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Modeling, analysis and dynamics of the human jaw system Ng, Francis Wai-Tsuen 1994

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Modeling, Analysis and DynamicsofThe Human Jaw SystembyFrancis Ng, Wai-TsuenB.Sc., The City University of New York, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS OF THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF ELECTRICAL ENGINEERTNGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAFebruary 1994© Francis Ng, Wai-Tsuen, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_________________________Depament ofThe University of British ColumbiaVancouver, CanadaDate___________DE-6 (2188)AbstractThis thesis deals with the modeling of the human jaw system. The model is acomputer model in which the nine pairs of facial muscles and the jaw itself arerepresented. The study leading up to the model includes expressive Object-OrientedProgramming (OOP) to encode the computer model. Different components in the jawsystem are defined as objects and used as building blocks of the system. Although thestudies in the thesis are confined to the human jaw system, various components of themodel are designed to permit continuous modification. Direct measurements ofmuscles’ activities are always invasive, or even impossible to measure. A dynamicsimulation model offers research workers a frame to improve the concept of thematters involved before measurements are made. Lastly, a jaw model can/may givesinsight into how patients will recover from facial and muscle injuries.Studies of the behavior of other biological systems have been made to discovermethods in which an artificial neural network (ANN) may contribute solutions to thedynamic control problem. Some useful results have been obtained which may indicatehow ANN could be incorporated in the dynamic jaw model of the future.The work is interdisciplinary involving the following fields: dynamic behavior ofmuscle; dynamic behavior of biological system; mechanical system simulation; and ANN.11Table of ContentsAbstract.iiTable of Contents iiiList of Tables viList of Figures viiAcknowledgment xChapter 1 Introduction 11.1 System and Model 21.2 Existing Simulation Model 31.3 Applications 41.4 Thesis Outline 51.5 Considerations of Hardware and Software Platform .. 7Chapter 2 Muscle Mechanics and the Human Jaw System .... 82.1 Methods of Studying the Actions of Muscles 82.2 The Hill-Type Muscle Model 102.3 Type of Contraction 112.4 The Mathematical Model 132.4.1 The Simulation Model 142.4.2 The Musculoskeletal Model 152.5 The Human Jaw System 162.6 Static Equilibrium Jaw Models 212.7 Structure of The Dynamic Jaw Model 22111Chapter,24.3Chapter Programming (OOP) 26The Evolution of Programming Style 26Chaos and Functional Programming 27Structured Programming and Data Abstraction 27Object-Oriented Programming 29The World According to Objects 29Class and Object 31Encapsulation, Inheritance and Polymorphism 32Design and Classification 33The Jaw System As An Object 34Digital Continuous Simulation Systems 36Numerical Integration Technique 37Considerations ofThe Muscular Tendon Parameters 40Elasticity 40Constants that Define a Muscle 41l,l and 12 41kj,k2andb 42Activation Level 46Simulation Proceduresand The Results 49Procedures of Test Running The Simulation Model .. 50Simulation Results 53Discussion 58ivChapter 6 Neural Network and Dynamic Control 636.1 Artificial Neural Network 646.2 Backpropagation Neural Network 666.3 Method for Improving The Performanceof Backpropagation Networks 676.4 Neural Network as A Digital Controller 716.5 Conclusions of Using Neural Networks 75Chapter 7 Conclusions 777.1 Limitations of The Current Model 787.2 Future Directions of The Jaw Model 79References 81VList of TablesTable 2.1 Muscle Attachment Coordinates 18Table 2.2 Tooth and Joint Coordinates 18Table 4.1 Stress-tension Relationships 43Table 6.1 Comparisons of The Root Mean Square Errors 71viList of FiguresFigure 1.1Figure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure 2.7Figure 2.8Figure 2.9Figure 2.10Figure 2.11Figure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6System and Model 3The Hill-Type Muscle Model 11The Simulation Model of Hill-Type Muscle 13Series Elastic Element 14Force Generator, Dash Potand Parallel Elastic Element 14A Simple Musculoskeletal System 15Lateral and Front View of The Human Jaw System ... 17Reference System used by The Model 18The Temporalis 20Frontal View of The Movement of The Mandible 23The Jaw Model 24The Artificial Bolus 25Functional Programming 27Structured Programming and Data Abstraction 29An Object 30Relationships Between Objects 31The Jaw as An Object 35Relationships Between Muscle Objectsand The Jaw Object 35viiFigure 3.7Figure 3.8Figure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 6.1Figure 6.2Figure 6.3Figure 6.4Figure 6.5Figure 6.6Structure ofA Digital Continuous Simulation Systems 37Numerical Integration Error 38Stress-strain Curve of Skeletal Muscle 43Stress-strain Curve of Tendinous Tissue 44Response of Mammalian Muscleunder Maximum Stimulation 45Activation Level 46B-spline Curves as The Activation Levels 48Structure of The Simulation Program 49Graphics Interface of The Simulation Program 50Comparisons of Activation Levels 51The Simulated Incisor Movement 54Incisor and Condyle Movement 55Reaction Force at Condyle 56Activation Level Patterns and Muscle& Tensions 57Typical Nerve Cell 63Artificial Neural Node 64The Sigmoid Function 64General Structure of An Artificial Neural Network ... 65Updating Procedures in Artificial Neural Node 66A Combined Artificial Neural Network 68viiiFigure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13The Crab Arm Example 69State Mapping 72Neural Network That Performs State Mapping 72State Mapping in Continuous Time Slices 73An Example of The Neural Network Controller 73The Casterian Product of S and C 74Simulation Resultsof The Neural Network Controller 75ixAcknowledgmentThe preparation of this thesis has been a long but exciting project and one whichwould not have been possible without the help and encouragement of my family, friends,and colleagues.Special thanks to my supervisor, Dr. M. P. Beddoes, for his patience,encouragement, and help have been beyond measure and generously given.The project is a cooperation with Dr. A. 0. Hannam and Dr. 0. E. J. Langenbachof The Dentistry Department. I am indebted to them for their helpful discussions andassistances.In addition, I would like to thank my parents for their support and understandingthroughout my graduate study.Finally, I wish to thank all those who have contributed in one way or another tothe completion of this thesis.xChapter 1IntroductionMuscles are biological machines that convert signals from the nervous systeminto chemical energy, force and mechanical work; it is only by the use of muscles thatwe are able to act on our environment -- to exert forces and to manipulate objects.Although there are computer simulation models [A4, A61 which define the propertiesof a single muscle and which use data collected from devices which record kinetics ofhuman motion, few of them [A3, B14, B16] are capable of describing the dynamics ofskeletal muscles that provide the internal force responsible for the movement of thebody. The thesis deals with the design of a dynamic computer simulation model of acomplex musculoskeletal system, the human jaw, for the use in the oral biology field.Different units in the simulation model are modular enough to allow its modificationand reuse. Thus, it can be easily converted to model other musculoskeletal systems.Studies of biological systems have shown new possible uses of artificial neuralnetworks. The central nervous system (CNS) of living animals is the most flexiblecontroller. The thesis will demonstrate how to provide control with neural networkswithout using the conventional control theory. Neural Networks offer newalternatives of approaching problems in dynamic control, but do not replace theconventional methods. In addition, a new method, Error-Adjusting Networks, is foundto improve the performance of neural networks.Components of the project involve the following fields: dynamic behavior ofmuscle and the biological systems, mechanical system simulation, and artficial1neural networks. The following sections in this chapter define the terms -- system andmodel. Terms used in modeling are also stated. Existing simulation models and theoutline of the thesis are presented next. The last section of this chapter providesinformation about computer hardware and software aspects of the project.1.11 System and ModelIn this section we will briefly discuss some essential concepts that are closelyconnected to the modeling and simulation approach. Terms discussed here will beused throughout the thesis.A system is an arrangement of units that function together to achieve a certaingoal. A system may be composed of one or more subsystems which consist again ofsome sub subsystems, and so on. Every system interacts with its environment throughinputs and outputs. Inputs have their origins outside the system and are not directlydependent on what happens in the system. Outputs, on the other hand, are generatedby the system and interact with the environment. Elements which are necessary tooutline the states of the system are defined as attributes (parameters and variables).Any process which changes the attributes of a system represents an action. Allexisting systems change with time, but when the rates of change are significant,systems are called dynamic systems. Their maifl feature is that their output at anyinstant depends on their history and not just on the current input. An experiment isthe process of extracting data (outputs) from a system by testing the system withvarious inputs.A model contains only essential aspects of an existing system or a systemwhich we want to build, and the model can substitute the system to conduct an2experiment (Figure 1.1). This definition does not imply that a model is a computerprogram. A simulation is an experiment performed on a model.Input OutputFigure 1.1System and ModelThe internal structure of the system and the initial state are usually known.With a complete system or model, we can perform one or both of the followingoperations:1. When all inputs are known as functions over time, the task of the experiment isto determine the response of the system from its outputs. This problem is calledthe direct problem.2. A second type of problem is where there is a set of desired outputs, and the goalis to solve for the unknown inputs. This is referred to as the inverse problem.The areas of inverse kinematics and automatic control in the robotics field aregood examples.1.21 Existing Simulation ModelsAlthough there are many muscle contraction models [A3, B14, B 161, they areusually limited by one or both of the following factors. First, they are designed towork as individual muscles instead of showing coordinate muscular actions that occur3in everyday acts such as raising the arm or chewing. Indeed, very few models havebeen developed to study integrated force from several different muscles. Second, theygenerally represent isometric contraction, in which muscle contracts without a changein length. However, despite these limitations, many existing models have producedrealistic simulation results.1.3 ApplicationsComputer simulation models that describe the dynamic behavior of themusculoskeletal system are very rare. For this reason, any new model offers severalpossibilities:1. Transplantation of muscle attachment sites is not an unusual procedure in clinicalsettings. Changes in muscular function that are produced by skeletal abnormalityor surgical corrections of abnormalities also occur. Hence, a dynamic simulationmodel which can be flexibly altered will give insight into how patients adapt todisorders, and how they might respond to surgical intervention.2. Muscles are the interface between the CNS and the skeletal system. Anunderstanding of the interface allows engineers to design prostheticneuromuscular stimulation systems to restore lost or impaired motor function.3. Direct measurements of muscle activity in living human beings are alwaysinvasive. Muscle activities that are located deep inside the human body may beimpossible to measure. Measurement results are sometimes based on subjectiveestimates of muscle activities, and therefore, can be misleading. A dynamicsimulation model can be used as a control against which to compare physiologicalrecordings.44. Study of artificial neural networks and methods to increase their performance mayprovide a possible general structure of automatic control, and can be comparedwith existing conceptualizations of nervous control systems in the CNS.1.4) Thesis OutlineIn Chapter 2, the study starts by defining a simulation model for the muscle,emphasizing how it contributes to the movement of the musculoskeletal system as it isattached to bone. The model is a simplified version of the real muscle but retains theessential factors to describe the biological behaviors of muscle. Hill is well known forpioneering work in muscle modeling, and the model reviewed and developed here isbased on a Hill-type model. We will concentrate on the basic mechanical structure ofa muscle and how its characteristics contribute to a musculoskeletal system. The wayin which muscle utilizes energy sources, the way it produces heat, and the natures ofthe proteins that generate the force are our concern here. The human jaw system,the existing simulation models and the basic structure of our new model will also bediscussed in this chapter.Chapter 3 introduces the concept of object-oriented programming (OOP).OOP allows one to program in the same way that one understands our world. Onemajor focus of the project is to use of OOP’s “expressive” power to model a complexmechanical system -- the human jaw. OOP is an abstract concept. In order to explainthe concept clearly, a casual but adequate definition of OOP will be used instead ofstating all the formal terminology of OOP. Efforts have been made to keep thediscussions short and precise. Accuracy of the numerical