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Dynamic musculoskeletal biomechanics in the human jaw Peck, Christopher Charles 1999

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D Y N A M I C M U S C U L O S K E L E T A L B I O M E C H A N I C S I N T H E H U M A N JAW by CHRISTOPHER CHARLES P E C K BDS, The University of Sydney, 1988 MSc(Dent), The University of Sydney, 1995 A THESIS SUBMITTED I N PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E O F DOCTOR OF PHILOSOPHY in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Oral Biology) We accept this thesis as confonning to the required standard ' T H E UNIVERSITY OF BRITISH COLUMBIA N O V E M B E R 1999 ® Christopher Charles Peck, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Q/-«J "fct'ftlo^  ( 0>oJ W^oJfL £cwu,o The University of British Columbia Vancouver, Canada Date 2°V . N W * — \ \ ^ DE-6 (2/88) ABSTRACT The high prevalence of functional disorders in the human jaw emphasises the need to understand better its dynamic behaviour. In the present studies, dynamic mathematical models based on typical physical properties of the human jaw and skeletal muscles have been developed. In the first three studies, a model of the entire jaw was created and utilised to predict jaw elasticity and viscosity, and to simulate muscle-driven symmetrical and asvmmetrical jaw movements. Specifically these models were constructed without "ligaments" (temporomandibular capsule or other accessory jaw ligaments) to determine whether or not plausible motion could be simulated in their absence. In the fourth study, a specific model of the temporomandibular ligament and outer wall of the TMJ capsule was created to investigate further these passive structures' perceived role in constraining jaw movement. Variations in their structure have been implicated in jaw hypermobility and joint disorders. In the fifth study, a specific model of the masseter muscle was developed and consisted of six contiguous muscle compartments in which muscle fibre orientations and lengths differed. The functional implications of this complex internal structure was investigated when the model was stretched in opening and lateral jaw movements. In the first three studies, the jaw models required low elasticity and heavy damping to match in vivo conditions, and consequently low levels of muscle activity (tone) were needed to maintain a clinical jaw rest position. In the absence of "ligamentous" constraints about the jaw, plausible symmetric, and asymmetric movements were possible. In study four, putative capsular regions about the TMJ were suggested to remain taut throughout an entire ipsilateral jaw movement, however for contralateral, opening and protrusive jaw movements, the capsule remained slack during the middle third of the movement. In study five, although theoretically capable of generating high passive tensions, the masseter muscle model generated low overall passive tension to stretch. Dynamic modelling suggests hypothetical relationships between the jaw's structural and functional variables. Jaw muscle coactivation generates varied movements, and together with passive tensions affords a degree of jaw stability. Muscle and "ligaments" probably cooperate to constrain jaw movement, although muscle appears predominant in the mid-range of jaw movements. The internal structure of the masseter muscle may allow maximum movement with minimum passive tension generation. ii T A B L E O F C O N T E N T S A B S T R A C T ii T A B L E O F C O N T E N T S iii LIST O F FIGURES ix LIST O F T A B L E S xiii A C K N O W L E D G M E N T S xiv 1 I N T R O D U C T I O N 1 1.1 Introduction to the thesis 1 1.2 Jaw Structure 2 1.2.1 The craniomandibular skeleton ; 3 1.2.2 Temporomandibular Joint : 4 1.2.3 Muscles 6 1.3 Jaw Function 7 1.3.1 Methodology for measuring j aw function 8 1.3.1.1 Measurement of j aw kinematics 8 1.3.1.2 Measurement of bite force and electromyography (EMG) 10 1.3.1.3 Animal Studies 11 1.3.1.4 Modelling 12 1.3.1.4.1 Static Jaw Modelling 13 1.3.1.4.2 Muscle modelling 14 1.3.1.4.3 Dynamic Jaw Modelling 15 1.3.2 Jaw Motion 17 1.3.3 Jaw Muscle Function 19 1.3.3.1 Muscle Tension Generation 20 1.3.3.1.1 Maximum Muscle Tension 20 1.3.3.1.2 Active Muscle Tension 22 1.3.3.1.2.1. Length-tension and velocity-tension relationships 22 1.3.3.1.3 Passive Muscle Tension 23 iii 1.3.3.2 Muscle Activity 25 1.3.4 Jaw Loading 28 1.3.4.1 Condylar loading 30 1.4 Summary 33 2 STATEMENT OF T H E PROBLEM : 35 3 DYNAMIC SIMULATION OF MUSCLE AND ARTICULAR PROPERTIES DURING WIDE JAW OPENING 38 3.1 ABSTRACT 38 3.2 I N T R O D U C T I O N 39 3.3 M E T H O D S 41 3.3.1 Detenriination of Forces Required to Attain Wide-Gape 41 3.3.2 Definition of the Jaw Model 42 3.3.2.1 Mandible and Dentition 44 3.3.2.2 Temporomandibular Joints 45 3.3.2.3 Muscles 47 3.3.2.4 Specification of Muscle Fibre/Tendon Ratios 47 3.3.2.5 Specification of Muscle Tension Properties 49 3.3.2.5.1 Passive Muscle Tensions: 49 3.3.2.5.2 Active Muscle Tensions: 51 3.3.3 Jaw Dynamics 52 3.3.3.1 Determination of the Mandibular Rest Position (Model 40RP) 52 3.3.3.2 Muscle-Activated MiclJine Jaw Opening (Models' 40LF & 40XF) 52 3.3.3.2.1 Use of Linear Force-time Functions for Active Muscle Tensions (Model 40LF) 52 3.3.3.2.2 Use of Expanded Linear Force-time Functions for Active Muscle Tensions (Model 40XF) 54 3.3.3.3 Opening with Reduced Condylar Guidance (Models' 25PF, 25LF & 25XF) 54 3.3.3.4 Asymmetrical Opening (MODEL 40LF-As) 55 3.4 Results 55 3.4.1 Forces Required to Attain Wide-Gape 55 iv 3.4.2 Definition of the Jaw Model 3.4.2.1 Specification of Passive Muscle Tension Properties 3.4.3 Jaw Dynamics 3.4.3.1 Determination of the Mandibular Rest Position 3.4.3.2 Muscle-Activated Midline Jaw Opening 3.4.3.2.1 Use of Linear Force-time Functions for Active Muscle Tensions (Model 40LF) 3.4.3.2.2 Use of Expanded Linear Force-time Functions for Active Muscle Tensions (Model 40XF) 3.4.3.3 Opening with Reduced Condylar Guidance 3.4.3.4 Asymmetrical Opening 3.5 Discussion 3.5.1 Modelling Assumptions 3.5.2 Muscle Tensions 3.5.3 Mandibular Rest Position 3.5.4 Jaw Opening 3.5.5 Articular Loading 3.6 Conclusions 4 FORCES RESISTING JAW DISPLACEMENT IN RELAXED HUMANS: A VISCOELASTIC P H E N O M E N O N 4.1 Abstract 4.2 Introduction 4.3 Methods 4.3.1 Mandibular Force-Motion Recordings 4.3.2 Mathematical Modelling 4.4 Results 4.4.1 Jaw Forces and Motions in Experimental Subjects 4.4.2 Mathematical Modelling 4.4.2.1 Critical Damping of the Mandible 4.4.2.2 Jaw Opening with Applied Force 4.5 Discussion 4.6 Conclusions 109 5 T H E INFLUENCE OF MUSCLE CONSTRAINTS O N JAW MOVEMENTS 110 5.1 Abstract 110 5.2 Introduction I l l 5.3 Methods 114 5.3.1 Initial Jaw Positions 116 5.3.2 Movement Tasks 117 5.3.2.1 Hinge Opening Movement 118 5.3.2.2 Protrusive and Lateral Movements: E M G Based-Muscle Activation 118 5.3.2.3 Lateral Movements: Muscle Activation According to Muscle Length 120 5.4 Results 122 5.4.1.1 Operator Guided Hinge Opening 122 5.4.1.2 Protrusion 122 5.4.1.3 Lateral Movements 124 5.4.1.3.1 EMG-Based Muscle Activation 124 5.4.1.3.2 Muscle Length-based Activation 131 5.5 Discussion 137 5.5.1 Jaw Modelling 137 5.5.2 Muscle-driven Jaw Motion 138 5.6 Conclusions 143 6 T H E EFFECT OF T H E LATERAL TEMPOROMANDIBULAR LIGAMENT AND CAPSULE O N JAW MOTION 144 6.1 Abstract 144 6.2 Introduction 145 6.3 Methods 147 6.3.1 Capsular Morphology 148 6.3.2 Mandibular Movement 150 6.4 Results 153 6.4.1 Opening Movement 157 6.4.2 Protrusive Movement 160 vi 6.4.3 Contralateral Movement 162 6.4.4 Ipsilateral Movement 163 6.5 Discussion ; 168 6.5.1 Assumptions 168 6.5.2 The Role of the Lateral Capsular Wall 169 6.6 Conclusions 174 7 A MODEL OF T H E PASSIVE TENSION PROPERTIES OF T H E MASSETER MUSCLE 180 7.1 Abstract 180 7.2 Introduction 181 7.3 Methods 183 7.3.1 Complex Muscle Models (Models C U & CD) 183 7.3.1.1 Complex Muscle Model Components 185 7.3.1.1.1 Muscle Thickness 185 7.3.1.1.2 Tendon Properties 191 7.3.1.1.3 Fibre Properties 191 7.3.2 Simple Muscle Model (Model S) 193 7.3.2.1 Simple Muscle Model Components 193 7.3.3 Muscle Dynamics 195 7.3.4 Mandibular Movement 195 7.4 Results 196 7.4.1 Jaw operiing 196 7.4.1.1 Resultant forces at superior (2ygomatic) muscle attachment 196 7.4.1.2 Fibre and tendon dynamics 197 7.4.2 Contralateral Jaw Movement 207 7.4.2.1 Resultant forces at superior (zygomatic) muscle attachment 207 7.4.2.2 Fibre and tendon dynamics 212 7.5 Discussion • 213 7.5.1 Modelling 213 7.5.2 Resultant Muscle Forces 219 7.5.3 Muscle Component Properties 220 vii 7.6 Conclusions 222 8 G E N E R A L D I S C U S S I O N 224 8.1 Jaw modelling 224 8.2 Jaw dynamics 227 8.2.1 Passive constraints 227 8.2.1.1 Jaw muscles , 227 8.2.1.2 Lateral capsular wall 229 8.2.2 Active constraints (muscle) 230 8.2.3 Condylar loading 231 9 G E N E R A L S U M M A R Y & C O N C L U S I O N S 233 10 F I N A L C O M M E N T S & F U T U R E D I R E C T I O N S 235 11 B I B L I O G R A P H Y 238 viii LIST O F FIGURES Page Figure 1 Anterolateral view of the basic model showing the muscle group actuators' lines of action 43 Figure 2 Temporomandibular joint analogues 46 Figure 3 Incisal point envelope of border movements produced by the kinematically-driven model 48 Figure 4 Generic passive muscle length-tension curve utilised for all muscle group actuators in (A) previous studies, and (B) current study 57 Figure 5 Comparison of rest position incisal gape for passive muscle tension function exponents between 10 and 0.0001 58 Figure 6 Effect of simple and expanded linear jaw-opener muscle activity on incisor opening pathway for 40° condylar guidance models 70 Figure 7 Effect of simple and expanded linear jaw-opener muscle activity on incisor opening pathway for 25° condylar guidance models , 71 Figure 8 Effect of simple linear, unilateral jaw-opener muscle activity (the left lateral pterygoid actuator has been removed) on incisor opening pathway for 40° condylar guidance model 72 Figure 9 Jaw-opener tensions plotted against time for 40° condylar guidance models: 40LF&C40XF 73 Figure 10 Jaw-opener tensions plotted against time for 25° condylar guidance models: 25LF & 25XF. 74 Figure 11 Passive muscle tensions plotted against incisal gape during jaw opening in Model 40LF 75 Figure 12 Passive muscle tensions plotted against incisal gape during jaw opening in Model 40XF 76 Figure 13 Passive muscle tensions plotted against incisal gape during jaw opening in Model 25LF 77 Figure 14 Passive muscle tensions plotted against incisal gape during jaw opening in Model 25XF 78 Figure 15 Representative plots of objective functions (condylar rotation/translation - 2°/mm) against incisal gape during jaw opening 79 ix Figure 16 TMJ loads plotted against incisal gape during jaw opening in: Model 40LF; Modd40XF; Model 25LF; Model 25XF; Model 40-As-right TMJ; Model 40-As-\eh TMJ 80 Figure 17 Passive muscle tensions plotted against incisal gape during asymmetric opening in Modd 40LF-A s 81 Figure 18 Passive muscle tensions plotted against incisal gape during asymmetric opening in Modd 40LF-As 82 Figure 19 Force and motion recording system 86 Figure 20 Single subject: anterolateral view of reconstructed force vector (arrow) and incisor motion (solid line) 92 Figure 21 Single subject: force (thick line) and gape (thin line) vs time for 5 second opening cycle 93 Figure 22 Force and gape vs time for 20 second opening in single subject and in model 94 Figure 23 Representative plots from 3 subjects of force vs gape for 5 second opening cycle 95 Figure 24 Representative plots from 3 subjects of force vs gape for 20 second opening cycle... 96 Figure 25 Pooled data: Temporal plots of applied force required to open each subject's jaw for F O cycles 98 Figure 26 Pooled data: Temporal plots of applied force required to open each subject's jaw for SO cycles 99 Figure 27 Pooled data: Temporal plots of mid incisor gape attained from applied forces in figure 25 for wide gape attained for F O cycles 100 Figure 28 Pooled data: Temporal plots of mid incisor gape attained from applied forces in figure 26 for wide gape attained for SO cycles 101 Figure 29 Pooled data: Temporal plots of normalised force curves, derived from data in figure 25, for F O cycles 103 Figure 30 Pooled data: Temporal plots of normalised force curves, derived from data in figure 26, for SO cycles 104 Figure 31 Anterolateral view of jaw model showing trajectories of mandibular centre of mass and incisor when the jaw is allowed to fall from IP to rest (under the influence of gravity) 105 Figure 32 Effect of damping on incisor gape as jaw passively attains a gravity-induced rest position from intercuspal position 106 Figure 33 Effect of postero-inferior "chin-point" force on jaw motion 123 x Figure 34 Effect of E M G based-muscle activation on protrusive jaw motion with tooth contact 125 Figure 35 Effect of E M G based-muscle activation on protrusive jaw motion without tooth contact 126 Figure 36 Effect of E M G based-muscle activation on lateral jaw motion with tooth contact 129 Figure 37 Effect of E M G based-muscle activation on lateral jaw motion without tooth contact 130 Figure 38 Relative shortening of muscles plotted against lateral jaw movement 133 Figure 39 Effect of muscle-length-based muscle activation on lateral jaw motion with tooth contact 134 Figure 40 Effect of muscle-length-based muscle activation on lateral jaw motion without tooth contact 135 Figure 41 Anterolateral outline of temporomandibular joint and putative lateral capsular wall location 149 Figure 42 Sagittal outline of regions in which putative capsular elements originate and insert, and their relationship to the mandibular condyle and temporal fossa 154 Figure 43 Antero-lateral view of mandibular movements in which the capsular lengths were assessed 155 Figure 44 Representative plot of 3 capsular elements' length change (as % of each element's maximum length) for jaw opening. Dotted horizontal line is at 95% of maximum element length 156 Figure 45 Sagittal outline of capsular elements which are within 10% of their maximum lengths throughout all jaw movements 158 Figure 46 Number of taut capsular elements (expressed as % of all taut elements for the particular movement) throughout each jaw movement (expressed as % of maximum movement) 165 Figure 47 Number of taut capsular elements (expressed as % of all taut elements for the particular movement) throughout each jaw movement (expressed as % of maximum movement) 166 Figure 48 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different jaw positions during opening 176 Figure 49 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different jaw positions during protrusion 177 xi Figure 50 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different positions jaw during contralateral movement 178 Figure 51 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different positions jaw during ipsilateral movement 179 Figure 52 Representation of masseter muscle architecture 184 Figure 53 Orientation of multiple musculotendon actuators within the masseter muscle (Models CU & CD) 186 Figure 54 Segmentation of multilayered masseter muscle (Models CU & CD) - Sagittal view. 187 Figure 55 Segmentation of multilayered masseter muscle (Models CU & CD) - Frontal view. 188 Figure 56 Orientation of musculotendon actuators for the simple muscle model (Modd S) 194 Figure 57 Force and moment magnitudes during jaw opening 198 Figure 58 Resultant force vectors and moments of models at wide jaw opening 199 Figure 59 Force vector components in the models during jaw opening 200 Figure 60 Force moment components in the models during jaw opening 201 Figure 61 Changes in relative positions of actuators as a result of wide jaw opening - Sagittal view 205 Figure 62 Changes in relative positions of actuators as a result of wide jaw opening - Frontal view 206 Figure 63 Force and moment magnitudes during contralateral jaw movement 208 Figure 64 Resultant force vectors and moments of models at maximum contralateral jaw positions 209 Figure 65 Force vector components in the models during contralateral jaw movement 210 Figure 66 Force moment components in the models magnitudes during contralateral jaw movement 211 Figure 67 Changes in relative positions of actuators as a result of contralateral jaw movement - Sagittal view 217 Figure 68 Changes in relative positions of actuators as a result of contralateral jaw movement - Frontal view 218 xii LIST O F TABLES Page Table 1 Muscle Properties 50 Table 2 Jaw models' structural (condylar guidance) attributes and functional (muscle tension variables) alterations to meet specific objectives 53 Table 3 Jaw motions, joint loads and muscle tensions at wide gape (Model 40XF, Model 25XF) and at maximum left lateral jaw deviation (Model 40XF-As) 68 Table 4 Expanded linear force functions assigned to the (A) Lateral Pterygoid actuator, and (B) Digastric actuator for the 40° (Model 40XF) and 25° (Model 25XF) condylar guidance models 69 Table 5 Gape and opening force data for 5 and 20 second opening cycles, and subjects' unassisted opening measurements 91 Table 6 Polynomial regression functions of pooled opening force vs time data 102 Table 7 Kinematics of lateral jaw movements from intercuspal jaw position and rest jaw position 121 Table 8 Tensions, in Newtons, developed in the model's muscle actuators 127 Table 9 Length changes (T increasing length; -l decreasing length) and tensions, in Newtons, developed in the model's muscle actuators for laterotrusive jaw movement tasks 136 Table 10 Tautness of specific capsular regions throughout jaw movement 167 Table 11 Musculotendon actuators' co-ordinates at intercuspal jaw position 189 Table 12 Properties of musculotendon actuators of Model CU for an opening jaw movement 203 Table 13 Properties of musculotendon actuators of Model CD for an opening jaw movement 204 Table 14 Properties of musculotendon actuators of Model CU for a contralateral jaw movement 214 Table 15 Properties of musculotendon actuators of Model CD for a contralateral jaw movement 215 Table 16 Model regions mean maximum fibre length reached during opening and contralateral jaw movements 216 xiii A C K N O W L E D G M E N T S I am extremely grateful to Dr Alan Hannam for his scientific guidance and inspiration that made this project such a rewarding experience. One could not ask for a better mentor and teacher, and I only hope that some of his brilliance has rubbed off onto me. I would like to thank Drs Bruce Blasberg and Douglas Romilly for their invaluable mstruction, constmctive criticism and guidance throughout my candidacy; from the initial planning of the proposal to the final stages of thesis compilation. I have been very lucky to enlist the expertise of Ms Joy Scott, who has provided direction and support for many of the computational aspects of my experiments. Her friendship is equally appreciated, as is that of the other members of the Craniofacial Biology Laboratory. I am very fortunate to have family and friends who have always been a constant source of encouragement and support. Special thanks go to Deborah, whom I have relied upon very much and who has somehow put up with me. x i v 1 INTRODUCTION 1.1 INTRODUCTION TO THE THESIS The human craniomandibular system is structurally and functionally complex. The components of this musculoskeletal system interact with external forces to accomplish a diverse range of normal functional tasks on a daily basis. The interactions of the variables at play in mandibular function are not well understood, which has resulted in questionable assertions regarding struaure-funaion associations. This speculation about, rather than demonstration of, jaw biomechanics has risked erroneous conclusions with respect to cause-effect relationships in functional disorders, reflecting adversely on their assessment, diagnosis and management. This negative impact of such speculation can not be illustrated more vividly than with the recent device recall of interpositional implants which have been used to treat intra-articular disorders of the human jaw. Their catastrophic failure is but one example of the need to understand the biomechanics of this musculoskeletal system, as there is controversy on the applicability and efficacy of virtually every treatment modality currently in use. Anthropometric data for the masticatory system shows there is enormous variation, and it is often difficult to obtain or interpret. In addition, the jaw and its associated structures comprise a collection of three-dimensional heterogeneous tissues which are dissimilar to those in the post-cranial skeleton making comparisons with other regions difficult. Since measurements of many of the functional variables, for example force, stress and strain, within the components of this system are impossible within the human, the experimental animal model has been heavily utilised. However, the uniqueness of the human temporomandibular joint (TMJ) and craniofacial form demand caution in interpreting and extrapolating data across species. A n alternative, indirect research approach to study human jaw biomechanics is mathematical modelling which has been used successfully in the other musculoskeletal regions of the human body. It applies principles of static or dynamic mechanics to understand better the physical environment of the system. Modelling the heterogeneous 1 nature of the human jaw is difficult and has been performed under static conditions revealing regional stress distributions consistent with experimental data. Muscle-driven jaw analogues of various complexities have been constructed recently, and offer an approach to three-dimensional analysis and simulation of the dynamic craniomandibular environment. Conceptually, they are hypotheses which link the physical properties of skeletal structures with factors like muscle tensions, skeletal motions, stresses, strains, and forces. They are however, only as good as their input data, which often must be assumed, as the values of some parameters are unknown and may never be obtainable. As well, the correctness and adequacy of the models must be evaluated by experiment before they will be accepted by either researchers or clinicians. Nevertheless, the strategy involving the design and analysis of a craniomandibular model which behaves plausibly in function, offers the ability to disassemble a dynamic system, and to explore the factors that shape its motion. Indeed, biomechanical simulation is the only practical way to study these variables in the human, and should be able to rationalise cause and effect, explain why given configurations operate as they do, and predict the likely outcome of an intervention to the system. 1.2 JAW STRUCTURE The human craniomandibular system comprises a diverse range of components including a mandible suspended from the maxilla and cranial bones by muscles, ligaments and other soft tissues. Contact between the cranial structures and mandible is afforded continually through the temporomandibular joints and intermittently (in the normal case) via the maxillary and mandibular dentition. This system has developed into a specialised unit which permits a variety of mandibular movements including suckling, swallowing, speech and masticatory jaw movements such as the incision and grinding of food. Amongst mammals there are quite large variations in mandibular, articular and muscular form (Dechow & Carlson, 1997), although interestingly the motor pattern of the masticatory muscles and the basic structure of the trigeminal system is similar amongst the different taxonomic groups (Song & Boord, 1993; Weijs, 1994). From an evolutionary perspective, the modern human jaw has seen a number of changes in structure from its hominid ancestors. These include reductions in mandibular and 2 tooth size, in masticatory muscle mass, and in cortical bone thickness, a dental arch shift from parallel tooth rows to a more parabolic form, and chin development (Wolpoff, 1975; Daegling, 1993). 1.2.1 The craniomandibular skeleton The structural diversity seen in the individual structures comprising the cranial skeleton results initially from the embryologic origins of the constituent tissues. For example, embryonic mesenchyme forms from neural crest cells which have migrated into the mandibular arch, and subsequently differentiated into multiple cell types to ultimately combine and form the mandible (Atchley, 1993). These condensations of various cell types, including odontoblasts, osteoblasts and secondary chondroblasts, are important in the eventual heterogeneous morphology of the mandible and dentition (Atchley & Hall, 1991). The structure of both jaws differ, with trabecular bone pattern predominating in the maxilla, and a thick external dense cortical bone with an internal trabecular framework in the mandible (Atkinson, 1964). The dentition is intimately related to both jaws by the specialised periodontal ligament tissue, which allows independent dental movement of approximately 0.3 mm in the healthy individual (Roberts et al., 1992). As compared to other mammalian teeth, humans have relatively flat occlusal surfaces, which has been suggested to provide adaptability for our omnivorous diet (Magid & Law, 1985). The dentition is often described by its interarch relationship in two-dimensions (GPT-7, 1999), which is generally inadequate when considering their complex three dimensional structure and relationships. The cranial skeleton has complex material properties, and is considered, like other calcified biological tissues, to be anisotropic (different material properties when measured in different directions) and inhomogeneous (Dechow et al., 1993; Ashman et al., 1994). Recent direct measurements of specific regions of the mandible show the mandible to be stiffest along its long axis (Dechow et al., 1993). The inertial properties, such as mass and mass moments of inertia, provide a description of the jaw's resistance to acceleration, and are essential properties when assessing the effects of external forces acting on the jaw (Nigg, 1994a). Inertial resistance of a body to linear acceleration depends on its mass, and its resistance to angular acceleration depends on 3 its mass moments of inertia, which are derived from the body's geometry and mass distribution (Andriacchi et al., 1997). Inertial properties for an anatomical object may be obtained experimentally (e.g., cadaveric measurements, volume displacements, moment table, imaging and impulse force experiments) or theoretically (mathematical models with varying complexities of mass distribution) (for review see Nigg, 1994a). In the case of the facial skeleton, the determination of these properties has been limited mostly to the mandible. Since biomechanical analyses have traditionally investigated mandibular motion relative to a fixed, "grounded" cranium, only the moving jaw has required assignment of properties (Koolstra & van Eijden, 1995; Langenbach & Hannam, 1999). Cadaveric mandibular specimens have been weighed to derive mass, and inertial properties approximated assuming uniform mandibular mass distribution (Koolstra & van Eijden, 1996). In a more accurate assessment, inertial properties have been estimated with a mathematical model (cited in Langenbach & Hannam, 1999). This method used finite element (FE) analysis, whereby the complex mandibular structure is discretised into a number of smaller elements. These "finite elements" were given material properties consistent with experimental findings, and although FE analysis is primarily used for the assessment of complex shape changes in structures, the computer algorithm was utilised to also derive the inertial properties for the entire mandible (Korioth & Versluis, 1997). Since all material properties of the facial skeleton were unknown, properties of similar tissue were used which consequently introduced a certain degree of inaccuracy to the result. More recently, inertial properties of a pig's jaw were derived from three-dimensional computed tomography (Zhang et al., 1999). The derived mass correlated closely with that of the actual mandible, and so this appears to be a valid and practical method by which these properties may be measured. 1.2.2 Temporomandibular Joint The human temporomandibular joint (TMJ) is a highly specialised synovial joint which permits a variety of mandibular movements. At birth, the immature TMJ includes a temporal bone and round condyle (in which cartilage predominates underneath fibrous articulating surfaces), and a flat, uniformly thick fibrous disc (Oberg et al., 1971; Bigland-Ritchie et al., 1992; Itoh et al., 1995). In the sagittal plane, the fossa-eminence is essentially flat, assuming its S-shaped morphology at around six years, and continuing in development to the 4 beginning of the second decade (Wright & Moffett, Jr., 1974; Bigland-Ritchie et al., 1992). The shape of the maturing disc conforms to the adjacent temporal and condylar articular surfaces, and apart from the predominant densely organised collagen fibres, the disc contains a fine branching of elastic fibres (Griffin et al., 1975) and cartilage-like proteoglycans (Axelsson et al., 1992). The growing condyle is characteristically ellipsoidal, and may undergo alterations in shape during late growth and early maturity (Solberg et al., 1985), so that in the adult, variations in structure are common (Yale et al., 1966). Islands of cartilage remain in the bony joint structures, although most are replaced gradually throughout adulthood (Carlson, 1994). These articular components are surrounded by an inelastic fibrous capsule which extends from superior attachments on the margins of the glenoid fossa and articular eminence to the condylar neck inferiorly. The capsule may not be a distinct entity, as one study found direct connections between temporal and mandibular bones on the lateral aspect only; other capsular regions consisted of upper and lower fibrous laminae of the articular disc attaching separately to either bone (Schmolke, 1994). Of note was the presence of elastic tissue in the postero-superior discal attachments (Ten Cate, 1994). The capsule's lateral wall is thickened with the temporomandibular ligament, a structure which classically is reported to have two definite collagen fibre orientations: one oblique band from the condylar neck to an anterosuperior region on the eminence, and a horizontal band from the lateral condylar pole to an anterior attachment on the eminence (Arstad, 1954; Griffin et al., 1975). Since relatively recent anatomical studies have not demonstrated these fibre orientations, the existence of a discernible lateral ligament must be questioned (Savalle, 1988; Luder & Bobst, 1991; Schmolke, 1994). Within the TMJ, the synovial fluid in which the highly viscous hyaluronic acid predominates, is involved in boundary lubrication by forming a molecular film over the articulating surfaces to help keep surfaces apart, and therefore decrease friction, during joint compression and motion (Israel, 1994). Together with weeping lubrication of the fibrous disc and articular surfaces, these properties have created an articular environment in which the coefficient of friction is suggested to be negligible (Osborn, 1985), and the joint surfaces are considered to be "several times as slippery as ice" (Charnley, 1959). Presumably, an 5 alteration in the molecular make-up of the synovial fluid, or articular surfaces would affect the frictional properties within the articulation (Stegenga et al., 1991). Immunohistochemical techniques have revealed a rich innervation to the capsule and the disc periphery (Morani et al., 1994), with many fibres located in the postero-lateral capsular region (Hannam & Sessle, 1994). These afferent nerves are carried mainly by the auriculotemporal, and to a lesser extent by the masseteric and deep temporal branches, of the mandibular division of the trigeminal nerve (Ten Cate, 1994). The possible presence of nociceptive-related neuropepetides (Johansson et al., 1986) and afferent activity with jaw motion (Klineberg, 1980) implicate these articular fibres in both nociception and proprioception. 1.2.3 Muscles Structural variation is the underlying theme in the jaw muscles which range from relatively simple parallel fibred units (e.g., digastric and lateral pterygoid muscles) to the complex multipennated masseter, medial pterygoid and temporalis muscles. In the pennated muscles of the jaw, fibres attach obliquely between broad intramuscular aponeuroses (tendinous sheets) so that their main line of action is angled to the long axis of the muscle (e.g., an average of 20° in the masseter van Eijden & Raadsheer, 1992). In relatively small spaces such as the compartments within the jaw muscles, pennation enables increased fibre numbers, although at the expense of fibre length (Gans, 1982; Gans & de Vree, 1987). With the complex orientation of these aponeuroses in some jaw muscles, it has been suggested that pennation angle should be expressed as a three-dimensional angle, rather than the usual description of a single angle of fibre angulation to the muscle's long axis (Lam et al., 1991). Although the jaw muscles have been divided into relatively simple functional divisions (e.g., masseter muscle: deep and superficial portions; temporalis muscle: anterior, middle and posterior portions), anatomical and histochemical studies, and regional and single motor unit electromyography suggest further task-dependent differentiation may be possible (Schumacher, 1961; Schumacher, 1982; Eriksson et al., 1984; Wood, 1986a & b; Belser & Hannam, 1986; Wood, 1987; Stalberg & Eriksson, 1987; McMillan & Hannam, 1991; Miller, 1991b; McMillan, 1993; Hannam & McMillan, 1994; van Eijden et al., 1995; Blanksma & van 6 Eijden, 1995). This differentiation is exemplified within the human masseter muscle, which has been anatomically divided by five internal aponeuroses with different fibre orientations between each (Schumacher, 1961); and unlike other skeletal muscles, has motor units which are small and in general, focally distributed to specific muscle compartments (McMillan & Hannam, 1991; McMillan &Hannam, 1992; Tonndorf & Hannam, 1994). In order to estimate a jaw muscle's line of action for biomechanical purposes, the average muscle angulation from an origin point to an insertion point is most often used (Weijs & van Ruijven, 1990; Hannam, 1994). Centres of muscle attachments have been approximated from dried skulls (Baron & Debussy, 1979; Faulkner et al., 1987), anatomical dissections (van Eijden et al., 1997; Koolstra & van Eijden, 1997a), cephalometric landmarks (Takada et al., 1984; Throckmorton & Dean, 1994; Kasai et al., 1994), and images of live subjects (Hannam & Wood, 1989; Koolstra et al., 1989; Koolstra et al., 1990). Although these methods produce an average line which represents the orientation of the muscle's force vector (only at the jaw position that landmark measurements were made), modifications would be necessary for muscles with curved fibres (Otten, 1988), such as in the posterior region of the temporalis muscle. 1.3 JAW F U N C T I O N The human jaw is involved in a number of diverse functional tasks including suckling, swallowing, speech and masticatory movements such as the incision and grinding of food. These tasks, especially rhythmical ones such as mastication, are generated in the central nervous system and modified by peripheral sensory feedback, including information from intraoral and TMJ receptors (Lund, 1991). Disorders of the jaw muscles and TMJ are embraced collectively under the term temporomandibular disorders (TMD), in which common signs and symptoms include impaired jaw function and movement (Dworkin & LeResche, 1992). T M D are a major health problem, and the prevalence of severe jaw dysfunction has been reported as high as 22% in the general population (see Carlsson & LeResche, 1995). Stability and loading of the TMJ and jaw are presumed to be important in jaw function (Storey, 1995), and alterations to these states have been implicated in T M D 7 (Milam, 1995; Sato et al., 1995), even though their mechanics are not well understood (Hannam, 1994). Aside from jaw kinematic studies there is a lack of direct human studies describing the mechanics of the functioning mandibular system (Hannam, 1994; Hannam & Langenbach, 1995; Storey, 1995; Hannam et al., 1997). Acquisition of human jaw muscle and TMJ loads is currently not possible, and therefore experimenters have relied on human bite force measurements and electromyography (Miller, 1991a), animal (Weijs & Brugman, 1989; Langenbach et al., 1991; e.g., Herring, 1993) and modelling experiments (see Hannam & Langenbach, 1995; Korioth, 1997) to examine the influence of forces on the system at rest (static assessment) or in motion (kinetic assessment) (Beer & Johnston, 1999). 1.3.1 Methodology for measuring jaw function 1.3.1.1 Measurement of jaw kinematics The study of jaw kinematics involves the analysis of motion without regard to the forces which cause it (i.e., the motion is imposed on the jaw) (Craig, 1986). The human jaw is capable of unique and complex tliree-dimensional motion (Posselt, 1952) and therefore instrumentation capable of recording with six degrees of freedom (the number of independant position variables needed to locate the whole jaw; Craig, 1986) should be used to capture fully the motion (Hannam, 1992b; Peck et al., 1997). Mandibular motion has been recorded by a variety of methods ranging from the very simple interincisal measurement of jaw displacement in the clinical setting (Dworkin & LeResche, 1992), to the sophisticated opto-electronic systems used in the research environment (Hannam, 1992b; Airoldi et al., 1994). Many studies have recorded the motion of a single point on or near the mandible, such as an incisor point or arbitrary condylar point (McMillen, 1972; Ahlgren, 1976; Hobo & Mochizuki, 1983), and subsequently attempted to deduce whole jaw motion or motion of "invisible" articular structures, without knowledge of their relationship to the recorded point (for review see Palla et al., 1997). This is erroneous when one considers the disparity in movement between different regions of the mandible; e.g., the incisor is able to translate maximally about 50 mm whereas the condyle's maximum 8 is in the vicinity of 16 mm (Posselt, 1952; Lotters et al., 1996). These incomplete recordings, together with the large variation in movement patterns observed between subjects (Merlini & Palla, 1988; Zimmer et al., 1991; Salaorni & Palla, 1993; Zwijnenburg et al., 1996b) partly explains the difficulty in discriminating between the motion of a healthy and disordered jaw system (Mauderli et al., 1988). To describe more completely the three-dimensional nature of jaw movement, motion of simple shapes representing the mandible (Peck et al., 1997) or of three-dimensional reconstructed anatomy, as determined from magnetic resonance images of the TMJ has been performed (Hagiwara et al., 1993a; Hagiwara et al., 1993b; Krebs et al., 1994; Krebs et al., 1995; Palla et al., 1997). In these latter studies, animation of the reconstructions enabled clear and comprehensive interpretation of regional motion variation. Recently, the helical axis has been computed for jaw movements in another attempt to describe more fully the motion of the mandible (Gallo et al., 1997). Here, the motion of a rigid body is expressed as a combination of translation along, and rotation about, an axis (Woltring et al., 1985). Thus jaw motion is described as a continuously changing (in position and orientation) "axis". This provides a complete description of jaw motion, although intuitively it is difficult to discern the actual motion from the axes motions. Recently recommendations for standardisation in the reporting of kinematic data of the whole body, and in particular of the TMJ have been suggested (Wu & Cavanagh, 1995; ISB standardization committee, 1999). Although in its infancy, standardisation of motion description by a recognised body such as the International Society of Biomechanics, should resolve many of the problems outlined above. The movement of the compliant articular disc has usually been described qualitatively, since it is difficult to define landmarks and quantitative measures of a deformable structure (Rohlf & Bookstein, 1990). Interest in its functional movement has arisen in the hope of alluding to possible mechanisms of uncoordinated movement between it and the mandibular condyle (Stohler, 1994). Apart from the manipulation of cadaveric specimens (Isberg-Holm & Westesson, 1982a; Isberg-Holm & Westesson, 1982b), the motion of the disc has been determined with cinearthrography (Scapino, 1997), arthroscopy (Stohler, 1994), and "fast scan" magnetic resonance imaging (Burnett et al., 1987; Maeda et al., 1992). Both cinearthrography and arthroscopy are invasive with the former requiring injection of contrast medium into the joint, and the latter using an endoscope inserted directly into the joint to 9 directly visualise motion. In "fast scan" imaging, images are obtained at successive increments of a jaw motion, and then sequenced to provide a "pseudo-kinematic" display. This technique has not been validated as of yet (Stohler, 1994), and the normality of the staged jaw motion must be challenged. 1.3.1.2 Measurement of bite force and electromyography (EMG) Human bite force recordings provide a global measure of the forces acting on the jaw at the level of the dentition, and although this force results from the activity of the jaw musculature, it must be remembered that bite force is not simply a sum of the muscle forces, since these forces are distributed also amongst the TMJs (see Hannam, 1992a). Nevertheless, because of the relative ease of recording bite force, a number of studies have been performed at both static positions and during masticatory function (reviewed by Hagberg, 1987a; Miller, 1991a). These force levels may indicate a subject's masticatory efficiency (Carlsson, 1974), however unless they have been recorded in all three dimensions, the resultant forces and torques may be missed (Paphangkorakit &C Osborn, 1997). Contracting jaw muscles have been studied widely with the use of intramuscular or surface electrodes to record the electrical signals emanating from a discrete region (e.g., single fibres or motor units) or a larger area (e.g., whole muscle) respectively (Miller, 1991a). These electromyographic signals have low voltages ranging between /xvolts and mvolts, and little current, and include noise from surrounding electrical interferences. Consequently, they are usually amplified, filtered and then frequently rectified and integrated to facilitate quantification of the recording (Loeb 8t Gans, 1986). There is a presumed linear relationship between an integrated electromyographic recording and the recorded muscle's isometric tension (Loeb & Gans, 1986), and thus jaw muscle E M G has been regularly related to bite force measurements (Moller, 1966; Manns et al., 1979; van Eijden, 1990; Christensen & Kundinger, 1991; Mao & Osborn, 1994). Unfortunately this is not entirely the case, as E M G does not reveal the number of motor units firing, their firing rate, nor the relative participation of slow and fast motor units with different force-velocity and excitation-contraction properties (van Ruijven & Weijs, 1990). Within a subject, E M G recordings for similar tasks on different occasions have demonstrated significant variation in muscle contraction activity levels, although they remained quite consistent with respect to recording 10 timing patterns in chewing (Burdette & Gale, 1990; Bakke, 1993). This latter point is important as most jaw funaion involves muscle coactivation, and hence knowledge of when individual muscles are activated is important. With internal jaw muscles like the lateral pterygoid, E M G recording is difficult because of limited access, and the possibility of injuries to surrounding tissue such as haematoma formation (Mahan et al., 1983). Electrodes are placed blindly via an intraoral or extraoral route, and then correct positioning may be evaluated by assessing the signals obtained for specific tasks in which the muscle is presumed active (Wood et al., 1986), or by imaging of the muscle and inserted electrodes (McMillan & Hannam, 1989; Orfanos et al., 1996). E M G recordings at single sites in or over multipennated jaw muscles (e.g., masseter, temporalis) is quite common, although these muscles have displayed functional heterogeneity (McMillan & Hannam, 1992; McMillan, 1993; Blanksma & van Eijden, 1995; Blanksma et al., 1997), and thus regional differentiation may be missed with this recording technique. 1.3.1.3 Animal Studies Although human jaw structure and function is unique (Creanor & Noble, 1994), laboratory animals such as the rat, rabbit, pig, dog, sheep and monkey have been used extensively to assess jaw biomechanics (e.g., Weijs & Dantuma, 1975; Herring, 1977; Hylander et al., 1987; Boyd et al., 1990; Bosanquet et al., 1991; Langenbach et al., 1991). They are considered an attractive approach because in vivo measurements are possible, the functional implications to structural changes, and vice versa, can be directly assessed. In a recent review, Herring recommends the pig's jaw as a "cost effective" practical model for the human (1995). Apart from structural differences with the human, the following functional differences in the other animals were suggested as too incompatible with the human. The rodent's resultant muscle force vector passes through the bite point, so that bite and muscles forces cancel resulting in no joint force. In the dog, the functional muscle force and joint force are retrusive, and in the rabbit and sheep the masticatory patterns are fundamentally different in that the molar teeth form inclined guiding planes that guide the power stroke of mastication. The remaining animals, the pig and monkey, were the best of the group, although they are not ideal, because of occlusal, muscle orientation, TMJ configuration and masticatory differences with the human (Herring, 1976; Byrd et al., 1978). Bone strain measurements at the condyle and other regions of the mandible and cranial bones have been 11 frequently obtained (Bouvier & Hylander, 1981; Hylander et al., 1987; Herring et al., 1996; e.g., Freeman et al., 1997). Indirect measurements including electromyography and jaw motion have also been acquired, often in conjunction with the direct strain measures (e.g., Weijs & de Jongh, 1977; Hylander & Crompton, 1986; Marks et al., 1997). Direct force measurements with a multidirectional force transducer have been performed on selectively stimulated jaw muscle motor units of anaesthetised rabbits (Turkawski et al., 1998), and in other skeletal muscles of both animals and humans, functional force recordings utilising buckle transducers or liquid metal strain gauges attached directly to tendons or ligaments have been performed (van den Bogert, 1994). 