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Post stroke arm impairment : motor variables and movement control McCrea, Patrick Heath 2003

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POST STROKE ARM IMPAIRMENT: MOTOR VARIABLES AND MOVEMENT CONTROL by Patrick Heath McCrea B .A.Sc , University of British Columbia, 1997 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Mechanical Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A June 2003 © Patrick Heath McCrea, 2003 U B C Rare Books and Special Collections - Thesis Authorisation Form Page 1 of 1 I n p r e s e n t i n g t h i s . t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r , C a n a d a D e p a r t m e n t 4VJO^ O - S /2ocTb . http://www.library.ubc.ca/spcoll/thesauth.html 6/25/2003 Abstract Upper extremity motor impairment is common following stroke and is due to changes in both the central nervous and the musculoskeletal systems. Multiple aspects of stroke induced motor impairment can interfere with one's ability to complete activities of daily living. Weakness (i.e., reduced ability to generate torque) and hypertonia (i.e., increased resistance to passive stretching) impairment dimensions are of particular interest to clinicians as are subsequent adaptations to the control and planning of arm movement. Thus, the purpose of this thesis was to characterize weakness and hypertonia motor impairments and evaluate the planning and control mechanisms underlying a reaching task. We conducted three parallel experiments using twenty persons with chronic arm impairment due to stroke and ten similarly aged healthy control subjects. The first experiment validated a linear spring-damper model of the passive torque response of the elbow and found that mechanical parameters of stiffness and damping were quantitatively related to clinical impairment measures of hypertonia. In the second experiment we characterized the ability to maximally generate torque about eight different joint actions of the upper extremity. We found magnitude and temporal impairments of torque ^ generation in not only the more affected arm but also the less affected arm of individuals with n stroke. The final experiment examined the muscle activation and joint biomechanics underlying natural hand motion during reaching movements to various targets at fast and self-paced speeds. Shoulder abduction was a prominent feature that was related to a clinical scale of motor impairment. Results suggested that post-stroke movement planning is similar to healthy (i.e., different joint trajectories achieved by time scaling joint paths) but that the repertoire of available movement patterns is neurally constrained. i i Table of Contents Abstract i i Table of Contents i i i List of Tables vi List of Figures vii Contributions of the Author x References x Acknowledgements xi Chapter 1 : Introduction 1 Biomechanics of Healthy Reaching 2 Upper Extremity Impairments Following Stroke 5 Reaching Biomechanics Following Stroke 8 Purpose and Overview of Thesis 11 Chapter 2 : Linear Spring-Damper Model of the Hypertonic Elbow: Reliability and Validity ... 14 Abstract 14 Introduction 15 Methods 16 Group Description and Clinical Evaluation 16 Experimental Setup 17 Analysis of Resistance Profiles 20 Statistical Analysis 23 Results 24 Surface Parameter Fit and Reliability 24 Comparison of Sides 24 Parameter Relationships to Clinical Measures of Hypertonia 26 Discussion 28 Conclusion 31 Chapter 3 : Time and Magnitude of Torque Generation is Impaired in Both Arms following Stroke 32 Abstract 32 Introduction 33 i n Methods 34 Participants 34 Torque generation assessment 35 Isometric Joint Torque Analysis 38 Statistical analysis 39 Results 40 Reliability 40 Peak Torque 40 Time to Develop Torque 42 Time to Reduce Torque 42 Relationship Between Muscle Parameters 45 Discussion 45 Peak Torque 45 Time-Dependent Changes 47 Limitations and Future Considerations 49 Clinical Implications & Conclusions 50 Chapter 4 : Compensatory Reaching Strategies are Neurally Constrained Post Stroke 52 Abstract 52 Methods 58 Participants 58 Experimental Setup: Reaching Task 61 Data Collection 61 Hand Kinematics 62 Biomechanical Model 63 Muscle Activation 66 Statistical Analysis 66 Results 69 Reliability 69 Hand Path & Trajectory 69 Joint Configurations 72 Kinetics 76 Muscle Activation 80 Speed & Height Effects 83 iv Discussion 85 Coordination of Movements: Non-Dominant and Less Affected Arms 86 Degrees of Freedom are Neurally Constrained ,87 •j Hemiparetic Adaptation to Static But Not Dynamic Demands 89 Limitations & Future Considerations 92 Conclusions & Clinical Implications 94 Chapter 5 : General Conclusions 95 General Findings and Future Work 95 Motor Planning, Control, and Learning Impairments in Stroke 97 Theoretical Framework of Upper Extremity Motor Impairment 99 References 102 Appendix I: Advertisement for Clinical Subjects 113 Appendix IT. Informed Consent Form 114 Appendix III: Clinical Assessment Scales 116 Modified Ashworth Scale 116 Fugl-Meyer Upper Extremity Function Scale 117 Appendix IV: Conceptual Development of Linear Spring-Damper Model 120 Appendix V : Anatomical Landmark, Marker, and Electrode Placement 122 Appendix VI: Point-to-Plane Method and Determination of Embedded Axes System 124 Point-to-Plane Method 124 Global Position and Orientation of Segments (Embedded Axes) 130 Appendix VII: Joint Kinematics and Kinetics 134 Joint Kinematics 134 Joint Kinetics: Calculation of Moment and Power 137 Appendix VIII: Scatterplots of Biomechanical and Electromyographic Parameters 144 v List of Tables Table 2-1: Between day reliability of Surface Parameters 26 Table 4-1: Participant Descriptions 60 Table 4-2: Statistical Analysis 68 Table 4-3: Intersession reliabilities 69 Table 4-4: Hand Kinematics 71 Table 4-5: Joint Configurations 75 Table 4-6: Power Absorption and Generation 79 Table 4-7: Percent of Muscle Activity ; 82 Table A V - 1 : Tracking Marker Locations 122 Table A V - 2 : Digitized Anatomical Landmarks 122 Table A V - 3 : Electrode Placement 123 Table AVI-1 : Empirical Formulas used For Embedded Axes 130 v i List of Figures Figure 1-1: Simple model of the neuromuscular system applied to a spastic hemiparetic arm during forward reaching. Junctions that sum or compare signals are represented by "®". Agonist and antagonistic muscles are indexed to m arid n respectively. Reaching impairment could arise at various components of the model, eg. inability to activate muscles due to decreased motor recruitment (A & I), inability to generate muscle force due to disuse atrophy (B), changes in muscle structure that result in increased viscoelasticity (C), and increased gain (sensitivity) to stretching of muscle receptors (hyperreflexia) (D) 8 Figure 1-2: Relation of experiments to neuromuscular model. Experiments 1 and 2 identified the motor characteristics of the upper extremity under zero (i.e., hypertonia) and maximal (i.e., weakness) motor input respectively. Planning and control mechanisms were inferred from reaching behaviour (Experiment 3) 13 Figure 2-1: Schematic of testing apparatus (not to scale). The transverse view on the left shows the testing direction while the side view on the right describes the testing apparatus 19 Figure 2-2: Windowing of raw profiles for low and high speeds. Speed and torque-resistance profiles are shown in the upper and lower graphics respectively. Upward pointing arrows denote the windowed region for 30 deg/sec and downward pointing arrows denote the windowed region for 180 deg/sec 20 Figure 2-3: Family of torque resistance-angle profiles for the more affected arm of one subject (SR09). Extension speeds vary from 30 to 180 deg/sec. Profiles are near parallel and increase with both angle and speed 21 Figure 2-4: Passive resistance data fit to linear spring-damper model for the more affected arm of one subject (SRI8). The upper curve is the least squares fit to extensions at different speeds. Residuals are plotted on the lower curve. The model slightly overestimates response torque for combinations of fast speed/small angle and slow speed/large angle while it slightly underestimates response torque for slow speed/small angle (i.e., angle- , speed interaction). Residuals are near zero elsewhere 25 Figure 2-5: Scatterplots of the M A S versus mechanical parameters of (a) stiffness, (b) damping,; (c) angular offset, and (d) viscoelasticity for the more affected arm 'o ' and the distribution of mechanical parameters for the less affected arm (mean and standard error bars on left of each graph) 27 Figure 3-1: Posturing for isometric testing. From left to right, the illustrations show postures for (a) elbow flexion/extension, (b) shoulder flexion/extension, (c) shoulder abduction/adduction, and (d) internal/external rotation. The mid-range isometric testing angle is labeled on each illustration. Additional posturing is described below each illustration 37 Figure 3-2: Torque profile regions 38 Figure 3-3: Normalized peak torque versus joint action for each arm condition 41 V l l Figure 3-4: Time to develop torque versus joint action for each arm condition. 43 Figure 3-5: Time to reduce torque versus joint action for each arm condition 44 Figure 4-1: Reaching tasks, Biomechanical Model, and Euler rotation sequence, (a) Reaching Tasks: Participants made reaching movements to one of three targets placed on a target board. Target distances were adjusted to the excursion distances of the more affected (or non-dominant) arm by translating the target board in the anterior-posterior directions, (b) Biomechanical Model: Local right-handed coordinate system embedded within each rigid segment, (c) Euler rotation sequence: Flexion/extension (around x axis), adduction/abduction (around y' axis), and internal/external rotations (around z" axis) 63 Figure 4-2: Tangential velocity profile of the hand for mild (dotted line), moderate (dashed line), and severe (dot-dash line) impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard deviation - faint dotted line). Velocity is shown on the vertical axis and normalized movement time on the horizontal axis. Notice how the profile becomes progressively more skewed and less smooth as impairment increases 70 Figure 4-3: Joint path profiles for (a) shoulder flexion-extension, (b) shoulder adduction-abduction, (c) shoulder internal-external rotation, and (d) elbow flexion-extension. Joint angle is shown on the vertical axis and normalized movement time on the horizontal axis. Profiles are shown for mild (dotted line), moderate (dashed line), and severe (dash-dot) line impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard deviation - faint dotted line). Notice how the profiles become progressively more abducted and internally rotated with impairment 73 Figure 4-4: Power profiles for planes defined by (a) shoulder flexion-extension, (b) shoulder adduction-abduction, (c) shoulder internal-external rotation, and (d) elbow flexion-extension. Joint power is shown on the vertical axis and normalized movement time on the horizontal axis. Power generation is positive and absorption is negative. Profiles are shown for mild (dotted line), moderate (dashed line), and severe (dash-dot) line impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard , deviation - faint dotted line). Notice how power shifts from the shoulder flexion-extension plane to the adduction-abduction plane as impairment increases 77 Figure 4-5: Normalized muscle activation profiles for the (a) anterior deltoid, (b) lateral deltoid, (c) biceps, and (d) triceps (long head). The percent of maximum voluntary contraction (PMVC) is shown on the vertical axis and normalized movement time on the horizontal axis. Profiles are shown for mild (dotted line), moderate (dashed line), and severe (dash-dot) line impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard deviation - faint dotted line). Notice how the P M V C patterns saturate and become irregular with increases in impairment 81 Figure 4-6: Speed and height effects on abduction angle. Mean values and 95% confidence interval, (a) Effect of height on abduction angle: Abduction increases with increasing height in each arm condition, (b) Effect of speed on abduction angle: Abduction angle is , invariant with speed condition 84 Figure 5-1: Neuromuscular model of movement in stroke. Module structures are based on healthy movement. Potentially important stroke induced changes to model components are indicated by bold letters. A - Increased number of submovements (Rohrer et al., 2002); B ; . -v i n Degradation of internal model formation (Takahashi & Reinkensmeyer, 2003); C -Increased neuromotor noise (McCrea & Eng, 2002); D - Changes to length-tension relationship of muscle (Ada et al., 2003). Dashed boxes outline the scope of each experiment in this study with their contributions to the literature bolded and italicized.... 100 Figure A l V - l : Conceptualization of spring-damper model 120 Figure AVI-1: Transformations between global (left graphic) and local rigid body (right graphic) coordinate systems 125 Figure AVTI-1: Transformation (TDP) between the embedded coordinate system of a proximal segment (P) to the embedded coordinate system of a distal segment (D). The - t : transformation between systems is composed of a translation, pop, and a rotation, R(a,p,y)i Note that unlike the Euler rotation angles, angular velocities and accelerations of the distal segment are described entirely within the orthogonal axis system of the proximal segment. 134 Figure AVTJ-2: Forces and Moments acting upon a segment body and the principal axis system attached to the segment body. In addition to the applied moments, force moments (i.e., r X F ) act on the body 137 Figure A VIII-1: Scatterplots of Motor Impairment versus hand path and trajectory parameters of (a) Directness, (b) Segmentation, (c) Medial-Lateral (ML) Deviation, (d) Skewness, (e) Inferior-Superior (IS) Deviation, and (f) Kurtosis for the more affected arm 'o'. Distributions (means and 95% confidence intervals) of the less affected (LA) and non-dominant (ND) arms are given on the right side of each graph for comparative purposes. 144 Figure AVHI-2: Scatterplots of Motor Impairment versus change in angle for (a) Shoulder Flexion(+)/Extension(-), Shoulder Adduction(+)/Abduction(-), Shoulder Internal(+)/External(+) Rotation, and Elbow Flexion(+)/Extension(-) for the more affected-arm 'o'. Distributions (means and 95% confidence intervals) of angular change for the less affected (LA) and non-dominant (ND) arms are given on the right side of each graph for comparative purposes 145 Figure AVIJJ-3: Scatterplots of the F M Motor Impariment Scale versus peak powers of (a) Shoulder Flexor Generation, (b) Shoulder Abductor Generation, (c) Elbow Flexor Generation, and (d) Elbow Flexor Absorption for the more affected arm 'o'. Distributions (means and 95% confidence intervals) of the peak powers for the less affected (LA) and • non-dominant (ND) are given on the right of each graph for comparative purposes 146 Figure AVLII-4: Scatterplots of Motor Impairment versus percent maximum voluntary contraction (PMVC) for (a) Anterior Deltoid, (b) Lateral Deltoid, (c) Biceps Brachialis, and (d) Long Head of Triceps for the more affected arm 'o'. Distributions (means and 95% confidence intervals) of PMVCs for the less affected (LA) and non-dominant (ND) arms are given on the right of each graph for comparative purposes 147 ix Contributions of the Author This thesis contains three experiments that have been conducted by the candidate Patrick H . McCrea, under the supervision of both Dr. Janice J. Eng (Associate Professor, Rehabilitation Sciences) and Dr. Antony J. Hodgson (Associate Professor, Mechanical Engineering). The collection, analysis, and documentation of all experiments were primarily the work of the candidate. The above statement was written by Patrick H . McCrea and agreed upon by the undersigned. Janice J. Eng Antony J. Hodgson References McCrea PH, Eng JJ, Hodgson A J (2002). Biomechanics of Reaching: Clinical Implications for Individuals with Acquired Brain Injury. Disability and Rehabilitation, 10: 534-541. McCrea PH, Eng JJ, Hodgson A J (2003). Time and Magnitude of Torque Generation is Impaired in Both Arms following Stroke. Muscle & Nerve, 28: 46-53. McCrea PH, Eng JJ, Hodgson A J (in press). Linear Spring-Damper Model of the Hypertonic Elbow: Reliability & Validity. Journal of Neuroscience Methods. x Acknowledgements I would like to thank my supervisors, Drs. Janice Eng and Antony Hodgson, for their joint mentorship and patience. Their diverse backgrounds and encouragement made for a dynamic and enjoyable learning experience. I would like to thank Dr. Eng further for all the resources that she has provided to make this study possible. I would also like to thank Drs. Elizabeth Croft and Ted Milner for their helpful recommendations throughout the course of this thesis. I am very grateful for all the help I received during data collection and for the useful suggestions from GF Strong clinicians and members of the Neuromotor Control and Rehabilitation Research Laboratories over the past two and a half years. I would particularly like to thank Willem Atsma, Maria Kim, Katherine Hepburn, Kelly Chu, Craig Tokuno, Jocelyn Harris, and Catherine Donnelly. M y family deserves special thanks for their constant support and encouragement in whatever endeavor I chase. M y friends and housemates have also been supportive during this process and have provided both inspiration and laughter - thank you. I am grateful to the Rick Hansen Institute for providing financial support. Finally, I am indebted to all the participants who happily volunteered their time without which this study would not have been possible. xi Chapter 1 : Introduction Patients with stroke incur high rates of impairment to the upper extremity with approximately 85% incurring acute impairment and 40% incurring chronic impairment (Parker et al., 1986). In over half of individuals with a stroke, the affected upper extremity remains severely impaired despite intensive and prolonged rehabilitation (Nakayama et al., 1994). Furthermore, in both stroke and traumatic brain injury patients, the upper extremity recovers less than the lower (Eng et al., in press). Stroke patients rate return of upper extremity function as a high priority (Bohannon et al., 1988) and failure to substantially recover upper limb function can lead to depression and withdrawal (Balliet et al., 1986). Reaching is a functional activity that requires the coordination of multiple joints and involves both the musculoskeletal and neural systems. Following stroke, movement analysis of reaching can identify changes in interjoint coordination or the quality of the hand path (e.g., directness, smoothness). In fact, kinematic measures of movement time, movement distance and interjoint coordination during a reaching task are strongly correlated (Levin, 1996) to functional measures of upper extremity function such as the Fugl-Meyer scale (Fugl-Meyer et al., 1975) in individuals with stroke. Kinematic and kinetic measures can be used not only to assess performance but also to elucidate the motor strategies used during a goal-oriented reach. In addition, movement analysis of reaching may be useful for the evaluation of existing (for review see: van der Lee, 2001) and developing upper extremity therapies in stroke such as the force use paradigm where the less affected arm is restrained to encourage use of the more affected extremity (Taub et al., 1993), the use of neuromuscular blocks (e.g., botulinum toxin) to upper extremity muscle to relieve spasticity (Gracies & Simpson, 2000), and robotic assisted reaching exercises (Volpe et al., 2000). 1 Despite the fact that reaching is one of the major functions of the upper extremity and has poor recovery in stroke (Parker et al., 1986), the biomechanics of this multijoint task are largely unexplored. This introductory chapter will (1) detail the biomechanics of reaching in healthy individuals, (2) describe stroke induced joint impairments that may affect reaching performance, and (3) and review the findings from studies of reaching biomechanics in persons with stroke. , Finally, this introductory chapter will outline the thesis goals and structure. Biomechanics of Healthy Reaching Reaching to a target within arm's length involves the shoulder, elbow, and wrist. Reaching to targets beyond arm's length involves movements at all these joints, as well as trunk and hip motion (Dean & Shepherd, 1997). These joints work together as a coordinated mechanical system in healthy individuals to accurately place the hand in a desired position. Understanding the biomechanical and neuromotor control processes underlying reaching in the healthy population can help clinicians to identify where deficits may occur in persons with stroke. Segments of the upper limb may move about seven possible degrees of freedom (DOF) (i.e., joint rotations), in the shoulder (3 DOF), elbow (1 DOF), forearm (1 DOF) and wrist (2 DOF), in addition to elevation/depression and protraction/retraction of the shoulder-scapular complex. This natural excess of joints affords the central nervous system (CNS) the ability to employ an infinite number of paths when reaching to a specific target. Despite the many available degrees of freedom, joint motion during reaching is similar for a given start position, end position, and hand orientation across the healthy population (Dean & Shepherd, 1997; Kaminski et al., 1995). Functionally, the redundancy of joints provides the ability to adaptively 2 and optimally control movements to account for internal and external environmental factors (Latash and Anson, 1996) such as compensating for an injury or altering the hand trajectory to avoid collision with an object. Neuromuscular control of reaching is computationally complex and requires the synchronization of muscle activation at all the moving joints as well as all the muscles involved in postural stabilization. The acceleration of each joint during a reaching movement depends upon both the net joint torque (i.e. rotational force) and inertia (i.e., resistance of an object to any change in motion); rotational inertias experienced by upper extremity joints are coupled by the movements and configurations of the upper arm, forearm, and hand (Gribble & Ostry, 1999). The net joint torque is due not only to muscle activity but also to the effects of gravity, joint viscoelasticity, and externally applied forces (e.g. the reaction force of a door on the hand as it is being opened). Gravitational effects depend upon the weight and general orientation of the arm segments. Viscoelasticity is the inherent mechanical property of passive tissues (i.e. muscles and tendons) to stabilize joint position. The central nervous system (CNS) planning of reaching movements may be considered as a hierarchical control in which spatial information is converted to motor patterns at the shoulder and elbow to move the hand through space. A series of transformations convert sensory signals into hand trajectories, then into corresponding joint trajectories, required muscular torques, and finally into the actual patterns of muscle activity (Scott, 2000). While there is general agreement regarding this motor control process, there are debates over the specific coordinate system used in planning reaching movements and whether or not the muscle torques, are explicitly represented by the CNS (Feldman & Levin, 1995). For example, some have suggested that at the highest level, planning could occur in terms of a joint angle co-ordinate 3 system (e.g., control of shoulder, elbow and wrist angles) (Hollerbach, 1990) or in terms of the final endpoint co-ordinates (i.e., target) (Morasso, 1981). The CNS uses both feedforward and feedback strategies to control reaching movements (Jeannerod, 1990). The first phase of reaching is feedforward (preplanned) controlled; sensory information is used to anticipate disturbances to limb dynamics and plan appropriate muscle activation based on experience. Feedforward control is characterized by a profile of continuous movement that contains one acceleration and one deceleration phase. The second phase of reaching is feedback controlled and corrects for discrepancies between where and how one wants to place the arm versus the current position and speed of the arm. In feedback control, signals from peripheral receptors provide information back to the nervous system about the events occurring in the muscles, joints and other tissues. Feedback control is characterized by a profile of discontinuous movement that contains multiple accelerations and decelerations of progressively shorter duration as the error between the hand and the target approaches zero (Brooks, 1986). Control of voluntary movements improves with practice as we learn to anticipate and correct for disturbances resulting from internal and external forces acting on the body (Shademehr & Moussavi, 2000). People of all ages exhibit this ability to adapt their reaching strategies to changing environmental and physiological factors (Yan et al., 2000). Normal multijoint reaching is characterized by a smooth bell shaped velocity profile with a peak velocity approximately halfway between the start and endpoints. The peak velocity corresponds to the changeover from the acceleration and deceleration phases and its location within the velocity profile is an indicator of strategy. As requirements for accuracy increase, the bell shaped velocity profile becomes skewed and the peak velocity occurs earlier in movement. Conversely, as requirements for speed increase, the peak velocity occurs later in movement. The 4 relationship between movement speed and accuracy during reaching movements is known as Fitts' law (Fitts, 1954) where an increase in accuracy (decreasing the target width) is related to a reduction in reaching speed. Hand paths during reaching movements are straight or slightly curved (Morasso, 1981). Producing such a path requires a subject to coordinate rotations of both shoulder and elbow joints, typically characterized by a roughly constant ratio of joint angular velocities (Flanagan et al, 1993; Lacquaniti, 1992). A measure of the straightness of the hand path (known as the hand directness) is the ratio of the actual path length to that of the direct path (Bastian et al, 1996). Straight hand paths require simultaneous rotation of the elbow and shoulder so that inter-joint coordination in healthy individuals is demonstrated by a near constant ratio of the elbow and . shoulder angular velocities throughout the reaching movement (Flanagan et al, 1993; Lacquaniti, 1992). Deviations from straight line paths is caused by reduced coordination of the shoulder and elbow joint movements. Analyses of interjoint coordination may be helpful in understanding the nature of movement deficits in individuals with CNS lesions (Flanders et al., 1992; Kelso & Tuller, 1981). Upper Extremity Impairments Following Stroke Reaching may be affected by a number of impairments following an stroke, including spasticity, a decreased range of motion (ROM), coordination difficulties and weakness resulting from peripheral muscle atrophy or decreased central motor recruitment (Colebatch & Gandevia, 1989). 