approximation technique usein the project, and other run-time considerations are also discussed.5In Chapter 4, parameters used in the muscle model and the nerve impulses thatfeed into the muscle model are discussed. This chapter will utilize the conclusions ofChapter 2 and 3 to design a possible simulation structure for the jaw system.Chapter 5 reports the simulation results, and the results are compared withknown values of human mastication. As we will see, the simulation results imply somenew hypotheses of movement in the musculoskeletal system.Chapter 6 addresses neural networks, and the possible structure of neuralnetwork for dynamic control. A neural network is an engineered computationalsystem modeled after or inspired by the learning abilities and parallelism of biologicalnervous systems. Neural networks are not programmed; they learn by example.Typically, a neural network is presented with a training set consisting of a group ofexamples (inputs and outputs) from which the network can learn. In response to this,the neural network compares its outputs to the standard outputs and adjusts the valueof its internal weights. Usually the set of training examples is presented many timesduring training to allow the network to adjust its internal parameters gradually. Themajor use of a neural network is to classify different input patterns. However, byneural network for control we mean neural network that goes beyond classifying theirinput signals to influencing them.Concluding remarks in Chapter 7 include current limitations of the model andsuggestions for possible future directions for the project. The possible future uses ofthe model with abnormal muscles and jaw configurations are discussed.61.5) Considerations of Hardware and Software PlatformThe computer simulation model is designed to be a stand-alone executableprogram that can be run on IBM PCs or compatibles. The simulation model is alsodesigned for use as a teaching tool in the oral biology field, therefore, a portableexecutable program that can run on PCs would be of great convenience.As the simulation model is tested with object-oriented language syntax to easecomplex system modeling, an object-oriented language is chosen for our purpose.C++ is found to be adequate because it is highly portable and powerful [D2, D3].Borland C++ 3.1 is chosen from all the compilers available for its excellent integrateddevelopment environment and debugging tools.7Chapter 2Muscle Mechanics and the Human Jaw SystemMuscles and tendons are the interface between the CNS and the linked bodysegments. An understanding of the properties of this interface is important toscientists who interpret kinesiological events in the context of coordination of thebody. Study of the musculoskeletal system with computer simulation models was notcommon until recently, and most studies have been based on biological measurementsmade in the past few decades. We start with summarizing the consequences ofbiological measurements as it is the basic of all the studies of biological movement.2.1) Methods of Studying the Actions of MusclesHuman motions and muscle properties have been studied extensively in thepast few decades, and methods of studying them are briefly summarized below:1. Anatomical -- Dissection is used to study the location and attachments of amuscle and its relation to the joint it spans. This method provides a basis forvisualizing the muscle’s potential movements. Histological examination providesdetails of muscle fiber and tendon composition, often assisted by differentialstaining or labeling to reveal different fiber properties.2. Physiological• Direct measurement of muscle length and tension changes are possible inanimal preparations or in excised muscle tissue.8• Electrical activity can be recorded directly from muscles, and part of muscles,in experimental animals and living human subjects. Electromyography (EMG) isbased upon the fact that a muscle generates electrical impulses when it contracts,and EMG is a technique of recording such impulses or action potentials. Surfaceor needle electrodes are placed close to the target muscle to do themeasurement. EMG measures muscle activities during reflex and voluntaryfunctions.• The properties of groups of muscles can often be inferred indirectly byrecording the displacement of bone, (e.g. limbs or jaw movement) or the forcesgenerated at some target site.3. Physical Model -- Elastic elements such as springs are fixed to the bones of askeleton in such a way as to represent muscles. Tensions that develop in thesprings and changes in their lengths can be demonstrated by moving the skeletonsystem manually, or by adjusting individual spring lengths.Besides their contributions to the biological field, conventional measurementmethods often fail to reveal correlated events in human living tissues, and limitednumbers of subjects are available for experimental purposes. The requirement ofexpensive equipment is another factor that forbids direct measurement. In comparison,computer models can be an alternative to measurement methods using today’sinexpensive computing power from PCs. Applications of the new models discussed inChapter 1 are also new possibilities that are not possible with current measurementmethods.92.21 The Hill-Type Muscle ModelDifferent models of muscle have been defined mathematically, and used toestimate muscle forces during different motor tasks. Most of the latest models ofmuscle are based on the microscopic properties of the muscle tissue. However, the“black-box” approach (a model which only needs to be based on an input-output [I/O]description of the tissue) is more appropriate for our purpose. The selection isjustified because our goal is to study the integrated force from a few different musclesinstead of determining how different microscopic tissues make up the muscle force.The Hill model [A4, A6] (Figure 2. la) has withstood the test of time and ischosen as our base model.OriginMuscleFibreDashport ParallelElement ElasticElementTend onInsertionFigure 2.la Figure 2.lbThe Hill-Type Muscle Model The Fusiform MuscleThe model comprises of a contractile element as a pure force generator (theactive state) in parallel with a dashpot element. The contractile proteins in muscle cellthat convert chemical energy into force and mechanical work make up the activestate. Since muscle contains a considerable amount of water, viscosity of waterSeriesElasticElement10accounts for the viscous property of the dashpot element. While the muscle tendonmakes up the series elastic component, the parallel elastic component resides in themuscle cell membrane, the connective tissue surrounding the muscle fibers, and theprotein filaments that produce the contractile force. Together the parallel and serieselastic components account for the passive tension properties of muscle [A4].Historically, anatomy texts designated attachments of the two ends of a muscleas “origin” and “insertion.” The origin is usually characterized by stability andcloseness of the muscle fibers to the bone. The insertion, on the other hand,frequently involves a relatively long tendon, and the bone into which the muscle’stendon inserts is usually the one that moves. A long tendon help prevents injury to themuscle during movement.Figure 2. lb illustrates a fusiform-shaped muscle. This shape is characterized byits rounded muscle and gradual lessening width at either end. This is what peoplecommonly perceive as the general shape of muscle. However, different structuralforms of muscle exist, and we will study them when we reveal the musculoskeletalstructure of the human jaw.Before we look into the mathematical model of the muscle, the next sectionexplains different types of contraction. This helps to explain the functional propertiesof muscle.2.3) Type of ContractionAlthough to contract literally means to “draw together” or to shorten, musclecontraction may exist when the muscle is shortening, remaining the same length, or11lengthening. A muscle contraction occurs whenever the muscle fibers generate tensionin themselves. The followings reveal the three most common types of contraction.Concentric Contraction - Concentric (toward the middle) contraction occurswhen the tension generated by the muscle is sufficient to overcome a resistanceand to move the body segment of one attachment toward the segment of itscounterpart. The muscle shortens and, when one end is stabilized, the other pullsthe bone to which it is attached and turns it about the joint axis. Usually, themuscle that undergoes a concentric contraction is directly responsible foreffecting a movement and is classified as the agonist muscle, and muscles thatcause the opposite movement from that of agonist are defined as the antagonist.2. Isometric Contraction - Isometric means “equal length.” In isometriccontraction, external resistance is equal to the internal force developed by themuscle, and there is no external movement. There are two different conditionsunder which isometric contraction is likely to occur. First, muscles that areantagonistic to each other contract with equal strength, thus balancing orcounteracting each other. The part affected is held tensely in place withoutmoving. Tensing the biceps to show off its bulge is an example of this.Furthermore, a muscle is held in either partial or maximal contraction againstanother force, such as the pull of gravity or an external mechanical or muscularforce. Holding a book with outstretched arm and attempting to move an objectthat is too heavy to move are good examples. Muscle undergoes isometriccontraction can be afixator, stabilizer or supporting muscle.3. Eccentric Contraction - When a muscle slowly lengthens as it gives in to anexternal force that is greater than the contractile force it is exerting, it is in12eccentric (away from the middle) contraction. In most instances in whichmuscles contract eccentricity, the muscles are acting as “brake” or resistive forceagainst the moving force of gravity or other external forces.2.4 The Mathematical ModelIn order to work interactively with other components of a musculoskeletalsystem, several things have been disregarded in our base muscle model. The musclemodel needs an interface to the outer environment. In a real muscle, the active state isactivated by nerve impulses from the CNS. While specialized sensor receptors knownas muscle spindles within many muscles detect change of length and rate of change oflength of the muscle, other receptors known as Goigi Tendon Organs in tendon detectthe tension in the muscle [A2]. Figure 2.2 shows the model with the interfacestogether with the variables needed to define the mathematical model.All, Ii’aTnerve endingIi12k2Figure 2.2The Simulation Model of Hill-Type Muscle132.4.11 The Simulation ModelIn order to model the muscle system for simulation, we start by identifyingsubsystems that can be moved independently. We now cut the system open at theinterfaces between the subsystems. The openings at both ends are replaced by twoforces equivalent to the force act between the subsystems. These two “internal forces”are always of the same size but of opposite in directions [Cl]. In our case, the musclesystem can be cut between the tendon (series elastic element) and muscle fibers(active state, dash pot and parallel elastic element). The muscle system can bedescribed with the following equations:The reaction force on tendon:614Figure 2.3Series Elastic Elementk2Al=T (2.1)The reaction force on active state, dash pot and parallel elastic element:Figure 2.4Force Generator, Dash Pot and Parallel Elastic Element14B4’+k1Al+F(a)=T . (2.2),,T—F(a)—k1AiB(2.3)(Note: if M <0, then kM = 0.)Equations (2.1) and (2.3) define the internal behaviors of a muscle and will be used asthe basis to define our simulation model of muscle in Chapter The Musculoskeletal SystemUp to this point, we have discussed the internal behavior of the muscle. In thissection, we will go through the mechanical behavior of a single muscle in amusculoskeletal system. The basic idea is illustrated by Figure 2.3.