1.3.1.4 Modelling Since measuring physical and functional variables is difficult, the data garnered from' human and animal experiments is incomplete, and consequently reveals only limited information on the biomechanics of the jaw (Storey, 1995). Physical and mathematical modelling can utilise this incomplete data, and provide hypothetical values for the missing variables (Hannam, 1994). Notwithstanding the need to evaluate the assumptions made in modelling, this approach can demonstrate the mechanics of the jaw, TMJ and muscles (Hannam & Langenbach, 1995). Physical models have utilised jaw specimens with or without attached soft tissues, and plastic or other material analogues, and generally have been greatly oversimplified with respect to their TMJ articulations and muscles (Mah et al., 1997). Nevertheless, they have provided a method to evaluate the plausibility of more complex mathematical models (Korioth et al., 1992). Mathematical models have developed in parallel with computational advances, and this form of biomechanical analysis is very common in all musculoskeletal regions of the human (Nigg & Herzog, 1994; Mow & Hayes, 1997). A problem in analysis of muscle and joint loads in the musculoskeletal system is that when the system is decomposed into a set of mathematical equations describing the interaction of biological forces, there are more unknowns than equations (An et al., 1997). Solution of this ^determinate problem has been approached by reduction and optimisation methods in the jaw system. A reduction approach 12 will make simpKfying assumptions in order to match the number of unknown variables with the number of equations to arrive at a single solution (An et al., 1997). For example, in the jaw these simplifications have included reducing the number of variables in the system by ignoring or grouping similar funaioning muscles (e.g., Ferrario & Sforza, 1992). Alternatively, the number of equations have been increased by assuming a specific relationship between the force distribution in muscles or TMJs (Faulkner et al., 1987). A more common approach is that of optimisation (Herzog & Binding, 1994) in which an objective function which iriinimises or maximises a process (e.g., TMJ loading) is utilised in an algorithm that searches for optimal values of variables (e.g., muscle forces) that meet this objective (Osborn, 1985; see Koolstra et al., 1988). Intuitively the use of optimisation seems valid, as it is not unreasonable to expect the neuromuscular system to learn a control process to minimise articular loads or utilise efficient muscle activity. In addition, the jaw system may be even more broadly optimised, as is suggested by E M G studies, so that the diversity of jaw function is maximised, without emphasis on loads or efficiency (e.g., Moller, 1974; Belser & Hannam, 1985) 1.3.1.4.1 Static Jaw Modelling A number of analyses on the human jaw have used static equilibrium theory to predict relative proportions of muscle, bite-point and joint loading, and therefore their solutions must satisfy the criteria that the sum of all forces and moments equals zero (Hannam, 1992a). The majority are simple rigid models which allow resolution of forces at single points, and thus neglect loading across broad regions at the dental, articular and muscle interfaces (Hannam & Langenbach, 1995). Finite element analysis provides complex flexible models which have regional physical properties consistent with known properties (Hart et al., 1992; Korioth & Versluis, 1997). These models have been loaded by simulated muscle tensions in a variety of jaw positions, to demonstrate the deformation and strain patterns of the mandible and the resultant differential loading pattern across the mandibular condyle (Korioth & Hannam, 1994b). The most advanced models are three-dimensional, and are constructed from computed tomographic images of an excised mandible. The TMJ has been represented as a two layer cap in which the first layer consisted of the combined thicknesses of the condylar, articular and temporal fibrocartilage, and the second consisted of temporal cortical bone (Korioth & Hannam, 1994b). Evaluation of these models involved comparing 13 actual surface strains recorded on the excised mandible with strains predicted by the model (Korioth et al., 1992). 1.3.1.4.2 Muscle modelling In order to assess the role of changing muscle tensions on musculoskeletal systems, functional muscle models have been realised. The dynamic attributes of the muscles have been modelled with varying degrees of complexity in the human body, and indeed the more elaborate could be considered a distinct model on their own (Zahalak, 1992). No muscle analogue behaves plausibly in every situation, and so a number of different modelling approaches have been undertaken (see Epstein & Herzog, 1998e) The constitutive equations used to describe the physical properties of muscle are not ideal because of incomplete experimental data, and because there is not one consistent mathematical equation which will describe all of the known properties of muscles (Fung, 1993b). There is a large variety of muscle models in existence from microscopic cross-bridge and sarcomere representations, to macroscopic whole muscle analogues (Zahalak, 1992). With the continual acquisition of experimental data, models continue to evolve, although the majority are based on two prototypes: the structural Huxley model (Huxley, 1988) based on the interaction of myofilaments via cross-bridges, and the phenomenological Hill-type model (Winters, 1990) which describes force behaviour for precisely defined contractile length and velocity conditions (Epstein & Herzog, 1998c). There are alternative models which have arisen as a result of questioning the current hypotheses of muscle mechanics, and which behave plausibly with respect to certain biological measures (see Pollack, 1990). Indeed, it has been suggested that the controversies surrounding muscle mechanics and the current models' neglect of some basic principles (e.g., long-lasting history dependent force behaviour following stretch or shortening), will see them replaced in the near future (Epstein & Herzog, 1998c). Generally, the mathematical complexity of the model increases as one attempts to model the microscopic events, and therefore the cross-bridge and sarcomere models are more intractable and not used frequently in macroscopic musculoskeletal biomechanics (Zahalak, 1990). The Hill-type models are derived from Hill's experiments that indirectly demonstrated a relationship between muscle force and contraction velocity (Zahalak, 1992). They are rheological models which contain spring and damping components to describe the muscle's mechanical behaviour. These viscoelastic muscle analogies usually consist of a 14 contractile element, an in-series elastic element and a parallel elastic element, although elements may be removed depending on the modelling circumstances (Huijing, 1998). The contractile element is described by force-length and force-velocity relationships which are derived from experiments of isometric and isotonic contractions of skeletal muscles (van den Bogert et al., 1998). The force-length properties are often represented by a parabolic function which has been verified in fully activated muscle fibres (Gordon et al., 1966; Huxley & Simmons, 1971), and the force-velocity properties during shortening and lengthening have been represented by parts of a rectangular hyperbola (Zajac, 1989). These properties are often linearly scaled to represent less than maximal activation, although the relationship to activation level may not be that straight forward (Rack & Westbury, 1969). Although tension developed in the contractile element is derived from force-length and velocity properties, in reality a unique relationship between force and velocity particularly in the muscle lengthening and sub-maximal activation case has not been found (Zahalak, 1992). In addition, the contractile element's force will be linearly scaled by a muscle activation level which is arbitrarily assigned or derived from E M G studies (Koolstra & van Eijden, 1995; Langenbach & Hannam, 1999; Koolstra & van Eijden, 1999). Experimental evidence suggests that this relationship is not linear for skinned fibres or whole muscles (Rack & Westbury, 1969; Huijing, 1998). It is not a simple matter to define the biological structures each of these elements represents. For example, the series elastic element models the mechanical response to rapid length changes, and the response will include variable amounts of tendon (both external and internal muscle) compliance, cross-bridge elasticity and myofilament elasticity (Epstein & Herzog, 1998c). The parallel elastic element presumably represents the passive tension properties of the stretched muscle, although there is controversy as to whether it has an extra- or intra-fibre origin (Epstein & Herzog, 1998d). 1.3.1.4.3 Dynamic Jaw Modelling Although static analyses of the jaw have suggested joint and muscle loads, the functional environment of the jaw advocates a dynamic appraisal to understand more fully the interaction between motion and muscle, articular and dental loads (Hannam et al., 1997). The study of jaw dynamics involves the analysis of motion of a jaw, with mass and rotational 15 inertia, which is subjected to applied forces (Craig, 1986). Since the tension in each jaw muscle influences the tension in the other muscles, analytical techniques cannot be used to derive an exact solution (Jeffrey, 1996). The jaw is defined as a collection of mixed nonlinear differential and algebraic equations, which are solved with numerical integration methods to provide an approximate (although often very accurate) solution to the set of equations Geffrey, 1996). Dynamic analyses are sparse in the dental literature. Combined finite element analysis and jaw kinematics have been attempted by Chen and X u (1994) who developed a two-dimensional finite element model of the TMJ and used it to demonstrate areas of compression and tension through the joint during a closing movement. Although a small alteration in condylar displacement did have significant effects on the magnitude of condylar reaction forces and discal stresses, it was a promising approach at combining relatively large jaw motions with the deformable articular structures. Recently a system has been described that creates a finite element and a three-dimensional kinematic jaw model with image data from a human subject (Maki et al., 1999). Although these are two separate models, the next logical step would be incorporation of both into a dynamic deformable structure. Only recently have truly dynamic muscle driven models been realised. A model of the rat's masticatory system was developed which in fact was several separate models which fed consecutively into each other (Otten, 1987). The units which contributed to the overall model included static force-length fibre and muscle models, a dynamic muscle model based on calcium dynamics, fibre type, velocity-force relations and the static models, a kinematic model of the jaw system and a three-dimensional reconstruction package. By deconstructing the model and the solution process, the computation of results was simplified, however the time required to compute an overall solution was lengthy. A two dimensional dynamic model of the human jaw has been developed to simulate chewing (Ng, 1994) and more recently three-dimensional jaw models have been created (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999). These models use rigid body mechanics, although they can mimic compression and distortions in the TMJ and muscles with "energy-storage" components such as spring-damper analogues. They use Hill-type muscle models, and articular contact has been represented by either a point ("condyle") to plane ("temporal articulating surface") contact 16 (Langenbach & Hannam, 1999) or sphere to curvilinear surface (Koolstra & van Eijden, 1996). Neither study included the articular disc since flexible structures such as this are not trivial to model (Hannam, 1994). The simpler articulation in the former study was offset by its more complex muscle activity patterns used for masticatory simulation. 1.3.2 Jaw Motion Despite the wide variation in human mandibular movement, simple measurement of incisor displacement continues to be one of the diagnostic tests used in T M D (Dworkin & LeResche, 1992). Attempts at classifying movement patterns according to functional status of the jaw has been generally unsuccessful (Mauderli et al., 1988). As a consequence of this poor diagnostic validity, it has been suggested that the use of movement recording devices for diagnosis is inappropriate (Lund et al., 1995). Movement of specific, albeit putative, mandibular landmarks representing muscle insertions or ligament attachments have been calculated from whole body motion (Osborn, 1989; Osborn, 1993; Kang et al., 1993; Osborn, 1995; Goto et al., 1995). Findings include the notion that masseter muscle insertions move quite differently to each other in function, and that the temporomandibular, sphenomandibular and stylomandibular ligaments constrain the motion of the mandible (Osborn, 1989; Osborn, 1993; Kang et al., 1993; Osborn, 1995). These findings are interesting, since the different movement of muscle insertions implies muscle fibres with varying ability to generate tension. In the other studies, the ligaments were modelled as single line structures, when in reality they consist of multiple collagenous fibres inserting into relatively broad attachment sites. Nevertheless, they offer an argument for jaw and TMJ stability from passive tissue constraints as opposed to a stabilising influence from active muscle control (Kornecki, 1992). Stability of the TMJ during function is particularly important, as hypermobility has been implicated as an aetiological factor in T M D (Westling, 1992). This is supported in autopsy studies in which capsular attachments were found lower on the mandibular condyle in adults when compared to children, and it was speculated that this enabled greater joint mobility (Oberg et al., 1971). In addition, lower attachments on the condyle were associated with condyles with multiple deviations in structural form (suggestive of bony remodelling) (Solberg et al., 1985). The latter authors 17 suggested that loose capsular attachments and irregular condylar form may lead to joint instability. In studies where jaw kinematics were matched with anatomical reconstructions in human subjects, condyle-fossa distances were measured across the articular surfaces to suggest condylar loading patterns (Palla et al., 1997). No association between joint loading and condyle-fossa distance has been shown as of yet, and so the distance may be indicative of only the interposing disc's thickness and not its degree of compression. Nevertheless, the study is an interesting attempt at analysing some stracture-function relationships in the jaw joint. Dynamic mathematical models have been used in an attempt to associate jaw motion with muscle activity (Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999). Chewing, open-close and lateral motions were simulated, although only Langenbach's model attempted to match closely the model motion with that in the human. In the open-close models, the jaw opened and closed very quickly (0.2 s), and reached a maximum incisal gape of only 35 mm (Koolstra & van Eijden, 1997b), and in the lateral movements the lateral translation of the condyle was excessive (Koolstra & van Eijden, 1999). Nevertheless, these are the only studies that have attempted to match three-dimensional motion with muscle activity, and offer exciting prospects in looking at these relationships. The architecture of the human TMJ ensures that the mandibular condyle is capable of rotation and translation in all three planes. With the interposition of the articular disc, it is said that there is predominantly rotation between condyle and disc, and translation between disc and articular eminence (Rees, 1954). During jaw motion, there is co-ordination between the movement of the disc and condyle (Burnett et al., 1987; Maeda et al., 1992). The mechanisms involved in this co-ordinated movement are not known, although it has been proposed that the tautness in discal attachments to the condyle and temporal bone, compressive anteriorly directed forces onto the discs thickened rim (Osborn, 1985), lateral pterygoid muscle activity , or negative intraarticular pressure are responsible (reviewed by Scapino, 1997). It is interesting to note that a number of these hypotheses require a pre-condition of compressive forces within the TMJ to enable disc movement. 18 1.3.3 Jaw Muscle Function The functional capability of the jaw elevator muscles, in which pennated fibres predominate, is quite different to the jaw depressors which have a parallel fibre architecture. In general, pennate muscles with their small fibre:tendon ratios and increased fibre numbers, generate relatively large tensions over a smaller range of muscle lengths (Gans, 1982; Gans & de Vree, 1987) and with a smaller maximal velocity of shortening (Spector et al., 1980). Their fibre length shortening is less than whole muscle length shortening; this has been demonstrated in the rabbit digastric which showed 0.7 mm fibre shortening for 1 mm whole muscle shortening (Muhl, 1982). Since parallel-fibred muscle have more sarcomeres in series, any muscle length change results in a smaller length change per sarcomere (Gans, 1982). The possible muscle length change in this situation is thus greater, than in a muscle of similar length but with fewer sarcomeres in series. Parallel fibred jaw muscles generally produce translational motion of a muscle and its bony insertion (Miller, 1991b), whereas the effect of pennation is expected, although presently not shown, to cause rotations and translations of the jaw's musculotendon junctions resulting in complex bending and shearing movements of internal muscular aponeuroses (Hannam & McMillan, 1994). This is partly supported by ultrasonography of the aponeuroses in the tibialis anterior muscle, which demonstrated significant independent movement when contracted as opposed to very little movement, separate to the muscle fibres when the muscle was moved whilst it was inactive (Fukunaga et al., 1997). Tendon stiffness has been reported to be two orders of magnitude larger than muscle fibre stiffness in the finger (Garcia-Elias et al., 1991), and in the rat and cat hind limb tendons demonstrate minimal compliance in the normal range of motion (Griffiths, 1991; Hawkins & Bey, 1997). At the extremes, the tendon compliance allowed greater range of muscle length for active tension generation and a greater muscle length before passive forces were generated in the muscle. It was suggested that they acted as a mechanical buffer to protect muscle fibres from damage during eccentric contractions (Griffiths, 1991). Although the tendons in these studies did not resemble the complex three-dimensional structure of tendons in muscles such as the masseter, presumably the jaw muscle tendons provide similar functional advantages. In the human jaw muscles, some differences between the parallel-fibred and pennated muscle have been proposed using the pterygoid muscles as examples, in which the parallel lateral 19 pterygoid produces 1.7 times larger displacements and velocities than the pennate medial pterygoid which produces 1.6 times more force (van Eijden et al., 1995). 1.3.3.1 Muscle Tension Generation Total muscle tension is a combination of tensions generated from active (contracting sarcomeres) and passive structures (sarcomeres and extra-fibre connective tissues) (Magid & Law, 1985; Brown et al., 1996; Epstein & Herzog, 1998b). 1.3.3.1.1 Maximum Muscle Tension Since tension measurements of individual jaw muscles are not possible, and muscular strength is determined by total muscle fibre number, the total cross-sectional fibre area of a muscle - physiological cross-section (PCS), is used to provide an indication of a muscle's maximal isometric strength (Schantz et al., 1983). This is an absolute value, and variations in actual muscle strength may be caused by differences in subjects' motivation, ability to fully activate muscles, to inhibit antagonist muscles and to ignore discomfort or pain (Kroemer & Man-as, 1980). PCS has been practically determined by two methods: 1. the ratio between total muscle weight and mean fibre length (Weber PCS)(Weber, 1846), and 2. total cross-section of teased muscle fibre bundles (Buchner PCS)(Weijs & Hillen, 1984b). For the jaw muscles, both methods correlated strongly, although the latter always provided lower values (Schumacher, 1961; Honee, 1972; Weijs & Hillen, 1984b). It has been speculated that differences between these two methods may be due to either an underestimation of fibre length because muscle fibres were broken short of their periosteal and tendinous attachments, or short fibres sliding past each other, and thus not measured in the Buchner PCS (Weijs & Hillen, 1984b). Muscle imaging has been used to derive PCS from live subjects. Computed tomography (CT) and particularly magnetic resonance imaging (MBS) both provide high 20 resolution and excellent muscle detail. Limb muscle cross-section has been measured with ultrasound, however for the jaw musculature, ultrasound lacks resolution, and is unable to depict the bony covered pterygoid muscles. Jaw muscle cross-sectional area has been measured with a planimeter on computer tomographic images, and PCS can be accurately predicted from these measurements by a specific linear regression equation for each muscle (Weijs & Hillen, 1984b; Weijs & Hillen, 1985a). To reduce radiation exposure, CT scans were limited to one for each muscle (masseter, medial pterygoid, temporalis), and were oriented parallel to the mean fibre direction of each muscle. In predicting PCS from imaged muscle cross-sections, error may be present from a variety of sources including determination of selected scanning planes, determination of the surface of the scans and in the use of regression equation, which has a residual error, to predict the PCS (Weijs & Hillen, 1984b). The final prediction has an error of 10-20%. It appears that PCS of the jaw muscles is larger in younger subjects. This may be due to the dentition status and/or age of the subjects (Schumacher, 1961; Weijs & Hillen, 1984b), as it has been reported that bite force reduction is associated with a loss of teeth (Atkinson & Ralph, 1973; Carlsson, 1974), and masticatory performance remains unchanged (Feldman et al., 1980) or diminishes (Baum & Bodner, 1983) with increasing age. The intrinsic strength of a muscle (force/unit of PCS) has been determined as between 30-100 Ncm"2 (Haxton, 1944; Ikai & Fukunaga, 1968; Fukunaga, 1973; Nygaard et al., 1983; Maughan et al., 1983). Generally this large variation was attributable to applying poorly standardised methods. In order to obtain acceptable intrinsic strength values, the isometric voluntary contraction and PCS should be at muscle optimum length, all relevant muscles forces should be considered, the determination of maximum strength should be standardised, and the measurement of mechanical advantage, force and PCS should be in the same subjects, or mean values obtained from the same population (Weijs & Hillen, 1985b). Recent values for skeletal muscle intrinsic strength of between 30-50 Ncm"2 have been established (Ikai & Fukunaga, 1968; Fukunaga, 1973; Nygaard et al., 1983). Weijs and Hillen obtained a value of 37 Ncm"2 for the human jaw muscles (masseter, temporalis and medial 21 pterygoid) of 26 healthy adult males (1985b). Measurements of PCS were derived from CT scans of the muscles at mouth closed position, and then adjusted to an open jaw position (anterior tooth separation 15 mm) where it was considered muscle length to be optimum. 1.3.3.1.2 Active Muscle Tension The generation of "active" muscle tension is dependent on the sarcomeres' length and velocity states and motor unit recruitment (Muhl et al., 1978). Although experiments demonstrating these sarcomere relationships have not been performed in the human jaw muscles, these relationships are widely accepted for skeletal muscles and have been corroborated in mammalian jaw muscle studies (Muhl et al., 1978; Herring et al., 1979; Muhl, 1982; Weijs & van der Wielen-drent, 1983; Anapol et al., 1987). 1.3.3.1.2.1. Length-tension and velocity-tension relationships In the human jaw, length-tension relationships have been examined indireafy with bite force studies in which maximum interocclusal forces, as a result of jaw muscle coactivation, were measured at different jaw gapes (Manns et al., 1979; Mackenna & Turker, 1983; Gelb, 1990). The relationship with maximum isometric muscle tension is not a direct one, as maximum voluntary bite force increases when the periodontium is anaesthetised, suggesting that it is modified by intraoral afferent activity (Orchardson & MacFarlane, 1980). Bite force has been shown to increase to a maximum at approximately 20 mm incisor gape, and then decreased with further gape; and it has been suggested that this jaw position of maximum bite force is the position where the muscles are closest to their optimal length and to their optimal muscle orientation (Koolstra et al., 1988). Interestingly with even further gape, the bite force has been shown to increase again to reach a maximum at approximately 40 mm gape (Fields et al., 1986). This may be explained on the basis that the bite force was a resultant of not one but several muscles, with differing orientations and gapes at which their maximum tensions were produced (Takada et al., 1984; Bakke, 1993). In addition, unless the force transducers measures three-dimensional bite forces, results may be indicative of only uniaxial forces without consideration of other axial forces and torques, and thus may not be representative of the resultant force. 22 Maximum active isometric tension of a sarcomere increases with increases in its length to reach a maximum tension at a specific optimal sarcomere length, followed by gradual tension reduction with further sarcomere lengthening (Herzog, 1994). Estimates based on myofilament lengths suggest active force production is possible for human sarcomere lengths between 1.27 and 4.24 /xm, which equates approximately to a range of 50-169% of the sarcomere's optimal length (Herzog, 1994). Further modifications to active muscle tension is achieved by velocity changes of the muscle whereby tension is increased (or decreased) with eccentric, lengthening (or concentric, shortening) contractions (Zajac, 1989). This force-velocity relationship is often scaled to represent less than maximum activation, however like the force-length relationship, the scaling may not be linear (Moss, 1986). In addition, preceding events affects this relationship; an example is that a prestretched muscle shortens more quickly than one without a stretching history (Cavagna & Citterio, 1974). For the whole muscle, the relationship between force, length and velocity is more complex, especially when heterogeneous sarcomere lengths and fibre lengths and orientations exist such as in many of the jaw muscles (van Eijden et al., 1997). In the rat, this heterogeneity has been shown to augment the range of muscle lengths for active tension production by 40% (Willems & Huijing, 1994). In addition, the notion that maximum fibre tension in each motor unit may not coincide with the optimal length of the muscle suggests fibre and sarcomere heterogeneity may impart a range of lengths, rather than a single specific muscle length at which maximal tension occurs (Wood, 1986a; Bigland-Ritchie et al., 1992). 1.3.3.1.3 Passive Muscle Tension Resting muscle is considered a viscoelastic structure when stretched (Fung, 1993c), although the contribution of viscous and elastic forces to overall passive muscle tension for the jaw is unknown. Only limited information exists on the relative contribution to overall tension by passive elastic elements in the jaw muscles (Lynn & Yemm, 1971; Miles et al., 1986). Presumably this component contributes in a similar fashion to other skeletal muscles so that passive tension is generated when the muscle is lengthened beyond its resting, slack length, (a 23 position which does not necessarily coincide with the muscle's optimal length), and increases exponentially with increasing muscle length (Woittiez et al., 1983; Brown et al., 1996; Scott et al., 1996). Passive tensions have not been recorded for individual human jaw muscles, rather collectively for the whole masticatory system (Lynn & Yemm, 1971; Miles et al., 1986). The overall tensions followed an exponential form when plotted against jaw gape, or against putative masseter muscle length changes. For wide jaw opening, the collective tensions generated were in the vicinity of 10 Newtons in one study (Lynn & Yemm, 1971) and 40 N in the other (Miles et al., 1986). It was suggested that this difference may have arisen because the former study did not use E M G feedback to reduce the likelihood of contribution from muscle depressor activity and in addition, their subjects' gapes may have been less (Miles et al., 1986). The relative contributions to passive tension from individual structures including connective tissues, sarcolemma, and sarcomere myofilaments within the muscles and adjacent connective tensions were not known. Nevertheless, at least one of the studies implies low tensions were generated within each of the stretched elevator muscles. The resistance to mouth opening was always larger than the assistance to mouth closing at any mouth gape, and the force-gape diagram appeared as an open loop or Lissajous figure. This pattern has been described in displacement of the finger, and interpreted as frictional and viscous influences in the system (Long et al., 1964). Alternatively Lynn and Yemm suggest that the mandibular elevators may have actively opposed the opening, and assisted the closure. The passive tensions generated at wide jaw gape in these studies essentially reflect the elastic nature of the muscle, as the opening was performed slowly thus reducing any velocity-related influences. Assessment of the viscous component of jaw stiffness has been attempted by inducing an alternating open-close torque to the mandible in 6 subjects (p. 125 Walsh, 1992a). When the force changed from an opening-directed to a closing-directed one, the jaw immediately moved in the closing direction but then started to decelerate at around 10 msec following the force reversal. No muscle activity was recorded in either elevator or depressor muscles during this period, and it was considered reflex events would not have contributed in this short time. In other studies, a rapid loss in bite force was consistently found in subjects who participated in unloading experiments (in which the resistance to a forceful static bite was suddenly removed). These relatively immediate decreases in force 24 could not be explained by muscle co-contraction or reflex activity (van Willigen et al., 1997; Slager et al., 1998). The above findings suggest the jaw is a relatively stiff system, and that processes at the sarcomere level may be responsible (e.g., heterogeneous behaviour of contracting sarcomeres, or history dependent properties; Slager et al., 1998). The previous state of a muscle could have a profound effect on its mechanical properties. A good example of this is the effect of movement history on a muscle's passive tension. Muscle thixotropy, i.e., behaviour as a solid below a certain applied shear force, and as a fluid at higher forces, has been used to describe the friction-like behaviour of passive muscle to movement (Lakie et al., 1979; Lakie et al., 1980; Lakie et al., 1984; Walsh & Wright, 1988; Walsh, 1992a & b; Proske et al., 1993; Simons & Mense, 1998). This effect has been explained by the formation of cross-bridges between actin and myosin filaments of muscles which are inactive for some time, and the subsequent breaking of these bridges when a muscle moves beyond a certain range (Hill, 1968; Hagbarth et al., 1985; p. 85 Walsh, 1992a). These properties were originally observed in skeletal muscle of the frog which displayed a tension increase in the initial 0.2% of muscle lengthening, and no increase in tension with further lengthening (Hill, 1968). This tension was not related directly to length or velocity. Thixotropic effects have been observed in the human finger, wrist, arm, hip and synovial fluid and suggested in postural control (Finlay, 1978; Lakie et al., 1980; Ivanenko, 1986; Lakie et al., 1986; Walsh & Wright, 1988; Safari et al., 1990; p. 101, Walsh, 1992a; Tal'nov et al., 1997; Hagbarth & Nordin, 1998). Indeed this physical phenomenon may explain partly the maintenance of the jaw's rest position with little or no observed muscle activity (Miller, 1991). 1.3.3.2 Muscle Activity In mammals, contraction of multiple muscles is necessary to effect normal functional jaw movements (Hannam & Wood, 1981; Gibbs et al., 1984; Wood, 1987; Miller, 1991b). The jaw has many more muscles than its degrees of freedom, and thus is considered mechanically redundant (Weijs & van Ruijven, 1990). One consequence of this redundancy is that to perform a certain task, the central nervous system has multiple combinations of muscles from which to select. Presumably then, the diversity in jaw function is partly a product of the selection of coactivating muscles, their individual timing patterns and level of motor drive (Lund, 1991). Interestingly, many tasks are produced by a relatively uniform motor patterns and an attempt has been made to group task specific muscles into triplets to 25 demonstrate common themes in motor control (Weijs, 1994). This approach of simplifying muscle recruitment has facilitated comparative mammalian studies, and offers promise in modelling studies since they prefer simpler rather than more complex muscle activity patterns (Nigg, 1994b). Mathematical models have demonstrated coactivation patterns required for masticatory (Langenbach & Hannam, 1999) and open-close (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b) tasks. In the former study, aaivity patterns were derived from E M G contraction profiles, whereas in the latter muscles were driven with a constant activation level. The muscles were represented by Hill type straight line actuators with force-length-velocity properties derived from empirical relationships of these variables (Zajac, 1989) or animal studies (van Ruijven & Weijs, 1990) and then scaled to the jaw muscles' maximum tensions. Of note is that neither of these models were able to open to incisor gapes of more than 35 mm, even when maximal activity was assigned to the depressor muscles. This suggests that assigning animal or even general skeletal muscle properties to the jaw muscles may not be appropriate. Animal E M G (e.g, Herring et al., 1979), human E M G (Belser & Hannam, 1986; McMillan, 1993; e.g., Blanksma & van Eijden, 1995) and modelling studies (van Eijden et al., 1988; e.g., Koolstra & van Eijden, 1999) have demonstrated the functional heterogeneity within the more complexly arranged jaw muscles which presumably adds even more diversity and adaptation to jaw function (Hannam, 1997). E M G studies of the pig masseter have demonstrated antero-posterior differences during the closing phase of mastication (Herring et al., 1979), and in the rabbit, regional heterogeneity during mastication has been shown (Weijs & Dantuma, 1981). In addition, rabbit motor unit stimulation demonstrated differences in force direction and magnitude as measured by a multiaxial force gauge attached to the superior insertion of the muscle (Turkawski et al., 1998). These differences can be explained partly by sarcomeres displaying different lengths throughout the masseter muscle, and thus the potential to generate different active tensions (Weijs & van der Wielen-drent, 1983). Regional and motor unit E M G has been recorded in the human temporalis and masseter for a variety of functional tasks (Belser & Hannam, 1986; Blanksma & van Eijden, 1990; van Eijden et al., 1993; McMillan, 1993; Tonndorf & Hannam, 1994; Blanksma & van Eijden, 1995). For example, regional E M G studies have divided the masseter into superficial 26 and deep portions (McNaughton & Georgiadis, 1986; Blanksma et al., 1992; van Eijden et al., 1993) and further divisions of the deeper portion have been suggested for specific tasks (e.g., incisal clenching & open-close tasks van Eijden et al., 1993; Blanksma & van Eijden, 1995). The motor unit activity within this muscle demonstrates further task dependent divisions(McMillan & Hannam, 1991), and the majority of motor units tend to be located within specific compartments bounded by aponeuroses (Tonndorf & Hannam, 1994). However there are motor units which disregard the anatomical boundaries and cross the entire muscle cross-section (Stalberg & Eriksson, 1987; McMillan & Hannam, 1991; McMillan & Hannam, 1992). These larger motor units complicate the issue further with regards to functional specialisation of muscle regions, but could partly explain smooth muscle function, which would be otherwise difficult to produce with many separate functional regions within the muscle (Hannam & McMillan, 1994). Although different studies have reported different task dependent regions in these muscles, this can probably explained by differences in recording methodologies (electrode type and placement), low sample size, and non-standardised functional tasks. In a static two dimensional jaw model in which anatomical positions were derived from a cadaver, a muscle vector was assigned to each of the major muscle portions, and its angulation was allowed to vary between the anterior and posterior limits of the muscle portion(van Eijden et al., 1988). Notwithstanding that the directions of the muscle vectors were aligned to anatomical and not functional regions of the muscle, this study demonstrated the "anatomical" heterogeneity of the muscles with its results of varying bite force magnitude and direction with varying muscle angulations. In a three-dimensional model of the human jaw, individual muscle portions which were expected to produce a lateral jaw motion were represented by single line actuators and "activated" separately (Koolstra & van Eijden, 1999). Although in their most constrained model which included temporomandibular ligament analogues, the lateral motion of the model's condyle was greater than that recorded in human kinematic studies (Peck et al., 1999b), the overall jaw motion compared favourably to a similar in vivo human study in which regions of the temporalis and masseter were elearically stimulated (Zwijnenburg et al., 1996a; Zwijnenburg, 1997). The effects of pennation and tendon extensibility were not considered in these models, however it would be expected that they would provide further functional heterogeneity (Hannam et al., 1997). 27 1.3.4 Jaw Loading Human bite force studies have suggested the human jaw can withstand high compressive loads (see Hagberg, 1987a). Indeed, although average maximum bite force is in the region of 60 to 75 kg (588-735 N), a maximum bite force of 443 kg (4340 N) has been recorded in one individual (Gibbs et al., 1986). Bite forces during mastication are generally lower with studies reporting values between 30 and 380 N (Anderson, 1956; Haraldson et al., 1979; Hagberg, 1987b), and are influenced by food consistency (harder food comminution requires higher forces) and state of dentition (Hagberg, 1987a). The variability in bite force between subjects can be attributed to variation in a muscle's strength, its moment arm length, voluntary inhibition of full muscle recruitment, and separation between teeth. There is wide variation in craniofacial structure in the human population, and although the inter-relationships between the components that make up the jaw are limited, increased facial width is associated with larger masseter, medial pterygoid and temporalis muscles (Weijs & Hillen, 1986; Hannam & Wood, 1989). Additionally, maximum bite force levels in long faced individuals were smaller than in normals, and since this could not be completely explained by differences in muscle cross-sectional size and orientation it was suggested that there were intrinsic muscle differences with regard to force generating capacity between these craniofacial types (van Spronsen et al., 1992; van Spronsen et al., 1997). Bite force at the first molars is typically double or more of that at the incisors (Hannam, 1994), which is a consequence of increased contraction by more of the jaw muscles and shorter bite point moment arms (van Eijden, 1991). The rationale for the latter is that for equivalent muscle forces, the anterior bite force must be less than a posterior one if the moments at the TMJ were to remain the same. The best studies use a three dimensional force gauge, instead of the simpler transducer that is aligned perpendicular to the occlusal plane (van Eijden, 1991). This is necessary as both in vivo and modelling studies have demonstrated maximum bite forces are produced in the medial and posterior directions, rather than in the vertical direction (Koolstra et al., 1988; van Eijden, 1991). The structural framework of the human jaw provides further indications that it is capable of withstanding high functional loading patterns. For example, the maxilla primarily transfers compressive occlusal loads to the cranial vault which is facilitated by a trabecular 28 bone pattern oriented primarily in line with the stresses, with modifications to provide support to the dentition (Atkinson, 1964). This pattern provides a framework which can withstand compressive forces with minimal mass (Atkinson, 1965). On the other hand, the mandible absorbs these occlusal forces, resulting in complex bending and twisting movements (Hylander, 1985a; Hylander & Johnson, 1994; Korioth & Hannam, 1994a). Its external dense cortical structure with internal trabecular framework is able to withstand these diverse loads whilst minimising its mass and sustaining the metabolic needs of the jaw (Cowin, 1981). The adaptation of bone to alterations in its mechanical environment has been well established (Cowin, 1981; Cowin, 1990; Judex et al., 1997), although quantitative data on this adaptation is lacking. Trabecular patterns and mechanical properties in the condyle of the pig have demonstrated anisotropy and suggested that the condyle is strongest and stiffest in the supero-inferior direction (Teng & Herring, 1995; Teng & Herring, 1996). Similarly, the sagittal orientation of trabecular patterns and differential bone density have been observed in human specimens (Werner et al., 1991). In primate jaws, strong positive correlations between certain craniofacial measurements have suggested that relatively large condyles are associated with relatively large masticatory muscles and relatively inefficient biomechanics (Smith, 1983). The latter suggestion was based on findings of large condyles in prognathic mandibles, suggesting relatively inefficient incisor mechanics. In the human the development of the articular eminence has been suggested to be associated with functional condylar loading which produces anterior loading onto the temporal bone (Nickel et al., 1997). This hypothesis is supported by the lack of eminence development in cases of condylar agenesis (Kazanjian, 1940). These observations of structural adaptation to loading conditions supports the hypothesis that the structure of the facial skeleton is optimised for countering and dissipating stress (see Hylander & Johnson, 1997). However, this hypothesis, which is based on the premise that the skeleton exhibits maximum strength with a minimum amount of bony material, has been disputed by in vivo strain measurements. Regional strain analysis in primates has shown certain regions of the mandible to support this hypothesis, but that other regions in the facial skeleton (e.g., posterior zygomatic arch and supraorbital region) demonstrate relatively large bone mass for the stresses they endure (Hylander, 1979a; Bouvier & Hylander, 1981; Hylander et al., 1991). It has been suggested that these regions 29 may be strengthened to avoid damage from an infrequent traumatic non-masticatory load which would severely compromise either masticatory function, or damage the orbit or cranial vault (Hylander & Johnson, 1997). Strain analysis has demonstrated the complex bending and twisting patterns that occur in the mandible. In the macaque during the masticatory power stroke, the distortion of the jaw was complex, and basically the working side corpus was twisted so that the lower border everted, and the balancing side demonstrated parasagittal bending (Hylander, 1979b). A finite element model of the human jaw which was evaluated with strain patterns from a fresh specimen of the human mandible, displayed similar distortions for a simulated unilateral clench (Korioth et al., 1992). 