5 Weakness from either peripheral (e.g., muscle atrophy) or central sources (e.g., reduced motor unit recruitment) may be the major impairment underlying the functional disability of the more affected upper limb in stroke injury (Bourbonnais et al., 1989; Colebatch & Gandevia, 1989; Gowland et al, 1992). Classifying muscle strength by manual testing (Medical Research Council, 1976) has limited sensitivity to strength deficits in stroke (Van der Ploeg et al., 1984). Muscle strength is better measured using dynamometry and quantified by the peak magnitude of force or torque that can be generated (e.g., Andrews et al., 1996). In addition to reductions in peak force generation, time-dependent properties of muscle contraction could be altered following stroke and could be potentially important for function. While such factors have i proven to be related to function in other neurological conditions (Corcos et al., 1996), they have not yet been investigated in stroke. Spasticity is one of the principal factors affecting rehabilitation (Levin & Hui-Chan, 1993) following an upper motor neuron lesion (1JMN). Spasticity has been defined as a velocity dependent increase in the tonic stretch reflex (Lance, 1980). Increases in muscle tone (an assessed using the Ashworth and modified Ashworth scales (Ashworth, 1964; Bohannon & Smith, 1987). The 5-point modified Ashworth scale (MAS) has a high inter-rater reliability for an extension movement of the elbow joint (Bohannon & Smith, 1987) but tends to cluster scores in the middle range rendering the scale insensitive to subtle changes that may result from treatment (Harburn et al., 1992; Katz & Rymer, 1989). The poor resolution of the M A S in quantifying hypertonia has been a motivating factor for developing continuously based scales of the mechanical response to stretch. These investigations (e.g., Katz et al., 1992) suggest that parametric descriptions of the resistive torque profile relate to the degree of hypertonia. 6 Mechanistic models of the torque response, however, have yet to describe the effects of velocity on the torque response or show reliability of model parameters. As weakness and spasticity reduce the responsiveness of the upper extremity to descending commands, it is important that they be accurately and fully characterized. The effect that these impairments may have on reaching can be elucidated in the context of a qualitative model of the neuromuscular system. Such models have been well used in simulating reaching movements in the healthy population (Winters & Stark, 1987). Consider the process of initiating and completing a reaching movement using a spastic hemiparetic arm in a qualitative model of arm movement (with permission: McCrea et al., 2002) - (Figure 1-1). Once a target is specified, the feedforward controller (A) generates patterns of muscle activation that are used to drive agonist muscles (B) (e.g., triceps brachii). However, decreased motor recruitment and disuse atrophy may limit the forces that agonist muscles can generate. As the hand moves towards the target, elbow extension and shoulder flexion may be restrained by increases in tone. Increased tone may be due to structural changes in muscles that result in elevated viscoelasticity (C). Increased tone may also be due to hyperreflexia (increased sensitivity to muscle receptor >-: stretching) (D), which causes antagonist muscles (e.g., biceps brachii) (E) to contract (Katz & Rymer, 1989). The resultant forces from muscle contractions, the environment, gravity (F), and viscoelasticity in addition to the inertias of the arm (G) determine the accelerations of the upper arm and forearm. If the original motor command does not adequately compensate for arm dynamics, the hand may not reach the desired target. New positions of the hand and joints wil l be detected by the sensory system (H) and iteratively corrected by the feedback controller (I). 7 Input Kinematics "Desired Target" Feedforward Controller Feedback Controller H Sensory Information B Environmental and Gravitational Forces Agonist 1 Agonist m Antagonist 1 Antagonist n viscoelasticity Muscle Receptor Stretching _ Output Kinematics "Hand Position" Figure 1-1: Simple model of the neuromuscular system applied to a spastic hemiparetic arm during forward reaching. Junctions that sum or compare signals are represented by "cg>". Agonist and antagonistic muscles are indexed to m and n respectively. Reaching impairment could arise at various components of the model, eg. inability to activate muscles due to decreased motor recruitment (A & I), inability to generate muscle force due to disuse atrophy (B), changes in muscle structure that result in increased viscoelasticity (C), and increased gain (sensitivity) to stretching of muscle receptors (hyperreflexia) (D). Reaching Biomechanics Following Stroke Although biomechanical analyses have been used to identify reaching characteristics in healthy individuals, basic principles such as Fitts' Law have yet to be evaluated in individuals with brain injuries during functional reaching tasks. Krebs et al. (1999) used kinematic analyses of hand paths to track the recovery pattern and identify adaptive strategies during unconstrained reaching tasks following brain injury. They found an improvement in twenty acute stroke survivors in both accuracy and smoothness in reaching movements and drawing tasks and the re-acquisition of bell-shaped velocity profiles over an 11 week period following their strokes. In addition, improvements of hand velocity in reaching during the acute period following stroke have also been reported (Trombly, 1993; Wing et al., 1990). 8 Kinematic analyses of hand paths have produced evidence that persons with chronic stroke may select a strategy that optimizes their environment and neuromuscular system (Cirstea and Levin, 2000; Roby Brami, 1997; Trombly, 1992). Trombly (1992) found that the kinematic profile of the non-paretic arm during reach is fast and continuous whereas the profile of the paretic arm is slow and discontinuous. She suggested that the CNS adapts a feedback control in the paretic arm to correct deviations from the desired trajectory. Roby-Brami (1997) tested reaching to cone shaped targets in the horizontal plane and found that individuals with chronic stroke selected strategies that compensated for their specific impairments; those with predominantly proximal impairments slid their hands along a supportive table while patients with predominantly distal impairments made downward stabs. Cirstea and Levin (2000) found that patients with moderate and severe impairments in the paretic arm would involve trunk c movements to targets that were within arm's length and that the recruitment of an extra degree of freedom may be related to the severity of the impairment. Goal-directed actions seem to produce significantly smoother and faster reaching movements of the non-paretic arm in persons with chronic stroke than "no object" conditions (Trombly & Wu, 1999). Moreover, practically preferred and meaningful targets such as food items have resulted in even faster and smoother movements (Wu et al., 2001). This suggests that movement quality may be enhanced by using functionally relevant target objects during goal oriented reaching. Elbow and shoulder coordination has been investigated in individuals with stroke using a reaching task in the horizontal plane with the arm supported by a table. During these tasks, kinematic measures of interjoint co-ordination (ratio of the shoulder-elbow velocity) were more strongly correlated with impairment as measured by the Fugl-Meyer test than with spasticity 9 scores (Levin, 1996). In addition, it has been suggested that individuals with stroke lack the required compensation for inertial torques (i.e., torques dependent upon movements from other joints) during fast reaching movements and consequently result in larger deviations between the initial direction of reaching movement and the actual target direction (Beer et al. 1999, 2000). These directional errors are associated with excessive rotation of the elbow with respect to the shoulder. Beer et al. (1999, 2000) suggested that the inability of patients to specify joint co-ordination may be partly due to decreased ability to predict limb dynamics in feedforward control. Elbow and shoulder coordination has also been investigated using reaching tasks in which the hand path is physically restricted to straight paths of specified direction (e.g., forward/backward, lateral/medial). These constrained tasks can provide complementary information to unconstrained natural movements. If the elbow and shoulder joints act in a coordinated fashion during a constrained task, the hand will accelerate towards the target. However, in individuals with stroke, altered coupling of the elbow and shoulder joints results in forces acting in directions other than the intended direction (Lum et al., 1999; Reinkensmeyer et al., 1999a, 2000). These forces, known as constraint forces, can differentiate between the pathological extensor and flexor synergies found in stroke (as defined by the Fugl-Meyer scale), (Reinkensmeyer et al., 1999a). The magnitude of these constraint forces increases when reaching movements are exerted against greater gravitational loads (e.g., reaching in increasingly upward directions) (Reinkensmeyer et al., 1999b, 2000). 10 Purpose and Overview of Thesis The use of biomechanical analysis techniques in assessing persons with stroke is still in its infancy, and much remains to be done to develop them further. Joint related impairments such as hypertonia and weakness might constrain the joint torque patterns that are necessary for making functional reaching movements. Weakness may be a multidimensional phenomenon. In addition to reduced magnitude, temporal features of torque generation could be impaired following stroke. Mechanical characterizations of hypertonia need to be shown to be reliable and need to also include velocity dependent factors. Assessments of weakness and hypertonia approximately correspond to fully active and inactive (i.e., passive) motor input states and together could be used to parametrically describe post-stroke musculosketal dynamics. The hand path and trajectory of a reaching movement is a function of the intrinsic musculoskeletal dynamics and the control and planning of movement. Early investigations have shown that this control and planning isxhanged following stroke. To date, however, the majority of reaching evaluations involve movements performed at one speed in the horizontal plane with the arm supported (e.g., Levin, 1996). The effects of different reaching conditions in stroke such as speed, effect of gravity (e.g., reaching upwards or downwards), accuracy, direction and sitting posture needs to be evaluated. Natural reaching movements and joint motions occur in 3-dimensional space. In order to better understand the control and planning of natural reaching movements of the impaired upper extremity, we need to analyze not only hand motion but also the underlying muscle activities and the 3-dimensional joint mechanics. The overall goal of this thesis was to identify stroke induced changes in the motor control of the upper extremity. We developed novel parametric descriptions of motor control and 11 extended upper extremity movement analysis into 3-dimensions to achieve this goal. As these descriptions of movement were new, an additional goal was to establish reliability and clinical validity of biomechanical parameters. We conducted three parallel experiments in this thesis using a cohort of persons with chronic stroke and similarly aged healthy control subjects1. The first two experiments were designed to identify characteristics of the impaired upper extremity; under passive (i.e., zero motor input) and fully active conditions. After identifying these characteristics, the purpose of the final experiment was to evaluate the planning and control underlying the emergent behaviour of the impaired neuromuscular system during natural reaching movements. The three experiments specifically addressed the following questions. 1. Can a mechanical model be used to describe increased passive resistance due to hypertonia impairment and is such a model reliable and clinically valid? (Experiment 1). 2. Does the weakness impairment have a temporal dimension? Do the torque generation characteristics of joints in the more and less affected arms of persons with stroke differ from those of healthy individuals? (Experiment 2) 3. Do persons with stroke exploit the joint redundancy of the upper extremity to compensate for upper extremity impairments and do they vary with task demands (i.e., speed and height)? (Experiment 3) Study recruitment notices (Appendix I) were posted within the GF Strong Rehabilitation Hospital and circulated among Lower Mainland stroke clubs (after a brief presentation by the investigator). Informed consent (Appendix II) was obtained from each participant. Clinical assessment scales used in all three experiments are described within' Appendix III. 12 The scope of each experiment and the relationship between experiments can be conceptualized by the following qualitative neuromuscular model (Figure 1-2). Movement Goal 'Desired State' Central Ivbtor Control and Planning Experiment 1: Zero Motor Input Hypertonia (Passive/Reflexive Dynamics) Reflexive Dynarrics Passive Joint Mechanics Muscle Actuator Dynarrics . i J Torque Experiment 2: Maximum Motor Input Weakness (Muscle Actuator Dynamics) Experiment 3: Reaching Neuromuscular System Behaviour Sensory Information Hand and Joint Mation 'Current State' Figure 1-2: Relation of experiments to neuromuscular model. Experiments 1 and 2 identified the motor characteristics of the upper extremity under zero (i.e., hypertonia) and maximal (i.e., weakness) motor input respectively. Planning and control mechanisms were inferred from reaching behaviour (Experiment 3). 13 Chapter 2 : Linear Spring-Damper Model of the Hypertonic Elbow: Reliability and Validity Abstract Hypertonia of the elbow joint complex is common in individuals with stroke and is related to the magnitude of the torque response (described by position dependent parameters) during constant velocity extensions. The objective of this study was to model position and velocity dependent characteristics of hypertonia. For both the more and less affected arms in 17 persons with chronic stroke, we measured the torque response to constant velocity stretches (30-180 deg/sec). The responses were combined in position-velocity space and parameters of stiffness, damping, and offset angle were determined from a linear spring-damper model of the torque profile. The model was assessed at three levels: (1) ability to describe the combined torque profile variance, (2) reliability of parameters, and (3) validity of parameters (i.e., clinical correlation). Model parameters fit the torque profiles of both arm groups well and exhibited day-to-day reliability. Stiffness (r=0.820), damping (r=0.816), and 'viscoelasticity' (r=0.909), a composite parameter index developed posthoc, were highly correlated to a manual assessment of hypertonia (Modified Ashworth Scale). Mechanically determined parameters of hypertonia graded along a continuum may have better discriminatory power than manual assessments and thus, may be better at tracking recovery and evaluating interventions. 14 Introduction Spasticity has been defined as ' . . . a velocity dependent increase in the tonic stretch reflex (muscle tone) with exaggerated tendon reflexes . . . ' (Lance, 1980). Spasticity may contribute to both impaired motion (Katz & Rymer, 1989) and reduced functional independence (Carey & Burghardt, 1993). Hypertonia is the increase in joint resistance to passive movement and results from spasticity (i.e., hyperactivity of the stretch reflex) and/or changes in the viscoelastic characteristics of muscular and connective tissues (Katz & Rymer, 1989). The Modified Ashworth Scale (MAS) (Bohannon & Smith, 1987) is the primary clinical measure of hypertonia. The M A S subjectively grades the sensation of resistance felt by an examiner (i.e., 'tone') when manipulating a relaxed joint through its passive range of motion. Limited reproducibility and resolution of the M A S (Pandyan et al., 1999) has been a motivating factor for objectively quantifying hypertonia through biomechanical evaluations of the torque response to passive movement. The most well used biomechanical alternatives to manual assessment are the 'pendulum test' (e.g., Lin & Rymer, 1991), sinusoidal motion (e.g., Agarwal & Gottlieb, 1977; Lehmann et al., 1989), and ramp and hold stretches (e.g., Powers et al., 1989; Katz et al., 1992; Given etal., 1995). In a ramp and hold stretch, a relaxed joint is stretched at a constant angular velocity over a predetermined angular displacement and hypertonia is quantified by the resistive torque generated by the stretched muscle (Powers et al., 1988; Katz & Rymer, 1989; Given et al., 1995). As ramp changes of position correspond to functional disturbances and avoid cyclical stretching effects, the magnitude and time course of responses during testing are highly related to the joint's natural behaviour (Kearney & Hunter, 1990). The response during these stretches has been 15 characterized by the threshold angle at which torque begins to rise, the slope of the angle-torque (stiffness) curve, and the peak resistive torque (Powers et al., 1988; Damiano et al., 2002). These biomechanical parameters correlate with clinical measures of hypertonia (Katz et al., 1992) and are dependent on the angular velocity of the passive stretch (Ju et al., 2000; Damiano et al., 2002). The neuromuscular behaviour of a healthy joint system (i.e., connective tissues, muscles, etc.) is commonly parameterized by not only position dependent (i.e., stiffness) but also velocity dependent (i.e., damping) terms (Kearney & Hunter, 1990). The mechanical response of hypertonic joints has yet to be described as such, despite its dependence on stretch velocity. These parameters would be useful for characterizing the resistance that is felt by clinicians during manual assessments and could be determined by combining the torque responses to ramp and hold stretches at a variety of velocities within a spring-damper model. If these parameters are reliable between days and are related to clinical measures (i.e., are valid) they would be useful for measuring recovery and evaluating interventions. In this study, we examined the ^ mechanical response of elbow flexors of persons with hypertonia due to chronic stroke to \\ determine (1) the ability of a linear spring-damper model to describe passive resistance, (2) the test-retest reliability of model parameters between days, (3) the relationship of these parameters and a composite parameter to a clinical assessment of spasticity. v--Methods Group Description and Clinical Evaluation Seventeen older adults (Mean Age=61.8, SD=5.84, Range=49-72 years; 11 males and 6'' females) with chronic stroke (Mean time since injury=3.9, SD=2.2, Range=l-8 years) were 16 recruited from the community with inclusion criteria of: 1) a minimum of one year post-stroke, 2) present with hemiparesis secondary to first cerebrovascular accident, 3) able to provide informed consent, 4) able to follow one and two step commands and 5) able to voluntarily flex/abduct their shoulder 45 degrees and extend their elbow 30 degrees. Exclusion criteria were any neurological condition aside from the stroke and any musculoskeletal conditions which might affect upper extremity function. The study protocol was approved by the local university and hospital ethics committees. The upper extremity portion of the Fugl-Meyer motor scale (Fugl-Meyer et al., 1975) was used to describe motor impairment of the more affected arm. The mean score was 37.5/66 (SD=18.3, Range= 13-64). Elbow flexor muscle tone was assessed by extending the participant's elbow over its entire range of motion and graded according to the M A S (Bohannon & Smith, 1987). The mean score of the more affected arm was 1.4 (SD=1.1, Range=0-4). Experimental Setup We measured the velocity dependent resistance of elbow flexors of the more and less affected arm using a seated isokinetic dynamometer system (KinCom, Chattanooga, TN) in passive mode. Isokinetic dynamometers can passively rotate joints in the same posture that is used during manual joint assessments of the M A S . These devices have been used to assess spasticity in both the lower (e.g., Lamontagne et al., 1997) and upper (e.g., Schmit et al., 2000) extremities in persons with chronic stroke. Subjects were seated with the torso supported by crossing lap belts and the upper arm rigidly stabilized by a trough so that the shoulder was abducted and flexed to 80° and 45° (i.e., • gravitationally neutral elbow flexion/extension). The forearm was fastened in mid 17 pronation/supination by an adjustable cuff attached to the lever arm of the dynamometer (see Figure 2-1). The cuff was wrapped snugly around to the forearm to minimize forces related to the human-cuff interaction (i.e., compression of cuff material and soft tissue of the forearm). The flexion-extension axis of the elbow was aligned to the rotary axis of the motor and the start and stop angles of the motor were adjusted to the full passive range of the more affected arm. The same angular range was used for tests of the less affected arm. Observations of the hypertonic torque response over broad angular ranges are preferable to smaller ranges (Schmit et al., 1999). Full elbow extension was defined as 180°. The start elbow angle ranged from 60 to 80 degrees while the stop elbow angle ranged from 140 to 165 degrees. Ramp and hold extensions were applied to the elbow through its available passive range at speeds of 30, 60, 90, 120, 150, and 180 7sec. The tested joint was protected from hyperextension by (1) mechanical stops, (2) a failsafe motor shutdown, and (3) and an emergency stop. Custom designed software was used to directly sampled angles from the potentiometer, angular velocity signals from the tachometer, and force readings from the load cell at 600 Hz; the rotational resistance (i.e., torque) was found by multiplying force readings by the distance between the elbow joint center and the contact point of the load cell. Three trials, separated by 1-minute breaks, were conducted at each speed. Ten of the participants were tested a second time 2-3 days following the first assessment to establish between-day reliability. 18 Upper Arm Trough Motor Coupling and Forearm Elbow Support Cuff Torso & Lap Belts and Chair Extension of Tested Joint Rotation Axis Tachometer, Potentiometer, and Motor Figure 2-1: Schematic of testing apparatus (not to scale). The transverse view on the left shows the testing direction while the side view on the right describes the testing apparatus. 