(x,Figure 2.5A Simple Musculoskeletal SystemResultant muscle force in the x and y-direction:T = T(x0—x1) (2.4)(x0 —x1)2+(y0—y)2T=T. oyj) (2.5)(x0—x1)2+(y —y)215Torque (r) due to the muscle force:r=T(x1—x)—T(yy) (2.6)T, T and r can be solved with simple trigonometric arithmetic, however, theabove equations can generate faster code. Although the above illustrates aconfiguration of two dimensions, it is implemented with a three-dimensional design inthe simulation model.2.5) The Human Jaw SystemThe jaw is one of the most complicated single moving parts in the humanmusculoskeletal system. The jaw consists of the jaw bone with at least nine symmetricpairs of muscles pulling at different angles, and with different strengths on each sideof the jaw [B 12, B 131. Figure 2.6a and 2.6b show simplified lateral and frontal viewsof the musculoskeletal structure of the jaw. Small circles in Figure 2.6a and Figure2.6b indicate the mandibular insertions of the muscles.The system was modeled within a triaxial coordinate system centered on theright mandibular condyle. Figure 2.7 shows the reference system used by the model.The z-axis lays on the intercondylar axis, the x-axis runs parallel to the dental occlusalplane, and the y-axis is orthogonal to both. Coordinates describing the relativepositions of vectors representing 18 principal jaw muscles, mandibular condyles andbite points are obtained from previously published data [B7, B14]. The nine muscles(or parts of muscles) on each side include the anterior, middle and posteriortemporalis, the supeificial and deep masseter, the medial pterygoid, the superior andinferior lateral pterygoid, and the digastric muscle. The attachment of the digastricmuscle to the hyoid bone is fixed in space in our model.16Lateral View of The Human JawFigure 2.6aSm superficial masseter, dm = deep masseter, mp = medial pterygoid,at = ant. temporalis, mt = medial temporalis, pt = posterior temporalis,ip = inf. head lateral pterygoid, sp = sup. head lateral pterygoid, dg digastric.Figure 2.6bSmall circles show the insertion ends of the muscles in the jaw system.mlFront View of The Human Jaw17Reference System used by The ModelVFigure 2.7The figure illustrates the reference systemand arrows indicate the positive quadrant.Table 2. la and 2. lb show the physiological and anatomical parameters foreach muscle group. (x0, Yo’ z0) is the coordinate of the maxillary origin and (xj, Yi’z) is the coordinate of the mandibular insertion. The first column containsabbreviations of muscles’ names. Each muscle is assigned a specific cross-sectionalarea, and a constant of 40 N/cm2 is then used to determine its maximum possibletension [B7, B 14]. MAXF is the maximum possible contractile force of the muscleand is summarized in Table 2.la and 2.lb.Table 2.2 shows the coordinates of a complete set of lower teeth. Themandible’s mass was assumed to be bOg, and the center of gravity is located at(0.04981, -0.048673, 0.045425). The moment of interia of the jaw is 6.O84e4kgm2when it rotates along the intercondylar axis. These parameters were estimated from adry human specimen. All the coordinates refer to a normal closed jaw and themeasurements are in standard SI units (meters and Newtons).zx18Muscle Attachment CoordinatesMAXF x0 y0 z0 x1 y z1rsm 190.4 0.041501 -0.005996 -0.00885 0.015616 -0.048498 0.001675rdm 81.6 0.017225 0.003167 -0.01245 0.024356 -0.01724 0.001625rmp 174.8 0.025997 -0.015502 0.025275 0.007963 -0.045255 0.00595rat 158.0 0.043005 0.041557 -0.0031 0.029027 -0.031155 0.00805rmt 95.6 0.006519 0.057006 -0.01435 0.033807 -0.001944 0.000425rpt 75.6 -0.02942 0.042005 -0.0161 0.03354 -0.002092 0.000275rip 66.9 0.026238 -0.011053 0.0230 0.002947 -0.00305 0.003025rsp 28.7 0.022312 0.001099 0.022775 0.003818 0.000931 0.0011rdg 40.0 0.037259 -0.076011 0.0337 0.069928 -0.071325 0.0420Table 2.laMAXF x0 y0 z0 x1 Yjism 190.4 0.041501 -0.005996 0.0997 0,015616 -0.048498 0.0891751dm 81.6 0.017225 0.003167 0.1033 0,024356 -0.01724 0.089225imp 174.8 0.025997 -0.015502 0.065575 0.007963 -0.045255 0.0849lat 158.0 0.043005 0.041557 0.09395 0.029027 -0,031155 0.0828lmt 95.6 0.006519 0.057006 0.1052 0.033807 -0.001944 0.090425ipt 75.6 -0,02942 0.042005 0,10695 0.03354 -0.002092 0,090575lip 66.9 0.026238 -0.011053 0.06785 0.002947 -0.00305 0.087825isp 28.7 0.022312 0.001099 0.068075 0.003818 0.000931 0.08975ldg 40.0 0.037259 -0.076011 0.05715 0.069928 -0.071325 0.049Table 2.lbTooth and Joint CoordinatesLeft RightXm Ym Xm Zcondyle 0 0 0 0 0 0.09085incisor 0.084058 -0.042117 0.045425 0.084058 -0.042117 0.045425incisor 0.08302 -0.041706 0.0417 0.08302 -0.041706 0.04915canine 0.079744 -0.040834 0.036425 0.079744 -0.040834 0.054425premolar 0,073044 -0.040482 0.030975 0,073044 -0.040482 0.059875premolar 0.06763 -0.040089 0.028025 0.06763 -0.040089 0.062825molar 0.061696 -0.039867 0.02585 0.061696 -0.039867 0.065molar 0,050855 -0.038728 0.023325 0,050855 -0.038728 0.067525molar 0.041741 -0,037669 0.0199 0.041741 -0,037669 0.07095Table 2.219Jaw muscles are usually flat and located close to each other. Some are locateddeep to the mandible. The temporalis, masseter and medial pterygoid muscles aremultipennate. That is they contain multiple, interleaved flat intramuscular tendonsheets to which muscle fibers insert obliquely. This close fiber packing is believed toimpart greater fiber density in a minimum space. Figure 2.8 shows that pt, mt, and atactually belong to one single muscle whose fibers radiate from a narrow attachment atone end to a broad attachment at the other. Studies have shown that the line ofactions of this muscle can be separated into three different parts as defined. (Musclesof this form are generally described as fan-shaped.) Partitioning also occurs in themasseter and lateral pterygoid muscles. The lines in the Figure 2.6a and 2.6b indicatethe lines of action rather than the anatomical shapes of various muscles.Figure 2.8Although the temporalis is a single muscle,the lines of actions show that the muscle can beconsidered as three separated parts as defined.The anatomical and functional complexities of the human masticatory systemmake it difficult to explain how muscles move the lower jaw and develop forcesbetween the teeth, how the jaw’s articulation works, and how growth, deviations inThe Temporalis20form, and surgical or prosthetic treatment alter this process. While it is possible tomeasure many aspects of structure and function in living subjects, for example byimaging, electromyographic samplings, bite force recording and jaw tracking, and toshape behavior by defining voluntary tasks [B13j, many important aspects ofmusculoskeletal function cannot be assessed because the methods used to study themare either impractical or invasive. Extrapolation of information drawn from nonhuman sources, an alternative approach, is unfortunately of limited value due to majorinter-species differences in the face and jaws. The problem is compounded byvariation in most human populations, which often makes it difficult to develop simple,working hypotheses to explain experimental observations. Increasingly, emphasis hasbeen placed on computer models for this purpose.2.6 Static Equilibrium Jaw ModelsStatic jaw models assume that the jaw is closed. Here the goal is to develop abite force at a given bite point, and It follows from the linear algebra that sixequations for static equilibrium of a rigid body have to be solved. However, there isno unique solution because the six equations contain more than six unknowns. Thejaw system is a fail-safe system and this is responsible for the extra unknowns.The idea of ‘cost’ is then introduced. Different costs are assigned to differentmuscles and joint forces, and the total cost of using the muscles and joint forces isdefined as follow:Total cost = (muscle force * cost of muscle force)+ >(joint force * cost ofjoint force)21The objective is to find the pattern of muscle tensions that minimizes the total cost.The ‘cost’ technique is widely used in other static models of different musculoskeletalsystems. Details of a typical static jaw model can be found in [B141.These simulations of jaw mechanics with static equilibrium theory are useful.The jaw muscles are often active in the isometric state during symmetric andasymmetric biting and clenching, and models can provide insights that are otherwiseunavailable. The expression of interactions between structure and function, includingvariables such as muscle activation, muscle tension, tooth and joint forces, can bedeveloped with formal physical principles, and the models then become workinghypotheses. They can predict results which are often testable. However, as mentionedearlier, a muscle driven dynamic model can offer a whole new dimension as comparedto the ‘cost’ model.2.7) Structure of The Dynamic Jaw ModelFew, if any, models have been developed to simulate the biology of jawdynamics, The most sophisticated was the jaw model of a rat [B 17], but the modelwas not based on formal physical principles.As jaw is very complex, a few assumptions are necessary to make the jawsystem feasible enough to model dynamically. The jaw model is a reduced version ofthe real thing, but still adequate to provide useful information.The temporalis muscles are the largest jaw muscles in carnivores, and providea large cutting force at the molars. The cutting action is mainly an up-downmovement of the jaw. On the other hand, temporalis muscles are of relatively little useto herbivores. Temporalis in herbivores is small. They use their premolar and molar22teeth for grinding their food. The strong pterygoideus muscles in herbivores providethis side-to-side movement. Humans are omnivorous; we need both the cutting forcesfrom the temporalis and grinding force from the pterygoideus. However, as stated inTable 2.1, temporalis are stronger than the pterygoideus in human. Figure 2.9 is anexample of the frontal view of the jaw movement in a normal chewing cycle measuredfrom the first incisor [B12]. The figure shows that magnitude of the up-downmovement in the human jaw is about 3.25 times greater than that of the lateralmovements. Therefore, the model will be concentrated on the up-down motion of thejaw as it is the major movement of a chewing cycle. A model that can describe boththe vertical and lateral movement at the same time would be excellent, but the motionaccording to the two joints of the jaw makes it extremely difficult to model. In fact,the vertical motion can reveal some of the most important information in the humanjaw system.Figure 2.9Measured at the lower central incisor teeth.Unit is in (mm).The up-down motion is not a pure rotation motion; the condylar heads of thelower jaw slide outward as it opens. Condylar guidance was simulated by providing aFrontal View of The Movement of The Mandible23—v+ Torque_due_to_CGIThe position of the first incisor is regarded as the first output of the computermodel; it has often been used as the reference point to measure the motion of the jaw.In addition, changes of muscle length and tension are also valuable outputs. Mostuseful of all is the joint force as output. This is not measurable in living humans.frictionless constraint along a line angled at 30 degrees to the horizontal referenceplane. Linear motion of the condylar center point was confined to this line. Anunlimited sliding surface to the joint was provided in order to determine the extent towhich condylar positioning could be controlled by muscle action alone. This isindicated in Figure 2.10. All muscular arrangements are expressed in three-dimensions.Figure 2.10The Jaw ModelAssume that the mass of the jaw is m, and the moment of interia is I. Thetranslational and angular acceleration (a and 0”) of the jaw are simply defined asfollows:dl’ ET cos30° —(YT +rng)cos6o° (2.7)di m(2.8)24Midline chewing on a fixed food bolus in the first molar region is simulated.During simulated chewing, the “food bolus” is introduced by placing a constant forceof 75N on the first molar bite point. The reaction force is effected on the first molaras it is the most common bite point, and 75N is well within the range expected duringmastication. When the jaw makes contact with the bolus, the direction of the reactionforce from the bolus is defined perpendicular to the line formed by the first andsecond molars. This reaction force remained at the same angle to the bite pointirrespective of jaw position, and had to be overcome by muscle action for the jaw toreturn to its initial starting position, defined as dental intercuspation, The “bolus” isinjected when the first molar bite point is 3mm from its initial, starting position duringclosing, and is removed when the opening cycle started. Figure 2.11 illustrates thearrangement of the bolus.Figure 2.9The Artificial Bolusmolar firstmolar25Chapter 3Object Oriented Programming (OOP)There is an extensive use of the object-oriented technology in the computerindustry recently. Although the new technology can be implemented in many differentareas (operating system and environment, computer hardware, etc.), the discussionhere will be concentrated on object-oriented programming (OOP). Because object-oriented design is a relatively young practice, it may mean different things to differentpeople. Therefore, the materials that follow will be based on a few different references[Dl, D2, D3] and my personal experience of using object-oriented programming.Although researchers claim that one of the main advantages of using OOP is toallow people to program the same way we understand our world, newcomers to OOPusually find the new concept difficult to learn (especially those who are alreadyfamiliar with structured programming). Discussions are kept to be short and precise;main ideas will be illustrated with diagrams.3.fl The Evolution of Prorammin2 StyleThe programming community has seen different programming techniques comeand go in its 40-year life span. The discussion will start with the review of the earlierprogramming styles then to our main subject -- OOP. A review of earlier styles isnecessary to show how different styles decompose problems.263.1.fl Chaos and Functional Prorammin2The earliest of programming styles is best described as chaos programmingthat has little organization either physically or logically, with jump and go-tocommands sprinkled liberally throughout.Functional Programming is the first major improvement over the chaos style,originally introduced as a way to reuse repetitive code. The most popular functionalprogramming languages are FORTRAN and COBOL, In Figure 3.1, we see thetopology of functional programming languages.DataSubprogramsFigure 3.1Functional ProgrammingApplications written in these languages exhibit a relatively flat physical structure,consisting only of global data and subprograms. The arrows in this figure indicatedependencies of the subprograms on various data. During design, one can logicallyseparate different kinds of data from one another, but there is little in these languagesthat can enforce these design decisions. An error in one part of a program can have adestructive effect across the rest of the system, because the global data structures areexposed for all subprograms to see.3.1.21 Structured Proprammin and Data AbstractionIn structured programming, the program is broken up into individualprocedures that perform discrete tasks in a larger, more complex process. These27procedures are kept independent of each other, and each with its own logic.Information is passed between procedures using parameters, and procedures can havelocal data that cannot be accessed outside the procedure’s scope. Procedures can bethought of as miniature programs that are put together to build an application.A powerful concept was introduced with structured programming: abstraction.Abstraction could be defined as the ability to look at something without beingconcerned with its internal details. In a structured program, it is sufficient to knowthat a given procedure performs a specific task. As long as the procedure is reliable, itcan be used without having to know how it completes its function. This is known asfunctional abstraction.Although structured programmers were supposed to pass all data into and outthrough arguments, without powerful data structures this was often not