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Evidence of biomechanical functional symmetry in the presence of lower extremity structural asymmetry… McBride, Margaret E. 1989

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EVIDENCE OF BIOMECHANICAL FUNCTIONAL SYMMETRY IN THE PRESENCE OF LOWER EXTREMITY STRUCTURAL ASYMMETRY DURING RUNNING By MARGARET E. McBRIDE B.A./B.P.H.E., Queen's University, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT O F THE REQUIREMENTS FOR THE DEGREE O F MASTER OF PHYSICAL EDUCATION in THE FACULTY OF GRADUATE STUDIES (School of Physical Education) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1989 © Margaret E. McBride, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of P#V\<;\CAL. £ hrViCAi\ b/Q The University of British Columbia Vancouver, Canada Date ^ f t i i - , , DE-6 (2/88) ABSTRACT The biomechanical analysis of human gait is typically characterized by the generation of large volumes of collected data. In an attempt to simplify the analysis of results, researchers have made the pragmatic decision to record force and cinematographical data from only one side of the body and assume symmetry between the left and right sides. This study was devised to address two topics related to the issue of assumed biomechanical symmetry in the study of human gait mechanics. The initial objective was to determine if the assumption of symmetry in kinematic and kinetic variables remained valid in a group of runners diagnosed with a leg length differential. It was postulated that lower extremity structural asymmetry in the form of leg length inequality would be manifested as functional asymmetry in biomechanical parameters. The second objective of this study was to determine if runners with a leg length inequality were characterized by common systematic patterns of asymmetry in kinematic and kinetic variables. If universal compensation strategies were identified, they may eventually be linked to etiological factors involved in the development of overuse injuries in runners with a difference in leg length. A group of ten asymptomatic male runners served as subjects in this study. Subjects were assigned to one of two experimental conditions based upon bilateral anthropometric determination of leg length. Leg length assessment was comprised of bilateral measurements of the distance from the anterior superior iliac spine to the lateral and medial malleoli as well as the distance from the greater trochanter to the floor. The five runners in the structurally symmetrical group were characterized by a leg length differential of less than 3 mm while the five runners in the structurally asymmetrical group demonstrated a leg length inequality of greater than 10 mm. Subjects were required to run barefoot at 4.88 m/s over a flush-mounted Kistler force platform imbedded in a straight 20 meter runway. After sufficient practice, six trials were collected from both the left and right legs. The three components of the ground reaction force were collected while a Locam 16 mm camera recorded each trial in the sagittal plane at 150 frames per second. Filtered kinematic and ground reaction force data were used as input into a mathematical model designed to estimate the joint forces and muscle moments occurring at each lower extremity joint during the stance phase of running. ii Bilateral comparisons were made on the range of motion at the hip, knee and ankle joints, mean vertical force peaks and net anterior-posterior impulses. Analysis of the internal kinetic variables included the mean vertical joint reaction force and the mean muscle moment of force for each joint averaged to every 20% of the total stance duration. Results for each runner were assessed for functional equality using a symmetry index. For each variable analyzed, this calculation provided the mean absolute difference between the left and right legs for members of the structurally symmetrical group and between the long and short legs for the structurally asymmetrical runners. Comparison of group results revealed functional equality in the majority of biomechanical measures analyzed. Analysis of individual results revealed that regardless of structural status, some runners demonstrated functional equality while others were characterized by functional asymmetry. The second portion of the study attempted to determine if runners with a leg length inequality were characterized by universal patterns of asymmetry in kinematic and kinetic variables which could eventually be linked to the etiology of overuse injuries. As the structurally asymmetrical group demonstrated functional equality in the majority of variables measured, it was not possible to detect common patterns of compensation utilized by all runners with a leg length differential. Based upon these results, the following conclusions were made: 1. Regardless of structural status, functional symmetry remained a valid assumption in the majority of biomechanical variables measured in this study. 2. Structural asymmetry in the form of a leg length differential is not necessarily manifested as asymmetry in the biomechanical measures analyzed in this study. 3. No universal compensation strategy was utilized by all subjects presenting with a leg length differential. 4. Pooling data concealed bilateral asymmetries which existed in individual profiles. iii TABLE O F CONTENTS ABSTRACT ii LIST O F TABLES vii LIST O F FIGURES viii 1. INTRODUCTION 1 Statement of the Problem 2 Hypotheses 2 Significance of the Study 3 Definitions of Terms 3 Delimitations • 4 Assumptions and Limitations 5 2. REVIEW OF LITERATURE 6 Gait Research Methodology 6 Kinematics 6 External Kinetics 8 Anthropometry 9 Link Segment Model 9 Internal Kinetics 10 Variability in Human Performance 11 Kinematic Variability 12 External Kinetic Variability 12 Internal Kinetic Variability 13 Evidence of Biomechanical Symmetry 14 Evidence of Temporal Symmetry 14 Evidence of Kinematic Symmetry.... 14 Evidence of External Kinetic Symmetry 15 Evidence of Biomechanical Asymmetry 15 Evidence of Temporal Asymmetry 15 iv Evidence of Kinematic Asymmetry 16 Evidence of External Kinetic Asymmetry 16 Evidence of Internal Kinetic Asymmetry 16 Leg Length Differences 17 Prevalence of Leg Length Inequality 17 Pathomechanics 18 Injuries related to Leg Length Inequality 19 Methods of Assessing Leg Length Differences 20 — Direct Methods 20 Indirect Methods 22 Sources of Errors 22 Technical Error of Measurement 23 Coefficient of Variation... 23 Median Score 23 3. PROCEDURES 24 Research design 24 Statistical Analysis 24 Subjects 25 Data Collection 25 Anthropometric Protocol 25 Kinematic Protocol 26 Kinetic Protocol 27 Data Analysis • 27 External Kinematics 28 External Kinetics • 28 Internal Kinetics 29 Individual Analysis 29 4. RESULTS A N D DISCUSSION 31 v Description of Subjects 31 Croup Kinematic Data 31 Croup Ground Reaction Force Data 36 Group Internal Kinetic Data 40 Joint Reaction Forces 40 Muscle Moments of Force 46 The Influence of Speed on Moment Coefficient of Variation 56 Integrated Analysis of Individual Data 57 Structurally Symmetrical Subjects 57 Structurally Asymmetrical Subjects 59 5. C O N C L U S I O N S A N D RECOMMENDATIONS 61 Conclusions 61 Recommendations 63 APPENDIX A - DETERMINATION O F LEG LENGTH 64 APPENDIX B - DESCRIPTIVE DATA FOR ALL SUBJECTS 67 APPENDIX C - BILATERAL LEG LENGTHS FOR ALL SUBJECTS 68 APPENDIX D - MEAN KINEMATIC VALUES 69 APPENDIX E - MEAN EXTERNAL KINETIC VALUES 71 APPENDIX F - MEAN INTERNAL KINETIC VALUES 73 APPENDIX C - COMPLETE GRAPHICAL SUMMARY O F T W O STRUCTURALLY SYMMETRICAL SUBJECTS 81 APPENDIX H - COMPLETE GRAPHICAL SUMMARY O F T W O STRUCTURALLY ASYMMETRICAL SUBJECTS 86 REFERENCES 91 vi LIST O F TABLES 1. Influence of Speed on Moment of Force Coefficient of Variation Values 55 v i i LIST OF FIGURES 1. Mean Ankle Angle - Structurally Symmetrical and Asymmetrical Groups 32 2. Mean Knee Angle - Structurally Symmetrical and Asymmetrical Groups 33 3. Mean Hip Angle - Structurally Symmetrical and Asymmetrical Groups 34 4. Mean Vertical Force - Structurally Symmetrical and Asymmetrical Groups 38 5. Mean Anterior-Posterior Force - Structurally Symmetrical and Asymmetrical Groups 39 6. Mean Ankle Joint Reaction Force - Structurally Symmetrical and Asymmetrical Groups 42 7. Mean Knee Joint Reaction Force - Structurally Symmetrical and Asymmetrical Groups 43 8. Mean Hip Joint Reaction Force - Structurally Symmetrical and Asymmetrical Groups 44 9. Mean Ankle Moment of Force - Structurally Symmetrical and Asymmetrical Groups 46 10. Mean Knee Moment of Force - Structurally Symmetrical and Asymmetrical Groups 47 11. Mean Hip Moment of Force - Structurally Symmetrical and Asymmetrical Groups 48 12. Mean Support Moment of Force - Structurally Symmetrical and Asymmetrical Groups 49 vm Chapter 1 INTRODUCTION The biomechanical analysis of human gait is often associated with time consuming and tedious processing of large volumes of collected data. Eighty variables are necessary to completely describe the kinematics of a simplified seven-segment anatomical model in the sagittal plane (Winter, 1987). Records of the three components of the ground reaction force and internal kinetic calculations would further contribute to the volume of data produced. In an attempt to limit the description of gait to a manageable level, compromises have been made in the quantity and nature of the data collected. As running is characterized as a uniform, coordinated interaction between the left and right legs, analyses have been simplified by assuming biomechanical symmetry. This implies that functional equality should be expected in the kinematic and kinetic profiles representing the left and right legs of each individual. It has become accepted protocol to collect force and film data from one side of the body and imply the results to the opposing limb. To date, the assumption of biomechanical symmetry has not been tested in individuals diagnosed with leg length inequality. The compensatory postural adaptations associated with leg length discrepancies, coupled with the dynamic overload experienced with every footstrike may eventually lead to the development of overuse injuries in runners. Clement et al. (1981) cite leg length inequality as one of the most prevalent etiological factors associated with the development of iliotibial band friction syndrome and tibial stress fractures. This implied causal relationship between inequality in leg length and specific overuse injuries suggests that a universal compensation strategy is utilized by all runners demonstrating a leg length differential. A bilateral biomechanical assessment of structurally symmetrical and asymmetrical runners would reveal the prevalence of left-right functional inequality in each selected sample and permit a statement on the validity of assumed functional symmetry. By documenting internal and external variables which demonstrate asymmetry and the level at which compensation occurs, mechanisms involved in the etiology of overuse injuries may be revealed. To date, the evaluation of the internal 1 kinetic measures such as joint forces and moments has not been applied to the study of running mechanics. Statement of the Problem This study was designed to address two issues related to the assumption of biomechanical symmetry in the general assessment of human gait. Initially, an attempt was made to determine if the assumption of biomechanical symmetry remained valid in the presence of lower extremity structural asymmetry. The second focus involved the attempt to ascertain whether runners adapt to a leg length inequality with a universal strategy of compensation which could be detected biomechanically and eventually linked to the etiology of overuse injuries. Hypotheses 1. It was hypothesized that the assumption of functional symmetry in biomechanical measures would prove valid only in the subjects who were classified as structurally symmetrical. 2. It was expected that structural asymmetry, in the form of a leg length differential, would be manifested as asymmetry in the external and internal biomechanical variables analyzed. 3. It was hypothesized that common compensatory strategies would be revealed as universal to the runners demonstrating an inequality in leg length. Significance of the Study This study served to test the validity of the widely accepted assumption of biomechanical symmetry in the study of human gait mechanics. The clinical significance of this study involved the attempt to reveal asymmetries in external and internal biomechanical variables resulting from leg length inequality. 2 By identifying the level at which compensation for this type of structural asymmetry occurs, insight into the mechanisms of overuse injuries in running may be possible. Definitions of Terms Functional Asymmetry. Left-right inequality in kinetic and kinematic measures, regardless of structural status of the individual. Structural Asymmetry. Left-right leg length inequality due to an actual shortening of one leg (anatomical), or to an apparent length difference due to conditions such as scoliosis, malalignment or subtalar joint movement (functional). Kinematics. The description of the observed spatial movement of segments and joints, without consideration of the forces causing movement. Variables such as linear and angular displacement, velocity and acceleration are usually obtained from digitization of cinematographical data. Kinetics. The analysis of forces which cause observed movement. External kinetics are analyzed in the three components of the ground reaction force. Internal kinetics include estimations of joint forces and muscle moments derived from the standard link segment model. Ground Reaction Force. The three orthogonal components of the ground reaction force are measured by a force platform. They represent the net vertical, anterior-posterior and medial lateral forces applied to the foot during the stance phase of gait. Link Segment Model. A mathematical model developed by Bresler and Frankel (1950) designed to indirectly estimate internal kinetic parameters such as joint forces and muscle moments. Full kinematic description, accurate anthropometric measures, external forces and center of pressure are required as input to the model. Muscle Moment of Force. The turning effect produced by a muscular force. The muscle moments acting across each joint represent the end result of all agonist and antagonist contractions as well as joint and ligament friction. Moment of force data may be calculated for the hip, knee and ankle by inverse dynamics using the standard link segment model. By convention, counter-clockwise moments calculated at the proximal end of a segment are positive, indicating that extensors or dorsiflexors are dominant at that joint. 3 Support Moment. The algebraic sum of the moments acting on the three major joints of the lower extremity. Although variations are evident at each joint, a consistent extensor motor pattern is observed in the support moment while the foot is in contact with the ground. This net extensor pattern produces erect posture during stance (Winter, 1980). Normalization. As subjects are unique in height, segment length, body mass and cadence, the researcher is challenged to normalize results to produce more universal patterns which may be compared across subjects. Temporal data expressed as a percentage of total stance duration, allow the relative timing of events to be assessed. Components of the ground reaction force and moments of force for each individual are normalized to body mass (Winter, 1987). Coefficient of Variation. The stride-to-stride variability in kinematic and kinetic profiles may be quantified by the Coefficient of Variation (C.V.). This calculation is equal to the root mean square of the standard deviation at each time interval divided by the mean magnitude of the signal over the entire stride. It is therefore a variability to signal ratio (Winter, 1983a). Technical Error of Measurement. The technical error of measurement (TEM) is an accepted anthropometric method of determining and documenting differences between repeated measures such as leg length. It is therefore an estimation of assessor reliability. Delimitations Results of this study were restricted to competitive male middle distance runners characterized as rearfoot strikers when running barefoot at 4.88 m/s. Accuracy of the results may have been affected by the constraints of the experimental environment and therefore may not accurately reflect natural running mechanics. Analyses were confined to the plane of progression so that distortion associated with movement out of the sagittal plane was ignored. Ground reaction force data for each leg were not collected as consecutive footfalls. A limited number of variables derived from the graphical representation of group and individual profiles were tested for equality using a symmetry index. Some discrete aspects of each profile which may have demonstrated asymmetry were unavoidably neglected. 