1.3.4.1 Condylar loading It has been suggested that condylar loads change during development, increasing from a model-predicted 10 N at birth to 140 N at 25 years for a maximal molar biting task (Iwasaki et al., 1997). During growth, it has been estimated that the area of loading on the mandibular condyle increases approximately 3VS times to 70 mm 2 in the adult (Iwasaki et al., 1997), and it is suggested that loads will be distributed across this area regionally depending on the congruency between condyle, disc and temporal bone (Nickel & McLachlan, 1994). A n autopsy study of young adults demonstrated good congruence medio-laterally between the eminence and the condyle, where a convex condyle was often associated with a concave tubercle and flat condyle with flat tubercle as seen in the frontal plane (Solberg et al., 1985). Specimens with departures from these forms illustrated more deviations in condylar form, which have been suggested as functional adaptations to differential loading (Solberg et al., 1985), and presumably will maintain regional loading patterns. Indeed, regional strain patterns predicted with F E modelling for symmetric and asymmetric clenching tasks demonstrate task specific, differential condylar loading patterns (Hart et al., 1992; Korioth & Hannam, 1994b). In the two tasks which resulted in greatest condylar loads, maximum regional compressive forces occurred in the medial condylar third region of both TMJs with incisal clenching and in the lateral condylar third region for contralateral molar clenching (Korioth & Hannam, 1994b). Total compressive forces was 30 around 125 N on each condyle for incisal clenching, and 145 N and 98 N on the balancing and working side condyles respectively for unilateral molar clenching. With asymmetrical clenching tasks, the balancing to working side condylar force ratios was 3:2 for unilateral molar clenching or group function with a balancing side contact on the second molar, and for group function alone the ratio was 2:1. These findings of compressive joint loads fits with those in human and animal studies and in other static rigid beam models. A number of static rigid mathematical models have investigated the load distribution between the condyles (see Storey, 1995), but unlike the F E models, the condylar forces are a resultant at a single point (usually condylar centroid). Model-predicted TMJ compressive forces have been estimated to be around 300 N and 250 N for maximum intercuspal and incisal positioned clenches (see Hannam, 1994), although the largest value exceeded 510 N (Koolstra et al., 1988). Interestingly, this suggests that the condylar loads may exceed the bite force. Similar to F E studies, static models of asymmetric molar clenching predicted higher balancing condyle compressive forces (330 N) compared to working side forces (210 N) (Koolstra et al., 1988). These static models' forces are higher than those reported from F E studies (see above) and are probably due to the different methods of assigning muscle properties. For example in the F E models, muscle tension was represented as a series of force vectors acting over a muscle attachment region on the mandible, whereas in static models, the total muscle tension is directed at a single muscle attachment point on the mandible. Here, the resultant muscle forces may be identical, but the moments of the forces, acting at the TMJ, will be quite different. In addition, the generated muscle tensions differed as they were either scaled levels of maximum possible tensions (related to a muscle's size) derived from E M G responses for specific clenching tasks (FE model of Korioth & Hannam, 1994a), or determined by optimisation techniques which deterrnined muscle activity patterns that would rninimise joint or muscle forces for a specific clenching task(Barbenel, 1983; Baragar & Osborn, 1987; Koolstra et al., 1988) The major drawback with static analyses is that they cannot assess the changing magnitude and direction of muscle tensions during function (Throckmorton & Dechow, 1994). Loading was measured indirectly in human subjects by measuring intra-articular pressure of the upper joint cavity (Nitzan, 1994). Although positive pressures were measured during clenching, and negative ones during jaw opening, these observations probably 31 reflected motion rather than loading. In an assessment of whiplash injuries and TMJ forces resulting from impact-related extension-flexion neck motion, four subjects participated as occupants in controlled rear-end motor vehicle collisions (Howard et al., 1995; Howard et al., 1998). By measuring the resultant rearward acceleration of the cranium and assuming the mandible was a free body (with assigned inertial properties) which was carried along with the head, peak compressive forces in the TMJ were estimated at around 10 N , and compression was not in both extension and flexion of the cranium. N o reflex muscle activity, tonic muscle activity, or passive visco-elastic constraints were considered, and so it is interesting that the forces generated by essentially applying an impact force to the head were so low. Further these results agreed closely to acceleration (and thus force) values obtained with a head-neck mathematical model of rear-end collision (Schneider et al., 1989). Direct measurement of strains near the condylar surface of monkeys and pigs have generally demonstrated greater compressive than tensile strains, higher balancing strains during mastication, and similar strain values between the two animals (e.g., Hylander, 1979a; Marks et al., 1997). These findings are not rigid, as variation between animals is common; for example in one study of macaques, most of the animals demonstrated higher average balancing strains, however in one animal, similar average strains between both condyles were produced (Hylander & Bays, 1979). In the pig study, loads were estimated to range between 135 N (chewing) and 227 N (maximum muscle stimulation), and well below the failure load of the condyle as measured on pig samples (Teng & Herring, 1996). Two points are worthy of note regarding the calculated condylar loads: firstly a single gauge was used in these studies, so out of plane strains may have been missed, and secondly, strain is a measure of the change in shape of the bone surface, which is a consequence of not only the applied force but also the bones resistance to deform (Throckmorton & Dechow, 1994). In contradiction to the above studies, a study in which a thin piezoelectric transducer was cemented onto the condylar surface of monkeys demonstrated higher working side than balancing side forces. However, since only one joint was measured, working to balancing side forces were not compared simultaneously (Boyd et al., 1990). Furthermore, mandibular movement was not recorded, and so there was some ambiguity in determining working from balancing sides. Notwimstanding these reservations, the results may be plausible since a recent dynamic jaw 32 model has demonstrated similar findings (see below). In addition, theoretical static studies predict, depending on left-right muscle force ratios, that working side condylar forces could be higher than balancing side for a unilateral clench or masticatory cycle (Smith, 1978; Greaves, 1978; Hylander, 1985b). For a working/balancing muscle recruitment ratio of approximately 1.5:1 or greater, the working side condyle is predicted to be under greater compression than the balancing condyle (Hylander, 1985b). The recruitment ratio would be expected to change in mastication and be partly dependent on bolus position and consistency and type of masticatory stroke. Dynamic models have some of the misgivings of the static models, such as a rigid mandible and condylar forces calculated at a single point (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999). For open-close movements and masticatory tasks, these models demonstrated continual, but changing condylar compression. TMJ forces were greater in opening (approximately 75 N posteriorly directed and 110 N inferiorly directed) compared to closing (approximately 15 N anteriorly 25 N interiorly directed) as measured at the centre of gravity of the jaw (Koolstra & van Eijden, 1997b). In a dynamic assessment of unilateral chewing, ipsilateral condylar loading (> 50 N) was higher than contralateral loading (< 20 N) when the bolus was "cornminuted", and it was suggested that this was a result of differential muscle activity and condylar motion since the higher joint loads occurred at the ipsilateral condyle when it was "static" in its fossa, and when muscle tensions were maximal (and higher on the ipsilateral side) (Langenbach & Hannam, 1999). It must be reiterated that the maximum incisor gape these models were able to attain was 35 mm, which in clinical dentistry is considered one indicator of a dysfunctional system (Dworkin & LeResche, 1992). Nevertheless, comparison of these models with typical human jaw motions suggests they produce a reasonably accurate simulation of jaw dynamics. 1.4 SUMMARY The human jaw has a unique structure including multiple muscles with complex internal architecture, two temporomandibular joints that maintain apposition with the cranial skeleton, and a dentition that mtermittently contacts the maxillary teeth at multiple points. This combination allows the jaw to engage in diverse functional tasks which result in 33 relatively large and elaborate three-dimensional movements. The variables which are involved in these movements are not well understood, and dynamic assessments are necessary to gain insight into their relationships. Animal studies and human kinematic and electromyographic studies have provided much understanding of mandibular function, however in vivo techniques such as these do not (and may never) expose all of the inter-relationships between the responsible biological components. Dynamic mathematical modelling techniques have been recently applied to musculoskeletal systems. They use mechanical principles to predict the role of structural and functional variables involved in movement. Although application in the human jaws has been limited since they are computationally demanding, the preliminary results are favourable and suggest this to be a feasible method for future biomechanical studies. 34 2 STATEMENT OF T H E PROBLEM The biomechanics of the human jaw during function are not clearly understood. Currently, experiments designed to measure individual muscle tensions, joint loads and joint capsule strains during function are highly invasive. Understandably, many of these experiments cannot be performed in the human, and even if they were, the nature of the experimental methodology would most probably alter any variable being measured. Experiments which determine global characteristics of the jaw such as bite force are important, but to extract the multitude of individual components involved in their makeup is presently difficult, if not impossible. Mathematical modelling offers an approach in which the jaw can be deconstructed, thus enabling study of the variables shaping its motion. It overcomes many of the problems inherent in direct human experimentation. Notably, jaw modelling that applies the principles of dynamic mechanics offers insight into the interaction of the jaw's structural components (e.g., temporomandibular joint and capsular morphology, muscle morphology) and changing muscle tensions during function. The method is computationally intensive however, and only recently has it been applied to three-dimensional biological structures. In the present work, the following key areas of jaw biomechanics were considered: 1. The feasibility of using mathematical modelling to simulate plausible jaw function. Such viable models would provide a useful way to study presently unrecordable structural and functional variables of the human jaw. 2. The role of active and passive muscle tensions on jaw motion and articular forces. This would help illustrate why previous jaw models have been unable to simulate wide jaw opening, or plausible lateral jaw movements, and whether articular compression and stability can be maintained with muscle tensions. 35 3. The role of physical damping and elasticity with respect to muscle and jaw mechanics. The relative contribution of damping and elastic resistances to jaw movement is not known, although it is important in modelling the jaw's dynamic behaviour. 4. The role of the lateral capsular articular constraints on jaw motions. This would support or oppose the unproven notion, that this region of the temporomandibular joint is a major constraint to jaw movement. 5. The role of the complex internal architecture of the masseter muscle on passive tension generation. This would provide insight into the complicated interactions between aponeuroses and muscle components of a multipennnated muscle, and suggest whether the structure influences passive tension generation. To address these issues, the following experiments were carried out: 1. Construction of a dynamic muscle-driven mathematical jaw model in a format suitable for manipulation of multiple structural and functional variables. This system was used to address the following specific hypotheses: • That muscle tensions alone (i.e., in the absence of ligamentous or capsular tissue) could restrain jaw motion during jaw opening. This is reported in Chapter 3. • That the damping required in the jaw would be similar to that needed to critically-damp free jaw motion, (i.e., the jaw-closing muscles would function near their critical damping frequencies). This is reported in Chapter 4. 36 • That muscle tensions alone could restrain jaw motion during lateral, protrusive, and hinge-opening jaw movements. This is reported in Chapter 5. 2. Construction of a kinematic model of the lateral capsular wall of the temporomandibular joint. This was used to address the specific hypothesis that parts of the lateral capsular wall would be taut throughout excursive jaw movements. This is reported in Chapter 6. 3. Construction of a three-dimensional dynamic mathematical model of the masseter muscle. This was used to address the following specific hypotheses: • That the effects of the masseter muscles internal architecture limits passive tension generation. This is reported in Chapter 7. • That simpler masseter muscle models (used frequently in whole jaw modelling) provide reasonable estimates of the muscle's passive tension. This is reported in Chapter 7. 37 3 D Y N A M I C S I M U L A T I O N O F M U S C L E A N D A R T I C U L A R P R O P E R T I E S D U R I N G W I D E J A W O P E N I N G 3.1 ABSTRACT Human mandibular function is determined in part by masticatory muscle tensions and various morphological restraints within the craniomandibular system. Since only limited information about interactions between them can be obtained in vivo, mathematical modelling is a useful alternative, for it allows causal relationships between structure and function to be simulated, and the demonstration of hypothetical events in functional or dysfunctional systems. In this study, we initially determined the externally-applied force required to reach maximum jaw gape in 5 relaxed subjects, and used this information, with other musculo-skeletal data, to construct a dynamic, muscle-driven, three-dimensional mathematical model of the craniomandibular system. The model was programmed to express relationships between muscle tensions and articular morphology during wide jaw opening. We found a downward force of 5N could produce wide gape in vivo. When we adjusted the model's passive jaw-closing muscle tensions to permit this, the jaw's resting posture was lower than that normally observed in alert subjects, and it was necessary to add low-level active tone in the closer-muscles to maintain a typical rest position. Plausible jaw opening to wide gape was possible when activity in the opener-muscles increased incrementally over time. When the model was altered structurally by decreasing its angles of condylar guidance, jaw opening required less activity in these muscles. Plausible asymmetric jaw opening occurred with deactivation of the ipsilateral lateral pterygoid muscle actuator. The model's lateral deviation was limited by ipsilateral medial pterygoid passive tensions which forced the jaw to return towards the rnidline as opening continued. For all motions, the temporomandibular joint (TMJ) components were maintained in continual apposition, and displayed stable pathways despite the absence of constraining ligaments. Compressive TMJ forces were present in all cases, and increased to reach maximum values at wide gape. Dynamic mathematical modelling seems a useful way to study such presently unrecordable events in the human craniomandibular system. 38 3.2 INTRODUCTION The mandibular motions accompanying human suckling, respiration, swallowing, speech and mastication take place in a space constrained by jaw muscle tensions, the temporomandibular joints (TMJs), ligaments, and contacts between the maxillary and mandibular teeth (Posselt, 1952). These constraints complement functional demands, and disorders may result when structural or functional adaptive capacities are exceeded (Carlsson &LeResche, 1995). While previous studies of the functioning human jaw have provided some insight into its biomechanics, the invasiveness of many experimental procedures limits the information obtainable from living subjects. Although animal models are useful substitutes, inappropriate conclusions can be drawn when data are extrapolated to humans, not least because human jaw and joint structure and function are unique (Creanor & Noble, 1994). Mathematical modelling is an attractive alternative in this respect, for it offers a means to deconstruct the system in question, to manipulate the variables shaping its actions, and to demonstrate behaviour consistent with such experimental measures of the human condition that are available (see reviews by Hannam & Langenbach, 1995; Storey, 1995). In static modelling, the mandible is usually represented as a rigid or flexible structure acted on by variable muscle tensions, and constrained from moving by reaction forces at designated sites. In dynamic modelling, the mandible is defined as a physical structure (with specific inertial properties) acted upon by forces which may be constant (e.g. gravity) or changing (e.g. act-specific muscle-tensions), and the jaw is free to displace until its motion is arrested by constraining forces. Difficulties encountered in mathematical modelling however include the simulation of complexly-layered, multipennated masticatory muscles (see Hannam & McMillan, 1994), flexible and compressible articular discs, and mandibles capable of deformation (Korioth & Hannam, 1994a). Moreover, assignation of the appropriate physical values to the various structural components is not straightforward, often requiring simplification, and the use of unverified data. In fact, some desirable information may never be obtainable from living humans. Despite these limitations, recent dynamic jaw models are sophisticated, and suggest, inter alia, that active and passive muscle tensions interact to cause 39 TMJ compression during plausible jaw motions (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Langenbach et al., 1996a; Koolstra & van Eijden, 1997b). Perhaps the most significant limitation of present models, however, is their inability to demonstrate plausible jaw-gapes caused by maximum activation of the infra-mandibular and inferior lateral pterygoid muscles. Typically, their maximum gapes have been around 35 mm, well below the reported mean value of 51 mm (Szentpetery, 1993). Koolstra and van Eijden (1997b) suggested this restricted opening might be due to over-shortening of the opening muscles, which decreases the digastric and inferior lateral pterygoid tensions to approximately 40% (25 Newtons) and 50% (24 Newtons) (Koolstra & van Eijden, 1997a) of their maximum tensions respectively, thereby reducing their ability to overcome the passive tensions of the jaw-closing muscles. They considered that hyoid movement during opening in vivo (a missing factor in their simulation) would normally sustain opener muscle-lengths adequate for the tensions needed to open the jaw widely. While this may be so, it would only apply to the digastric muscles, since the lateral pterygoids have immobile origins. However maximum gape can also be reached by applying external forces of less than 10 Newtons to the jaws of relaxed subjects with inactive digastric muscles (Lynn & Yemm, 1971). Thus it seems that appropriate length-tension curves in the jaw-closing muscles would be needed to accommodate jaw opening under these conditions. The same curves would also have to accommodate other jaw positions believed to be influenced or maintained by passive muscle tensions, including the mandible's gravitational rest position (Oishi, 1967; Lynn & Yemm, 1971; Yemm, 1976; Miller & Chierici, 1977), which is believed to occur at an interincisal separation of 3-5 mm (Brill & Tryde, 1974). The rest position also fluctuates 2-3 mm during recording sessions (Dibdin & Griffiths, 1975) and is influenced by low levels of mandibular elevator activity in the alert subject (Kawamura et al., 1967; McNamara, Jr., 1974; Mailer, 1976). In summary, it would seem that plausible dynamic models should have length-tension properties assigned to closing muscles which satisfy the twin criteria of permitting gapes of 50 mm with a 10 Newton external force exerted on the mandible, while at the same time producing a gravity-determined jaw resting posture consistent with known behaviour. Consequently, it is possible that the jaw-closing muscles in such models may require different length-tension properties than have been assumed until now. 40 Mandibular translations and rotations affect jaw muscle attachments differently (Goto et al., 1995). Thus the balance between active and passive tensions can be expected to alter dynamically during different functions, and in response to any structural changes (which may also alter reaction forces). The predictions of a given human jaw model therefore have to be plausible for a variety of functional acts, and remain so for various boundary morphologies, e.g. in the temporomandibular articulation. A n appropriate dynamic "balance" between active and passive muscle tensions for a given system is critical here, since tensions are major determinants of jaw position within the functional envelope of motion. If this "balance" does not occur, ligamentous or some other external constraints must be invoked to control jaw motion. In the present study, our initial aim was to verify the externally-applied force needed to reach maximum jaw gape in relaxed subjects (i.e., to confirm the suggestions made previously by Lynn & Yemm, 1971). We then constructed a dynamic, muscle-driven mathematical jaw model that could duplicate both this behaviour, as well as a plausible, gravitational resting posture. We suspected these twin requirements might demand modification of the passive length-tension curves used in previous studies. On the premise that we could design such a model, our second aim was to determine whether muscle tensions alone (i.e., in the absence of ligamentous or similar passive restraints) could restrain jaw motion during wide midline opening, and during opening with a lateral deviation. Finally, we were interested in whether the model remained stable when systematic alterations were made to articular morphology. 3.3 METHODS 3.3.1 Determination of Forces Required to Attain Wide-Gape To confirm behavioural parameters associated with externally-induced jaw-opening, we measured the magnitude and angle of the force needed to attain maximum gape in five healthy adults (4c?, 1 ?; age range 25-31 yr.). In each subject, a customised acrylic clutch, fixed to the lower dental arch, provided a rigid platform over the mandibular incisors. A 10 cm shaft, extending from a hand-held digital force-gauge (Accuforce Cadet, Ametek, Largo, FL), was fixed to the clutch with a universal joint, allowing the mandible to be pushed or 41 pulled with a known force in any direction on the midsagittal plane. Calibrated, linear scales were attached separately to the mandibular clutch, the transducer's shaft, and a cranially-supported spectacle-frame worn by the subject. The relative positions and orientations of the scales were recorded continuously with a fixed video camera (Hi8 VM-H38A, Hitachi-Canada, Quebec) which was aligned with its optical axis perpendicular to the parasagittal plane. The recording sessions were performed in an isolated room. Each subject was seated in a slightly reclined dental chair, and instructed to remain as relaxed as possible. With a restraining hand on the subject's forehead, the operator slowly depressed the mandible with the force gauge until maximum gape was attained. Throughout the movement, the operator used the camera's microphone to record verbally (and continuously) the value of the force displayed digitally on the gauge. In this way, cranial, jaw and shaft positions and orientations could be correlated with the applied force. After each recording session, single video frames at the beginning and end of opening were digitised via a UNIX-based workstation (TRIS Capture 1.3.3, SGI, Mountain View CA). Screen pixel co-ordinates corresponding to all scale-markers were extracted individually from these images (IRIS ImgView 2.1, SGI, Mountain ViewCA). The marker positions were used to calculate (i) the linear distance travelled during opening by the shaft's attachment site on the clutch, and (ii) the direction of the applied force (i.e., the orientation of the shaft), relative to the occlusal plane. The average direction and magnitude of this applied force was input into the jaw model to help determine passive muscle tensions at wide gape (see below in Specification of Passive Muscle Tension Properties). 3.3.2 Definition of the Jaw Model The model was based on previously published descriptions of musculoskeletal geometry (Baron & Debussy, 1979) and muscle physical properties (van Eijden & Raadsheer, 1992; van Eijden et al., 1995; van Eijden et al., 1996; van Eijden et al., 1997). It allowed six degrees-of-freedom motion, shaped by forces from 16 craniomandibular muscle groups, two TMJs, and gravity (Figure 1). We developed it with commercially available software written specifically for the design, visualisation and analysis of dynamic models common in 42 Figure 1 Anterolateral view of the basic model showing the muscle group actuators' lines of action. Muscle groups: 1-anterior digastric; 2-superficial masseter; 3-medial pterygoid; 4-deep masseter; 5-lateral pterygoid; 6-posterior temporalis; 7-middle temporalis; 8-anterior temporalis. 4 3 mechanical engineering (ADAMS; MDI, Ann Arbor, ML). We ran the program on an Indy RS4000 workstation (Silicon Graphics Inc., Mountain View, CA). A D A M S defined the system as a collection of mixed nonlinear differential and algebraic equations, and subsequently solved them with numerical integration methods. Briefly, this involved a two-phase predictor-corrector technique, whereby initially a solution was estimated at a point in time in the analysis by fitting a polynomial through solutions at previous points in time and extrapolating forward. To improve upon this predicted solution, the corrector phase is implemented where time is held constant temporarily and the predicted solution is iteratively improved upon using the numerical integration algorithm. These iterations continue until either differences in successive iterations are below a user-defined tolerance, or the user-specified number of iterations have been performed. If the former occurs whereby the corrector has converged all displacement variables to within the tolerance before the number of iterations have been performed, then the solution is accepted and the process continues by initiating another predicted solution at a step forward in time. If the latter occurs, the predicted solution has not converged and is rejected, and the predictor-corrector technique backs up to a point in time closer to the previous acceptable time step than that just used in the failed solution estimate. In addition, the order of the polynomial used to predict a solution is also reduced to assist in finding an acceptable solution. 3.3.2.1 Mandible and Dentition The mandible was defined as a rigid body with a mass of 200 g. It was located in the midline (10 mm below the second molar bite point), and had the following moments of inertia: L^: 92.2, l^: 182.2 and 1^ : 125.2 Kgm 2 . These properties were derived from a finite-element model of an intact human jaw previously developed in our laboratory (see Langenbach & Hannam, 1999). The mandible was positioned in a gravitational field of 9.8 ms"2 to simulate a head in upright posture. The dentition was represented by flat maxillary and mandibular occlusal planes without cusps. Vertically-directed reaction forces on the mandibular teeth (1000 N/mm) simulated the occlusal interface, and prevented further jaw-closing. 44 3.3.2.2 Temporomandibular Joints The TMJs were ellipsoidal, canted condylar shapes that rotated and slid against frictionless, curvilinear surfaces (Figure 2). Each condyle measured 20 mm mediolaterally, 10 mm supero-inferiorly and 10 mm antero-posteriorfy (Oberg et al., 1971). We used physical constants to define the resistance, i.e., the functional boundary, formed by each articular fossa and its disc. The lateral profile of this boundary was represented by the function, y = 5* cos^— * 7rj — 5, where x and y were the anteroposterior and supero-inferior co-ordinates respectively. The boundary consisted of seven contiguous plates that provided a curvilinear surface boundary with anterior, inferior and lateral dimensions of 19 mm, 10 mm and 24 mm respectively, and a condylar path inclination of approximately 40° to the occlusal plane (Lundeen et al., 1978). The sagittal plane inclination of each fossa/disc boundary was 20° to the mid-sagittal plane, so that the medial pole of the condyle was posterior to the lateral pole (Yale et al., 1966). To investigate the relationship between structure and function, a second pair of TMJs was developed with similar morphologies to the above, except that the condylar path inclination in each was reduced to approximately 25° to the occlusal plane (Figure 2). Each condyle was monitored for possible contact with its functional fossa-disc boundary, by fmding intersections between these two objects' geometries. When contact was detected, and if the computed post-contact velocity was below a nominal 1 mm/sec, then the contact between the two bodies was assumed to be persistent. If contact were intermittent, an impulse-based, momentum-balance computation was performed, which resulted in the objects separating with an instantaneous change in velocity, i.e., colliding and rebounding. In the constant contact case, an instantaneous constraint was applied between the two objects, but if the force at the constraint indicated the objects were trying to separate, the constraint was removed. Since material properties were unavailable for these combined bone-collagen objects, we assigned values previously described for bone and fibrocartilage, i.e., we used a Young's modulus of elasticity, Poisson's ratio and density at 0.2 GPa, 0.35 and 1.8 g/cm3 respectively (Wong & Carter, 1988; Dechow et al., 1993). The value for the coefficient of restitution was one, denoting an elastic collision, with conservation of momentum and 45 Figure 2 Temporomandibular joint analogues. Joints with 40° condylar guidance (upper) and 25° condylar guidance (lower). energy. Each condyle could distract freely from its boundary, and there were no ligamentous or soft tissue constraints. 3.3.2.3 Muscles The masseterj temporalis, medial and lateral pterygoid and digastric muscles were divided into 18 functional groups for which physiological data were available. The jaw-closing muscles were represented by anterior, middle and posterior temporalis, superficial and deep masseter, and medial pterygoid muscle groups. The opening muscles were represented by anterior digastric and lateral pterygoid (inferior head) groups. The muscles (and then-subgroups) were simulated with Hill-type, flexible, single-line actuators (Zajac, 1989). Each had a fibre and a tendon component, together producing active and passive tensions. Apart from the digastric muscle, all muscle attachment sites were derived from the work of Baron and Debussy (1979), which was based on five human skulls. The actuator orientations represented the central axis of the body of each muscle or subgroup from origin to insertion (Figure 1). Special consideration was given to the digastric muscle, because its line of action is influenced by the position of the hyoid bone. The hyoid position changes during function (Winnberg, 1987; Winnberg et al., 1988; Haralabakis et al., 1993; Hiiemae et al., 1995) with a weak correlation relative to the mandible in its closed and maximum-open positions (Muto & Kanazawa, 1994). The angle between the mandibular plane and hyoidale varies between 10° and 17° during jaw opening (Pancherz et al., 1986; Winnberg et al., 1988), but to simplify the model, we chose a fixed line of action for the digastric actuator, which was 15° to the mandibular plane. We found it necessary to damp each muscle actuator (10 Nsm"1) to prevent high-frequency internal oscillations. We considered this represented muscle and other soft tissue damping likely to be present in vivo. 3.3.2.4 Specification of Muscle Fibre/Tendon Ratios A major criterion of the model was that it could undergo the full range of typical jaw motion under the influence of muscle-derived forces. During its construction, we utilised kinematic data to define the jaw's extreme range of motion, i.e., in each case, we produced typical border movements, as described by Posselt (1968), at the mandibular incisor and condyles (Figure 3). Invariably, these simulations showed that at the position of wide gape, 47 fc o H O c o ca ° > s E o i n C o •« o u s S3 , "3 ca ca 'spi o H O -fc c o s OS o c ca u O 6 E o S s .o '55 3 60 C l l c '5 8.1 lo1 ca o > E E o '5b ca c ca E E 60 a 60 |<S IS? *>l .5 c 1 1 c 'S lo & E S CO C 2 2 a o .2 » ~ ca T3 1 a w ID .2 a -o3 ca c I ca o e-a E . g OO o <u .. T 3 >^ C -o O C o o 60 ° C 60 o .S c ±i ca u-"ca o 2 -o 6 o u c c a .2 £ g a c .2 .2 W j a CO GO c c ca ca 1- u. .2 .2 <L> <U •*-» -fcj c c ca ca E E E E CN O oi .. J J - o >^  C T3 O C o o 60 ° C 60 o .S ca u. PQ i> 60 C '% I •2 § is S •2 3 -rt u. S 3 ca o > E E o i n ca '5b ca o e o ja _ca 00 CO C C ca ca c o o 60 ca E E oo jo >, -a c o o 60 60 c '% o = c c2 -2 ^ co 60 =S c o ! S O £ •a o S > 2 « -° « c a .2 S 2 3 & JO I c2 s 1 i ^ « 1 ^ .SP 4> S cu co S « u ^ .9 tS O Dh .2 £ u u « I n> <u on 3 6X 48 all jaw-closing muscles attained their individual maximum lengths. We set the maximum length for all closing muscles norninauy at 150% of their optimal length, in accord with typical values for skeletal muscle (Zajac, 1989). Although ranges of motion vary between different muscles, and indeed between individuals for the same muscle (Brown et al., 1996), we reasoned that 150% is the largest lengthening that most skeletal muscles would be expected to undergo. Selecting a larger rather than smaller relative maximum muscle length change meant that we always assigned the shortest optimal length possible to limit gape at any rest position derived from the passive muscle tensions alone. With the jaw at maximum gape (i.e. an inter-incisal opening of 50 mm, and a sagittal-plane rotation of 30°, Salaorni & Palla, 1993; Peck et al., 1997), we calculated the lengths of the muscle fibre and tendon components which would enable each muscle to reach its total length at maximum gape, while retaining fibre, tendon and sarcomere length-ratios consistent with the literature (van Eijden & Raadsheer, 1992; van Eijden et al., 1995; van Eijden et al., 1996; van Eijden et al., 1997). For these calculations, all length changes were assumed to occur within the fibre component. Tendons were modelled as inextensible elements because their functional lengths have been reported to change less than 4% (Curwin & Stanish, 1984). Components calculated this way meant, when the jaw was in the dental intercuspal position, that sarcomere lengths averaged 9% less than the 2.73 /zm previously assumed to be an optimal sarcomere length (Muhl et al., 1978). The properties we used are summarised in Table 1. 3.3.2.5 Specification of Muscle Tension Properties 3.3.2.5.1 Passive Muscle Tensions: Each muscle's passive tension, Fp, was represented by the function: ( musclelength ^ g maxjnusclelenglh j Fp = ^ exp , i.e. passive tension increased exponentially with increasing muscle length (Hill, 1953; Gordon et al., 1966; Woittiez et al., 1983). The maximum muscle length, maxmusclelength, was derived from the kinematic model's data (Figure 3 & Table 1), and is expressed as the muscle length change beyond 49 *(Fmax*factor) Passive Tension WO AST 2.28 0.98 2.10 1.90 1.15 0.91 Active tone at RP<(N) 0.35 0.15 0.31 0.28 0.17 0.14 190.4 81.6 174.8 158.0 95.6 75.6 66.9 40.0 S i 4.76 2.04 4.37 3.95 2.39 1.89 1.67 1.00 Proportion of whole muscle (%) o r\ o m o o T-H oo ON m o o o T-H Tendon length (mm) 23.67 8.40 26.09 37.77 31.59 39.17 * Z N—' CH nO •«*• ON CN NO o m oo T-H in u 5 S3 H 8,8 Sarcomere Length-IP* (um) 2.63 2.32 2.41 2.66 2.27 2.51 & iscle tn) 66.88 44.85 50.63 95.92 93.36 101.08 Muscle Length-u •* uinr 51.46 29.07 40.51 75.54 65.81 77.11 Muscle Group Superficial masseter Deep masseter Medial pterygoid Anterior temporalis Middle temporalis Posterior temporalis Lateral pterygoid Anterior Digastric U a o u u u 3 2 H 4> c o 50 optimal muscle length. Maximum passive muscle force, F^, and scaling factor, factor, were derived as outlined below. The exponent was raised to the power of exp to change the slope of the exponential function, and consequently the rate which passive tension developed with respect to muscle length. This latter variable was altered when we were determining the jaw model's rest position. Passive force began to increase at optimal muscle length (musdelengh = 0), and was greatest at maximum length {pwsddengh = maxjnusdden^h). Its maximum value (F^, was proportional to the muscle's cross-sectional size, and was determined by multiplying the muscle's physiological cross-sectional area (PCS) with an appropriate constant (Ikai & Fukunaga, 1968; Fukunaga, 1973; Pruim et al., 1980; Nygaard et al., 1983; Weijs & Hillen, 1985a; Fitts et al., 1991). Thus, for each muscle, F^ = PCS * 40 Ncm"2. The PCS values were obtained from whole muscle cross-sections (Weijs & Hillen, 1984a; Weijs & Hillen, 1984b) according to proportions derived by Nelson (1986) (see Table 1). To assign an appropriate length-tension curve to each muscle, each of the elevator's F^ was scaled by an identical factor in the following manner. We constructed a parametric jaw model with ADAMS, in which we specified this factor as the design variable. Factor was changed incrementally in a series of analyses, until passive length-tension curves were found which enabled the jaw, (with an externally-applied force as determined above from our experiment on five healthy adults, and in the presence of gravity), to reach stable equilibrium at a maximum gape of 50 mm. 3.3.2.5.2 Active Muscle Tensions: Each muscle's maximum-possible active tension also depended on its cross-sectional size, i.e. F^. However, the instantaneous active tension actually developed in each muscle as a consequence of neural drive was expressed by the linear'function: F = F,*r , , where Fx is the greatest force generated by the actuator for the task, and is < F^ , and is time of actuator activity. 51 In an attempt to improve the opening trajectory of the model for miiscle-activated midline jaw opening, the function expressing the digastric and/or lateral pterygoid actuator activity was then expanded to: Ft - F, *t, + F2 *t2... + Fn*tn , where Ft = original force as above, and F2... „ = additional force applied at time tz „ and t0<t1<t2<... tn<tf. 3.3.3 Jaw Dynamics For the model and its modifications (see Table 2) correlated dynamic properties were obtained, including predictions of loads between the condyles and disc/fossa boundaries, passive and active tensions in the muscle actuators, and displacements at the mandibular incisor and condyles. 3.3.3.1 Determination of the Mandibular Rest Position (Model 40RP) To determine the rest position, we allowed the model described above to reach a state of equilibrium, influenced by gravity and passive muscle tensions alone. In this model (Modd 40RP, see Table 2), we altered the variable exp in the passive tension function for each muscle in an attempt to reach the target rest position of an inter-incisal opening of 3-5 mm (Brill & Tryde, 1974). We postulated that if the jaw stabilised at a wider inter-incisal separation than this, it would be necessary to add steady-state active drive to all jaw-elevator actuators to achieve an acceptable rest position. Under these circumstances, any additional active muscle "tone" was specified as a constant fraction of each muscle's F^. It was determined by parameterising the model with tone as the design variable, and increasing this variable incrementally in a series of analyses until a typical rest position was achieved. 3.3.3.2 Muscle-Activated Midline Jaw Opening (Models' 40LF & 40XF) 3.3.3.2.1 Use of Linear Force-time Functions for Active Muscle Tensions (Modd 40LF) We coactivated the digastric and lateral pterygoid actuators on the above model to simulate jaw opening (Modd 40LF, see Table 2). A n optimisation technique was performed 52 H O W O l-l > Z o I—I z w H w 1-1 U y Q i 1 *3 -a CU d ^ O 1/6 JU (U II •1) tL) o S o 4) •8 1^-HH o •3-fe T3 CU B o >-c - i - i S cu rt d !_, cu o. d x <U <u i.3 to <u OA •a CM "N <N <L> CU 1 •73 y a o :s CO o a, T3 CO ,2 K ^ cu <u 6 f-8-6 H a to determine these actuator forces (modified method of feasible directions ADAMS, 1994a). A parametric model was defined by specifying digastric and lateral pterygoid actuator forces as design variables. Screening analyses were performed in which these design variables were systematically altered between zero force and F^. In this way, we determined a 5 - 10 N window within which each actuator would have to work when opening the jaw to maximum gape (50 ± 5 mm inter-incisal separation) in approximately one second, against passive tensions in the jaw closing actuators. Our objective was jaw-opening at a rate as close as possible to 2° rotation per mm of anterior condylar translation in the sagittal plane (Salaorni & Palla, 1993). This was expressed as the objective function, ^,yj{R IT — 2) 2 , where R = sagittal plane jaw rotation, and T = anterior condylar translation at each time step of the model simulation from intercuspal position to wide gape. We then invoked the optimisation algorithm to drive the actuators within the range determined by our screening analyses, so that this objective function was minimised and the function's derivative approached zero. This algorithm was constrained to a maximum inter-incisal gape between 48 and 52 mm, with an opening duration of 0.5-1 s. 3.3.3.2.2 Use of Expanded Linear Force-time Functions for Active Muscle Tensions (Modd40XF) Once the model had been optimised as above, we attempted to obtain a better opening trajectory by selectively adding digastric and/or lateral pterygoid actuator activity at points along the opening path where condylar rotation/translation varied by ± 0.5°/mm from our objective of 2%nm {Model 40XF, see Table 2). We detennined additional actuator activity with the same procedure; namely a screening analysis, followed by optimisation, on successive increments of the opening path. 3.3.3.3 Opening with Reduced Condylar Guidance (Models' 25PF, 25LF & 25XF) These models were developed to observe the effect of altered structural guidance by the articulation. Here, the antero-inferior condylar path inclination was reduced to approximately 25° relative to the occlusal plane (Figure 2). To achieve this, the disc/fossa boundary of the original model was rotated 15° upwards in the sagittal plane. In other 54 respects, the initial model (Modd 25PF, see Table 2) was identical to Modd 40XF, including the model's digastric and lateral pterygoid actuator activity, and wide jaw opening was attempted. To obtain a more typical opening trajectory, we again followed the sequence outlined above; a new model (Modd 25LF) was constructed with linear force-time functions for the active muscle tensions, and another (Model 25XF) constructed with expanded linear force-time functions for the active muscle tensions. These force functions were computed by the same procedure as above, i.e., design studies, followed by optimisation to minimise the objective function. 3.3.3.4 Asymmetrical Opening (MODEL 40LF-As) We constructed this model to observe the effect of an altered function on the system. We changed the task to asymmetrical jaw opening (still without ligamentous constraints). It was identical to Model 40LF, with the original antero-inferior condylar path inclination of 40°, and utilised linear force functions for the opener actuators. In this case however, the left lateral pterygoid actuator was deactivated so that the jaw moved to the left during opening (Modd 40LF - As). 3.4 RESULTS 3.4.1 Forces Required to Attain Wide-Gape Our measurements of the force needed to attain wide gape in relaxed, conscious subjects indicated that maximum, passively-guided jaw-gapes in excess of 45 mm could be achieved with levels of applied external force ranging from 4.5 N to 5.5 N (individual forces were: 4.5, 4.5, 5.1, 5.3, 5.5 N; at 87, 81, 81, 82, 84° respectively to the occlusal plane), thus confinriing Lynn and Yemm's conclusions (1971) that forces well under 10 N were sufficient to open the relaxed jaw fully. For modelling purposes therefore, we specified that the jaw should be able to reach an interincisal wide gape of 50 mm when a downward and backward-directed force of 5N was applied to the lower incisors, at 83° to the occlusal plane. 55 3.4.2 Definition of the Jaw Model 3.4.2.1 Specification of Passive Muscle Tension Properties At wide gape, the maximum passive tension in each of the muscles was calculated to be 1.2% (defined as factor'in the passive muscle tension function) of each muscle's (Table 1). With these passive tensions in the jaw closing actuators, plus gravity and a 5 N vertically-directed force applied to the model, equilibrium could be achieved at wide gape. The generic passive muscle length-tension curve used is seen in Figure 4, and examples of passive force-length relationships generated by the jaw elevators in the different models are seen in Figures 11 -14. 3.4.3 Jaw Dynamics 3.4.3.1 Determination of the Mandibular Rest Position Under the influence of gravity and passive muscle tension alone, the Modd 40RP reached rest positions (measured at the mandibular incisor) between 11-38 mm, when the exp variable (which determines the slope of the exponential function) ranged from 10 to 0.0001 (Figure 5). As values of exp below 0.1 provided only minor reductions in rest position, we selected this exp value, which provided a rest position gape of 11 mm. To raise this rest position gape to our target 3 - 5 mm inter-incisal opening, active tone was needed in each of the jaw closing muscle actuators. This corresponded to 0.18 % of each muscle's F^ (Table 1). 3.4.3.2 Muscle-Activated Midline Jaw Opening 3.4.3.2.1 Use of Linear Force-time Functions for Active Muscle Tensions (Modd 40LF) To simulate a plausible wide gape derived from activity of the jaw opening muscles, the series of screening analyses initially performed on Modd 40LF reduced the active tensions in the jaw opening actuators from their maximum range (ON-F^J to a range of 2 - 6 N for the digastric actuators, and 8 - 12 N for the lateral pterygoid actuators. To achieve typical jaw opening to wide gape, these reduced ranges of actuator values were utilised by the optimisation algorithm to open the jaw at a rate of 2° sagittal-plane jaw rotation/mm of 56 57 c G G o a 3 <u .5: 6D <2 G o S "I (A o <y o o o G T3 O -« 2 " g 8 S O tu -g W3 '—1 irj G « <u 55 £ y C o E 8 P anterior condylar translation. The optimised digastric and lateral pterygoid actuators' force functions were FDG=3.2*t] and FLP = 10.1*/, respectively (Figure 9). With these functions, wide gape was attained in 0.95 s, and tension in the lateral pterygoid muscle was more than three times that in the digastric muscle, the actuators reaching maximum force values of 9.6 N and 3.0 N respectively. Apart from the posterior temporalis which reached a maximum of 7.0 N , all passive muscle tensions were relatively low during the opening movement, with values less than 2.5N (Figure 11, Table 3). Condylar loading increased as the jaw opened, and peaked at 15.8 N at wide gape (Figure 16, Table 3). At various points along the opening path, Modd 40LF deviated by more than ± 0.5°/mm from our objective of 2°/mm, and indeed this objective was not reached until 0.48 seconds after opening commenced (Figure 15). Although wide gape was attained with these optimised actuator functions, the trajectory of the mandibular mid-incisor point in opening displayed a marked translatory component at approximately 2/3 gape (Figure 6). This movement coincided with the condyle's transition from the relatively vertically-oriented posterior wall to the horizontally-oriented crest of the eminence of the disc/fossa boundary. At this transition point, the condylar forces had increased to a maximum of 8.8 N , then remained relatively constant as the condyle negotiated the eminence's crest, and finally increased with further gape. 3.4.3.2.2 Use of Expanded Linear Force-time Functions for Active Muscle Tensions (Modd40XF) To improve the opening trajectory of Modd 40LF, we selectively added digastric or lateral pterygoid actuator activity when the objective function deviated by more than 0.5°/mm from our objective of 2°/mm. As the optimised objective function from Modd 40LF did not reach its goal of 2°/mm until 0.48 s of opening, we optimised the model for the initial 0.25 s of opening. It was then necessary to add additional lateral pterygoid actuator activity at 0.2 s, 0.4 s and 0.54 s, and to add additional digastric actuator activity at 0.48 s and 0.58 s. The resulting jaw trajectory and objective function can be seen in Figures 6 & 15 respectively; the final optimised, expanded linear functions for the lateral pterygoid and digastric actuators are presented in Table 4 and Figure 9. With these functions, wide gape of 50 mm was attained in 0.6 s, with the digastric and lateral pterygoid actuators reaching 59 maximum force values of 11.6 N and 16.8 N respectively. Apart from the passive muscle tension of the middle temporalis (which reached a maximum of 10.1 N), all passive muscle tensions remained below 4.6 N throughout the opening movement (Figure 12, Table 3). These maximum tensions coincided with maximum gape. The temporomandibular joints were compressively loaded throughout the opening movement: individual joint forces increased to a maximum of 28 N at 44 mm, and remained at this force level to wide gape (Figure 16). 