19 Analysis of Resistance Profiles For each trial, the torque resistance-angle profile was windowed for the region of constant rotation speed (i.e., zero inertial dependent torque) (Lamontagne et al., 1997); the windowed region decreased slightly with speed because of prolonged acceleration effects (see Figure 2-2). Angle (Degrees) Figure 2-2: Windowing of raw profiles for low and high speeds. Speed and torque-resistance profiles are shown in the upper and lower graphics respectively. Upward pointing arrows denote the windowed region for 30 deg/sec and downward pointing arrows denote the windowed region for 180 deg/sec. 20 The rotational torque resistance of the elbow was ensemble averaged over three trials at each extension speed; ensemble-averaging reduced artifacts and preserved the highly repeatable shape and magnitude characteristics of individual trial profiles. In addition to verifying a positive association of passive torque resistance with extension angle and speed, preliminary analysis of torque resistance-angle profile families (i.e., the set of torque resistance-angle profiles to increasing extension speeds) identified three key response characteristics (see Figure 2-3). 70 90 110 130 150 Angle (Degrees) Figure 2-3: Family of torque resistance-angle profiles for the more affected arm of one subject (SR09). Extension speeds vary from 30 to 180 deg/sec. Profiles are near parallel and increase with both angle and speed. 21 Firstly, the majority of torque-resistance-angle profile families consisted of near parallel torque resistance-angle profiles; this parallel relationship within families suggested that the interaction effect between speed and position on passive resistance was minor. Secondly, individual resistance-angle profiles were consistent with the classic linear hypertonic response to stretching of the elbow (e.g., Given et al., 1995). Finally, a linear effect of velocity was indicated by increases of resistance that were proportional to increases in extension speed at each extension angle. Given the predominant linear characteristics of profiles, we constructed a linear spring-damper model in terms of the angular position, 9, and the angular velocity, d9/dt to describe the passive torque response,! to extensions (see equation 2-1). Note, a full development of equation 2-1 is presented within Appendix IV. T ( 0 > d % ) = k 0 + b d % + r° =H0 -0O) + bd%t Equation 2-1 Here, k is the stiffness, b is the damping, and To is a constant; the constant, T 0 , was then converted into offset angle (i.e., spring displacement), 9o. The offset angle can be interpreted as the spring-damper analogue of the threshold angle that is used in spring-offset models. Stiffness (N-m/deg), damping (N-nrsec/deg), and angular offset (deg) parameters were found by applying a least-squares fit of the spring-damper model to position, velocity, and torque data; this least-squares method was independent of starting parameters and search paradigm because of the linearity of the model (Strang, 1988). Specifically, the fit solved for x (stiffness, damping, and. angular offset parameters) by minimizing the total squared error, E 2 , between model estimates and measured values of torque (b) for position and velocity data (A) (i.e., E2=||Ax-b||2) (Strang, 22 1988). To facilitate comparisons between subjects and account for the effect of elbow flexor muscle mass on passive resistance (Given et al., 1995), both stiffness and damping parameters were normalized by participant mass. Statistical Analysis For both the more and less affected arms of each subject, the ability of the linear spring-damper model to describe passive resistance torque data was measured by the squared multiple correlation, R , goodness of fit measure (Tabachnick, 2001). Relative reliability using intraclass correlations, ICC(l.l) (Shrout & Fleiss, 1979) and absolute reliability using the standard error of measurement (SEM) (Eliasziw et al., 1994) was determined between days for stiffness, damping, and offset angle parameters; the ICC was used in the S E M calculation and SEMs were expressed t as a percentage of mean scores. Subsequent analyses used parameter values from tests on the first day. Concurrent and construct validity were tested for the parameters. The most common evidence in support of construct validity is provided when a test can discriminate between conditions known to have the trait and those who do not (Portney & Watkins, 2000). The effect of arm condition (i.e., more versus less affected arm) on parameters of normalized stiffness, normalized damping, and offset angle was assessed by two-tailed t-tests. T-tests were conducted with equal variances not assumed because a preliminary Levene's Test of Equality of Variance indicated that arm condition had an effect on variance. Concurrent validity is the relationship of one measure to another and is quantified by correlation (Portney and Watkins, 2000; Streiner & Norman , 1995). The relationship between clinical hypertonia, as measured by the M A S , with parameters of offset angle, stiffness, and damping was calculated by Spearman rank correlations. The robustness of the correlations was quantified by the leverage of influential data points (i.e.,-; 23 effect of removing a data point) (Wilcox, 1998). Correlation leverage (CL) was documented by the range of correlations that occurred when single data points were removed. Non-parametric f correlations were used because of the non-normal distribution of scores and the non-equivalence of M A S ordinal grade intervals. For purposes of statistical coding, '1+' on the M A S was assigned a value of 1.5. A l l statistical tests were conducted at a significance level of p=.05. Results Surface Parameter Fit and Reliability Across all the subjects, the R values of the model fit to the torque profile for the less * j affected arm ranged from 0.58 to 0.96 with a mean value of 0.83. For the more affected arm, R values ranged from 0.79 to 0.99 with a mean value of 0.94. Typical features of the linear spring-damper model fit are illustrated by Figure 2-4. The between-day reliabilities of model parameters are in table 2-1. Comparison of Sides There was a significant effect of arm condition on stiffness, t(32)=3.56, p<.05, with the mean stiffness of the more affected arm (4.81*10A-4 N-m/deg-kg) greater than twice that of the . less affected arm (2.08*10A-4 N-m/deg-kg). There was also a significant effect of arm condition on damping, t(32)=2.32, p<.05, with the mean damping of the more affected arm (14.38*10A-5 N-m-sec/deg-kg) also greater than twice that of the less affected arm (6.29*10A-5 N-m-sec/deg-kg). There was also a significant effect of arm condition on the offset angle, t(32)=2.55, p<.05, with the mean offset angle of the more affected arm (76.1 deg) reduced from that of the less affected arm (107.4 deg). Resistive viscous and elastic forces can be computed 24 from spring-damper model parameters given body mass, forearm length, and a specified extension angle and velocity. Consider a person exhibiting the mean spring-damper parameter values above, weighing 100 kg with a forearm length of 0.25 m, whose elbow is extended to 120 deg at a velocity of 100 deg/sec. For the more affected arm the resulting viscous and elastic resistances would be 5.8 N and 8.4 N respectively. Parameters of the less affected arm translate as smaller viscous and elastic forces of 2.5 N and 1.0 N . Figure 2-4: Passive resistance data fit to linear spring-damper model for the more affected arm of one subject (SR18). The upper curve is the least squares fit to extensions at different speeds. Residuals are plotted on the lower curve. The model slightly overestimates response torque for combinations of fast speed/small angle and slow speed/large angle while it slightly underestimates response torque for slow speed/small angle (i.e., angle-speed interaction). Residuals are near zero elsewhere. 25 Table 2-1: Between day reliability of Surface Parameters Parameter More Affected Less Affected ICC % S E M ICC % S E M Stiffness .983 9.9 .909 21.0 Damping .862 28.5 .882 37.0 Offset .740 18.6 .902 8.2 Parameter Relationships to Clinical Measures of Hypertonia The M A S was not significantly correlated, p>.05, with the offset angle (r=0.408; C L = 0.289 - 0.446) but was significantly correlated, p<.001, with stiffness (r=0.820; C L = 0.765-0.848) and damping (r=0.816; C L = 0.766 - 0.853). Given the complexity of interpreting many mechanical parameters of hypertonia simultaneously, clinicians may find it easier to grade hypertonia by a single measure. This motivated us to generate a composite descriptor of muscle tone, 'viscoelasticity', by multiplying stiffness and damping parameters. A combined score is advantageous because the intrinsic randomness of related variables is reduced when they are combined; multiplication of parameters (as opposed to addition) generates scores that are unbiased to parameter units. The M A S was significantly correlated, p<.001, with viscoelasticity (r=0.909; C L = 0.882 - 0.939). Parameter values are graphed against the M A S in Figure 2-5. 26 C/3 < co > Q o O -o 0 <, O O - m CO > o O -o o CO O o o o o o o 13 o o CO >> c r © # 41 TS es s-"« u CO O IS o I D © V J T m - H (§>I ¥ §3p/33S^UI>j) S"vOT x Su idu iBQ o I D o o o ID 6"vOI x ^PRSBiaoDsiA o o o o po o Oo OBS ooo r - H CO < co > <u .^o <+-< _cS t>0 o o o p 00 d o o o OdB o 1 ' 1 1 0 O 1 , 1 1 CS u u CO o it JS TS eu s o I D I D © 00 o o ( S j ^ S a p / u i u ) f - v O I x SS3UJJIJS ( § 3 p ) a es *o * w <U -8 S s w es = is Sr*. "O o fl es <fl 3 CS 5P « SS co S3 Jtf ^ 0> be i« .9 M S -2 a CS s-cs co d £ CS co js w w *s s £ 'S fl o o US CS o ' f l es -fl o <u a -a fl cs co S co S-OJ cs »« es © © g « « D O A J3 co O i . e s A £ * es «<-i h w > . o c« .-fl3 £ IT) -.2 » r i T3 ^ es -2 1 -3 » S a . o f w fl 27 Discussion The purpose of this study was to test the reliability and validity of a linear spring-damper model of elbow flexor hypertonicity in persons with chronic stroke. Spring-damper parameters fit resistive torque profiles well, were reliable between days, and were capable of differentiating hypertonia from normal muscle tone. Stiffness, damping, and viscoelasticity, but not offset angle, were strongly and robustly correlated with increases in hypertonia as graded by the M A S . These results were found in our dataset which had a wide distribution of elbow flexor M A S scores. The smaller number of data points at higher M A S grades may have reduced the power of our correlation analysis. However, the tight range of correlations found when potentially influential data points were removed demonstrates robust relationships between mechanical parameters and clinical scores of hypertonia. Furthermore, the distribution of our dataset is similar to many studies (e.g., Watkins et al., 2002; Johnson, 2002; Katz et al., 1992) which indicate that only a small percentage of individuals with chronic stroke exhibit scores at the upper two levels of the M A S under passive extension of the elbow. A second limitation of this study is that we did not use electromyography to identify the presence of hyperactive stretch reflexes. The identification of hyperactive stretch reflexes has been used to separate the mechanical contribution of hyperreflexia from the changes to the intrinsic viscoelastic characteristics of soft tissues (i.e., muscle and tendon) (Zhang et al., 1997). Subdividing hypertonicity, however, may not be practical or of clinical use as the reflex response has been shown to be insignificant when compared to changes in the natural viscoelastic joint resistance (Lee et al., 1987). A final limitation of this study is that our spring-damper model did not 28 accommodate for possible non-linear features of the response profile. While the addition of non-linear terms may have potentially improved the model fit to response data, it is unlikely that non-linear parameters would improve the model's already excellent clinical correspondence (i.e., correlations) to hypertonia. Our spring-damper model of hypertonicity compares favorably with other biomechanical studies. On average, 90% of the variance (R 2) in the torque response profile was explained by the three spring-damper parameters. With the addition of a single damping parameter to account for changing extension velocities, our model is capable of explaining a percentage of variance that is similar to linear parameterizations (84%) of torque responses at isolated velocities (Pandyan et al., 2001). Although it is not possible to make exact comparisons between different studies due to different subject characteristics and protocols, the ability of the linear spring-damper model to explain a similar percentage of variance calculated from single speeds suggests that that the relationship between response torque and stretch velocity can be characterized as linear. The few hypertonic profiles that demonstrated reduced response linearity (i.e., smaller R 2 values) may have been associated with a 'catch'. Catches are a transient increase in the passive resistive torque, are non-linear with position, and their fit to linear functions is reduced (Pandyan et al., 2001). The validity of this spring-damper model is limited to the direction, angles and speeds that lie within the testing range as geometrical constraints (i.e., bone contact) and a different rotation direction will cause the hypertonic response to diverge from linearity. Reliable measures are crucial for determining changes that may occur during natural recovery or as a result of therapeutic intervention. Despite this, there is little information on the reliability of biomechanical and neurophysiological measures of hypertonia between days. In our study, the relative reliabilities of stiffness (ICC=0.983) and damping (ICC=0.862) 29 parameters but not the offset angle (ICC=0.740) were high in comparison to the reliability calculated for the M A S (Kappa=0.826) (Bohannon & Smith, 1987); reliability calculations by Kappa and ICC statistics are similar or identical (Streiner & Norman, 1995). There was more variability in the absolute reliability of damping (28.5%) than offset (18.6%) and stiffness (9.9%). Whereas damping is a velocity dependent parameter, both offset and stiffness parameter are position dependent. Thus, it is possible that increased variability in damping estimates is related to the resolution of torque data which is decreased across speeds (6 speeds) when compared to data across angles (several hundred data points). Construct validity of the spring-damper model was demonstrated by the sensitivity of its parameters to arm condition (i.e., more versus less affected arm) and concurrent validity was demonstrated by the high correlation of parameters with clinical measures of hypertonia. In addition to finding a correlation of stiffness with the M A S (0.820) that is comparable to those previously reported (0.778-0.873, Katz et al., 1992), this is the first study to show a correlation between the M A S and a damping parameter (0.816). We also found that compressing mechanical parameters into a single biomechanical index, 'viscoelasticity' can improve clinical correlations (r=0.909). Other methods of compressing biomechanical parameters such as principal components analysis may be useful in isolating a single index, particularly i f several mechanical parameters are determined from the torque response to stretch. We expected that in hypertonic elbow flexors, mechanical parameters values would shift so as to cause a more resistive spring-damper model (i.e., increases in stiffness and damping and a decrease in offset angle). This was the case for stiffness and damping parameters, as both were larger in the presence of hypertonia and both increased with its clinical grading. In addition, elbow flexors graded as having 'normal' muscle tone had comparable stiffness and damping 30 parameters to the less affected arm. While the offset angle was significantly smaller for hypertonic elbow flexors, it was not as reliable as stiffness and damping measures and did not decrease with increasing clinical grades as we had anticipated. This unexpected result may have been due to non-linear features of the torque response profile that were not taken into account by the linear model or the slight bias of the offset angle calculation to the larger amounts of data available at lower extension velocities. However, the high goodness of fit measures associated with the spring-damper model, particularly in the more affected arm, would suggest that these are not problems. Alternatively, the differences in start angle between participants may have affected the response mechanics and the onset of the stretch reflex (Wolf et al., 1996) and thus, the calculation of the offset angle. A third possibility is that clinical gradings of hypertonia may not be related to the angle at which resistance is first felt but to the sensations associated with stiffness and damping. Conclusion Combining the torque responses to a variety of extension speeds can lead to improvements in the mechanical characterization of a hypertonic joint. A spring-damper model describes both the position and velocity dependence of hypertonia with parameters that are strongly correlated to clinical measures. The increased resolution of these mechanical descriptors could be useful for detecting small but clinically meaningful changes in hypertonia for which the Ashworth and M A S scales are insensitive. 3 1 Chapter 3 : Time and Magnitude of Torque Generation is Impaired in Both Arms following Stroke Abstract Muscle strength, usually measured as the peak torque during maximal contraction, is impaired in persons with stroke. Time-dependent properties of muscle contraction may also be altered but have not been quantified. We quantified both magnitude (peak torque) and time-dependent parameters (times to develop and reduce torque) in eight different isometric joint actions. Parameters were compared among the more and less affected arms of 20 persons with chronic stroke and the non-dominant arms of 10 similarly aged healthy persons. Torque-generation parameters were independent from one another (i.e., low correlations) and highly reliable between trials and days. A l l parameters were impaired in the more affected arm, whereas peak torque and time to develop torque were impaired in the less affected arm. Following stroke, torque generation impairments include both magnitude and time-dependent properties and exist not only in the more but also in the less affected arm. Clinicians attempting to improve upper extremity function should employ therapeutic exercises that challenge patients to improve both their strength and speed of muscle contraction. 32 Introduction Muscle strength, the ability to generate muscular force, is generally measured by the magnitude of force or torque (e.g., peak torque) that can be generated, whereas weakness is defined as a decrease in the maximum voluntary torque or force when compared to normative values (Bohannon, 1995). The inability to generate torque is recognized as a primary obstacle to recovery following a stroke (Andreassen & Rosenfalck, 1980) and is related to decreased function of the upper (Bohannon et al., 1991) or lower (Kim & Eng, 2003) extremities. The magnitude of force generated is the most common measure of muscle contraction. However, time-dependent properties of muscle contraction may also be altered by neurological disease and are potentially important for function. For example, the rate of force generation is impaired and related to functional performance in individuals with Parkinson's disease (Corcos et al., 1996). The speed with which the torque profile rises and falls may also be an important descriptor of muscle contraction after a stroke. In healthy individuals, peak torque is achieved within 1 second of the initiation of a maximum voluntary contraction and is consequently available for use in everyday tasks (Canning et al., 1999). During the acute stage of stroke, however, a reduced peak torque is accompanied by a prolonged time to generate peak torque for knee extensors (Bohannon & Walsh, 1992) and elbow flexors/extensors (Canning et al., 1999). Given the structural muscle changes associated with chronic stroke, including a relative decrease in fast-twitch fibers (Toffola et al., 2001), we hypothesized that persons with chronic stroke would also exhibit an increase in the time required to generate torque. In persons with stroke, the magnitude of and joints affected by deficits in peak force production varies across 33 individuals (Andrews & Bohannon, 2000; Colebatch & Gandevia, 1989), depending on lesion site and volume. However, the nature and anatomical distribution of deficits in time required to generate torque are unknown for muscles of the upper extremity. It is also unknown whether impairment in the time required to generate torque is accompanied by impairments in the time to reduce torque. Lastly, the relationship between the magnitude of torque production and time-dependent muscle properties (i.e., time to develop and reduce torque) has not been defined. Joint torque parameters represent the collective behaviour of active muscles and characterize the net output of the neuromuscular system during a task. We have evaluated torque-generation by measuring both the magnitude (peak torque) and time-dependent parameters (time to develop and time to reduce torque) in eight different isometric joint actions across four conditions: (1) the more and (2) less affected side of individuals with chronic stroke, and (3) the dominant and (4) non-dominant sides of healthy control participants. The objectives of the study were to compare these torque parameters across the four conditions and across upper extremity muscle groups within each condition, and to determine the relationship between the magnitude of peak torque and the time-dependent variables. Methods Participants Twenty older adults (mean 60.9, SD 6.1, range 49-72 years, 13 men and 7 women) were recruited from the community with the following inclusion criteria: (1) a minimum of 1-year post-stroke, (2) present with hemiparesis secondary to first stroke, (3) able to provide informed consent, (4) able to follow one- and two-step commands, and (5) able to voluntarily flex/abduct 34 the shoulder 45 degrees and extend the elbow 30 degrees. For this group of 20 adults with stroke, 12 had ischemic strokes and the other had hemorrhagic strokes, 17 were right hand dominant prior to their stroke, 13 had hemiparesis on the right side of the body, and the time since stroke was a mean 4.3, SD 2.6 years. Ten healthy adults of similar age (mean 61.0, SD 9.0, range 51-77 years) and gender (6 men and 4 women) were recruited from the community. Musculoskeletal or neurological conditions (in addition to the stroke for the test participants) that would affect upper-extremity function were exclusion criteria for all participants. The study protocol was approved by local university and hospital ethics committees, and all participants gave informed consent. The level ofmotor impairment for the more affected arm in participants with stroke was assessed by the upper extremity portion of the Fugl-Meyer scale (Fugl-Meyer et al., 1975) (maximum function=66) and by the modified Ashworth Scale (MAS) for spasticity (Bohannon & Smith, 1987) (0=no increase in muscle tone and 4 = affected part rigid in flexion or extension). The Fugl-Meyer score was 38.2 (SD 19) and M A S was 1.3 (SD 1.1). Twelve participants with stroke were evaluated a second time, 2 to 3 days following the first assessment, to establish intersession reliability. Torque generation assessment Torque generation was measured using the isometric mode (static contractions) of a seated dynamometer system (KinCom, Chattanooga, TN). In this mode, both the joint and the distal point of force application (lever) are stabilized and supported by straps or an arm trough, depending on the movement direction. The trunk was restrained by a set of crossing seat and lap belts; further stabilization at the level of the clavicle was applied by a clinician. Maximal voluntary isometric contraction of eight different upper-extremity joint actions was tested in 35 midrange in the shoulder (flexion, extension, abduction, adduction, internal and external rotation), and elbow (flexion and extension) (see Figure 3-1). We measured torque generation in four conditions: (1) the more and (2) less affected arms of participants with stroke, and in (3) the non-dominant and (4) dominant arms of healthy participants. For each trial, participants started in a relaxed state and were instructed: "At the sound of the tone (an auditory cue), quickly push as hard as you can (in the appropriate direction). Immediately stop pushing at the second tone." Participants understood that in each trial they were required to (1) develop torque as fast as possible, (2) sustain a maximal level of torque (i.e., peak), and (3) reduce torque as fast as possible. Within each trial, participants received continuous visual feedback about the rate and level of force production via a bar graph displayed on a computer monitor. This information was removed from the computer screen at the end of the trial. Verbal encouragement was used to ensure the best performance. Three contractions (each of 3 seconds) were performed for each joint action, and rest breaks of 1 minute between trials were given to minimize fatigue. A 3-minute rest was given between joint actions. Blood pressure and heart rate were monitored with a digital blood pressure cuff (Lifesource, Milpitas, CA) throughout testing to ensure that it remained within the exercise testing guidelines of the American College of Sports Medicine (ACSM, 2000). 