4 Assumptions and Limitations It was assumed that each runner was accustomed to the experimental environment and protocol prior to data collection. The joint markers used for cinematographical recording were assumed to be accurately placed over the anatomical joint centre and remained fixed during movement. The accuracy of results were limited by the assumptions inherent to the biomechanical linked segment model. These limitations were documented by Winter (1979). 5 Chapter 2 REVIEW O F LITERATURE A rudimentary understanding of the techniques utilized in the biomechanical assessment of human gait must be developed before the research findings can be fully appreciated. In recognition of the requirement, the review of literature will be divided into the following subsections: (a) gait research methodology; (b) variability in human performance; (c) evidence of biomechanical symmetry; (d) evidence of biomechanical asymmetry; (e) prevalence and significance of leg length differentials; (f) methods of assessing leg length differences. Gait Research Methodology The complete analysis of human gait mechanics ideally includes the examination of external kinematic and kinetic measures and the mathematical estimation of internal kinetic variables. This extensive biomechanical profile demands an appreciation of kinematics, anthropometry, external kinetics, the link segment model and the calculation of internal kinetics. Kinematics. The description of the spatial movement of the body and its segments without consideration of the forces which cause the activity is termed kinematic analysis (Winter, 1979). Variables analyzed are the segmental linear and angular displacement, velocity and acceleration. Typically, angular displacement data are collected by means of electrogoniometers or high speed film and the angular velocity and acceleration are derived by first and second order differentiation. The majority of research concerned with the kinematic description of human gait adhere to a protocol comprising of high speed cinematographical recording of the event, translation of the film image to cartesian coordinates representing each surface marker, digitally filtering the raw coordinate data, and eventually determining the higher differentials of velocity and acceleration. Each of these procedures will be briefly reviewed. The most frequently used method of recording human motion involves the use of a high speed 16 mm camera. The camera is usually positioned to record the activity in the sagittal plane with the subject progressing from left to right. Adherence to this biomechanical convention ensures 6 consistency in displacement measures and enables the subsequent calculation of kinematic and internal kinetic variables (Winter, 1987). The film record of the activity must be translated into digital data before further calculations may be performed. The visual film image for the recorded activity is projected onto a digitizing tablet one frame at a time and the cartesian coordinates for each surface marker are determined. The absolute angle of a segment relative to the horizontal is easily determined once the coordinate data from the anatomical markers at each end of the segment are known. By convention, all angles are positive in the counter-clockwise direction with the horizontal equal to zero degrees. When the position of two adjacent segments are known, the relative angle of the joint between them is logically derived. By convention, all angles in flexion or dorsiflexion are designated positive (Winter, 1979). The collection and reduction of cinematographical data inevitably results in the raw digitized coordinate data being composed of the actual marker displacement data and a random component of the signal identified as noise. The indirect determination of linear and angular velocities and accelerations by means of differentiation of displacement data serve to amplify the errors which exist in the original data. As the noise is spread equally across all harmonics, the displacement data must be smoothed prior to first and second order differentiation (Winter, 1987). Spectrum analysis reveals that the desired signal occupies the lower component of the frequency spectrum while the noise occupies the higher frequency. The selected filter should be designed to pass over the lower frequency spectrum without affecting the signal and attenuate the high frequency noise component. A low-pass Butterworth filter is commonly used to digitally filter raw coordinate data prior to differentiation. By comparing RMS difference between filtered and unfiltered film data, an indication of digitization noise may be obtained (Wells and Caldwell, 1982). The process of digital filtering introduces a phase lag into the output which must be overcome if filtered data are to be compared or synchronized with unfiltered data. A solution is provided by filtering the data once in the forward direction and once in reverse. This produces an equal and opposite phase lag so that the net shift is zero. The technique of digital filtering has been validated by Pezzack, Norman and Winter (1977). 7 Once the marker displacement data are suitably filtered, velocity may be simply determined by the finite difference between adjacent samples divided by the time interval between the samples (Winter, 1979). When velocity is calculated in this manner, the result does not accurately represent the velocity at either sample time. Winter (1979) recommends that the slope be calculated over two sample intervals so that velocity may be defined at each sample time. Similar differentiation of velocity-time data produce acceleration profiles. The kinematic parameters of joint angular displacement, velocity and acceleration are merely descriptors of human gait, insight into how or why the observed motion occurred is not possible. Insight into the actual driving mechanisms responsible for the observed movement is possible through the analysis of internal kinetic variables. Kinematic data in conjunction with external forces experienced by the musculoskeletal system serve as valuable input into the link segment model for the eventual calculation of internal kinetic measures. External Kinetics. The analysis of external forces acting on the body is termed external kinetics. This type of evaluation depends primarily upon the use of a force platform to measure the ground reaction forces (CRF) which act on the foot during stance. This force consists of a vertical component and two shear forces which are usually resolved into anterior-posterior and medial-lateral components (Dainty and Norman, 1987). Although the analysis of ground reaction forces do not provide insight into the internal mechanisms which cause movement, they do serve to illustrate the end effect of the mass-acceleration products of all body segment during stance (Winter, 1987). The typical force platform consists of piezoelectric crystals mounted at right angles to each other in the four corners of the plate. Any force applied to the platform surface results in the mechanical deformation of the crystals which alters their electrical conductivity. The change in the electrical signal is proportional to the magnitude of the force applied (Dainty and Norman, 1987). This permits the determination of force-time curves for the three orthogonal components of the ground reaction force and the location of the resultant force vector. Existing literature indicate that the vertical component of the resultant force is the largest in magnitude and of primary concern in the etiology of running injuries (Williams, 1985a; Frederick and Hagy, 1986). It is also this component which supplies the force input to the link segment model for 8 the calculation of muscle moments for flexion and extension. Consequently, it is this component of the ground reaction force which receives the most attention in gait mechanics literature. Factors which influence the magnitude of the ground reaction forces include; running speed (Hamill et al., 1983; Nigg et al., 1987), shoe composition (Clarke et al., 1983; Cavanagh et al., 1981), foot strike pattern (Cavanagh and Lafortune, 1980) and mass (Frederick and Hagy, 1986). It would appear that accurate insight into external kinetic variables is restricted to data obtained from a homogeneous group of barefoot runners characterized by the same foot strike pattern while performing at a strictly maintained horizontal velocity. The variability in force data resulting from different subject mass is overcome by normalizing all forces to individual body mass. Thus, each component of the ground reaction force should be expressed as N/Kg to facilitate between subject comparisons. Anthropometry. The basic anthropometric description of body segment parameters is necessary in the kinematic analysis of the total body center of gravity and as input into the mathematical model used in the approximation of muscle moments and joint reaction forces. Normative values derived from cadaveric research are often utilized to estimate appropriate values for living subjects. Dempster's (1955) extensive analysis of eight cadavers serves as the most frequently used set of normative values in biomechanics research. The author was able to determine the relative weight of each segment expressed as a percentage of the total body weight and the location of the segmental center of mass expressed as a percentage of the total segment length. Tables summarizing the normative values for these parameters are available in most biomechanics reference books and manuals. The validity of applying cadaveric values to the study of healthy athletic subjects has been questioned (Hay, 1985). Link Segment Model . The indirect calculation of internal parameters such as joint forces and muscular moments is possible with the use of a mathematical link segment model. Input required by the model include synchronized force and kinematic data in conjunction with the anthropometric 9 properties of each segment. Ultimately, the accuracy of internal kinetic values is determined by the precision of the input measurements. The lower extremity is modelled as a series of rigid segments and standard link segment equations developed by Bresler and Frankel (1950) are applied to each joint initiating from the point of force application at the foot and progressing proximally towards the trunk. Joint forces and net muscle moments are therefore calculated at each successive joint. A number of assumptions have been made to simplify analyses using the link segment model. The segmental center of mass is represented as a fixed point located at the segmental center of gravity. The location of the segmental center of gravity is considered to remain fixed during movement. All joints are modelled as pure hinge or pin joints. During movement, the mass moment of inertia of each segment is assumed to be constant about its proximal joint (Winter, 1979). It is also assumed that only one muscle group is active at any time and is therefore solely responsible for the observed movement. The accuracy of results obtained from the biomechanical link segment model are further limited as joint and muscle friction are considered to be negligible. Regardless of these assumptions and limitations, the error associated with this type of analysis is reported to be an acceptable 10 percent (Pierrynowski, 1982). The Biomech Computer Package developed by researchers at the University of Waterloo is frequently used in the mathematical modelling of human movement (Winter, 1983c; Pierrynowski, 1982; Winter and Robertson, 1978). The validity of muscular moments and joint reaction forces obtained by such models has not been fully verified but partial support is demonstrated in the correlation between muscular electrical activity and the predicted value of the muscular force (Dainty and Norman, 1987). Internal Kinetics. Internal kinetic variables such as joint forces and muscle moments serve as driving mechanisms for all externally observable variables. Researchers acknowledge that the moment of force-time history is one of the most valuable kinetic patterns used in the assessment of human gait mechanics (Winter, 1980). The moment of force patterns represent the net effect of all agonist and antagonist muscle activity at each joint. It has been postulated that examination of internal kinetic factors may shed light onto the mechanisms involved in the development of overuse injuries in 10 runners (Winter, 1983c). Joint reaction force calculations have been used to assess the magnitude of forces tolerated by the body during repetitive impact activities such as running (Dainty and Norman, 1987). The description of muscle moments follow a specific biomechanical convention. Counter-clockwise moments calculated at the proximal end of a segment are positive while clockwise moments are negative. As the standard link segment model assumes that only one muscle group is active at any time, the net effect of co-contracting agonist and antagonist muscles and frictional forces are reported as the resultant muscle moment. It is not possible to determine the relative contribution of each muscle group to the resultant moment. The muscle moment is described by the action of the dominant muscle group at each joint. An ankle plantarflexor moment would indicate that the muscles which act to plantarflex the ankle are creating a greater moment about the ankle than the dorsiflexors. The net effect of all muscle activity may be classified as either concentric or eccentric, based upon the direction of the angular velocity of the limb segment relative to the direction of the moment of force (Winter, 1979). For example, a eccentric knee flexor moment would mean that the knee flexor muscles were exerting a greater moment of force than the knee extensors but that the shank segment was moving forward into extension. As a positive muscle moment may describe a dominant flexor activity at the knee and net dorsiflexor activity at the ankle, it is advantageous to report all extensor moments as positive (Winter, 1987). This decision permits the identification of a single control pattern termed the support moment which is defined as the algebraic summation of extensor moments at the hip, knee and ankle (Winter, 1980). The support moment is consistently positive during the stance phase of gait due to the net extensor moment which must occur at each joint to maintain upright posture. Variability in Human Performance Coordinated human movement involves the integrated contribution of many muscles which influence motion at many joints. The result of this complex interaction between internal and external mechanisms is tremendous motor flexibility. The presence of agonist and antagonist muscle co-contraction and muscles which act upon more than one joint enable the production of the same kinematic movement from a variety of possible neuromuscular patterns. Variability in most measures 11 should therefore be expected even when conditions are carefully controlled and the activity is well learned (Kinoshita et al., 1983). The issue of cycle-to-cycle variability both within and between subjects must be addressed before a statement may be made on the functional status of an individual with a leg length inequality. Normal individual variability in gross motor patterns may be too large to statistically detect functional asymmetry in biomechanical measures. The coefficient of variation (C.V.) has been utilized to assess stride-to-stride variability in both kinematic and kinetic data. This statistic represents a variability to signal ratio and is equal to the root mean square of the standard deviation at each time interval divided by the mean magnitude of the signal over the entire stride (Winter, 1983a). Low coefficient of variation values, representing low variability, are generally reported for external kinetic and kinematic stance profiles while internal kinetic motor patterns are characterized by high C.V. values and are therefore relatively inconsistent. One coefficient is calculated to represent the total variability of the motor pattern over the entire stride. As a result, this statistic fails to identify periods of high and low variability. Consequently, identical C.V. values reported for two individuals may reflect medium variability throughout stance for one subject and high variability at heel strike followed by extreme consistency for the remainder of stance for the other individual. The coefficient of variation is also influenced by the magnitude of the signal which it describes. Although the absolute variability for two measures may be identical, the C.V. value would be higher for the variable with the greater magnitude. Kinematic Variability. Sagittal plane joint angle profiles collected from repeat trials on one subject demonstrate extremely consistent patterns during natural walking cadence. This uniformity is reflected in C.V. values of 12%, 7% and 25% for the hip, knee and ankle respectively (Winter, 1987). Joint angle data recorded from 19 individuals walking at a natural cadence illustrate the effect of intersubject variability with C.V. values of 52%, 18% and 68% at the hip, knee and ankle (Winter, 1987). External Kinetic Variability. Vertical and anterior-posterior components of the ground reaction force are characterized by highly uniform patterns from stride to stride. One subject walking at a natural cadence exhibited a vertical force C.V. value of only 7% while the anterior-posterior force C.V. was 20% (Winter, 1984a). When ground reaction force data were collected from 19 subjects, the 12 variability measures doubled but still remained relatively low (vertical force C.V .