3.4.3.3 Opening with Reduced Condylar Guidance In our first attempt at jaw opening with reduced condylar guidance angles, we used the expanded linear force-time functions from Model 40XF to define activity in the jaw opening actuators. This model (Modd 25PF) attained a gape of only 34 mm, and a sagittal plane jaw rotation of 24°, at which point the condyles had translated beyond their anterior limit of 20 mm in 0.48 s. The objective function resulting from this simulation did not approach the goal of 2° sagittal-plane jaw rotation/mm of anterior condylar translation. In our next attempt to simulate a plausible wide gape with reduced condylar guidance, we initially used linear actuator force functions (Modd 25LF), in which the optimised digastric and lateral pterygoid actuators' forces were F^ =3.0*^ and FLP = 6.0*tl respectively. Here, a wide gape of 50 mm was attained in 0.87 s (Figure 7), and tension in the lateral pterygoid muscle was twice that of the digastric muscle, with the actuators reaching maximum force values of 5.2 N and 2.6 N respectively (Figures 7 & 10). A l l passive muscle tensions were relatively low during the opening movement, with values less than 2.4N (Figure 13, Table 3). These passive tensions were maximal just prior to wide gape (superficial and deep masseter, and medial pterygoid tensions) or at wide gape (anterior, middle and posterior temporalis tensions). Condylar loading increased as the jaw opened and peaked at 10.0 N at wide gape (Figure 16, Table 3). As this model deviated by more than ± 0.5°/mm from our objective of 2°/mm at various points along the opening path, we subsequently selectively added more digastric or lateral pterygoid actuator aaivity to the simple linear force functions (Modd 25XF). The resulting jaw trajectory can be seen in Figure 7. The final optimised, expanded linear 60 functions for the lateral pterygoid and digastric actuators are outlined in Table 4 and Figure 10. Here, a gape of 48 mm was attained in 0.68 s, with the digastric and lateral pterygoid actuators reaching maximum force values of 3.4 N and 6.4 N respectively. Apart from the posterior temporalis muscle's passive tension of 12.2 N at wide gape, all passive muscle tensions remained below 2.0 N throughout the opening movement (Figure 14, Table 3). Superficial and deep masseter, medial pterygoid and anterior temporalis actuators reached their maximum tensions just prior to wide gape, whereas the middle and posterior temporalis actuators reached their maxima at wide gape. The temporomandibular joints were compressively loaded throughout the opening movement: joint forces increased to a maximum of 10.7 N at 40 mm, and then increased sharply to 17.9 N at wide gape (Figure 16), and followed the general form of passive tensions in superficial and deep masseter, medial pterygoid and anterior temporalis actuators. 3.4.3.4 Asymmetrical Opening Plausible eccentric jaw opening (Figure 8) was obtained by simply deactivating the left-sided lateral pterygoid actuator, and activating the right-sided lateral pterygoid and bilateral digastric actuators with the simple linear functions from Modd 40LF (Figure 9). In this case, the jaw opened, and moved to its extreme lateral position in 0.6 s, such that the mandibular incisor displaced 21 mm interiorly and 11 mm laterally. At this position, apart from tension in the left (ipsilateral) medial pterygoid muscle (which rose sharply to 4.5 N as the model approached this extreme lateral position), all left-side muscles' passive tensions were lower than right-side tensions (Figures 17 & 18, Table 3). Both condyles were compressively loaded throughout the movement, although unevenly so, with maximum values for the right and left condyles of 7.3 N (contralateral) and 4.1 N (ipsilateral) respectively (Figure 16, Table 3). The condyles remained in stable positions despite the absence of "ligaments" or any other constraints. After reaching its most lateral position, the jaw commenced a medial movement while continuing to displace interiorly (Figure 8). At this time, the left condyle began to move antero-inferiorly along the posterior wall of the eminence. The left medial pterygoid passive tension remained around 4.5 N , while those in the other closers remained fairly constant, or gradually increased (Figures 17 & 18). 61 3.5 DISCUSSION 3.5.1 Modelling Assumptions Computer models have been used widely to study muscle tensions, skeletal forces, motions, stresses, and strains in the back, lower limb, shoulder, elbow and jaw (e.g., McGill, 1992; Hawkins, 1992; van der Helm et al., 1992; Kuo & Zajac, 1993; Gonzales et al., 1993; Korioth & Hannam, 1994a; Osborn, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b). Al l such models are simpler than the systems they emulate, and ours is no exception, for it included a rigid mandible, a fixed hyoid bone, and single-line actuators instead of complex muscles. In addition, we were forced to estimate many unknown muscle and inertial parameters. Other parameters were simplified to permit workable mathematical solutions and computation times (see Table 1). We suggest our assumption of mandibular rigidity was reasonable, since skeletal distortion during jaw motion has been reported to be less than 1.5 mm at the first molar (de Marco & Paine, 1974). We also consider our treatment of articular disc and fossa restraint as a single, compressible surface boundary against which the condyle functioned as reasonable in context; modelling a separate articular disc during jaw opening was not computationally practicable, since it would have required combining large-motion rigid body mechanics with flexible-structure, finite-element modelling. While finite-element modelling has provided valuable insight into static jaw mechanics (Korioth & Versluis, 1997), only Chen and X u (1994) seem to have attempted dynamic finite-element modelling within the jaw. In their study, which was localised to the TMJ, a two-dimensional model was driven with joint motion data. Although the magnitudes of condylar reaction forces and discal stresses in this instance were very sensitive to small alterations in joint motion, stress distributions in the disc remained relatively unchanged. We fixed the position of the hyoid relative to the mandible, with digastric lines of action approximately 15° relative to the lower border of the mandible. The hyoid changes position during function (Winnberg, 1987; Winnberg et al., 1988; Haralabakis et al., 1993; Hiiemae et al., 1995), but its range of motion is not great, and in any event data regarding its position at maximum gape are sparse. Though the relative actions of the digastric muscle with respect to the hyoid apparatus were not the focus of this study, we have demonstrated 62 previously that digastric and lateral pterygoid actuators move the jaw on surprisingly similar trajectories to maximum gape whether or not the hyoid is depressed (Langenbach et al., 1996b). Hyoid motion would have had a negligible effect on jaw-closing muscle tensions. While hyoid depression must, of course, change the digastric's angle of attack (requiring a minor compensatory change in lateral pterygoid drive to maintain a given incisor-point trajectory), we consider its omission did not detract significantly from the study's conclusions, especially those related to maximum gape evoked (in the absence of muscle contraction) by means of an external force applied to the lower incisor region. Our simplification of the multipennate jaw-closing muscles as sets of single-line actuators was clearly not ideal. The human masseter alone contains at least five, interleaved, aponeurotic septa running at various angles, and it can contract regionally (van Eijden et al., 1993; Hannam & McMillan, 1994). Nevertheless, we are presently unaware of a better method for simulating internal fibre and tendon mechanics in complex muscles, and our approach is consistent with recent work by others on jaw muscle dynamics (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b). The actuators we used produced tensions proportional to each muscle's regional cross-sectional area, and they incorporated jaw muscle fibre-tendon ratios consistent with the literature. Also, in the case of the masseter and temporalis muscles, several actuators operated between attachment sites within the same muscle. They simulated different amounts of regional muscle stretch and the changing action lines dictated by the wide insertions of these muscles. Our specification of maximum muscle-lengths in the jaw closers as those at wide gape differed from those used in other recent models (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b). Our maximum muscle stretch invariably occurred at 150% optimal muscle fibre length, and it was uniform for all closing muscles. In vivo however, it is possible that different proportions of stretch occur among the different muscles at maximum gape (and indeed in the same muscle among different subjects) (Brown et al., 1996). The tension correlates for such length changes in hving human jaw muscles are however unreported, and it is difficult to visualise an experiment which could reveal them. While the complexities of internal organisation may evoke changes in fibre length which differ from those we assumed, it remains possible that the overall behaviour of each muscle as a whole approximates that of our actuator (or 63 actuator sets). We speculate, however, that the system more likely includes fibre and whole-muscle length-tension characteristics which are unique to each muscle. Notwithstanding these reservations, we propose that the more models display behavioural characteristics which mimic those known inwx>, the more plausible they become (Zajac, 1989), in this case providing a starting point for appraising what must be achieved by functioning human jaw muscles, and for experimenting with their properties. Viewed this way, our model predicted realistic spatial parameters for jaw-opening caused by opening muscles working against passive tensions in the closers. 3.5.2 Muscle Tensions By definition, maximum active muscle tension in each of our closers would develop at incisal gapes between 4 and 10 mm. Collectively, the muscles' optimal lengths occurred at different gapes which, if true, suggests the masticatory system is able to produce relatively large forces over a useful range of gapes. This gape at which the optimal length of the closers occurs is lower than the reported incisal gape of between 13 and 21 mm when maximum molar bite force is produced (Manns et al., 1979; Mackenna & Turker, 1983). However, our actuators had defined optimal muscle fibre lengths 2/3 of maximum fibre length, as this produced the maximum fibre stretch skeletal muscle is believed to undergo (Brown et al., 1996). If we reduced our assumed fibre stretch (which may indeed occur), then our optimal fibre length would be set at a wider gape, and agree more closely with values in the literature. By altering the model this way however, our rest position without activity in the jaw-closers would occur at an even wider gape, requiring more closing muscle tone to maintain a clinical rest position of 3 - 5mm. We were somewhat surprised that a force of only 5 N was needed to open the jaw widely in living subjects, though this confirmed earlier work in which a similar, low force of 0.65 kg (6.4 N) was reported (Lynn & Yemm, 1971). Low passive resistance has also been found in the rat tibialis muscles, where minimal passive tensions were generated within the muscles normal range of motion (Hawkins & Bey, 1997). Our rigorous requirement that the model should meet this specification, i.e., that the passive tensions of the closer actuators should permit wide gape with a 5 N external force, differs from previous work. Others have 64 assigned passive tension properties to the closing muscles by calculating the tensions as an exponential function of the sarcomere length (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; see Figure 4). These models however were unable to attain inter-incisal distances > 35 mm. Although this limited gape (at least in one study) was attributed in part to incorrect jaw-opener tensions at wide gape (Koolstra & van Eijden, 1997b), an attractive alternative explanation is that the passive tensions in the jaw-closers were too high. In these limited-gape studies, a one-to-one relationship between sarcomere length and whole muscle length change was used. For pennated muscles like the jaw closers however, sarcomere length change represents approximately 70% of the whole muscle length-change (Muhl, 1982; van Ruijven & Weijs, 1990). If this ratio were used in these studies, passive muscle forces would be expected to be lower than those reported. In addition, the values used in an exponential function to compute passive muscle tensions were derived from adult rabbits. As the passive muscle tension properties among young and adult rabbits (Weijs et al., 1989), and rats (Woittiez et al., 1986) differ, they may also be dissimilar from those in humans. The model behaved in a stable manner during asymmetric jaw opening, during which it required no modification of closing-muscle passive tension properties. This reinforces our impression that complex masticatory muscle behaviour can be represented, albeit crudely, with multiple actuators. 3.5.3 Mandibular Rest Position The gape requirements of the model meant that active closer-muscle tensions were needed to maintain a plausible mandibular resting posture. Our inability to find length-tension curves which simultaneously satisfied the twin criteria of maximum gape with a 5 N force applied to the jaw, and a normal clinical "rest position" of 3 - 5 mm incisal separation, implies that low-level muscle activity is indeed needed to establish the freeway space in the awake subject. This idea is not new, since it is consistent with previous studies on the plasticity of the position, and its dependence on alertness (Yemm, 1976; Rugh & Johnson, 1984). It is notable however that the additional tension needed in the closers was very low, and did not restrict muscle-driven jaw-opening when left "on". 65 3.5.4 Jaw Opening Normally, jaw opening includes digastric and lateral pterygoid coactivation. Matching jaw motions induced by our digastric and lateral pterygoid actuators were chiefly sagittal plane rotation and anterior jaw translation respectively (Langenbach et al., 1996a). Digastric activity (complemented by gravity) overcame the predominantly upward-directed jaw closer passive tensions, and lateral pterygoid activity caused anterior translation of the jaw, with wide jaw opening at a rate of 2° sagittal-plane jaw rotation per mm of anterior condylar translation. The active tensions in these muscles increased with time, so active jaw opening occurred over one second. The digastric and lateral pterygoid actuators reached a maximum of 11.6 N and 16.8 N respectively, which equates to approximately 30% and 25% of their respective (Table 3). Although the maximum tension a muscle is able to generate depends on its length and velocity (Zajac, 1989), these relationships were not incorporated into our actuators since their tensions never approached F^. Presumably F^ would be reached in these muscles during jaw-opening against resistance, in which case the active length-tension and velocity-tension relationships would have to be considered. 3.5.5 Articular Loading Direct studies in mammals suggest the temporomandibular joint is compressively loaded during function (Hylander, 1985b; Boyd et al., 1990; Nitzan, 1994), but there is some disagreement regarding when and where maximum articular loads occur (Hylander, 1985b; Boyd et al., 1990). Direct experimental measurement of articular loading is sparse (Hylander, 1979a; Hylander, 1985b; Boyd et al., 1990; Nitzan, 1994; Marks et al., 1997), though primate articular loads have been reported to range between 6-175 N for chewing, drinking and aggressive vocalisation (Boyd et al., 1990). In our model, increasing, compressive loading of both condyles took place during the entire phase of midline and eccentric opening, and consequently might be expected to maintain continual apposition of condyle, disc and fossa if its predictions apply in vivo (Figure 16). Maximum loads of 28 N occurred during midline opening in our model with steeper (40°) condylar guidance. This value is less than that reported in another study (approximately 75 N posteriorly-directed and 110 N inferiorry-directed forces with respect to 66 the mandibular centre of gravity (Koolstra & van Eijden, 1997b). One explanation is that our muscle activation of the jaw openers was significantly less than the 100% used in this previous work. It is particularly interesting that during the eccentric jaw opening caused by right-sided lateral pterygoid action and bilateral digastric activity, both condyles sustained compressive (though uneven) loads, and remained in apposition with the articular restraints despite the absence of "ligaments". The apparent appositional functioning within our model's two articulations during widely-excursive tasks reinforces our impression that for these acts at least, muscle tensions are a prime factor in mamtaining articular integrity during function. 3.6 C O N C L U S I O N S Movements like jaw opening involve a complex interaction between passive muscle tensions, active muscle tensions and craniofacial form. In this present study we were able to simulate plausible midline, and eccentric jaw opening by utilising available morphological and functional data in a three dimensional mathematical model. This model required active tone in the jaw-closers to maintain a simulated clinical rest position. Our results suggest that for these tasks, jaw function can be maintained in the absence of ligaments, and occurs in the presence of compressive articular loading. Tensions in the jaw-openers and -closers, and the resultant articular forces remained reasonably low, and would presumably increase if resistance to motion was encountered. 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CM PH cu rt CA •is cu cu u o 5 c5 _G 8 CO S 3 41 OH O .rg CO J-j cG "O J3 G O u O .ti vG £ •1-3 1 g u, G CO S •Sir CM CU 3 cu b .3 v _ Q <U G G cu G CM <U « C ' M 13 O -T3 3 1 o l-C a a • f l CO s § CO 8 ^ .s VV ^ W (I) 79 80 81 o u 4 F O R C E S R E S I S T I N G J A W D I S P L A C E M E N T I N R E L A X E D H U M A N S : A V I S C O E L A S T I C P H E N O M E N O N 4.1 ABSTRACT Forces opening the relaxed human jaw are resisted by intrinsic restraints, including passive tensions in the jaw-closing muscles. These muscle tensions have been modelled as viscoelastic elements, and static measurements suggest the elastic portion contributes approximately 5 N resistance to wide gape. However, viscous damping properties, which affect the jaw's dynamic behaviour, are unknown. Since dynamic models should match their human counterparts, and since dynamic human data are unavailable, we measured temporal changes in the forces required to open the jaw to full gape at two different opening rates. We used these data to determine the optimum muscle damping needed in a previously-described model of the average human jaw. Six normal subjects were taught muscle-relaxation techniques, and custom-fitted with a removable, acrylic, mandibular dental clutch linked to a bi-directional force-gauge which moved the jaw. Motion was recorded with a six degrees-of-freedom opto-electronic tracking system which measured the motion of the cranium, mandible and force-gauge. In each subject, simultaneous recordings of applied force and jaw motion were obtained for two repeated opening cycles, each lasting 5 or 20 seconds. This data was then used to drive a 3D dynamic jaw model in order to determine optimum damping properties of the masticatory system. During 5 second and 20 second opening, relatively low forces were required (6.7 + 3.3 N and 3.9 ± 2.43 N respectively, at 50% gape). Forces increased to reach maximum gape (mean: 49+2 mm), and more than doubled for 5 sec. relative to 20 sec. opening (20.9 ± 4.9 N vs. 8.2 ± 2.2 N). It was possible to reduce the force without decreasing jaw opening once wide gape was attained. The model determined damping constant needed in each jaw closer muscle was 150 Nsm"1, approximately 25% lower than calculated critical damping constants. This study suggests low forces are required to open the jaw in relaxed humans, and that passive and dynamic muscle properties assigned to models permit them to perform realistically when compared with living subjects. While these properties are presently impossible to verify in vivo, they offer a hypothetical construct for future experiments. 83 \ 4.2 INTRODUCTION Although the spatial limits of human jaw opening have been described previously (Posselt, 1952), the forces required to sustain them are unknown. Jaw opening involves interactions among active and passive tensions in the closing and opening muscles, and passive restraints by other tissues. It has been simulated in biomechanical models (see Chapter 3). Generally, these have utilised data specific to the human jaw, though in some cases properties have been extrapolated from more distant sites (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b). For example, the jaw's inertial properties (i.e., mass, centre of mass and moments of inertia) have been estimated from cadaveric specimens, from images of living subjects, and by finite element analysis (for review see Korioth & Versluis, 1997). Muscle drive patterns and muscle tensions have been based on task-related electromyography, general velocity-tension curves for skeletal muscle (Zajac, 1989) and specific measurements of cross-sectional muscle size (Koolstra & van Eijden, 1995; Langenbach & Hannam, 1999) (see Chapter 3). Passive muscle tensions, which resist muscle lengthening, have been derived from computed sarcomere length changes, length-tension curves from the rabbit (van Ruijven & Weijs, 1990), and the jaw's resistance to maintaining wide gape (Chapter 3). In simulation studies, passive muscle tension is usually represented by a viscoelastic spring-damper which imparts length (spring) and velocity (damper) dependent resistive forces to muscle stretch (Zajac, 1989). Thus in the jaw, the spring component of the closer-muscles determines the opener-muscle forces needed to maintain wide gape. The damper component of the closer-muscles affects the path of opening. A lightly-damped system will introduce vibratory motion. Heavy damping will eliminate vibrations, but impede motion. A critically-damped system can be assumed to be non-vibratory, and hinder motion minimally. Damping is often applied uniformly to the individual muscles in the system (Langenbach & Hannam, 1999) (Chapter 3), but it can also be applied to the jaw in toto (Koolstra & van Eijden, 1995). Presumably arbitrary damping risks compromising the accuracy of models expected to predict the jaw's dynamic behaviour. Recent dynamic models suggest passive length-tension curves in the closing muscles may be unusual in order to satisfy two jaw positions of clinical significance, i.e., the postural 84 resting position, and maximum jaw gape (Chapter 3). Theoretical predictions, as well as one report of static force at full gape in relaxed subjects, suggest relatively low external forces (around 5 -10 N) are sufficient to sustain full opening (Lynn & Yemm, 1971) (Chapter 3). In this study, we measured the dynamic forces required to open the jaw to full gape. We expected these forces would be low when opening was performed slowly. We then used a dynamic model of jaw mechanics (Chapter 3) to determine the muscle-damping needed to match the experimental data. We hypothesised it would be similar to that needed to critically-damp free jaw motion, i.e., we postulated the jaw-closing muscles would function near their critical damping frequencies. 4.3 METHODS 4.3.1 Mandibular Force-Motion Recordings The experiment had ethical approval from The University of British Columbia Clinical Research Ethics Board, and was performed on six normal healthy subjects (5 <$, 1 $) aged 21 - 36 years. Each attended two or more 30 - 45 min sessions. In the first session, dental impressions and intra-oral records were taken to permit construction of a full-coverage, removable, mandibular dental clutch. It was made with light-cured resin (Triad, Dentsply, Pennsylvania), and was retained on the lower dental arch by undercuts due to the buccal heights of contour and embrasures of the teeth. Occlusal contacts maintained a stable initial vertical jaw position. The clutch had a midline, anterior spherical connecting link (Swivel Ball Link, Dubro, Wisconsin) to the extension rod of a bi-directional force-gauge (AccuForce, Ametek, Florida). Thus we could move the jaw in any direction when force was directed along the gauge's long axis, and due to the design of the linkage, the recorded force was collinear with the transducer's long axis, i.e., directed perpendicularly to the spherical contact on the clutch. Customised spectacle frames with reference markers (stabilised with moulding putty) and markers on the gauge itself, monitored the extension rod's angulation three-dimensionally (see Figure 19, and below). At the end of this session, each subject was taught progressive relaxation and deep-breathing 85 LU a : 60 u .*.s CO u a a 86 muscle-relaxation techniques (Fried, 1993; Bernstein & Carlson, 1993). Finally, inter-incisal measurements of unassisted, voluntary, wide gapes were obtained for later comparison with those evoked by applying force to the mandibular clutch. In the next session, each subject semi-reclined in a quiet, dimly-lit room, and using the practised techniques, relaxed for five minutes. The dental clutch was inserted, and jaw-opening cycles were rehearsed. Opening forces were applied to the clutch by means of the force-gauge, and although the force gauge was not constrained to any particular plane, jaw opening was achieved with a postero-inferiorly directed force (relative to the subjects' mandibles). Simultaneous recordings of applied force magnitude and direction, and jaw motion, were obtained for repeated cycles of fast jaw-opening (FO) and slow jaw-opening (SO) to wide gape (lasting five and 20 seconds respectively). Jaw motion was recorded with a six degrees-of-freedom, opto-electronic tracking system (MacReflex, Qualisys, Partille). This had a precision of 0.03 mm, and an accuracy of 0.3 mm (Hamborg & Karlsson, 1996; Josefsson et al., 1996). Two infrared cameras recorded the motion of three reflective markers on the spectacle frame, and of three on the mandibular clutch. Two more markers on the force-applicator rod monitored its orientation (Figure 19). We used co-ordinate transformations (with articulated dental casts as fixed references) to express the motion of the lower jaw relative to the maxillary occlusal plane (defined by the mesio-buccal cusp tips of the maxillary first molars, and mesio-incisal edge of the right central incisor). The direction of force was defined as the angle the force gauge rod made with the mandibular occlusal plane, so that a 0° direction was posteriorly directed and parallel to the occlusal plane, and a 90° direction interiorly directed and perpendicular to the occlusal plane. Initially this was coincident with the maxillary occlusal plane when the upper teeth were in contact with the clutch. The force gauge's range was 0 - 90 N , and it had an accuracy of + 0.45 N . It was calibrated prior to, and following, each experimental session. The forces were sampled with a PC-based data-acquisition system (HPVEE, Hewlett-Packard, California). Al l forces and motions were recorded at 50 or 10 frames/second (five and 20 second tasks respectively). 87 The combined data were edited and analysed in a spreadsheet (Excel, Microsoft, Washington). Temporal plots of the jaw force and jaw displacements for the six subjects were then used to derive best-fit, polynomial regression curves. 4.3.2 Mathematical Modelling The jaw model was based on previous descriptions of musculoskeletal geometry (Baron & Debussy, 1979) and muscle physical properties (van Eijden & Raadsheer, 1992; van Eijden et al., 1995; van Eijden et al., 1996; van Eijden et al., 1997). It allowed six degrees-of-freedom of jaw motion which was shaped by forces from 16 craniomandibular muscles, two temporomandibular joints, and gravity (Figure 1). The model was created with commercially-available software written specifically for the design, visualisation and analysis of dynamic models used in mechanical engineering (ADAMS; MDI, Ann Arbor, MI). A D A M S defined the system as a collection of mixed nonlinear differential and algebraic equations, and subsequently solved them by numerical integration. The program ran on an Indy RS4000 workstation (Silicon Graphics Inc., Mountain View, CA). The mandible was defined as a rigid body, with inertial properties that were derived from a finite-element model of an intact human jaw (see Langenbach & Hannam, 1999). It was positioned in a gravitational field of 9.8 ms"2 which could be altered to simulate the head in various postures. The dentition was represented by flat maxillary and mandibular occlusal planes without cusps. Vertically-directed reaction forces were developed on the mandibular teeth (with a stiffness of 1000 N/mm) when the jaw reached the occlusal vertical dimension, preventing further jaw-closing. The TMJs were ellipsoidal, canted condylar shapes that rotated and slid against frictionless, curvilinear fossa/disc boundaries. These had anterior, inferior and lateral dimensions of 19 mm, 10 mm and 24 mm respectively, and provided condylar path inclinations 40° to the occlusal plane (Lundeen et al., 1978). The sagittal plane inclination of each fossa/disc boundary was 20° to the mid-sagittal plane, i.e., the medial pole of the condyle was posterior to its lateral pole (Yale et al., 1966). 88 The jaw-closing muscles comprised the anterior, middle and posterior temporalis, superficial and deep masseter, and medial pterygoid (bilaterally). They were simulated with Hill-type, flexible, single-line actuators (Zajac, 1989). Each had a fibre and a tendon component, together producing active and passive tensions. A l l muscle attachment sites were derived from Baron and Debussy (1979). The actuator orientations represented the central axis of each muscle or muscle subgroup from origin to insertion. A l l muscle length changes were assumed to occur within the fibre component. Tendons were modelled as inextensible elements because their functional lengths have been reported to change less than 4% (Curwin & Stanish, 1984). Each muscle's passive tension component consisted of an elastic and a viscous damping element. The elastic element's force increased exponentially with increasing muscle length (Gordon et al., 1966; Hill, 1953; Woittiez et al., 1983) and reached its maximum at wide gape. This maximum was proportional to the muscle's individual cross-sectional size; in the presence of gravity, it enabled the jaw to maintain wide gape when an inferiorly-direaed opening force of 5 N was applied at the mandibular incisor region (Chapter 3). The damping element resisted motion by providing a frictional force directly proportional to the muscle's lengthening velocity, and parallel to its passive tension vector. We defined critical damping as the muscle damping necessary for the jaw, when driven by gravity from the jaw closed position with light intercuspal tooth contact (TP), to reach a stable resting position, without oscillating, in the shortest possible time. We determined this by means of a design study, in which a design variable, representing damping, was applied equally to each closer muscle, then increased, from an initial value of 0 Nms"1, by 10 Nms"1 increments in successive dynamic analyses until the mandible opened to, and remained at, its resting position in the shortest possible time. We then performed a second design study to calculate the damping needed to open the jaw with the same forces, and at the same rates of opening, as the group of experimental subjects, i.e., the incisal force functions matched the best-fit polynomial curve for group-averaged F O and SO cycles respectively. Muscle damping was increased successively by 10 Nms"1 increments, from an initial value of 0 Nms'1, until the jaw-opening durations were identical to those recorded experimentally. These muscle damping constants needed to 89 match the F O and SO cycles were then compared with the constants required to critically-damp the muscles. 4.4 RESULTS 4.4.1 Jaw Forces and Motions in Experimental Subjects In each subject, operator-evoked jaw opening was similar to voluntary opening without assistance (Table 5). Wide gape was attained within 3 seconds and 8 seconds for F O and SO cycles respectively. In each instance, subjects maintained a wide gape for the rest of the opening cycle. In each subject, the opening forces were directed approximately 35° to the mandibular occlusal plane, and although the force gauge's orientation could be changed, as it was rotationally unconstrained at the spherical joint on the mandibular clutch, it remained in the mid-sagittal plane during the opening cycles (Table 5). Figure 20 is a kinematic animation of the raw data from one subject, and illustrates a typical force-gape relationship for a single SO cycle. It shows the average direction of the force applied to the incisor region and the resulting opening path followed by the mandible. Figures 21 and 22 illustrate typical F O and SO cycles expressed in time. In both cases, similar maximum gapes were reached after an initial rapid increase in force and corresponding jaw separation. However, the force needed to maintain gape decreased with time. This was most evident in SO cycles, where repeated on and off-loading of the jaw had little effect on maximum gape. In Figures 23 and 24, force is plotted against gape for three representative subjects. Both F O and SO cycles are shown. The force recordings commenced at 10 mm incisal gape because, in all subjects, the jaw opened to this gape under the passive weight of the force gauge. Though group mean mid-incisor gapes for F O and SO were 48.7 mm and 48.9 mm respectively, the forces needed to reach them differed considerably; those for the SO being less than half those for FO. Again, the figures indicate applied force could often be lessened considerably after initial opening without reducing gape. 90 5 second cycle 20 second cycle Unassisted opening INTER-INCI range: mean: SAL WIDE GAPE 45-51 mm 48.7 ± 2 . 1 mm 45-51 mm 48.9 ± 2 . 0 mm 45-52 49.0 ± 2 . 1 mm FORCE AT range: mean: l/VIDE GAPE 14.9-29.3 N 20.9 ± 4.9 N 7.3-19.6 N 4.7-10.6 N* 13.8 ± 2 . 0 N 8.2 ± 2 . 2 N* FORCE AT range: mean: 50% GAPE 2.6-12.4 N 6.7 ± 3.3 N 1.2-8.3 N 3.9 ± 2.4 N FORCE GA range: mean: JGE INCLINATIC 26.3-50.5° 36.2 ± 4 . 8 ° )N§ 25.8-46.4° 35.4 ± 5.0° * lowest force required to maintain wide gape 5 force gauge inclination is direction of opening force, in the sagital plane, relative to the mandibular occlusal plane. As inclination increases, force direction becomes more vertical. Table 5 Gape and opening force data for 5 and 20 second opening cycles, and subjects' unassisted opening measurements 91 Figure 20 Single subject: anterolateral view of reconstructed force vector (arrow) and incisor motion (solid line). The figure is taken from an animated kinematic model using data from a 20 second cycle. The orientation triad is located at the incisal intercuspal position in the occlusal and midsagittal planes. Each axis represents 10 mm. (N) aojo-j o O CO o CM CM OO . . o CD d) E CM (uiui)dde£) (N) SOJO-J o o 10 o CM in o ^" E in (uiui)adeg •3 -fl u Ot too 2 3 94 o Pooled opening-force and jaw displacement data plotted against time are shown in Figures 25 and 26, and Figures 27 and 28 respectively. Least-squares polynomial regression curves were fitted to these data, i.e., 3 r d and 4 t h order polynomial equations described the opening force profiles for F O and SO (Table 6), with R 2 values of 0.73 and 0.47 respectively. The fitted and normalised force data demonstrated similarities in the temporal pattern of force application to the subjects' jaws (Figures 29 and 30). This was reflected in increased R 2 values of 0.92 and 0.93 for F O and SO respectively (Table 6). 4.4.2 Mathematical Modelling 4.4.2.1 Critical Damping of the Mandible Underdamping caused the model to oscillate about its final rest position for 8 seconds (Figure 31a). Critical damping was achieved when 200 Nsm"1 was applied to each of the jaw muscles, and the model came to rest in 5 seconds (Figure 31b). Overdamping delayed the model's final rest position for more than 10 seconds (Figure 31c). Figure 32 shows the effect of damping on incisal point motion for these three instances. 4.4.2.2 Jaw Opening with Applied Force When the polynomial function was used to define the F O force, uniform muscle damping of 150 Nsm"1 was required to attain wide gape in three seconds. When the polynomial function defined SO, the same muscle damping constants (150 Nsm"1) allowed the jaw to open widely in 8 seconds. We simulated on and off loading of the jaw model, and in a similar fashion to the human experiment, a force reduction had litde effect on maximum gape (Figure 22 - right plot). 4.5 DISCUSSION Conscious and/or unconscious muscle activity was not monitored in this study. While it is theoretically desirable to eliminate active muscle contraction as a source of viscoelastic stiffness, it is impossible to sample all muscle regions capable of resisting jaw motion in conscious human subjects, and the demonstration of minimal to no activity in sampled 97 T 3 CU ' H "a, OH £ CU C 3 <u OH )H O CA c CA U o u CA , 0 HJ ^ O T J 5 a * ^ • -H h u m O C ( N OH rt cu g cu C CU & 1 3j H S o « « «i .3 rt~ cu <U c ° ^ o in ^ O <N no OH cu «J So « <N 0 <u <U S CA W 3 <» <A PU vg OH 100 oo O N o + X 1—1 in m in I V o o NO CN I V rn \ 0 vO o o cu 0£ -o c o u <u o rv I V m o o o I V o 1—I o o I oo o o o o II O N s CU OX •a o u cu oo m <N rv O N 3 I V 1—I OO OO II O o 1 h3 SI m iv •>*• o d + x T-H m oo o m m m d oo m I V o II I o OH <N O N a o cu a . o 0) OH O •a o u 0) > U oC g "S (U OH O *o O OH CA C o a v3 a o VH O *o &H NO CU « 102 o CO 105 regions does not therefore exclude the possibility of active contributions from unrecorded sites. The only way to ensure a complete absence of muscle activity would be to perform the experiment on anaesthetised subjects, which is not a trivial task. Thus it is possible that our subjects could have activated either the jaw closers to resist, or the openers to assist, jaw opening. Since all subjects were given relaxation training, and the shapes of the force-gape plots were very consistent, we think background muscle activity was not a major factor, although we cannot discount its presence. The slow rates of opening we used are unlikely to have evoked jaw-closing stretch reflexes, which are predominantly rate-sensitive (Hannam & Sessle, 1994). If it can be assumed there was insignificant muscle activity, we suggest our force data are a measure of the resistance to jaw opening largely provided by passive structures such as muscles, ligaments and other facial soft tissues. In any event, we suggest our measurements are typical of human performance in a conscious, but fully-relaxed state. At the commencement of recording, each subject's jaw opened to approximately 10 mm incisal gape. Little or no opening-force was applied by the experimenter. This is consistent with the notion that a 'relaxed' jaw rest position is greater than the normal 'alert' jaw rest position of 3-5 mm incisal gape (Brill & Tryde, 1974). For this clinical position to be maintained, jaw elevator muscle tone is required (Kawamura et al., 1967; McNamara, Jr., 1974; Mailer, 1976). The maximum gapes reached in our experiment are similar to those found in normal clinical practice (Peck et al., 1997). We found low opening forces (around 8 N) were sufficient to attain maximum jaw gape. This is in agreement with our previous study (Chapter 3) and another by Lynn and Yemm in which a similar, low opening force of 0.65 kg (6.4 N) was reported (1971). The observation has significant implications for dynamic jaw models driven by muscle activity. When designed with "best-available" sarcomere length-tension data for passive muscle tension properties, human jaw models do not open more than 35 mm, even when the opener muscles are driven maximally (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999). Although such limited gapes have been attributed in part to incorrect jaw-opener tensions at wide gape (Koolstra &C van Eijden, 1997b), an alternative explanation is that passive tensions assigned to the jaw-closers were too high, implying the complex masticatory muscles cannot be modelled 107 as simple single-line actuators with tensions derived from sarcomere length tension properties (Chapter 3). Experimentally, the force required to open the jaw increased in a nonlinear fashion, not unlike the muscle length-tension curves used in dynamic models (Chapter 3). However, the F O sequences produced forces at maximum gape approximately twice as great as those produced during SO. It is possible that our subjects may have actively resisted the more rapid FO. A n alternative explanation is that the system behaves in a rate-sensitive, viscoelastic manner consistent with known muscle properties. Notably, the lower forces recorded during SO could be reduced even further at stable maximum gape. Our model replicated this phenomenon, and was due (at least in the model) to the stiffness of the jaw elevator muscles. These elevator muscles were assigned properties so that they would generate 5 N of passive elastic force at wide gape. This level of elasticity was derived experimentally in a previous study (Chapter 3). In the current model, opening was generated with forces greater than this, however since the passive (elastic) tensions rise rapidly at wide gape, no noticeable increase in jaw gape is realised. Conversely as long as the tensions remain at or above the rninimum necessary to maintain wide gape, there will be no decrease in gape with decreasing opening force (Figures 22). Our study suggests the relationship between jaw opening rate and jaw opening force can be largely explained by the viscous properties of the masticatory system. Although we have applied viscosity uniformly to the jaw closer muscles in our model, viscosity is likely to vary with muscle size and composition, and may also be attributed to the motion of sliding fascial planes and tendon plates between muscles and of other, adjacent soft tissues. Indeed, viscous damping is unlikely to arise within muscle fibres as simple frictional resistance, rather than viscosity, has been shown in relaxed frog muscles undergoing small movements (Hill, 1968). Nevertheless, our method of damping provided temporally-dependent gapes consistent with experimental recordings. To reproduce these results, the model's damping constants were 150 Nsm"1, approximately 25% lower than the model's critical damping constants. Underdamping is known to exist in the wrist, where it has been suggested to facilitate reduction of unwanted oscillations, while minimally impeding voluntary movements (Lakie et al., 1984). For similar reasons, it is therefore possible that the human jaw is slightly underdamped. The thixotropic properties of muscle (i.e., muscle stiffness inversely related to 108 past movement history) may also help eliminate small perturbations of the jaw. These properties contribute to the relatively high stiffness of the jaw, which may provide protection to the temporomandibular joints and prevent uncontrolled contact of the opposing dentition when the jaw is subjected to accelerations/decelerations such as in running or in sudden, unexpected bolus fracture (Walsh, 1992a; Slager et al., 1998). In the clinical environment, an argument could be made to assess muscle trismus, contracture, and the clinical end-feel associated with jaw motion, by simultaneously measuring any forces applied to the mandible, and its resulting displacement, since it should be feasible to establish changes in viscoelastic components quantitatively, e.g., to reduce the effects of viscosity, jaw velocity should be kept low, and vice-versa. It was quite surprising to us that the model-determined damping for the F O case was the same as that needed in the SO task. This suggests that the viscous forces in the jaw are linearly related to the velocity (or at least the two velocities at which we opened the subjects' jaws) of the mandible. Our results suggest models can perform realistically when compared with living subjects. While many of their properties remain impossible to verify in vivo, they nevertheless offer a useful hypothetical construct for future experiments. Methods of experimentation in which a virtual prototype is constructed and tested prior to in vivo experimentation provides several advantages including the ability to design, model, visualise and improve hypotheses which can be tested experimentally. This method is used widely in mechanical engineering, including the automobile and aerospace industries, and is gaining increased attention in musculoskeletal biomechanics. 4.6 CONCLUSIONS Although this study suggests the jaw is underdamped, it nevertheless appears that it, and presumably its muscle set is quite heavily damped, yet has quite low passive elastic resistance to stretch. This may provide the jaw, dentition and temporomandibular joints some protection to sudden unexpected changes in velocities, whilst also providing rninimal resistance to controlled and slow movement tasks. 