36 O fi <D -+-» X fi <u 3 o a o o T3 I O O a e 2 oo a o ' in C3 o W ^3 s 6"N 5 4: 3 o "a S a "a a-a © •*•» Vi fl a 5 <u o •+"> Vi X — ii a a g> .2 g x >-* a 2 « £ ja *> H c a -2 o •S "S * S 2 -2 5 « ja «i a w o t . c s G- 9> » 2 is 5 * s o 89 a X! <*> C — o •*•> •** "3 a _ i. u w *• 2 , w on s—' 4> S -8 T) 3 a vi S * ' £ > 5 a g j> .2 C 2 2 •** ~5 e g § « .2 © • " •** 'S3 S u „ s -o M s a a 2 .® tS g « <u o u ~ tS .2 " 3 O O C3 .2 *B 4 1 t« a a ,2 -2 ° WD « 4> .S a » i- o x B *a -2 p ea •-« 2 w> is -a a a vi .3 •2f ^tS 37 Isometric Joint Torque Analysis Resultant torque profiles for each contraction were corrected for gravity. Peak torque was defined as the maximum torque value that could be sustained for a period of 250 ms (Dewald & Beer, 2001). Peak torques were normalized by body mass. Gender and age, two other factors that affect strength, were not statistically different in their means or distribution between the healthy and stroke participants. The locations of 10% and 70% peak torque values were identified on the ascending and descending portions of the torque profile. These values were used to divide the contraction into five segments: pre-contraction, activation, plateau, deactivation, and post-contraction (Figure 3-2). The times to develop and reduce torque were calculated as the durations between the 10 and 70% thresholds; these parameters are useful for characterizing the shape of the torque profile and are independent of peak torque. Trials that had segmented or noisy profiles were eliminated from further analysis. The percentage of trials that were eliminated was < 1%. 251 1 r 51 i i i i i I 1 2 3 4 5 6 7 T i m e (s) Figure 3-2: Torque profile regions. 38 Statistical analysis Statistical analyses were performed on the three torque generation parameters (peak normalized torque, time to develop torque, and time to reduce torque). Relative reliability using intraclass correlations, ICC(1,1) (Shrout & Fleiss, 1979) and absolute reliability using the standard error of measurement (SEM) (Eliasziw et al., 1994) of the parameters was determined for each muscle group across the three trials (intrasession) and across the two days (intersession) for the stroke participants; SEMs were expressed as a percentage of mean scores. Subsequent analyses used the mean values from tests on the first day. Preliminary analyses found no difference between the non-dominant and dominant arms of the healthy participants for any of the three parameters, so further analyses included only the non-dominant arm. The effect of arm condition (more and less affected side of individuals with chronic stroke, and non-dominant side of healthy control participants) on peak normalized torque, time to develop torque, and time to reduce torque was evaluated using an A N O V A followed by post-hoc Duncan's multiple comparison tests. Within each condition, the effect of the eight different muscle groups on the muscle contraction parameters was tested by an A N O V A followed by post-hoc Duncan's multiple comparison tests. Finally, the relationship of parameters (i.e., times to develop and reduce torque and peak torque) was evaluated by performing three Pearson product correlations for each arm condition. For the correlational analyses, data for all eight muscle groups were included within each arm condition. A l l statistical calculations were performed on SPSS 11.0 (Statistical Package for the Social Sciences, Chicago, Illinois) using p=0.05. 39 Results Reliability For brevity, only the averaged values of intersession reliabilities across joint actions are reported. For the more affected arm, the mean ICCs were 0.97, 0.91, and 0.94 for peak torque, time to develop torque, and time to reduce torque respectively; the associated S E M percentages were 12.3%, 12.4%, and 18.4%. For the less affected arm, the mean ICCs were 0.98, 0.88, and 0.94 and the S E M percentages were 7.9%, 14.2%, and 15.6%. Peak Torque There was a significant effect of condition on the peak normalized torque [F(2,397)=72.72,p<.001] (Figure 3-3). The post-hoc multiple comparison Duncan test separated the condition means such that the healthy non-dominant arm was the greatest (0.406 Nm/kg), followed by the less affected (0.350 Nm/kg), and then the more affected (0.191 Nm/kg) condition. There was a significant effect of joint action on the peak normalized torque on the non-dominant arm [F(7, 72)=10.45, p<.001], less affected condition [F(7,152)=6.11, p<.001], and the more affected condition [F(7,152)=4.80, p<.001]. For all three conditions, the post-hoc analyses resulted in similar ranking of joint actions; the peak normalized torque values were largest for shoulder flexion and elbow flexion joint actions and smallest for internal and external rotation joint actions. The peak normalized torque values associated with shoulder abduction and adduction, shoulder extension, and elbow extension were intermediate to these values. 40 41 Time to Develop Torque There was a significant effect of arm condition on the time to develop torque [F(2,397)=21.88, p<.001; Figure 3-4]. The post-hoc test separated the condition means such that the more affected (0.548 s) arm was slower than the less affected arm (0.413 s), whereas the healthy non-dominant arm (0.339 s) was the fastest. There was no significant effect of joint action on the time to develop torque (p > 0.05) for any of the arm conditions. Time to Reduce Torque There was a significant effect of arm condition on the time to reduce torque, [F(2,397)=8.71, p<.001; Figure 3-5]. Similar to the time to develop torque, the post-hoc test separated the means such that the more affected arm was the slowest (0.653 s) of the three arm conditions; there was, however, no statistical difference between the times of the less affected arm (0.501 s), and the healthy non-dominant arm (0.536 s) conditions. There was no significant effect of joint action on the time to reduce torque for the non-dominant or more affected arms (p> 0.05), but there was a significant effect of joint action on the time to reduce torque for the less affected condition [F(7,152)=2.19, p<.05]. 42 (s) anbuoj %Q£ dopxzQ oj a u i i x 43 44 Relationship Between Muscle Parameters No significant correlations were found amongst any of the parameters (i.e., times to develop and reduce torque and peak torque) in the non-dominant arm. In the less affected arm, significant (p<.01), but low correlations were found between peak torque and time to reduce torque (-0.322) and between time to develop torque and time to reduce torque (0.275). A l l correlations among the torque parameters were significant (p<.01) but low within the more affected arm: peak torque and time to develop torque (-0.301), peak torque and time to reduce torque (-0.329), and time to develop torque and time to reduce torque (0.275). Discussion The purpose of this study was to compare the torque characteristics of the more and less affected arms of persons with stroke to the non-dominant arm in otherwise healthy persons. We characterized the torque generating capabilities of eight joint actions by measures of peak normalized torque, time to develop torque, and time to reduce torque. The results showed that all measures were highly reliable and sensitive to arm condition. Moreover, pairwise-correlations between the three parameters were low, indicating that they all provided valuable and complementary information about deficits in muscle contraction. Peak Torque In comparison to the non-dominant arm of healthy participants, the magnitude of joint torque (peak normalized torque) was impaired by 53% in the more affected arm and 45 by 15% in the less affected arm in persons with stroke. This finding confirms and extends recent evidence (Andrews & Bohannon, 2000; Colebatch & Gandevia, 1999; Jung et al., 2002) that strength is also impaired in the less-affected upper extremity following stroke. The apparent weakness of the less affected side may be due to the small percentage of descending cortical tracts that originate from the lesion site and remain ipsilateral (Dewald & Beer, 2001) or from the generally sedentary lifestyle of a person with stroke who may fail to maintain the strength of a more regularly exercised non-dominant arm of a healthy person. We found differences in the peak torque across the eight joint actions within the healthy participants that are likely dependent on the sizes and moment arms of muscles contributing to the movement. The relative ranking of the magnitudes of the peak torques for the eight joint actions was the same for all three conditions, i.e., the strongest joint actions in the more affected condition were also the strongest joint actions in the less affected and non-dominant arm conditions; moreover, the weakest joint actions were the same in all three arm conditions. This agrees with other studies (Andrews & Bohannon, 2000, Colebatch & Gandevia, 1989) that have not found evidence supporting the clinical belief that strength deficits increase in the proximal-to-distal and the flexor-to-extensor directions in the upper limb following stroke. It could be argued that the distribution of strength deficits in chronic stroke is individual and related to the size and the location of the brain lesion, but this individualized weakness cannot be detected when data are averaged over a large sample size uncontrolled for lesion size or location. 46 Time-Dependent Changes We found that the times to develop and reduce torque, indicators of the ability to modulate muscle force in a timely fashion, are impaired in chronic stroke. Time to develop torque was impaired by 61% in the more affected arm and by 22% in the less affected arm of persons with chronic stroke, compared to the non-dominant arm of healthy persons. We also found that the time to reduce torque was impaired by 22% in the more affected arm condition compared to the less affected arm and non-dominant arm conditions. There is a natural slowing of force generation and muscle activation that occurs with age resulting from factors that include a reduction in motor drive and a decrease in the ability of aged skeletal muscle to generate tension rapidly (Lewis & Brown, 1994). Reduction in the number of fast-fatigable muscle fibers (type II), and their denervation with age (Faulkner et al., 1995) may also contribute to natural declines in the speed of muscle contraction, as the loss of type II muscle fibers would specifically produce difficulty in the initiation and achievement of rapid and high-force movements. Accelerated type U fiber atrophy caused by a sedentary lifestyle and reduced muscle activity (Miller, 1995) may contribute to the moderate slowing of torque development times observed in the less affected arm. The further slowing of torque development in the more affected arm is likely due to motor unit loss of up to 50% (Dattola et al., 1993; McComas et al., 1973) that is specific to motor units associated with type II fibers (Dattola et al., 1993; Dietz et al., 1986; McComas et al., 1973). In addition to muscle inactivity, Dattola et al. (1993) suggested that mechanisms contributing to this type II atrophy may include transsynaptic degeneration of type II motoneurons, collateral 47 reinnervation, and motor unit transformation. Other factors contributing to reduced torque control following stroke include motor unit recruitment deficits and decreased firing frequency (Rosenfalck & Andreassen, 1980). The inability to respond quickly to changes in force requirements may also relate to abnormal motor unit discharge patterns. Persons with stroke also demonstrate atypical electromyographic interspike intervals that could manifest clinically as a difficulty in maintaining a steady force or in adapting to rapid changes in force requirements (Andreassen & Rosenfalck, 1980; Gerperline et al., 1995; Shahani et al., 1991; Yan et al., 1998). In contrast to our results, Canning et al. (1999) did not find deficits in the time to develop torque during isometric elbow flexion and extension movements in older adults who were 25 weeks post-stroke. There are two major methodological differences that we believe improved our ability to detect differences in time to develop and reduce torque. First, they used time to 90% of peak torque, which we found in pilot work to be less reliable than time to 70% of peak torque. The torque profile tends to both fluctuate and flatten out near the peak torque, inherently making unrealiable time-dependent measurements near the peak. Second, we used a larger sample size (20 vs. 10) and compressed values over multiple muscle groups, thus enabling us to increase our ability to detect differences among arm conditions. Impairments in the time to reduce torque, unique to the more affected arm, may be due to changes in motoneuron membrane firing behaviour. Changes in neuromodulators as a consequence of stroke can shift the synaptic current - frequency relations so that a cell can maintain a prolonged tonic firing rate following a brief period of excitation (Kiehn & Eken, 1998). Both animal (Bennett et al., 1998; Hounsgaard et 48 al., 1988; Lee & Heckman, 1998) and human (Gorassini et al., 1998) studies suggest that this behaviour, known as a 'plateau potential (Hoimsgaard et al., 1988), plays a facilitating role in the regulation of motor unit firing rates. It follows that slower torque relaxation times of the more affected side during isometric contractions are associated with motoneurons that self-sustain tonic firing when a descending neural stimulus is removed. No joint action had significantly faster times to develop or reduce torque within any of the arm conditions, suggesting that anatomical location or muscle size did not influence time-dependent contraction parameters in the tested proximal upper-extremity muscles. The significant correlations between time-dependent parameters and peak normalized torque production in persons with stroke may be in part related to a selected atrophy of type II fast-twitch muscle fibers and a concomitant behavioural transition of type I-associated motoneurons that results in plateau-potential firing patterns. These changes would affect not only the peak force but also the rate at which it is generated and reduced. However, these correlations were very low, only accounting for less than 10% of the variability, suggesting that time-dependent parameters are largely unrelated to peak torque and represent a different dimension of joint action. Limitations and Future Considerations We measured the ability to generate torque under isometric conditions. Functional activities naturally require muscle to be working under concentric or eccentric conditions and so dynamic strength tests (isokinetic or isotonic) may be more functionally relevant. Isometric strength tests of the upper extremity, however, correlate well with the results from isokinetic and isometric tests (Knapik et al., 1983). 49 Furthermore, the identification of time-dependent torque profile characteristics during dynamic tasks is complicated by the muscle length-tension and velocity effects on torque generation (Mayer et al., 1994). This study was a comprehensive evaluation of joint torque for eight upper extremity joint actions involved in gross motor arm function. In future studies, it would be clinically useful to characterize the joint actions of the more distal wrist and hand as they are critical for the orientation of the hand and the manipulation of objects. In fact, because of the natural proximal-to-distal gradient of increasing fast-twitch fiber content (Jozsa et al., 1978), it is likely that comparisons between hand and arm joint actions would yield significant differences in both magnitude and time-dependent parameters of muscle contraction. It would also be beneficial to evaluate the relationship between the muscle contraction parameters with participation and activity restrictions. Clinical Implications & Conclusions Conventionally, the magnitude of peak torque has been recognized as an indicator of impaired muscle contraction within the stroke population (Colebatch & Gandevia, 1989). Conversely, in other neuromotor pathologies such as Parkinson's disease, slowness of movement has been recognized as a key component of disability (Corcos et al., 1996). We found that in the chronic stroke population, torque generation is impaired not only in terms of the magnitude of the peak torque but also in terms of the ability to develop and reduce torque. The heterogeneity of lesion type, side, and location in this study support the robustness of this finding and suggest that this multidimensional deficit is common within persons with stroke. Clinicians may want to improve upper extremity 50 function by integrating therapeutic exercises that challenge clients to improve both their strength and speed of muscle contraction. 51 Chapter 4 : Compensatory Reaching Strategies are Neurally Constrained Post Stroke Abstract Stroke induced impairment is associated with changes to hand path and trajectory during reaching movements. However, these effects may be lessened by central planning and control adaptations that take advantage of redundant joints within the upper extremity. We expected that multiple compensation strategies would exist in a cohort of persons with stroke given the variety of impairment manifestations (e.g., weakness, decreased range of motion, and spasticity). The purpose of this study was to identify these compensatory strategies. A second purpose was to examine the effects of target height and reaching speed on compensation. We compared hand motion, joint motion, joint kinetics, and muscle activation during sagittal reaching tasks among the more and less affected arms of twenty persons with chronic stroke and the non-dominant arm of ten age-matched healthy individuals. Within each arm condition, we examined the effect of target height and reaching speed on the set of joint paths. Descriptive and statistical techniques were used to identify changes to biomechanical and electromyographic profiles. Measures were reliable between trials and days. Reaches of the non-dominant arm condition were executed using joints that lie within the sagittal plane; the less affected arm condition was associated with a small increase in abduction angle. Reaching movements of the more affected arm condition were stereotypically executed using abduction and internal joint movements that increased with impairment. Changes in speed had no effect on joint paths in any of the arm conditions while changes in height 52 (gravitational load) resulted in mild, moderate, and pronounced increases in abduction angle in the non-dominant, less affected, and more affected arm conditions. Stereotypical reaching movement in the more affected arm condition was taken as evidence that functional synergies are neurally constrained following stroke. The combination of increased load-dependent effects on and speed-invariance of joint paths suggests that multiple trajectories can be executed by time scaling a set of joint paths (kinematic planning) possibly determined by the kinetic and muscular capabilities of the impaired upper extremity. Joint based analyses of movement are more sensitive to neuromotor impairments than hand movement. 53 Introduction Persons with stroke and traumatic brain injury incur high rates of impairment to the upper extremity with approximately 85% incurring acute impairment and 40% incurring chronic impairment (Parker et al., 1986). In persons with stroke, upper extremity motor impairment is strongly correlated to the magnitude of spatial-temporal, kinematic (Levin, 1996; Kamper et al., 2002), and kinetic parameters (Lum et al., 1999) during reaching. Examination of these parameters can help elucidate the construction and execution of motor commands in both healthy and persons with stroke. Following stroke, clinical descriptions of abnormal synergies (Brunnstrom, 1966), multi-axial force, and E M G recordings during isometric tasks indicate that torque development is pathologically coupled between joints (Dewald & Beer, 2001) and that individual muscles are recruited over a broader range of movement directions (i.e., unintentional co-activation) (Dewald et al., 1995). This suggests that motor commands may flow through lower motor pathways with diffuse muscle innervation as an adaptation to a reduction in the number of functional higher motor outflow pathways (e.g., corticospinal and corticobulbar) (Colebatch et al., 1990). Under normal conditions, higher pathways are used to control independent joint movement through selective muscle activation. Reliance on motor pathways that have distributed innervation would limit the flexibility of the neuromuscular system to use task appropriate movement patterns during voluntary reaching, with potential aberrations occurring not only in the path and trajectory of the hand but also in joint motion, joint kinetics, and muscle activation within the upper extremity. 54 Indeed, when confined to a specific trajectory, hemiparetic arms inappropriately generate joint torques that result in hand forces perpendicular to the intended direction of movement (Lum et al., 1999; Reinkensmeyer et al., 1999a,b). Unconstrained but supported planar reaching movements also give evidence for dis-coordinated joint dynamics (Beer et al., 2000) and kinematics (Levin, 1996) that result in misdirected hand trajectories (Beer et al., 2000; Levin, 1996). Other features of supported movements by hemiparetic arms include decreased elbow (Wing et al., 1990) and hand (Roby-Brami et al., 1997) velocities, segmentation (Roby-Brami et al., 1997; Krebs et al., 1999), and decreased movement distance (Levin et al., 1996). Unrestricted movements in 3-dimensional space can be characterized by hand trajectories that are slow, segmented (Trombly, 1992; Archambault et a l , 1999; Kamper et al., 2002), indirect (Archambault et al, 1999; Kamper et al., 2002), and have a reduced excursion (Kamper et al., 2002). Concomitant E M G measures during unrestricted reaching movements suggest that muscles work closer to their maximal capacity in persons with stroke (Trombly, 1992). The planning and control of joint motion underlying hand trajectories during unrestricted reaching movements has not been elucidated in persons with stroke. These 'natural' movements are likely controlled differently than supported/constrained movements which restrict the repertoire of movement patterns available to the central nervous system (CNS). There is a natural excess of joints that may contribute to reaching movements and despite the many available degrees of freedom, joint motion is similar across the healthy population (Kaminski, 1995). Functionally, the redundancy of joints provides the ability to control movements adaptively and optimally to account for both internal and environmental factors (Latash, 1996). Bernstein (1967) proposed that during 55 the performance of any act, the many relevant subsystems are grouped into functional units (i.e., synergies). Functional unit organization may realize an optimal solution to indeterminacies that develop in transforming a movement from the conceptual level to specific kinematic, kinetic, and muscle activation patterns. In kinetic terms, unconstrained reaching movements in 3-D space are associated with both quasi-static (antigravity) and dynamic costs. If dynamic costs are minimized alone, the optimal posture at any speed depends solely on the geometry of the mass distribution of the arm (note that the peak torque increases quadratically with speed). Conversely, i f reaching was optimized for the total energetic cost, then slow arm movements would be associated with the formation of nearly sagittal forearm - upper arm planes (minimizes antigravity torques at the shoulder) with speed increases resulting in increasingly non-sagittal shoulder movements. In healthy individuals, 'synergistic' arm postures (i.e., joint angles) formed at the end and sequenced throughout an unsupported reaching movement are found to be invariant with speed and depend only on the initial posture (Nishikawa et al., 1999). This suggests that motor planning indeterminacies in healthy individuals are solved by the optimization of independent antigravity and dynamic force drives (Soechting et al., 1995; Nishikawa et al., 1999). Control and planning schema, however, are intrinsically constrained by the capacity of the neuromuscular system and may need to be adapted following the occurrence of stroke. Kinetically observable impairments such as increased passive resistance (Chapter 2) and reduced ability to generate torque (Chapter 3; McCrea et al., in press) may prevent the use of joint torque patterns that are necessary to carry out a movement plan. In fact, the effort required to just support the arm against gravity during 56 reaching tasks may require the full capacity of the upper extremity muscles; increasing gravitational demands (i.e., arm pitch) during both guided (Reinkensmeyer et al., 1999a) and unrestricted reaching (Kamper et al., 2002) movements typically result in decreases in reaching excursion. The subsequent restructuring of action plans (i.e., schema) to compensate for injury may result in programming changes to 'natural' transformations that occur between any of the sensorimotor levels (see Saltzman, 1979 for discussion of levels of sensorimotor representations). Ultimately, such changes will be reflected by altered muscle activation patterns but also may be observable by changes in the bodily segments involved, the trajectory of the hand/fingertip, joint-motion (i.e., kinematics), or joint torques (i.e., kinetics). Following stroke, the type of disturbed motor control may vary as it depends on the size, location, and severity of the lesion along with the manner of compensation employed by each person (Perry, 1969). Compensatory mechanisms have been identified at many levels of the action plan following stroke. During gait, for example, increased co-activation of non-paretic muscles (Lamotagne et al., 2000) and increased hip abduction moments (i.e., hip hiking) of the paretic limb (Kim & Eng, in press) may compensate for abnormal muscle activation patterns (i.e., phasing, coactivation, and/or decreased recruitment) (Knuttsson & Richards, 1979) and deficits in hip flexion moment (Kim & Eng, in press). Similarly, restrictive upper extremity joint motion may be compensated for by involving proximal segments such as the trunk and hip to achieve a reaching task (Cirstea and Levin, 2000). However, the use of compensatory reaching strategies internally available within the upper extremity has yet to be made clear, nor have the effects of task demands on the nature of compensatory strategies. 