= 18%; A-P force C.V .= 43%). Internal Kinetic Variability. In the presence of consistency in external measures, the internal kinetic factors which actually cause movement demonstrate large variability from stride-to-stride. Joint moment of force curves for one individual walking may be fairly consistent at the ankle (C.V. = 16%) but variance is evident at the knee (C.V.= 53%) and the hip (C.V.= 92%) (Winter, 1987). When joint moment data are averaged over 16 subjects, the coefficient of variation values increase to 45%, 150% and 144% for the ankle, knee and hip respectively (Winter, 1984a). The source of this large variability may be partially explained by the presence of large muscles such as the quadriceps, gastrocnemius and hamstring complex, which have opposing functions at adjacent joints. These biarticulate muscles introduce flexibility to the motor patterns at these joints which is reflected in the coefficient of variation measures (Winter, 1984a). The lower variability at the ankle may be due to the predominance of single joint muscles controlling movement at this joint (Winter, 1984a). The consistency of joint moment of force patterns improves as speed of locomotion increases. Joint moment C.V. calculations for the hip, knee and ankle improve from 207%, 171% and 45% for slow walking to 77.5%, 45.3% and 36.2% for slow jogging (Winter, 1983b, 1983c). The author rationalizes that walking at a natural cadence is accomplished well within the extremes of forces tolerated at each joint and is loosely controlled without conscious effort. The reduced variability which occurs as the speed of locomotion increases is thought to be due to "the more conscious CNS control over the motor commands plus the fact that the muscle forces increase (as a percent of their dynamic range) thus leaving less room for a flexible exchange between muscle groups" (Winter, 1982 p.50). The indeterminancy of motor patterns and the difficulty associated with establishing representative moment profiles at each joint is illustrated by an example provided by Winter (1983a). While the foot is flat on the ground, the knee angle is controlled by muscle moments acting about the hip, knee and ankle. These three moments are the net effect of all forces generated by the various combinations of muscles acting on each joint. Consequently, an infinite number of motor pattern combinations may produce the same knee angle history from one stride to the next (Winter, 1984b). 13 It is therefore unrealistic to expect predictable muscle patterns even in the presence of highly consistent external measures. In spite of the variability in moment of force patterns demonstrated at each joint, the support moment is found to be consistently replicated. Support moment calculations reveal a highly consistent and symmetrical extensor moment during the stance phase of walking at various cadences (Winter, 1983b). The coefficient of variation is reported to be 14% for repeated trials recorded from one subject and 56% for group data (Winter, 1987; 1984a). The consistency in support moment patterns has been presented by Winter (1984a) as evidence that "neural control during walking involves a total lower limb pattern rather than control over individual joints" (p.72). The flexibility demonstrated in muscle moment of force patterns confound the assessment of gait as there is no unique solution to a given kinematic pattern. The considerable cycle-to-cycle variability exhibited in biomechanical parameters necessitate the collection of several trials to establish reliable mean values for each individual. Evidence of Biomechanical Symmetry As human gait is characterized by a uniform, coordinated interaction between the left and right legs, lower extremity functional symmetry is frequently assumed. Researchers and clinicians have equated symmetry with normalcy by utilizing functional equality between legs as a baseline in assessing pathological gait. The assumption of symmetry is strengthened by evidence of functional equality in temporal, kinematic and external kinetic measures. Evidence of Temporal Symmetry. Buckalew et al. (1985) utilized the 1984 pre-OIympic trials to collect bilateral kinematic data from elite female marathon runners. Utilizing bilateral temporal measures such as stride length, stride rate, support time and non-support time, the top ten finishers were compared to the women who placed from position thirty to forty. The authors concluded that all runners were functionally symmetrical and that no differences existed between experimental groups. The method of establishing symmetry was omitted and the statistical procedure utilized to support this conclusion was not described. Evidence of Kinematic Symmetry. Hannah et al. (1984) used electrogoniometers to measure hip and knee motion in the sagittal, coronal and transverse planes for 12 subjects walking barefoot. 14 Mean values from several strides were normalized in time and indices of symmetry were developed in both the time and frequency domains. These researchers concluded that high symmetry in lower extremity kinematics is to be expected in normal human locomotion. They further suggested that equality be used as the optimal state in the assessment of pathological gait. Evidence of External Kinetic Symmetry. Hamill et al. (1984) identified 20 ground reaction force measures designed to summarize the peak forces and impulses which occur during the foot to ground interphase. Means values from 10 trials were calculated for each leg in five walking subjects and five running subjects. Results were grouped and no significant differences (p<0.05) were found between the left and right legs. The pattern of external kinetic symmetry remained when the data were rearranged to reflect the difference between the preferred and non-preferred limb. Balakrishnan and Thornton-Trump (1982) developed a symmetry index which utilized the integrated GRF curves for each leg and divided the value obtained from the left leg by that recorded from the right. The results suggest that although external kinetic data are not exactly symmetrical in normal subjects, they are very similar. Although support for functional equality is scarce, the assumption of symmetry continues to exist in the clinical and biomechanical assessment of gait. The following section summarizes the literature which demonstrate bilateral asymmetry in the general description of gait. Evidence of Biomechanical Asymmetry Biomechanical evidence which refute the validity of assumed functional symmetry exists in the general assessment of human gait. Bilateral assessment of normal individuals has confirmed asymmetry in temporal, kinematic, external and internal kinetic measures. Evidence of Temporal Asymmetry. Utilizing a symmetry index, normal subjects have been shown to demonstrate inequality in stance duration, foot angle and stride length (Chodera, 1974; Dewar and Judge, 1980). Attinger et al. (1987) applied a temporal asymmetry index to a diverse group of asymptomatic individuals in an attempt to establish normative profiles. Slight asymmetries in force and temporal measures were found in the majority of subjects. Analysis of variance technique was utilized by Rosenrot (1980) to statistically demonstrate that a high degree of temporal asymmetry existed in the double support time of normal individuals. In a 15 comprehensive evaluation of running kinematics and kinetics, Williams (1985a) found that some individuals exhibited significant differences between left and right sides in measures of contact time, stride width and foot abduction angle. Although Williams (1985a) found no statistically significant mean absolute difference in stride length, the large relative difference of 6.1 cm was considered functionally significant. Evidence of Kinematic Asymmetry. Significant asymmetries have been reported during walking in lower leg angle and achilles tendon angle (Vagenas and Hoshizaki, 1988). The angular displacement histories for the foot and shank also revealed a distinct asymmetry between legs. Rearfoot angles calculated for the first 130 ms after footstrike illustrated asymmetry in both the fatigued and unfatigued conditions in two elite middle distance runners (Cavanagh et al., 1985). Kinematic asymmetries in arm motion have also been reported (Riley et al., 1977). Evidence of External Kinetic Asymmetry. A symmetry index was utilized by Herzog et al. (1989) to establish a ratio between the left and right legs for variables describing the peak forces and impulses collected from the three components of the ground reaction force. Not one of the 62 subjects demonstrated perfect symmetry (as indicated by a ratio of zero). The asymmetries noted for the vertical and anterior-posterior components of the ground reaction force and stance duration were very small, with deviations from zero of less than 4 percent. Evidence of kinetic inequality in two individuals is provided by Cavanagh et al. (1985), who report that one subject exhibited a vertical force profile typical of a rearfoot striker on the left side while the right leg was characterized by a midfoot strike pattern. In another subject, the peak vertical force and the loading rate for the right leg was almost twice the magnitude of the left. Although Munro et al. (1987) found no significant bilateral differences in pooled data describing the stance time, average vertical CRF, loading rate and braking impulse for normal subjects, analysis of individual subject data revealed significant differences between the right and left legs. Williams (1985b) also found that when data from several subjects were averaged, individual differences in temporal and CRF variables were obscured. Evidence of Internal Kinetic Asymmetry. To date, the issue of left-right functional asymmetry has not been applied to the study of joint forces and muscle moments. Pierrynowski et al. (1980) 16 studied the energy flow between the drive motor of a treadmill and a number of subjects. Results collected over 50 strides from both the left and right legs indicated that the peak energy flows for each leg were statistically different for all subjects (p <0.01). Asymmetrical partitioning of work output from each leg was found to be a typical feature during cycle ergometry which was unrelated to lower limb dominance (Daly and Cavanagh, 1976). Functional asymmetries have also been observed in the strength of lower extremity musculature (Rosenrot, 1980). No attempt has been made to identify mechanisms which may be causally related to observed functional asymmetry in many biomechanical measures. One may speculate upon the influence of anatomical asymmetries on the functional status of an individual. Structural inequality in the form of a leg length differential may logically be manifested as functional asymmetry in biomechanical measures. Leg Length Differences Leg length asymmetry may result from structural or functional inequality or a combination of both. Structural asymmetry is due to an actual discrepancy in bone length resulting from factors such as unequal development, fracture, dislocation or epiphyseal irritation with lengthening (Blustein and D'Amico, 1983). Functional asymmetries occur in response to altered lower extremity mechanics which give the appearance of a short leg. Etiological factors include malalignment, joint laxity, genu valgum, genu varum or pelvic imbalance. An individual may therefore present with a measurable leg length discrepancy in the presence of symmetry in bone length. Prevalence of Leg Length Inequality. The reported prevalence of leg length asymmetry in the normal population ranges from as low as 4 - 8% to as high as 90 - 95 % (Rush and Steiner, 1946; Stoddard, 1954 and Nichols, 1960 in Gross, 1983). The low incidence of leg length inequality is demonstrated in 50 asymptomatic subjects recruited by Giles and Taylor (1981). Only 8% were found to have a leg length discrepancy greater than 9 mm when measured by erect posture radiography. Evidence of high prevalence of leg length differentials is presented in several studies (Friberg and Kvist, 1984; Pappas and Nehme, 1979; Blustein and D'Amico, 1985). The random assessment of bilateral leg length in 266 army conscripts revealed structural asymmetry in 85% of subjects (Friberg 17 and Kvist, 1984). Of these individuals, 21.7% had an leg length differential greater than 10mm. This observation lead the authors to suggest that inequality in leg length should be considered a normal variant. An average leg length difference of 1.1 cm was reported in 95.5% of the 376 normal subjects measured in a survey performed by Pappas and Nehme (1979). Estimations of the prevalence of leg length differentials are hampered by the lack of unanimity surrounding the definition and determination of leg length inequality. The controversy involves whether the definition should include all measurable leg length differences or only those which disrupt normal function. There is also a lack of consensus concerning the degree of inequality required to cause postural adaptation and associated pain. A survey of orthopedists failed to identify a critical differential beyond which pain indicating corrective intervention could be expected (Cross, 1978). While some authors believe that a leg length discrepancy of less than 5 mm may be mechanically related to pathologies of the hip, pelvis and spine, others claim that differences of over 12 mm are not clinically significant (Woerman et al., 1984). Tolerance would appear to be influenced by individual response to the inequality and to the stresses imposed upon the lower extremity. The reported ability of the human body to painlessly adapt to leg length differentials varies from one to three inches in the inactive population to 1/8 inch in the running community (Beekman et al., 1985). Leg length inequality has been associated with a well documented pattern of postural adaptations. Pathomechanics. Blustein and D'Amico (1985) summarize the compensatory gait mechanics associated with a leg length discrepancy. The adaptations to the longer leg involve a prolonged stance phase and maximal pronation of the subtalar joint. This modification serves to effectively shorten the limb by plantarflexing and adducting the talus and everting the calcaneus, causing a decrease in calcaneal inclination. In the normal foot, the midtarsel joint locks to provide a stable foot during the period of maximum locking. Compensatory pronation of the long leg serves to delay this locking mechanism. The extrinsic musculature of the unstable pronated foot is eventually overstressed in the attempt to resupinate the foot against body weight. Postural adaptations to the short limb involve subtalar joint supination which causes an increase in calcaneal inclination and a decrease in talocalcaneal angle and talar declination. These compensations serve to effectively lengthen the shorter limb and rebalance the pelvis (Blustein and 18 D'Amico, 1985). Compensation may also be manifested as disrupted motor patterns further up the kinetic chain. This is illustrated by the presence of pelvic drop and scoliotic spinal deviation to the shorter side. Ultimately, increased stress is experienced by the lower back musculature and vertebrae. An asymmetric increase in electromyographic activity in several muscle groups in the lower back has been reported with a leg length differential of 10 mm (Taillard and Morscher, 1965 in Friberg, 1983). Leg length inequality may not be detected until injuries occur resulting from prolonged postural adaptation. Compensatory pathomechanics in the presence of subtle leg length differentials, combined with the potentially destructive forces transmitted to the foot with every heelstrike have been linked to the development of overuse injuries (Gross, 1983; James et al., 1978; Cavanagh and Lafortune, 1980). Injuries related to Leg Length Inequality. The myriad of symptoms related to leg length inequality reveal the range of compensations experienced by the body as it attempts to return to a state of symmetry. Related injuries include collapse of the medial longitudinal arch, medial plantar fasciitis, anterior tibial shin splints, chrondromalacia patella, iliotibial band strain, sciatica, unilateral calluses and hip osteoarthritis, intervertebral disk herniation, nerve root compression syndromes and degenerative joint disease (Blustein and D'Amico, 1985; Subotnick, 1981). In a survey of 1500 army conscripts identified with a leg length differential, Friberg and Kvist (1984) concluded that unilateral stress fractures and sciatic nerve pain occurred in the longer lower extremity in 70 - 80% of subjects while knee pain occurred on the short side in 73% of cases. The authors concluded that even subtle leg length differences in individuals exposed to heavy physical stress and loading of the lower limbs may be clinically significant. Leg length inequality has been identified as one of the most prevalent etiological factors associated with the development of overuse injuries in runners (Clement et al., 1981). In opposition to these finding, Gross (1983) reported that 14% of a group of 35 asymptomatic marathon runners exhibited a leg length differential greater than 12 mm. Although no statistical analysis was performed, the author concluded that leg length inequality between 5 and 25 mm was not found to be functionally detrimental. 