possible. Withdata abstraction, data elements could be bundled together into more easily identifiedstructures (Pascal calls these RECORDs; C calls them structs). Data abstractiondoes for data what functional abstraction does for operations.For larger programs, logically related subprograms are grouped together toform modules. The overall goal of the decomposition into modules is the reduction ofsoftware cost by allowing modules to be designed and revised independently. Itshould be possible to change the implementation of one module without knowledge ofthe implementation of other modules and without affecting the behavior of othermodules.Although modules are used to group logically related operations, the samedata structures may be used in a few different modules as the arrows indicate. Figure3.2 illustrates the topology of this style. As program grows in size, data types are28processed in many procedures within different modules. When changes occur in thosedata types, modifications must be made to every location that acts on those data typeswithin the program. This can be a frustrating and time-consuming task in programsthat contain thousands of lines of code and hundreds of functions.Defined DataStructuresModules(make up of logicallyrelated subprograms)Figure 3.2Structured Programming and Data AbstractionWhat will happen if only one module will act on a single data structure? Thefollowing sections will answer this question.3.1.3) Object Oriented ProgrammingWhile structured programming decomposes the problem into a set ofoperations, and modules are used to group logically related operations, OOP requiresa different way of thinking about decomposition. The fundamental change is that anobject-oriented program is designed around the data being operated upon, rather thanupon the operations themselves. The next few sections will explain the abovestatement in more details. A definition of ‘object’ will also be given, followed by theterminology. The World According to ObjectsWe experience our world largely as a vast collection of discrete objects, actingand reacting in a shared environment. An object in the real world can be simply29defined as something that can be identified and felt. Identity is the property of anobject which distinguishes it from all other objects. The object should have a way ofinteracting with others in order to be felt, and behaviors are how an object acts andreacts to the outer environment. In addition, the states of an object record all thestatic and dynamic properties of the object, and states of an object can only be alteredby its behaviors [Dl]. Message passing to other objects is common behaviors of anobject. Figure 3.3 illustrates the above ideas of an object:r Iden.IflyBehcMorsFigure 3.3An ObjectConsider a pop machine that dispenses soft drinks (i.e., the object’s identity isa pop machine). The interface of this object consist of a slot for feed in of coins, a fewbuttons for user to make selection, and an opening for the emerges of drinks. The popmachine is usually in a state of “not ready for selection.” However, the state changesto “ready for selection” after the right amount of coins are fed in. The total quantity ofcoins and number of pops the machine holds also make up the states of the machine.An object may contain other objects as the pop machine contains pops; it can alsointeract with other objects as the pop machine can interact with users.Figure 3.4 shows a graph (not tree) structure with a few different objectsinteract with each other in the world they exist:30Figure 3.4Relationships Between ObjectsThere are three different using relationships possible between objects. ‘A’ is aserver object as it is only operated upon by others. ‘B’ and ‘D’ only operate upon otherobjects and are defined as the actor objects. Agent objects can both operate uponother objects and be operated upon by other objects, and ‘C’ is an agent object.An object should represent an individual, identifiable item, unit, or entity,either real or abstract, with well-defined role in the problem domain. As you can see,almost everything in the world can be described as an object. Class and ObjectIn OOP, a class is a template that describes both the data structures (states)and the valid actions (behaviors) for data items. When a data item is declared to be amember of a class, it is called an object. Assume we have the following C statement;mt i, j, k;mt is the class while i, j and k are objects of the mt class. Those functions thatare defined as valid for a class are known as methods (such as +, —, * and / ininteger), and they denote the way in which an object may act and react, and thusconstitute the entire static and dynamics outside view (behaviors) of the object.313.1.3.3) Encapsulation Inheritance and PolymorphismThere are three main properties that characterize an OOP language:encapsulation, inheritance and polymorphism.Encapsulation is the process of hiding all the details of an object that do notcontribute to its essential characteristics. It focuses on the outside view of an object,and separates an object’s essential behavior from its implementation. Actually,encapsulation and abstraction are complementary concepts.With struct in C, we can define the structure and build specific operationsand these specific operations only to manipulate the defined structure as in what wedo with C++. In another words, it is possible to create objects with C. However, thereis no compulsion in C to enforce this design. In addition, two more properties,inheritance and polymorphism are required to construct a complete OOP language.Inheritance is the property that allows you to build new class from one or morepreviously defined base classes while possibly redefining or adding new data andactions. This creates a hierarchy of classes instead of building separated classes withsimilar properties. Besides encouraging reuse of existing codes and data structures,the main idea of inheritance is to capture the way that people classify things. Weconstantly relate new concepts to existing ones. We like to conceptualize the world asa tree-like structure, with successive levels of detail building on earliergeneralizations. This is an efficient method of organizing the world around us.Traditionally, operations are forced to use different names even they logicallyperform similar operations. In order to construct programs in a more natural way,objects are allowed to respond to the same operation (the “same” here means different32operations with the same name) with their own unique behavior. This characteristic isknown as polymorphism in OOP.Although OOP offers many new useful properties, you can use the structuredprogramming style or even the chaos programming style to program whatever you canachieve from OOP. In fact, more computer programs have been developed withstructured programming as compared to OOP. However, the advantages of usingOOP are usually smaller codes. Well-defined classes are also much easier to beunderstood, maintained, and reused.The followings show how a complex mechanical system can be decomposedinto simpler objects. Behaviors will be assigned to the objects which make it possiblefor different objects function together as a complete system.3.2) Design and ClassificationA structured approach to programming is essential in OOP. In a structuredprogram, up-front analysis is important to organize the application’s functionseffectively. You can use the same technique to do an object-oriented analysis of aproject. You can’t design classes unless you know the details about how the program’sdata is organized and processed.In addition, it can require a substantial amount of preliminary work to createeffective class libraries for a particular application. Defining the right set of classes foran application is critical to the effectiveness of the program. Unfortunately, there is noexact path to classification, nor the perfect class structure. Booch is well known in theOOP field and has written an excellent book on object-oriented design and analysis[Dl].33To identify classes in the jaw model, however, is quite straight forward. Thesystem basically consists of the mandible and muscles. The repetitiveness of musclesin a musculoskeletal system makes them difficult to model with conventionalprogramming techniques as there are too many variables to be considered at the sametime. This is responsible for the absence of a musculoskeletal system model that isdirectly driven by muscles. On the other hand, the ‘repetitiveness’ and ‘similarity’properties of muscle make them easy to define as a class. As long as the muscle classis reliable, muscle objects define with this class can be used as building blocks of thejaw model.There is only one moving part in the system -- the mandible. It is not acommon practice to construct a class with only one object defining with it. In ourcase, however, by defining moving parts as a class makes the programming style moreconsistent and easier to cope in the complete model.One more class is needed to handle continuous system simulation. Instead ofphysical existence, a process can also be an object. The following sections will explainthe above designs in more details.3.3 The Jaw System As An ObjectThe interface of the jaw system to the outer environment is simple. As anobject, the input to the jaw consists of a bundle of nerves that activate differentmuscles in the system, and the useful outputs are the current status of the mandibleand the muscles of the jaw system. This includes the angular and displacementinformation of the mandible, and muscles’ tensions. Mathematical details of thesedisplacements and tensions have already been defined in Section 2.5 and Section 2.8.34Activation CurrentLevels Status of theJaw SystemFigure 3.5The Jaw System as An ObjectThe jaw in turn contains eighteen muscle objects and a mandible object. Eachmuscle is defined with the muscle origin, muscle insertion and maximum possiblecontractile force in the beginning. The first dynamic input to a muscle should be theactivation level, and outputs are tension and torque on the mandible. In return, themandible moves together with the insertion ends of the muscles. Therefore, themessages pass from the mandible to the muscles are change of insertion end locations.Figure 3.6 illustrates these relationships. The dynamic behaviors of the muscles andmandible have been defined in (2.1), (2.3), (2.4), (2.5), (2.6), (2.7) and (2.8). (2.1)and (2.3) are embedded as the internal behaviors of the muscle object. The results ofusing objects are that we can manipulate with the clearly defined interfaces of objectsinstead of a whole collection of mathematical equations. Objects can simply be used asbuilding blocks to construct a complex system.Li Muscles Tensions,chaTorquesinsertion EndLocationsFigure 3.6Relationships Between Muscle Objects and The Jaw Object35C++ is not a simulation language. Therefore, we have to include our owndynamic system module. The next section will discuss the concept of digitalcontinuous simulation systems.3.4 Digital Continuous Simulation SystemsWe usually model dynamic system with a set of ordinary differential equations(ODEs), in general:x’(t) = f(t,x(t))In turn:x(t)= fx’(t)dtWhenever we use a digital computer to simulate a continuous-time model (aset of ODEs), we must discretize the time axis in some way [Cl, C2j. For instance, ifsimulation operates with constant independent-variable increments At (calculationinterval), we can discretize the time axis so that differential equations becomedifference equations:x(t + At) — x(t)= f(t x(t))Atorx(t + At) = x(t) + f(t,x(t))AtThe discrete event simulation is given by a two-step interation: the first stepconsists of the evaluation of all derivatives and the second includes the integrationprocedure, which evaluates the state variables for the next calculation interval. Thistwo-step iteration is usually implemented in simulation systems with two subprograms(or behaviors in object) -- DERIV and INTEG [C2]. The basic concept of digitalsimulation systems is shown in Figure 3.7.36t DERIVx(O) derivatives evaluationx’(t) x(t+At)INTEGintegrationOUTPUTresultsFigure 3.7Structure of A Digital Continuous Simulation SystemsDuring simulation the integration procedure requires many evaluations of statederivatives (depending on the integration algorithm). In the prescribed time instantsthe control is given to the OUTPUT subprogram which supplies the user withsimulation results.Besides the basic mechanisms of digital continuous simulation system, our jawmodel should not be contained much more than specifying the relationships betweendifferent muscle objects and the mandible object by calling the according DERIV,1NTEG and OUTPUT behaviors of the objects.3.5) Numerical Integration TechniqueThe integration algorithm chosen here is the simple Euler method [C2]:+ hy,where n = 0, 1, 2There are more efficient integration algorithms available. However, the workshere are concentrated on how different features of a complex system can be37distributed into different objects, and the Euler method is easier to implement for ourpurpose.No matter how good an integration algorithm is, it only gives approximationvalues to the true solution. Numerical approximation errors are limitations from theintegration algorithm [C2]. However, a smaller calculation interval can reduce thiserror. On the other hand, smaller calculation interval will introduce another error --the roundoff error. In practice, integration algorithms are implemented by computerarithmetic with finite precision (number of bits). This leads to the roundoff errors.Roundoff errors accumulate and become increasingly serious with decreasingcalculation interval, since a smaller interval means more calculation intervals for giventmax - to. Figure 3.8 shows the relations between the numerical approximation error,the roundoff error and the total error.Numerical Integration ErrorError“Total NumericalroximationRoundoff—‘—-ErrorCalculationIntervalFigure 3.8Total Error = Numerical Approximation Error + Roundoff ErrorIn Borland C++, there are three type of floating point numbers with differentaccuracy. They are float (32 