57 Understanding the effect of stroke on the expression of reaching movements may illuminate neuromotor planning and control in both healthy and stroke populations. In this study, we therefore characterized reaching movements of the upper extremity using kinematics, inverse dynamics, and electromyography analyses within four groups: 1) more and 2) less affected side of individuals with chronic stroke and 3) dominant and 4) non-dominant sides of healthy control participants. We studied the effect of a stroke and the differential effects of speed and task demands (i.e., height of target) within stroke and healthy persons on the control and execution of unrestricted reaching movements. Given the diversity of impairments that may occur following stroke (e.g., weakness, spasticity, and contractures) and the freedom of the CNS to execute tasks within a redundant mechanical system, we hypothesized that multiple compensatory strategies would exist amongst persons with stroke and could be identified with changes in muscle activation and joint mechanics. We expected that increasing levels of motor impairment would result in strategies that increasingly differed from the healthy population. We further hypothesized that changes in speed and task demands would cause changes to reaching strategies by persons with stroke (not seen in healthy subjects) that reflected an optimization of the total kinetic effort as indicated by changes in the path of joint configurations. Methods Participants Twenty older adults (Mean=60.9, SD=6.1, Range=49-72 years, 13 males and 7 females) were recruited from the community with the following inclusion criteria: 1) a 58 minimum of one year post-stroke, 2) present with hemiparesis secondary to first cerebrovascular accident (CVA), 3) able to provide informed consent, 4) able to follow one and two step commands and 5) able to voluntarily flex/abduct their shoulder 45 degrees and extend their elbow 30 degrees. Subjects with stroke were excluded i f they presented with hemispatial neglect as confirmed by the line bisection test (Schenkenberg et al., 1980). Ten healthy adults of similar age (Mean=61.0, SD-9.0, Range=51-77 years) and gender (6 males and 4 females) were recruited from the community. Musculoskeletal or neurological conditions (in addition to the C V A for the stroke participants) that would affect upper extremity function were exclusion criteria for all participants. The characteristics of the participants with stroke are described in Table 4-1. The study protocol was approved by local university and hospital ethics committees. The level of motor impairment for the more affected arm in participants with stroke was assessed by the upper extremity portion of the Fugl-Meyer scale (Fugl-Meyer et al., 1975) and by the Modified Ashworth Scale (MAS) for spasticity (Bohannon & Smith, 1987). Twelve participants with stroke were evaluated a second time two to three days following the first assessment to establish inter-session reliability. 59 "> I-i I Xl O CD o c S o I P O0 CD o ,u CD I-I o o oo o + —i + T - I <N —i 10 vo bo u fe X W r - l V O U - l V O C N r - l f n ^ O ( N r O T f \ O r O l r ) r - l r ^ r - l CD ' o t i I s N CD < J CO ^ £ CD ^ 00 r- vo <q vo VO vo ^  y> 2 fe 2 2 fe" fe r - - o \ o o m r x o \ O r H M i o N 0 . v o fe fe fe fe tNr<-)'<*iovor-ooa\0'— ics cu — c N f n ^ t - i n o o o s o [ T 3 O O O O O O O r - - , - , |U OOryjoor^ryjryDC^ryjryjryDwry^ryDW n rs £j 60 Experimental Setup: Reaching Task Participants were seated in a chair with their arm relaxed and their hand resting on their ipsilateral thigh (i.e., shoulder adducted, elbow in mid-flexion, and forearm pronated) and reached to one of three targets (3x3 cm squares) in a para-sagittal plane (passing through the glenohumeral joint). A l l targets were located just inside the reaching workspace limits of the more affected (or non-dominant) arm. The first target was at the height of the glenohumeral joint and the second and third targets were at heights 0.5 and 1.0 times the participant forearm length higher (i.e., eye level and slightly above head). (See Figure 4-la). Participants performed five unconstrained reaching movements to each target at (1) comfortable (i.e., self-paced) and (2) ballistic (i.e., fast - maximum) speeds. For each trial, participants started in a relaxed state and were instructed: "At the sound of the tone (an auditory cue) reach and touch the target at a comfortable pace or as fast as possible." Participants touched the target with their pointing finger (index finger tip or index distal interphalangal joint i f unable to extend the interphalangal joint). The torso was supported by crossing lap belts to prevent trunk and hip compensation (Cirstea and Levin, 2000). Data Collection Muscle activation was detected by surface electrodes placed on the anterior and lateral heads of the deltoid, the long head of the triceps, the biceps brachium, and the brachioradialis. Electromyograms (EMGs) were collected at 600 Hz (analog prior to sampling) and low-pass filtered at 100 Hz. 61 Three non-collinear infrared emitting diodes (IREDs) were placed on each upper limb segment (hand, forearm, and upper arm). Anatomical landmarks were digitized and registered relative to IRED locations. A full description of anatomical landmark, tracking marker, and electrode locations is provided in Appendix V. All movements were represented in terms of the right arm; movements of the left arm were converted to right arm equivalents by reflecting IRED and anatomical landmarks across the sagittal plane. IRED movements were tracked by an optoelectronic sensor (Northern Digital) at 60 Hz and then filtered using a second-order acausal Butterworth low-pass filter at 10Hz. Hand Kinematics Movement initiation and cessation were identified from the velocity profile of an IRED attached to the pointer. Movement was deemed to begin when the tangential velocity rose above 5% of the peak velocity and cease when the velocity fell below 5% of the peak velocity. Movement time was calculated as the difference between initation and cessation. Various kinematic descriptors were computed from the path and trajectory of each profile. The path of each trial was characterized by dimensionless indices of directness and mean path displacement. Path directness was defined as the ratio of the direct path to the actual path (Bastian et al., 1996). At each instant in time, the displacement of the actual path from the direct path was calculated (i.e., vector orthogonal to direct path and passing through the current hand position). This vector was then averaged over time, normalized by the length of the direct path, and decomposed into medial-lateral (ML) and inferior-superior (IS) components; lateral and superior directions are taken to be positive. 62 The tangential velocity profile was characterized by segmentation and statistical definitions of skewness and kurtosis (Zar, 1999). Segmentation was defined by the number of velocity peaks and troughs (i.e., minima and maxima). Skewness and kurtosis were used to quantify deviations from normality. Kurtosis is an index of the extent to which a distribution is peaked (positive), normal (zero), or flat (negative); increasing measures of kurtosis are synonymous with reductions in the ability to initiate and terminate movement. As requirements for accuracy increase, the velocity profile becomes positively skewed (i.e., peaks shift earlier) due to the need to control the deceleration region. Biomechanical Model Rigid body calculations were used to determine the global location and orientation paths of the three segments. A local right-handed coordinate system was fixed within each segment according to the anatomical position (i.e., arms hanging at sides with palms facing forward) so that ZL=inferior-to-superior direction (longitudinal axis), XL=medial-to-lateral direction, and Y L = posterior-to-anterior direction. X L and Z L axes were determined from anatomical landmarks and Y L by cross ( Z L , X L ) ; an orthogonal system was obtained by correcting X L by cross ( Y L , Z L ) . The corrected X L was less than 10° from the initial X L for each participant and segment. A full description of the mathematical techniques used to specify embedded coordinate systems can be found in Appendix VI. The coordinate systems of adjacent segments were allowed to translate and rotate with respect to one another (i.e., unconstrained six-degree of freedom joints -see Figure 4-lb). 63 o a CT , w fl o -t-» l £ I-l l l o CQ . t o t o IH fl O cd I <o. N N cu 7 3 _ C3 fl S .2 « u a s .2" * V S. 0 C3 S OX) cs fl CO fl •2 A w .2 fa « CU JS eu es & g s § • 2 eu "O a " f t 3 OX) CO H fl . o -a "fl 2 es es "S 0 5 -I - CU « DX) I-W 73 es fl fl es o — 73 cu <u 73 W O es 2 "S N 73 fl fl O es CO fl # o * f l es •w o u "es fl i~ cu cu is es fl 1-cu +3 73 fl cu 3 2 w o OH O i W .2 ~ 1- a cu CU fl e es OX) eu Sa — co e es *- B .fl OX) fl >-es 5 8 JS ~ y eu cu eu fi H PQ "5 « 2 S co O « O OX) co • f l fl A cu 8 i cu cu fl OX) -« 5 la A es w 0 es £1 « - M fl cu w>5 42 £ cu no JS cu * - 73 OX) 73 fl eu .2 S co CU es £ s- cu . CO >' >. mO CO S +* i- es es fl S fe W 2 - w 73 73 "2 1 fl fl es 2 * fl z I - A S.Sf> 73 i fl « eu o «S -cs . * eu "3 § 0 S § •a 13 eu 73 fl es X es V. 73 fl S © 1M w fl CU S 73 JH es "fl o 73 73 es es X 73 fl S o im es fl _© "co fl cu •*•» .cu "fl o *s cu ^ s 4 w> eu .2 fe 5 eu ox) es S £ 2 £ •= E 0 scu -A cu eu fl g .a -2 73 PQ cu eu fl cu fl cr CU co 64 Local joint angles, velocities, moments, and powers were described as the relative motion of the distal segment to the more proximal segment. Joint angles were described by a sequential Euler ( X , Y ' , Z" ) rotation sequence (see Figure 4-lc). These angles are referred to as a, P, and y and correspond approximately to clinical descriptions of flexion/extension, ad/abduction, and in/external rotation angles (Grood & Suntay, 1983) and have been used to describe motions in the upper extremity (Biryukova et al., 2000; Prokopenko et al., 2001). Muscle moments were determined by a recursive Newton-Euler method (Meglan, 1991). Joint powers were computed as the product of joint velocity and moment. Joint moment and power analyses during reaching have previously been shown to be sensitive indicators of neurological impairment (e.g., Riener & Straube, 1997). Development of kinematic and kinetic equations can be found in Appendix VTL While our model accounts for movements from all seven joints of the upper extremity, preliminary inspection of biomechanical profiles indicated that - regardless of arm condition - reaching tasks in this protocol were executed largely without rotations of the wrist or forearm. As such, we restricted our analyses to flexion-extension of the elbow and the three rotational axes of the shoulder. To facilitate comparisons between subjects, kinetic profiles (i.e., powers and moments) were normalized by subject mass. From individual profiles we calculated joint configuration (maximum change in joint angle) and kinetic (power peaks - peak generation and absorption) parameters. A l l profiles were then converted to a time base that ran from 0 to 100% of movement to further facilitate comparisons between subjects. Representative profiles from individual trials of the more affected arm (mild, moderate, and severe impairments) were graphed with ensemble-averaged biomechanical profiles of healthy arms. 65 Muscle Activation E M G profiles were normalized by maximum voluntary contractions (MVCs) and the mean percentage of muscle activation (PMVC) was determined across the entire movement. In preliminary analysis, P M V C measures were shown to be more reliable than mean values of unnormalized E M G profiles. A l l profiles were then converted to a time base that ran from 0 to 100% of movement to further facilitate comparisons between subjects. Representative activation profiles of the more and less affected arms were graphed with ensemble-averaged activation profiles of healthy arms. Statistical Analysis Statistical analyses were performed on hand path/trajectory, posture, kinetic, and muscle activation parameters. Relative reliability using intraclass correlations, ICC(1,1), (Shrout & Fleiss, 1979) and absolute reliability using the standard error of the measurement (SEM) (Eliasziw et al., 1994) of the parameters was determined for each parameter across the five trials (intra-session) and across the two days (inter-session) for the stroke participants; SEMs were expressed as a percentage of mean scores. Subsequent analyses used the mean values from tests on the first day. Preliminary analyses indicated that there was little difference in any of the parameters between the non-dominant and dominant arms of healthy participants, so further analyses included only the non-dominant arm. The use of multivariate analysis protects against substantial inflation of finding differences between conditions by chance which occurs when running multiple univariate analyses (i.e., maintains chosen magnitude of type I error). It also provides a more powerful method of finding differences between conditions when predicted variables are 66 correlated and when differences of each predicted variable are too small to be detected alone (Zar, 1999). Used in combination, multivariate and univariate analyses allow for the global protection of type I error while being able identify differences in individual parameters. Multivariate analyses of variance (MANOVAs) were used to assess the effect of arm condition (more and less affected side of individuals with chronic stroke and non-dominant side of healthy control participants) on hand path/trajectory, joint configuration, kinetic, and muscle utilization parameters; height and speed conditions were also entered as factors within these M A N O V A s . Using the same model designs, analyses of variance (ANOVAs) were run for each parameter. This statistical analysis is summarized in Table 4-2. Post-hoc Duncan's comparison tests were used to identify differences among arm conditions. Within the more affected arm condition we evaluated the relationship between motor impairment (Fugl-Meyer) and hand path/trajectory, configuration, kinetic, and muscle utilization parameters using Pearson product correlations. Scatterplots of parameters and motor impairment can be found in Appendix VHI. Prior to testing the effects of height and speed conditions (i.e., fast vs. self-paced) on neuromotor planning, we conducted A N O V A s in each arm condition to confirm that speed condition indeed had an effect on movement speed (i.e., peak hand velocity). We then performed 2-factor M A N O V A s to examine the effects of changing static (height) and dynamic (speed) task demands on neuromotor planning as evidenced by joint configuration parameters. Concurrent A N O V A s were completed for each parameter. 67 CD 13 ti T3 O u-'3b . d cd l-i o d o CD X W I-I o cl >> o O r=j CD I-1 O C! 3 o S CD fe 2 ' S 13 Q I-I o •c CD 12 ' 3 13 Q 13 IH CD 13 o CS r H ffl CO OH CD O s cd cd r H o r S o cd r H PQ CO DH CD O 'P. H CfH o Td cd CD rC| Cl o h-1 +3 CD S £ •H ° .a g -2 fe r H o CO CD CD o r d © u fe X r H o H - » o d r H TJ l5J o r d r H o -4-» o T3 r H o t3 r H r — CD cd 3 fi 3 CD rB ^  cc) fi CD r H o co d !S - ^ H o x r O ^ W g X fe d o d CD CO CD l-i, & l ti I T3 CD 1 3 If* 13 iS r^ l "3b . d 'to cd CD r H d o U . d ' 3 co CD 'MI 3 d o CO 3 x I f . 2 X r 2 fe I-I CD o r d 00 d o o d 1 O o d <3 cd d o 'U +-» o r H ^ CD 3 fi oo pq r ^ S cd fi CD d o CO d 1 * I w S d 2 'x r3n fe CD CD Cd' |H H le d ^ o <L> I CO J> 1 3 w PH X r-H 3 ffi CD ^ _! X CO - H co co CD d +-» o CD I-i d CD fi CD O r 3 "PH co Q i - l d CD CD J "EH CO 00 d o d CD H—I V / J 2 M CD 00 > O < > O <zo>< -> 6 8 Results Reliability There was less intra-session than inter-session parameter variability so for brevity only the inter-session reliabilities have been reported. Both relative and absolute reliabilities have been averaged across directions, joints, or muscles where appropriate (see Table 4-3). In the more affected arm condition, the reliability of the brachioradialis muscle P M V C (ICC=0.16, S E M % =106.4) was substantially less than other muscle groups and was therefore removed from subsequent comparative analysis. Table 4-3: Intersession reliabilities Parameter More Affected (n=12) Less Affectet (n=12) ICC % S E M ICC % S E M Directness 0.96 1.13 0.78 4.12 Displacement 0.82 31.63 0.64 33.50 Skewness 0.75 205.74 0.71 267.90 Kurtosis 0.97 1.18 0.56 0.53 Segmentation 0.74 14.56 N / A J N / A J Angular Change2 0.96 15.54 0.68 36.19 Kinetic Power Peaks2 0.96 7.72 0.83 15.00 Mean P M V C 2 0.87 21.26 0.96 13.26 Hand Path & Trajectory In both the non-dominant and less affected arm conditions the path was slightly curved and the velocity profile was (See Figure 4-2) substantially bell shaped. Kinematic descriptors, particularly the directness parameter, were significantly affected by arm 2 Averaged Reliabilities reported 3 All segmentation scores in this grouping were 1 so reliability statistics were undefined. 69 condition and correlated with impairment level (see Table 4-4). The multivariate Wilks' Lambda statistic of 0.630 was significant, Multivariate F (12,526) =11.349, p < 0.001. % Movement Figure 4-2: Tangential velocity profile of the hand for mild (dotted line), moderate (dashed line), and severe (dot-dash line) impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard deviation - faint dotted line). Velocity is shown on the vertical axis and normalized movement time on the horizontal axis. Notice how the profile becomes progressively more skewed and less smooth as impairment increases. 70 es E H A es es H o CN T 3 <L> o o C N CD o CO co u a o Q fl o Z C N fl o '§ t i o u i n a s ¥ o oN i n O N O O C O o O N C O O N O O C N O N O O ro O N co O N O N © O N 0 0 O N O O c--O N o O N O N oo o 06 15 r o c o O o o C N o © , O N C N O V O o o o o o 0 0 o o © C N o © o » O N O O o © o C N o o o "3-o o o o o C O o © r o C N o © o -*-» IT) C N o C N r o O fl a CO Q 0 O r o CN © O N C N 0 0 C N C N O O I 0 0 o o o oo r o oo O o o O N C O fl a Hi a a CO Si 00 r-0 0 r o ©' r--c o IT) I odl o -4—» l/-> C N V O r o I vd 0 0 o 0 0 r o O O IT) r o C N l - H O O C O r o I C N O IT) o vo vo C O r-O N C N O -*-» O N C N i n O N C Hi C a D 00 O oo m oo r o m c o IT) O N C N co O a C3 O is 71 Joint Configurations In the non-dominant arm condition, the upper arm was raised using primarily shoulder flexion (See Figure 4-3). Shoulder flexion was consistently coupled with small increases in the abduction angle (~0-15°) early in movement and decreases in the abduction angle (~0-10°) late in movement; internal-external rotation was always small, variable in direction and not generally coupled with shoulder flexion. Elbow movement was consistently bi-phasic with slight flexion (5-15°) occurring early and extension (10-40°) near the end of the movement. Movements of the less affected arm were qualitatively similar to those of the non-dominant arm. Elbow movements of the more affected arm were also bi-phasic but unlike the non-dominant and less affected arm conditions, there were prominent abduction and internal rotation movements. While the absolute timing and magnitude of abduction and internal rotations varied between participants, events characterizing these movements and those of the elbow were coupled. Abduction was associated with elbow flexion and internal rotation was associated with elbow extension. Abduction peaked with elbow flexion early in movement (i.e., < 50%) before decreasing slightly midway through movement. Internal rotation was initiated at the same time as elbow extension and increased gradually until the end of movement. Events typifying elbow flexion and extension phases occurred earlier in the overall movement than the other arm conditions reflecting the skewed velocity profile of the hand. Joint rotations of the more affected arm were also characteristically less smooth than those of the other arm conditions. 72 < - u o i p n p p v - u o i p n p q v - » ( S 9 9 J § 3 Q ) $ j s p j n o q s <—uoixsij-uoisuarxg—> ( S 9 9 J § 3 Q ) TO Avoqjg <-UOIX9JJ-UOISU9JXg-> ( S 9 9 J § 9 Q ) » J9p]noqs o o <-JBUJ9}UI-[BUJ9JXg—> (S99J§9Q) k igpinoqs s o cu - a 5 *-.9 a ! - r > 2 s o ™ «o .9 O a IT s a a -a ts a ^ l § u -a s a T3 CS -s <» ? -a a « o — V C es 3 £ 2 « 1 3 3 O co p s O J 3 s —' co B .S .2 « -•^ CS ^ ** V 3 3 O .2 ^ * . »2 3 u '5 -S 3 3 3 o cu f l — <u C o <~ St •3 I 2 ^ .3 O S --a H J CS 1 2 3 OJ wo -S E 8 i j -2 3 w es a 9 > g » s a - O es -S e a cu co 3 r H •a cu CU CS 5 M W <w § CJ >• ^ 3 -a "3 cu S 3 es ^ 2 « ts ^ 3 5 | : 2 3 ^ v S 2 .S « « TS 2-5 « CU X! C >• es JJ o 2 & a a 8 .^ " X! 3^ o « .SS ^S Xi co _ ~ co 3 _ cu > O I . 2 TJ O w es fll « a a co 5 o o a * CO Or © 'a « 5, es ,eu eu > 3 O .a © o o -a 5 I XI >5 73 Joint configuration variables, most noticeably the abduction and internal rotation angles, were significantly affected by arm condition and correlated with impairment level (see Table 4-5). The multivariate Wilks' Lambda statistic of 0.573 was significant, Multivariate F (8, 528)=21.22, p < 0.001. 74 CN II O -*-» o <+H < o o C N h 3 on cl o U U in ON CD U \ ° in ON a o |Q i l | M H C N C N in ON CD CD 'o „ u p . 00 in o o C N C N in o -4-» r o r n ON vd T f , oo o ON T f m oo oo r-^  T f o w> vq c o T f ^ in in T f C N CO in vo C N ON T ^ O C N C N in m T f vd Cl cl o ,o 'x '% CD O GO ^ r--o oo o VO ON VO VO ON ON r o ON ON C N vd T f VO O i CO 00 C N r o VO in in T f vo © r o C N V O in vo vq od ON C N O o o T f V O C N C N r-oo CO o as ON oo C N VO oo T f © T f 00 o r o CD 2 t\ 6 • f l ii ON in T f C N VO O © o C N ON r o c o C N C N in T f r o © o vo m vo o in C N t--T f C N © l - H I o o VO l - H vd o C N r o T f T f C N T f o v 'x o --H co 75 Kinetics In the non-dominant arm, shoulder moment was predominantly flexor. In the early phase of movement, this moment was primarily due to joint acceleration and then asymptotically approached a value that was largely determined by the gravitational moment of the arm. The moment at the elbow was always flexor, increasing during elbow flexion (peak at ~ 15-30% of movement time) and decreasing during elbow extension. Moment profiles of the less affected arm were qualitatively similar to those of the non-dominant arm. In the more affected arm, there was a reduced flexor moment that coincided with a large increase in abduction moment; this compensation was particularly evident early in the movement profile. The flexor-extensor moment pattern of the elbow was similar to the non-dominant and less affected arms but more variable. Internal-external moment profiles of all three arm conditions were bi-phasic (first internal then external) but were small in magnitude. In the non-dominant and less affected arm conditions, shoulder power (see Figure 4-4) was primarily flexor and concentric (generation) in origin with a peak occurring slightly after the midpoint of movement. Elbow power was bi-phasic and, as expected, primarily along the flexion-extension axis; this power was initially concentric (generation) while the elbow flexed and eccentric (absorption) as the elbow extended under the force of gravity. Changes in the power profile of the more affected arm were consistent with changes in the moment profile. There was a large increase in abductor generation power that coincided with a large reduction in flexor generation power. Elbow power remained bi-phasic but with substantially reduced generation and absorption peaks. 