19 The lack of consensus in many of the issues related to leg length inequality is largely due to differences in defining and determining lower extremity differences. The following section summarizes the various clinical methods of determining leg length differentials. Methods of Assessing Leg Length Differences Leg length determination may be achieved by either direct or indirect methods. The direct evaluation of leg length assesses the linear distance between two anatomical landmarks either on a roentgenologic image or the skin surface. The practitioner is then able to estimate bone length, calculate the differential and identify the specific region of the length discrepancy. Leg length may be determined indirectly by placing wedges under the shorter limb until the pelvic obliquity associated with leg length asymmetry is eliminated. This method of assessment produces a measure of the effective length differential of the each limb but does not enable the researcher to determine whether the cause of the leg length difference is structural or functional. Direct Methods. Direct measurements of leg length may be performed in either the supine or weight bearing position. As upright posture is maintained during gait, leg length determinations obtained in this position would ensure a more accurate assessment of the postural status of the individual during running. A summary of several methods of directly determining leg length are provided below. (a) roentgenologic techniques: In cases where leg length must be determined within millimeters, roentgenological methods are recommended. This procedure involves either x-ray of the entire length of both legs simultaneously (teleradiography) or the exposure of a metal ruler and the joint areas of each leg while the subject is in the supine position (orthoroentgenography). The leg length differential is measured as the difference in heights of the bone ends at each joint (Morscher and Figner, 1977). The accuracy of different methods of determining leg length are frequently evaluated by comparing results with those obtained from radiographic methods but the errors associated with this method are often not reported. The disadvantages to the various X-ray procedures encompass extended exposure to powerful rays, careful positioning of the subject and the occasional restriction of assessment in the supine position (Clarke, 1972; Woerman et al., 1984). Errors result from imprecise 20 centering of the roentgen ray, varying thickness of the soft tissue layer, and poor contrast in the vicinity of the ankle joint (Morscher and Figner, 1977). Exposures are typically performed in the frontal plane which may artificially produce an image of a short leg if the knee is slightly flexed. When this technique is performed properly, the degree of accuracy is reported to be as low as 3 mm (Rothenberg, 1988). (b) Tape measure: An inflexible tape measure may be used to obtain the linear distance between two marks on the skin surface. The results obtained by using a metal tape measure to evaluate the distance from the ASIS to the medial malleolus have been reported to be reliable and valid by Gogia et al. (1986) and Nicols and Bailey (1955). Conversely, this method has been acknowledged as inaccurate in several studies (Morscher and Figner, 1977; Woerman et al., 1984). Obvious sources of error include tape flexibility, inaccuracy in locating landmarks, pelvic tilt, muscular asymmetry and movement of the skin while measuring. In a study reported by Clarke in 1972, a tape measure was used to estimate the distance between the ASIS and the medial malleolus in 50 structurally asymmetrical subjects assessed in the supine position. Two trained examiners were within 5 mm of the leg length values obtained from weight bearing radiographic results in 40% of the subjects. Methodological errors associated with this study include the different positions used in each measurement condition. Functional leg length inequalities would not be detected with the supine tape measurement but would become evident in the erect position used for the radiographic evaluation. (c) anthropometer: The recommended instrument for this type of assessment is the Siber-Hegner G P M anthropometer. The anthropometer is comprised of a calibrated beam with one stationary wand and one mobile wand able to move along the length of the beam. Anatomical landmarks defining the ends of each segment are determined and marked. The beam is positioned parallel to the long axis of the segment with the tip of the stationary blade touching one segment end and the moving blade manipulated to reach the other segment end. The measurement of segmental length is read from the calibrated beam. A footplate replaces the stationary blade for the determination of landmark heights from the standing surface. 21 (d) Biplanar computed tomography (CT) scan technique: This method of leg length assessment involves the patient lying supine on a moving bed while a stationary x-ray beam scans in both the frontal and sagittal planes (Class and Poznanski, 1985). This circumvents the problem of erroneously detecting leg length inequality due to a flexed knee. Indirect Methods. The indirect methods of determining leg length rely upon the observed pelvic tilt towards the shorter leg in asymmetrical individuals. (a) wedges: Leg length may be indirectly determined in the standing position by placing calibrated wedges under the shorter limb until pelvic obliquity is perceived to be eliminated. The height of the lift inserted indirectly measures the extent of the leg length discrepancy. This method of assessment does not enable the researcher to determine whether the cause of the differential is due to an actual discrepancy in bone length or the result of malalignment. Woerman et al. (1984) evaluated five methods of clinically measuring leg length and compared the results to those obtained from radiographic procedures. The wedge method was reported to be the most accurate and precise means of establishing the leg length differential. Errors linked to this method include the possibility that asymmetries in pelvic architecture may erroneously be detected as leg length inequality. (b) orthotractor: This device incorporates a carpenter's level to objectively determine the angle and distance between the two anterior-superior iliac spines (Okun et al., 1982). The orthotracter enables the practitioner to distinguish between functional and structural asymmetry by performing measurements in both the neutral and relaxed calcaneal positions. Again, the possibility exists that asymmetries in pelvic architecture may imitate leg length inequality. Sources of Errors. External methods of determining leg length rely upon an approximation of the unknown actual anatomical length. Standard techniques and protocols have been developed in an attempt to reduce the discrepancy between obtained and true values. In spite of these efforts, large residual errors occur with some regularity in any anthropometric survey (Johnston et al., 1972). Errors associated with the determination of leg length include inaccuracy in palpating and marking anatomical landmarks, movement of the skin, random fluctuations of the measurement instruments, 22 recording errors and postural adaptations of the subject. An accepted anthropometric method of determining and documenting assessor reliability is the technical error of measurement. Technical Error of Measurement. The technical error of measurement (TEM) is calculated to express differences between repeated measures and therefore may provide an estimation of assessor reliability. A correlation coefficient could also be used to provide a relative measure of precision but this statistic merely reflects how well the repeated trials vary together (Ross and Ward, 1985). The TEM calculation represents the absolute difference between repeated trials. The technical error of measurement is defined by Hermanussen et al. (1988) as: (sum (xn - ~ 1 ) 2 + sum (x 2 -"x"2)2 / K (n-1))** 0.5 where x= variable measured k= the number of subjects measured, and n = the number of pairs of repeated measures. Coefficient of Variation (C.V.). Johnston et al. (1972) recognized that the TEM value was directly proportional to the size of measurement. Thus, measurements producing lower average readings were mistakenly associated with greater observer reliability. When the TEM was expressed with respect to the appropriate mean, a measure of the relative error was obtained with the same units of measurement as the variable being analyzed. Coefficient of Variation = (TEM x 100) / mean of variable. Median Score. Although the mean value is statistically the most reliable measure of central tendency with repeated measures, the median value is selected in anthropometry. It has been proposed that the median value is more resilient to the effects of mislocated landmarks, misreading, arithmetic and round-off errors (Ross and Ward, 1985). This contention was tested by Ward (1989) when gross errors were programmed into a set of triplicate anthropometric (skinfold) measures. The technical error of measurement between the actual criterion value was compared to the criterion value from the erroneous data set. The median score was consistently shown to be the most resilient measure to this imposed error. 23 Chapter 3 PROCEDURES The objective of this study was to address two issues related to the assumption of biomechanical symmetry in human gait. First, to determine if the general assumption of biomechanical symmetry remained valid in individuals with lower extremity structural asymmetry. Secondly, to determine if runners adapt to a leg length inequality with a universal compensation strategy which could eventually be linked to the etiology of overuse injuries. Research design Subjects were assigned to either the structurally symmetrical or structurally asymmetrical group based upon anthropometric determination of leg length. Lower limb kinematic, ground reaction force and internal kinetic data were collected from each leg for all subjects. For the symmetrical group results of the left leg were compared to those obtained for the right, while in the asymmetrical group data from the long leg were compared to the data collected from the short leg. The ratio of one leg to the other was assessed as a symmetry index. Mean symmetry index values for selected kinematic, external kinetic, joint force and muscle moment features were pooled for each group. This allowed a general statement to be made on the assumption of biomechanical functional symmetry in the presence of structural inequality. This analysis would also reveal common compensation strategies in the structurally asymmetrical group if they existed. It was recognized that the analysis of group profiles may obscure functional asymmetries which may exist in the biomechanical profile of each individual. To investigate this possibility, an integrated biomechanical assessment was performed on two runners from each of the experimental groups. Statistical Analysis The commitment of time and money associated with the complete biomechanical assessment of human gait mechanics logistically limits the number of subjects analyzed. As a review of the literature failed to provide any indication of the impact a leg length inequality may have on the biomechanical profiles collected from each leg, the researcher was reluctant to limit the number of 24 variables assessed. Consequently, many kinematic and kinetic variables were evaluated for both experimental groups. It was assumed that an inequality in leg length would be manifested as asymmetry detected in biomechanical measures. The attempt was therefore made to reveal evidence of functional asymmetries in the descriptive assessment of graphical data. Each experimental group was assessed for equality using a symmetry index. This calculation produced the absolute difference between mean values calculated for each leg. This differential was then evaluated relative to the maximum value measured for each variable and a statement on the functional significance of the inequality was provided. For example, the absolute difference between the long and short legs for the variable of first vertical force peak may be 0.5 N/Kg. This difference would not be considered functionally significant in light of the fact that the maximum vertical force experienced during stance may exceed 30.0 N/Kg. If this type of analysis exposed one variable which demonstrated functional asymmetry, subsequent analyses may utilize traditional statistical techniques in the attempt to determine the impact an inequality in leg length may have on this one variable. Subjects The subjects were 10 competitive male middle distance runners training in excess of 50 km per week. All subjects were characterized as rearfoot strikers. The structurally symmetrical group was composed of five runners with a measured leg length differential of less than 3 mm. The structurally asymmetrical group consisted of five runners demonstrating a leg length discrepancy of 10 mm or greater. A complete history of lower extremity injuries affecting training in the previous 12 months was recorded. At the time of testing, all athletes were free of any musculoskeletal complaints. Prior to data collection, each athlete was informed of the nature of the study and consented to participate. Data Collection Anthropometric Protocol. Subjects underwent a series of anthropometric measurements involving three repetitions of bilateral leg and lower extremity segment lengths. One individual was responsible for the determination of leg length in all 10 runners. As the purpose of the study was to investigate the biomechanics of runners in an erect position, weight bearing anthropometric measures 25 were selected. The anatomical landmarks selected and the techniques utilized are summarized in Appendix A. Anthropometric data were required for the determination of leg length asymmetries and as input to the link segment model. Leg length assessment was based upon bilateral measurements of the anterior superior iliac spine to the medial and lateral malleolus as well as the distance from the greater trochanter to the floor. No attempt was made to distinguish between structural and functional leg length inequality. This decision was based upon research by Woerman et al. (1984) who state that the "mechanical effects on the kinetic chain are potentially the same for either" (p.230). For the purposes of this study, it was theorized that evidence of any form of leg length asymmetry would result in detectable asymmetry in measured biomechanical variables during running. With the intent of determining tester reliability, the anthropometric protocol was repeated in an independent sample of two volunteers for six consecutive days. An estimation of tester precision was provided in the technical error of measurement (TEM) for each measurement performed (Ward, 1989). As recommended by Hermanussen et al. (1988), the first measurement in the series was omitted from the TEM calculations. The calculated TEM values ranged from 3.28 mm for trochanteric height to 3.59 mm for the ASIS to the medial malleolus. These results are in accordance with values reported in the literature (Cameron, 1978). Based upon these results, the criterion value for leg length differential in this study was determined to be 10.0 mm. Kinematic Protocol. Video recording was utilized to categorize subjects based upon the region of initial contact between the foot and the floor. Only runners classified as rearfoot strikers while performing at a 4.88 m/s (5:30 min/mile pace) were accepted for this study. A Locam 16mm camera was positioned 7.85 m from the force plate centre with the optical axis perpendicular to the plane of progression. Cinematographical data were recorded at 150 frames/sec. The camera was activated by photocells prior to force platform contact to ensure that full operating speed was achieved before the subject entered the field of vision. Background coordinates painted at known intervals on the adjacent wall provided information necessary to correct for perspective and parallax error. High contrast markers were affixed to both the left and the right sides of the body on the following anatomical landmarks: toe, heel, ankle (lateral malleolus), knee (lateral femoral epicondyle), hip (greater trochanter 26 of the femur). A marker affixed to the lateral aspect of the trunk at the level of the bottom rib served as the proximal marker for the trunk. Kinetic Protocol. The collection of external kinetic data involved a Kistler Model 9261-A force platform flush mounted in a straight 20 metre indoor runway. Sufficient practice was permitted to ensure that contact with the force platform was made in a smooth, unbroken running stride at the required running speed. Subjects performed