bits, 7-digit precision), double (64 bits, 15-digitprecision) and long double (80 bits, 19-digit precision). The type long38double is chosen in our simulation to minimize the roundoff error. Differencecalculation intervals have been tested, and a O.Olms calculation interval producesstable solutions for the simulation model. A smaller interval may produce a betterapproximation, but O.Olms is a good compromise for efficiency and accuracy. Withthe calculation interval unchanged, the system has been tested by replacing longdouble with double and float. There is a big difference between the outcomesof using long double and float. However, the difference between the resultsof using long double and double are insignificant. We can assume that theroundoff error has been taken care of by the extra precision with double. Allfloating point numbers in the model are implemented with long double for betterconsistency of solutions.The model has been tested with different input values, and is believed togenerate reasonable outputs with the above setup. Details of the results can be foundin Chapter 5. Long running time are penalties of using the Euler method; a smallcalculation interval and a long floating number are needed for better accuracy. Theprogram is complied C++ code, and a total simulation time interval of O.5s takes a486 33MHz PC approximately two minutes to yield the simulation results.39Chapter 4Considerations of the Muscular Tendon ParametersIn the last few chapters, we have discussed the mathematical and programmingconcerns of the jaw model. The mathematical model is defined and different parts ofthe model are clearly organized with objects. However, before we can performsimulation, the simulation model needs a few more pieces of information. First, asdefined in Section 2.5, constants k1, k2, 1, ij, 12 and B are needed to define a muscle.Second, we need an input signal, activation level, to activate the muscle. Before welook into the constants use in the muscle model, a few terms that are used to describeelasticity are defined in the next section. Different constants that define a muscle andthe activation level will be presented next.4.1’) ElasticityWhen a force acts on a body or material, resisting forces within the body react.These resisting forces are called stresses. Stress is measured by the force applied perunit area which produces deformation in a body. The unit of stress is expressed asN/rn2. Thus:FStress = -The ratio of length after stress is applied, to original length, is defined as a strain.Because it is a ratio of length, strain has no dimensions or units.AlStrain =40The numerical relationship between stress and strain was first discovered byRobert Hooke. Hooke’s Law states that there is a constant or proportionalarithmetical relationship between force and elongation. The modulus of elasticity isdefined as the stress required to produce one unit strain.F/A FtModulus of elasticity= / =The above relationship holds until the elongation reaches a point known as the elasticlimit. The elastic limit is the smallest value of stress required to produce permanentstrain in the body. Below the elastic limit, materials return to their original lengthwhen the deforming force is removed. However, the result of applying a force beyondthe elastic limit is that the stressed material will not return to its original length whenthe force is removed. In addition, materials elongate much further for each unit offorce above the elastic limit. Elastic materials in biological systems such as musclesand tendons are arranged to work in conditions that the tissues always operate belowtheir elastic limits. Beyond the elastic limit will cause injuries to the tissues [Al].4.21 Constants that Define a MuscleConstants k1, k1, 1, l,‘2 and B are needed to define a muscle. The next sectionwill define 1, i and 12 which describe the dimension of the muscle, k1, k1 and B thatdescribe the dynamic behaviors of the muscle will be followed next.4.2.1) 1 i, and ‘2Muscles are believed to be under small amount of passive tensions when theyare attached to the skeleton system. If they are removed from the skeleton system, themuscle length will usually be shortened by almost ten percent as compared to the41original length. The original length of an uncontracted muscle is defined as the restinglength, and the length of an isolated muscle is defined as the equilibrium length.To simplify implementation, the muscles in the jaw system are assumed to beunder no tension in a completely closed jaw. The muscle insertion and origin of aclosed jaw define the total length, 1, of the muscle. In fact, the absolute resting lengthsof different muscle are difficult to predict mathematically.A complete muscle is made up of muscle fibers and muscle tendons. Asdefined in Section 2.4, ij is the length of the muscle fibers and 12 is length of themuscle tendons. Informal measurement indicates that the ratio of the fibers to tendonsis about 5:1, and this ratio is used in every muscle of our model. There is no exactvalue for this ratio as there is a fuzzy edge between the muscle fibers and the tendons,and an exact value is not necessary either. Our concern here is to simulate the generalmoving pattern of a jaw pull by a set of muscles, but not the detailed internalbehaviors of specific muscles.4.2.21k1d2 and Bk1, k2 and B are directly proportional to the thickness or size of the muscle. Inturn, the size determines the maximum contraction force possible of the muscle.Therefore, the following assumptions can be made:k1 = maximum contractionforce * constant1,k2 = maximum contractionforce * constant2,B = maximum contractionforce * constant3.The approximation values of these constants can be obtained from the behaviors ofthe biological tissues.42Muscles for mastication always operate within the elongation range of 45%,and muscles are stretched by about 20% in a normal chewing cycle. Figure 4.1 showsan estimated stress-strain curve of the masseter muscle [A5].Stress-strain Curve of Skeletal Muscle1210820Elongation %Figure 4.1(y-axis in glmm2)Base on the stress-strain curve, we have Table 4.1.Stress-tension RelationshipsElongation Stress Length Area Tension0% 0 1 1 010% 0.2 1.1 0.909 0.181820% 0.4 1.2 0.863 0.416530% 1.1 1.3 0.769 0.845940% 2.2 1.4 0.714 1.870850% 5.2 1.5 0.67 3.48460% 11.25 1.6 0,625 7.03125Table 4.1Column 2 and 5 indicate the relationships between stress and tension.Columns 3, 4 and 5 are the length, cross sectional area and the passive tension of amuscle. As these three columns represent ratios and they do not refer to any particularmuscle, units are not necessary. Assuming that the muscle will reach the elastic limitwhen it is stretched by 50% of the original length and it can withstand its own0 10 20 30 40 50 6043maximum contractile force at that point, the magnitude of the passive tension on thesame muscle that is stretched by 20% is:= 0.4165/3.484 * maximum contractile force,= 0.1195 * maximum contractile force.The force required to stretch a normal spring obeys the following equation:F=kzixIn this expression Ax denotes the amount by which the spring is stretched from itsunstrained length. The term k is a proportionality constant called the spring constantand has dimensions of force per unit length (N/m). If the muscle operates within theelongation range of 20% and assumes that the passive tension and strain have a linearrelationship in this range, this equation can be implemented as following:F 0.1195 * maximum contractile force * (A11/l) / 0.2ork1 = 0.5977 * maximum contractile force / iTendinous tissues are much stiffer than muscle fibers, and Figure 4.2 showsthe stress-strain curve of the tendinous tissues [A5].Stress-strain Curve of Tendinous Tissue654U,b120102Eloqigaion %Figure 4.2(y-axis in kg/mm2)44Assume that a tendon is under the maximum contractile force when it isstretched by 4%, the passive force from the tendon can be described as follow:F = maximum contractile force * (l2/ 12) / 0.04or= 25 * maximum contractile force / 12However, the ratio of the cross section area of tendinous tissue/muscle fiber in themastication muscle is roughly four times higher than most other skeletal muscles, k2implemented in the model is:— 100 * maximum contractile force / 12The last constant, B, defines the response time of the muscle, and Figure 4.3shows the response of a mammal muscle when it is fully activated.Response of Mammalian Muscle Under Maximum Stimulation.zzI:: /Time (s)Figure 4.3(y-axis is tension in %)The graph shows that the muscle will reach its maximum strength at around O.14safter it is fully activated. Simulation of the isometric contraction of a single muscleshows the magnitude of B is approximately (5 * maximum contractile force) in orderto satisfy the above criteria.45This section reveals a possible way of defining the approximate values for k1,k2 and B, but this is by no means that there is only one way to define these values.Data gathered for biological tissues vary a lot, and sometimes contradict each other.The method discussed above is believed to be direct and easy to implement. There arelimitations with the constants defined here; they are all non-linear functions in realbiological system instead. However, k1, k2 and B define here are more adequate forthe first test run of the model.4.3 Activation LevelThe jaw movements of the model are considered the result of voluntary driveby the CNS, and studies have shown that control signals from the CNS for voluntarymovement can be change as fast as fifty to sixty times per second, therefore, thefrequency of the activation levels is chosen to be 50Hz in our model.In addition, the activation levels from the CNS are usually quite continuous.Figure 4.1 shows a possible measured raw EMG graph and the shape of the activationlevels after it is rectified and filtered. The rectified and filtered signal is believed to bethe original activation levels from the CNS._______________________________________________Figure 4.1Activation LevelIn order to define the activation levels freely for the model, the activationlevels are designed to be defined with a B-spline curve. In drafting terminology, a46spline is a flexible strip used to produce a smooth curve through a set of plottedcontrol points. The term spline curves, or spline functions, refer to the resultingcurves drawn in this manner.Given an input set of n+1 control points Pk with k varying form 0 to n, wedefine points on the approximating B-spline curve as:P(u) = pkNk.t(u)where the B-spline blending functions Nkt can be defined as polynomials of degree t1. The blending function is recursively defined as:N zi—f1 if(uku<uk+I)k,1’ “ 0 otherwiseNkl (ii)= u— Uk Nkt_l (u) + Uk+t— ‘Nk÷l...l (u)Uk+t_1 — Uk Uk+t — Uk+lAny terms with value of 0 as the denominators are assigned the value 0 during therecursive calculations.The defining positions U for the subintervals of u are referred to asbreakpoints. Breakpoints can be defined in various ways. A uniform spacing of thebreakpoints is implemented here and is defined as:=0 ifj<t,Uj j-t+] iftjn,=n-t+2 ifj>n.for values ofj ranging from 0 to n+t.The B-spline curve implements in the model has five control points. Figure 4.5shows an example of activation level curve generated with five control points. Morecomplex form of activation levels can be generated by joining a few different B-splinecurves.47o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0TimeFigure 4.5B-spline Curve as The Activation LevelWith the final information described here, we are ready to test run oursimulation model of the jaw. The next chapter consists of procedures of test runningthe model and details of the simulation result, Although the model is designed tohandle abnormal settings of the jaw and activation levels, the first run is concentratedon working with a normal setting of the jaw. The model is convincing if it respondsfavorably, under normal circumstances, in a way compatible with the literature [B 1,B12, B13].48Chapter 5Simulation Procedures and The ResultsBecause of the complexity of the model, it is separated into three computerprograms. ACTGEN takes the control points as inputs and generates the activationlevels for different muscles. The activation levels are then fed into SIM, and SIMsimulates the jaw system according to the input activation levels. The final result canbe visualized with the graphics interface -- SHOW, or imported to a spreadsheetprogram. The ACTGEN and SIM can be put into a batch program to simulate a fewdifferent patterns. The structure of the programs is shown in Figure 5.1.Figure 5.1Structure of The Simulation ProgramSHOW is a graphics interface that shows informations about the jaw anddifferent muscles, and most of the effort has been spent on SIM that performs thesimulation. However, the graphics interface helps people to understand the simulationresults much better. Figure 5.2 shows the output of the graphics interface.49CurrentTimeWindow thatperms visuatzation Muslceof the movement Tensionsof the musclesand the jaw.Displacement,velocity andaccelerationof the condyle.Current angle,angular velocityand accelerationof the jaw.The first incisorlocation.Figure 5.2Graphics Interface of The Simulation Program5.1) Procedures of Test Running The Simulation ModelThe computer simulation model of the jaw was fully tested in the Faculty ofDentistry’s Craniofacial Laboratory at UBC, and provided satisfactory results. Thepatterns of muscle activations for simulated chewing by the model are shown as heavylines in Figure 5.3. Where possible, comparisons have been made with muscleactivation patterns derived from Moller [B 13] as indicated with the light lines in thefigures. Moller’s measurements of the muscle activations in the chewing cycle arebelieved to be the most accurate and complete in the oral biology field.The duration of the chewing cycle was fixed at 700ms in our simulation model,representing a value within ranges reported in the literature [B 1 (600-1 000ms), B 13(435-865ms)]. Chewing cycle durations depend upon the nature of the food, tougherand stickier foods requiring longer times [B 1]. The duration selected for this study istypical for apple and gum