76 M .2 o fl <: A s T 3 < t> 3 o .fl O O cu A _o ' Lo fl CD •*-> X w fl o CD s-l CD T3 3 o .fl 00 io o Q; cn co • O L •*—' iK cu ^ ^ T 3 > CO CO = O g j g i C ) i i i i i t i i \ V b < — U O T J B J 3 U 9 £ ) - uondiosqv-» < - U O T J B J 9 U 3 0 - uoudiosqv-» ( § > [ S / U I -JS[) J 9 A V 0 J ( § } [ - S / U I - N ) J 9 A V O J fl fl CD w fl o -x CD o -fl CD w a CD fl" CD 00 fl 9 O - f l s» ^  - . a 5 a -= £ 2 2 © A 2 JS « s. <» 5 © cu 73 fl S ? fl ts fl w ,-3 .2 « « A *B p 3 W PH 2 "« • * '-3 >: u u '** V u « 73 >• W) s S fl CO fl — ^ O A 6 fl -2 ^ p-a © ** .2 -fl 2 a w -Q § .2 « s 2 ? * SI fl o a, o a > 'R *S ' f l ,2 .S 'S C o o fa --s ft -S • a fl .2 5 o S .2 .fl fl A co CJ CS — A. X 4 1 a 2 CU 73 ^ A eu-o -a s U V ^ s g « i 4) ^ PH 73 O . co £ .a 5 ^ w .2 T3 73 « S o fl o «fl « # g CU fl o 3 -2 -fl 2 -2 -fl s» »• fl eu p-j O £ § cu PH « .S « fl _V CU fl s = £ « W O * % E .s a eu S -fl 2 o «« +•» cu « i a * 0 co a s Lm CO « U -2 | 5 o, « o CU A 1 8 a -fl £ 8 © ^ « co S b cu 73 -2 a A -s S 2 ^ a .1 .s *a flf a / — s fl 5 0 o * -« 'A 2 ? A fl -fl > -2 ^ a w ^ .2 P fe A S -o g " A - 3 73 * ? fl ^ fl «^ r.2 S fl 3 fl 05 A 73 73 es 2 O es „ es O S | 2 CU CU 2-1.2 cu ® -cu co eu 73 § « 5 " « 2 eu eu « fl >• tJ a « cu CJ -fl S A S .2 o es X 3-f l^ 77 Our descriptive analysis of power profiles indicated functionally relevant power peaks (i.e., contributing substantially to total movement power) of shoulder flexor generation, shoulder abductor generation (particularly in the more affected arm condition), elbow flexor generation, and elbow flexor absorption. These peak power variables were significantly affected by arm condition and correlated with impairment level; the shifting of power generation from flexor to abduction origin was particularly noticeable (see Table 4-6). The multivariate Wilks' Lambda statistic of 0.480 was significant, Multivariate F(8, 528)=29.307, p < 0.001. 78 a jo C5 S-<U a <u O a es a © © Vi X i < o PH VO I TT JO X l « o <N -rn o <£ O H <, CO t-i o o C N CO o CO CO O i-H o Q I fi o r-C N co . , S 8 ? co, o PPI d o «3 CO u ON 9 ca U m ON VO m vo o as o o T f VO 00 TJ-vo <N O O -t-» r -co C N o o VO CN ON ON CN © o -rn CN VO C N © 00 CN co T f I 2 S d .2 § g x § 3 co cn T f VO o oo T -H C O o o o -r-» vo T f <N o d , CN O O CN o ON CN © © o vo o o C O ON O O UO vo o ON t-H CN O o d d o o -*-» -+-» r- vo o r--© o o d , d , vo vo i n CO o CN o o © d co C N C O GO " J H i o ?3 d i s O <! oo vo T f vo CO o d o -4—» VO r -CN o d , o CN CO o CN oo wo o d o -«-» i n ON T f o ON C O i n o d co o d T f I .2 § a • SH CO -rn 4 - * S x s * d oo vo o d C O C O <N o o O C N O C O o vo o T f o T f C O o d o T f T f o ON CN VO o T f 00 T f o ON ON vd i n W d i ° • r H co d d o CO • r H •+_» • ° r - H < E a OS 00 o ca y >H OH o ca * o E « S l T3 O £ U 9. <** 5§ ° ca 0 1 ) bO T3 o -a tn ca ca a £! o C H - U T3 O 1=1 6 "O o '$ & rn - r t P 00 O — 1 CJ T3 *H cj H-» 0 o .S3 o C cn ca w & " 1 o JB o o w S £ o -2 ^ 1 l l 79 Muscle Activation The pattern of muscle activities was similar across the non-dominant arms of healthy participants and unaltered by ensemble averaging. Consistent with previous studies of reaching in three dimensions (Flanders, 1991) and the sagittal plane (Flanders et al., 1996), waveforms exhibited both phasic (speed-related) and tonic (gravity-related) components. Deltoid activity was characterized by increased tonic activity at movement termination and by phasic bursts occurring early and late in movement; the magnitude of the phasic and tonic activities was largest for the anterior head and smallest for the lateral head. The same activation pattern was shared by biceps brachii. Brachioradalis had a phasic burst at movement initiation. Triceps (long head) activity was characterized by a single burst occurring midway throughout movement. Activation patterns of the less affected arm were similar to the non-dominant arm of healthy participants. The clear tonic and phasic activities in the non-dominant and less affected arm conditions were not present in the more affected arm condition. Activation patterns were highly variable across participants and included pattern abnormalities such as segmented activation, co-activation, prolonged firing, and changes in recruitment and burst timing (See Figure 4-5). For all muscles, the percent of maximum voluntary contraction increased significantly for the more affected arm condition with increases correlated to impairment level (see Table 4-7). The multivariate Wilks' Lambda statistic of 0.574 was significant, Multivariate F (8,418)=13.36, p <0 .001. 80 (a) Anterior (b) Lateral Deltoid u 1 o 50 100 % Movement (c) Biceps Mild(SR10) 1 Moderate (SR12) — • Severe (SR19) Healthy Average Healthy Std. Dev. 0.5 A / V. / " * \ & ^ « ^ ~ / 0 0 50 100 % Movement (d) Long Head of Triceps Figure 4-5: Normalized muscle activation profiles for the (a) anterior deltoid, (b) lateral deltoid, (c) biceps, and (d) triceps (long head). The percent of maximum voluntary contraction (PMVC) is shown on the vertical axis and normalized movement time on the horizontal axis. Profiles are shown for mild (dotted line), moderate (dashed line), and severe (dash-dot) line impairments of the more affected arm compared to the healthy average (solid line) and range (1 standard deviation -faint dotted line). Notice how the PMVC patterns saturate and become irregular with increases in impairment. 81 o CN cu -t-» o < CD S-H O O CN T3 CU -4—» o <: C O C O cu o T o Q o co HH CN C N C U + -cu OH O 13 tl o O CU o uo O N uo ¥ cd o CC5 r H PQ m , P H cu o • r H PQ ON © • c/3 « oo .S3 o 82 Speed & Height Effects Increases in height had a significant multivariate effect on joint angles in the non-dominant F[(8,102)=28.48, pO.OOl], less affected [F(8,208)=12.96, pO.OOl], and more affected [F(8,206)=10.00, pO.OOl] arm conditions. Across all arm conditions, univariate tests revealed that increases in height were significantly related to increased shoulder flexion, shoulder abduction, and elbow extension (all pO.OOl) but not to internal rotation of the shoulder (all p>0.05). Figure 4-6(a) shows that abduction angle increases with target height and that these increases are largest in the more affected arm condition. 'Fast' reaching speeds were significantly greater than 'self-paced' reaching speeds in the non-dominant [F(l,58)=13.25, pO.OOl], less affected [F(l,lll)=16.15, pO.OOl], and more affected [F(l , l 10)=9.34, pO.OOl] arm conditions. Across all arm conditions, reaching speed (i.e., fast vs. self-paced) had neither multivariate nor univariate effects on joint angles (p>.05). In one sense, the lack of evidence for speed effects amounts to acceptance of the null hypothesis (that movement speed has no effect on joint configuration). Therefore, we computed the power of our statistical analyses to reject the null hypothesis when it is false (Zar, 1999). The multivariate powers for the non-dominant, less affected, and more affected arm conditions were 0.593, 0.120, and 0.103 respectively. In contrast to the effects of target height, Figure 4-6(b) indicates that abduction angle does not change with reaching speed. 83 84 Discussion The purpose of this study was to assess the effects of arm condition and the differential effects of speed and height within arm conditions on the control and execution of unrestricted reaching movements. We used hand path and trajectory, joint configuration, kinetic, and muscle activation measures to characterize movement. In general, the absolute reliabilities of these measures were excellent in both the more and less affected arms (note that the zero centering of skewness and displacement scales tended to inflate their respective normalized S E M measures). The relative reliabilities of measures were also excellent in the more affected arm but were reduced in the less affected arm, most likely reflecting the similar functional status of arms within this condition. The poor reliability of P M V C measures in the brachioradialis muscle of the more affected arm may have been a reflection of abnormalities in the recruitment of hemiparetic muscle (Gemperline, 1995). A l l measures were sensitive enough to find an effect of arm condition (with more affected always being different). Joint configuration was independent of speed but dependent on height in all arm conditions; joint configuration changes of the more affected arm condition with height were more pronounced (i.e., larger change in angles) then those of other arm conditions. As observed in this study and other studies of stroke, differences in both arm condition and task requirements result in simultaneous and moderately related (e.g., Kamper et al., 2002) changes to several neuromechanical parameters. Our approach to describe movement patterns in a multivariate sense is consistent with the presentation of such coupled parameter changes. 85 Coordination of Movements: Non-Dominant and Less Affected Arms Unrestricted movements of the upper extremity are executed with seven mechanical degrees of freedom. Reaching tasks in this study specified the terminal position of the hand (i.e., target) but not the posture of the arm. In addition, the central nervous system was free to use any hand and joint trajectories between the start and end of movement. With the initial posture of the upper limb in the same para-sagittal plane formed by the targets and starting position, reaching tasks could have been accomplished entirely through shoulder and elbow extension. The net joint movement (i.e., stop-start) of healthy participants was consistent with this prediction. However, the elbow flexion that preceded the required elbow extension suggests that the control of joint motion is not strictly predicted by external spatial factors. This early elbow flexion could be secondary to the initial use of biceps (a bi-articular flexor) to power shoulder flexion but the co-activation of brachioradialis suggests that elbow flexion was planned. In fact, elbow flexion is advantageous because it temporarily reduces the shoulder lever arm to the upper limb center of mass and thus the required shoulder flexor torque. The non-involvement of wrist and forearm joints found in preliminary inspection of healthy is likely because the primary functional use of these joints is in orienting rather than positioning the hand. The resulting hand kinematics of the non-dominant arm were characteristically direct, non-segmented and unskewed. Hand path and trajectory measures of the less affected arm were similar to those of the non-dominant arm although there were small but significant changes to joint path and kinetic patterns (i.e, increased abduction). The ability to generate torque in the less affected arm is reduced relative to healthy persons (Chapter 3; McCrea et al., in press). 86 The combined abduction-flexion movement likely facilitated a wider recruitment of muscle fibers across the deltoid so that a sufficient shoulder torque could be developed. The fact that hand kinematics were seemingly unaltered points to the adaptability of the CNS to exploit the mechanical redundancy of the neuromuscular system. Degrees of Freedom are Neurally Constrained Wrist and forearm joints remained uninvolved in reaching movements of the more affected arm. Because motor impairment following stroke typically increases in the proximal to distal direction (Colebatch & Gandevia, 1989), it is unlikely that distal joints would be used to compensate for reduced function of proximal joints. Despite the redundant mechanical degrees of freedom available in the arm and the variety of impairments that may occur after stroke, compensatory movements were stereotypical and described by increasing abduction and internal rotation related to level of impairment. The temporal couplings of abduction with elbow flexion and internal rotation with elbow extension were also stereotypical. These couplings are consistent with the description of flexor (elbow flexion, abduction, and external rotation) and extensor (elbow extension, adduction, and internal rotation) pathological synergies that emerge following stroke (Brunnstrom, 1966). Unlike the less affected arm, there were concomitant deficits in the quality of hand kinematics which suggest that abnormal joint couplings were neither purposeful nor favorable. We believe that the common patterning of joint motion provides evidence that the occurrence of stroke neurally constrains the inventory of joint synergies that may be expressed. In addition to operating muscles near their capacity, changes in temporal (segmentation and prolonged activation), and spatial (co-activation) features observed in 87 the more affected arm during reaching would specifically limit neural coordination strategies. Neural restrictions have been previously proposed as the mechanism that leads to a loss of directional hand control during reaching movements in severe motor impairment (Reinkensmeyer et al., 2002). Certainly this is the case during hemiparetic isometric force generation as the inability to isolate torque generation to selected joints (Dewald & Beer, 2001) coincides with abnormal co-activations between elbow flexors and shoulder abductors and between elbow extensors and shoulder adductors (Bourbonnais et al., 1989; Dewald et al., 1995). Abnormal neural coupling could be due to altered descending commands from the cortex, or a greater reliance on brainstem pathways with more diffuse connectivity that span several motor neuron pools (Colebatch et al., 1990). Abnormal coupling could also be due to a spinal mechanism, caused by a change in the tonic firing level of interneurons, thereby increasing the excitability of selected motor neuron pools (Lundberg, 1975). Reduced levels of sensation could also constrain neural control and planning because it would limit the afferent information (i.e., feedback from muscle spindles, Golgi tendon organs, and tactile sensors) that is used to form and update motor plans. Alternatively, the common patterning of joint rotations for reaching movements of the more affected arm could result from geometric limitations on joint range (i.e., contractures) as it has been shown that small reductions in joint ranges results in large reductions in the number of potential movement synergies that can be expressed (Kamper & Rymer, 1999). However, participants were excluded from the study i f they had significant impairments in the active range of the shoulder and/or elbow. In addition, while not reported in this study, we found that the passive ranges of shoulder and elbow 88 joints were largely unimpaired in the more affected arms. Another possibility is that stereotypical pathological reaching patterns could emerge i f the distribution of upper extremity muscle weakening was similar across participants and movement planning compensated for kinetically based deficits (Also see the following section). This is also unlikely because weakness distributions following stroke tend to be individualized (Colebatch & Gandevia, 1989) and our participants demonstrated heterogeneity in lesion type, side, and location. Hemiparetic Adaptation to Static But Not Dynamic Demands In each arm condition, flexion, abduction, and elbow extension angle (but not internal rotation) increased with height. Similar changes in mean shoulder flexion and elbow extension angles were observed across the different arm conditions and can be predicted by the geometrical implications of increasing the target height. Changes in shoulder abduction angle, however, allow for loads to be distributed across a larger muscle mass (i.e., use of lateral deltoids) and are likely favorable planning adaptations to increased neuromuscular demands. This adaptation was mild in the non-dominant arm condition, moderate in the less affected arm condition, and pronounced in the more affected arm condition. This graded increase in abduction angle with arm condition coincided with increases in the peak abductor generation power. The near saturated levels of shoulder flexor and abductor muscle activity suggest that this adaptation was necessary in the more affected arm condition. According to our hypothesis that movement would be optimized for the total kinetic effort, we should have observed larger abduction angles in the 'fast' condition than in the 'self-paced' condition. We found, however, no statistical effect of speed 89 condition. In addition, while our power analyses were weak, they represented the ability to reject the null hypothesis in favor of a statistical effect that contrasted the kinetic optimization theory (i.e., increasing abduction angles are associated with slower movements) because of the slight data trend. The results of this statistical analysis, we believe, suggest that joint configurations are likely invariant with movement speed. This observation was made across all arm conditions, regardless of the task. For the non-dominant arm condition, this finding is consistent with rigorous studies of speed invariance during planar (e.g., Atkeson & Hollerbach, 1985; Soechting & Lacquaniti, 1981) and 3-dimensional reaching movements (Nishikawa et al., 1999; Soechting et al., 1995) but for the more and less affected arms of persons with stroke this finding is novel. In healthy individuals, speed-invariant hand and joint paths have been taken as evidence for kinematic based motor planning (Bizzi et al., 1992; Feldman, 1966). In kinematic planning, a variety of movement speeds are achieved by time-scaling joint and hand paths. Recently, it has been shown that kinematic based motor planning may result from the optimization of separately driven antigravity and dynamic force drives (Nishikawa et al., 1999; Soechting et al., 1995). Speed-invariance occurs because the dynamically optimal posture depends only on the geometry of the mass distribution of the arm, with movement following the path of least inertial resistance. Biomechanically, this partitioned optimization is disadvantageous when compared to optimizing the drives together (i.e., minimum dynamic + gravitational torques) because it requires more kinetic and thus more muscle related consumption of metabolic energy (Hogan, 1984) to execute movements. 90 The observation of speed-invariant postures following stroke indicates a preservation of kinematic (or partitioned kinetic) motor planning schema in the presence of motor impairment. From a computational and motor learning perspective, kinematic based planning is advantageous because a family of joint trajectories (i.e., common paths) needs only one inverse dynamics computation with linear scaling in speeds related to quadratic increases in joint torque demands (Sciavicco & Sicilano, 2000). This is also advantageous for learning because speeds can be increased without changing visual-aspects of arm movements. While movement scaling seems to occur on a kinematic basis it does not preclude kinetic factors such as peak available torque from acting as factors in path planning. In fact, our finding that increased gravitational demands (i.e., higher targets) relate to progressively more distributed activation of muscles and shared loading strategies reflects the importance of such kinetic factors. One possible motor planning scheme that we favor (for its consideration of both kinematic and kinetic planning) would have the speed-invariant joint path set decided from a kinetic optimization of the neuromuscular demands of a ballistic paced reaching movement (presumably the most demanding). The resulting path could then be time-scaled for any sub-ballistic reaching speed as slower movements along the same path would require less kinetic output (i.e., maximum joint torques). Other factors such as the net joint pain/comfort over a movement (Cruse, 1986; Cruse et al., 1990) may supercede the importance of kinetic variables and may ultimately be the determining factor in choosing path invariant families. 91 Limitations & Future Considerations This study examined the differences in reaching characteristics among arm conditions without matching reaching speeds and one may argue that such differences are related to the naturally slower movements of the more affected arm condition. To examine the potential confounding effects of reaching speed (and not arm condition) contributing to differences in parameter values, we also ran multivariate and univariate analyses of covariance using peak tangential hand velocity as a covariate. The F-scores of models with the covariate remained significant between arm conditions but because multiple comparison post-hoc tests are not well established for covariate models we have not reported these results. By using hand speed as a covariate, we were not only able to account for this effect but we were also able to have participants move at their natural speeds. In addition, the speed invariance of posture formations observed within each arm condition suggests that the same parameter differences would have been observed i f healthy participants had matched their reaching speeds to those by participants with stroke. Another possible limitation of this study is the scope of our inverse dynamics model. During free reaching movements, the net torque at joints is due not only to muscle activation but also to the effects of gravity, joint viscoelasticity, and 'interactive' torques that develop from movement at other joints. Our inverse dynamics analysis determined the net muscle and visoelastic torque at each joint that would produce the observed motion but did not independently report the contributions of interactive torques. While important to anticipate during supported horizontal tasks (Beer et al., 2000), the impact of interactive torques on movement patterns in sagittal tasks is likely reduced 92 because of the increased muscular forces needed to support the arm against gravity. Our inverse dynamics analysis also did not partition torques due to passive viscoelastic tissue properties from active muscle contractions or sub-divide the torque contributions of antagonistically acting muscle groups. Determining the contribution of these factors to upper extremity biomechanics during reaching requires modeling of both joint viscoelasticity in hypertonia (e.g., Chapter 2) and the natural joint impedances. Our measures of muscle activity, however, give an indication of how muscle torques change at each joint during movement and do not require extensive testing (likely tiring the participant) to determine model parameters. Muscle activity causes torque generation producing joint motion that results in hand motion. While we did not explicitly examine this intrinsic causal flow between neuromechanical variables, we did observe changes in variables at each sensorimotor level that were proportional to impairment. Statistical (correlations and path analyses) and neuromuscular models could be used to specifically examine how changes (i.e., impairment) at higher levels manifest as changes at lower levels. Decreases in movement quality occur not just as targets increase in height but also as targets move more forward and contralateral (Kamper et al., 2002; Levin, 1996; Reinkensmeyer et al., 2000). Future studies also need to investigate the joint biomechanics and muscle activity that underlie these directionally dependent changes as activities of daily living often require movements in non-sagittal planes. With a wider variety of tasks and through the use of discriminant analyses, it may be possible to identify movement pattern sub-groups within the more affected arm condition - possibly related to lesion location. Our study, 93 however, suggests that movement patterns would not be discretized as such but would follow a continuum related to motor impairment. Conclusions & Clinical Implications Despite the variety of impairments that may occur following stroke, reaching movements of the more affected arm are executed in a predictable fashion in which joint motions are pathologically linked. This indicates that the synergies of the neuromotor system are constrained following stroke. Similar to healthy and less affected arms, the joint paths of the more affected arm during reaching movements are speed-invariant while changes in response to increased gravitational demands (i.e., height) are more pronounced. This adaptation to static but not dynamic demands suggest that neuromuscular capacities may play a role in the selection of an appropriate set of joint paths which can be time scaled for a range of hand trajectories. Improved function may result i f more specific motor pathways can be utilized and i f the response characteristics of muscles are improved. Targeted strength training may provide a means to improve the speed and magnitude of muscle contraction. Plastic re-mapping of cortical regions (Ramachandran et al., 1992) through forced use of the arm (Taub et al., 1993) may facilitate more specific control of these muscles. 