an average of 50 practice trials for each leg before being asked to rehearse barefoot. Rearfoot strike patterns were confirmed by visual inspection of the characteristic biphasic profile of the vertical component of the ground reaction force. Running speed was monitored within 5% of the desired pace by photocells positioned at trunk height on either side of the force platform. The braking and propulsive impulses for each trial were monitored on an oscilloscope to determine if the subject was accelerating or decelerating during the step sampled. Trials which differed more than 5% from the desired speed, demonstrated inequality in the anterior-posterior impulses, or for which targeting was evident were rejected. A total of 12 successful trials were retained for analysis. Half of the trials were performed with the right foot contacting the platform and the remainder involved the left foot. Consequently, data recorded for each leg were not obtained from consecutive footfalls. The force platform output was sampled through a 12-bit analog-to-digital converter at a rate of 500 Hz/channel by a DataCeneral MicroNova MP200 computer. Data Analysis A computer software package resident in the University of British Columbia mainframe computer performed digital filtering of digitized coordinate data, estimations of noise, full kinematic analysis, and the internal kinetic calculations of joint forces and muscle moments. This procedure is outlined by Winter (personal communication, 1989). Kinematic and kinetic data from each leg were assessed for functional equality using a symmetry index. For the structurally symmetrical group, the value from the right leg was subtracted from that for the left leg for each of the variables analyzed. The symmetry index value would be zero if complete functional symmetry existed between the two legs. A positive value would indicate that the value for the left leg was greater than that for the right, 27 while a negative symmetry index value would represent a greater value for the right leg. In the structurally asymmetrical group, the value for the short leg was subtracted from that for the long leg. External Kinematics. The complete stance phase of each trial was analyzed by projecting the visual film image onto the digitizing tablet one frame at a time using a L.W. International (model no.224A) 16 mm projector. The cartesian coordinates for each marker were digitized by a Numonics graphics calculator interfaced with a Data General MicroNova MP200 computer. Data were then transferred to The University of British Columbia mainframe computer where raw coordinate data for each trial was scaled and corrected for perspective and parallax error with a matrix transformation adapted from that described by Woltering (1975, 1976). The raw coordinate data were filtered with a 4th order, zero lag low-pass Butterworth filter with a cut-off frequency of 10.0 Hz. This reduced the high frequency noise component of the signal associated with filming and the digitization process. The appropriate filter cutoff frequency was determined by comparing the RMS difference between filtered and unfiltered data as the cutoff frequency was manipulated from 4.0 to 12.0 Hz (Wells and Caldwell, 1982). By plotting filter cutoff frequency against RMS residual, the point at which the signal and noise occurred at the same frequency was determined to be 10.0 Hz. Coordinate data from segment end points were used to calculate the joint angles at the hip, knee and ankle. In an attempt to disclose possible asymmetries in the kinematic data, variables describing the maximum range of motion in flexion and extension at the hip, knee and ankle were calculated for the left and right legs of each subject. A symmetry index was utilized for the individual assessment of functional equality between legs. The mean value for the left leg was compared to that for the right in the structurally symmetrical group while the asymmetrical group compared the long leg to the short leg. The symmetry index values for each individual were averaged to produce a group mean index of symmetry for each of the variables analyzed. This data allowed a statement to be made on the general assumption of functional symmetry in kinematic measures. The kinematic variables of segmental angular velocity and acceleration were not assessed for symmetry, but served as input into the link segment model. External Kinetics. Initial manipulation of ground reaction force data was performed on a Data General Micronova MP200 computer. To facilitate intersubject comparisons, the total stance duration 28 was normalized to 100% and the three components of the ground reaction force were normalized by individual body mass. Ensemble averages of ground reaction force profiles from six trials were calculated for the left and right leg of each subject. Values describing the total stance duration, mean first vertical peak force, mean second vertical peak force, net braking impulse and net propulsive impulse were calculated for each subject and functional equality was determined by the symmetry index. The left leg was compared to the right in the structurally symmetrical group while the asymmetrical group compared the long leg to the short leg. The symmetry index values for each individual were averaged to produce an estimate of symmetry for both experimental groups. This data allowed a statement to be made on the general assumption of functional symmetry in kinetic measures. The normalized ground reaction force data were then transferred to the Amdahl computer for synchronization with the appropriate kinematic data and the eventual determination of internal kinetic data. Internal Kinetics. Filtered marker coordinate data were synchronized with the appropriate anthromopetric and normalized ground reaction force data and applied to a standard link segment mathematical model. Equations developed by Bresler and Frankel (1950) were applied to each joint initiating from the point of force application at the foot and progressing proximally towards the trunk. For each subject, bilateral estimations of vertical joint force and net muscle moments were produced for each lower extremity joint during the stance phase of running (Bresler and Frankel, 1950; Pierrynowski et al., 1980). Joint reaction force and muscle moments of force values for every 20% of stance were retained from each leg and assessed for functional equality using the symmetry index. The left leg was compared to the right in the structurally symmetrical group while the asymmetrical group compared the long leg to the short leg. The symmetry index values for each subject were then averaged to produce an estimate of functional symmetry for both experimental groups. This data allowed a general statement to be made on the assumption of functional symmetry in internal kinetic measures. The net support moment data was compared in the same manner. Individual Analysis. It was recognized that averaging individual data to produce a mean profile representing the entire group may obscure evidence of functional asymmetry in individual data. To investigate the possibility of functional asymmetry in individual data, a comprehensive biomechanical 29 assessment was employed on two subjects from each experimental group. The four subjects selected represented the two extremes of the compensation spectrum. One individual from each experimental group was characterized by relative functional equality on all levels of analysis. The remaining two runners demonstrated functional asymmetry at most levels of evaluation. Analysis of the data collected from the two structurally asymmetrical runners was employed to determine if universal strategies were utilized by both runners in an attempt to compensate for an inequality in leg length. 30 Chapter 4 RESULTS A N D DISCUSSION The results and discussion are presented under the following headings; (a) Description of the subjects; (b) Group kinematic data; (c) Group external kinetic data; (d) Group internal kinetic data; (e) The influence of speed on moment coefficient of variability values; (f) Integrated analysis of individual data. Description of Subjects Ten competitive asymptomatic, male runners characterized as rearfoot strikers served as subjects in this study. The mean age, height and mass of all subjects were 26.0 +/- 6.88 years, 177.86 +/- 6.04 cm, and 70.17 +/- 4.82 kg respectively. Complete descriptive data for each subject are tabulated in Appendix B. The two experimental groups were differentiated by the amount of structural inequality in lower extremity length. All members of the structurally symmetrical group demonstrated a leg length differential of less than 3 mm, while the asymmetrical group were characterized by a leg length difference of greater than 10 mm. The bilateral leg length measurements for each subject are presented in Appendix C. Group Kinematic Data The angle profiles for the ankle, knee and hip for each experimental group are summarized in Figures 1-3. Each curve represents the ensemble average of 30 trials collected from five different subjects. The abscissa of all plots are expressed as a percentage of the total stance duration from heel strike (at 0%) to toe off (at 100%). The symmetrical group compared the results of the left leg to those obtained from the right, while the asymmetrical pool contrasted the data from the long leg to that collected from the short leg. Visual inspection of the graphs revealed varying degrees of symmetry at each joint for both structurally symmetrical and asymmetrical group of runners. Graphically, left-right asymmetry appeared to be greater in the structurally symmetrical group of subjects. As the total range of motion at each joint was similar for both groups, the significance of each curve will be described together. A near neutral ankle position was maintained at heel strike with the ankle gradually becoming more dorsiflexed during weight acceptance. Plantarflexion began to occur at approximately 50% of 31 40 -20 0 SYMMETRICAL 20 40 60 PERCENT STANCE 80 100 40 30 + (J LU R 2 0 •20 0 ASYMMETRICAL 0 = S H 0 R T C. V. = 3 2 . 2 7 . X = L 0 N G C. V. = 2 6 . 2 '/. -t-20 40 60 FERCENT STANCE 80 100 Figure 1 (a) Mean Ankle Angle - Structurally Symmetrical Croup. (b) Mean Ankle Angle Structurally Asymmetrical Croup. 32 60 SYMMETRICAL LU-LU § 2 0 + 0 = R I G H T C . V.= 1 8 . 67 . X = L E F T C . V . = 8 . 5 V. 10' 60 LU § 2 0 20 40 60 PERCENT STANCE ASYMMETRICAL • - S H O R T C . V. = 1 5 . 37-X = L O N G C . V . = 1 4 . • 7. 80 100 10- > » - • ' — i — i — i — • — • — i— 20 40 60 PERCENT STANCE 80 100 Figure 2 (a) Mean Knee Angle - Structurally Symmetrical Croup. (b) Mean Knee Angle - Structurally Asymmetrical Croup. 33 20 40 60 PERCENT STANCE 100 40 3 0 -LD 2 0 " U J a U J 10 + _i LD Z < 0 + ^ 1 0 --20 ASYMMETRICAL 0 = S H 0 R T C . V . = 2 7 . 4 7 X = L 0 N G C . V . = 3 6 . 7 ' / . > - ' T 20 40 SO PERCENT STANCE 80 100 Figure 3 (a) Mean Hip Angle - Structurally Symmetrical Group. (b) Mean Hip Angle - Structurally Asymmetrical Group. 34 the total stance duration in preparation for push off. The mean ankle profiles closely reflect the range of motion reported in the literature for fast walking (Winter, 1987). It is possible that the limit to the dynamic range of motion at this joint is reached during fast walking and further increases in speed of locomotion would be reflected in the kinematic patterns at the knee and hip. In the general overview of running biomechanics, Williams (1985a) concluded that no systematic changes were apparent in the range of motion at the ankle joint with increases in speed. During stance, the knee angle curves reflect the typical pattern of flexion as weight is accepted and the downward movement of the total body center of mass is slowed and stopped, followed by extension during the later portion of stance. Extension at the knee contributes to the thrust which accelerates the body away from the ground. In contrast to fast walking, the knee does not reach full extension during running (Winter, 1987). The total range of motion at the knee is approximately 3 0 ° for both walking and running, but the motion occurs from a position of greater flexion during fast running. During stance, the hip gradually moves from a position of approximately 3 0 ° flexion at heel strike into an extended position at toe-off. The total range of motion recorded at the hip in this study corresponds closely to that described for fast walking although the movement occurs in a position of greater flexion during running (Winter, 1987). This may be due to the greater trunk inclination observed in fast running. Although slight asymmetries between legs and between groups were noted in the visual inspection of joint angle plots, the differences were small. This is illustrated by the group symmetry index values for the maximum range of motion in flexion and extension at each joint which are tabulated in Appendix D. As the symmetry index represents the absolute difference between legs, functional asymmetry is indicated by any value not equal to zero. Analysis of results reveal that functional asymmetry is found in both experimental groups for all kinematic measures, although differences range from 0 . 5 ° for the variable of maximum ankle plantarflexion for the symmetrical group to 5 . 5 ° for maximum hip flexion in the same group. In the structurally symmetrical group, the left leg experienced a greater range of motion for all variables except hip extension. In the group of 35 runners characterized by leg length inequality, the long leg demonstrated a greater range of motion for knee flexion and extension as well as hip extension. Kinematic profiles assembled for each experimental group demonstrated movement patterns which approximated symmetry. No obvious differences were noted between groups in the symmetry index values for the variables analyzed. Thus, given these kinematic data, the assumption of functional symmetry appears to remain valid even in the presence of measurable lower extremity structural asymmetry. Group Ground Reaction Force Data The group mean profiles for the vertical and anterior-posterior (A-P) components of the ground reaction force are presented in Figures 4 and 5. Prior to establishing group results, individual data were time and amplitude normalized. Group profiles were therefore presented with force normalized to body mass and time normalized to percent stance duration. Visual inspection reveals that both groups demonstrated some degree of functional asymmetry in both components of the ground reaction force analyzed. Individual values for the variables of first and second vertical peak forces, braking and propulsive impulses and total stance duration were assessed for equality using the symmetry index. The individual data were then averaged to produce group results for the structurally symmetrical and asymmetrical pools. Individual and group data are summarized in Appendix E. The vertical component of the ground reaction force depict the typical biphasic profile characteristic of rearfoot strikers. The initial peak vertical force occurs as a result of heel strike and the second inflection is due to push-off. The peak vertical forces experienced by the foot approach 30 N/Kg during fast running. This is approximately three times the magnitude of force reported for walking at a natural cadence (Winter, 1987). The group symmetry index values calculated for the vertical impact peak force were 0.4 (+/- 3.9) N/Kg and 0.6 (H-/-8.5) N/Kg for the symmetrical and asymmetrical groups respectively. As these differences represent only 1.6% of the average vertical force experienced during heel strike, the disparity between legs was not considered to be functionally significant. The difference between the left and right leg for the second vertical peak force was 5.4 (+/-13.5) N/Kg for the structurally symmetrical group. 36 PERCENT STANCE Figure 4 (a) Mean Vertical Force - Structurally Symmetrical Group. (b) Mean Vertical Force - Structurally Asymmetrical Group. 37 Figure 5 (a) Mean Anterior-Posterior Force - Structurally Symmetrical Croup. (b) Mean Anterior-Posterior Force - Structurally Asymmetrical Croup. 