109 5 T H E I N F L U E N C E O F M U S C L E C O N S T R A I N T S O N J A W M O V E M E N T S 5.1 ABSTRACT Although articular ligaments and muscle activity have been suggested to constrain mandibular motion, the relative significance of each is unknown. This is important clinically since some treatments for "hypermobile" jaws involves surgery or other therapies aimed at "tightening" temporomandibular capsular ligaments. Recent mathematical modelling has suggested symmetrical and asymmetrical jaw opening can occur in the absence of articular ligamentous constraints, however investigations into possible constraining mechanisms during other jaw motions are lacking. In this study, we attempted to simulate plausible protrusive and lateral jaw movements with and without tooth contact, and hinge jaw opening with a dynamic muscle-driven human jaw model, devoid of articular or accessory jaw "ligaments". Hinge jaw-opening was simulated with a postero-inferiorly directed force applied to the chin point of the mandible. Jaw muscle coactivation, derived from published electromyography (EMG) studies, generated the remaining tasks. In addition, lateral jaw movement was attempted by activating only those jaw muscles which shortened during the task. Hinge jaw opening was limited to 15 mm gape by the passive tensions generated in the medial pterygoid, superficial masseter and anterior temporalis actuators; further opening demonstrated an anterior translation component. Plausible protrusive and lateral jaw movements were possible with EMG-based muscle recruitment, however lateral jaw movements were not plausible when the "muscle-shortening" muscle recruitment strategies were attempted. Reasonable jaw motion was produced with this strategy and additional ipsilateral medial pterygoid actuator activity. For all movements, muscle activity remained below 40% of maximum possible tensions, and articular compression (<30 N) occurred during all tasks, and was asymmetrical during lateral jaw movements. This study suggests muscle tensions (active and passive) may play an important role in constraining the jaw (and condyle). Further, since similar jaw motions were produced with different muscle patterns, individuals may be able to learn different muscle recruitment strategies to shape articular and/or muscle loads. 110 5.2 INTRODUCTION Condyle and disc positions are affected by active and passive muscle tensions, dynamic articular forces, and perhaps by temporomandibular and accessory ligaments (Hesse & Hansson, 1988; Osborn, 1993; Osborn, 1995; Sato et al., 1995). The relative importance of each of these variables in constraining mandibular motion is controversial, as both ligaments and muscle activity have been implicated as major controllers of various mandibular movements. Proponents advocating a predominantly ligamentous constraint have suggested that inadequate capsular and ligamentous structures may result in TMJ subluxation or dislocation, and that the ensuing joint hypermobility may be related to temporomandibular disorders (for review see Sato et al., 1995). In posterior (border) opening motion of the mandible, the transition from hinge-like opening to full posterior opening has been attributed to the tautness of the temporomandibular (lateral) ligament, compression of the soft tissues behind the angle of the mandible, or stretching of the masseter muscle (Posselt, 1968). A possible ligamentous contribution has been modelled with single inextensible links representing the temporomandibular (TML) and sphenomandibular ligaments (SML) constraining the motion of the condyle against an articular fossa plane (Osborn, 1993; Osborn, 1995). This model was tested with anatomical landmarks from six skulls, and in each case plausible opening was possible by constraining the motion with the ligament analogues. In each of the six cases, the individual ligaments affected the movement differently; and acted at different stages of the opening path. The T M L controlled the early phase of the movement, either by rotating about its inferior attachment to the condylar neck, or by allowing the condyle to slide down the eminence while the jaw simultaneously rotated about the inferior T M L attachment, and 111 swung about its superior attachment. The middle phase of opening was achieved with rotation about the inferior TML attachment, until the SML tautened and the jaw rotated or swung about its sphenoid attachment. Conversely however, dynamic muscle-driven models devoid of ligaments have recreated plausible jaw opening, and demonstrated compressive forces through the temporomandibular joints (TMJs) throughout the task (Koolstra & van Eijden, 1995, Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Chapter 3). The craniomandibular system was represented by a three-dimensional model. The mandible had plausible inertial properties, and was constrained by multiple forces including gravity, non-linear muscle actuators with active and passive tension properties, and contact forces at the TMJs. The lateral pterygoid and infra-mandibular actuators provided opening torques resisted by passive tensions generated in the stretched jaw closer actuators, about a mass centre located in the midline and the second molar region. Although no ligamentous or capsular constraints were present, the condyles did not distract from the fossa or eminence in any of the studies. For other jaw motions, the literature is more sparse, though the controversy about their constraints exists. Some studies have suggested the T M L and/or accessory ligaments (stylomandibular and sphenomandibular ligaments) limit excursive jaw motions (Rees, 1954; Rossow, 1968; Burch, 1970). These studies were performed by mimicking human mandibular movements on cadaver specimens or skulls, and examining the motion of intact ligaments or the distance between ligament attachment sites. The concept that ligaments are not the only constraints for lateral motions has been suggested with data from dynamic muscle-driven models without capsular or ligamentous constraints, which have produced 112 plausible laterally-directed opening movements (Chapter 3). Here lateral motion was limited by the passive tensions of the stretched ipsilateral medial pterygoid muscle. In addition, Koolstra and van Eijden investigated the effects of T M L on muscle-driven lateral movements (1999). Al l muscles suitably oriented to contribute to right lateral motion were activated (simultaneously or separately) to 10% of their maximum. This sensitivity study explored the effects of passive muscle tensions and temporomandibular ligaments on the jaw motion. This model, complete with ligaments and passive tensions, demonstrated a lateral deviation of 12 mm at the mid-incisor point and 4 mm at the condyles. Deviation at the condyles remained similar when the passive muscle tensions were removed, and doubled in the absence of the ligaments, suggesting a constraining role attributable to the TML. Although a lateral condylar motion of 4mm, with ligamentous and passive muscle tensions, is somewhat extreme compared to actual average human data of 2 mm (Peck et al., 1999b), the Koolstra and van Eijden study provides a theoretical foundation for the biomechanical roles of various structures in the craniomandibular system. Since the mandibular condyles moved excessively in these models, those structures which constrain jaw motion continue to elude us. It was our present aim to simulate, utilising a dynamic, muscle-driven mathematical human jaw model, plausible lateral, protrusive (each with and without tooth contact) and hinge-opening movement tasks. We hypothesised that muscle tensions alone (i.e., in the absence of ligamentous or capsular tissue) could restrain jaw motion for these tasks. 113 5.3 M E T H O D S We simulated protrusive, lateral and hinge-opening jaw movements with a mathematical model of the human mandible. The model definition has been described previously (Chapter 3). We developed it with commercially available dynamic modelling software (ADAMS; MDI, Ann Arbor, MI) which ran on an Indy RS4000 workstation (Silicon Graphics Inc., Mountain View, CA). The model was based on previously published descriptions of musculoskeletal geometry (Baron & Debussy, 1979) and muscle physical properties (van Eijden & Raadsheer, 1992; van Eijden et al., 1995; van Eijden et al., 1996; van Eijden et al., 1997). It allowed six degrees-of-freedom of jaw motion, shaped by forces from 16 craniomandibular mustle groups, two TMJs, and gravity (Figure 1). From the forces representing muscle tensions, TMJ contact, gravity and the inertial properties of the jaw, Newtonian mechanics were used to compute the mandibular accelerations. Specifically, numerical integration methods provided a solution to this problem, by predicting an initial solution, then iteratively improving on this with a numerical integration algorithm The final solution was accepted once differences in successive iterations fell below a user-defined tolerance (Jeffrey, 1996). The mandible was defined as a rigid body with a mass of 200 g, centred in the midline and 10 mm below the second molar bite point, and moments of inertia: 1 :^ 92.2, L^: 182.2 and 1^ : 125.2 Kgm 2 (see Langenbach & Hannam, 1999). The TMJs were canted ellipsoidal condylar shapes that rotated and slid against frictionless, curvilinear surfaces which provided a condylar path inclination of approximately 40° to the occlusal plane (Lundeen et al., 1978). Contact between the ellipsoidal condyle and curvilinear disc-fossa surface was determined by finding intersections between these two geometries. No capsular or ligamentous constraints 114 were present, enabling each condyle to distract completely from its functional disc-fossa boundary. The mandible was positioned in a gravitational field of 9.8 ms"2 to simulate a head in upright posture. The dentition was represented by flat maxillary and mandibular posterior occlusal planes without cusps and guidance in the incisor and canine regions. Whenever the maxillary and mandibular dentition "collided", vertically-directed reaction forces were produced on the mandibular teeth (1000 N / m m indentation) to simulate the posterior occlusal interface. Similar reaction forces produced anterior dental guidance, except these were directed perpendicular to the palatal surface of the anterior dentition. The incisor guidance was located at the maxillary central incisors, oriented perpendicular to the mid-sagittal plane and inclined antero-inferiorfy 45° to the frontal plane, and extended 3.0 mm from intercuspal position. The canine guidance was located at the right maxillary canine, oriented perpendicular to the frontal plane and inclined latero-inferiorfy 45° to the sagittal plane, and extended 3.0 mm from intercuspal position. The masseter, temporalis, medial and lateral pterygoid and digastric muscles were divided into 16 functional groups for which morphological physiological data were available (Figure 1). The groups were left and right anterior, middle and posterior temporalis (AT, MT, PT respectively), superficial and deep masseter (SM, D M respectively), medial pterygoid (MP), inferior head of the lateral pterygoid (LP), and anterior belly of the digastric (AD) muscles. The muscles (and their subgroups) were simulated with riill-type, flexible, single-line actuators (Zajac, 1989). Each had a fibre and a tendon component, together producing active and passive tensions. Al l length changes within the actuator occurred within the fibre component, and tendons were modelled as inextensible elements, since their functional 115 lengths are relatively constant (Curwin & Stanish, 1984). The passive tensions in each muscle increased exponentially with muscle lengthening. The active tension, developed as a consequence of motor drive in each muscle, was a proportion of the muscle's maximum possible tension, F^, (determined by its cross-sectional size x 40 N/cm 2 ) (Weijs & Hillen, 1985a; Fitts et al., 1991). For each muscle, this tension was expressed as a step function in time. Thus, Active tension = Muscle activation amplitude x F^ x ((time/OA)2 x (3-2x(time/0A))), i.e., tension developed gradually over the first 0.1 second to reach a constant activation level. In this function, Muscle activation amplitude, measured as %, was the only variable which was altered for each active muscle. We damped each lengthening muscle actuator (150 Nsm"1) to represent muscle and other soft tissue damping likely to be present in vivo (Chapter 4). 5.3.1 Initial Jaw Positions Since the resting jaw model (under the sole influence of gravity and passive muscle tensions) remained at an interincisal opening of 11mm (Chapter 3), it was necessary to add steady-state active drive to all jaw-elevator actuators to achieve a clinical rest position of 4 mm incisal gape (Brill & Tryde, 1974) or an intercuspal position. According to a previous study, we needed jaw elevator "tone" corresponding to 0.18 % of each muscle's possible maximum tension to simulate a clinical rest position (Chapter 3). It is not known what elevator activity is necessary to maintain IP. We applied steady-state active drive in all jaw-elevator actuators to achieve this position. This active muscle 116 "tone" was specified as a constant fraction of each muscle's possible maximum tension, and was determined by parameterising the model with tone as the design variable, and by increasing it by 0.25% increments in a series of analyses until an IP with light tooth contact was achieved. When tone was added to the model, compressive dental forces increased in a linear fashion with increasing elevator activity, so that at 0.5%, 1%, 2% and 4% activities, compressive forces were 2.1 N , 5.9 N , 13.1 N and 27.4 N respectively. As tooth contact was not attained until elevator muscles were activated to 0.5% of their respective maximum tensions, we selected this as the activity to maintain intercuspal position. Active muscle tone was maintained throughout all lateral and protrusive movements commencing from an intercuspal or clinical rest position. It was not maintained for the hinge-opening movement since we simulated operator-guided movement on a relaxed individual. 5.3.2 Movement Tasks Operator guided hinge-opening, and muscle-driven protrusive and lateral jaw movements from a "jaw rest position" (RP) with incisor separation of 4 mm were simulated. Protrusive and lateral jaw movements were also begun from a jaw closed position with light intercuspal tooth contact (IP). Muscle activation profiles for protrusive and lateral jaw movements were initially derived from published electromyographic studies for these movements (Gibbs et al., 1984; for review see Miller, 1991b). To gain further insight into the complex relationship between muscle activity and lateral jaw motion, we modelled an additional muscle activity strategy to perform this motion. In this strategy, we assumed those 117 muscles which shortened during the lateral motion were participants in the movement, and activated them to levels relative to their length changes. 5.3.2.1 Hinge Opening Movement To simulate an operator-guided hinge opening movement (Stroud, 1997), the model was set in the clinical rest position, and an external postero-inferiorly directed 5 N force with a rise-time of 0.1 seconds was applied to the chin point for 1 second. To ensure initial sagittal plane condylar rotation, we parameterised the model, and set the inclination of this external force with respect to the mandibular occlusal plane as a design variable, which was altered in a series of analyses until early hinge opening occurred. To simulate a relaxed individual, all active muscle drive was absent; thus only this opening force, passive muscle tensions and gravity were present. 5.3.2.2 Protrusive and Lateral Movements: EMG Based-Muscle Activation Activity levels in muscles responsible for each of the movement tasks were derived from elearomyographic studies (Gibbs et al., 1984; Miller, 1991b). Only muscles recruited at moderate or maximum activation levels were used in the model. The rise-time at onset of contraction was constant for all muscles (0.1 seconds). Multiple screening analyses, in which the activation levels of these muscles were systematically altered between 0 and 100% of their respective maximum possible tensions, were performed. These analyses provided a range of values for the active muscles which caused jaw movement in approximately 1 second. Then, in a subsequent design study, we altered these muscle activation levels to meet specific objectives for our protrusive and lateral movements (see below). For movements from IP we permitted tooth contact until an edge to edge position was attained. For movements from RP, we allowed no tooth contact. Like most models of the human musculoskeletal 118 system, our model was an indeterminate system as there were an infinite number of muscle tension combinations that could satisfy our motion objectives (An et al., 1997; Andriacchi et al., 1997). To reduce the number of analyses we adopted the following strategies. The drive from any muscle combination patterns had to complete the jaw motions in approximately 1 second, and any coactivation strategies which completed the jaw motions in under 0.5 or over 1.3 seconds were rejected. We felt this time period was plausible for the tasks, and was not too rapid so as to involve significant reflex muscle activity (Matthews, 1972). We assumed any minor reflex activity from muscle stretch was represented in our passive viscoelastic parameters of the actuators (Gottlieb, 1996). To reduce the number of analyses in our design studies, we reduced the number of design variables (active muscles) to three. For the remaining active muscles we assigned activity levels which we felt appropriate. Our result was a pattern of muscle activity (which certainly was not unique) that provided us with desirable jaw motion. For protrusion, LP, M P and A D muscles were activated bilaterally to produce symmetric incisor motion of 10 mm without jaw opening rotation. For lateral jaw movement, the ipsilateral A D , AT, and M P muscles and contralateral LP, M P and A D muscles were activated. In this case there were six muscles which could be activated to produce a lateral motion. To simplify the solution, the variables were reduced initially by fixing the bilateral MP muscle activity to 5%, and the contralateral LP to 15% of their respective maximum possible tensions. The activity in the remaining muscles (ipsilateral A D , A T and contralateral AD) were altered systematically to achieve lateral jaw motion of 10 mm at the incisor point, and a bodily side-shift of the mandible of 2 mm or less. If needed, the motion was further refined by "tweaking" individual activity levels of all six muscles. 119 5.3.2.3 Lateral Movements: Muscle Activation According to Muscle Length In this strategy, muscle activity was based on each contributing muscle's length change during the motion. We derived muscle length changes from a previous kinematic model, in which lateral jaw motion was simulated (Chapter 1). This kinematic model had identical morphology (muscle attachments, joint size and shape) as the mathematical model in the present study. For lateral motion from an intercuspal tooth position, where both condyles were initially within the fossae, the ipsilateral condyle rotated about a vertical axis through its centroid, and the contralateral condyle translated downwards forwards and inwards along a pre-defined condylar path (Table 7). For lateral motion from rest position, the jaw started its movement from an inter-incisal opening of 3.5 mm with condyles displaced 2.4 mm (1.7 mm anteriorly and inferiorly) from their intercuspal positions. With commencement of motion, the ipsilateral condyle moved upwards into the fossae, and the contralateral condyle moved downwards, forwards and medially along a predefined path (Table 7). From these kinematic models we calculated muscle length changes during the lateral motions. We expressed each muscle's length change during the movement as a percentage of its initial length at the start of the movement, and used a spline function using the standard cubic method of interpolation (ADAMS, 1994b) to represent its activation profile. It was deemed that if a muscle shortened, it must have done so actively, and if a muscle lengthened it did so in the absence of active tension generation. In this way, shortening muscles developed active tensions, and lengthening muscles developed passive visco-elastic tensions. The activity profile of each shortening muscle was represented by its spline function. To produce active tension in each muscle, each of these muscles' spline functions was scaled equally in the following manner. We constructed a parametric jaw model with ADAMS, in 120 Ipsilateral condylar rotation 0 RZ T—1 d Ipsilateral condylar rotation 0 RY o Ipsilateral condylar rotation 0 RX o Contralateral condylar translation (mm) N q i 1 Contralateral condylar translation (mm) Contralateral condylar translation (mm) X T-H LO Incisor point translation (mm) N -9.8 -10.6 Incisor point translation (mm) o T-H Incisor point translation (mm) X <N CN From IP FromRP T 3 CD CL) U 1) ion. <u OJO ion. -Q UTS * J • P H 00 X clo po bout oo bout N Pi a + o -*-» CO •d U > <H o 0 •o W a cu CS « oo a a p o o o <x • B O 'co 1j CL) O 8 OH 5 3un "P « 3un c CU p^ o, C/J S I a o •a 4-1 o 1-1 121 which we specified the scaling factor (applied to each muscle) as the design variable. This factor was changed incrementally in a series of analyses, until the model moved laterally 10 mm under the influence of the scaled spline functions. The goal here was simply to produce a pattern of plausible muscle tensions which would create the desired jaw motions. 5.4 R E S U L T S 5.4.1.1 Operator Guided Hinge Opening Hinge-opening of the model occurred when an external force was applied to the incisors postero-inferiorly at 80° to the occlusal plane (Figure 33). In this scenario, all muscles were inactive. Parasagittal incisor-point motion demonstrated a transition at 15.0 mm gape from pure condylar rotation (8.6°) to combined rotation and translation. At this point the externally-applied force was 2.0 N and passive tensions in the S M , M P and A T muscles had increased to 1.1 N , 0.9 N and 0.8 N respectively. Condylar compressive forces gradually increased to reach 1.8 N at this transition point. As the jaw and condyles began to move forward, these passive and condylar forces dropped slightly, then increased with further opening. 5.4.1.2 Protrusion We simulated plausible jaw protrusion, with tooth contact, and achieved our objective of symmetric incisor motion of 10.0 mm with no sagittal plane opening rotation in 1.3 seconds with 25%, 7% and 5% activity (of possible maximum tension) in the L P , A D and M P actuators respectively (Figure 34 & Table 8). The condyles translated 9.8 mm along the anterior fossa wall, and rotated 4.2° in a closing direction, which resulted in a slightly 122 <7j -3 C 123 superiorly directed incisal path in the latter portion of the motion. The length of LP decreased from 33.0 mm at IP to 26.3 mm at the end of the movement. Tensions (a combination of tone and passive tensions) in the remaining muscles remained below 2.9 N (Table 8), with slightly more tension developed in the temporalis group (AT: 1.1 N , MT: 0.8 N , PT: 1.0 N) than in the masseter groups (DM: 0.5 N , SM: 0.9 N). Compressive joint forces increased to reach a maximum of 13.3 N at the limit of protrusion. Tooth contact remained, with incisal forces of 4.4 N , until the mandibular incisors had moved anteriorly past the maxillary incisal edges. From this point, protrusion continued in the absence of dental contact. We could simulate protrusion wdoout tooth contact with 25%, 7% and 6% activity in LP, A D and M P actuators respectively (Figure 35 & Table 8). The incisor point translated 10.0 mm anteriorly in 0.8 seconds, as the condyles translated 10.5 mm, and rotated 1.8° in a closing direction. Tensions in the temporalis groups (AT: 1.3 N , MT: 1.6 N , PT: 2.0 N) were at least twice as large as those in the masseter groups (DM, SM each 0.6 N). Compressive joint forces reached a maximum of 14.6 N at the end of the movement. The mandible closed slightly as it approached its extreme protrusive position. 5.4.1.3 Lateral Movements 5.4.1.3.1 EMG-Based Muscle Actuation We simulated plausible lateral movement, with tooth contact, in 1 second with 17%, 6%, 5%, 13%, 5% and 4% activity (of respective maximum possible tensions) in the contralateral LP, A D , MP and ipsilateral A D , MP, and M T / P T actuators (Figure 36 & Table 8). Although initially we added equal activity to the ipsilateral temporalis groups, we inactivated the A T muscle to reduce the supero-anterior component of the motion (AT: 0.3 124 52 • — T3 to .a ^ .a s & - <o E 2 ^ ^ PL, << PQ v3 125 126 H CN CN CN T f CN T f CN T f CN i CN IT) T-t AD r-; rn IT) T f 00 CN 00 CN MP O N 11.2 o O N 10.2 LP 16.7 16.7 10.8 O N H CN CN CN T f CN 00 T f T f T f CN T f o T f o AD l O T f O N T f MP i> O N 11.2 CO O N ON oo LP 16.7 16.7 T f T-H CO PRO-IP PRO-RP LAT-IP LAT-RP 5 H -TH S3 .9 "5 "H -S =3 :s <a > a o 127 N , MT: 4.0 N , PT: 3.9 N). Tensions generated in the contralateral masseter (DM: 0.8 N , SM: 1.1 N) and temporalis (AT: 1.1 N , MT: 1.0 N , PT: 1.1 N) groups and ipsilateral masseter groups (DM: 0.1 N , SM: 0.3 N) each remained below 1.1 N . Tooth contact remained, with canine forces of 4.9 N , until the mandibular canine had moved lateral to the maxillary incisal edges. Condylar compressive forces increased during the tooth contact phase to reach 6.8 N in the ipsilateral joint and 11.2 N in the contralateral joint. From this point the movement continued in the absence of dental contact, and ipsilateral condylar forces rose quickly to reach a maximum of 11.0 N and contralateral joint forces increased marginally to 12.8 N . The incisor point translated 9.8 mm (9.2 mm laterally and 2.4 mm anteriorly), and the contralateral condyle translated 7.5 mm along the anterior fossa wall, with 4.8 mm, 5.5 mm and 1.5 mm anterior, inferior and medial displacements respectively. The ipsilateral condyle shifted laterally 1.2 mm, and rotated 4.0°, 3.3° and 0.5° in the frontal, horizontal and sagittal planes respectively. For lateral motion, without tooth contact, the same strategy was employed, namely setting the above tensions for the bilateral MP and contralateral LP, and varying the remaining active tensions to produce a plausible motion (Figure 37). We met our objective in 1 second with 15%, 5%, 7.5%, 15%, 5% and 2% activity (of respective maximum possible tensions) in the contralateral LP, A D , MP and ipsilateral A D , M P and M T actuators respectively (Table 8). Tensions in the ipsilateral temporalis actuators were modified by removing activity in the A T and PT actuators to reduce the superior component of the motion (AT: 0.3 N , MT: 4.0 N , PT: 0.1 N). Tensions generated in the contralateral masseter (DM: 0.5 N , SM: 1.0 N) and temporalis (AT: 0.9 N , MT: 0.7 N , PT: 0.8 N) groups and 128 129 a o u a w o <! .3 130 ipsilateral masseter groups (DM: 0.5 N , SM: 1.0 N) each remained below 1 N . Compressive condylar forces increased to 8.7 N in the ipsilateral condyle and 13.1 N in the contralateral condyle. The incisor point translated 9.7 mm (9.2 mm laterally, 2.2 superiorly and 2.1 mm anteriorly), and the contralateral condyle translated 7.2 mm along the anterior fossa wall, with 4.2 mm, 5.2 mm and 2.7 mm anterior, inferior and medial displacements respectively. The ipsilateral condyle shifted laterally 2.4 mm, and rotated 3.8°, 2.5° and 0.1° in the frontal, horizontal and sagittal planes respectively. 5.4.1.3.2 Muscle Length-based Activation The relative length changes of the muscle actuators (when compared to their initial lengths), derived from a kinematic model, during lateral jaw motions from IP and RP are shown in Figure 38. Those muscles which shortened were considered active and their length changes, defined as cubic spline functions, were used as the basis for the muscle activity to drive laterally our mathematical jaw model. The lengthening muscles could only contribute with passive length- dependant and velocity-dependant tensions. For lateral movement from IP, the following muscles shortened: ipsilateral masseter (DM, SM) and temporalis (AT, MT, PT) actuators and contralateral pterygoid (LP, MP) actuators. For lateral movement from RP, these same muscles and the ipsilateral digastric shortened (Table 8). A lateral jaw motion from IP, of 10.4 mm (incisor motion), was attained with the spline functions of the shortening muscles scaled by a factor of 1. With this scaling, the shortening muscles used the complete profile of their respective spline functions to drive the jaw to its extreme lateral position. Although the incisor motion was typical, overall jaw movement was not plausible as condylar lateral side-shift was 7.2 mm (Figure 39a). The tensions developed in the muscles are shown in Table 9. These tensions can be further 131 subdivided in the ipsilateral masseter (DM: 8.3 N , SM: 1.9 N) and temporalis (AT: 2.2 N , MT: 2.8 N , PT: 4.4 N) groups, and the contralateral masseter (DM: 2.8 N , SM: 2.6 N) and temporalis (AT: 2.7 N , MT: 3.4 N , PT: 3.6 N) groups. Compressive forces increased to 10.6 N in both joints. This model was modified further with the addition of activity in the ipsilateral M P in an attempt to limit the lateral bodily shift of the jaw. Using 15% of this muscle's maximum tension, and scaling of the spline functions by a factor of 1.5, the lateral motion became more plausible (Figure 39b). Incisor motion was 10.0 mm (8.6 mm laterally and 4.9 mm anteriorly) and the contralateral condyle translated 8.2 mm along the anterior fossa wall, with 5.1 mm, 6.0 mm and 2.3 mm anterior, inferior and medial displacements respectively. The ipsilateral condyle shifted laterally 2.0 mm, and rotated 3.8°, 2.4° and 2.6° in the frontal, horizontal and sagittal planes respectively. A n upward component of the muscle tensions maintained tooth contact for the entire motion: initially by canine contact, and then by posterior tooth contact, and resulted in occlusal forces of 20.6 N . Compressive condylar forces increased to 27.2 N in the ipsilateral condyle and 14.6 N in the contralateral condyle. Muscle tensions are shown in Table 9. The tensions in the masseter and temporalis groups can be further subdivided into the ipsilateral actuators (DM:12.3 N , SM: 2.7 N , AT: 3.1 N , MT: 4.1 N , PT: 6.3 N), and the contralateral actuators (DM:3.8 N , SM: 3.1 N , AT: 3.2 N , M T : 3 . 9 N , P T : 3.9 N). A lateral jaw motion, from RP, of 10.9 mm, was attained when the spline functions were scaled by a factor of 1. However as above, the jaw motion was not typical as there was a lateral bodily shift of the jaw of 6.9 mm. In addition, the jaw moved upwards to tooth contact (Figure 40a). The model was modified with the activation of ipsilateral MP (8 %) and A D (25 %) and maintenance of the unity scaling of the spline functions (Figure 40b). With these muscle tensions, incisor motion was 8.6 mm (7.4 mm laterally and 4.3 mm anteriorly) and the contralateral condyle translated 5.8 mm along the anterior fossa wall, with 2.6 mm, 3.9 mm and 3.4 mm anterior, inferior and medial displacements respectively. The ipsilateral condyle shifted laterally 3.3 mm, and rotated 2.8°, 1.3° and 1.8° in the frontal, horizontal and sagittal planes respectively. Compressive condylar forces increased to 24.8 N in the ipsilateral condyle and 9.3 N in the contralateral condyle. Muscle tensions are shown in Table 9 . The tensions in the masseter and temporalis groups can be further subdivided into the ipsilateral actuators (DM:9.4 N , SM: 3.9 N , AT: 2.9 N , MT: 5.1 N , PT: 4.3 N), 132 A IP • F u l l lateral -20 J B RP • Full lateral Figure 38 Relative shortening of muscles plotted against lateral jaw movement. Muscle length (ordinate) calculated from a kinematic jaw model moving from A) intercuspal position (IP) to full lateral excursion with tooth contact, and B) rest position (RP) to full lateral excursion without tooth contact. Muscles numbered on plots are 1: Contralateral medial pterygoid; 2: contralateral lateral pterygoid; 3: ipsilateral posterior temporalis; 4: ipsilateral middle temporalis; 5: ipsilateral anterior temporalis; 6: ipsilateral superficial masseter; 7: ipsilateral deep masseter; 8: ipsilateral anterior digastric. 133 134 u O "t3 cu o 8 2 -9 •a -=3 3 fee •5 <-> _ o C oo 0 g g < 13 g b :a 1 . GO « o — OH O {* 22 o PQ h to i j bp _ to J-, O O " cu rj cu > CU . O .fc -t-> C J « (A I O rj Wi CU S T3 - U CO U 3 co C ° a U O 2 s O O & II CU 1 1 & fc. ^•2 ^ J cu ""3 « u .2 a •3 Is* O T 3 3 ^ O CO 5 *> J=8 -5 -5 -o cu CU O £> u *o 3 <u oo H cu O H i CU "0 00 1 135 CO a o • i H CO G <u H IS u t H H - » c o u CO G o « P H CO C <u H JH "u CO S C4 I-I OS • »H OH H < — C S 11.0 C S L O < — T f L O C s S O 0 0 C O AD <- T-H T f ' 0 0 T f 0 0 C O MP — » T f O © CO © LP — » 17.3 26.0 16.2 H — > T t -C S 13.5 12.3 10.2 15.0 13.3 AD - > £r < — s o C N O s CN 12.4 MP < — T-H C N 00 CN 15.3 LP < — 0 0 o O Length LAT-IP LAT-IP* LAT-RP* •3 ,p ••a « _T u • S3 ^  If go' •a H * .3 136 and the contralateral actuators (DM: 2.0 N , SM: 1.8 N , AT: 1.7 N , MT: 2.0 N , PT: 2.2 N). 5.5 DISCUSSION 5.5.1 Jaw Modelling Mathematical models such as the one used in this study, provide a unique method to understand the biomechanical environment of a specific system. Computational advances have enabled the design and analysis of complex three-dimensional mathematical models, whose structural and functional attributes may be altered to explore relationships in asymmetrical tasks such as lateral jaw motion. Of course these models are only as good as the input used in their construction, and always simpler than the systems they emulate. For example, occlusal contacts were limited to horizontal flat plane posterior contacts, and inclined flat plane anterior contacts throughout the excursive movements. Consequently, we simulated an anterior protected occlusion, with guidance located in the canine region for lateral movements and in the incisor region for protrusive movements. In future studies, this contact scheme could be altered to simulate any type of occlusal pattern. Measurement of joint loads and muscle tensions are not readily available for humans, and have largely been inferred from muscle size, electrical aaivity, and properties derived from animal studies (Oberg et al., 1971; Baron & Debussy, 1979; e.g., Weijs et al., 1989; Fitts et al., 1991; van Eijden et al., 1997). In part of this present study, muscle activity was derived from published electromyographic muscle recordings for lateral and protrusive jaw movements. E M G signals do not determine muscles' passive tensions, and they may not be directly related to active tensions (Loeb & Gans, 1986; Miller, 1991a; A n et al., 1997). In addition, E M G signals.can vary considerably from trial to trial for a single task in one individual. The closest correlation between muscle activity and muscle tension occurs in static studies when the muscle contracts isometrically (e.g., clenching) (Miller, 1991a). Extrapolating muscle tension from E M G signals depends on a number of factors including source of the signal, distance of source to electrode, electrode area and impedance etc. We minimised these shortcomings by using E M G signals to determine muscle activity but not muscle tensions. 137 There is wide variation in human morphological and functional data (Yale et al., 1966; Hannam & Wood, 1989; Miller, 1991b), so the use of an "average" human jaw has its limitations. Nevertheless, we believe the construction and analysis of our generic model allows, at least, a first-order investigation of interactions in the masticatory system. 5.5.2 Muscle-driven Jaw Motion The present study, suggests coactivation of masticatory muscles, combined with their passive tension components, provides resultant forces which act to move the mandible in a plausible manner for lateral and protrusive motions. For all motions we attempted, compressive joint forces were present, and activity in each muscle remained below its possible maximum tension. While our study does not discount a role for the temporomandibular ligament in restraining jaw motion, it suggests several motion characteristics previously attributed to this ligament may be accounted for by muscle action alone. In posterior border opening of the mandible, for example, explanations for the transition from hinge opening to further posterior opening have included the tautness of the temporomandibular ligament (Arstad, .1954; Posselt, 1968), compression of the soft tissues behind the angle of the mandible (DuBrul, 1980) and stretching of the masseter muscle . We found we could simulate the initial part of this border movement by applying a postero-inferiorly directed force at the model's chin-point, and in the absence of a temporomandibular ligament. In our model, the transition point in the posterior border path was distinct, and caused by changing passive tensions in the SM, M P and A T muscles, presumably interacting with the aarvilinear constraints of the articular fossae. If this transition in trajectory primarily results from passive muscle tensions, then it seems this position in individuals may vary with changes in muscle compliance (e.g., muscle contracture). The significance of anterior translation of the mandibular condyle has been cited as a mechanism to prevent airway impingement by the tongue and mandibular angle (Smith, 1985), or alternatively, as a mechanism to rriinimise sarcomere length changes in the masseter and medial pterygoid by moving the instantaneous centre of rotation of the jaw towards the masseter-medial pterygoid complex (see Hylander, 1992). By minimising sarcomere length 138 changes, these muscles are able to remain at lengths at which they can generate active tensions. The present study appears to support the latter hypothesis since forward condylar translation was necessary to minimise excessive stretch (and consequently maintain these muscles within their active functional range) of the SM, MP and A T muscle actuators. In mammals jaw muscle coactivation for many tasks is produced by a relatively uniform motor pattern, and an attempt has been made to group muscles (as triplets) according to phases of masticatory cycle (Weijs, 1994). This novel approach at grouping task specific muscles, which can be used for any jaw movements involving muscle coactivation, is one method whereby muscle recruitment can be simplified. We adopted a similar approach by assigning activity to particular muscles. For example, we used bilateral muscle triplets consisting of the inferior head of the lateral pterygoid, anterior digastric and medial pterygoid muscles, to produce an entire protrusive motion. Future detailed studies of muscle activity matched to motion should allow more complex muscle recruitment strategies, and consequently different triplets specific for particular phases of jaw motion. Protrusive jaw motion in our model was consistent with published kinematic studies (Sigaroudi & Knap, 1983; Slavicek, 1988; Zimmer et al., 1991; Theusner et al., 1993). Almost identical activation levels in the LP, A D and MP actuators were used for protrusion with or without tooth contact. In the task without tooth contact, the limit of protrusion was attained in 0.8 seconds, whereas with tooth contact, protrusion lasted 1.3 seconds. The tooth contact phase, with postero-inferiorfy directed forces on the mandible of 4.4 N , would appear to be responsible for this difference in movement duration. Tensions in the passive muscles were slightly greater for motion without tooth contact, reflecting their length and velocity-dependency. The condyles were compressively loaded throughout both tasks and reached similar levels of approximately 14 N , an order of magnitude less than hypothesised maximum joint loads (Hannam, 1994). Plausible lateral motion, as measured at the incisor, was possible for a variety of muscle recruitment strategies derived either from published E M G studies or from the relative shortening in the muscles during a lateral movement (Figures 36 - 40). This is consistent with findings of Koolstra and van Eijden who demonstrated plausible laterally-direaed incisor motion with artivity of single masticatory muscles (1999). They concluded that lateral 139 movements of the jaw are primarily dependent on the orientation of the contributing active muscles. This may be true, however even in their most constrained model in which the temporomandibular ligament was included, lateral condylar displacement was excessive (Hobo, 1986; Curtis, 1989; Theusner et al., 1993; Peck et al., 1999b). To simulate plausible jaw motion (as measured at both the incisor and condyles) we had to apply specific tension levels to our recruited muscles. Using the EMG-based muscle activities, the models from both IP and RP displayed plausible motions, and the lateral motions of the incisor point and ipsilateral condyle were approximately 10 mm and 2 mm respectively. The lateral jaw motion, resulting from muscle activation according to muscle length, was implausible as lateral translation of the condyles was in the vicinity of 7 mm. In addition the resultant muscle forces included a closing-directed component so that movement without tooth contact was impossible (Figure 40a). Addition of activity to the ipsilateral MP made the motion more realistic. Incorporation of this muscle not only reduced the lateral shift of the condyles, but also the lateral movement of the whole jaw. In the model without tooth contact, ipsilateral digastric activity was added to counteract the closing influence of the other active muscles. Although these muscle recruitment patterns may or may not be realistic, they suggest different activation strategies may evoke similar jaw motions, with quite different articular loading patterns. Thus, it may be possible to teach muscle recruitment strategies to temporomandibular disorder patients to shape joint loading patterns. In both protrusive and lateral jaw movements, the medial pterygoid muscle played an important role. The muscle's multipennation allows relatively large tension generation in a small muscle (Woittiez et al, 1983; Gans & de Vree, 1987), and the wide attachment sites offer divergent fibre orientations and the possibility of task versatility by differential activity (Hannam & McMillan, 1994). In all of our lateral jaw movements, activation of the ipsilateral medial pterygoid muscle was necessary, and this artivity has been supported by electromyographic studies (Gibbs et al., 1984). It provided a restraining influence on the lateral displacement of the ipsilateral condyle, enabling a lateral jaw motion with rotation about a vertical axis in the vicinity of the ipsilateral condyle (Hobo, 1984b; Peck et al., 1999b). 140 For all lateral jaw motions, more analyses were required to optimise the jaw motions without tooth contact than the motions with tooth contact. It appears that dental guidance provides a platform upon which a number of recruitment strategies will move the mandible in a similar fashion. Without dental guidance the motion of the mandible was much more susceptible to changes in muscle activity, resulting in the need to tune more finely the muscle activities. In lateral motions obtained from our model with EMG-based muscle activity, contralateral condylar forces were higher than ipsilateral forces throughout the motion, in agreement with previous primate and theoretical studies (Ffylander, 1985b; Throckmorton et al., 1990; Korioth & Hannam, 1990; Korioth, 1997). It has been suggested that the articular loading patterns are sensitive to the ratio of ipsilateral:contralateral closing muscle forces, and that a ratio lower than 1.75 : 1 will produce higher contralateral loads (Hylander, 1985b). Our models appear to support this differential loading relationship. The model of lateral motion with tooth contact appears to have a greater ratio of ipsilateral:contralateral muscle forces and correspondingly, less difference in ipsilateral and contralateral articular loads (Table 8). In all of our models with muscle activity based on muscle length, there were high ipsilaterakcontralateral closing muscle tension ratios, which resulted in greater ipsilateral than contralateral articular forces (Table 9). Joint reaction forces seem to counteract tensions generated in the inferior head of the lateral pterygoid. In our case, the contralateral LP generated greater tension than its counterpart, and presumably contributed to the increased contralateral articular loads. In the model at a jaw position where ipsilateral tooth contact was present, the difference in joint loads was more marked, as the upwardly directed muscle tensions were distributed between the dental contact and the joint reaction forces. Although this study suggests plausible motions are possible with only muscle tension constraints, we do not reject the role of other structures as possible constraints. Extreme positions may be locations where the ligaments and articular capsule come into play as constraints. The thesis that these ligamentous tissues limit the extent of motion has been put forward previously for the human TMJ (Osborn, 1993; Osborn, 1995), and also for other human joints (Viidik, 1990; Frank & Hart, 1990; Ten Gate, 1994). In a recent dynamic study, 141 addition of single element lateral capsular ligaments limited ipsilateral condylar motion (Koolstra & van Eijden, 1999). In the mid-portion of symmetrical motions (opening and protrusion), it appears that the relatively inelastic articular tissues (capsule and accessory ligaments) are unable to physically remain taut (Rossow, 1968; Hesse & Hansson, 1988). E>uring this phase of motion, when the condyle is compressed against the central area of the inclined surface of the anterior fossa wall, muscle appears to be the major constraining influence. Forward directed muscle forces and/or opening torques during these movements compressed the condyle into the disc and fossa wall and thus presumably provide the requisite articular, and jaw stability. E)uring lateral motion the condyles are also compressed against disc and fossa, however there are also laterally-directed force components predominantly from the contralateral medial and lateral pterygoid muscles acting on the condyles. Unlike the symmetrical movements, the disc and fossa are not able to resist the influence of these laterally-directed muscle forces on both condyles. Thus additional constraints are necessary, and they appear to include coactivation of the ipsilateral medial pterygoid muscle. Further, as cited above, the lateral capsular wall of the ipsilateral TMJ appears to provide a constraining influence, and so, throughout asymmetrical motions it appears that muscle coactivation, together with the passive constraints of muscles and capsular/ligamentous tissues guide the mandible. Muscle and ligamentous/capsular constraints acting synergistically in this way must provide a system with enhanced stability during function. If this were the case, then both muscle and ligamentous integrity must play major roles in articular hyper/hypomobility. Constraints at the end of protrusion may also include physical obstruction of the coronoid process of the mandible anteriorly by the zygomatic process of the maxilla, or the inability of the inferior head of the lateral pterygoid to generate force as it is overshortened and below its functional length. The latter possibility is probably not the case as calculation shows the LP, at the limit of protrusion, was still able to generate approximately 29% of its maximum tension with muscle properties consistent with published force-length relationships and sarcomere lengths (Muhl et al., 1978; Koolstra & van Eijden, 1996; van Eijden et al., 1997; Koolstra & van Eijden, 1997a). In all motions in this study, the LP activity remained below this level. At the limit of lateral motion, the contralateral lateral pterygoid could also be below its functional length (although for the same reason as in 142 protrusion it probably is not), the medial capsule may constrain the contralateral joint, or the lateral surface of the posterior maxilla may physically obstruct further medial motion of the contralateral ramus of the mandible. J 5.6 CONCLUSIONS Typical protrusive and lateral movements, with and without tooth contact, can be produced with a muscle-driven mathematical model of the human jaw which does not require accessory or articular capsular ligaments. For all motions, muscle activity can remain well below possible maximum tensions, and the incisor point and condyles move similarly to reports in previous human kinematic studies. The condyles remain compressively loaded for all movements, due to the active and passive muscle tensions. Similar lateral jaw motions can be achieved with quite different muscle recruitment strategies. Muscle tensions may not only provide drive for specific jaw motions, but may also constrain the jaw and limiting motions. The muscles probably work in co-operation with other passive constraints such as the TMJ capsule/ligaments and bony morphological constraints. Individuals may be able to learn novel muscle recruitment strategies to shape articular and/or muscle loads. 