chewing, and very close to the duration cycle of the meanelectrical activity for several jaw muscles published by Moller, (1966).50,,00’510>G)0>>C)(‘380706050403020100-0.1 0.0 0.1 0.2 0.3 0.4 0,5 0.6 0.7 0.8-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8at. pterygoid inf.digastric/,.,..juFigure 5.3Comparisons of Activation Levelstime (s)Moller (1___Simulated3020966)patternsup. masseter30med. pterygoid\, ,ant. temporais20100temporalis\post.151030504030201051Initially, each activation level was generated by assigning the onset, 50% peak,peak amplitude, 50% peak, and cessation of activity from published, meanelectromyographic data [B 13, p.103, Fig. 143]. Straight-line curve fits between thesepoints were smoothed with a simple three-point averaging filter. Moller’s data did notinclude values for the middle temporal muscle or deep masseter, nor did theydistinguish between activity in the upper and lower heads of the lateral pterygoidmuscle. Therefore values were assigned to the middle temporal muscle which werebetween those for the anterior and posterior parts. Since activity in the deep masseteris similar to that in the anterior temporal muscle during gum chewing [B2] values forthe deep masseter were matched accordingly. Although Moller’s data describebiphasic activity in a single lateral pterygoid muscle, newer data suggest that theinferior part of the muscle is inactive in jaw closing during mastication [B5, B12,B22]. The upper and lower parts thus activate reciprocally, i.e., the superior lateralpterygoid is activated synchronously with the anterior temporal muscle during theclosing phase of the chewing cycle [B5]. In the present study, Moller’s data for theopening phase was assigned to the inferior lateral pterygoid, and his data for theclosing phase to the superior part of the muscle. Since mid-line chewing wassimulated, all muscle groups were considered to act symmetrically, i.e., they wereactivated in matching pairs on the right and left sides.The model was driven from a position of assumed rest where there was noactivity in any muscle. Motion of the jaw was analyzed from the lateral aspect, withemphasis on the incisor point and the center of the mandibular condyle. Minorcorrective changes were then made to overall muscle amplitudes (but not timing) tocreate an incisor point trajectory which fell within the mean range of data publishedfor human chewing [BI]. Minor scaling was considered acceptable, becauseelectromyographic data itself is a relative measure of muscle activation. Since52condylar motion was unconstrained except for angle, muscle “balance” became criticalduring the last part of the closing sequence. Many muscles were active, each with adifferent line of action, and the goal was to bring the mandible to its start pointwithout sliding past it. Accordingly, small adjustments, especially to the temporalismuscle group, were important in this phase. Figures 5.3 illustrates the similaritybetween the simulated patterns of contraction, and those believed to occur in thebiological jaw. Notable features include slight differences in symmetry between thedigastric and inferior head of the lateral pterygoid muscles during jaw opening, andearly activation of the medial pterygoid, coupled with relatively late peaking ofactivity in the temporalis muscles during jaw closing. The small, early burst of activityin the middle and posterior temporal muscles was needed in the model to maintain agood trajectory of jaw movement when the bolus was hit, and may or may not bepresent in human electromyographic responses when a similar bolus is used. Once thefirst open and close sequence of chewing was achieved, the model was allowed tocycle by driving it repetitively with the same muscle activation patterns. This wasdone to observe any effect of phasic changes in muscle properties on subsequentcycles.5.21 Simulation ResultsThe shape and temporal characteristics of the chewing stroke produced by thismuscle drive are shown in Figure 5.4. The opening and closing strokes nearlysuperimposed, and were angled towards posteriorly at approximately 70 degrees tothe dental occlusal plane. The gape at maximum jaw opening was 20.9mm. Themovement trajectory, which completed one cycle every 700ms, reached maximumgape at 360ms. The opening phase was slower than the closing phase, which showedcharacteristics of natural chewing such as a pause in closing when the bolus was hit,53slowed movement through the bolus, and the dwell phase in the “intercuspal” or startposition before opening began for the next cycle.Figure 5.4The Simulated Incisor MovementFigure 5.5 illustrates changes in position and linear velocity of both the incisorand condylar points during the same cycle. At the incisor point, the linear velocity was91mm/sec when the jaw was approximately halfway open, and reached 192mm/secwhen it was between a third and halfway closed. At the condyle, the peak openinglinear velocity was 26mm/sec about halfway through forward condylar translation,which reached 5.2mm at maximum gape. During closing, condylar velocity reached56mmlsec at the same time as the incisor point reached its peak velocity. Both theIE4-,C0E0U(‘3Q.41.‘3)>0—10-200-10-20I . I-10 0hor. displacement (mm>0.0 0.2 0.4 0.6 0.8time (s)54incisor and condylar closing velocity curves showed second, smaller peaks coincidentwith the molar’s passage through the “bolus.”velocityposition50—501 start of opentng-1502 maximal open3 bolus hit4 start of occiusal phaseFigure 5.5Incisor and Condyle MovementChanges in force on the condyle are shown in Figure 5.6. Condylar force wasessentially biphasic, reaching a peak of 43N towards the end of condylar translation,and a slightly greater peak of 55N when the jaw reached its initial starting position,i.e., at the end of “bolus” compression. A third, transient peak of the same magnitudeoccurred when the “bolus” was struck.1 2 341inc. point(mmls)(mm>0—•10—2050condyl e--0-50550.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)Figure 5.6Reaction Force at CondyleRecently, researchers have had success in gaining access to animalmusculotendious units to measure their tensions, but these techniques are available inhumans in isolated instances only. The simulation model, however, provides estimatedvalues for the jaw muscle. In Figure 5.7, changes in muscle tension (continuous lines)have been superimposed on the muscles’ corresponding activation curves (bar lines).In addition, displacement curves for the incisor point are provided for comparison.The elevator muscles all showed marked increases in tension during the openingphase, and again during the closing and compressive phase of the cycle. Theamplitudes and timing of these changes were unique to each muscle. Theclosing/opening tension ratios were noticeably greater in the superficial masseter,medial pterygoid and anterior temporal muscles, but approached unity in theremainder, i.e., the opening and closing tensions were roughly equal. With theexception of the medial pterygoid, all the elevators showed least tension (approachingor reaching zero) before, and at the time the “bolus” was struck, i.e., just after jawclosing velocity reached its maximum. This effect was particularly evident in the threetemporal muscles, especially in the anterior temporalis. Another decrease in tensionwas observed at the end of the “dwell” phase, just before jaw opening.56Figure 5.7Activation Levels and Muscles’ Tensionsmt:hi1dg575.3 DiscussionDespite simplification of the biomechanics, the model produced a very realisticchewing cycle when known patterns of muscle activation were chosen to drive themandible through a simple resistance. Many features of the simulated cycle comparedfavorably with known values for human mastication.In the model, the movement trajectory, jaw gape, and condylar motion were alldetermined by the timing and amount of activity in the inferior lateral pterygoid anddigastric muscles, both working with the assistance of gravity against the combinedpassive tensions of the jaw-closing muscles. These passive tensions differed accordingto each muscle’s cross-sectional size, location and length, although they sharedcommon length-tension curves and visco-elastic characteristics. The pattern ofactivation in the inferior lateral pterygoid and digastric muscles during jaw openingcreates unique movement trajectories at each closing muscle’s insertion, and thevarious differences between the muscles’ sizes and insertion sites then cause theirlengths and shortening speeds to vary. The passive tensions are therefore specific andtask-dependent.The model’s prediction of low to zero tensions in several closing muscles(particularly the temporalis group) at maximum closing velocity, just before the“bolus” is hit, may indicate a tendency rather than an actual event in the biologicalsystem. The behavior of the model is explained as follows. The induction of fastclosing by the medial pterygoid (which did not show any decreased tension) createdphase lag in muscles not yet activated to the same extent. Their insertions wererapidly displaced so as to slacken muscles which at best were marginally active. Thiseffect was most obvious in the anterior temporalis, which was the most susceptible58due to its location and length. Although possible, the phenomenon of “slackness” isunlikely to occur in the biological jaw. Differences in muscle properties comparedwith the model, or low levels of activity in the muscles concerned (possibly reflex-driven), could maintain low muscle tensions irrespective of any actions of the jawsystem. The maintenance of residual tensions would have considerable advantage, forexample more efficient force coupling and faster response times when the bolus isstruck. In the model, these zero tensions could be avoided by earlier activation of themuscles concerned, but the trajectory of the closing cycle changed when this wasdone.The model shows how interrelated muscle activation patterns andmusculoskeletal mechanics must be. Any patterned drive to the inferior lateralpterygoid and digastric muscles that is intended to produce a particular jaw movementhas to do so under the influence of passive tensions in the closing muscles. Thistensioning system responds differently according to the direction and the speed thejaw is driven. Thus, both rate and position-dependent factors of the mandible must betaken into account when the goal is to move the jaw into a particular position within aset time. Although at best an approximation, our model provides at least some idea ofthe way these tensions alter during function, and it invites speculation regarding theway the central nervous system learns to select the appropriate pattern of activation inadvance.The jaw-closing speed in our simulation was faster than that reported byAhlgren [Bi] for unrestrained human mastication (about 75 mm/sec for carrotchewing) but is consistent with that reported previously for forced rapid chewing,which can be as high as 274 mm/sec [B6]. Jaw-closing speeds vary considerablyaccording to food type. The kind of “chopping strokes” simulated in this study are59more like shorter duration chewing cycles than the wider, more ruminant strokes usedin the mastication of hard foods [B 121.When the “bolus” was struck, 50-6Oms passed before combined muscle tensionreached a sufficient magnitude to overcome the resistance and move the jaw upwards.In practice, most foods do not present such an abrupt transition, and a softened“leading edge” to the onset of force would alter this movement-time relationship. Thethickness and resistance profile of the bolus has a critical relationship to the timing ofmuscle activation and most important, the generation of muscle tension. Theactivation pattern has to be generated with an expectation of probable jaw velocity,muscle tension on impact, and tension required to compress a given bolus in a preselected direction ofjaw movement. Failure to tune the model in this way produced anunwanted trajectory of jaw movement. Nevertheless, surprisingly small modificationsto the average muscle pattern provided by Moller, (1966) were needed to “chew” thebolus in a typical manner.When the initial starting position of the jaw was reached at the end of closing,the drive to most elevator muscles had begun to decrease, although their tensionsremained. This was required to complete “bolus” penetration, and the tensions had todissipate before the next opening stroke. Dissipation occurred when the jaw becamestationary in a spontaneous “dwell” phase, which is also a characteristic of mammalianand human mastication [Bi, B6, B9]. It is significant that force dissipation in this“dwell” phase was so balanced between the different muscles that the jaw remainedstationary despite the location of its “condyle” on an inclined plane with no posteriorlimit. Mutual balance between elevator muscle groups obviates the need for aposterior limit. The condylar head can move and resist forces during opening, closingand bolus compression into an assumed “intercuspal” position without any passive60articular restraints, other than rear slope of the articular eminence itself. Here, thesuperior lateral pterygoid muscle had a critical role. Unless this muscle contractedsynchronously with the closing muscles, the condyle continued to slide posteriorly andupwards beyond its starting position as closing muscle tensions decreased. Thesuperior lateral pterygoid is generally considered to tension the articular disk,stabilizing it during bolus and tooth compression [B5, B 10, B 15]. Although manyfibers of the superior lateral pterygoid attach to the condyle itself [B 12] there are fewopinions about the role of this attachment, The model suggests that the muscleprovides an anterior tension vector to the condyle at a critical time in the late closingphase. Without this, a posterior limit to condyle movement e.g. by a ligamentousrestraint would be essential. The alternative possibility would be for the inferior lateralpterygoid to contract biphasically (i.e., be active in both the opening and closingphases) as originally proposed by Moller, (1966), but this notion is not supported bythe current literature.A tedious aspect of working with models is developing muscle contractionstrategies. However, the process is educational in that it provides one with insight intothe problems facing a central nervous system, and a major advantage of the model isthat the generation of muscle activation patterns is a contained operation. Theavailability of many descriptors such as changes in muscle tension and length, jointtranslation and rotation, movement velocities and articular forces, makes it readilypossible to derive variables used as feedback by the central nervous system. It wouldbe comparatively simple to use these data to simulate neural sensory information, andbuild this into a separate, linked model of the nervous control mechanisms responsiblefor jaw movement. Thus any future models of the nervous system, perhaps includingaspects such as artificial intelligence, can readily be added to the system.61The next chapter will discuss an existing artificial neural network architecture,a method of improving it, and a feasible dynamic controller with neural network thatcould be used to control the jaw model in the future.62Chapter 6Neural Network and Dynamic ControlNeural networks provide a unique computing architecture that can be used toaddress problems that are unmanageable with traditional methods. These newcomputing architectures, inspired by the structure of the brain, are radically differentfrom the computers that are widely used today. Neural network architectures aremotivated by models of our own brains and nerve cells. Although our currentknowledge of the brain is limited, the basic anatomy of an individual nerve cell orneuron is known. A typical nerve cell in the human brain is shown in Figure 6.1.OedllonofDseddtes .. .