94 Chapter 5 : General Conclusions Impaired upper extremity motor control is common following stroke and can interfere with one's ability to complete activities of daily living. Multiple aspects of impairment are related to activity limitations (Harris & Eng, 2003). It is therefore important to understand the physiological nature of these impairments and their contribution to motor behaviour so that effective theory based interventions can be developed. In a series of three experiments, this work has identified specific disruptions to the controllability and responsiveness of the neuromuscular system in persons with chronic stroke. Here, we outline the findings of these experiments and then integrate our work with other studies in stroke and recent findings in motor control and learning within a theoretical model of post stroke upper extremity motor impairment. General Findings and Future Work In the first experiment we validated a linear spring-damper model of the passive torque response of the elbow to extension stretch and found that mechanical parameters of stiffness and damping were quantitatively related to clinical impairment measures of hypertonia. The second experiment characterized the active torque responses of eight upper extremity joint actions to maximal voluntary increases, maintenance, and reductions in neural input. We found magnitude and temporal impairments in torque response characteristics of not only the more but also the less affected arms when compared to healthy individuals. When considered in functional terms, the motor variables determined from experiments 1 and 2 indicate that a decreased ability to 95 modulate joint torque would limit the timely responsiveness of the neuromuscular system. The final experiment examined the muscle activation and joint biomechanics underlying natural unrestricted hand motion. Results suggested that movement in stroke is planned in a similar fashion to healthy (i.e., time scaling of path) but that the expression of movement strategies is neurally constrained; the degree of neural constraint increasing with motor impairment. We made qualitative inferences between identified musculoskeletal deficits (experiments 1 and 2) and changes to the control and planning of movement (experiment 3). Quantitative predictions of how changes in weakness and hypertonia affect reaching behaviour have yet to be made. As suggested in the discussion of the final experiment, certain behavioural parameters of reaching such as peak velocity and abduction angle (i.e., an abducted joint path) may well be determined from interactions between task difficulty and musculoskeletal impairments. Mechanical models (e.g., Nadeau et al., 1996) and correlation analysis could be used to establish clinically important associations between motor variables and behavior so as to guide interventions. Reaching (and many other upper extremity) movements occur over a small period of time so changes in temporal factors (i.e., generation and relaxation times) may be particularly important. Another potentially important dimension of torque generation (not examined in this study) is change in the length-tension relationship of muscle in persons with stroke (Ada et al., 2003). Future studies also need to investigate how musculoskeletal parameters change with interventions (conventional therapy, neuromuscular blockers, and constraint induced therapy) and how control and planning mechanisms adapt to such changes. 96 Motor Planning, Control, and Learning Impairments in Stroke Arm motion is regulated by the sum of feedforward and feedback controller motor commands. Following stroke, there is an increased reliance on the feedback control of reaching (Trombly, 1992). Studies of healthy individuals suggest that the feedforward controller specifies a motor command using an inverse model of the arm (and environment); in parallel, a forward model predicts the next state given the current state and motor command. Together these models are referred to as an internal model. A n internal model is trained (learned) by minimizing the difference between actual movement and its prediction. Reduced compensation for interaction-based torques (Beer et al., 2000) and poorer adaptations to perturbations (Takahashi & Reinkensmeyer, 2003) suggest a reduced ability to form an appropriate internal model. Decreased learning automaticity may be due to not only damage to areas of the brain where the model is tuned/formed but also to increased response complexity to neural commands (e.g., spasticity and neuromotor noise) and poorer state estimations of arm position. Because of time delays, the true state of the system is never known. State estimations of arm position are generated from an optimal blending of internal state predictions and sensory feedback (i.e., vision and proprioception). Sensory deficits could also lead to the formation of internal models which are inconsistent with arm behaviour. While state estimations are continuously available, sampling and acting on the differences between desired and current states may occur at discrete time intervals; movement being the summation of overlapping submovements that result from discrete motor commands (Burdet & Milner, 1998). In healthy individuals, submovements increase with accuracy requirements (Burdet & Milner, 1998) suggesting a modulation of 97 either the sampling rate or comparator error threshold with increased internal attention to extrinsic demands. Recovery from stroke is associated with reductions in the number submovements (Krebs et al., 1999; Rohrer et al., 2002). This reduction would indicate an appropriate tuning of the internal model or a reduction in the variability (noise) of motor commands. The inherent signal-to-noise ratio of the neuromotor system (Clammam, 1969) also plays a role in planning as extrinsic demands (i.e., spatial tolerance) constrain the allowable movement variability and thus movement signal. In a related study to this thesis (McCrea & Eng, 2002), we found kinematic evidence for decreases in the signal-to-noise ratio in persons with stroke. It would seem that optimal reaching movements should consider not only the physics of the arm but also the variability of its response. Indeed, hybrid models that minimize movement error are consistent with experimental observations of smooth hand and joint paths (Harris & Wolpert, 1998). Functional recovery of the upper extremity following stroke requires the re-acquisition of motor control under a variety of contexts. In healthy individuals, interference occurs when attempting to learn multiple dynamic (Brashers-Krug et al., 1996; Gandolfo et al., 1996) or visumotor patterns (Krakauer et al., 1999) over a short period of time but not when separated by several hours. This suggests that not only are multiple task specific internal models formed but also that tuning these models requires a period of consolidation in which time they are fragile to disruption. Limited memory storage requires methods to readily generalize movement from previously generated internal models. By blending the contribution of individual internal models, each weighted by their contextual relevance, situation appropriate motor commands and behaviours could be generated (Wolpert & Kawato, 1998). Thus, a set of multiple 98 internal models could be regarded as motor primitives and the building blocks (i.e., basis functions) used to construct a repertoire of movements. Experiments in the frog's spinal cord support the concept that inexpensive motor control is achieved by combining proportions of these basis functions rather than individually controlling each muscle (Giszter et al., 1993). Accordingly, abnormal co-activations observed post stroke may represent a decrease in the functional space spanned by motor primitives. Our observation of a prevailing pathological synergy during reaching movements suggests that this loss occurs not directly from the lesion but indirectly by disrupting any of the neuroanatomical subsystems that maybe used to reinforce and recall the set of internal model structures; disuse may lead to further internal model degradation as their relevance diminishes. Theoretical Framework of Upper Extremity Motor Impairment Impairments to any of the various central and peripheral components that contribute to movement will limit the behavioural flexibility of the neuromuscular system. The collective effects of stroke related impairments on emergent movement properties can be elucidated by a neuromuscular model; results from our experiments and other recent findings have been integrated in such a model (see Figure 5-1). 99 'S-S TO ^ .ra 3 £ s; P" o 3 : i t 3 cz «o o a} w K •S i § o » 2. T3 " ' p 2 R l >S I eg e 111 "S .«-a a>.S ™ a > 1 I * S o i l iS 5 § c LU <u ^ q> * . § 6 a < o g T3 U . ° i.1 CO CO IS w a — cu a> cu 1 8 H co zj O HH I o T3 cu a s-cu cu cu g 3 to CA HM> eS CU TS 1. CU CU XI c a M § <^  *> . co -es X cu u es co — £1 3 - ° § 5 CN 3^ 3 es « TJ cu cu es 2 T3 O < -c a s «*H w3 o „ ft XI cu •»» cu a co 3 cu 3 -*H 3 .3 tS XI o co a 3 ~ 2 es >, es « .2 s A -cu es a "3 .a © TS tS — « 2 CU 3 S 'C O 5 3 a 2 CU U * - JH X *cu O 3 o 1 . be tS § -3es eg o ^ CO — . — CU a _ CU co 3 U O x 3 cu cu cu es 8 cu o s s c « s & 2 H 2 3 ^ I CU CU co 3 MH 3 ns i T 9 3 fN o o H g O 3 fN CU O r. ^ * "3 CO " CO > ~ i cu -o M l 3 3 ^H « «> -3 .a ' 3 Q ^ 3 ° s ° -e fN >-3 & cu es es cu a »H {-I § ° W CJ 4 . " .a ^ 3 4) S- 3 •8 , ' 3 V> S3 U 3 2-3 WD S* 5 J ) H 5s © O co &_ CU cu o 3 X 100 Successful reacquisition of motor skills following stroke may be facilitated by multifaceted therapies that address identified component deficits. For example, early rehabilitation efforts may be best focused by spacing mass practice of different movement tasks/contexts to avoid learning interference between internal models; the acquisition of these movements may be improved through mental imagery (Jackson et al., 2001) during the memory consolidation period which in brain injured cortexes occur within one hour (Fraser et al., 2002). With a diverse set of movements established (i.e., an orthogonal set of motor primitives), focus may shift to improving the retention of learned actions by introducing variability into movements. Concurrent strength training therapies targeted at the extremes of joint range and at higher contraction speeds may contravene structural and cellular muscle changes that are associated with spasticity (Friden & Lieber, 2003; Lieber & Friden, 2002). Motor impairments in stroke are related directly to changes in the central nervous system (CNS) caused by the lesion and to subsequent changes to the musculoskeletal system. Movement impairments are not limited to the hemiparetic arm but may also occur in what is considered as the 'good' arm. The cortical topography of limb muscles can be altered when forced to relearn movement following stroke (Liepert et al., 2000). Muscle tissue, at least in healthy individuals, also adapts to task specific training (Jones et al., 1997). A theoretical framework of post-stroke upper extremity motor impairment may lead to the development of therapeutic interventions that exploit the plasticity of both the neural and the muscular subsystems. This thesis has made modest contributions to such a theoretical framework. 101 References Ada L, Canning CG, Sheau-Ling L (2003). Stroke patients have selective muscle weakness in shortened range. Brain, 126: 724-31. Agarwal WC, Gottlieb G L (1977). 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IEEE Transactions on Biomedical Engineering, 44:1192-1209. 112 Appendix II: Informed Consent Form I N F O R M E D C O N S E N T F O R M : M e a s u r i n g A r m F u n c t i o n i n P e r s o n s w i t h A c q u i r e d B r a i n I n j u r y Principal Investigator Dr. Janice Eng School of Rehab Sciences University of British Columbia (604) 714-4105 Co-Investigator Patrick McCrea Masters of Applied Science Student University of British Columbia (604) 714-4108 B a c k g r o u n d : I understand that I am being invited to participate in this study because I have weakness of left or right side due to brain injury. I understand that my arm movement wil l be evaluated. P u r p o s e : The purpose of the study is to measure arm movements during rehabilitation in persons who have sustained a brain injury resulting in weakness of the upper extremities. S t u d y P r o c e d u r e s : I wil l be asked to move my arm in a reaching motion in different directions while sitting in chair. I wil l be asked to perform up to 100 reaching motions per session and I understand that there wil l be up to eight sessions. Sessions will occur up to once per week during my stay at the G.F. Strong Rehab Centre for a maximum of eight sessions. I understand that my arm movement will be evaluated only i f I can move my arm by myself. Rest breaks can be taken at any time. Electrodes will be put on me to measure muscle activity and markers will be put on me to measure movement patterns. I understand that each test session will take less than one hour. M y medical records wil l be used to acquire the following information: age, duration of injury, and severity and type of injury. E x c l u s i o n s : S u b j e c t s w h o h a v e h a d t h e i r t r a u m a t i c b r a i n i n j u r y o r s t r o k e l e ss t h a n 12 m o n t h s before testing will be excluded from this study. Subjects with prior history of brain injury wil l be excluded fro the study as will subjects who have previously had or currently have musculoskeletal injury to the upper extremity. Individuals will be excluded from the study i f they are younger than 19 years old. Page 1 of2 114 Risks: There is a slight chance that I may feel fatigued or experience some muscle soreness at the end of the evaluation due to muscle soreness. There is a rare chance (less than 1 in 200) that I may develop some skin irritation due to the electrode or tape. Benefits: There are no direct benefits for myself for this study. It is hoped that this information wil l contribute to the understanding of movement in the upper extremity following brain injury. Confidentiality: Any information resulting from this research study will be kept strictly confidential. A l l documents wil l be identified only by a code number and kept in a locked filing cabinet. I wil l not be identified by name in any reports of the completed study. M y medical record may, however, be inspected by the Health Protection Branch (HPB Canada) in the presence of the Investigator or her designate. Copies of relevant data which identify me only by code number may be required by the HPB, but I will not be identified by name, initials or date of birth. Remuneration/Compensation: In order to defray the costs of transportation, I will receive an honorarium in the amount of $50.00 once I complete the program. Contact: I understand that i f I have any questions or desire further information with respect to this study, or i f I experience any adverse effects, I should contact Dr. Janice Eng or one of her associates at (604) 714-4105. If I have any concerns about my treatment or rights as a research subject I may contact the Director of Research Services at the University of British Columbia, Dr. Richard Spratley at 822-8598. Patient Consent: I understand that participation in this study is entirely voluntary and I may refuse to participate or I may withdraw from the study at any time without any consequences to my continuing medical care. I have received a copy of this consent form for my own records. I consent to participate in this study. Subject Signature Date Witness Signature Date Investigator Signature Date Page 2 of2 115 Appendix III: Clinical Assessment Scales Modified Ashworth Scale Grade Description 0 No increase in muscle tone 1 Slight increase in muscle tone, manifested by a catch and release or by minimal resistance at the end of the range of motion when the affected part(s) is moved in flexion or extension 1+ Slight increase in muscle tone, manifested by a catch, followed by minimal resistance throughout the remainder (less than half) of the range of motion 2 More marked increase in muscle tone through most of the range of motion, but affected part(s) easily moved 3 Considerable increase in muscle tone, passive movement difficult 4 Affected part(s) rigid in flexion or extension Adapted from: Bohannon RW, Smith M B . (1987). Interrater reliability of a modified Ashworth scale of muscle spasticity. Physical Therapy, 67, 206-207. 116 Fugl-Meyer Upper Extremity Function Scale Upper Extremity - Sensation/Proprioception and Joint Range Test Scoring Criteria Max Score Sensation - Light Touch 0 - Anaesthesia 1 - Hyperaesthesia/dyesthesia 2 - Normal 4 Upper Arm 2 Palm of Hand 2 Proprioception 0 - No sensation 1- 3/4 of answers correct but large difference between sides 2 - A l l answers are correct, little or no difference 8 Shoulder 2 Elbow 2 Wrist 2 Thumb 2 Joint Pain/Motion Test in Supine Motion Scoring 0 - Only a few degrees of motion 1 - Decreased passive range of motion 2 - Normal passive range of motion Pain Scoring 0 - Marked pain at end of range or pain through range 1 - Some pain 2 - No pain 24/24 Shoulder - Flexion 2/2 Shoulder - Abduction to 90 2/2 Shoulder - External rotation 2/2 Shoulder - Internal rotation 2/2 . . . Elbow - Flexion 2/2 Elbow - Extension 2/2 Wrist - Flexion 2/2 Wrist - Extension 2/2 Fingers - Flexion 2/2 Fingers - Extension 2/2 Forearm - Pronation 2/2 Forearm - Supination 2/2 Upper Extremity Assessment - Motor Test Scoring Criteria Max Score I Reflexes 0 - no reflex 2 - reflex elicited 4 . . . . Biceps 2 Triceps 2 Ha Flexor Synergy Contralateral knee to ear 0 - cannot be performed 1 - performed partly 2 - performed faultlessly 12 Elevation 2 Retraction 2 Abduction (at least 90) 2 External Rotation 2 117 Elbow Flexion 2 Forearm Supination 2 lib Extensor Synergy Ear to contralateral knee.(outside) 0 - cannot be performed 1 - performed partly 2 - performed faultlessly 6 Adduction/Intern. Rotation 2 Elbow Extension 2 Forearm Pronation 2 III Mixing Synergies 6 Hand to Lumbar spine 0 - No specific action performed 1 - Hand passes anterior superior illiac spine 2 - Action is performed faultlessly 2 Shoulder Flexion to 90, elbow at 0 0 - Arm immediately abducted or elbow flexes 1 - Abduction or elbow flexion occurs late in motion 2 - Faultless motion 2 Pronation/Supination of forearm with elbow at 90 and shoulder at 0 0 - Incorrect position and/or no pronation/supination 1 - Correct position with minimal pronantion/supination 2 - Correct position and complete pronation and supination 2 IV Out of Synergy 6 Shoulder abduction to 90, elbow at 0 and forearm pronated 0 - Initial elbow flexion or deviation from pronated forearm 1 - Motion performed partly or i f during motion elbow is flexed or forearm not kept in pronation 2 - Faultless motion 2 Shoulder flexion, 90 - 180, elbow at 0, and forearm in midposition 0 - Initial flexion of elbow or shoulder abduction occurs 1 - Elbow flexion or shoulder abduction, occurs during shoulder flexion 2 - Faultless motion 2 Pronation/Supination of forearm elbow at 0 and shoulder between 30-90 of flexion 0 - Supination/Pronation not possible or elbow and shoulder postion cannot be attained 1 - Elbow and shoulder properly positioned, pron/supin limited 2 - Faultless motion 2 V Normal Reflex Activity ***Only evaluated if stage IV has a score of 6*** 2 Biceps and/or finger flexors and triceps 0 - at least 2 of the 3 reflexes are hyperactive 1 - one reflex is hyperactive or 2 reflexes are lively 2 - no more than one reflex is lively and none are hyperactive 2 VI Wrist 10 Stability, elbow 90, shoulder 0 0 - Cannot dorsiflex wrist to required 15 1 - Dorsiflexion is accomplished, but no resistance is taken 2 - Position can be maintained with some resistance 2 Stability, elbow 0, shoulder 30 2 118 Flex/Ext elbow 90, shoulder 30 2 Flex/Ext elbow 90, shoulder 0 0 - Volitional movement does not occur 1 - Cannot actively move wrist joint through out total R O M 2 - Faultless smooth movement 2 Circumduction 0 - Cannot be performed 1 - Jerky or incomplete circumduction 2 - Complete motion with smoothness 2 VII Hand 14 Finger mass flexion 0 - No flexion occurs 1 - Some flexion, but not full motion 2 - Complete active flexion (compared with unaffected hand) 2 Finger Mass Extension 0 - No extension occurs 1 - Patient can release an active mass flexion grasp 2 - Full active extension 2 G l : M P joints ext and PIPs & DIPs flexed. 0 - Required position cannot be performed 1 - Grasp is weak 2 - Grasp maintained against reasonable resistance 2 G 2: Adduct thumb, IP & M P O 0 - Function cannot be performed 1 - Paper (can, ball) can be held in place but not against a tug 2 - Paper (can, ball) is held against tug 2 G 3: Thumb oppose indexfinger 2 G 4: Grasp can 2 G 5: Grasp tennis ball 2 Co-ordination/Speed 6 Tremor - Finger to nose 0 - Marked tremor 1 - Slight tremor 2 - No tremor 2 Dysmetria - Finger to nose 0 - Pronounced or unsystematic dysmetria 1 - Slight or pronounced dysmetria 2 - No dysmetria 2 Speed - Finger to nose 0 - Activity is more than 6 seconds longer than unaffected hand 1 -2 -5 seconds longer than affected hand 2 - less than 2 seconds 2 Total 66 Adapted from: Fugl-Meyer AR, Jaasko L, Leyman I, Olsson S, Steglind S. (1975). Poststroke hemiplegic patient: evaluation of physical performance. Scandanavian Journal of Rehabilitation Medicine, 7, 13-31. 119 Appendix IV: Conceptual Development of Linear Spring-Damper Model The resistive response of a joint to stretch has dependence on position, velocity, and acceleration and can be conceptualized as a mass-spring-damper system (Figure AIV-1). Upper Arm Rotational Stiffness Rotational Damping Inertia e 0 e Figure AIV-1: Conceptualization of spring-damper model. When stretched at a constant velocity, the torque due to acceleration (i.e., inertial) becomes zero. The most general response torque to a constant velocity can be described by a mixed polynomial of position and velocity terms (see equation AIV-1). M%)=z*1(«-^ )f+zl:-v(»-*;('%-%0)'+t*>%-%.)' Equation AIV 1-1 Here, angular position is 0 and angular velocity is d6/dt. Position, velocity, and mixed coefficients are represented by k,b, and m respectively. Polynomials of order i and 120 j are expanded about 'neutral' offsets - denoted by the subscript 0; these neutral offsets respectively correspond to null position and velocity dependent torques. Preliminary inspection of resistance profiles indicated broadly proportional relationships between changes in torque with either position or velocity, in addition to a dependence on the interaction between position and velocity (see Chapter 2). As such, we kept only the 1 s t order terms within the model of the torque response and assumed the velocity offset to be zero (i.e., no resistance at zero velocity). The remaining terms represented a one way spring-damper (i.e., equation unidirectionally valid) in which elastic forces are offset by an angular offset (see equation AJY-2). r(*,<%Me-*o)+*<% Equation AIV-2 Stiffness, damping, and angular offset parameters were determined using a least-squares fit of the spring-damper model to position, velocity, and torque data; this least-squares method was independent of starting parameters and search paradigm because of the linearity of the model (Strang, 1988). Specifically, the fit solved for x (stiffness, damping, and angular offset parameters) by minimizing the total squared error, E 2 , between model estimates and measured values of torque (b) for position and velocity data (A) (i.e., E2=||Ax-b||2). 121 Appendix V: Anatomical Landmark, Marker, and Electrode Placement Segments were considered rigid and motion of each segment was tracked with arrays of three markers. Markers were placed on bony landmarks to minimize skin translation with the underlying rigid body (e.g., Small et al., 1992) and in a wide triangular pattern to minimize computational errors in determining the planar orientation of the rigid body. The segments and corresponding marker locations are given in Table V - l . The locations of specific anatomical landmarks were digitized during a still pose (used to describe position and orientation). These landmarks are given in Table A V - 2 . Table AV-1: Tracking Marker Locations Marker # Segment Location 1 Upper Arm Lateral projection of glenohumeral joint 2 Upper Arm Mid Upper Arm (over humerus) 3 Upper Arm Lateral Epicondyle 4 Forearm Olecranon 5 Forearm Mid Forearm (over radius) 6 Forearm/Hand (Duplicate) Styloid Process of Radius 7 Hand Ring Knuckle (K) (Proximal Head of 4 t h Phalange) 8 Hand/Finger (Duplicate) Index Finger Nail (Distal Head of 2 n d Phalange) Table AV-2: Digitized Anatomical Landmarks Landmark # Segment Location 1 Finger Tip of Index Finger (Distal Head of 2 n d Phalange) 2 Hand/Forearm Styloid Process of Radius (RS) 3 Hand/Forearm Styloid Process of Ulna (US) 4 Forearm Olecranon - tip of Ulna 5 Upper Arm Lateral epicondyle (LE) 6 Upper Arm Medial epicondyle (ME) 7 Upper Arm/Trunk Glenohumeral Joint (GH) 9 Trunk (Reference) Xyphoid 10 Trunk (Reference) Sternal Notch (SN) 122 Electrodes were placed over the bellies of muscles that contribute significantly to reaching. In the cases where several muscles contribute to the same action, we chose the muscle which was most superficial to the surface in order to maximize the quality of the muscle activity that was being measured. Table AV-3 describes the muscle groups, their involvement in a reaching action, and electrode placement. Table AV-3: Electrode Placement Muscle Reaching Action Electrode Placement Anterior Deltoid Shoulder flexion Palpate the greater tubercle of the humeral head. Place electrodes on muscle mass immediately medial. Biceps-Brachium Elbow flex & Shoulder flex Electrodes placed immediately lateral to the center of muscle mass of the upper arm when in flexion. Triceps - Long Head Elbow ext. & Shoulder ext. Palpate the division of upper arm flexors and extensors near the axilla. Place the electrodes immediately posterior to division parallel to muscle. Triceps -Lateral head Elbow extension Palpate the division of triceps muscle superior to the olecranon. Place electrodes on lateral side of division. Brachioradialis Elbow flexion (monarticular) Electrodes placed on muscle mass just distal to the elbow while resisting elbow flexion with wrist in neutral postion (50% pronated). Lateral-anterior side. Latissimus Dorsi Shoulder extension Electrodes placed immediately medial to the posterior side of the axilla near the lateral border of the scapula. Lateral Deltoid Shoulder Abduction Electrodes placed on lateral aspect of upper arm about 3 cm below the acromion. 