143 6 T H E E F F E C T O F T H E L A T E R A L T E M P O R O M A N D I B U L A R L I G A M E N T A N D C A P S U L E O N J A W M O T I O N 6.1 ABSTRACT The role of the temporomandibular ligament (TML) in mandibular function is uncertain, although alterations to its integrity have been implicated in the aetiology of temporomandibular disorders. It is believed, although unproven, to be a major constraint to jaw movement. Since a distinct TML, separate from the lateral joint capsule, is questionable, any biomechanical investigation of the relationship between its structure and function should include the entire capsular wall. We developed a mathematical model of the lateral wall of the temporomandibular joint capsule to test the hypothesis that parts of the lateral capsular wall were taut throughout excursive jaw motions, and thus able to provide a constraining influence on the mandibular condyle. The lateral capsule was modelled as 12540 straight-line elements between putative temporal and mandibular attachment regions. For typical opening, protrusion and laterotrusive jaw movements, we computed the movement of the mandibular attachments, and the length changes and maximum lengths of the capsular elements. A n element was considered taut (and a constraint) when it was within 5% of maximum length. For all jaw movements, taut capsular regions were present at the jaw closed position and at maximum excursive positions. For an ipsilateral movement, elements could be found which remained taut throughout the entire motion, however for contralateral, opening and protrusive jaw movements, taut elements were lacking during the middle third of the movement. Although many of the taut capsular elements were oriented similarly to the classical description of the oblique portion of the TML, the other capsular regions were variously taut throughout the jaw motion. It is suggested that future analyses of the T M L should include the entire lateral capsular wall. Further, it is suggested that the structure of the lateral capsule/TML does not allow it to constrain all jaw motions, and that other (e.g., neuromuscular) controls are necessary. 144 6.2 I N T R O D U C T I O N The role of the T M L in mandibular function is uncertain, although alterations to its integrity have been implicated in the aetiology of temporomandibular disorders (Westling, 1992; Osbom, 1995; Harkins et al., 1995). For example, plication surgery of a lax T M L has been indicated in an attempt to reduce mandibular hypermobility (Boudreaux & Spire, 1968; Poswillo, 1974), and conversely, ligament reconstruction with an alloplastic patch has been performed on excessively taut TMLs (Feinberg & Smilack, 1988). This all seems plausible if the T M L is like other inextensible ligaments in the body; i.e., non-elastic collagenous structures which restrict and limit the movements a joint can make (Ten Cate, 1994). Unfortunately however, measurements of many functional variables, for example stress and strain, are impossible within the human TML, and thus its function has been speculated upon rather than demonstrated (Sato et al., 1995). Most of our insight into structure-function relationships of the T M L has been obtained from cadaver experiments and mathematical modelling, however the results have been equivocal (for review see Sato et al., 1995). It has been suggested that non-neuromuscular controls; the T M L together with the articular eminence and accessory ligaments, constrain the opening movement of the mandible (Rees, 1954; Osborn, 1989; Osborn, 1993; Kang et al., 1993; Osborn, 1995). Conversely, dynamic jaw models under the sole influence of active and passive mandibular muscle tensions, have demonstrated plausible jaw opening in which the condyle maintains apposition with a disc-fossa interface whilst moving towards and beyond the articular eminence (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b) (Chapter 3). In support of a restraining influence by the TML, jaw opening simulations on cadavers demonstrated a taut T M L (Arstad, 1954; Rees, 1954). These studies have limitations including the non-physiological nature of the specimen and the imposition of movements by the operator which may not necessarily result in a movement comparable to that in the live subject. In a mathematical model, the ligament has been shown to constrain opening, whereby the condyle rotated about the lowest attachment of the T M L to the condyle, and swung about the most posterior attachment of the ligament to the articular tubercle, resulting in a specific rotation/translation relationship (Osborn, 1989; Osborn, 1993). This model was 145 tested further with specific morphological relationships derived from six skulls, albeit actual ligament attachments and jaw motion were obviously surmised. Nevertheless, the early phase of opening was constrained by a taut TML, whereas the later phase was constrained by a taut sphenomandibular ligament with or without a taut T M L (Osborn, 1993). Passive muscle tensions of the jaw closing musculature were not considered, although these tensions could have a constraining effect on the joint (Weijs et al., 1989). Interestingly, in another mathematical model (Kang et al., 1993), the length change between putative T M L attachments, during jaw opening, was found to be greater than the few percent exhibited by normal ligamentous tissue. The T M L attachments were at their maximum separation with the jaw at an opening angle of approximately 16 - 18°, and were at least 20% closer at a jaw closed position and 9% closer at wide opening (opening angle of 28°), which suggests a T M L is slack (and therefore not a constraint) at these positions. In the above mathematical models, each ligament was modelled with single attachment points, however in reality the ligament is often a broad band with a wide attachment area to bone (Luder&Bobst, 1991; Schmolke, 1994). Indeed there is controversy as to the existence of a temporomandibular joint ligament per se, which is distinct from the capsule surrounding the articulation. The classical description is of a ligament that originates on the lateral aspect of the articular eminence, and passes downward and backwards to insert into the neck of the condyle (Arstad, 1954; Griffin et al., 1975; Piette, 1993). Griffin et al. (1975), describe the ligament consisting of horizontal and oblique bands, and their insertion is into the lateral pole as well as the neck of the condyle. Schmolke (1994) describes the lateral ligament as a reinforcement of the capsular wall in the central and central-anterior parts of the joint. Luder and Bobst (1991) described a lateral thickening, however only one of their eighteen specimens was found with a structure looking like a classical ligament, and Savalle (1988) found only 3 of 16 specimens with a discernible lateral ligament. Similar controversy exists with collagen fibre orientation, as the TML's collagen, which is the tissue's major component, has been shown to have no discernible orientation (Savalle, 1988; Sato et al., 1996). This haphazard orientation may impart reduced resistance to tension, or indeed provide multi-directional tensile resistance in this tissue (Fung, 1993a). Thus it seems wise to consider the ligament as thickenings of the 146 capsular wall, and any biomechanical assessment should consider the entire lateral capsular attachment between temporal bone and mandible. For the lateral capsule to constrain condylar and therefore jaw motion, a part of the capsule must be taut at each stage of the motion. Thus three constraining situations are possible: 1. the entire capsule remains taut and constrains jaw motion, 2. a particular region of the capsule remains taut and constrains the motion, or 3. particular regions of the capsule are taut at different stages of jaw movement, and thus the constraining influence of the capsule is transferred from one region to another throughout the movement. The purpose of this study was to develop a mathematical model of the lateral wall of the TMJ capsule in which we could determine regional tautness of this wall during opening, protrusive and lateral excursive jaw motions. We hypothesised that parts of the lateral capsular wall were taut throughout these jaw motions, and thus able to provide a constraining influence on the mandibular condyle 6.3 METHODS A mathematical model of the lateral capsular wall of the temporomandibular joint was developed in which we were able to calculate the length changes between putative capsular origin (temporal attachment) and insertion (mandibular attachment) sites for various mandibular movements. In this study, all mandibular movements were relative to a fixed cranium, and thus the capsular insertions moved relative to the capsular origins. In this model, the mandible was modelled as a rigid body, and thus standard linear transformations could be used to calculate the motion of capsular insertions from the motion of the mandibular condyle. The model was oriented in a right-hand co-ordinate system so that the 147 antero-posterior (X) axis was parallel to the occlusal plane and mid-sagittal plane , the medio-lateral (Y) axis was perpendicular to the X axis and parallel to the occlusal plane, and the supero-inferior (2) axis was mutually perpendicular to the X and Y axes. Further, the positive X, Fand 2 axes were directed anteriorly, medially and superiorly respectively from an origin at the lateral condylar pole. 6.3.1 Capsular Morphology The regions that were expected to contain origin and insertion points for the lateral capsular wall were derived from published adult human temporomandibular joint anatomical studies (Angel, 1948; Oberg et al., 1971; Ingervall, 1974; Luder & Bobst, 1991; Schmolke, 1994). Although it is known that the bony attachments of the capsule are broad, the precise locations of these attachments are unknown (Savalle, 1988; Luder & Bobst, 1991). We selected extensive areas about the TMJ which we believed would contain the attachments. The capsular origins were expected to be contained within a rectangular box with a volume of 3780 mm 3 and which extended 21 mm along the X axis, 12 mm along the Faxis, and 15 mm along the 2 axis. With respect to the origin (the lateral condylar pole), this region extended 16 mm anteriorly, 5 mm posteriorly, 10mm superiorly, 5 mm inferiorfy, 6 mm laterally and 6 mm medially (Figure 41a). The capsular insertions were expected to be contained within a rectangular box of volume 864 mm 3 which extended 12 mm along the X axis, 12 mm along the Y axis, and 6 mm along the 2 axis. With respect to the lateral condylar pole, this region extended 6 mm in each of the anterior, posterior, inferior, medial and lateral directions (Figure 41b). 148 149 We modelled the capsule as multiple straight line links between the capsular origin and insertion regions. Attachment points were selected at 3 mm increments in each of these volumes, resulting in 240 origin and 72 insertion attachments. Each and every origin attachment point connected to each insertion attachment point resulting in a lateral capsular mesh of 18000 capsular elements (Figure 41c). Some of these elements would be completely implausible; e.g., at the jaw closed position elements with coincident origin and insertion attachments or with an origin attachment more than 6 mm medial to the insertion attachment. Our final capsular mesh consisted of 12540 elements. Of note is that our capsular mesh allowed elements with insertion attachments located up to 6 mm laterally and up to 12 mm medially with respect to the origin attachments. These extremes may not be plausible, although this has not been documented in the literature, and in any case would depend on a particular joint's morphology. Nevertheless, we did make note of any elements with large medio-lateral differences when reporting on the results of this study. 6.3.2 Mandibular Movement The relative motion of the putative capsular insertions and length change of the capsular elements were calculated for the following four typical jaw movements: opening, protrusion, ipsilateral and contralateral excursion. There is much variability to human jaw motion (Peck et al., 1997; Peck et al., 1999a & b), however we selected plausible "average" values for mandibular condylar motion from the literature to represent the various motions. We constructed a kinematic model of. the human jaw with a dynamic modeller (ADAMS, MDI, Michigan) in which the condyles followed their pre-determined paths for each particular jaw movement. 150 In opening, the curvilinear condylar paths, in the sagittal plane were represented by the function: Z = 5 * cos fx > * TC V13 j 5 , where X is the antero-posterior translation with a range of 1-13 mm, and 2 is the supero-inferior translation. Sagittal plane rotation of the condyle simultaneously occurred and was represented by: i? = 30* , where R is the opening-directed rotation, in degrees. Thus, the sagittal V13y plane condylar path inclination was approximately 40° to the occlusal plane, and at wide gape the condyles had translated 13 mm anteriorly and 10 mm inferiorly, and rotated open 30°, and the incisor point had translated 50.0 mm. These values are in accord with kinematic data from human jaw opening (Lundeen et al., 1978; Salaorni & Palla, 1993; Peck et al., 1997). For the protrusive task, the condyles followed the same curvilinear path as in opening, however unlike opening, they did not reach the height of the eminence (Ingervall, 1972; Theusner et al., 1993). To allow the jaw to move forwards with minimal opening, sagittal plane rotation was represented by the following function: R = -3* f X^ In this case the condyles translated 7.8 mm anteriorly and 6.5 mm V7.8y inferiorly, rotated closed 3° and the incisor point had translated 10.0 mm (Sigaroudi & Knap, 1983; Slavicek, 1988; Zimmer et al., 1991; Theusner et al., 1993). Although the condyles followed the same path as in opening, they did not reach the height of the eminence as in opening For lateral movements, the ipsilateral condyle was able to rotate, but not translate about its centroid. It rotated +1.9°, +1.7° and +4.0° about medio-lateral, antero-posterior 151 and supero-inferior axes respectively, so that from the side the condyle rotated in a closing direction, and from the front and top it rotated in counter-clockwise directions. This motion enabled the contralateral condyle to follow the same airvilinear path as in opening, except that it also moved medially 1.0 mm. This resulted in plausible lateral jaw motion consistent with human kinematic data (Aull, 1965; Lundeen et al., 1978; Hobo, 1984a; Hobo, 1984b; Peck et al., 1999a). Each jaw movement was divided into 15 equal steps and standard matrix transformations describing the translational and rotational motion of the mandible with respect to a fixed cranium were calculated at each step (Craig, 1986). Utilising the relative position of the putative capsular insertion attachments on the mandible, we were able to calculate their motions with the transformation matrices. The length of each capsular element was determined throughout a particular jaw movement using: Ll=J(X,-XeY+(Y,-YeY+(Zl-Zey where Xj, Y> Zi are the antero-posterior, medio-lateral and supero-inferior positions respectively of the capsular insertion when the jaw has moved to position i from z-1. X^ Yc, 2C are the antero-posterior, medio-lateral and supero-inferior positions respectively of the capsular origin, which did not change position during the jaw movement task. As each task was divided into 15 steps, 16 length values (including the length at jaw closed position) were obtained for each capsular element. For each capsular element, we determined its maximum length attained during all jaw motions. Then, for each jaw movement, or part of a jaw movement, whenever an element reached, or was within 5% of its maximum length , it was considered taut and therefore a restraint to that particular jaw movement. In this way we allowed capsular elements which 152 were taut to undergo stretch which was consistent with collagenous ligament tissue (Viidik, 1990; Woo et al., 1997). To describe possible restraining elements' locations and orientations, we divided each element's attachment sites into 4 origin regions: antero-superior (AS), anteroinferior (AT), central (C) and posterior (P) and 2 insertion regions: posterior condylar (PC) and anterior condylar (AC) (Figure 42). In this way we could categorise each capsular element into one of the following groups: AS-PC (2376 elements), AS-AC (1584 elements), AI-PC (2376 elements), AI-AC (1584 elements), C-PC (1782 elements), C - A C (1188 elements), P-PC (990 elements), P-AC (660 elements). Each jaw movement was divided into early (beginning 1/3 of movement), middle (middle 1/3) and late (last 1/3) segments. For each segment of motion we determined whether or not any of the groups of elements were taut, and if so when in that motion segment they were taut. 6.4 R E S U L T S The mandibular movements in which the capsular lengths were assessed are shown in Figure 43. The entire capsule did not remain taut for all movements, nor for any one particular movement. For example, the lengths of three different capsular elements during jaw opening can be seen in Figure 44. In this figure, element 1 (belonging to AS-PC group) is directed antero-superioriy from the condylar neck region to the articular eminence in a similar fashion to the reported oblique band of the TML. Element 2 (belonging to AI-PC group) is directed horizontally from the condylar neck region to the eminence in the region of the reported 153 154 C3 ,6 8 155 o O O 00 O CD O O <u - S o s i * G .g T 3 W S3 9i E g . S _w fa S .2 (lunwixew jo %) imouai juaiuaje C ty o o g g bo if IS" <o O <u 156 horizontal band of the TML. Element 3 (belonging to C-PC group) is directed superiorly from the condylar neck to the height of the fossa. N o capsular elements remained taut for all mandibular movements, although if we relaxed our criteria for a taut element to include any lengths which were within 10% of its maximum length, then there were 33 elements (0.3% of lateral capsular mesh) which fit the criteria as possible constraints. Al l were AS-PC elements, and Figure 45 shows their sagittal plane orientation. In the frontal plane, and with respect to their origin attachment, 39% of these elements were inclined laterally, 48% inclined medially, and 13% oriented in a parasagittal plane. The medio-lateral position of the elements' insertions with respect to their origins extended through the entire allowable range, i.e., up to 12 mm difference between attachments. For these capsular elements the length changes ranged between 8.1% and 10.0%, and average (± standard deviation) maximum and minimum lengths were 26.2 ±1.4 mm and 24.6 ± 1.5 mm respectively. 6.4.1 Opening Movement Two capsular elements remained taut and thus were able to constrain the condyle throughout the opening task. Both were AS-PC elements, obliquely inclined in a postero-infero-medial direction from their origins, with insertion attachments 12 mm medial to their origin attachments. Overall, 9495 capsular elements (76% of the lateral capsular mesh) were taut at some stage of the opening movement (Figures 46 & 47), and on average were taut for 19.3% of this movement. Apart from the two elements which were taut for the entire opening task, taut elements could be found for each stage of opening, except when the jaw was at 1/3 open position. Forty-three capsular elements were taut for 75% or more of the opening movement, and all were AS-PC elements. Of note is that all of these elements were taut at the beginning of early-opening (up to 20% gape) and in the middle of mid-opening (after 45% gape). In thirty-six of these elements, origin and insertion attachments were within 6 mm of each other along the medio-lateral axis. Interestingly, there were only seven capsular elements which were taut at some stage when the jaw was between 20 - 45% of its maximum gape (early to mid-opening transition), and in each, the insertion attachment was 9 mm or 157 more medial to its origin attachment. For the remainder of jaw positions during opening, taut elements were found in the complete range of medio-lateral orientations (i.e., the capsular elements' insertions were located anywhere between 0-12 mm medially or between 0-6 mm laterally with respect to the element's origin attachment). Of the 652 elements taut during early opening, the majority (86.2%) were AS-PC elements, with the remainder belonging to the AI-PC (13.5%), and C-PC (0.3% or 2 elements) groups. In these latter 2 elements, insertions were 9 and 12 mm medial to their origins. No taut elements were found originating in the posterior region of the joint, or inserting into the anterior condylar region. On average, the elements were taut for only 36.7% of this stage of the movement, and this occurred predominantly at the beginning of early opening, where all elements were taut at the jaw closed position (Table 10). At each stage of early opening, there was an AS-PC element which was taut, however an AI-PC element was taut only for the initial stages (first half of early opening) and a C-PC element was taut only at the commencement of movement (at the jaw closed position). Further, if we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then AS-PC elements were taut for the initial 67% of early opening, AI-PC elements were now taut for the initial 33% of early opening, and C-PC elements were not taut for early opening. Of the 446 capsular elements taut during mid-opening, the majority (93.3%) were AS-PC elements, and the remainder (6.7%) were AI-PC elements. N o taut elements were found originating in the central or posterior regions of the joint. A l l of these elements inserted into the posterior condylar region. On average, the elements were taut for 33.5% of this stage of opening. This occurred predominantly during the latter stage of mid-opening at which point all elements were taut (Table 10). At each stage of mid-opening, there was an AS-PC element which was taut, however an AI-PC element was taut only for the latter stages (latter 40%) of mid-opening. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then AS-PC elements were taut for the latter 80% of early opening, and AI-PC elements were still taut for the latter 40% of early opening. 159 Of the 9141 capsular elements taut during late opening, 17% were A S - A Q 15% were AS-PC, 14% were AI-AC, 4% were AI-PC, 13% were C - A Q 14% were C-PC, 10% were P-A C and 135 were P-PC elements. These elements were, on average, taut for 59.5% of late opening, and this occurred predominantly during the latter stage of this phase (Table 10). At each stage of late opening, there were AS-AC, AS-PC, AI-AC, AI-PC and C-PC elements which were taut. It was only in the latter stages (latter 80%) of late opening that C - A C and P -AC and P-PC elements were taut. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then all regions, except for P - A C elements, were taut for the same stages in late opening as above. The P - A C elements were taut in the latter 60% of late opening. 6.4.2 Protrusive Movement One capsular element remained taut and thus was able to constrain the condyle throughout protrusion. It was an AS-PC element, obliquely inclined in a postero-infero-medial direction with an insertion attachment 12 mm medial to its origin attachment. Overall, 858 capsular elements (6.8% of lateral capsular mesh) were taut at some stage of the protrusive movement (Figures 46 & 47), and on average were taut for 30.6% of this movement. Apart from the element which was taut for the entire protrusive task, there was not a combination of taut elements which constrained the entire protrusion, as no element was taut when the jaw was 40 - 60% protruded. Therefore a combination of elements, each taut at a particular stage of the protrusion, could not be found for the entire movement. Five capsular elements were taut for 75% or more of protrusion, and all were AS-PC elements. These elements were taut in early and late protrusion, and all had origin and insertion attachments at least 9 mm apart along the medio-lateral axis. In addition, other elements in combination could be found which were taut in the early and late phases of protrusion, and these elements were found in the complete range of medio-lateral orientations. Of the 670 elements taut during early protrusion, the majority (90.4%) were AS-PC, and the remainder (9.6%) were AI-PC elements. N o taut elements were found originating in 160 the central or posterior regions of the joint (Table 10). On average, the elements were taut for only 53% of this stage of the movement, and this occurred predominantly at the beginning of early protrusion from the jaw closed position, at which point all elements were taut. There were 3 elements which were taut for the entire phase of early protrusion; they all were AS-PC elements with insertion attachments at least 9 mm medial to origin attachments. At each stage of early protrusion, there was an AS-PC element which was taut, however an AI-PC element was taut only for the initial stages (initial 67%) of early protrusion. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then AS-PC elements were taut for the initial 83%, and AI-PC elements were taut for the initial 50% of early protrusion. Ten capsular elements were taut during mid-protrusion, and all were AS-PC elements with insertion attachments at least 9 mm medial to origin attachments. On average, the elements were taut for only 30% of this stage of protrusion. At each stage of mid-protrusion, there was an AS-PC element which was taut, however if we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then there were no taut AS-PC elements in mid-protrusion. Of the 231 capsular elements taut during late protrusion, 93.5% were AS-PC, 0.4% (1 element) were AI-PC, and 6.1% were C-PC elements. These elements were, on average, taut for 65.6% of late protrusion, and this occurred predominantly during the latter stage (Table 10). At each stage of late protrusion, there was an AS-PC element which was taut, however only during the latter 80% and 60% of late protrusion were taut AI-PC and C-PC elements present respectively. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then taut AS-PC and C-PC elements were still present at the same stages as above, however no AI-PC elements were taut during late protrusion. 161 6.4.3 Contralateral Movement During a contralateral movement, no capsular elements remained taut throughout the complete motion. Overall, 3404 capsular elements (27.1% of lateral capsular mesh) were taut at some stage of the contralateral movement, and on average, the elements were taut for only 14.7% of this movement. N o elements were taut during the middle 1/3 of the movement (Figures 46 & 47). The capsular element which was taut for the greatest amount (62%) of the contralateral movement was taut during early and late stages of the motion. It was an AS-PC element with an insertion 12 mm medial to its origin. A combination of elements, each taut at a particular stage of the contralateral movement, could be found for the early and late stages of the contralateral motion. These elements were found in the complete range of medio-lateral orientations. Of the 683 elements taut during early contralateral motion, the majority (88.3%) were AS-PC, and the remainder (11.7%) were AI-PC elements. On average, the elements were taut for only 37.3% of this stage of the movement (Table 10), and this occurred at the beginning of early contralateral motion from the jaw closed position, at which point all elements were taut. For the initial 83% of early contralateral movement there was an AS-PC element which was taut, and for the initial 50% there was an AI-PC which was taut. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then taut AI-PC elements were still present for the initial 50%, and AS-PC elements were present for the initial 67% of early contralateral movement. As stated above, no elements were taut during any part of the middle stage of the contralateral movement (Table 10). Of the 3247 capsular elements taut during the late segment of contralateral motion, 40.9% were AS-PC, 4.8% were AI-PC, 29.6% were C-PC and 23.7% were P-PC and 1% were P-AC elements. 162 These elements were, on average, taut for 40.0% of the late segment, and this occurred predominantly during the latter stage of this segment (Table 10). At each stage of late contralateral motion, there was an AS-PC element which was taut, however an AI-PC element was taut only for the final 60% and C-PC, P-PC and P - A C elements were taut for the final 40% of this segment of the movement. Further, when limiting our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, taut AS-PC, C-PC, P-PC and P -AC elements were still present at the same stages as above, however AI-PC elements were now taut during the final 40% of late contralateral motion. 6.4.4 Ipsilateral Movement Throughout the ipsilateral movement, 487 elements were taut during the entire motion. Of these, 435 were AS-PC and 52 were AI-PC elements. In all, insertions were located at every possible medio-lateral position. Overall, 3671 capsular elements (29.3% of lateral capsular mesh) were taut at some stage of the ipsilateral movement (Figure 46 & 47), and on average were taut for 59.7% of this movement. Interestingly, apart from the 487 elements which were taut for the entire ipsilateral task, there was not a combination of taut elements which constrained the entire ipsilateral movement, as no element was taut at the commencement of movement in the jaw closed position. For all other stages of the movement, elements, or combinations of elements could be found which remained taut. Excluding those elements taut for all of the movement, 697 capsular elements were taut for 75% or more of the ipsilateral movement; 55.7% of these were AS-PC elements, 43.8% AI-PC elements, 0.3% (2 elements) A I - A C and 0.3% C-PC elements. Of note is that all of these elements were taut for the latter part of the movement, and insertions were found at every possible medio-lateral position. Apart from those which were taut for the entire ipsilateral movement, there were 918 elements taut during the early phase of ipsilateral motion. These were divided approximately in half between AS-PC (50.5%) and AI-PC (48.7%) elements, with the remainder consisting of AI-AC (4 elements) and C-PC (3 elements) elements. In these latter three elements, insertions were 9 mm and 12 mm medial to their origins. N o taut elements were found 163 originating in the posterior region of the joint. On average, the elements were taut for only 47.4% of this stage of the movement, and this occurred in the latter stage of early ipsilateral motion (Table 10). For the latter 83% of early ipsilateral movement there were AS-PC and AI-PC elements which were taut, and for the latter 67% and 50% of the early movement there were AI-AC and C-PC elements respectively which were taut. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then taut AS-PC, AI-PC and A I - A C elements were still present at the same stages as above, but no C-PC elements were taut for early ipsilateral movement. Taut elements originating from the antero-superior and antero-inferior joint region were found for the latter 80% of early ipsilateral motion. Taut elements originating from the central region were found for the latter 60% of this segment of ipsilateral movement. Apart from those which were taut for the entire ipsilateral movement, 2537 capsular elements were taut during the middle phase of ipsilateral motion. The majority (67.5%) were AI-PC elements, with the remainder divided amongst AS-PC (23.4%), A I - A C (5.7%), C-PC (3.2%) and AS-AC (0.2%) elements. On average, the elements were taut for 72.0% of this stage of the movement, and this occurred predominantly during the latter stage of middle segment at which point all elements were taut (Table 10). At each stage of mid-contralateral motion, there were elements from each of the above groups which were taut. If we limited our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis, then taut AS-PG, AI-PC, A I - A C and C-PC elements were still present at the same stages as above, however A S - A C elements were now taut during the final 40% of the middle phase of contralateral movement. There were 3184 capsular elements taut during the late segment of ipsilateral motion, and of these, 63.4% were AI-PC elements, 18.7% were AS-PC, 11.4% AI-AC, 6.4% were C-PC and 0.2% AS-AC elements. N o taut elements were found originating in the posterior region of the joint. On average, the elements were taut for 97.7% of this late stage of motion, and this occurred predominantly during the latter stage of the late phase of the motion at which point all elements were taut. At each stage of late contralateral motion, all 164 opening 100 80 60 40 20 13 2D 27 33 40 5 3 6 0 6 7 7 3 8 0 8 7 9 3 100 Jaw position as % of full movement protrusion ? 100 Jaw position as % of full movement Figure 46 Number of taut capsular elements (expressed as % of all taut elements for the particular movement) throughout each jaw movement (expressed as % of maximum movement). This page shows data for opening and protrusive motion. Overleaf is data for contralateral and ipsilateral jaw motion. 1 contralateral 55 100.. Jaw position as % of full movement ipsilateral 3? 100-. Jaw position as %of full movement Figure 47 Number of taut capsular elements (expressed as % of all taut elements for the particular movement) throughout each jaw movement (expressed as % of maximum movement). This page shows data for contralateral and ipsilateral jaw motion. 166 Capsule group Early segment Middle segment Late segment A B C D A B C D A B C D Opening AS-PC I 37.8 100 67 F 34.3 100 80 F 85.8 100 100 Opening AS-AC F 63.2 100 100 Opening AI-PC I 30.1 50 33 F 22.7 40 40 F 67.2 100 100 Opening AI-AC F 49.6 100 100 Opening C-PC I 85.3 17 0 F 57.7 100 100 Opening C-AC F 47.7 80 80 Opening P-PC F 52.0 80 80 Opening P-AC F 51.7 80 60 Protrusion AS-PC I 53.9 100 83 F 30 100 0 F 66.9 100 100 Protrusion AS-AC Protrusion AI-PC I 44.5 67 50 F 80.0 80 0 Protrusion AI-AC Protrusion C-PC F 45.7 60 60 Protrusion C-AC Protrusion P-PC Protrusion P-AC Contralateral AS-PC I 38.1 83 67 F 46.4 100 100 Contralateral AS-AC Contralateral AI-PC I 31.3 50 50 F 32.2 60 40 Contralateral AI-AC Contralateral C-PC F 35.3 40 40 Contralateral C-AC Contralateral P-PC F 36.6 40 40 Contralateral P-AC F 40 40 40 Ipsilateral AS-PC F 76.1 100 100 F 95.5 100 100 I,F 100 100 100 Ipsilateral AS-AC F 56.0 40 40 I,F 100 100 100 Ipsilateral AI-PC F 47.2 100 100 F 68.2 100 100 F 98.8 100 100 Ipsilateral AI-AC F 33.3 67 67 F 38.9 100 100 F 91.8 100 100 Ipsilateral C-PC F 33.3 50 0 F 40.0 100 100 F 91.1 100 100 Ipsilateral C-AC Ipsilateral P-PC Ipsilateral P-AC Table 10 Tautness of specific capsular regions throughout jaw movement. For each movement segment (early, middle & late): A) The stage of the segment (initiaLl, finaLF) at which a specific capsular group is taut. B) The average amount, in percent, of that segment in which a specific capsular group is taut. C) The amount, in percent, of that segment in which taut elements could be found. D) As in C, but elements whose attachments are not within 6mm mediolaterally of each other are excluded 167 AS-PC and AS-AC elements were taut, and one or more elements from each of the remaining groups listed above were taut (Table 10). We did not change the stages during the motion that these elements were present by limiting our plausible elements to those whose origin and insertion attachments were within 6 mm of each other along the mediolateral axis. 6.5 DISCUSSION 6.5.1 Assumptions In this study, a theoretical model of the temporomandibular joint was developed in which putative lateral capsular insertions on the condyle and condylar neck were able to move, with respect to the capsular origin attachments on the temporal bone, for various mandibular movements. We modelled the capsular elements as straight line links between insertion and attachment points, although in reality, regions of the capsule may be curved, especially below and behind the lateral condylar pole. Both jaw motion and joint morphology show large variation in the human population (Yale et al., 1966; Oberg et al., 1971; Solberg et al., 1985; Salaorni & Palla, 1993; Palla et al., 1997), and ideally this study would be conducted on individually matched motion and morphology data. Although an individual's jaw motion has been matched to image-obtained TMJ morphology (condyle, articular eminence) (Palla et al., 1997), specific capsular attachments were not derived. This is currently not possible, as high resolution imaging of the joint's soft tissue structures have not differentiated capsular wall from other soft tissue structures (muscle, tendon, disc). Nevertheless this differentiation may be possible in the near future as successful segmentation of soft tissue structures within the orbit from magnetic resonance images has recently been performed (Ettl et al, 1998). In this study we chose typical mandibular movements and attempted to include all possible capsular attachments by assigning relatively large volumes for the origin and insertion regions. These regions were derived from average joint dimensions, and for a specific individual subject these regions would presumably be smaller, and thus not contain all capsular elements we have included. It must be emphasised that our capsular mesh is not 168 a direct representation of the lateral capsular wall, rather a region in which the capsule is expected to exist. Afterall, our mediolateral dimensions for both origin and insertion attachment regions were 12 mm; capsular attachments throughout these entire regions would result in excessively thick, unnatural capsular tissue. We intentionally minimised reporting on the tautness of specific elements and instead reported on a group of elements as a whole and their possible constraining influence. In this way we assumed that if a number of elements were taut within a group, then at least some of these taut elements would be plausible in an individual. We divided each jaw movement into 15 discrete points, and although we determined whether the putative capsular elements were taut at each of these jaw positions, we do not know the element's length between these discrete points. Although the element's would have become less or more taut between these discrete points, we do not believe it would have affected the overall outcome of this study as the jaw motions were smooth and evenly distributed between the 15 positions. Therefore these discrete jaw positions were a good representation of the entire movement. We only examined the lateral aspect of the capsule because it has been reported that capsular elements which connect the temporal bone with the mandible are only found on the lateral side of the joint (Schmolke, 1994), and many functional speculations have been aimed at this region (Arstad, 1954; Boudreaux & Spire, 1968; Sanders & Newman, 1975; Griffin et al., 1975; Savalle, 1988; Feinberg & Smilack, 1988; Osborn, 1993; Kang et al., 1993; Sato et al., 1995). 6.5.2 The Role of the Lateral Capsular Wall We chose specific opening, protrusive, contralateral and ipsilateral jaw movement tasks and found no part of the capsule which remained taut throughout all of these movements. However when we relaxed our definition of taut capsular regions to include those elements which were within 10% of their maximum length, then we found AS-PC elements which could conceivably constrain all motions. This finding must be interpreted with caution. A 10% strain (relative length change) is relatively large for taut collagenous connective tissue, and in fact has been cited as the nominal value after which rupture occurs in these types of 169 tissue (Viidik, 1990). In fact, laboratory investigations have shown, during normal function, that the safety margin of collagenous connective tissue is considerable and that the working range of these tissues is well below this strain level (Viidik, 1990). Although unlikely, the lateral capsular wall of the TMJ, with its haphazard collagen architecture (Sato et al., 1996), may not display the same mechanical properties as these more regularly oriented collagenous structures, and so may extend to 10% strain during normal function. These elements comprised only a very small proportion (0.3%) of our lateral capsular meshwork. It would be expected however that tissue responsible for constraining all jaw movements would consist of more elements than the few we found here. These possible constraining elements extended, in the sagittal plane, from the antero-superior corner above the articular eminence to the postero-inferior corner, at the back of the condylar neck (Figure 45). These attachment points make them the longest elements in our capsular mesh, enabling these elements to lengthen more, while still remaining within 10% of their maxima, than any of the other (shorter) elements. If the capsular attachments did not extend to these regions, then there would be no elements remaining within 10% of their maximum length for all movements. Nevertheless, these attachment locations provide this functional advantage, and interestingly the reported oblique fibres of the T M L are oriented in a similar fashion to these elements (Griffin et al., 1975). We assessed opening, protrusive and lateral movements from jaw closed to maximum excursive positions. Elements from each of the capsular regions were taut at various stages of the jaw movements. This, together with anatomical studies which indicate no particular tissue orientation in the capsule (Savalle, 1988; Luder & Bobst, 1991), supports a proposal to consider the whole lateral capsule as a ligament (Ten Gate, 1994). In our study there was a preponderance of taut AS-PC elements (which were oriented similarly to the oblique TML) throughout the jaw movements, and so it would not be unreasonable to expect fibres oriented similarly in anatomical specimens. However, jaw movement variations, which are large in the human population, could very well alter the capsular regions containing taut elements. This may in part explain the variation in fibre orientation of the lateral capsular wall in human specimens. More of the capsular mesh was taut during opening than for any of the other movements (open: 76% of mesh, ipsilateral: 29.3%, contralateral: 27.1% and protrusion: 170 6.8%). Interestingly however, during opening, protrusion and contralateral motion those elements which remained taut did not remain this way for the entire movement as only 0.3% (43 elements), 0.04% and 0% of the mesh remained taut for 75% or more of the movements respectively. For the ipsilateral movement, 9.4% of the mesh remained taut for 75% or more of the movement. Apart from the ipsilateral movement where the elements remained taut for an average of 59.7% of the movement, the elements remained taut, on average, for less than 1/3 of the movement. In all jaw movements there were regions of the capsule which were taut at the beginning (jaw closed position) and end of the movement. This finding suggests that the TMJ, at the jaw closed position, is in a 'close-packed position' as there is optimum congruency between joint surfaces and a tautened capsule (Barnett, 1971; Brown, 1975). This position should impart maximum joint stability as no further movement (closing) should be possible. Unlike other articulations, the TMJ was considered previously not to possess a close-packed position (Hesse & Hansson, 1988). For the ipsilateral movement, there were a number of AS-PC and AI-PC group elements which remained taut throughout this movement. Even if the sum total of elements was reduced by limiting attachment sites to 6mm or less along the mediolateral axis, taut elements from these two groups were still present. The ipsilateral jaw movement is a special case as there were not only many single elements which were taut throughout the whole motion, but there were also other elements which were taut throughout each segment of the movement. For example, although taut elements from AS-PC and AI-PC groups predominate in the early segment, throughout the middle and late segments of this motion, elements from the AI-AC, AS-PC and C-PC groups remain taut. Even when the element numbers are reduced by limiting attachment sites to 6 mm or less along the mediolateral axis, many of these elements remain (Table 10, Column D). This suggests a large proportion of the capsule, from the central to anterior regions, is able to share a constraining effect to this motion. Although we chose a specific lateral movement, in reality the laterally directed mandible is able to move in an envelope of lateral positions ranging from antero-lateral to postero-lateral movements. Perhaps the arrangement of the capsular wall is able to constrain all of these possibilities. 