•... impulse:.. Cell .Body (OflFigure 6.1Typical Nerve CellThe output area of the neuron is a long, branching fiber called the axon. An impulsecan be triggered by the cell, and sent along the axon branches to the ends of the fibers.The input area of the nerve cell is a set of branching fibers called dendrites. Theconnecting point between an axon and a dendrite is the synapse. When a series ofimpulses is received at the dendritic areas of a neuron, the result is usually anincreased probability that the target neuron will fire an impulse down its axon.636.1) Artificial Neural NetworkA great deal of biological detail is eliminated in the computing models.However, the artificial neural networks retain enough of the structure observed in thebrain to provide insight into how biological neural processing may work. Figure 6.2illustrates an example of a typical processing unit for an artificial neural network.Figure 6.2Artificial Neural NodeOn the left are the multiple inputs which are connected to the processing unit; eacharriving from another unit. Each interconnection has an associated connectionstrength. The processing unit summing up all the inputs and uses a nonlinear thresholdfunction to compute its output. The calculated result is sent along the outputconnections to the target cells. The nonlinear threshold is usually implemented withthe sigmoid function. The equation for the sigmoid function is:1Figure 6.3The Sigmoid FunctionWnInputsOutputs1f(X)=i+e_x-5 -4 -3 -2 -1 0 1 2 3 4 564Figure 6.4 shows an example of neural network with two layers of processingunits, a typical organization of the neural network known as feedforward network.IN1OUT1N2Figure 6.4General Structure of An Artificial Neural NetworkFirst is a layer of input units. The input patterns are represented as vectors to thenetwork. The middle, “hidden,” layer of this network consists of “feature detectors” --units that respond to particular features that may appear in the input pattern.Sometimes there is more than one hidden layer. The activities of the last layer are readas the output of the network. In the example, there are two inputs, four hidden nodesand one output, however, configurations may be different for different applications.Despite the complex form of the network, it can be easily implemented asfollows:4.177 -85336OUT = sigmoid (sigmoid ( 3.9223 -1.7201 [10.8646 -5.8806 .20.7456 6.1682]LNJ -6.3929 -6.2253\, \ 799 3.6412Assume that IN1 and 1N2 are ([0, 0], [0, 1], [1, 0], [1, l]}, OUT will be (0.017719,0.980323, 0.980321, 0.025326} accordingly, indicating that the neural network isperforming the XOR function. The problems remaining are to find the right4.110.86463.641:65connection weights for the desired function in the neural network. The next sectionwill briefly discuss a training algorithm which is commonly used in artificial neuralnetwork.6.2) Backpropaation Neural NetworkBackpropagation neural networks are the most widely used of the neuralnetwork models and have been applied successfully in a broad range of areas.Backpropagation neural networks can handle any problem that requires patternmapping. Given an input pattern, the network produces an associated output pattern.A backpropagation neural network is also one of the easiest networks to understandbecause its learning and update procedure is a relatively simple concept. If thenetwork gives the wrong answer, then the errors back-propagate along theconnections. The weights of the connections are corrected so that the error islessened. Figure 6.5 illustrates these updating procedures.WIaAWI=iOÔI 0Figure 6.5Updating Procedures in Artificial Neural Nodewhere= activation level= error valuewji = connection weight= learning rateIn the context of such training, the feedforward network is often referred to a“backpropagation neural network.”66Although biological systems have neurons that perform a type of summation ofinputs, and have varying interconnection strengths, direct back-error propagationalong the same nerve has not yet been identified (actually not possible) in biologicalsystems. However, the uses of a trained net are completely forward in order, as inbiological systems.Backpropagation neural networks have a few disadvantages. First, the largestdrawback with backpropagation appears to be its long training time. Second, becauseof the long training time, on-line retraining of the net is not easy. Finally,backpropagation is susceptible to training failures in which the network neverconverges to a point where it has learned the training set.6.3 Method for Improving The Performance of Backpropaation NetworksBackpropagation networks are layered, and usually with each layer fullyconnected to the layers below and above. Backpropagation networks do not have tobe fully interconnected, but, most applications that work have used fullyinterconnected layers. The more complex the training patterns, the bigger the net wehave to use. This is true to a certain extent, but simulations show that there will be noimprovement after the network reaches a certain size. Instead of holding everything inone fully interconnected network, the biological neural networks tend to storeinformation in a more distributed manner. Therefore, I suggest a way of combiningartificial neural networks. Figure 6.6 illustrates the structure.Two neural networks in parallel make up this new configuration. One of thetwo networks is to train on the original training pattern, while the second network isto train on the error of the first network. The second network is named the Error67Adjusting Network (EAN) because its function is to minimize the error of the firstnetworkFigure 6.6A Combined Artificial Neural NetworkNeural networks tend to learn patterns that are more continuous in the initialtraining state that is fast, and slow down as only less continuous patterns are leftbehind, The less continuous patterns are responsible for the inconsistent performanceof a neural network. EAN can deal with these situations.The results of using the parallel structure are shorter training time and smallernetwork. The new structure is even able to handle more complex patterns that don’tconverge with a single network. The major drawback of a neural network is that itonly gives approximate solutions, and is not good for precise controlling. The newconfiguration also shows a possible way to adjust the precision of a neural network toan acceptable level.The uses of the above structures are illustrated with solving the inversekinematics of a two-jointed crab arm. Figure 6.7 shows the arrangements of the crabarm. Although the structure of the crab arm here is not common in artificial robotarm, the purpose of the crab arm model is to illustrate the performance of the newconfiguration of the neural network.68The trajectory of the open end of the arm is specified with the angle 0 and thedistance d. By specifying 0 and d, we want to know the values for 01 and 02respectively. If the inverse kinematics of the crab arm is solved with conventionaltechniques, there is no reason to replace it with a neural network. Therefore, thetraining data for the neural network is generated with the direct kinematics that isstraight forward as compared to inverse kinematics. As long as we have the input andoutput patterns, neural networks don’t care how the patterns are generated. Thetraining patterns should characterize the complete range of the input and outputpatterns, and a powerful feature of neural networks -- generalization -- will fill inappropriate values in the empty gaps that are not included in the training patterns.Figure 6.71 = length of the proximal arm12 length of the distal arm0, 02: 300 - 1200(shaded lines indicate the possible areaof movement as constraint by 01 and 02)The Crab Arm Example69The training patterns are generated as follows:for 0 30° to 120°, step 5°for 02 = 30° to 120°, step 5°1/ direct kinematics equation of/1 the crab armx =l1cos(0) +l2cos(01+0) + 2y =l1sin(02) + sin(0+0 + 10 = atan(y/x)d = (x2+y)°5Angles 0 and 02 are separated into two neural networks. Neural networkswhich are fully connected have the configurations of two inputs (0 and d), two hiddenlayers and each with eight nodes, and one output. The neural networks that are builtfrom two networks in parallel have a different configurations. Each of them have twohidden layers with four nodes. Although there are the same number of nodes in bothconfigurations, there are 88 connections in the first configuration as compare to 56 inthe second.In the new configuration, the first network is trained until the root meansquare error reaches 0.08 and the second network will pick up the rest. With half thetraining time, two networks in parallel still work considerably better than the standardconfiguration. The root mean square errors of these two different networks arecompared in Table 6.1.70Comparisons of The Root Mean Square ErrorsRMSinO1 RMSinO2Standard Configuration 0.002928 0.00 1809Two Networks in Parallel 0.000242 0.00074Table 6.1As indicated in Table 6.1, error in the new configuration could be up to tentimes smaller than the standard configuration. The running time of the newconfiguration is also faster as there are 32 fewer connections as compared to the first.On-line retraining is also possible because we can always add a second network inparallel with the first. In addition, there is a better chance for the neural networks toconverge because informations can be distributively stored in different networks.These are all significant improvements to the standard backpropagation networks.6.4) Neural Network as A DiitaI ControllerThere is much research in the area of neural networks for control. However,most of them depend on feedback controller, and the neural network learns from thecontroller and finally replaces it. Again, there is no reason to replace a conventionalcontroller with a neural network controller. The best a neural network can do is tocopy the function of a conventional controller and the performance will never bebetter but only worse than the original controller.In feedback control, the parameter that is being controlled is continuallymeasured (feedback), and compared to a reference (error calculation), and the actionmodified according to a control law to overcome the error. However, one has to thinkin terms of pattern mapping when working with neural network. The objective is to71map the current state and the desired “next” state to the according control signal. In otherwords, we want to determine the correct control signal that will transform the system fromthe current state to a desired new state. Figure 6.8 illustrates this relationship.State Mappingdesired-newstatecurrentstateAtFigure 6.8The objective is to determinethe correct control signal to transform the systemfrom the current state to the desired new state.The input and output connections of the neural network that performs this functionis simple. Figure 6.9 shows this configuration.current stateof the system controldesired new signalstate of lInesystem after AtFigure 6.9Neural Network That Performs State MappingThe training set is prepared with forward dynamics. With different possiblestates of the system, different possible control signals are fed in to the system and theoutcome is a set of possible “next” state of the system. The neural network is trained72with the current state and the “next” state as inputs, and the according control signalas output as indicated in Figure 6.9.Continuous controlling can be performed by dividing the time axis intodifferent time slices, and each time slice can be considered as separate pattern to theneural network. The idea is illustrated in Figure 6.10.Figure 6.10State Mapping in Continuous Time SlicesAs the neural network controller always tries to give a control signal that matches thedesired path in different time slices, the error is not cumulative.The above idea is illustrated with the isometric contraction of a single muscle.Figure 6.11 shows the complete arrangement of this example.neural tensionneIworkTenS0nFigure 6.11An Example of The Neural Network ControllerAt•• AtM At MAT73In the above example, the only variable that defines the state of a muscle is the tensionand the possible control signal is the magnitude of the neural drive. With the currenttension known, we want to find out the magnitude of the activation level to generate adesired tension after At.Recently, there are studies that the neural network controller learns from itsenvironment. These methods are based on a trial-and-error scheme and are passiveand slow. Instead of the passive trial-and-error scheme, the data is generated once andfor all. A complete set of training patterns can be generated by the cartesian productof S and C in which S is made up of elements within the possible initial states of thesystem and C is the set of possible control signals that can be fed into the system.Figure 6.12 illustrates the cartesian product of S and C in the previous example.Tension ActivationLevelmax. 