123 Appendix VI: Point-to-Plane Method and Determination of Embedded Axes System The global positions and orientations of segments were calculated in a two-step procedure. First, the locations of specific anatomical landmarks were digitized and meshed with the locations of tracking markers in a still pose (chosen to be the starting position). This registration provided a fixed but local spatial relationship between tracking markers and anatomical landmarks attached to the same 'rigid' segment. A point-to-plane method was developed and applied to (1) establish the coordinates of a landmark relative to 3 points on a rigid body given both the global coordinates of the anatomical landmark and the global coordinates of the 3 points on the body and (2) establish the global coordinates of a landmark given both the global coordinates of 3 markers attached to a rigid body and the fixed relationship between these markers and an anatomical landmark. Second, landmark locations were used to determine an axis system embedded within each segment. Point-to-Plane Method Consider an arbitrary point in space, Po (representing an anatomical landmark of interest), and the plane P123 defined by points P i , P2, P3 (representing the locations of tracking markers attached to the same segment as the anatomical landmark). The vectors between points P i , P2, P3 are given by Y\2, v 2 3 , and v 3 i (Figure AVI-1). 124 Figure AVI-1: Transformations between global (left graphic) and local rigid body (right graphic) coordinate systems. As any of the three vectors between these three points lie within the plane, the cross product of any three of these vectors (when normalized) gives the unit normal (n, note ±) to the plane (see Equation AVI-1). n _ V 12 X V 2 3 _ V 2 3 X V 31 _ V 31 X V 12 V 1 2 X V 2 3 V 2 3 X V 3 1 V 3 1 X V 1 2 Equation AVI-1 The geometrical relationship between Pi23 and Po can be expressed in terms of the point-to-plane distance (P123-P0) and the location of the point, pPo, where the normal vector going through P 0 pierces Pi23- The point-to-plane distance can be found by the dot 125 product of the unit normal with the vector between Po and any point internal to the plane (chosen to be any one of Pi, P2, or P 3 ) - see equation AVI-2. PPD = P 1 2 3 -P 0 =n. Equation AVI 2 The position of pPo can be calculated by scaling the unit normal by the point-to-plane distance and subtracting this vector from the point Po (see equation AVI-3). The relative position of the pierced point in the plane can be determined with respect to any point in the plane providing that both the connection between the point in space and the plane are rigid - this can be expressed using a local coordinate system. This local coordinate system is most conveniently centred about one of the three known markers with two co-planar but orthogonal axes defined by the vectors to the remaining two marker positions. For demonstration purposes, this process is developed about Pi and the direction of the first axis is chosen as the self-normalized vector, Ui(i)= V12/IV12I. The direction of the second axis, U2(i), is the normalized component of V23 that is orthogonal to v ^ ; this basis is determined via the Gram-Schmidt process (Strang, 1988) -see equation AVI-4. pP0=PQ-u-PPD Equation AVI-3 v 23 • V 12 u 2(1) u = V 23 - V 12 -» u 2(1) -u 2(1) Equation AVI-4 126 The point-to-plane process gives the fixed local rigid body coordinates of Po in terms of an orthogonal axis set (n, ui(i), U20). The calculation of global coordinates for Po during motion requires this process to be carried out in reverse. In order to reduce estimation errors caused by skin translation, Po was determined from weighted estimations from axes centred on each of the triangular vertices of Pi, P2, or P3 (weighting was dynamic and changed during movement). Elastic deformation (e), the strain between static and dynamic lengths, was used to weight the estimations. The weight of each estimate was exponentially proportional to the elastic deformation of the side opposite to the current vertex (i.e., weight decreasing with increasing strain). For demonstration purposes, this weighting calculation is shown about Pi (see equation A VI-5). V 2 3 ( . v ) V23(d) V 2 3 ( . v ) —>• w, = exp(- sx) Equation AVI-5 127 Below is the main source code (matlab) for generating these rigid body transformations, (for a fully annotated version see point2plane.m on cd). point2plane.m %'golocal' INPUT: 3 markers (3x3 matrix),global point in space (1x3 vector) %'golocal' OUTPUT: Local position estimat e (3x4 matrix) %'goglobl' INPUT: 3 markers (3x3 matrix), local point in space (3x4 matrix) %'goglobl' OUTPUT: Global position estimate (1x4 vector) function [output_position]=point2plane(mode,plane,input_position) %Current plane matrix, the vectors along the sides, and the lengths of each side plane_vect=[plane(l,:)-plane(2,:);plane(2,:)-plane(3,:);plane(3,:)-plane(l,:)]; triangle_len=[norm(plane_vect( 1,:)) ;norm(plane_vect(2,:)) ;norm(plane_vect(3,:))]'; %The normal to the plane - any 2 of the plane vectors will give the same result n=cross(plane_vect(l,:),plane_vect(2,:))/norm(cross(plane_vect(l,:),plane_vect(2,:))); i f mode=-golocal' PO=input_position; Dpp=dot(n,PO-plane(l,:)); pP0=P0-Dpp*n; for i=l:3 vl=plane_vect(i,:); ifi<3 v2=plane_vect(i+l,:); len=triangle_len(i+l); else v2=plane_vect(l,:); len=triangle_len( 1); end u l=vl ; u2=v2-ul*dot(v2,ul)/(vl*vl'); ul==ul/norm(ul); u2=u2/norm(u2); pPO_ul=dot(ul,pPO-plane(i,:)); pP0_u2=dot(u2,pP0-plane(i,:)); local_P0(i,:)=[pP0_ul pP0_u2 Dpp len]; end output_position=local_PO; end 128 i f mode='goglobr local_PO=input_position; for i=l:3 v 1 =plane_vect(i,:); dv 1 =abs(norm(v 1 )-triangle_len(i)); ifi<3 v2=plane_vect(i+l,:); dv2=abs(norm(v2)-triangle_len(i+l)); else v2=plane_vect(l,:); dv2=abs(norm(v2)-triangle_len(l)); end u l=vl ; dul=dvl; u2=v2-ul *dot(v2,ul)/(vl *vl'); du2=dv2+dul *dot(v2,ul); rel_du 1 =du 1 /norm(u 1); rel_du2=du2/norm(u2); ul=ul/norm(ul); u2=u2/norm(u2); global_pPO(i,:)=plane(i,:)+local_PO(i,[l 2])*[ul;u2]; global_P0(i,:)=global_pP0(i,:)+n*local_P0(i,3); relative_elasticity(i)=sum(local_PO(i, [12]).* [rel_du 1 rel_du2]); weight(i)=exp(-relative_elasticity(i)); end output_position=weight*global_PO./sum(weight); output_position(4)=sum(relative_elasticity); ************************************************************** 129 Global Position and Orientation of Segments (Embedded Axes) The global position and orientation of each segment was measured as the translation and rotation between an embedded orthogonal axis system and the global frame of reference origin. The embedded orthogonal axes correspond to medial-to-lateral (X), posterior-to-anterior (Y), and distal-to-proximal directions (Z) when in the anatomical position. In combination with empirical equations relating internal joints to surface landmarks (Yeadon & Marlock, 1989), specific anatomical landmarks were used to define the distal-to-proximal direction and an estimate of the medial-to-lateral direction (see Table AVI-1). Table AVI-1: Empirical Formulas used For Embedded Axes Segment Medial-to-Lateral Vector Proximal-to-Distal Vector Upper Arm (LE-ME) PJ-DJ = C9*GH+.1*SN)-(.5*LE+.5ME) | L E - M E | |PJ-DJ| |(.9*GH+.1*SN) - (.5*LE+.5ME)| Forearm (RS-US) PJ-DJ = f.5*LE+.5*ME)-C5*RS+.5*US) |(RS-US)| |PJ-DJ| |(.5*LE+.5*ME) - (.5*RS+.5*US)| Hand (RS-US) |(RS-US)| PJ-DJ - C5*RS+.5*US) - M K |PJ-DJ| |(.5*RS+.5*US) - M K | The posterior-to-anterior axis was then determined by the cross product between the distal-to-proximal and medial-to-lateral axes. The medial-to-lateral axis was then 130 corrected by taking the cross product between the posterior-to-anterior and distal-to-proximal axes to create a fully orthogonal set of axes (see equation AVI-6). Y = ZxX, est x = YxZ ZxX, est \YxZ E q u a t i o n A V I - 6 The directions of the embedded axis system were entered as columns in a rotation matrix between the global and embedded system. For example, column 1 corresponds to how the x-axis of the new coordinate system is seen in the global (reference) coordinate system; columns 2 and 3 are representations of the new y and z axes. Proximal, distal, and centre-of-mass (com) coordinate systems were generated. In each segment, the scaled translation vector (STV) defining the position of the com relative to the distal joint was taken from previous anatomical studies (Yeadon & Marlock, 1989). STVs for the upper arm, forearm, and hand were [0 0 0.564], [0 0 0.57], and [0 0 0.5] respectively. The displacement to the com in the global coordinate system was calculated as the product of the rotation matrix, R g , the segment length (long axis), and the STV. The rotation (R g=[X Y Z]) and position, p g, of each coordinate system was represented in terms of a 4x4 matrix. See equation AVI-7 for an example of the matrix representation at the com. COM'g) * ^ PcOM(g) 0 0 0 1 E q u a t i o n A V I - 7 131 Below is the main source code that was used to generate to generate the systems of embedded axes (for a fully annotated version see pr_axes2.m on cd). pr_axes2.m function [PA_pjc,PA_com,PA_djc,del_xdeg,seglen,Xcross,Xanat,Zdot]=pr_axes2(global_anatloc at) %FUNCTION INPUT: This function inputs the global anatomical positions %(global_anatlocat nxmx4). %FUNCTION OUTPUT: The nx4x4 matrix representation of the principle set of axes %located on the proximal joint (PA_pjc), the nx4x4 matrix representation of the %principle set of axes located at the center of mass of the segment (PA_com). %This function also outputs 3D angle (delxdeg) between the orthogonally corrected %x-axis and the x-axis estimate based strictly on anatomical landmarks - small %angle values are desired!!! define_arm_model; for seg=l:num_segments clear seg_global_anatlocat R seg_global_anatlocat(:,:)=global_anatlocat(seg,:,l:3); last_lm=size(seg_global_anatlocat, 1); p_prox(seg,: )=seg_global_anatlocat( 1,:); p_dist(seg,:)=seg_global_anatlocat(2,:); i f seg=base_segment dp_vect=base_dprot*seg_global_anatlocat(3:last_lm,:); else dp_vect=p_prox(seg,: )-p_dist(seg,:); end trans(seg)=norm(dp_vect); seglen(seg)=trans(seg); ml_vect=ml_weights(seg, :)* seg_global_anatlocat(3: lastlm,:); x_est(seg,: )=ml_vect/norm(ml_vect); z_dir(seg,: )=dp_vect/norm(dp_vect); end for seg=l:num_segments clear R R(3,:)=z_dir(seg,:); curr_x=x_est(seg,:); 132 R(2,:)=cross(R(3,:),curr_x)/norm(cross(R(3,:),curr_x)); R(l,:)=cross(R(2,:),R(3,:))/norm(cross(R(2,:),R(3,:))); del_xdeg(seg)=(l 80/pi)*acos(dot(R(l ,:),curr_x)); %transform columns into rows so we have the correct format as specified in 2. R=R'; rel_com_disp=-trans(seg)*R*d_com(seg,:)'; %If the segment is 1 (ie - the trunk) reset the rotation matrix to 0. This %wil l eliminate any errors from poor digitization i f seg=base_segment R=eye(3); end seg_PA_pjc=R; seg_P A_pj c( 1:3,4)=p_prox(seg,:)'; seg_PA_pjc(4,:)=0; seg_PA_pjc(4,4)=l; seg_PA_com=seg_PA_pjc; seg_PA_com(l :3,4)=seg_PA_com(l :3,4)+rel_com_disp; seg_P A_dj c=seg_PA_pj c; seg_P A_dj c( 1:3,4)=p_dist(seg,:)'; PA_pjc(seg,:,:)=seg_PA_pjc; P A_dj c(seg,:,: )=seg_P A_dj c; P A_com(seg,:,: )-seg_P A_com; end 133 Appendix Vll: Joint Kinematics and Kinetics Joint Kinematics Segment kinematics were described as the relative movement of the more distal segment to the more distal segment (for general reference see: Sciavicco & Siciliano, 2000). Specifically, the relative movement was defined by the transformation, TDP, between the global coordinates of the distal joint of the proximal segment, Tp(Dj,g), and the global coordinates of the proximal joint of the distal segment, TD(pj,g) (see Figure AVII-1). Figure AVII-1: Transformation (TDP) between the embedded coordinate system of a proximal segment (P) to the embedded coordinate system of a distal segment (D). The transformation between systems is composed of a translation, pop, and a rotation, R(a,p\y). Note that unlike the Euler rotation angles, angular velocities and accelerations of the distal segment are described entirely within the orthogonal axis system of the proximal segment. Y D X P 134 The relative rotation, R D P , and translation, pop, between segments was abstracted from the transformation matrix and represent the orientation and position of the distal segment within the proximal segment's coordinate system (see equation AVLI-1). The translation vector was used as a measure of joint distraction and the true location of the joint was assumed to lay midway between proximal and distal segment estimates of the joint center. The transformation matrices describing the relative movement of the distal segment com were calculated in a similar fashion. 1D(g) 1DP1P(g) ^ DP 1D(g)IP(g) Equation AVII-1 Joint angles were abstracted from the rotation matrix according to an Euler ( X , Y ' , Z " ) rotation sequence. With V and 'c ' referring to sin and cosine, the resultant rotation matrix that corresponds to rotations by angles of a (flexion-extension), p (adduction-abduction), and y (internal-external rotation) is given by equations AVJJ-2. RDP=R(a,j3,y) = RxR,Rz,.= 1 0 0 0 ca -sa 0 sa ca c/3 0 s0 0 1 0 -s/3 0 cj3 cy -sy 0 sy cy 0 0 0 1 R D P -ri3 r23 r3\ r32 r33 cfi-cy -cp-sy s/3 sa • s/3 • cy + ca • sy - sa • s/3 + ca • cy -sac/3 - ca • s/3 • cy + sa • sy ca • s/3 • sy + sa • cy ca-c/3 Equation AVII-2 135 Angles were determined from the matrix by comparing the ratio of internal elements (see equation AVIJ-3). a = atan2(-r 2 3 ,r 3 3) ; p = atan2(r13,A/r23 +r 3 3 ) ; / = a tan2(-r ] 2 , r u ) Equation A V I I - 3 Linear, v=[vx v y v z], and angular, co=[cox % coz], velocities of the distal segment axis system were calculated with respect to the orthogonal set of axes in the proximal segment. Linear velocities were calculated by taking the derivatives of the translation vector p=[px P y P z ]• Angular joint velocities were determined from the skew symmetric components of the 3x3 matrix found when multiplying the time derivative of the rotation matrix, dR/dt, by the transpose of the rotation matrix, R T (see equation AVII-4): 4 » , CO, CO. • h 0 - co„ 0 coy 0 dR T dR d : — R ; = — dt dt dt r "'ii rn r . 3 ~ r22 r23 V / 3 1 r32 r 3 3 . ) Equation A V I I - 4 Linear a=[ax a y az] and rotational accelerations a=[ax a y az] were calculated as the time derivatives of linear and rotational velocities respectively. 136 Joint Kinetics: Calculation of Moment and Power The dynamical equations of motion were determined using a recursive Newton-Euler method in local coordinates (Meglan, 1991). Consider the forces (F) and moments (M) acting upon a segment body (with a principal coordinate system, q) can come from distal segments (d), proximal segments (p), or may be of external origin (e) - see Figure AVII-2. Figure AVII-2: Forces and Moments acting upon a segment body and the principal axis system attached to the segment body. In addition to the applied moments, force moments (i.e., r X F ) act on the body. 137 The reaction forces, F=[FX F y F z ] , and moments, M=[M X M y M z ] , of each segment (i.e., the forces and moments transmitted through tendon and muscle at a joint) are a function of not only the forces and moments acting upon the body but also the emergent kinematics (v=[vx v y v z], ©=[cox coy coz], a=[ax a y az], and a=[ccx a y a z]) and segment mass (m) and inertias, I=[Ix I y Iz]. In our model we used anthropomorphic measurements of upper limb segment perimeters and lengths in combination with empirically derived models to (Yeadon & Marlock, 1989) to estimate segment masses and inertias. Force and moment equilibrium equations were developed at each joint and solved inwardly (i.e., balance at the wrist, then the elbow, and finally the shoulder). The net force at each joint, F=ma, was given equation AVII-5. » » = F , , - ^ + F M + m - G » ma - ml E q u a t i o n A V I I 5 This equation was solved for the proximal joint force, F q p (see equation AVH-6). Vq,p=ma-m-Gq-¥q.e+Vq4 E q u a t i o n A V I I - 6 The net angular moment at each joint, L , and the solution for the proximal joint moment, M q p are given by equations AVII-7ab. 138 L = r ? > e x Fqe + M„> e -xq 4 x Fq4 -Mqd + rqp x Fqp + Mqp y<°g,: Iq,x-aqtX+{lq^-I(l,y)-o}q - aq,y + ( 7 ^ - ^ , J - ® , , z ® , , . tg,, • a g , z + { I g , y ~ 1'g,x\ <°g,*<°g M9.P = L "  rg,e x F„,e + M 9 ] £ + rq4 x Fq4 + Mq<d - vq,p x Equation AVII-7ab Joint forces and moments transmitted by muscles and tendons were represented in terms of the distal joint reaction of the more inward segment (using its coordinate system) to the proximal joint loading of the current segment. This representation of joint moments was consistent with joint kinematics (i.e., shoulder adduction moment is in reference to frontal plane of trunk, elbow flexor moment is in reference to the sagittal plane of the upper arm, etc.). The distal joint reaction of the more inward segment, coordinate frame: q+1, is given in terms of the proximal joint force and the rotation matrix between coordinate frames, Rq+i;q (equations AVII-8ab). ^g+\,d ^-q+\,g^g,p Equation AVII-8ab In addition to determining the anatomically relevant joint loadings, the transformation of loads to the more inward segment was used to initiate the next iteration 139 of the Newton-Euler formulation. Note that the gravitational component of force and moment can easily be calculated by setting velocities and accelerations to zero. Joint powers were also used to describe movement kinetics. Powers P=[PX P y P z] were calculated about each rotational axis (i.e., flexor/extensor power, adductor/abductor power, and internal/external power) by taking the product between joint moments and angular joint velocities (see equation AVJJ-9). P = [PX PY P\=[MX-OJX My-coy Mz-a>\ Equation AVII 9 This representation of joint powers has been used previously to describe lower extremity kinetics (Eng & Winter, 1995) and is representative of the power generated/absorbed by muscle groups associated with the specific anatomical action. 140 Below is the main source code (matlab) used for the Newton-Euler method (for a fully annotated version see three_RNE.m on cd). three_RNE.m function [PORF,PORM,PORFST,PORMST]=tb^ heck) %Conventions -%q=Principal Axis system %G=gravity %e=external %p=proximal %d=distal %r=vector %a=acceleration %aa=angular acceleration %w=angular v elocity %R=rotation matrix % %c=principal axis system of current segment %cp=principal axis system of proximal segment %cd=principal axis system of distal segment defme_arm_model; numframes=size(LT,l); Gg=[0; 0; -9.81]; for f=l :numframes %clear frame loop variables (for checking purposes) clear qFd qMd qG qrd qrp qre c M A cMqG L qreXqFe qrdXqFd qrpXqFp qMd qMp qFc qMc qpF qpM qFe(l :num_segments,l :3)=0; qMe(l :num_segments,l :3)=0; qFeSt(l :num_segments,l :3)=0; qMeSt(l :num_segments,l :3)=0; for d=l :num_segments %since for loop wil l not work in reverse set up a dummy %variable up first 141 s=num_segments+1 -d; %clear segment loop variables (for checking purposes) clear c l c M cTl cRl cTg cTph w aa v a Rpc %***** Abstract current (c) values of parameters*********** cl(:,:)=ln(s,:,:); cM=M(s); cTl(:,:)=LT(f,s,:,:); cRl(:,:)=cTl(l:3,l:3); cTg(:,:)=GT(f,s,:,:); cRg(:,:)=cTg(l:3,l:3); w(:,:)=W(f,s,:); aa(:,:)=AA(f,s,:); v(:,:)=V(f,s,:); a(:,:)=Acc(f,s,:); %**Find the distal forces and moments acting on the segment** %**opposite in direction to the i f s=num_segments qFd(s,l:3)=0; qMd(s,l:3)=0; qFdSt(s,l:3)=0; qMdSt(s,l:3)=0; else qFd(s,:)=-qpF(s+l,:); qMd(s,:)=-qpM(s+l,:); qFdSt(s,:)=-qpFSt(s+l,:); qMdSt(s,:)=-qpMSt(s+l,:); end %**Determine vector directions on the current segment******** qG(s,:)=(cRg'*Gg)'; %gravity - originally (cRg'*Gg)'; qrd(s,:)=([0 0 l]-d_com(s,:))*seglen(f,s); qrp(s, :)=-d_com(s, :)*seglen(f,s); qre(s,:)=[0 0 0]; Rpc=cRl'; % cMA(s,l)=cM*(a(l)+v(3)*w(2)-v(2)*w(3)); cMA(s,2)=cM*(a(2)+v(l)*w(3)-v(3)*w(l)); cMA(s,3)=cM*(a(3)+v(2)*w(l)-v(l)*w(2)); cMqG(s,:)=cM*qG(s,:); qFp(s,:)=cMA(s,:)-cMqG(s,:)-qFd(s,:)-qFe(s,:); L(s,l)=cl(l,l)*aa(l)+(cl(3,3)-cl(2,2))*w(2)*w(3); L(s,2)=cl(2,2)*aa(2)+(cl(l,l)-cl(3,3))*w(3)*w(l); L(s,3)=cl(3,3)*aa(3)+(cl(2,2)-cl(l,l))*w(l)*w(2); 142 qreXqFe(s,:)=cross(qre(s,:),qFe(s,:)); qrdXqFd(s,:)=cross(qrd(s,:),qFd(s,:)); qrpXqFp(s,:)=cross(qrp(s,:),qFp(s,:)); qMp(s,:)=L(s,:)+qrdXqFd(s,:)+qrpXqFp(s,:)+qreXqFe(s,:)-qMd(s,:)-qMe(s,:); c^*******# S H * * * * * * * * * * * * * * * * * * * * * * * * * * * * %*******Partition the forces and torques into static, velockty dependent, %*******and acceleration dependent terms!!M***************************** %Note this requires unique identification of forces and torques at each %joint so spurious moments/forces are not carried through qFpSt(s,:)=-cMqG(s,:)-qFdSt(s,:)-qFeSt(s,0; qreXqFeSt(s,:)=cross(qre(s,:),qFeSt(s,:)); qrdXqFdSt(s,:)=cross(qrd(s,:),qFdSt(s,:)); qrpXqFpSt(s,:)=cross(qrp(s,:),qFpSt(s,:)); qMpSt(s, :)=qrdXqFdSt(s, :)+qrpXqFpSt(s, :)+qreXqFeSt(s, :)-qMdSt(s, :)-qMeSt(s,:); O^st ; * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * %**Transformation of Force and Moment to inner segment PICS** qFc=qFp; qMc=qMp; qFcSt=qFpSt; qMcSt=qMpSt; qpF(s,:)=(Rpc'*qFc(s,:)')'; qpM(s,:)=(Rpc'*qMc(s,:)')'; qpFSt(s, :)=(Rpc'*qFcSt(s,:)')'; qpMSt(s,:)=(Rpc'*qMcSt(s,:)')'; end %Full Forces and Moments PORF(f,:,:)=qpF; PORM(f,:,:)=qpM; %Static Forces and Moments PORFST(f,:,:)=qpFSt; PORMST(f,:,:)=qpMSt; 143 Appendix Vlll: Scatterplots of Biomechanical and Electromyographic Parameters (a) Directness (b) Segmentation ,°g8 8 I 2 o o 6> oo OOOQD (c) M L Deviation (d)Skewness ° o o °° ° o ° ° " A s (e) IS Deviation (f) Kurtosis ...O-o 00 o a ° . o Goc*> 22 44 6 6 LA ND FM Motor Impairment -0.3 „ -0.8 O t 5 -1.3 -1.8 O CD o 22 44 6 6 LA ND FM Motor Impairment Figure AVIII-1: Scatterplots of Motor Impairment versus hand path and trajectory parameters of (a) Directness, (b) Segmentation, (c) Medial-Lateral (ML) Deviation, (d) Skewness, (e) Inferior-Superior (IS) Deviation, and (f) Kurtosis for the more affected arm 'o\ Distributions (means and 95% confidence intervals) of the less affected (LA) and non-dominant (ND) arms are given on the right side of each graph for comparative purposes. 144 (a)Shoulder Flexion/Extension o O' ° o o c QD O O O ° •i i (b)Shoulder Adduction/ Adduction 10 ° o -10 -20 -30 oo CD' ,00 QD C® O O (c) Shoulder Internal/External Rotation (d) Elbow Flexion/Extension o o o ° o O o o o ° ° ° ° o°°g i. * 22 44 66 LA ND FM Motor Impairment 35 15 -25 ° o o O T O <§> O o f ° ° o ' O x 0 22 44 66 LA ND FM Motor Impairment F i g u r e AV I I I-2: S c a t t e r p l o t s o f M o t o r I m p a i r m e n t v e r s u s c h a n g e i n a n g l e f o r (a ) S h o u l d e r F l e x i o n ( + ) / E x t e n s i o n ( - ) , S h o u l d e r A d d u c t i o n ( + ) / A b d u c t i o n ( - ) , S h o u l d e r I n t e r n a l ( + ) / E x t e r n a l ( + ) R o t a t i o n , a n d E l b o w F l e x i o n ( + ) / E x t e n s i o n ( - ) f o r t h e m o r e a f f e c t e d a r m V . D i s t r i b u t i o n s ( m e a n s a n d 95% c o n f i d e n c e i n t e r v a l s ) o f a n g u l a r c h a n g e f o r t h e l ess a f f e c t e d ( L A ) a n d n o n - d o m i n a n t ( N D ) a r m s a r e g i v e n o n t h e r i g h t s i d e o f e a c h g r a p h f o r c o m p a r a t i v e p u r p o s e s . 145 (a) Shoulder Flexor Generation (b) Shoulder Abduction Generation ~ 0.3 1 5, 0.2 i ^ 0.1 0.12 ..oo. o o o (c) Elbow Flexor Generation 22 44 66 LA ND FM Motor Impairment 0.12 0.08 0.04 o o o 8 o o O Oo o CP a , Otg (d) Elbow Flexor Absorption 0 22 44 66 LA ND FM Motor Impairment Figure AVIII-3: Scatterplots of the FM Motor Impariment Scale versus peak powers of (a) Shoulder Flexor Generation, (b) Shoulder Abductor Generation, (c) Elbow Flexor Generation, and (d) Elbow Flexor Absorption for the more affected arm 'o\ Distributions (means and 95% confidence intervals) of the peak powers for the less affected (LA) and non-dominant (ND) are given on the right of each graph for comparative purposes. 146 (a) Anterior Deltoid (b) Lateral Deltoid 2.4 1.8 1.2 0.6 o O O o o >ocP i i 1.5 1 0.5 0 o o o ° o ° o 6 o o ° o I 5 1.2 0.8 > 0.4 (c) Biceps Brachialis o -°- o o o o o 22 44 66 LA ND FM Motor Impairment 1.2 0.8 0.4 (d) Long Head of Triceps o o o ° o ° o ° ©JO o o 00 o° I I 0 22 44 66 LA ND FM Motor Impairment Figure AVIII-4: Scatterplots of Motor Impairment versus percent maximum voluntary contraction (PMVC) for (a) Anterior Deltoid, (b) Lateral Deltoid, (c) Biceps Brachialis, and (d) Long Head of Triceps for the more affected arm 'o\ Distributions (means and 95% confidence intervals) of PMVCs for the less affected (LA) and non-dominant (ND) arms are given on the right of each graph for comparative purposes. 147 

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