38 This large discrepancy is due to considerable functional asymmetry in one runner. The magnitude of the anterior-posterior (A-P) force experienced during fast running approach 4.0 N/Kg, which is approximately 1.5 times greater than that reported for normal walking (Winter, 1987). Assessment of the A-P force profiles demonstrate near equality in the net braking and net propulsive impulses for each group. This is evidence that as a group, the runners maintained a constant horizontal velocity during the data collection. Propulsive and braking impulses were calculated and assessed for functional equality using the symmetry index. The largest discrepancy between legs was 0.071 (+/-0.102) Nsec/Kg for the braking impulse of the asymmetrical group. Results indicate that functional asymmetry occurred in both experimental groups for all external kinetic measures analyzed, but these differences were small and not considered to be functionally significant. No obvious differences were noted between groups in the symmetry index values for the variables analyzed. These data suggest that the assumption of external kinetic functional symmetry remains valid even in the presence of measurable lower extremity structural asymmetry. Group Internal Kinetic Data The group internal kinetic data were divided into joint reaction forces and muscle moment of force patterns for the ankle, knee and hip. All joint forces and muscle moments are normalized to body mass on the ordinate and to percent stance duration on the abscissa. Joint Reaction Forces. Bilateral joint reaction force values were recorded from each subject for every 20% of the total stance duration. The symmetry index was utilized to test for functional equality in each of these measures. The symmetrical group compared the magnitude of the joint forces from the left leg to results collected from the right. The structurally asymmetrical group compared the absolute differences between the long and short leg at every 20% of the stance period. The individual symmetry index values were then averaged to produce a ratio between legs for each experimental group. Individual and group results are presented in Appendix F. The joint reaction force graphs for each experimental group are presented in Figures 6 - 8. Visual inspection of the joint reaction force plots reveal bilateral functional equality for all three joints in both experimental groups. The stride-to-stride consistency of these measures at the ankle, knee and hip is 39 20 ^ i n X 5 n -40 20 -40 SYMMETRICAL 0=R IGHT C. V. =23. 17. X=LEFT C. V. =14. 87. 20 • 40 60 PERCENT STANCE ASYMMETRICAL 0=SH0RT C. V. =22. 07, X=L0NG C. V. =19. 9 7. 20 40 60 PERCENT STANCE 80 100 80 100 Figure 6 (a) Mean Ankle Joint Reaction Force - Structurally Symmetrical Croup. (b) Mean Ankle Joint Reaction Force - Structurally Asymmetrical Group. 40 20-SYMMETRICAL 1 0 -CD is: ^ 0 0 = R I G H T C . V . = 2 5 . 1 7. X = L E F T C . V . = 1 5 . 3 7 . -40 0 20-20 40 60 PERCENT STANCE ASYMMETRICAL 80 100 1 0 -^ 3 0 " 0 = S H 0 R T C . V . = 2 3 . 5 7 . X = L 0 N G C . V . = 2 3 . 5 7. -40 0 20 40 60 PERCENT STANCE 80 100 Figure 7 (a) Mean Knee Joint Reaction Force - Structurally Symmetrical Croup. (b) Mean Knee Joint Reaction Force - Structurally Asymmetrical Group. 41 SYMMETRICAL 0=RIGHT C. V. = 29. 07. X=LEFT C. V. =15. 9 7. •+-20 40 60 PERCENT STANCE 80 100 ASYMMETRICAL 1 0 -CD + * 0 0=SH0RT C. V. =27. 27-X=L0NG C. V. =42. 07. 0 20 40 60 PERCENT STANCE 80 100 re 8 (a) Mean Hip Joint Reaction Force - Structurally Symmetrical Group. (b) Mean Hip Joint Reaction Force - Structurally Asymmetrical Group. 42 greater vertical forces at each joint during the first 50% of stance. As a group, the left leg also demonstrated less consistency from stride-to-stride, as illustrated by the higher C.V. values. In the structurally asymmetrical group, it was the short leg which was subjected to slightly greater vertical forces at each joint during the first 50% of stance. This observation is in opposition to theories which suggest that the long leg experiences greater forces during running and is therefore more susceptible to overuse injuries (Friberg and Kvist, 1984). A subconscious defensive mechanism may serve to protect the long leg from excessive impact forces. The bilateral symmetry observed visually in the graphical representation of the data is also evident in the symmetry index values calculated for each group. In the symmetrical group, the mean left-right differences range from a low of 0.10 (+/- 3.2) N/Kg for the hip at 60% stance to a high of 3.90 (+/- 5.5) N/Kg for the knee at 80% stance. As the mean maximum forces experienced at the hip and knee are approximately 27.0 N/Kg and 24.5 N/Kg respectively, the difference between legs was not considered to be functionally significant. Analysis of the long-short differences calculated for the structurally asymmetrical group reveal evidence of absolute functional symmetry for the ankle joint reaction force at 80% of stance. The largest difference between the long and short leg was 11.0 (+/- 13.4) N/Kg recorded for the hip force during the last 20% of stance. The maximum bilateral difference reported in joint forces represent approximately 44% of the peak knee joint reaction force experienced during stance. Analysis of individual joint reaction force data reveal that this large asymmetry was produced by substantial functional inequality in one individual. Joint reaction force profiles assembled for each experimental group demonstrated patterns which approximated symmetry. No obvious differences were noted between groups in the symmetry index values calculated for every 20% of stance. Based upon these results, the assumption of bilateral symmetry in joint reaction force profiles remain valid in even in the presence of lower extremity structural asymmetry. Although asymmetry in joint reaction forces are frequently cited as an etiological factor 43 Figure 9 (a) Mean Ankle Moment of Force - Structurally Symmetrical Croup. (b) Mean Ankle Moment of Force - Structurally Asymmetrical Group. 44 CD E 2 LU a ' 2 : LU -5 5 4 3 2 0 a SYMMETRICAL 0=RIGHT C. V. =51. 8 7. X-LEFT C. V. --52. 2 7. -+-20 40 60 PERCENT STANCE 80 100 ASYMMETRICAL 0-SHORT C. V. =68. 5 7. X=L0NG C. V . -51. 6 7. 20 40 60 PERCENT STANCE 100 Figure 10 (a) Mean Knee Moment of Force - Structurally Symmetrical Croup. (b) Mean Knee Moment of Force - Structurally Asymmetrical Croup. 45 -10 0 2 0 4 0 6 0 P E R C E N T S T A N C E 8 0 1 0 0 x - 8 -A S Y M M E T R I C A L X - L O N G C . V . = 4 4 . 9 / . 0 = S H O R T C . V . = 5 8 . 7'/ - 1 0 • 2 0 4 0 6 0 P E R C E N T S T A N C E 8 0 1 0 0 Figure 11 (a) Mean Hip Moment of Force - Structurally Symmetrical Group. (b) Mean Hip Moment of Force - Structurally Asymmetrical Group. 46 LD \ E z: 1 5 10-LU a QL a o_ ZD cn S Y M M E T R I C A L • - R I G H T C . V . =22 .8 ' / . X = L E F T C . V . = 2 0 . 9 V. 20 40 60 P E R C E N T S T A N C E 100 cn E Z 15 ASYMMETRICAL • = S H 0 R T C . V . = 3 0 . 2 7 . X = L 0 N G C . V . = 2 6 . 3 7. 20 40 60 P E R C E N T S T A N C E 100 Figure 12 (a) Mean Support Moment of Force - Structurally Symmetrical Croup. (b) Mean Support Moment of Force - Structurally Asymmetrical Croup. 47 associated with overuse injuries in runners with a measurable leg length differential, this hypothesis is not supported by the results of this study. Muscle Moments of Force. Bilateral joint moment of force values were recorded from each subject for every 20% of the total stance duration. The symmetrical group compared the magnitude of the joint moments from the left leg to results collected from the right. The structurally asymmetrical group compared the absolute differences between the long and short leg at each interval. The symmetry index was utilized to test for functional equality in each of these measures. The individual symmetry index values were then averaged to produce a ratio between legs for each experimental group. Individual and group results are presented in Appendix F. Croup mean moment of force graphs for each joint and overall support moment are presented for the structurally symmetrical and asymmetrical groups in Figures 9 -12. All moment data were amplitude normalized so that moments were expressed as Nm/Kg. In agreement with Winter (1984a), the lowest values for the coefficient of variation were found at the ankle, with variability in motor patterns increasing at the knee and hip joints. The larger C.V. at the knee compared to the ankle is accounted for by a larger absolute variability and the fact that "the average magnitude of the knee moment is considerably less than that generated at the ankle" (Winter, 1984a, p.60). The influence of many biarticular muscles crossing both the knee and hip joints have been cited as factors contributing to the greater stride-to-stride variability in moment patterns at these joints. An adjustment made at one joint unavoidably affects the moment profile at the adjacent joint, ultimately causing an increase in cycle-to-cycle variability at both joints. The ankle moment profiles approximate symmetry in both groups. Although the ankle is actually dorsiflexing during the first 50% of stance, a large plantarflexor moment is maintained at this time. The muscle is therefore lengthening under tension or eccentrically contracting. This enables the storage of elastic energy in the plantarflexor muscles. The release of this energy may contribute to the plantar-flexion motion which occurs in the later part of stance in preparation for push-off. Winter (1983c) reports a peak stance ankle plantarflexor moment of force of 2.03 Nm/Kg for one subject 48 jogging at 2.72 m/s. The plantarflexor ankle moments of force presented in this study peak at approximately 5.5 Nm/Kg for subjects running 1.8 times faster. The ankle moment of force patten is relatively consistent across subjects as illustrated by the low C.V. values for each group. This consistency in ankle moment patterns and the bilateral symmetry observed in the visual inspection of the graphs is supported in the symmetry index calculations for each experimental group. The absolute differences between legs for the moment of force values calculated every 20% of stance were considered to be minimal. The symmetry index values for the ankle moment patterns in both groups ranged from 0.03 (+/- 0.72) Nm/Kg to 0.77 (+/- 1.05) Nm/Kg. As the maximum difference between legs represented only 12.8% of the mean maximum ankle moment of force, the discrepancy was not considered to be functionally significant. Ankle moment of force patterns for both experimental groups could be considered functionally symmetrical. Immediately after heel strike, the knee flexes under the influence of weight acceptance. The rapid rise in knee extensor moment towards midstance serves to arrest this flexion, decelerate the backward rotating shank and eventually extend the knee (Winter, 1983a). In the analysis of one subject jogging slowly, Winter (1983c) found that a peak knee extensor moment of 2.78 Nm/Kg occurred at 40% of the stance duration while no knee flexor moments were reported. Data presented in the present study also demonstrate a peak knee extensor moment occurring at approximately 40% of the stance, but the magnitude of the moment averaged only 1.5 Nm/Kg. In contrast to the profiles presented for slow jogging, a net flexor moment occurred for the last 35% of the stance period. Powerful involvement of the hip extensor muscle group during fast running may influence motor patterns at the knee by producing a net knee flexor moment. The long leg in the structurally asymmetrical group experienced a greater knee extensor moment of force during weight acceptance than did the short leg. In the symmetrical group, it was the left leg which experienced greater knee extensor moment. Kinematically, both the long and the left legs demonstrated a greater amount of flexion than the contralateral limb during the first 50% of stance. Perhaps a greater knee extensor moment is required to arrest this additional flexion. Although slight asymmetries were noted in the knee moment of force patterns for both groups throughout the stance duration, functional symmetry was approached in the later portion of 49 stance. The group mean symmetry index values were similar for both groups with values calculated for midstance equal to 0.34 (+/- 1.11) Nm/Kg for the symmetrical group and 0.17 (+/- 0.86) Nm/Kg for the structurally asymmetrical group. The largest absolute difference between legs was 0.858 (+/- 0.83) Nm/Kg recorded for the first 20% of stance for the structurally asymmetrical group. This difference represents approximately 69% of the mean maximum knee moment experienced during this portion of stance. The knee moment of force patterns for each group provide evidence that functional symmetry may not be a valid assumption in the measurement of some internal kinetic variables. During slow jogging, the hip moment of force demonstrates a net extensor action until midstance when a flexor moment of force serves to "decelerate the backward rotating thigh and reverse the thigh's direction to drive it forward into swing" (Winter, 1983c p.95). The peak moments in both flexion and extension are reported to be close to 1.0 Nm/Kg for slow jogging. The data presented for fast running demonstrate an overall extensor activity for the duration of the stance phase for both experimental groups. In the structurally symmetrical group, a peak hip extensor moment of 3.5 Nm/Kg occurred at approximately 35 % of stance for both legs. A similar pattern was found for the long leg of the structurally asymmetrical group, but the short leg demonstrated a peak hip extensor moment of approximately 5.1 Nm/Kg at 15% of the total stance duration. There was no evidence of a hip flexor moment. The dominance of the hip extensor moment during fast running may be explained by the greater demands for trunk stability at higher running speeds. The hamstring muscle group influence the moment of force patterns at both the hip and the knee, but the mechanical advantage is two times greater at the hip (Winter, 1983c). These muscles may exert a greater influence during fast running. Results of the symmetry index calculations for the hip moment patterns indicated periods of relative equality between mean values for both legs, as well as periods of substantial functional asymmetry. The first 20% of stance for the structurally symmetrical group is characterized by a mean absolute difference between the left and right legs of only 0.01 (+/• 1.01) Nm/Kg. In contrast, the hip moment of force pattern for the asymmetrical group recorded during the same portion of stance represent a mean absolute difference between the long and short leg of 1.39 (+/- 1.58) Nm/Kg. This value represents almost 28 % of the maximum hip extensor moment experienced during stance. The 50 hip moment of force patterns for each group provide evidence that functional symmetry may not be a valid assumption in the measurement of some internal kinetic variables. The knee moment of force data revealed that the long leg of the structurally asymmetrical group experienced greater extensor moment of force during weight acceptance. In contrast, the short leg experiences a grater hip extensor moment of force during this period. The opposing moment of force patterns observed at the knee and hip may be evidence of the dual role Particulate muscles, such as the hamstrings and quadriceps, play in the motor patterns at these joints. The interaction which occurs between the hip and knee joints to produce a highly replicable kinematic pattern is evident in the flexible trade-off between moment of force patterns at these two joints. For example, the hamstrings may be recruited to extend the hip and stabilize trunk position, but activation of this muscle group would serve to create a flexor moment at the knee (Winter, 1984a). A high negative correlation has been reported from cycle-to-cycle between the hip and knee moments (Winter and White, 1987). The mutual exchange between the moment of force patterns at the hip and knee signifies that "on any given stride there is a one-for-one trade-off of moment of force contributions, but the total contribution at these two joints is constant" (Winter and White, 1987 p.367). This consistent relationship contributes to the low variability noted in support moment of force calculations. The support moment of force represents the sum of the moments acting on the three major joints of the lower extremity. Although stride-to-stride variations are evident at each joint, a consistent extensor support moment of force is observed during stance. The support moment profiles for the structurally symmetrical and asymmetrical groups are presented in Figure 12. The characteristic net extensor pattern is evident in both plots. Visual inspection of these graphs reveal relative functional equality between legs. The consistency in this pattern from stride to stride is evident in C.V. values under 30%. The Particulate muscles which are responsible for the flexible interaction between the hip and knee moments contribute to the consistency of support moment of force patterns. During the stance phase of slow jogging, the support moment reflects a net extensor activity which reaches a peak of approximately 4.05 Nm/Kg at 40 % of stance (Winter, 1983c). In fast running, a peak extensor moment of close to 9.0 Nm/Kg occurred at 50% stance. This amplification of moment 51 of force values with increasing speed is in agreement with observations on different walking cadences (Winter, 1984a). A slight flexor moment has been reported in support moment profiles immediately prior to push-off during slow jogging (Winter, 1983c). In contrast, no flexor pattern was found in the support moment profile for runners performing at 4.88 m/s. This should not be surprising given the dominant extensor patterns evident at the ankle and hip throughout the stance period. The flexor moment exhibited at the knee during the last 35% of stance is not large enough to overcome the extensor moments contributed by the ankle and hip to the calculation of the support moment. The symmetry index values calculated for the support moment of force reveal values which approximate symmetry at every 20% of stance. The