1Figure 6.12The Cartesian Product of S and CPlease note that the above figure shows the cartesian product of S and C instead of atime slice, and the neural network is trained with patterns that are generated asfollows:for current tension = 0 to max tension, step maxtension/5for activation level = 0 to 1, step 1/5new_tension = tension after At (current_tension,activation_level);74Change in tension as according with time is planned (Figure 6.11), and Figure6.13 illustrates the simulation result. 6.13Simulation Results of The Neural Network ControllerThe white dots in Figure 6.13 indicate the desired tensions at the specified time, andthe curve indicates the tension developed within the muscle with the control of neuralnetwork. The outcome at O.08s does not match the requirement as it is not possible todevelop maximum tension of the muscle within this short period of time (O.02s), however,the neural network controller will always try to provide the best match to the requirement,As indicated in Figure 6.13, the simulation results are quite good with this simple test.6.5) Conclusions Reardin Neural NetworksThis chapter has demonstrated how to perform inverse kinematics and dynamiccontrol with neural networks in a direct manner. Neural networks that handle inversekinematics and dynamic control are not designed to replace the conventionalalgorithms. Indeed, no matter how accurate a neural network is, it only gives anapproximate solution to the problem. Therefore, an error will always be presented. Ono o 0 0 0 0 0 0 0 0Time75the other hand, conventional techniques are more accurate and predictable. A neuralnetwork should be used when the solutions are impractical to solve with theconventional algorithms, and when approximate solutions are acceptable.In our example, there is only one variable that defines the state of the muscle.However, no matter how many variables that define the state of a system, it makes nodifference to the way in which the neural network performs. One of the strongestpoints of a neural network is that it can deal with multi-dimensional inputs as well astwo or three-dimensional inputs.In addition, EAN is believed to improve the performance of neural networks toa more acceptable level. Although the demonstrations here only show the combinationof two neural networks, there is no reason to limit the number of neural networks totwo. Instead, different neural networks should be thought of as the building blocks ofa more complex system.76Chapter 7ConclusionsThe simulation results from the computer model in Chapter 5 are realistic inthe following way. The model produces trajectories of opening and closingmovements in the incisor region which resemble those reported in the literature forhuman mastication, both in time and space. This kind of dynamic simulation, can helpexplain the interplay between active and passive muscle tensions during jaw motion,the physical consequences of muscle coactivation, and loads upon the mandibularcondylar during translational and rotational motion. The basic design can be modifiedto explore the question of articular stability, the action of specific muscle groups onarticular function, and wider associations between patterns of muscle contraction andcraniofacial shape. Long-term goals might include the simulation of an active neuralcontrol system, mandibular mechanics during whiplash injury, and prosthetic designsfor joint replacement.Although studies in the project are confined to the human jaw, the completedmuscle model is flexible enough to model other mammalian musculoskeletal systemsas well. The jaw model that utilized the muscle model provided valuable informationwhich was not obtainable in any other way, and it could do the same for any othermusculoskeletal system developed with it.Studies of the biological system seemed to indicate a way of increasing theperformance of an artificial neural network. Neural networks may provide a feasiblestructure for automatic control, and could be incorporated into future musculoskeletal77system model of the kind developed in this study. The examples in Chapter 6 aresimple, but the structures of the neural networks suggested are sufficient for generaluse.7.1) Limitations of the Current Jaw ModelThere are several limitations in the present jaw model. They includesimplifications of the form and properties of the jaw muscles, the adoption of anartificial food bolus, reduction of the condylar guidance to an unlimited andfrictionless sliding surface, assumptions regarding the center of gravity and moment ofinteria, and the limitation of jaw movement within a two dimensional space.Human jaw-closing muscles are all multipennate (containing radiating patternsof individual muscle fibers), and they are notable for their relatively wide areas ofattachment. It is also possible that all the closing muscles are capable of at least somedegree of regional activation, depending upon the task being performed [B3, Bi 1,B21, B22J. Given their complexity, various of attachment sites, and the possibly local,graded patterns of intramuscular activation, it is presently difficult to predict the truenature of active and passive length-tension curves for individual human jaw muscles.The relatively simple assumptions for muscle-tendon actuator behavior in this studywere based on data available for whole skeletal muscles generally, and did not takespecific pennation patterns into account. Although the muscle model may not be theideal, approximating to the actual system, it provides reasonable estimate of thegeneral qualitative changes which occur in the biological system. However, the factthat the jaw model with realistic patterns of muscle activation produced jawmovement patterns which closely resembled those in the literature suggests that ourassumptions regarding muscle properties were quite reasonable first approximations.78A similar argument can be proposed for regarding the mass, center of gravityand moment of interia of the human lower jaw. The estimation of jaw weight is likelyto have been low, since it was based on a dry specimen, and the measurement of themandible’s true center of gravity and moment of interia is not simple. However, bothvary in life, and it would be simple to modify these constants when better data becomeavailable. Again, the behavior of the model system indicated that the values used werenot unreasonable. Even in the absence of other variables, such as the passive viscoelastic properties of other soft tissues in the region and the weight of the tongue, themodel was still able to behave well. With the great strength of the jaw muscles, thesefactors seem to have only minor effects on the jaw.7.2) Future Directions of The Jaw ModelThe model was designed to permit continuous modification and improvement.The muscle attachments which were modeled three-dimensionally can be altered toproduce different musculoskeletal configurations. Similarly, muscle constants can bealtered as data change. The specification of “bolus” properties can be changed toinclude different thicknesses, different bite point locations, and different compressiveproperties. Elements of friction can be introduced at the dental occlusal level, andwithin the temporomandibular articulation. The shape of the articular eminence can bemade curvilinear if desired, and various forms of posterior buttressing and elasticitycan be added. Conversion of the model to accommodate three-dimensional jaw motionis not as simple a proposition as the above changes even though the construction of atwin-joint system is a very desirable goal.It would be a comparatively simple matter to use many of the behavioraldescriptors such as changes in muscle tension and length, joint translation and79rotation, movement velocities and articular forces as variables describing feedback bythe central nervous system, and to build these into a separate, linked model of thenervous control mechanisms responsible for jaw movement. Future models of thenervous system, including control of muscle drive by artificial intelligence, can readilybe added to the system which invites further development.80ReferencesThe references are classified into five sections, labeled from A to E.A) Muscle Mechanics1. Alexander R. M. (1988). Elastic Materials. In: Elastic Mechanisms in AnimalMovement. Cambridge University Press, pp 1-21.2. Alter M. J. (1988). The Neurophysiology of Flexibility: Neural Anatomy andNeural Transmission. In: Science of Stretching. Human Kinetics Books, pp 43-50.3. Jongen H. A. H., Denier van der Gon J. J. and Gielen C. C. A. M. (1989).Activation of Human Arm Muscles During Flexion/Extension andSupination/Pronation Tasks: A Theory on Muscle Coordination, BiologicalCybernetics 61: 1-9.4. McMahon T. A. (1984). Fundamental Muscle Mechanics. In: Muscles, Reflexes,and Locomotion. Princeton University Press, pp 1-26.5. Yamada H. (1970). Locomotor System. In: Strength of Biological Materials. pp82- 105.6. Zajac F. E. (1989). Muscle and Tendon: Properties, Models, Scaling, andApplications to Biomechanics and Motor Control. Crit Rev Biomed Eng 17:359-404B) Human Jaw System1. Ahlgren J (1976). Masticatory Movements in Man. In: Mastication (eds. AndersonDJ and Matthews B). John Wright and Sons Ltd., Bristol, Great Britain, pp 119-130.2. Belser UC and Hannam AG (1986). The Contribution of The Deep Fibers of TheMasseter Muscle to Selected Tooth-clenching and Chewing Tasks. Journal ofProsthetic Dentistry 56: 629-636.3. Blanksma NG and van Eijden TMGJ (1990). Electromyographic Heterogeneity inThe Human Temporalis Muscle. Journal of Dental Research 69: 1686-1690.814. Blanksma NG, van Eijden TMGJ and Weijs WA (1992). ElectromyographicHeterogeneity in The Human Masseter Muscle. Journal of Dental Research 71: 47-52.5. Gibbs CH, Mahan PB, Wilkinson TM and Mauderli A (1984). EMG Activity ofThe Superior Belly of The Lateral Pterygoid Muscle in Relation to Other JawMuscles. Journal of Prosthetic Dentistry 51: 691-702.6. Hannam AG, Dc Cou RE, Scott JD and Wood WW (1977). The RelationshipBetween Dental Occlusion, Muscle Activity and Associated Jaw Movement inMan. Archives of Oral Biology 22: 25-32.7. Korioth TWP, Romilly DP and Hannam AG (1992). Three-dimensional FiniteElement Stress Analysis of The Dentate Human Mandible. American Journal ofPhysical Anthropology 88: 69-96.8, Korioth TWP and Hannam AG (1990). Effect of Bilateral Asymmetric ToothClenching on Load Distribution at The Mandibular Condyles. Journal of ProstheticDentistry 64: 62-73.9. Lund JP (1991). Mastication and Its Control by The Brain Stem. Critical Reviewsin Oral Biology and Medicine 2: 33-64.10. Mahan PE, Wilkinson TM, Gibbs CH, Mauderli E and Brannon LS (1983).Superior and Inferior Bellies of The Lateral Pterygoid Muscle EMG Activity atBasic Jaw Positions. Journal of Prosthetic Dentistry 50: 710-718.11. McMillan AS and Hannam AG (1992). Task-related Behavior of Motor Units inDifferent Regions of The Human Masseter Muscle. Archives of Oral Biology 37:849-857.12. Miller AJ (1992). Craniomandibular Muscles: Their Role in Function and Form.CRC Press Inc., Boca Raton, Florida, USA.13. Moller B (1966). The Chewing Apparatus: An Electromyographic Study of TheAction of The Muscles of Mastication and Its Correlation to Facial Morphology.Acta Physiologica Scandinavica 69, suppl. 280: 1-229.14. Nelson GJ (1986). Three Dimensional Computer Modelling of Human MandibularBiomechanics. MSc. Thesis, University of British Columbia.15. Okeson JP (1993). Functional Anatomy and Biomechanics of The MasticatorySystem. In: Management of Temporomandibular Disorders and Occlusion, MosbyYear Book Inc., St. Louis MO, pp. 2 1-27.8216. Osborn JW and Baragar FA (1985). Predicted Pattern of Human Muscle ActivityDuring Clenching Derived From A Computer Associated Model: SymmetricVertical Bite Forces. Journal of Biomechanics 18: 599-612.17. Otten E (1987). A Myocybernetic Model of The Jaw System of The Rat. Journalof Neuroscience Methods 21: 287-302.18. Smith DM, McLachlan KR and McCall WD (1986). A Numerical Model ofTemporomandibular Joint Loading. Journal Dental Research 65: 1046-1052.19. Throckmorton GS (1985), Quantitative Calculations of Temporomandibular JointReaction Forces. II. The Importance of The Direction of The Jaw Muscle Forces.Journal of Biomechanics 18: 453-461.20. Throckmorton GS and Throckmorton LS (1985). Quantitative Calculations ofTemporomandibular Joint Reaction Forces. I. The Importance of The Magnitudeof The Jaw Muscle Forces. Journal of Biomechanics 18: 445-452.21. van Eijden TMGJ, NG Blanksma and P Brugman (1992). Amplitude and Timing ofEMG Activity in The Human Masseter Muscle During Selected Motor Tasks.Journal of Dental Research 72: 599-606.22. Wood WW, Takada K and Hannam AG (1985). The Electromyographic Activityof The Inferior Head of The Human Lateral Pterygoid Muscle During Clenchingand Chewing. Archives of Oral Biology 31: 245-253.CI Continuous System Simulation1. Francois E. Cellier (1991). Principles of Planar Mechanical System Modeling. In:Continuous System Modeling. Springer - Veriag, pp 79-109.2. Matko D., Karba R and Zupancic B (1992). Simulation and Modeling ofContinuous Systems. Prentice Hall.DI Object-Oriented Analysis and Prorammin1. Booch G. (1991). Object Oriented Design with Applications. The Benjamin ICummings Publishing Company, Inc..2. Davis S. R. (1992). C++ Programmer’s Companion. Addison Wesley.3. Ladd S. R. (1990). C++ Techniques & Applications. M & T Books.83El Artificial Neural Network1. Levine D. S. (1991). Introduction to Neural and Cognitive Modeling. LawrenceErlbaum Associates, Inc..84


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