171 The individual variation in ipsilateral condylar movement is large, with some individuals displaying rotation about the condylar centre (as in our model), and others displaying an additional lateral bodily shift of the condyle (Peck et al., 1999b). This translation of the condyle may occur in joints with a slightly slack capsular wall at the jaw closed position, so that as lateral motion occurs the condyle translates laterally, and tautens the capsular wall. Alternatively, muscle tensions (active and/or passive) may restrain, in combination with the capsule or alone, the condylar movement (Jimenez, 1987; Kornecki, 1992). The combined restraining influence of muscle and capsule is an attractive hypothesis, as golgi tendon organs have been found in the capsular wall (Thilander, 1961). Afferent activity from these slowly adapting mechanoreceptors is seen at the extremes of mandibular movement when significant stresses are generated within the capsule (Zimny, 1988). In addition, the capsule is associated physically with adjacent muscle, as part of the capsule inserts into the temporal fascia (Schmolke, 1994), and electromyography studies suggest medially-directed forces result from the ipsilateral medial pterygoid muscle during lateral movements (Gibbs et al., 1984). In opening there were only two elements (AS-PC), in protrusion there was only one element (AS-PC), and in contralateral motion there were no elements which remained taut throughout each of these movements. The three elements which were taut throughout opening or protrusion may be implausible because their insertion attachments were 12 mm medial to their origin attachments, or simply because capsular attachments did not exist at these three sites. Thus if we discount these three elements, then there were no other elements which, in combination, could constrain the opening, protrusive or contralateral movements. Interestingly, taut elements were lacking in the middle segments for each of these movements. When the jaw was at 1/3 opening, and during the entire middle segment of protrusion and contralateral motion, no capsular elements were taut (Figures 48 - 51). This is important as these middle regions of the motions are functional regions of mastication (Ahlgren, 1976), and it would be expected that at these positions, constraints are necessary. Interestingly, the end stage of each of the movements was constrained by capsular elements, suggesting the elements have a limiting role to extreme mandibular movement. This study does not discount the notion of differences in end-feel between the active and passive ranges of mandibular movement (Friedman & Weisberg, 1984; McCarroll et al., 172 1987), nor movement increases (Posselt & Thilander, 1965; Klineberg, 1980) or condylar distraction (McMillen, 1972) following articular or general anaesthesia. Our study may be considered as one of passive jaw movements in which the capsule limits the motion, whereas active jaw movements, performed by the conscious individual, may be limited predominantly by neuromuscular control, and thus rarely approaches the capsular-constrained jaw positions. McMillen (1972) found that following administration of a muscle relaxant, pantographic tracings demonstrated that condyles dropped an average of 2.43 mm (range 0.9-5.5 mm), and also increased their range of movement laterally. It was therefore suggested that the T M L is slack at the jaw closed position. Although he did not use a consistent force when manipulating the mandibles of his subjects, when comparing condylar range of motion with and without muscle relaxant, or correlate vertical and horizontal condylar displacements, our study suggests that this distraction is possible with taut capsular elements in the jaw closed position. We have shown that at the jaw closed position, taut AS-PC and AI-PC elements predominated. These elements, whilst remaining taut could allow the condyle to move downwards and forwards as it rotated about the elements' insertions and swung about their origins as postulated by Osborn in his mathematical study of opening (1993). Of note is that although the translatory condylar movement in maximal opening is greater than in protrusion (and contralateral motion), taut capsular elements were found at the limit of protrusion. This present study supports the notion that the rotation associated with opening frees the joint from the biomechanical constraints of the lateral capsular wall which are taut during maximum protrusion; and thus allows further anterior extension of the condyle (Theusner et al., 1993). If, as we have suggested in this study, capsular tissue does not constrain the entire motion, then what does constrain the motion segments in which we found no taut capsular elements? It has been suggested in other studies that accessory ligaments, such as the sphenomandibular and stylomandibular ligament, may play a constraining role throughout mandibular motion (Rossow, 1968; Hesse & Hansson, 1988; Osborn, 1993; Kang et al., 1993; Osborn, 1995), (Burch, 1970). The sphenomandibular ligament has been implicated as a constraint during late opening (Osborn, 1993; Osborn, 1995), as a constraint in lateral motion (Rossow, 1968), or as a negligible constraint to any motion (Williams, 1989). Similar controversy exists with the stylomandibular ligament, as it has been suggested to limit 173 contralateral and protrusive jaw motion (Burch, 1970), or alternatively to play no role in constraining any jaw movements (Rossow, 1968). Unfortunately the biomechanical function of these ligaments is uncertain, however even if they were to constrain motion as outlined above, then the middle segment of opening still appears to be without a ligamentous or capsular constraint. Dynamic muscle-driven models of the human jaw suggest muscle tensions are capable of constraining mandibular motions (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Koolstra & van Eijden, 1999). These complex three dimensional models, in which muscle tensions are represented by non-linear passive length-dependant forces, and active task-dependant drive, have shown that the mandible is able to move in a plausible manner, in the absence of periarticular ligamentous or capsular constraints. These models do not discount a role for a constraining capsule, but do suggest that if it exists, then it works in unison with the muscles to constrain motion. This co-operation has been shown in the rat knee, where passive muscle tensions and the anterior cruciate ligament were both responsible for constraining the motion (Aune et al., 1994). Our study suggests an interesting hypothesis that the capsule predominantly limits the extremes of opening, protrusive and contralateral motion, i.e., at the jaw closed and maximum excursive positions, and that muscle tensions play a major restraining role between these positions. 6.6 CONCLUSIONS In this study we have assessed the length changes of putative lateral capsular wall elements of the TMJ for opening, protrusive and lateral jaw movements. We determined the movement segments in which these elements were taut (i.e., within 5% of the elements maximum possible length) and subsequently suggested putative capsular regions which constrained particular segments of each motion. For all jaw movements, taut capsular regions were present at the jaw closed position and at maximum excursive positions. For the ipsilateral movement, capsular elements also constrained the whole movement. For the other movements, there were stages within the 174 middle segment of the motion in which no capsular elements were taut, suggesting that the capsule has no constraining influence during these movement stages. It seems appropriate to infer that other constraints, such as muscle tensions, are responsible for constraining these stages. Although many of the taut capsular elements belonged to the AS-PC region (located similarly to the oblique portion of the TML), the other capsular regions were variously taut throughout the jaw motions and so we suggest the whole lateral capsule, instead of the classically described temporomandibular ligament, be considered a ligament'. 175 Figure 48 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different jaw positions during opening. A. Jaw closed position, B. 1/3 opening, C. Full opening. 176 Figure 49 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different jaw positions during protrusion. A. Jaw closed position, B. Entire middle 1/3 of protrusion, C. Full protrusion. 177 Figure 50 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different positions jaw during contralateral movement. A. Jaw closed position, B. Entire middle 1/3 of movement, C. Full excursion. 178 A Figure 51 Sagittal representation of TMJ demonstrating taut (straight lines) and slack (curved lines) capsular regions for different positions jaw during ipsilateral movement. A. Jaw closed position, B. Entire middle 1/3 of movement, C. Entire latter 1 /3 of movement. 179 7 A MODEL OF T H E PASSIVE TENSION PROPERTIES OF T H E MASSETER MUSCLE 7.1 ABSTRACT Many of the masticatory muscles, including the masseter muscle, have complicated internal architectures, however the functional implications of this complexity are not known. In this study we constructed three-dimensional, dynamic mathematical models of the human masseter muscle. The aim was to illustrate the effects of a more complex internal architecture on passive tension generation by the muscle during opening and contralateral jaw movements. "Complex" models were created with 12 musculotendon actuators in which tendon and sarcomere stretch contributed to passive tension generation. In one model (Model CU), sarcomere lengths were assigned to muscle regions uniformly, and in the other they were assigned differentially (Model CD) according to anatomical descriptions. In addition, a much simpler muscle model (Model S), used frequently in whole jaw modelling, was created with a "deep" and a "superficial" straight line actuator. When typical jaw opening was simulated, passive tensions remained similar for the complex models (maximum in each: 5.1 N), but lower than the simpler model (maximum: 8.0 N). This trend was repeated but less noticeable for the contralateral movement (complex maximum: 3.9 N , simple: 4.0 N). Resultant moments were very low in all models for both jaw movements. For both movement tasks in the complex models, deep muscle fibres lengthened significantly more than superficial fibres (p < 0.05), and "aponeuroses" appeared to bend and shear, and muscle fibres altered their direction of pull. Whilst the effect is likely to be more complicated in vivo than in our 12 actuator model, this model does provide insight into the interactions of tendon and fibre components in the multipennated masseter muscle. Although the complex model involves greater structural detail than the simple model, the similar tensions generated in both types of models suggests that a simple two-line actuator may reasonably represent the tensions generated in the masseter muscle for the passive tasks simulated in this study. However a complex muscle would be needed to investigate differential activation within the muscle, or the effects of structural alterations such as muscle asymmetry. 180 7.2 INTRODUCTION The masticatory muscles are both architecturally and functionally complex. To accomplish diverse oral tasks, these muscles are required to move the mandible in an environment of constantly changing forces, including amongst others, such active and passive tensions developed by antagonist muscle groups. The relationship amongst such variables has been assessed in animal and human studies, and more recently it has been studied with virtual, biomechanical models (Miller, 1991b; Hannam & Langenbach, 1995). For a variety of reasons, including the difficulty in obtaining and interpreting adequate physiological data, structural and functional properties of the muscles have had to be simplified. For example, whole muscle tension has commonly been described often as a single force vector between an "average" origin and insertion attachment, although in reality many of the masticatory muscles display broad bony and tendinous attachments, and a multipennated, compartmentalised internal architecture (Hannam & McMillan, 1994). Further, regional and functional specialisation within the muscles (Eriksson et al., 1984; Belser & Hannam, 1986; Stalberg & Eriksson, 1987; McMillan & Hannam, 1991; Tonndorf & Hannam, 1994) suggests accurate control of muscle tension level and direction may occur through selective activation (Herring et al., 1979; Turkawski et al., 1998). The masseter muscle exemplifies these characteristics. Although often considered to consist of a deep and superficial part, more complete topographical descriptions depict a muscle compartmentalised by (5 or more) aponeuroses aligned approximately in the parasagittal plane, and attached in an alternating fashion to the 2ygomatic arch and mandible (Ebert, 1939; Schumacher, 1961; Lam et al., 1991). In living subjects, each aponeurosis has a unique orientation (revealed by magnetic resonance imaging; Lam et al., 1991), with muscle fibres attached between aponeuroses, or between the aponeuroses and bone (Schumacher, 1961). Although most motor unit territories in the masseter are confined to discrete compartments (Tonndorf & Hannam, 1994), a few units map quite large territories (Stalberg & Eriksson, 1987; McMillan & Hannam, 1991), presumably enabling the muscle to produce both fine jaw movements and large forces. Task-dependent, differential activation patterns have been demonstrated in specific regions of the masseter (Belser & Hannam, 1986; Tonndorf et al., 1989; Blanksma & van Eijden, 1995; Blanksma et al., 1997). 181 Regional differences in masseter fibre and sarcomere lengths have also been reported (van Eijden & Raadsheer, 1992; van Eijden et al., 1997), and the muscle's mandibular attachments have been suggested to move differentially with jaw motion (Goto et al., 1995). Given the muscle's complex internal architecture, this suggests differential fibre and sarcomere length changes result from jaw motion. Regional sarcomere measurements have been obtained at different jaw positions in the rat and pig (Nordstrom et al., 1974; Herring et al., 1979). In humans, sarcomere length changes during jaw motion have been predicted with theoretical models (van Eijden & Raadsheer, 1992). During opening, for example, it has been suggested that sarcomeres in the anterior region of the muscle stretch more, due to interactions between moment arm length, initial sarcomere length at the closed jaw position, and the number of sarcomeres in series (van Eijden & Raadsheer, 1992). The effect of mobile attachments, such as non-rigid aponeuroses (which can move independently of the mandible) was not considered, however since active and passive muscle tensions are dependent, in part, on sarcomere length, they might also be expected to differ regionally. If so, there would seem to be some support for previous recommendations that a proper analysis of the complete masseter muscle contraction mechanics should involve its partitioning into more than two independent elements (Herring et al., 1979; van Eijden & Raadsheer, 1992). In humans, direct assessment of dynamic tensions in the masticatory muscles is presently not feasible. In the dynamic models which have been developed, simplifications have been made to cope with unavailable input data, or with mathematical solution times which are excessive (Chapters 3 & 5) (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999; Koolstra & van Eijden, 1999). In these cases, the masseter muscle is represented by two straight-line force actuators which directly connect the origin and insertion attachment sites of the superficial and deep portions of the muscle respectively, or which divide each of the two muscle parts into a tendinous and fibre component connected by a "dummy" part with minimal mass properties. Although plausible muscle-driven jaw motions are possible with these simulations, problems have been encountered with the overall performance of these models. For example, when "whole" passive muscle tensions were derived from sarcomere length-tension curves, jaw depressor actuators were unable to overcome the 182 passive resistance generated in the jaw elevator actuators, and maximum jaw opening was limited to 35 mm incisal gape (Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Langenbach & Hannam, 1999). It is possible that this is the direct result of ignoring the influence of internal fibre and tendon orientation and compliance on total passive tensions in muscles like the masseter. In this study we constructed a three-dimensional, dynamic mathematical model of the human masseter muscle. Our goal was to illustrate the putative effects of a more complex internal architecture on passive tension generation by the muscle during opening and contralateral jaw movements. In addition, we wanted to compare these dynamic properties with those obtained from a simpler masseter muscle analogue used previously in whole jaw modelling (see Chapters 3 & 5). 7.3 METHODS 7.3.1 Complex Muscle Models (Models C U & CD) Two mathematical models of the right masseter muscle were developed with commercially available software written specifically for the design, visualisation and analysis of dynamic models common in mechanical engineering (ADAMS; MDI , Ann Arbor, MI). We ran the program on an Indy RS4000 workstation (Silicon Graphics Inc., Mountain View, CA). A D A M S defines a system as a collection of mixed nonlinear differential and algebraic equations, and subsequently solves these with numerical integration. The complex multi-layered muscle models were constructed according to topographical descriptions by Schumacher (1961). They were identical in every respect except for assigned initial sarcomere lengths (see below). In each case, the muscle was divided into five tendinous aponeuroses aligned approximately in the parasagittal plane. Muscle "fibre" bundles were assumed to run obliquely between adjacent aponeuroses and/or between an aponeurosis and the mandible (Figure 52). In this multipennation representation, tensions in one fibre group affected the orientations and locations of those in adjacent groups, and ultimately influenced the passive tension generated by the whole muscle. Al l 183 Figure 52 Representation of masseter muscle architecture. Frontal view depicting masseter muscle arrangement from zygomatic origin (Z) to mandibular insertion (M). The muscle is divided by aponeuroses (solid lines) which are interconnected with muscle fibres (dashed lines). Lateral is to the right of the figure, and superior is towards the top. 184 "tendon" and "fibre" attachments were oriented in a right-hand co-ordinate system with its origin at the condylar centre. The +x axis was directed anteriorly and parallel to the occlusal plane, and the +y and +z axes were perpendicular to this axis, and oriented superiorly and to the right (laterally) respectively. The tendinous aponeurotic sheaths were used as dividing landmarks, and the masseter muscle was partitioned into six layers (viewed in the frontal plane). Layer 1, the outermost layer, consisted of the outer aponeurosis (originating from the zygomatic arch) and its attached muscle "fibres" which inserted onto the mandible. Layer 2 consisted of this aponeurosis, the adjacent aponeurosis (attaching to the mandible) and interconnecting muscle "fibres". This layering continued to the innermost layer (Layer 6) of the muscle, which included the inner aponeurosis (originating from the zygomatic arch) and attached "fibres" inserting on the mandible (Figures 53 - 55). 7.3.1.1 Complex Muscle Model Components Each layer of the two complex muscle models was represented by two musculotendon actuators, resulting in identical 12-actuator muscle models. The outermost actuators were labelled M T l l and MT12, and this nomenclature continued to the deepest layer, which contained actuators MT61 and MT62 (Table 11). Seven of these actuators represented tendon-fibre-tendon complexes, i.e., each represented a muscle "fibre" attached between two aponeuroses. The remaining five actuators represented a tendon-fibre complex, in which the muscle "fibres" attached between an aponeurosis and the mandible or zygomatic arch (Figures 54 & 55). Within each actuator, the tendon and fibre components each generated passive tensions upon stretch, and the in-series pair collapsed when shortened passively below their initial combined lengths. 7.3.1.1.1 Muscle Thickness Since our masseter muscle models were three-dimensional representations, we needed some estimation of any changes in muscle thickness which occur when the masseter is stretched. Although masseter muscle thickness measurements have been made with the jaw at a tooth contact position (Kiliaridis & Kalebo, 1991; Raadsheer et al., 1994; Kiliaridis et al., 1995; Raadsheer et al., 1996), we found no reports of the muscle thickness at excursive jaw positions such as wide gape. We assumed, that overall, the masseter muscle would stretch 185 8 c/> T) cu J3 cu ^ fij U co O I ^ m ca d w £ 6 2 "2 o a 3 S u C o •o a u 3 a T3 O •3 On ,2 3 CO o CJ c o a, O -d d « o o -a 11 a h c i ! CU u o ••H « C« r: s TO <w n flj -4-1 -»-» 4_i ^ o <u cu •5 2 CM •••<N <N 3 C S S E o T3 « b o u 4-1 •So S 187 a o fe CN CN CN u CO 3 a u CU *J CU CO CO CS 13 a. IT CN cm O a o •a « i CU C/3 I I I fe [L, O 188 V. E o SJ3 N N <N o 6 c o o o O u a o C 3 u 3 <u i l l « y ii & ^ g « § *> ^ •£ 13 O £ - o .a .2 .3 "53 5-5 ^ 2 3 3 ii a <L) ^ c3 u ^ I i II' c« T3 -g 1) , —i O V o *« 53 <u C . a Q_ *H A) u fcr* <u X <u maximally at wide jaw opening (see Chapter 3), and consequently would show its greatest change in thickness between this position and the jaw closed position. To establish the extent to which the actual muscle would be expected to change in mediolateral thickness during maximum jaw gape, we made ultrasonographic measurements on a sample of living subjects. A real time ultrasound scanner (Pie medical scanner 480, 7.5Mhz linear array transducer) was used to obtain images of the masseter muscles in 5 normal human subjects (1 ? 4 c?, age 30-36 years) at two jaw positions: jaw closed with light intercuspal tooth contact (IP), and wide jaw gape (WG). We measured muscle thickness in the mid-third of the muscle at these two jaw positions. At IP, we located the mid-points of the muscle attachments on the zygomatic arch and inferior mandibular border, and bisected a line joining these attachments. This position was marked on the subject's skin and was defined as the mid-point of the masseter. The anterior border of the masseter was palpated and marked on the subject's skin, and the transducer was then aligned perpendicular to this border, and over the mid-point of the masseter, and the region was scanned. Then at WG, we redetermined the mid-point and anterior border of the muscle and repeated the scan. In both scans, the muscle thickness, defined on the scanned image as the largest perpendicular distance from the ramus of the mandible to the lateral border of the muscle, was measured. For five subjects, muscle thicknesses at IP were 0.96, 1.25, 1.32, 1.23, 0.84 cm; at WG, they were 0.86, 1.32, 1.39, 1.18, 1.03 cm respectively. The relative changes in muscle thickness were -10.4%, 5.6%, 5.3%, -4.1% and 8.9%, where a negative value indicates a decrease in muscle thickness from IP to W G . Subsequently, we represented this variation in the models by allowing each musculotendon junction freedom to move ±10 %, from its position at IP, along an axis perpendicular to the mandibular ramus. We modelled this allowable thickness change at each musculotendon junction as a "slot", i.e., the musculotendon junction was able to move freely as long as it did not attempt to move beyond the confines of the "slot". If it did, a viscoelastic force was generated, perpendicular to the ramus, to ensure the musculotendon junction remained in the allowed mediolateral region. The elastic constant for this restraining force was arbitrarily set at 104 Nm' 1 , with a viscous damping constant to 104 Nsm"1. In this 190 way, the muscle was allowed to become thicker or thinner during stretch according to the demands of its internal passive force vectors. 7.3.1.1.2 Tendon Properties Tendons exhibit a complex relationship between applied tensile forces and resulting strain (relative length change). At low strain levels, the tissue is compliant, and displays a non-linear force strain relationship, whereas with greater force application the relationship becomes more linear (Fung, 1993a). Since experimental force-strain relationships at low strain levels show large variation (Viidik, 1990), we modelled the tendon component in each actuator with a generic linear force-strain function, in which tendon strain, defined here as the amount of tendon stretch over its resting length, was nominally set at 3.3% when the tendon's tensile force reached the maximum tension of the muscle (22.7 N in each "tendon", see below) (Zajac, 1989). The direction of the strain was always assumed to be coaxial "with fibre" orientation at the fibre-tendon junction for each fibre group. No force was generated in the "tendon" when it was at its resting length, which we set to coincide with the jaw closed position. To facilitate numerical solutions when the "tendons" were in the region of no strain, a smooth onset of tension with early strain was implemented by representing the "tendon's" force with a step function during the initial 0.5% "tendon" strain. Thus for these strain levels, the force produced was not linear but a product of the linear function and (S)2x(3-2xS), where S was the proportion of the initial 0.5% strain, and ranged between 0 (no strain) and 1 (0.5% strain). 7.3.1.1.3 Fibre Properties The passive tension properties of the muscle fibre component were derived from animal studies (Weijs et al., 1989; van Ruijven & Weijs, 1990) used in previous human jaw modelling studies (Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; van Eijden & Koolstra, 1998; Koolstra & van Eijden, 1999). In these studies, the passive tension was modelled to increase exponentially with increasing muscle length, and its instantaneous value, Fp, was calculated according to the formula: 191 6.<V2-73> FP = Fmax* 0.0014 *e 2 73 , where e was Euler's number (2.718...), Ls was the sarcomere length (in jim) at that instant and Fmax was the maximum possible tension in the fibre (in N). Ls was determined by setting initial sarcomere lengths and assuming their length change was proportional to the fibre length changes during the jaw movement tasks. The optimum sarcomere length was assumed to be 2.73/mi (Muhl et al., 1978; Lieber et al., 1994). In our initial model (Model CU), we based the sarcomere lengths on a human anatomical study (van Eijden et al., 1997), so that at E?, sarcomere length was uniformly set at 2.45 /mi. In the second model (Model CD), differential sarcomere lengths were assigned to reflect regional differences according to van Eijden and Raadsheer (1992)(Table 11). We estimated sarcomere lengths from their anatomical study, and assigned them regionally to reflect the locations from which they measured. In both models, Fm3X, was proportional to the muscle's cross-sectional size, and was calculated as the product of the muscle's physiological cross-sectional area (PCS) and 40 Ncm"2 (Ikai & Fukunaga, 1968; Fukunaga, 1973; Pruim et al., 1980; Nygaard et al., 1983; Weijs & Hillen, 1985a; Fitts et al., 1991). The PCS value for the masseter muscle, obtained from whole muscle dissections, ranged between 6.80-10.31 cm 2 (Weijs & Hillen, 1985a; van Eijden et al., 1997), which resulted in the masseter's Fm3X range of 272-412.4 N for the muscle. In our masseter models we selected the lower end of this range as this was obtained from a younger adult population (Weijs & Hillen, 1985a). We distributed this tension evenly amongst the 12 musculotendon actuators, so that each actuator's Fm3X was 22.7 N . We arbitrarily distributed a mass of 1.3 grams at each fibre-tendon junction to impart a total muscle mass (24.7 grams) consistent with anatomical findings (Koolstra & van Eijden, 1997a). With this mass distribution, the centre of mass was located in the middle of the muscle (x, y, z co-ordinates: 25.0, -28.1, 20.6), and had the following moments of inertia: L^: 4.07, Xfy- 2.31 andl^: 5.19 Kgm 2. In agreement with a previous study (see Chapter 4) in which we required 300 Nsm"1 in the masseter muscle to perform realistic jaw opening, and assuming this was divided evenly 192 throughout the model, we applied uniform viscous damping of 25.0 Nsm' 1 to each actuator to simulate soft tissue viscosity and reduce unwanted oscillations. 7.3.2 Simple Muscle Model (Model S) We compared the multipennated models described above, with the masseter actuators used in previous jaw model studies (Chapters 3 & 5). In those studies, the muscle's complexity was reduced. This simple masseter model's geometry and derivation of physical properties have been reported previously (see Chapter 3). 7.3.2.1 Simple Muscle Model Components The masseter was represented by two straight-line actuators which modelled the deep and superficial portions of the muscle respectively (Model S) (Figure 56). The origin and insertion positions for these actuators were determined by dividing the complex masseter model into deep (MT41-MT62) and superficial (MT11-MT32) portions, and averaging their attachment co-ordinates (Table 11). In each actuator the instantaneous passive tension, Fp, was represented by the function, musclelenglh ^ ^ ^ ^ ~ ' *{Fwa) g max musclelenglh j FWG is the maximum passive tension of the muscle portion at wide jaw gape, maxjnusddengh is the maximum length the muscle attains, and musddengh is the instantaneous muscle length. FWG was calculated from human experimental data, in which wide jaw opening occurred under the influence of gravity and a vertically-applied 5 N force in the incisor region. In the model, each of the jaw elevator's FWG was scaled by an identical factor to resist this 5 N force, and maintain the jaw at wide gape. Consequently, the FWG for the superficial and deep portions of the masseter was 2.28 N and 0.98 N respectively. The maxjnusdelengh for each actuator was derived from a kinematic study in which the jaw was moved along typical border movement pathways and the distance between the actuators' attachments were calculated. The superficial masseter increased its length from 64.7 mm at 193 194 IP to 83.1 mm at WG, and the corresponding lengths for the deep masseter were 41.2 mm and 55.3 mm. The resultant passive tension in each actuator increased exponentially with increasing muscle length (Hill, 1953; Gordon et al., 1966; Woittiez et al., 1983). We applied viscous damping of 150 Nsm"1 to each actuator as this was necessary to reduce unwanted oscillations and produce plausible jaw motions in a previous study (see Chapter 4). 7.3.3 Muscle Dynamics Dynamic properties during opening and contralateral jaw motions were correlated with those for the simple model (Model S). The comparisons included predictions of passive tensions and displacements of the muscle actuators, muscle "fibre" and sarcomere length changes, and resultant tensions of the whole muscle. The latter properties were expressed as a resultant at a point in the middle of the muscle origin on the zygomatic arch, and thus represented the overall tension the muscle applied to its superior bony attachment. The Student's t-test was used to compare regional mean maximum "fibre" lengths attained during the movements. We compared "fibre" lengths between superficial (MTU, 12, 21, 21, 31, 32) and deep portions (MT41, 42, 51, 52, 61, 62), and also between anterior (MT12, 22, 32, 42, 52, 62) and posterior portions ( M i l , 21, 31, 41, 51, 61) of the muscle model. 7.3.4 Mandibular Movement The relative motion of the muscle model components were computed for a symmetrical opening movement, and for a contralateral excursion, both made within one second. Since there is much variability to human jaw motion (Peck et al., 1997; Peck et al., 1999a & b), we selected plausible "average" values for mandibular condylar motion from the literature for the various motions. We then constructed a kinematic model of the human jaw in A D A M S in which the condyles followed their pre-deterrnined paths for each particular jaw movement. 195 In opening, the curvilinear condylar paths, in the sagittal plane were represented by the function: Z = 5* cos f x ^ * n J 5 , where X is the antero-posterior translation with a range ,13 of 1-13 mm, and 2 is the supero-inferior translation. Sagittal plane rotation of the condyle simultaneously occurred and was represented by: ( X\ i? = 30* — , where R is the opening-directed rotation, in degrees. Thus, the sagittal plane condylar path inclination was approximately 40° to the occlusal plane, and at wide gape the condyles had translated 13 mm anteriorly and 10 mm inferiorly, and rotated open 30°, and the mandibular incisor point had translated 50 mm. These values are in accord with kinematic data from human jaw opening (Lundeen et al., 1978; Salaorni & Palla, 1993; Peck et al., 1997). For the contralateral movement, the ipsilateral condyle was able to rotate, but not translate about its centroid. It rotated 1.9, 1.7 and 4.0° about medio-lateral, antero-posterior and supero-inferior axes respectively. This motion enabled the contralateral condyle to follow the same curvilinear path as in opening, except that its movement was reduced to 8.0 mm translation which included a 1.0 mm medial component, and incisor motion of 9.8 mm laterally. This resulted in plausible lateral jaw motion consistent with human kinematic data (Aull, 1965; Lundeen et al., 1978; Hobo, 1984a; Hobo, 1984b; Peck et al., 1999a). 7.4 RESULTS 7.4.1 Jaw opening 7.4.1.1 Resultant forces at superior (zygomatic) muscle attachment For all 3 muscle models, the resultant force at the muscles' zygomatic origin increased with jaw opening and was directed in an infero-postero-medial direction (Figures 57 & 58). In all three models, this resultant force reached a maximum at approximately 50% gape, and then decreased with further opening. Throughout opening, Model S produced a greater passive resultant force than the other models, reaching a maximum of 8.0 N (-4.2 N , -6.5 N , 196 -2.1 N along x, y & z axes respectively) (Figure 59). Model C U and C D , whose forces were remarkably similar throughout opening, each reached maxima of 5.1 N (-2.6 N , -4.1 N , -1.7 N along x, y & z axes respectively) (Figure 59). At wide gape, the orientation of the resultant passive muscle forces for the three models was similar (Figure 58). Al l models were maintained at wide gape for 0.5 seconds. The average resultant forces at this stationary position were 2.7 N (-1.1 N , -2.2 N , -1.1 N along x, y & z axes respectively) for both Models C U and CD, and 3.1 N (-1.8 N , -2.4 N , -0.7 N along x, y & z axes respectively) for Model S. In each of the models, the moment of the resultant force at the zygomatic attachment was low during opening, however it did not display the same form in each model (Figure 57). Whereas the moment peaked close to wide gape in Models C U and C D (0.019 N m & 0.015 N m respectively), its maximum value occurred around mid-gape in the simple masseter model, Model S (0.017 Nm). The moment about each of the individual axes was similar for Models C U and CD, with maximum values about the x, y and z axes of -0.003 Nm, -0.013 Nm, 0.014 N m (Model CU), and -0.003 Nm, -0.012 Nm, 0.009 N m (Model CD) respectively (Figure 60). This resulted in a clockwise torque in the frontal and horizontal planes, and early-clockwise, late-counter-clockwise torque in the sagittal plane during opening. In Model S, the moment's sense was quite different with maximum values about the x, y and z axes of -0.009 Nm, 0.006 N m and -0.013 N m (Figure 60). This resulted in a clockwise torque in the frontal and sagittal planes, and a counter-clockwise torque in the horizontal plane. Thus at wide jaw gape, the sense of the moments about Y and Z axes was opposite between the complex and simple models (Figure 58). When these models were maintained at wide gape for 0.5 seconds, the average resultant moments were 0.017 N m (-0.002 Nm, -0.010 Nm, 0.014 N m about the x, y, z axes) for Model C U , 0.013 N m (-0.002 Nm, -0.009 Nm, 0.010 N m about the x, y, z axes) for Model CD, and 0.011 N m (-0.002 Nm, 0.004 Nm, -0.010 N m about the x, y, z axes) for Model S. 7.4.1.2 Fibre and tendon dynamics During opening, the overall shape of the muscle models changed similarly in models C U and CD, as both models became thinner by 10%. In Models C U and C D , each of the musculotendon actuators demonstrated different relative length changes and generated different tensions during jaw opening (Tables 12 & 13). In Model C D , the muscle fibre 197 Figure 57 Force and moment magnitudes during jaw opening. Resultant passive muscle forces and moments, calculated at a point in the centre of the muscle's zygomatic attachment, plotted against jaw gape (incisal separation). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. Deflections seen on curves are due to rapid internal musculotendon movements (vibrations). 198 crj 3 CO C/3 199 -2.5 J Figure 59 Force vector components in the models during jaw opening. X, Y & Z component forces, resulting from passive muscle tensions as calculated at a point in centre of the muscle's zygomatic attachment, plotted against jaw gape (incisal separation). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. +X, +Y & +Z are directed anteriorly, superiorly and laterally respectively Deflections seen on curves are due to rapid internal musculotendon movements (vibrations). 200 0.002 -n 50 mm E z -0.002 -~ -0.004 -a> | -0.006 S -0.008 --0.01 J Opening 0.01 n ~ 0.005 E z > " n rTT 50 mm - u 4-1 | -0.005 -o S -0.01 --0.015 -* • irl ' ^ ^ ^ ^ ^ ^ Opening—, y 0.02 -, -0.015 Opening ^. Figure 60 Force moment components in the models during jaw opening. X, Y & Z moments, resulting from passive muscle tensions as calculated at a point in the centre of the muscle's zygomatic attachment, plotted against plotted against jaw gape (incisal separation). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. +X, +Y & +Z are directed anteriorly, superiorly and laterally respectively Deflections seen on curves are due to rapid internal musculotendon movements (vibrations). 201 components lengthened between 13.54 and 72.71 % of their initial length, though some "fibres" collapsed between 0.05 and 1.73% at some stage of the movement. The deep region lengthened significantly more than the superficial region in these models (51±15 mm & 30±14 mm respectively, P < 0.05), and although the same trend was seen between the anterior and posterior regions, there was no statistical significance (44±13 mm & 36±20 mm respectively, P > 0.4) (see Table 16). Muscle fibre component tensions, resulting from length and velocity changes, averaged between 0.16-0.54 N , and reached maximum tensions of between 0.27-0.89 N . As expected, the muscle fibre component which demonstrated the greatest length change (in this case MT51) also displayed the greatest mean and maximum tensions. When the model was allowed to come to rest at wide gape, the "fibre" tensions dropped to a range of 0.07 and 0.82 N . Al l tendon components lengthened between 0.14 and 0.28 % of their initial length, although at some stage of the movement, all "tendons" shortened between 0.11 and 7.31 % of their initial length. "Tendon" tensions averaged between 0.08 and 0.79 N , and reached maximum values of between 0.17 and 1.11 N during the movement. When resting at wide gape, the "tendon" tensions dropped to between 0 and 0.99 N . In Model C U , these properties were qualitatively similar. When the same actuator was compared between models however, the actuator with the smaller initial sarcomere length generated less tension and vice versa. Thus, in Model C U , all musculotendon actuators (apart from MT41, 51, 61 and 62) which were assigned shorter initial sarcomere lengths generated slightly lower tensions (Table 12). The motions of the different layers of the complex models generally included a slight posterior rotation, (with lateral displacement in the inner sheets and medial displacement of the outer sheet) of the superiorly-attached aponeuroses and a postero-inferior translation (with posterior rotation) of the inferior aponeuroses (Figures 61 & 62). These inferior "tendon" sheets displayed some lateral motion as well (in particular the inner sheet) and the anterior border appeared to fold outwards on itself (Figures 61 & 62). 202 'I 4-» a o 'I u fe bO <0 o (SO 4) a bp u a M -d o bo u a M u a J a! U cr cr cr CM o to CM CM c\ CM 00 ON 00 00 I CM so o o SO d o o d s o d o CO Cs d o d o o d CM to CM O CM SO d o o d co o CM CS SO o d CM lO d 5 o CM d 5 IT) d CM d l«N CM d C S d s o CM d o d CO CO 8 o d o o S O d o d o CM 9 CM CO d so u-i o o © © d 8 lO ht-© in CM o o o CO 8 8 CM d o o d CO IT) I f i CO OS CS I © CM CM CO so CO 00 © o o d OS I CO | d CN CM d d o o d o to d o o d oo o CO so LO LO CM O d CM CO d CM CN H S i OS m o o CO CN H CM so Cs 00 CM o d so d U") |3 Cs 5 d CN L O H CM d © in S i o o d Cs d SO I co so CM CM o d Tj-to o o d to | CM © I CM S O H a 6 u > o o a J5 2 o 3 •»-> u C o a u 3 u CO 3 o -S •SL -S CJ CJ ^ CJ O ^ CO u ii Oh o H ' 3 s fei) cu max i i 0.14 0.20 0.19 0.24 0.15 0.26 0.28 0.25 t i « Len chang min i i -0.50 -2.39 -1.10 -0.11 -7.31 -0.68 -1.34 -0.47 i i ti tendc cr cu i i 0.01 0.13 0.02 0.53 0.00 0.57 0.99 0.39 i i nsertioi CU max i i 0.17 0.47 0.40 0.75 0.22 0.98 1.11 0.87 i i Fore min i • 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 i i X i 0.08 0.32 0.22 0.61 0.02 0.66 0.68 0.52 i i Length change (%) max 0.17 0.21 0.15 0.19 0.17 0.22 i 0.22 0.27 0.27 0.19 0.27 Length change (%) min -0.41 -0.46 -5.07 -2.78 -1.02 -0.12 i -0.18 -0.86 -3.54 -1.61 -3.54 tendon cr CU 0.02 0.13 0.02 0.16 0.01 0.45 • 0.42 0.91 0.51 0.11 0.51 Origin Force (N) max 0.33 0.52 0.21 0.44 0.29 0.62 i 0.59 1.02 1.07 0.42 1.07 Force (N) min 0.00 0.00 0.00 0.00 0.00 0.00 I 0.00 0.00 0.00 0.00 0.00 X 0.16 0.38 0.09 0.31 0.16 0.52 i 0.45 0.62 0.79 0.28 0.79 Length change (%) max 13.51 33.53 20.99 36.16 18.73 54.57 44.33 59.53 72.71 56.59 44.60 26.37 Length change (%) min -0.05 -0.11 -0.21 -0.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1.73 Fibre cr CU 0.07 0.14 0.08 0.16 0.08 0.44 0.13 0.44 0.82 0.38 0.11 0.07 Fibre CU max 0.37 0.54 0.27 0.45 0.27 0.59 0.41 0.65 0.89 0.58 0.41 0.38 Fore min 0.00 0.00 0.00 0.00 0.02 0.02 0.01 0.02 0.02 0.02 0.02 0.00 X 0.16 0.41 0.16 0.32 0.17 0.50 0.28 0.49 0.54 0.46 0.28 0.23 MTll CN T - H MT21 MT22 MT31 MT32 MT41 MT42 MT51 MT52 MT61 MT62 1 O cu -r> 204 205 00 lo 206 7.4.2 Contralateral Jaw Movement 7.4.2.1 Resultant forces at superior (zygomatic) muscle attachment In all three muscle models, the resultant force at the muscles' zygomatic origin increased with contralateral jaw motion and was directed in an infero-postero-medial direction (Figures 63 & 64). In contrast with symmetrical jaw opening, the resultant forces reached their maxima at the end of the movement and were similar in magnitude (Model C U , CD, S: 3.9 N , 3.9 N , 4.0 N respectively). Throughout the movement Model S produced a greater resultant force than the other models, though it only attained about half the magnitude it produced during jaw opening. Model S reached maxima of -1.2 N , -3.5 N , -1.6 N along x, y & z axes respectively which directed its vector more postero-infero-laterally than that of the complex models. Model C U and C D both reached maxima of -0.7 N , -3.1N, -2.3 N along x, y & z axes respectively (Figure 65). When all models were maintained at the extreme lateral position for 0.5 seconds, the average resultant forces were 1.1 N (-0.02 N , -0.9 N , -0.6 N along x, y & z axes respectively) for both Models C U and C D , and 0.6 N (-0.2 N , -0.5 N , -0.2 N along x, y & z axes respectively) for Model S. In each model, the moment of the resultant force at the zygomatic attachment was low, and dissimilar for the complex and simple models (Figure 63 & 64). Although the moment peaked at the end of the movement in all models, Model C U and C D displayed larger moments (maxima of 0.038 N m & 0.037 N m respectively), than Model S (0.005 Nm). This difference was reflected in the moments about each of the x, y, z axes where the moments were similar for Models C U and C D and predominant in the horizontal and sagittal planes (maxima of -0.004 Nm, -0.023 Nm, 0.031 N m and -0.004 Nm, -0.022 Nm, 0.029 N m respectively) (Figure 66) In Model S however, low moments were produced in all planes with slightly larger values in the frontal plane (-0.005 Nm, -0.001 Nm, 0.002 Nm). These moments resulted in all three models displaying a clockwise torque in the frontal and horizontal planes, and counter-clockwise torque in the sagittal plane during lateral motion (Figure 64). When the models were maintained at extreme lateral position for 0.5 seconds, the average resultant moments were 0.020 N m (-0.002 Nm, -0.012 Nm, 0.016 N m about the x, y, z axes) for Model C U , 0.019 N m (-0.002 Nm, -0.012 Nm, 0.015 N m about the x, y, z 207 r Laterotrusion • 0.045 -0.04 -0.035 ->ment (Nm) 0.03 -0.025 -0.02 -*• - * s 0.015 -0.01 -0.005 -n u Laterotrusion — — • 1 10 mm Figure 63 Force and moment magnitudes during contralateral jaw movement. Resultant passive muscle forces and moments, calculated at a point in the centre of the muscle's zygomatic attachment, plotted against contralateral jaw movement (incisal lateral displacement). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. Deflections seen on curves are due to internal musculotendon movements (vibrations). 208 CO a o CO O Oh u "3 a o o u o a 6 a 73 C o •t-> u > u u .o -3 c co U —i I jr1 ca n 209 Laterotrusion 0.5 n 0 10 mm ————' -0.5 z -1 >- -1.5 -o -2 o u. -2.5 -3 -3.5 -4 Laterotrusion — • 0.5 0 -10 mm — — -z -0.5 -N -1 -CD a o u. -1.5 --2 -2.5 -Laterotrusion — • Figure 65 Force vector components in the models during contralateral jaw movement. X, Y & Z component forces, resulting from passive muscle tensions as calculated at a point in the centre of the muscle's zygomatic attachment, plotted against jaw movement (incisal lateral displacement). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. +X, +Y & +Z are directed anteriorly, superiorly and laterally respectively Deflections seen on curves are due to rapid internal musculotendon movements (vibrations). 210 0 001 -j 0 --0 001 --0 002 --0 003 --0 004 --0 005 -10 mm Laterotrusion • E z CD E o 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 10 mm Laterotrusion 0.035 n 0.03 -•merit Z (Nm) 0.025 -0.02 -0.015 -0.01 -u E 0.005 -u -0.005 -Laterotrusion 10 mm — • Figure 66 Force moment components in the models magnitudes during contralateral jaw movement. X, Y & Z moments, resulting from passive muscle tensions as calculated at a point in the centre of the muscle's zygomatic attachment, plotted against jaw movement (incisal lateral displacement). Thin line: Model S; Thick line: Model CU; Dotted line: Model CD. +X, +Y & +Z are directed anteriorly, superiorly and laterally respectively Deflections seen on curves are due to rapid internal musculotendon movements (vibrations). 