greatest absolute mean difference between legs in support moment values occurred at 80% of the total stance for the structurally symmetrical group. The difference of 0.95 (+/- 1.52) Nm/Kg represents less than 10% of the mean maximum support moment experienced during stance. The results of this study indicate that the assumption of functional symmetry remains valid in the bilateral assessment of the net support moment. A summary of the kinematic and kinetic data for each experimental group reveal that even in the presence of inequality in leg length, functional symmetry remains a valid assumption in the majority of biomechanical measures analyzed. It was originally postulated that structural asymmetry in the form of a leg length difference would be manifested as detectable asymmetries in external and internal biomechanical measures. Analysis of the results collected from individuals running at 4.88 m/s reveal that this hypothesis was not supported. Bilateral functional symmetry was evident in the majority of kinematic and kinetic variables analyzed in this study. The assumption of biomechanical symmetry was not supported in either group for the knee or hip moment of force data. The possibility that functional asymmetry in individual data may have been obscured by grouping results, will be addressed later in this chapter. The Influence of Speed on Moment Coefficient of Variation. Winter (1983b) calculated joint and support moment of force profiles for subjects walking at slow, natural and fast cadences. The coefficient of variation values for all joints were highest for the slow walk and lowest for the fast walk. Winter (1983b) proposed that slow and natural walking occurred without conscious effort and well 52 within the range of tolerable forces at each joint. "The human motor system at slow and natural cadences is quite "sloppy" at the knee and hip, but as speed increases the motor patterns at these joints tighten up" (Winter, 1983c p.95). This hypothesis was illustrated by joint and support moments calculated for subjects jogging slowly (Winter, 1983c). During fast walking and slow jogging higher levels of force are experienced at each joint and movement is achieved by consciously controlling motor patterns. The neural control patterns become more consistent especially at the knee and hip where the large Particulate muscle act (Winter, 1983c). This improved consistency in motor patterns as speed of locomotion increases is demonstrated by a corresponding decrease in C.V. values. Coefficient of variation values for walking at slow, natural and fast cadences and slow jogging are combined with data from the present study and presented in Table 1. Coefficient of variation values for the first three conditions represent the variability calculated over the entire stride (Winter, 1983c, 1987). The variability in motor patterns change throughout the stride with high variability occurring during the stance phase of gait and fairly consistent motor patterns characterizing the swing phase. As the C.V. values for the two running conditions represent the variability measured only during the stance phase, the values are expected to be higher than if they were calculated for the entire stance cycle. 53 Table 1 Moment of Force C.V. Values at Various Speeds Ankle Moment Knee Moment Hip Moment Support Moment Slow Walk (0.995 m/s) 45.0% 208.0% 176.0% 55.0% Natural Walk (1.360 m/s) 42.0% 50.0% 44.0% 53.0% Fast Walk (1.750 m/s) 42.0% 101.0% 80.0% 49.0% Slow Jog (2.720 m/s) 36.2% 45.3% 77.5% 20.8% Fast Run (4.880 m/s) 19.6% 51.8% 28.1% 20.9% Integrated Analysis of Individual Data The results presented in this section summarize the integrated analysis of kinematic and kinetic data for two structurally symmetrical and two asymmetrical runners. These individuals were selected because they represented opposite ends of the compensation spectrum. O n e subject from each group was classified as functionally symmetrical while his counterpart in the same group demonstrated functional inequality in most measures. Individual assessment involved visual inspection of graphical data and the calculation of symmetry index values for each variable. As functional asymmetry has been implicated in the development of overuse injuries in runners, this portion of the analysis will focus upon those subjects demonstrating inequality in biomechanical measures. Structurally Symmetrical Subjects. A complete graphical summary of the two structurally symmetrical subjects selected for extensive biomechanical analysis is presented in Appendix C . This includes kinematic, ground reaction force and internal kinetic data for the ankle, knee and hip joints. 54 Only the prominent features of these curves which may be related to the development of injuries or possible compensation mechanisms will be presented. Although structurally symmetrical, one subject exhibited functional asymmetry in the kinematic profiles at each joint. In the kinematic assessment, it was observed that the left leg displayed greater flexion at the hip and knee and greater dorsiflexion at the ankle. This leg was also characterized by lower variability from stride to stride as indicated by the lower coefficient of variation. The symmetry index values for this individual further demonstrate the magnitude of the difference between the left and right legs. The mean maximum angle of ankle plantarflexion was 10.6 degrees greater for the left leg. As the total range of motion in plantarflexion is only about 15 degrees, this discrepancy may be considered functionally significant. Visual assessment of the ground reaction force plots revealed relative equality between the left and right legs of this individual. This observation is supported by the symmetry index values calculated for each external kinetic variable analyzed. The left leg demonstrated an initial vertical peak force which was only 1.5 N/Kg greater than the right leg. The impulse and stance duration calculations were virtually equal for both legs. During the first 50% of stance, this individual experienced greater vertical joint forces at the hip, knee and ankle of the left leg. At 15% of stance, the mean absolute difference between the left and right legs is 1800 N. The symmetry index value indicated a mean absolute difference in ankle force of 17.0 N/Kg. This is 7.26 times greater than the group average for this variable. The magnitude of the difference in maximum joint vertical force at the knee and hip range between 1600 N and 1300 N. Bilateral discrepancies in vertical forces experienced at each joint have been implicated as a possible cause of overuse injuries in runners (Friberg and Kvist, 1984). The mean absolute difference in ankle moment values for the left and right legs during the last 40% of stance are approximately 3.3 times greater than the group means. The pattern of large left-right differences continues in the moment profiles for the knee and hip. A knee extensor moment of force was noted for the left leg between 15% and 45% of stance which was almost twice the magnitude of the value measured for the right leg. This large knee extensor moment in the presence of greater knee flexion may expose the extensor musculature to detrimental stresses. The moment of 55 force patterns at the hip reveal a contrasting pattern, with the greater net extensor pattern evident in the right leg. Although described by equal leg lengths, this athlete demonstrated functional inequality in most of the biomechanical variables measured. It is possible that functional inequality in this runner may be the result of compensation to asymmetries in muscle strength, joint range of motion or any number of anatomical, physiological or anthropometric factors which were not documented in this study. One leg experienced greater joint forces and muscle moments, but this individual reported no musculoskeletal injuries which affected training. Compared to his more functionally symmetrical counterpart, this runner exhibited greater stride-to-stride variability in his motor patterns as illustrated by the greater C.V. values. Structurally Asymmetrical Subjects. A complete graphical summary of the two structurally asymmetrical subjects selected for extensive biomechanical analysis is presented in Appendix H. This includes kinematic, ground reaction force and internal kinetic data for the ankle, knee and hip. Only the prominent features of these curves which may be related to the development of overuse injuries or possible compensation mechanisms will be presented. The subject selected to represent functional asymmetry demonstrated kinematic profiles which approximated equality for the ankle joint. Symmetry index values for this individual support this claim with the mean absolute difference between the long and short leg equal to 0.1 degrees for maximum dorsiflexion and 1.01 degrees for maximum plantarflexion. Patterns at the knee joint indicate that the long leg experienced a range of motion in flexion which was 3.4 degrees greater than the short leg. The mean difference in the maximum angle of hip extension was 12.8 degrees greater for the short leg. This represents 58% of the total hip range of motion in extension for this individual and may be related to the development of injuries in runners. Although the long and the short leg appeared to experience equal loading of vertical forces, braking was definitely performed by the longer leg. The functional asymmetry evident in the A-P forces may be linked to the development of injuries in the long leg. Internal kinetic analysis for this structurally asymmetrical subject revealled relative symmetry in joint veritcal reaction force patterns at all joints. Consistency was noted in the ankle moment of force 56 curve with C.V. values equal to 9.1% and 13.9% for the long and short legs respectively. The knee moment profile illustrated that a net extensor moment is not generated for the short leg. A greater hip extensor moment was noted for this leg. As the hip extensors also serve to create a knee flexor moment, it is not known how the knee extends during the later portion of stance. The injury history for this individual does not provide a reason for the lack of knee extensor involvement for the short leg. 57 Chapter 5 C O N C L U S I O N S A N D RECOMMENDATIONS This study was designed to address two topics related to the issue of assumed biomechanical symmetry in the study of human gait mechanics. The initial focus was to determine if the assumption of symmetry in kinematic and kinetic variables remained valid in subjects demonstrating a measurable leg length differential. It was hypothesized that the assumption of functional symmetry in biomechanical measures would prove valid only in the subjects who were classified as structurally symmetrical. Analysis of the results revealed functional symmetry in both the structurally symmetrical and structurally asymmetrical groups for the majority of biomechanical measures analyzed. In light of these findings, it was concluded that regardless of structural status, functional symmetry remainded a valid assumption in the general assessment of gait. It was postulated that structural asymmetry, in the form of a leg length differential, would be manifested as asymmetry in the external and internal biomechanical variables analyzed. Although slight asymmetries existed in the graphical representation of grouped data, functional symmetry was observed in the majority of biomechanical variables assessed. Functional equality was observed between the mean profiles for each leg in the kinematic patterns at each joint, the data for two components of the ground reaction force, and the joint reaction forces at the hip, knee and ankle. Bilateral functional symmetry was also found for both groups in measurements of the ankle and support moment of force patterns. The only evidence refuting the assumption of biomechanical symmetry was found in the moment of force patterns for the hip and knee assembled for each group. It was hypothesized that common compensatory strategies would be revealed as universal to the group of runners classified as structurally asymmetrical. This aspect of the study attempted to determine if runners with a leg length inequality were characterized by systematic patterns of asymmetry in kinematic and kinetic variables which could eventually be linked to the etiology of overuse injuries. If such universal compensation patterns existed, they should have been revealed in the analysis of group results. As no such patterns were detected, the theory which implies that specific overuse injuries occur as a result of predictable and common compensation strategies is not supported by the results of this study. This indicated that each individual utilized a personal strategy in 58 adapting to a discrepancy in leg length. In an attempt to reveal evidence of functional asymmetry in individual data which may comprise personalized compensation strategies, two runners were selected from each group for a more comprehensive analysis. Individual assessment of four subjects revealed that regardless of structural status, some runners demonstrated functional equality while others were characterized by functional asymmetry. No systematic or consistent pattern of compensation was detected in either of the two runners characterized by a leg length difference. In the present study, no attempt was made to identify the cause or site of the leg length inequality in the structurally asymmetrical runners. Consequently, it is possible that one runner may present with a short femur, one subject may demonstrate malalignment at the knee, while another runner may suffer from subtalar joint laxity. All three conditions would result in the diagnosis of a short leg. The possibility of diverse causes and sites of the leg length differential, may contribute to the inability to detect a common pattern of functional asymmetry in the selected group of structurally asymmetrical runners. It is possible that individuals in both experimental groups may have been compensating for left-right differentials in muscle strength, range of motion, joint geometry or any number of anatomical, physiological or anthropometric asymmetries which were not measured in this study. The influence of these factors may have hindered the ability to identify specific neuromuscular compensation mechanisms related to leg length inequality. Based upon these results, the following conclusions were made: 1. In a group of subjects demonstrating lower extremity structural asymmetry, functional symmetry remained a valid assumption in the majority of biomechanical variables measured in this study. 2. Structural asymmetry of the lower extremities is not necessarily manifested as inequality in kinematic or external kinetic measures. 3. No universal compensation strategy was detected for the structurally asymmetrical group of subjects. The theory which implies that specific overuse running injuries occur in runners with leg 59 length inequality as a result of predictable and common compensation mechanisms was not supported by the results of this study. 4. Pooling data concealed bilateral asymmetries which existed in individual profiles. Recommendations Directions for future research could include the implimentation of a comprehensive biomechanical analysis on a group of runners presenting with a unique or specific overuse injury. Analysis of kinematic and kinetic variables may reveal a common biomechanical mechanism of injury. No attempt was made in the present study to identify the cause or site of the leg length inequality in the structurally asymmetrical runners. It is recommended that a complete biomechanical analysis be pursued in a group of runners with the same cause or site of leg length differential. An effort should be made to recruit subjects with a leg length inequality which exceeds the criterion in the present study. 60 APPENDIX A Anatomical Landmarks and the Determination of Leg  and Segmental Lengths As the surface measurements are an attempt to estimate bone length, precise anatomical landmarks must be selected which correspond closely with the ends of the long bones. Documentation dedicated to the procedure of locating each anatomical landmark is supplied by Ross and Ward (1985) and Cameron (1978). Both investigators recommend the landmarks, instruments, and protocol used in this investigation. Procedure Anatomical landmarks were palpated bilaterally and the overlying skin marked with permanent ink. The subject stood barefoot on a flat measuring platform throughout the testing procedure. An erect posture was maintained with arms relaxed at the sides and weight equally distributed on both feet. Bilateral segment lengths, the height of specific landmarks from the floor and the linear distance from the ASIS to the lateral and medial malleolus were recorded. Each estimation was performed by alternating between the left and right sides with the calipers returned to zero after each measurement. Values were repeated and recorded by an assistant. Equipment Anthropometric tape: A non-extendible, flexible measuring tape calibrated in metric units was used to determine the linear distance between the ASIS and both the lateral and medial malleoli. Anthropometer: A standard Martin design anthropometer manufactured by Siber-Hegner C P M was used in the determination of the length of each lower extremity segment. The calibrated shaft of the anthropometer was positioned parallel to the long axis of the segment with the tip of the stationary blade touching the one end of the segment and the moving blade manipulated to reach the other segment end. The measurement of segmental length was read from the calibrated beam. A footplate replaced the stationary blade for the determination of landmark heights from the standing surface. 