211 axes) for Model CD, and 0.001 N m (-0.001 Nm, 0.000 Nm, -0.001 N m about the x, y, z axes) for Model S. 7.4.2.2 Fibre and tendon dynamics During contralateral jaw movements, the overall shape of Models C U and C D changed differently as Model C D thickened slightly (+4%), and Model C U became thinner (-10%). The musculotendon actuators in both Models C U and C D demonstrated different relative length changes, and generated different tensions during contralateral jaw movement (Tables 14 & 15). In Model C D , some muscle fibre components lengthened between 0.05 and 63.48% of their initial length, and some collapsed between 0.30 and 5.59% during the movement. The deep region lengthened significantly more than the superficial region in these models (25+19 mm & 1±2 mm respectively, P < 0.05), and although the same trend was seen between the posterior and anterior regions, there was no statistical significance (19±23 mm & 7±8 mm respectively, P > 0.2) (see Table 16). During lengthening, tensions resulting from length and velocity changes averaged between 0.04-0.46 N , reaching maximum levels between 0.16-1.01 N . Again, like jaw opening, the muscle fibre components which demonstrated the greatest length change (in this case MT51) also displayed the greatest mean and maximum tensions. For the "fibres" that collapsed, muscle tension generally fell to zero from an already low level of 0.02 N at the beginning of the movement. When Model C D was allowed to come to rest at the end of the lateral movement, the "fibre" tensions dropped to a range of 0.00 and 0.56 N . Al l tendon components displayed minimal lengthening between 0.02 and 0.31 % of their initial length, and also shortened between 0.49 and 7.99 %. "Tendon" tensions averaged between 0.00 N and 0.60 N , and reached maximum values of between 0.00 and 1.39 N during the movement. When resting at wide gape, the "tendon" tensions dropped to between 0.00 and 0.69 N . In Model C U , these properties were similar, and like jaw opening, actuators with smaller initial sarcomere lengths generated less tension and vice versa. The motion of the different layers of the complex model generally exhibited an anterior and medial displacement of the aponeuroses, and the inner inferior aponeurosis 212 appeared to "twist" about a vertical axis so that its anterior border folded inwards. (Figure 67 &68). 7.5 DISCUSSION 7.5.1 Modelling Modelling has been applied to all regions of the human musculoskeletal system in an attempt to analyse and simulate mechanical properties of joints, muscles, ligaments and bones (e.g., Fung, 1993d; Mow et al., 1993; Nigg & Herzog, 1994; Mow & Hayes, 1997). The human craniomandibular system is not lacking in biomechanical studies, although only recently have investigations in the dynamic environment been attempted (Hannam, 1994; Hannam & Langenbach, 1995; Koolstra & van Eijden, 1995; Koolstra & van Eijden, 1996; Hannam et al., 1997; Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; van Eijden & Koolstra, 1998; Langenbach & Hannam, 1999). Apart from mylohyoid muscle mechanics (van Eijden & Koolstra, 1998), most studies have investigated whole jaw mechanics and simplified the masticatory muscles to single line actuators. Both the simple straight-line model and complex multi-layered models of the masseter muscle used in the present study are essentially "black boxes" with deterministic relationships between force and elongation histories (Zajac, 1989; Epstein & Herzog, 1998a). Our models did not consider aspects such as sarcomere dynamics (see Zahalak, 1990). The properties we assigned were designed to mimic collectively the passive tensions associated with tendons and aponeuroses, the cross-bridge and myofilaments and the connective tissue structures surrounding the muscle fibres and fascicles. This approach is not unusual (Huxley & Simmons, 1971; Woo et al., 1993; Zuurbier et al., 1994; Irving, 1995), for it is believed that resting muscle behaves in a viscoelastic manner (Thompson, 1994). Our model was based on a Kelvin body viscoelastic model in which the viscous damping component was arranged in parallel with an elastic component (representing muscle and fascia properties), and both of these components were arranged in series with another elastic component (representing tendinous tissue) (Hof, 1990; Winters, 1990). In order to simplify models, the parallel elastic component has often been neglected because forces developed in this element in skeletal muscle have been insignificant except at extreme non-physiological lengths (e.g., over 1.2 X the resting muscle length; 213 Length change(%) max i i 0.14 0.14 0.16 0.18 0.11 0.24 0.31 0.16 t • Length change(%) min i i -1.16 -4.08 -1.60 -1.82 -3.78 -0.98 -1.86 -1.77 i i i tendo cr CU i i 0.01 0.00 0.03 0.05 0.00 0.15 0.70 0.05 i i lsertior Force (N) max • i 0.20 0.17 0.25 0.35 0.08 0.73 1.40 0.26 i i Force (N) UTUI i i 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 i • X i i 0.01 0.00 0.03 0.07 0.02 0.34 0.60 0.10 i i 'Eh cu max 0.13 0.15 0.00 0.10 0.16 0.18 i 0.17 0.28 0.26 0.20 0.26 Len chang min -0.24 -2.26 -6.84 -4.14 -2.15 -1.25 i -1.30 -1.19 -7.38 -1.82 -7.38 tendon cr cu 0.01 0.03 0.00 0.00 0.03 0.05 i 0.06 0.64 0.16 0.11 0.16 Origin e(N) max 0.16 0.23 0.00 0.07 0.27 0.34 t 0.29 1.19 0.90 0.49 0.90 Foro UTUI 0.00 0.00 0.00 0.00 0.00 0.00 i 0.00 0.00 0.00 0.00 0.00 X 0.01 0.02 0.00 0.00 0.03 0.07 i 0.14 0.54 0.28 0.27 0.28 Length change (%) max 0.00 0.00 0.06 0.00 1.48 5.64 23.46 17.95 63.51 15.54 27.03 0.00 Length change (%) min -0.98 -0.82 -1.50 -1.46 -0.69 -0.55 -0.42 0.00 0.00 0.00 0.00 -5.61 Fibre cr <u 0.00 0.00 0.03 0.00 0.03 0.05 0.11 0.07 0.56 0.07 0.08 0.00 Fibre (N)3 max 0.02 0.02 0.15 0.02 0.24 0.33 0.47 0.36 1.01 0.36 0.47 0.02 Foro min 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.02 0.02 0.02 0.02 0.00 X 0.01 0.01 0.03 0.01 0.05 0.09 0.24 0.18 0.45 0.16 0.27 0.01 MTll MT12 MT21 MT22 MT31 MT32 MT41 MT42 MT51 MT52 MT61 MT62 6J0 214 Length change(%) max i i 0.16 0.15 0.15 0.17 0.10 0.23 0.31 0.16 i i Length change(%) min i • -3.54 -4.56 -1.60 -1.59 -3.88 -0.97 -1.88 -1.71 i i i tendc e q i • 0.01 0.00 0.03 0.05 0.00 0.14 0.69 0.05 i i tisertior Force (N) max i • 0.28 0.23 0.23 0.32 0.08 0.72 1.39 0.26 i i Force (N) min i i 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 i i i • 0.01 0.01 0.03 0.08 0.02 0.34 0.60 0.10 i i -a ^ max 0.11 0.15 0.07 0.02 0.16 0.17 i 0.17 0.28 0.26 0.20 0.26 Len chang UTUI -1.20 -1.86 -7.99 -3.69 -0.49 -2.32 i -1.34 -0.54 -7.15 -1.83 -7.15 tendon cr <u 0.01 0.04 0.00 0.00 0.04 0.05 i 0.06 0.64 0.15 0.07 0.15 Origin cu max 0.10 0.24 0.03 0.00 0.28 0.32 i 0.29 1.19 0.90 0.46 0.90 Foro min 0.00 0.00 0.00 0.00 0.00 0.00 i 0.00 0.00 0.00 0.00 0.00 X 0.01 0.02 0.00 0.00 0.04 0.08 t 0.14 0.54 0.28 0.26 0.28 Length change (%) max 0.00 0.05 0.07 0.00 1.46 5.66 23.57 17.92 63.48 15.47 27.03 0.00 Length change (%) min -1.22 -0.99 -1.53 -1.81 -0.76 -0.76 -0.30 0.00 0.00 0.00 0.00 -5.59 Fibre cr CU 0.00 0.04 0.04 0.00 0.04 0.05 0.09 0.07 0.56 0.07 0.05 0.00 Fibre cu max 0.02 0.25 0.16 0.02 0.25 0.31 0.45 0.36 1.01 0.36 0.44 0.01 Foro min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.02 0.02 0.02 0.00 0.01 0.06 0.04 0.01 0.06 0.10 0.23 0.19 0.46 0.17 0.26 0.12 MTll MT12 MT21 MT22 MT31 CN rO MT41 MT42 MT51 MT52 MT61 MT62 215 C2?> Q a 1—c CS • » h o C/3 * * * o CN CN ^-O o o o b b b b oo VO CO CO Gv Cv r - H T-H T-H +1 +1 +1 +1 o ON 00 00 VO VO LO LO b b LO LO CN CN LO CO CO T-H VD O ^-o +1 + | CN b o oo +1 +1 VO LO O T-H Os C \ CN CN CN CN O u u Q V U U cU U o o •a 1 1 o o If I 1 •a •a c« (H *c3 <H CU u u a a T-» O O cO b VO b oo CN b ( N a a o *C CU T-> w 0 CU 5 b CN +1 Cs vq LO fO ON b CN +1 00 LO CO o CN CN +1 VO CN Cs O r-~ CN CN +1 CN C\ u O •c cU o CA CN +i o LO T h T h U T3 O o VO oo I CN +1 VO 4 CO LO +1 CN LO VO Q U "o3 *o o s •a CU a O u -0 o i CO tH <U •w CS J o LO +1 CN LO VO Q U "u o i <H u T-> 216 217 .2 o a, 218 Winters, 1990). We retained this component in the model because the masseter muscle seems to reach these "extreme" lengths in many normal functional activities. Obviously, constitutive equations we have used to describe these physical properties of muscle are not ideal, partly due to unavailable experimental data, and partly because there is not one consistent mathematical equation which will describe all of the known properties of muscles (Fung, 1993b). Nevertheless, we reduced the variables at play by lirniting our models to passive properties of the masseter muscle only, and we have constructed it with sufficient flexibility to be upgraded as new data become available. 7.5.2 Resultant Muscle Forces In an earlier experiment, we calculated viscoelastic jaw properties for the model to simulate wide opening produced by an external force applied to the mandibular incisors of relaxed human subjects (Chapter 4). The viscosity was assigned uniformly to each of the model's jaw closer muscles, and the elasticity was assigned according to the muscle's cross-sectional size. These experimental data were used in the present simple masseter model which enabled it to generate 5-8 N during jaw opening and contralateral movement (Model S). Our complex models produced qualitatively similar, but quantitatively lower resultant forces. Although each of the tendon and fibre components in the muscle's 12 actuators was able to generate up to 22.7 N elastic force when stretched, the maximum tension attained was 1.2 N (in either muscle "fibre" or "tendon"). These low tensions which are related to muscle stretch were calculated with exponential functions derived from animal studies, and as such may not be applicable to humans. As important however, is the ability for at least some musculotendon junctions to move independently of the mandible. This is seen in the representations of the aponeuroses at wide gape and lateral positions (Figures 61,62,67 & 68), and supplements a recent study which predicted movement of putative muscle insertions with jaw function (Goto et al., 1995). The ability of these intramuscular tendinous sheets to translate and rotate would rninimise fibre tensions in the muscle, and thus reduce stretching in muscle fibres and adjacent structures in cases such as rapid jaw opening (Sato et al., 1992). Such complex behaviour is very different to that of a straight line actuator that simply stretches between rigid attachments on the cranium and moving mandible. 219 Overall, all our models produced greater passive tensions during opening than for contralateral jaw motion. It is the result of greater muscle stretch for this task. Although the moments of these forces were different in magnitude and sense, it must be emphasised that these torques were very small. To put this in perspective, the largest moment of 0.038 N m which occurred during contralateral movement in Model C U is comparable to the added moment produced at the elbow when holding a toothbrush (assuming the toothbrush is 15 grams and 30 cm from the elbow, and the forearm is parallel to the ground). 7.5.3 Muscle Component Properties For both movements, Models C U and C D demonstrated similar properties in their musculotendon actuators. Fibre component tensions increased when the components length increased beyond its initial length, and this increased tension predictably affected the tension within the connecting tendons. The tensions generated however, were individually quite low and collectively they were reasonably consistent with experimental findings of the resistance needed to restria passive jaw opening in humans (Chapter 4). Although the force and length properties were similar in the two complex models, it is probably wise to maintain the concept of heterogeneous sarcomere lengths in future jaw muscle models. This would seem especially prudent in the active muscle state, as sarcomere heterogeneity has been shown to increase a muscle's length range for force production by about 40% (Willems & Huijing, 1994). Although the simple masseter muscle model demonstrated continuous actuator length increases (and consequently continuous tension for both the opening and contralateral jaw movement), this was not the case for all components within the complex muscles. Whilst tension was generated by the complex models, some "fibres" and "tendons" lengthened, others collapsed and some did both at different stages during motion. This was particularly noticeable during contralateral jaw movements. Our "tendons" demonstrated a maximum stretch of 0.3 % over their initial length, which resulted in a maximum tension of 1.11 N . We used a generic stress-strain linear relationship for this tissue, and to facilitate numerical solutions in our model, this relationship increased gradually for the initial 0.5% strain with a polynomial function. Although this function was intended for improved mathematical 220 performance of the model, it had the added benefit of providing a "toe region" in the force-strain relationship. It resulted in higher tissue compliance at low tensions, consistent with experimental data for tendinous tissues (Fung, 1993a). Compliance is likely to vary throughout the muscle due to the large range in tendon lengths and thicknesses which we have not accounted for presently (Ker et al., 1988). Tendon stretch is inextricably linked to muscle length change, and therefore influences length-related properties of muscle such as active and passive tension generation (Hill, 1950; Hill, 1951). For isometric muscle contractions, tendon compliance has resulted in muscle fibre shortening of the order of 28% in the cat gastrocnemius muscle (Griffiths, 1991). In our model, wide gape resulted in M T 51 actuator "fibre" strain as high as 73%, though most "fibre" groups stretched much less than this. If the masseter muscle's active force-length properties are similar to those suggested by van Ruijven and Weijs (1990), then at fibre strains greater than approximately 47% of optimal length, fibres would be unable to generate active tension. However in the active state, tendon compliance might allow enough muscle fibre shortening to return highly stretched fibres to their active functional ranges. This would be consistent with the notion that tendon compliance does not alter muscle properties appreciably over the normal range of motion, but does affect the muscle's ability to generate forces at extremes of motion (Hawkins & Bey, 1997). The complex organisation of the masseter, suggests it should be considered as a number of separate muscles, with tendon compliance working separately in each muscle region. Since we modelled sarcomeres in series in each muscle "fibre", any relative length change in a fibre component implies a similar effect on sarcomere length change. In general, for jaw opening, "muscle fibres" in the anterior region stretched more than those in the posterior region, and deep muscle "fibres" stretched more than the superficial ones. Length changes in "fibres" were not as profound for contralateral jaw motion. Whilst deeper "fibres" tended to stretch more than those more superficially, there did not appear to be any marked differences between anterior and posterior fibre components. In all jaw movements the fibre component in MT51, located in the posterior deep region of the muscle, stretched the most, and also produced the greatest passive tension, a predictable consequence of its relatively short initial length. This was not a direct relationship however, as fibre tension production resulted not only from muscle length change, but also from the component's lengthening velocity. Our length-change findings are 221 in reasonable agreement with those of van Eijden and Raadsheer (1992), in which masseter measurements in cadavers were combined with extrapolated jaw movement. Differences between their study and the present one are most likely due to their omission of the role of tendon extensibility during fibre lengthening, and the different motions assigned to then-model and ours. Van Eijden and Raadsheer (1992) also investigated the proposition of equivalence in sarcomere length changes (and thus the resultant tensions) in a moving muscle (Gans & de Vree, 1987). They were unable to support this theory for the human masseter, and our differing residual tensions in each of the actuators at wide jaw gape, and at an extreme lateral jaw position do not support it either. It is difficult to verify dynamic biological models as there is a dearth of matching physiological data. This is particularly the case with the internal architecture of the human masticatory muscles (Hannam & McMillan, 1994). The complex orientation of masseter aponeuroses in live subjects has been visualised with magnetic resonance imaging (MRI), however no dynamic assessment of these tendon sheets has been performed (Lam et al., 1991). This may be possible with cfynamic-MRI and sonography (Herbert & Gandevia, 1995), which would permit experiments on live subjects. The internal architecture of moving muscles has been shown to be quite different to the structure of cadaveric specimens (Fukunaga et al., 1997). 7.6 CONCLUSIONS Different passive movements among putative intramuscular components suggest a complex dynamic arrangement of the human masseter muscle during function; the aponeuroses appear to bend and shear, and muscle fibres alter their direction of pull. Whilst the effect is likely to be more complicated in vivo than in our 12 actuator model, this model does provide insight into the mteractions of tendon and fibre components in the multipennated masseter muscle. Although the complex model provides insight at a greater structural level than the simple model, the similar tensions generated in both types of models suggests, for the passive opening case at least, that a two-line actuator may reasonably represent the tensions generated in the masseter muscle. However a complex muscle would 222 be needed to investigate differential activation within the muscle, or the effects of structural alterations such as muscle asymmetry. 223 8 G E N E R A L D I S C U S S I O N 8.1 JAW MODELLING Biomechanical mathematical modelling is one approach in which the interaction between structural and functional variables of a musculoskeletal system may be evaluated. Indeed at present, it may be the only way that certain internal behaviours such as changing muscle tensions or articular loads in the human jaw may be predicted. A model attempts to represent reality (Nigg, 1994b), although it is always a simpler version of the actual biological object. Simplifications and assumptions are necessary because experimental data may be lacking, or the complexity of mathematical calculations need to be reduced. For example, since biological tissues demonstrate complex mechanical behaviours that are dependent on a plethora of variables whose inter-relationships are not always known, it is not possible to formulate mathematical equations that define these structures exactly (Fung, 1993b). Indeed, if this were possible, a model would be isomorphic with, and equivalent to, the structure it represents and therefore redundant (Zahalak, 1992). In the present studies, simplifications included a rigid mandible, TMJs in which the fossa and disc were incorporated into one unit, and the condyle was a simple ellipsoidal object, and whole muscle portions represented by straight-line muscle actuators with simple active and passive tension representations. In the complex muscle model, we divided the muscle by 5 "aponeuroses", and represented each muscle layer with only two musculotendon actuators with tendon and fibres aligned in an average direction to those in vivo. A model's reduction in biological detail is not altogether disadvantageous since it facilitates understanding and manipulation of the processes involved in human function by eliminating those variables which are unimportant. In addition, a model that is simpler mathematically, will accelerate the computational process that is utilised in solving these equations (Zahalak, 1990). This latter issue will facilitate model design, analysis and simulation phases since modelling is in itself an active process, which requires continual modifications as new biological data emerges, or indeed as modelling predictions arise and challenge previous hypotheses. The challenge then is to develop "adequately" complex 224 models which retain the essential biological detail to fulfil scientific goals, yet which are also tractable with regards to manipulation and interpretation (Zajac & Winters, 1990; Zahalak, 1992). This challenge is exemplified in the human jaw, which is comprised of complex material and physiological properties (Dechow et al., 1993; Hannam & McMillan, 1994), and is able to achieve a variety of functionally diverse tasks (Moller, 1966; Ahlgren, 1976). A better understanding of the variables at play in the jaw system will ultimately offer predictions on stmcture-function relationships of the jaw, and cause-effect associations in jaw disorders (Hannam, 1994). In modelling, it is important to "walk before you run"; and therefore the mechanics of the jaw system should be understood prior to predicting the implications of altered structure or function. We followed this adage by understanding the passive tensions in the jaw prior to examining muscle coactivation strategies (Chapters 3 & 5) or altered TMJ morphology (Chapter 3). The progression of the current studies demonstrates the process of model development, the model's ability to enhance biological comprehension, and the emphasis on tractability. Take for example the determination of passive tension properties in the jaw muscles. In the early design phase of our dynamic modelling experiments, the jaw muscles were represented with single line actuators with generic muscle properties derived from skeletal muscle (Zajac, 1989). In other jaw dynamic studies, mechanical properties of the jaw muscle actuators were obtained similarly, or from animal jaw muscle studies (Koolstra & van Eijden, 1996; Langenbach & Hannam, 1999). However a major problem was encountered in that all of these models were unable to simulate wide jaw opening, even with maximal activation of the jaw opener muscles. These models predicted that the passive tension generated in the muscles opposing opening were too high, and indeed our experiments on opening forces required to reach wide gape verified this (Chapter 1). We then used modelling to comprehend the mechanisms of passive resistances offered by the jaw muscles during motion. We hypothesised that this excessive tension could be attributed to unique passive muscle behaviour in the human jaw that is dissimilar to other skeletal or animal muscles. Alternatively, the assigned properties may indeed be correct, and the extra tension could be caused by incorrectly representing the complex dynamic internal architecture of many of the jaw muscles with simplified single line muscle actuators. Our early results 225 suggest that the passive tension properties of "whole" jaw muscles are quite different to other skeletal muscles, and therefore cannot be represented by animal-derived or generic skeletal muscle properties (Chapter 3). Furthermore, our complex muscle model with multiple musculotendon actuators behaved, at least in passive tension generation, remarkably similar to a single line actuator (Chapter 7). This suggests the internal architecture imparts unique properties to the overall muscle, but that the passive tension properties may be represented by a "black box" single line actuator that disregards the structural mechanisms at work. In this example, modelling has provided insight and made predictions of the mechanisms in passive muscle tension generation. Answers to questions such as these, allows one to predict system behaviour, which may then be assessed in vivo. For example, if the relationship between muscle tensions is more clearly understood through modelling, the dynamic environment of different craniofacial skeletal types may be predicted, and then tested experimentally. These types of experiments are not trivial, since they involve simultaneous measurement of multiple variables. Nevertheless, it would be expected that the process would be greatly facilitated with the development of a "virtual jaw prototype " in which the variables of interest have already been manipulated, and the behaviour of a system inferred. In the present studies modelling was used to comprehend behavioural phenomena unique to the human jaw in function, such as the role of active and passive muscle tensions in symmetric and asymmetric jaw motions, the constraining influence of the temporomandibular ligament, and the influence of the complex architecture of the masseter muscle on its passive tension generation. The observations from these models must be credible in both a qualitative and quantitative sense (Zahalak, 1992). In essence, model evaluation or "validation" requires that the model predicts the phenomena of interest, that it identifies the mechanisms responsible, and that these predictions are quantitatively accurate. The models which examined symmetric and asymmetric jaw motions (Chapters 3 & 5) were required to simulate credible movement patterns in a plausible time frame, using muscle recruitment patterns consistent with those observed experimentally for those movements, and with muscle activity which remained within realistic limits. We predicted the viscosity of the muscles in a model whose 226 motion (specifically motion duration and velocity) matched that of experimental data. This model's robustness was enhanced as it was shown to simulate two experimental scenarios: slow and fast opening (Chapter 4). In this way, the model predicted a range of phenomena (jaw motion), which provided presumptive evidence that it included the most significant (and correct) physics for these tasks (Zahalak, 1992). In the TMJ capsule and the complex muscle model of the masseter (Chapters 6 & 7), the approach was opposite in that we attempted to increase the confidence in these models by including more detailed anatomical structure and functional data (and assumed we included the important physics for these scenarios). This was necessary as no experimental data exists for either capsular motion or the dynamic internal architecture of the masseter (or indeed of other jaw muscles). In any case, as more functional data of the human jaw emerges, it shall be easier to demonstrate whether a model is strong and powerful for the task for which it has been designed. 8.2 JAW DYNAMICS 8.2.1 Passive constraints 8.2.1.1 Jaw muscles Our findings suggest the human mandible is heavily damped yet not very stiff, since our experimental observations indicated that the jaw could be opened with an externally applied 5 N force, and that this force could be increased substantially by increasing the opening velocity. Our model duplicated these results when each muscle was assigned elastic forces of 1.2% of their respective maximum possible tension and uniform damping of 150 Nms"1. As expected, passive muscle tensions remained low for all movement tasks because elasticity was low and movements were accomplished slowly in a time of around one second. It is well recognised that muscle elasticity increases exponentially with increased muscle lengthening (Hill, 1953; Gordon et al., 1966; Woittiez et al., 1983). We retained this relationship in our muscles, as it has been shown that the passive elastic resistance to jaw opening increases in this way with increasing gape (Lynn & Yemm, 1971; Miles et al., 1986; our unpublished observations) in the jaw. 227 Of note is that we simplified our assignment of damping by applying it uniformly to each muscle, and that although we only determined the damping properties of the jaw in the opening direction, we assumed that the assigned values were valid for the other movements we generated. This could be an erroneous assumption, since damping of the jaw may be different for different movements such as laterally-directed movements. We did not attempt a laterally directed damping experiment on subjects because of the difficulty in stabilising and relaxing the jaw and then moving it laterally. The damping in the jaw presumably helps stabilise the jaw against sudden unexpected rapid jaw movements. This notion of heavy damping in the jaw is supported by Walsh (1992) who cites common events such as jogging in which forces are transmitted from the body to the jaw. Although changing forces are transmitted through the jaw from a runner's body that accelerates and decelerates vertically, no tooth contact occurs. This control system probably involves multiple mechanisms, with the overall stability provided by the viscosity of the system with further adjustment by active tone augmented by reflex loops. Thus passive muscle tensions provide an efficient mechanism to control jaw position, however unlike muscle activity, it has not been recorded during function. The present studies have suggested the dynamic influence of passive tensions, although these length- and velocity-tension relationships did not include any of the complex associations with movement history which have been demonstrated experimentally (Huijing, 1998). Unfortunately these relationships have not been assessed (knowingly) in the human jaw. Other dynamic models have demonstrated excessive restraint by the passive elasticity in the closing muscles (Koolstra & van Eijden, 1997a; Koolstra & van Eijden, 1997b; Langenbach & Hannam, 1999). For example in one of the models, combined elasticity in these muscles reached about 50 N when the model was at 70% of its maximum gape (Koolstra & van Eijden, 1997b). Tensions of this magnitude will have a marked effect on the level of muscle activity needed to generate jaw motion. It is suggested from the current findings that these tension levels are too high. Firstly, our experimental observations demonstrated low externally-applied opening forces could overcome these passive elastic resistances in the jaw closers and maintain the jaw at wide gape. Secondly, the passive tensions generated in the multi-layered masseter model, which used muscle length-tension properties in each of its 12 actuators similar to those in the above high passive tension study, 228 were collectively, much lower than those in the above studies. High elastic stiffness in the jaw in these other studies may have imposed incorrect constraints on the jaw, and thus masked the real restraints that actually contribute to jaw motion. In the present studies, although the elasticity in the jaw muscles was low, it did have an effect on jaw movements. When asymmetrical opening was attempted with simple activity of a contralateral lateral pterygoid and both digastric actuators, lateral opening was limited by passive tension generation in the ipsilateral medial pterygoid actuator (Chapter 3). In addition, when a hinge-opening movement of the jaw was simulated, jaw rotation (in the sagittal plane) was limited by the combined passive tensions in the superficial masseter, medial pterygoid and anterior temporalis muscle actuators 8.2.1.2 Lateral capsular wall The notion that passive ligamentous tissue constrains jaw movements has been the justification for plication surgery of slack temporomandibular ligamentous tissue and the more dubious treatment of injecting intracapsular sclerosing solutions (see Sato et al., 1995). The presumed constraining role of the temporomandibular ligament is based on anecdotal evidence, and some simple mathematical modelling in which the ligament was represented by a few inextensible linear structures (Osborn, 1989; Osborn, 1993; Osborn, 1995). The present study demonstrated dynamic simulation of a number of excursive jaw movements (symmetrical and asymmetrical opening, protrusion, lateral and hinge-opening jaw movements), in the absence of temporomandibular or accessory ligaments. These motions ensured that the mandible, and its condyles, moved to their limits in the anterior, lateral and inferior directions. In Chapter 6, a kinematic appraisal of the lateral capsular wall was performed, and although taut capsular regions were present at the jaw closed position and at maximum excursive positions, the study suggested that the capsule was slack during the middle third of contralateral, opening and protrusive jaw movements. Interestingly, the jaw may be under considerable and complex loads during mastication in these "unconstrained" jaw positions (Moller, 1966). This and the previous findings of muscle limited movements, suggest that both muscle (active and passive) and ligaments operate synergistically to constrain the motion of the jaw. 229 8.2.2 Active constraints (muscle) Electromyography of the jaw muscles has demonstrated that activity of multiple muscles is required for jaw function (Miller, 1991b). The simulated tasks in the current studies reinforce the importance of muscle coactivation in producing jaw movement. It was not possible to replicate plausible jaw motion with the activity of a single muscle; and indeed for the more complex lateral tasks, a number of muscle patterns were attempted before plausible jaw movement was achieved (Chapter 5). Although plausible mandibular incisor point translatory motion was accomplished with a number of different muscle recruitment patterns, the motion of the entire jaw was not. This supports previous recommendations (Hannam, 1992a; Palla et al., 1997) that jaw motion should be described with six degrees of freedom (i.e., a 3 component translation vector and rotations about 3 axes), and not three as is common practice in clinical studies (e.g., Mauderli et al., 1988; Hayashi et al., 1994; Harper & Schneiderman, 1996). In these studies muscle activity required for each of the jaw movements simulated was low. Apart from one movement task, active tension remained below 26% of each muscle's maximum isometric tension as derived from muscle cross-sectional area. In lateral jaw movement using muscle activity proportional to muscle shortening (Chapter 5), the contralateral lateral pterygoid tension reached 38% of its maximum. Therefore, there was ample tensions remaining to effect a more rapid movement, or a movement against resistance. These active tensions increased smoothly in time with a polynomial function, and the recognised relationships with muscle velocity and muscle length were not considered (Zajac, 1989). Since the tensions produced in our muscle actuators were low, omitting these relationships probably did not affect our overall results. However for tasks that utilise large muscle tensions (e.g., mastication, resisted movements), muscle length and velocity would presumably have an effect. The major simplification was the representation of the complexly layered and functioning muscles as single line actuators. Many muscles demonstrate differential activity (Hannam & McMillan, 1994), and hence the single force vectors generated from the straight line actuators in the model are supposed to represent the resultant of the different active regions of the muscles in vivo. 230 8.2.3 Condylar loading The adaptation of articular tissues to compressive loads has been investigated at the cellular level, however the distinction between healthy loading and degenerative loading states is unknown (Milam, 1995). This distinction is affected by a number of factors at the microstructural level, and presumably by larger scale factors such as dentition status, bite force, and left and right muscle force ratios (e.g., Hylander, 1992). In the present studies, the condyles were compressively loaded for all tasks in these studies. Maximum articular loads were 28 N (jaw opening; Chapter 3), and for each task the forces increased with the movement. In lateral movements, asymmetrical loads were generated, and load differentiation appears to be related to ipsilateral and contralateral muscle activity as has been suggested in static analyses (see Hylander, 1985b). The advantage of dynamic studies is that changing loads with function can be demonstrated. For example, in Chapter 5 in which lateral movement with tooth contact was simulated, condylar loads were markedly asymmetric (contralateral: ipsilateral ratio 2:1), however when the jaw moved further laterally beyond tooth contact ipsilateral joint loads increased markedly so that at the limit of this movement both joint forces were almost the same. The ability to predict changing articular loads with changes in structure (e.g., dental contacts) is advantageous especially when one considers the controversy surrounding the stmcture-function relationships such as the association between the occlusion and temporomandibular disorders (McNamara, Jr. et al., 1995). Although these models are significantly simpler representations than the actual dental interface, they nevertheless offer insight into the role of functional occlusion in jaw dynamics. These models all demonstrated articular stability without ligamentous constraints such as the temporomandibular ligament, articular capsule or accessory ligaments (sphenomandibular and stylomandibular ligaments). This stability resulted from the interaction of active and passive muscle tensions and the condylar compression into the disc fossa boundary of the TMJs. Although contact between these joint surfaces was considered frictionless, in reality it would be expected that this would change with increased loading conditions which would improve the congruency between the surfaces (Iwasaki et al., 1997), and thus presumably increase the stability of the jaw. In the movements with tooth contacts, the dentition also contributed to this stability, since it was easier to select muscle activities 231 that would generate a laterally directed movement, in the tooth contact case as compared to the movement from rest position. Furthermore, the capsule of the TMJ would be expected to participate in constraining the condyle, as is suggested from the kinematic analysis of the putative lateral capsular wall (Chapter 6). This study suggested its role may be predominantly in the extremes of jaw motion, and throughout an ipsilateral movement, and consequently it appears that both muscle and capsular constraints work collaboratively to afford articular stability. 232 9 GENERAL SUMMARY & CONCLUSIONS The approaches available to assess the clynarnic biomechanics of the human jaw are limited. Mathematical modelling is an expanding field, that seems to offer a viable and current method in which jaw dynamics may be addressed. However it must be emphasised that it is an indirect technique that is limited by the simplifications and assumptions necessary because of incomplete biological data, the inability to formulate complete constitutive equations of biological tissue and limited computational power. In time, these limitations will presumably lessen, although never completely. The jaw, its TMJs and muscles are, individually, all complex structures, but when combined become overwhelming to the computational modelling technique and indeed the modeller. The initial design phase of the jaw model, in which simplifications were initially chosen, was laborious and time intensive. It was not uncommon in the early stages of model development for the solution process to last days. With the reduction in complexity, this time decreased substantially, thus enabling increased model permutations to be investigated. This is important, especially in the early stages of the modelling process, when the effects of specific components (both in the model and the modelling process) on jaw dynamics needs to be established. It seems that the model is a good tool to be used in conjunction with direct investigations, and indeed, it would seem to be advantageous to drive experiments with model findings. In this way the model is evaluated by offering hypotheses testable by in vivo experimentation. The dynamic jaw models demonstrated the plausibility of jaw movements under active and passive muscle tensions. Activity within each muscle remained well below its maximum, indicating that if necessary much greater drive could be generated for a particular task. The passive tensions were low, in both single line actuators and this was reinforced with similar findings in the complexly layered analogue of the masseter muscle. The internal structure of the masseter appears to be unique as our model representation was theoretically capable of generating high passive tensions, however with simulated jaw movements in which the muscle elongated these tensions remained low. The condyle demonstrated compressive loading which was even for symmetrical tasks and generally uneven for asymmetrical tasks. These loads changed with changing muscle activity and/or jaw position. Although the condyle remained apposed with the disc fossa boundary at all times, the lateral wall of the 233 capsule could presumably impart more stability to the jaw in function. This is reinforced with the findings of taut capsular regions during particular movement tasks. Dynamic assessment of musculoskeletal systems is necessary, since functional tasks shall be influenced by, among other things, changing muscle tensions and articular loads. There is no single method available which provides the definitive explanation of the relationship between structure and function. The best approach appears to combine methodologies in such a way that they complement each other and further our understanding of functional behaviour. Dynamic mathematical modelling is an innocuous approach which can augment other techniques such as direct experimentation. The results from mathematical modelling are promising and can only improve in the future with advances in numerical and computational techniques, and further biological structural and functional data. 234 10 FINAL COMMENTS & FUTURE DIRECTIONS Dynamic mathematical modelling would appear to have a bright future since it is a relatively "cost-effective" approach to explore the structure and function in the musculoskeletal system. Impending computational advances, and further evaluation of this method with directly obtained experimental data will only improve its applicability. Jaw function is relatively poorly understood, and professional health bodies have recommended the need for future detailed biomechanical investigation in this area (Bryant & Sessle, 1995). Specifically in the case of dynamic mathematical modelling of the human jaw, further evaluation against biological data should be undertaken. Morphological and functional variation is large in the jaw, and thus one approach for future work would entail model design which matched an individual's specific structural and functional data. This is not trivial, although with recent advances in biomedical imaging and functional data acquisition, it may be possible. In essence it would require whole jaw imaging, with greater detail at the temporomandibular joints, to provide structural data such as key landmarks and inertial properties of the jaw. Simultaneously obtained functional data including bite force recordings, electromyography of as many of the masticatory muscles as possible, and jaw motion recording would provide information which could be used to build and subsequently evaluate the model. Furthermore, for comparative studies, it would be advantageous to obtain this data from individuals with greatly differing craniofacial types. For example, this could include patients who have undergone radical jaw resections, or simply normal subjects with extreme differences in facial height. Thus two or more models could be constructed, which have unique skeletal, muscle and joint profiles with functions derived from matched muscle activity patterns and bite force measurements. This is an enormous undertaking both from the direct experimentation and modelling perspectives, but would certainly substantiate any findings derived from the model. In many of the other musculoskeletal systems in the human, the modelling approach has been to simplify either muscle structure and function and investigate articular biomechanics or vice versa. This approach may be feasible for the human jaw, so that a resultant force profile for a particular task may be deduced from the combined muscle 235 activity for that particular task. This simplifies the number of equations in the model which will reduce computation time. In this way, more emphasis may be directed at constructing a more realistic TMJ analogue. It should be possible in the near future to incorporate flexible structures into "rigid" mathematical models. The articular disc may then be modelled, and simulations of the normal, but large, motions of it attempted. "Pseudo-kinematic" magnetic resonance imaging of the TMJ have demonstrated the stepped motion of the disc. If three dimensional images of true motion of the disc and condyle eventuate, then this will become an ideal method to evaluate an articular model's dynamics. This would have important implications in the field of temporomandibular disorders since friction or irregularities on the functional path of the condyle may be incorporated and the mechanisms of structural derangements between the condyle and articular disc may be inferred. There is much controversy regarding the relationship of dental occlusion with temporomandibular disorders. The present models represented the occlusion as a maxillary tooth "plane", over which the mandibular tooth "point" travelled. A more detailed occlusal set-up may be simulated that more closely matches the variety of guiding planes present in vivo. In this case, the implications of alterations to the dentition and its effects on the articulations may be suggested. Although we modelled a representation of a complex multipennated muscle, we only examined the generation of passive tensions when the muscle was stretched. A n assessment of the active capabilities of such a muscle and the implications on jaw movement and articular loading would be interesting. If functional images of the internal muscle become possible, this data could be utilised in a model to help match muscle activity with internal stractural changes. These data may help explain whether or not specific aponeuroses undergo significant strains in function and implicate specific tasks that are potentially more damaging to the muscle. This type of experiment may be ideally driven by a model derived hypothesis, which suggests associations that may be examined directly. Assigning muscle drive to dynamic models is a complex and time consuming task. Common methods include optimisation procedures or a simple assignation of values by trial and error. A promising alternative is artificial neural networks which utilise a number of input patterns (e.g., muscle activity levels) matched to output patterns (e.g., jaw motions) and 236 utilise a training algorithm to characterise the relationship between the complete range of input and output patterns. Once the network is "trained", and it encounters an input value which it is not familiar with, it will select an appropriate value determined from the previous relationships. This of course requires knowledge of inter-relationships between variables responsible for motion, but as data is acquired and fed into the network, the system becomes more and more powerful at predicting specific variables. A n artificial neural network would not only assist in selecting appropriate values of variables for a particular task in dynamic models, but may also be useful in a teaching environment where a trained network could provide fast solutions and be able to demonstrate cause and effect. 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