61 Landmarks The following anatomical landmarks were used in this study and are defined by Ross and Ward (1985) and Cameron (1978). Iliospinale: The most anterior point on the anterior superior iliac spine (ASIS). The undersurface of the tip of the ASIS was palpated and not the most frontally curved aspect. This feature is easily located in most subjects. Trochanterion: The most superior point on the greater trochanter of the femur, not the most lateral point. Tibiale laterale: The lateral border of head of tibia located inferior to the patellofemoral gap. Sphyrion: The most distal tip of the malleolare medialis (tibialis) and not the outermost point of the malleolus. Sphyrion fibulare: The most distal tip the malleolare laterale (fibularis). Anthropometric Measurements Thigh: The direct linear distance between the anterior aspect of the greater trochanter and the horizontal lateral border of the tibial tuberosity. Shank: The direct linear distance between the lateral aspect of the tibial tuberosity and the tip of the lateral malleolus. Foot: The direct linear distance between the most posterior point on the heel and the most anteriorly projecting toe. Trochanterion height: The height of the trochanterion from the standing surface. Tibial height: The height of the tibiale laterale from the standing surface. 62 ASIS to Lateral Malleolus: The direct linear distance from the iliospinale to the malleolare laterale (fibularis). ASIS to Medial Malleolus: The direct linear distance from the iliospinale to the medial border of the tibia. In accordance with the suggestion by Johnston et al. (1972), technical error of measurement and the coefficient of variation were the statistics adopted in this study to estimate assessor reliability of the various anthropometric measures used. 6 3 APPENDIX B General Descriptive Data for all Subjects (a) Structurally Symmetrical Croup; subj. Age Height (cm) Mass (Kg) Most Prevalent Injury 1 25 172.00 61.81 t i b i a l pain (R) 2 21 185.42 76.72 b i l a t e r a l p l a n t a r f a s c i i t i s 3 24 180.34 72.58 shin s p l i n t s (R) 4 25 173.99 69.96 none 5 29 181.61 71.76 knee pain (L) Mean SD* 24.8 2.86 178.67 5.55 70.57 5.49 * Standard Deviation (b) Structurally Asymmetrical Croup; Subj. Age Height (cm) Mass (Kg) Most Prevalent Injury 1 26 177.50 74.85 ankle sprain (R) 2 20 181.61 70.59 none 3 44 167.64 62.09 p l a n t a r f a s c i i t i s (L) 4 26 172.72 71.76 none 5 21 185.42 70.34 ankle sprain (L) X SD 27.4 9.69 176.98 7.04 69.93 4.73 64 APPENDIX C Median Bilateral Leg Length Measurements for Both  Experimental Groups (a) Structurally Symmetrical; Floor to Greater ASIS to L a t e r a l ASIS to Medial Trochanter Malleolus Malleolus 1 R 87.80 92.20 91.20 L 87.40 92.40 91.20 2 R 100.40 108.10 106.20 L 100.30 107.90 106.20 3 R 91.60 96.50 94.30 L 91.50 96.20 94.30 4 R 89.40 94.00 92.00 L 89.50 94.40 92.30 5 R 93.95 99.70 96.60 L 94.15 99.50 96.50 (b) Structurally Asymmetrical; Floor to Greater ASIS to L a t e r a l ASIS to Medial Trochanter Malleolus Malleolus 1 R 92.70 98.70 96.20 L 91.75 97.00 95.00 2 R 94.45 101.00 100.10 L 93.60 99.50 98.40 3 R 85.45 91.10 89.00 L 84.24 88.90 88.00 4 R 89.05 94.40 93.40 L 89.75 95.60 94.40 5 R 95.80 102.60 101.70 L 94.65 101.20 100.30 65 APPENDIX D Mean Kinematic Values (a) Structurally Symmetrical Croup; Joint Variable Leg 1 2 3 4 5 ANKLE max D.F. R 22.3 21.3 23.5 21.5 23.5 (degree) L 25.9 35.6 25.7 26.7 25.7 max P.F. R 5.5 15.0 5.7 8.5 5.7 (degree) L 1.0 10.2 6.3 19.1 6.3 KNEE max f l e x . R 47.1 44.7 48.4 47.2 48.4 (degree) L 51.2 44.2 49.6 52.3 49.6 max ext. R 21.8 13.8 23.2 18.8 23.2 (degree) L 25.1 20.0 23.6 21.0 23.6 HIP max f l e x . R 32.9 31.8 23.2 28.7 23.2 (degree) L 33.2 35.6 31.0 36.6 31.1 max ext. R 7.9 18.9 11.0 3.8 11.0 (degree) L 12.6 10.2 9.2 6.1 9.2 (b) Structurally Asymmetrical Group; Joint Variable Leg 1 2 3 4 5 ANKLE max D.F. R 25.6 22.9 15.4 23.2 26.5 (degree) L 25.5 24.2 19.3 23.0 28.7 max P.F. R 15.3 15.1 21.7 4.4 9.1 (degree) L 16.4 19.7 27.4 9.6 10.1 KNEE max f l e x . R 54.4 46.1 41.2 51.5 51.0 (degree) L 51.0 45.5 43.0 53.8 52.9 max ext. R 16.8 20.2 14.5 18.9 20.2 (degree) L 17.1 19.8 12.1 26.5 21.0 HIP max f l e x . R 45.4 33.0 29.8 33.5 25.8 (degree) L 40.1 37.2 40.3 42.4 27.8 max ext. R 11.4 6.8 7.5 3.0 14.1 (degree) L 24.2 3.5 5.2 6.5 1.1 66 Kinematic Symmetry Index Values (a) Structurally Symmetrical Croup (Left-Right); Joint Variable 1 2 3 4 5 Mean SD ANKLE max D.F. max P.F. 3.6 14.3 2.2 5.2 2.2 -4.5 -4.8 0.6 10.6 0.6 5.5 5.07 0.5 6.23 KNEE max f l e x . max ext. 4.1 -0.5 1.2 5.1 1.2 3.3 6.2 0.4 2.2 0.4 2.2 2.31 2.5 2.41 HIP max f l e x . max ext. 0.3 3.8 7.8 7.9 7.9 4.7 -8.7 -1.8 2.3 -1.8 5.5 3.42 -1.1 5.10 (b) Structurally Asymmetrical Croup (Long-Short); Joint Variable 1 2 3 4 5 Mean SD ANKLE max D.F. max P.F. 0.1 -1.3 -3.9 -0.2 -2.2 -1.1 -4.6 -5.7 5.2 -1.0 -1.5 1.62 -1.4 4.26 KNEE max f l e x . max ext. 3.4 0.6 -1.8 2.3 -1.9 -0.3 0.4 2.4 7.6 -0.8 0.5 2.38 1.9 3.43 HIP max f l e x . max ext. 5.3 -4.2-10.5 8.9 -2.0 -12.8 3.3 2.3 3.5 13.0 -0.5 7.71 1.9 9.27 67 APPENDIX E Mean Ground Reaction Force Values (a) Structurally Symmetrical Group; Variable Leg 1 2 3 4 5 1st Fz Peak R 26.0 23.8 21.5 38.4 22.8 (N/Kg) L 22.8 29.8 18.0 39.9 23.8 2nd Fz Peak R 30.2 27.0 28.8 28.7 29.0 (N/Kg) L 31.1 25.3 27.0 28.8 58.5 Braking Impulse R .260 .194 .214 .228 .158 (Nsec/Kg) L .262 .226 .200 .246 .185 Propul. Impulse R .203 .206 .242 .217 .214 (Nsec/Kg) L .188 .222 .253 .229 .196 Stance Duration R .135 .145 .145 .135 .137 (sec) L .130 .150 .150 .140 .140 (b) Structurally Asymmetrical Group Variable Leg 1 2 3 4 5 1st Fz Peak R 30.8 37.4 30.6 25.6 22.8 (N/Kg) L 31.0 50.1 31.0 33.4 31.1 2nd Fz Peak R 28.2 31.3 29.0 31.0 26.0 (N/Kg) L 28.9 31.4 31.9 29.1 26.0 Braking Impulse R .166 .187 .203 .211 .237 (Nsec/Kg) L .050 .198 .187 .206 .214 Propul. Impulse R .146 .213 .192 .183 .221 (Nsec/Kg) L .167 .202 .183 .197 .214 Stance Duration R .155 .135 .120 .135 .155 (sec) L .155 .130 .118 .135 .148 68 Ground Reaction Force Symmetry Index Values (a) Structurally Symmetrical Group (Left-Right); Variable/Subject 1 2 3 4 5 Mean SD 1st Fz Peak 2nd Fz Peak Braking Impulse Propul. Impulse Stance Duration -3.2 6.0 -3.5 1.5 1.0 0.9 -1.7 -1.8 0.1 29.5 .002 .032 -.014 .018 .027 -.015 .016 .011 .012 -.018 -.005 .005 .005 .005 .003 0.4 3.9 5.4 13.5 .013 .019 .001 .016 .003 .004 (b) Structurally Asymmetrical Group (Long-Short); Variable/Subject 1 2 3 4 5 Mean SD 1st Fz Peak 2nd Fz Peak Braking Impulse Propul. Impulse Stance Duration -0.2-12.7 -0.4 7.8 8.3 0.7 0.1 2.9 -1.9 0.0 .116 .011 -.016 -.005 -.230 .021-.011 -.009 .014 -.007 .000-.005 -.002 .000 -.007 0.6 8.5 0.4 1.7 -.071 .102 .002 .015 -.003 .003 69 APPENDIX F Internal Kinetic Descriptors (a) Structurally Symmetrical Croup; (i) Joint Reaction Force (N/Kg); Subj. Leg 20% 40% 60% 80% 100% ANKLE 1 R -18.8 -28.3 -28.2 -16.5 -1.0 L -15.9 -28.6 -29.8 -18.2 -1.4 2 R -12.6 -25.1 -25.0 -15.2 -0.3 L -13.7 -24.0 -23.9 -14.2 -0.7 3 R -12.6 -23.1 -27.7 -21.1 -6.0 L -11.6 -22.5 -25.3 -17.9 -3.6 4 R - 4.6 -19.6 -27.5 -25.0 -10.1 L -21.6 -26.2 -27.6 -16.4 -0.9 5 R -17.0 -27.7 -26.8 -15.4 -1.4 L -14.5 -26.5 -26.5 -15.5 -1.2 KNEE 1 R -17.7 -27.8 -26.5 -15.0 0.1 L -15.2 -28.1 -28.0 -16.6 -0.3 2 R -11.2 -24.6 -22.0 -12.9 0.4 L -13.1 -23.4 -22.2 -13.2 -0.1 3 R -11.5 -22.9 -26.2 -19.1 -5.2 L -10.6 -22.3 -23.6 -16.5 -3.2 4 R - 3.4 -19.0 -23.7 -26.6 -9.2 L -20.1 -26.0 -25.5 -15.2 -0.2 5 R -16.1 -27.3 -24.9 -14.0 -0.8 L -13.7 -27.0 -20.7 - 6.4 -0.5 HIP 1 R -15.6 -26.0 -23.4 -12.6 0.9 L -13.5 -26.7 -24.6 -14.1 0.6 2 R - 7.8 -23.1 -14.8 - 9.1 -1.0 L -11.5 -22.3 -19.4 -11.3 0.1 3 R -10.5 -21.6 -23.9 -15.8 -4.1 L - 9.2 -21.5 -21.3 -13.8 -2.3 4 R - 2.1 -17.5 -25.1 -19.3 -7.7 L -17.4 -25.6 -21.6 -12.8 0.2 5 R -14.7 -25.7 -22.0 -11.5 -0.1 L -12.1 -24.7 -22.0 -11.5 0.0 70 (ii) Joint Moments of Force (Nm/Kg) Subj. Leg 20% 40% 60% 80% 100% ANKLE 1 R -1.39 -3.89 -5.48 -4.27 -0.76 L -1.35 -4.70 -6.70 -5.21 -0.88 2 R -1.16 -4.39 -6.19 -5.19 -0.84 L -1.54 -4.37 -5.75 -4.23 -0.41 3 R -0.34 -2.59 -5.22 -5.48 -2.28 L -0.59 -3.07 -5.12 -4.77 -1.36 4 R -0.35 -2.25 -4.94 -5.68 -3.04 L -0.60 -2.53 -4.41 -3.64 -0.52 5 R -1.52 -4.44 -5.87 -4.44 -0.84 L -1.12 -4.02 -5.55 -4.21 -0.74 KNEE 1 R 0.16 1.29 -0.16 -1.68 -0.96 L 0.16 0.45 -1.04 -2.29 -0.96 2 R -0.12 -0.03 -2.02 -3.17 -1.04 L 0.22 0.77 -0.62 -1.55 -0.35 3 R -0.19 1.45 0.47 -1.50 -1.50 L -0.09 0.82 -0.36 -1.65 -0.98 4 R -0.45 0.95 0.57 -0.72 -1.50 L 1.09 2.92 1.68 -0.35 -0.58 5 R 0.52 0.91 -0.24 -1.53 -0.77 L 1.00 1.80 0.68 -0.94 -0.65 HIP 1 R -3.21 -3.40 -2.97 -2.56 -0.64 L -3.24 -5.11 -4.47 -3.35 -0.45 2 R -2.20 -4.02 -4.09 -3.16 -0.17 L -2.46 -2.84 -2.28 -1.96 0.61 3 R -2.93 -3.81 -3.61 -3.06 -1.50 L -2.25 -3.57 -2.95 -2.27 -1.04 4 R -1.16 -2.03 -2.88 -2.28 -1.48 L -2.66 -1.64 -0.93 -0.95 0.02 5 R -2.49 -4.27 -3.02 -2.17 0.04 L -1.34 -2.61 -1.46 -1.08 0.33 SUPPORT 1 R 5.06 8.53 8.26 5.12 0.34 L 4.75 10.26 10.13 6.27 0.37 2 R 3.24 8.37 8.26 5.17 -0.02 L 4.23 7.97 7.41 4.64 -0.54 3 R 3.08 7.85 9.30 7.04 2.28 L 2.75 7.47 7.71 5.40 1.43 4 R 1.07 5.24 8.39 7.24 3.03 L 4.35 7.09 7.02 4.25 -0.08 5 R 4.52 9.61 8.65 5.08 0.02 L 3.24 8.43 7.69 4.36 -0.24 71 (b) Structurally Asymmetrical Group; (i) Joint Reaction Forces (N/Kg); Joint Leg 20% 40% 60% 80% 100% ANKLE 1 R -20.0 -27.2 -25.8 -14.4 -1.1 L -23.4 -27.7 -24.5 -12.8 -1.2 2 R -18.1 -29.9 -28.3 -17.3 1.5 L -21.6 -30.0 -28.8 -16.5 -1.1 3 R -11.6 -23.2 -28.1 -22.7 -4.1 L -19.3 -29.2 -30.0 -21.5 -6.2 4 R -16.5 -23.3 -29.5 -21.5 -6.2 L -17.8 -25.6 -27.5 -18.4 -2.7 5 R -12.2 -22.9 -24.9 -16.6 -1.2 L -15.2 -23.3 -24.9 -17.2 -1.7 KNEE 1 R -18.8 -26.9 -23.9 -12.9 -0.3 L -22.3 -27.3 -22.9 -10.7 -1.1 2 R -17.5 -29.1 -26.2 -20.6 10.8 L -20.8 -29.3 -26.6 -15.4 -0.3 3 R -10.5 -22.5 -26.8 -23.6 1.9 L -17.9 -28.3 -28.3 -20.0 -5.2 4 R -15.0 -23.3 -27.9 -19.6 -5.3 L -16.4 -25.5 -25.6 -16.9 -1.9 5 R -11.6 -22.4 -23.2 -15.1 -0.4 L -14.1 -22.9 -23.3 -15.6 -0.8 HIP 1 R -16.4 -25.7 -21.1 -10.4 0.6 L -19.6 -26.5 -20.1 - 7.3 -1.5 2 R -16.1 -27.3 -22.5 -29.4 31.4 L -19.3 -27.9 -22.4 -13.5 0.3 3 R - 9.1 -20.2 -24.8 -26.1 14.1 L -15.4 -26.2 -25.6 -17.8 -4.3 4 R -13.2 -22.3 -25.0 -16.5 -4.5 L -14.5 -24.7 -22.3 -14.4 -1.0 5 R - 9.7 -21.5 -20.6 -12.0 -0.4 L -11.9 -21.9 -20.6 -12.4 0.2 72 (ii) Joint Moments of Force (Nm/Kg); Joint Leg 20% 40% 60% 80% 100% ANKLE 1 R -1.86 -4.24 -5.05 -3.44 -0.54 L -2.55 -4.90 -5.36 -3.04 -0.58 2 R -1.42 -4.58 -6.07 -4.70 -0.43 L -2.20 -4.97 -6.33 -4.53 -0.51 3 R -1.17 -3.34 -5.19 -5.07 -1.68 L -2.35 -4.43 -5.63 -4.77 -1.69 4 R -0.95 -2.60 -5.18 -5.23 -2.30 L -1.48 -3.81 -5.80 -5.00 -1.32 5 R -0.10 -2.94 -4.92 -4.29 -0.81 L -1.42 -3.65 -5.22 -4.54 -0.96 KNEE 1 R -0.30 1.17 0.95 -0.20 -0.53 L -2.54 -1.23 -0.74 -0.37 -0.39 2 R 0.22 0.62 -0.73 -1.91 -1.41 L 0.03 0.66 -0.53 -1.56 -0.42 3 R -0.20 0.53 -0.33 -1.54 -1.67 L -0.42 0.52 -0.32 -1.41 -1.06 4 R -1.27 1.38 0.59 -1.03 -1.75 L -0.45 1.15 0.15 -1.35 -1.11 5 R 1.72 2.14 0.66 -0.94 -0.85 L 0.87 1.95 0.85 -0.69 -0.87 HIP 1 R -5.04 -4.64 -1.96 -0.09 0.15 L -9.10 -8.16 -4.46 -0.25 0.28 2 R -3.92 -4.67 -3.67 -5.33 -0.62 L -4.02 -4.08 -2.91 -1.99 0.32 3 R -1.58 -2.35 -2.54 -2.93 -1.00 L -3.11 -3.00 -2.21 -1.47 -0.58 4 R -4.41 -3.34 -3.71 -1.91 -1.86 L -3.90 -4.27 -3.15 -2.59 -0.71 5 R -1.06 -1.95 -2.17 -1.67 0.38 L -1.80 -1.75 -1.64 -1.25 -0.07 SUPPORT 1 R 6.60 10.06 7.95 3.33 -0.14 L 9.11 11.83 9.09 2.92 -0.09 2 R 5.56 9.87 9.01 8.12 -0.36 L 6.25 9.70 8.72 4.96 -0.23 3 R 2.55 6.22 7.39 6.46 1.00 L 5.04 7.95 7.51 4.83 1.21 4 R 4.10 7.31 9.47 6.11 2.41 L 4.93 9.23 9.10 6.23 0.92 5 R 2.89 7.03 7.75 5.03 -0.42 L 4.09 7.35 7.71 5.11 0.17 73 Internal Kinetic Symmetry Index Values (a) Joint Reaction Force; (i) Structurally Symmetrical Croup (Left-Right); subj. 20% 40% 60% 80% 100% ANKLE 1 2 3 4 5 2.9 -0.3 -1.6 -1.7 2.4 -1.1 1.1 1.1 1.0 -0.4 1.0 0.6 2.4 3.2 2.4 -17.0 -6.6 -0.1 8.6 9.2 2.5 1.2 0.3 -0.1 0.2 Mean SO -2.3 -0.8 0.4 2.2 2.8 8.3 3.3 1.5 4.0 3.8 KNEE 1 2 3 4 5 2.5 -0.3 -1.5 -1.6 -0.4 -1.9 1.2 -0.2 -0.3 -0.5 0.9 0.6 2.6 2.6 2.0 -16.7 -7.0 -1.8 11.4 9.0 2.4 0.3 4.2 7.6 0.3 Mean SD -2.6 -1.0 0.7 3.9 2.1 8.1 3.4 2.6 5.5 4.0 HIP 1 2 3 4 5 2.1 -0.7 -1.2 -1.5 -0.3 -3.7 0.8 -4.6 -2.2 1.1 1.3 0.1 2.6 2.0 1.8 -15.3 -8.1 3.5 6.5 7.9 2.6 1.0 0.0 0.0 0.1 Mean SD -2.6 -1.4 0.1 1.0 2.1 7.5 3.8 3.2 3.5 3.3 74 (ii) Structurally Asymmetrical Croup (Left-Right); Subj 20% 40% 60% 80% 100% ANKLE 1 2 3 4 5 3.4 0.5 -1.3 -1.6 0.1 3.5 0.1 0.5 -0.8 2.6 7.7 6.0 1.9 -1.2 2.1 -1.3 -2.3 2.0 3.1 3.5 3.0 0.4 0.0 0.6 0.5 Mean SD 3.3 0.9 0.6 0.0 1.8 3.2 3.1 1.4 1.9 1.4 KNEE 1 2 3 4 5 3.5 0.4 -1.0 -2.2 0.8 3.3 0.2 0.4 -5.2 11.1 7.4 5.8 1.5 -3.6 7.1 -1.4 -2.2 2.3 2.7 3.4 2.5 0.5 0.1 0.5 0.4 Mean SD 3.1 0.9 0.7 -1.6 4.6 3.1 2.9 1.3 3.2 4.5 HIP 1 2 3 4 5 3.2 0.8 -1.0 -3.1 2.1 3.2 0.6 -0.1 -15.9 31.1 6.3 6.0 0.8 -8.3 18.4 -1.3 -2.4 2.7 2.1 3.5 2.2 0.4 0.0 0.4 -0.2 Mean SD 2.7 1.1 0.5 -5.0 11.0 2.7 3.0 1.4 7.3 13.4 75 (b) joint Moments of Force; (i) Structurally Symmetrical Group (Left-Right); Subj. 20% 40% 60% 80% 100% ANKLE 1 2 3 4 5 0.04 -0.81 -1.22 -0.94 -0.12 -0.38 0.02 0.44 0.96 0.43 -0.25 -0.48 0.10 0.71 0.92 -0.25 -0.28 0.53 2.04 2.52 0.40 0.42 0.32 0.23 0.10 Mean SD -0.09 -0.23 0.03 0.6 0.77 0.31 0.47 0.72 1.09 1.05 KNEE 1 2 3 4 5 0.00 -0.84 -0.88 -0.61 0.00 0.34 0.80 1.40 1.62 0.69 0.10 -0.63 -0.83 -0.15 0.52 1.54 1.97 1.11 0.37 0.92 0.48 0.89 0.92 0.59 0.12 Mean SD 0.49 0.44 0.34 0.36 0.45 0.62 1.17 1.11 0.84 0.39 HIP 1 2 3 4 5 -0.03 -1.71 -1.50 -0.79 0.19 -0.26 1.18 1.81 1.20 0.78 0.68 0.24 0.66 0.79 0.46 -1.50 0.39 1.95 1.33 1.50 1.15 1.66 1.56 1.09 0.29 Mean SD 0.01 0.35 0.90 0.73 0.64 1.01 1.29 1.43 0.86 0.53 SUPPORTl 2 3 4 5 -0.31 1.73 1.87 1.15 0.03 0.99 -0.40 -0.85 -0.53 -0.52 -0.33 -0.38 -1.59 -1.64 -0.85 3.28 1.85 -1.37 -2.99 -3.11 -1.28 -1.18 -0.96 -0.72 -0.26 Mean SD 0.47 0.32 -0.58 -0.95 -0.94 1.77 1.38 1.40 1.52 1.25 7 6 (ii) Structurally Asymmetrical Croup (Long-Short); Subj. 20% 40% 60% 80% 100% ANKLE 1 2 3 4 5 0.69 0.66 0.31 -0.40 0.04 0.78 0.39 0.26 -0.17 0.08 1.18 1.09 0.44 -0.30 0.01 -0.53 -1.21 -0.62 0.23 0.98 1.32 0.71 0.30 0.25 0.15 Mean SD 0.69 0.33 0.14 -0.08 0.25 0.73 0.90 0.43 0.30 0.41 KNEE 1 2 3 4 5 2.24 2.40 1.69 0.17 -0.14 0.19 -0.04 -0.20 -0.35 -0.99 0.22 -0.01 -0.01 -0.13 -0.61 0.82 -.023 -0.44 -0.32 0.64 0.85 0.79 -0.19 -0.25 0.02 Mean SD 0.86 0.58 0.17 -0.18 -0.22 0.83 1.09 0.86 0.21 0.62 HIP 1 2 3 4 5 4.06 3.52 2.50 0.16 -0.13 0.10 -0.59 -0.76 -3.34 -0.94 1.53 0.65 -0.33 -1.46 -0.42 0.51 -0.93 0.56 -0.68 1.15 0.74 -0.20 -0.53 -0.42 0.45 Mean SD 1.39 0.49 0.29 -1.15 0.02 1.58 1.79 1.33 1.36 0.81 SUPPORTl 2 3 4 5 -2.51 -1.77 -1.14 0.41 -0.05 -0.69 0.17 0.29 3.16 -0.13 -2.49 -1.73 -0.12 1.13 -0.21 0.83 1.92 -0.37 0.12 -1.49 -1.20 -0.32 0.04 -0.08 -0.59 Mean SD -1.21 -0.35 -0.26 0.95 -0.49 1.39 1.53 0.55 1.32 0.59 77 APPENDIX C Complete Kinematic, Ground Reaction Force and  Internal Kinetic Data for Two Structurally  Symmetrical Individuals 78 50 40 30 20 10 0 -10 -20 -30 -40 SYMMETRICAL ONE 0-R1GHT CV»12 . 4 7. X - L E F T C V - 9 . 2 A 20 40 60 80 PERCENT STANCE 100 50 40 ~ 30 u ui S 20 L U 10 _ J " „ z 0 < 0 . -10 X - 2 0 -30 -40 —~ m $ 5—— SYMMETRICAL TWO O-RIGHT CV-17 . 0 7. X - L E F T CV-16 . 5 / . 20 40 60 80 PERCENT STANCE 100 79 8 0 SYMMETRICAL ONE 20 40 60 80 PERCENT STANCE 500 100 20 40 60 80 PERCENT STANCE 81 HIP MOMENT <Nm" K N e E MOMENT <NnO ANKLE MOMENT (Nin; CD to APPENDIX H Complete Kinematic, Ground Reaction Force and  Internal Kinetic Data for Two Structurally  Asymmetrical Individuals 83 40 3 30 ui • 20 ui s! o z < •10 -20 0-LONG C V - 6 . 9 7. X-SHORT CV-11 . 7 7. 20 40 60 80 100 PERCENT STANCE 40 •10 -20 ASYMMETRICAL TWO 0-LONG C. V. - 9 . 9 y. X-SHORT C. V. - 17 . 5 7. 20 40 60 80 PERCENT STANCE 100 60 10 ASYMMETRICAL ONE 0-LONG CV-4 . 1 '/. X-SHORT C V - 9 . 5 7. 20 40 60 80 100 PERCENT STANCE 60 LU a UJ 40 _j u z Z30 LU z 20 10 ASYMMETRICAL TWO 0-LONG CV-4 . 7 / . * \ X-SHORT CV-17 . 7 7. \ j 20 40 60 80 100 PERCENT STANCE 50 LU a 20 u z < -20 -30 -40 ASYMMETRICAL ONE 0-LONG CV-10 . 27. X-SHORT C V - 1 1 . 7 /. 20 40 60 PERCENT STANCE 80 100 50 40 ~ 30 u LU a 20 LU 10 + -J z 0 0 .-10 5 - 2 0 -30 -40 20 ASYMMETRICAL TWO 0-LONG CV-14 . 9 7. X=SHORT CV-92 . 6 / 40 60 PERCENT STANCE 80 100 84 85 86 200 U J - 4 0 0 + z < - 6 0 0 ASYMMETRICAL ONE 0-LONG CV-13. 8 7. X-SHORT CV-9 . 5 / . 20 40 60 BO PERCENT STANCE 100 200 -600 ASYMMETRICAL TWO 0-LONG CV-9. 17 X-SHORT c v - i : 20 40 60 80 PERCENT STANCE 100 400 200 E Z Z UJ z a i_ ui ui z 200 + - 4 0 0 20 ASYMMETRICAL ONE 0-LONG C V - 2 1 . 7 7. •SHORT CV-29. 4 V. 40 60 80 100 PERCENT STANCE 400 200 + E Z - 4 0 0 ASYMMETRICAL TWO 0-LONG CV-30. 6 7. X-SHORT CV-39. 1 7. 20 40 60 80 PERCENT STANCE 100 200 -£-200 z £-400 Q. I - 6 0 0 -800 20 ASYMMETRICAL ONE 0-LONG CV-23. 1 V. 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