1 QUANTIFICATION OF ASYMMETRICAL STEPPING POST-STROKE AND ITS RELATIONSHIP TO HEMIPARE TIC WALKING PERFORMANCE By CHITRA LAKSHMI KINATINKARA BALASUBRAMANIAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008
2 2008 Chitra Lakshmi Kinatinkara Balasubramanian
3 To Mummy, Appa and Anjan
4 ACKNOWLEDGMENTS I would like to express my hear tfelt gratitude to my advisor Dr. Steve Kautz for opening the doors of science to me, his im peccable scientif ic vision and for kindling the fire of curiosity in me. I cannot thank him enough for his unrelenting support and for his constant belief in me to explore my strengths that I was myself unsure of I am also indebted to the exceptional members on my committee Dr. Andrea Behr man, Dr. Craig Velozo and Dr. James Cauraugh for their invaluable support, belief in my work and for inspiring th e art of being a scientist. Thanks go to each and every person in the lab: Ryan, Kelly and Naresh for all their hard work and assistance in data analyses; Mark and Erin for their help in data collection and for putting in that extra effort on my behalf during the home stretch. A special thanks goes to Erin for being my Angel! I would also like to tha nk Maria Kim and Lise Worthen for collecting and helping me access the data for my first study that jumpstarted my research. I want to thank Dr. Richard Neptune and Dr. Felix Za jac for their invaluable commen ts and contributions to my research. I have learnt a lot from the two of th em! I want to thank all subjects who volunteered to participate in my research studies. None of of my research pursuits would be possible without them. My research pursuits would not be a possibi lity without the str ong infrastructure and resources provided by UF for graduate education. Th anks go to UF also for inspiring the spirit of being a familythe gator family! I am grateful to the UF Alumni Association for granting me the Alumni fellowship that funded my education for four years. I am also thankful to NIH and VA Medical Center for their grant funding to Dr. St eve Kautz that helped build and maintain the HMPL where I pursued all my research. Faculty a nd staff in the Rehabili tation Science Doctoral (RSD) Program and Physical Therapy Departme nt have been an essential support system throughout my doctoral studies. Sp ecial thanks go to fellow RSD graduate students and the
5 people at Brain Rehabilitation Re search Center mostly for bei ng my home away from home! Thanks go to all my friends here in the US and in India for their wonderful friendships that made this my time as a graduate student so much better. None of this would be possible if it we rent for my parents Drs. Shyamala and Balasubramanian. From the time I can remember, Mummy and Appa have given me the freedom to explore my potential and always encouraged me to seek the best in the academic arena. I want to thank them for selflessly l oving and supporting me and for providing me with everything and much more! Special thanks go to Mummy for the rock of support and love she is to our family and for being my role model in life. My dissertation work is dedicated to her! I am extremely thankful to my loving sist ers Pooja and Vidya a nd my brother-in-law Karthik for always sticking together in times of trials and tribulat ions that have helped me focus and prioritize my education here in the US. They are my backbone! A special thanks goes to my partner in sin.my aunt (Mangalam) for her belief in my abilities and for her love. I also want to thank my parents-in-law Retired Lieutenant Commander Padmalochan Das and Runu Baruah for loving me as their daughter and selflessly en couraging me to pursue my endeavors. I am grateful that my time as a graduate student was shared w ith my darling husband Anjan. His unconditional love and encouragement have been pivotal to keep me going throughout my graduate studies. I am short at words to thank him for putting my dreams before his and constantly moving around the globe (litera lly!) to be with me and help me pursue my education. He has shared with me times of hope and despair, frustrati on and exhilaration, and everything in-between. I thank him for being my best friend throughout this journey! Finally, thank you God for giving me the stre ngth and courage to go after my dreams and for bringing these wonderful people into my life during my doctoral education.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ........10 LIST OF FIGURES.......................................................................................................................11 ABSTRACT...................................................................................................................................13 CHAP TER 1 INTRODUCTION..................................................................................................................15 2 LITERATURE REVIEW.......................................................................................................18 Introduction................................................................................................................... ..........18 Part 1: Overview of Walking Function................................................................................... 18 Neuromotor Control of Healthy Gait..............................................................................18 Quantifying Gait: Phases in the Healthy Gait Cycle....................................................... 19 Walking Capacity after a Stroke...................................................................................... 19 Stroke: incidence and consequences........................................................................ 19 Pathophysiological basis of the lo comotor disorder post-stroke ..............................20 Nature and rate of walking recovery........................................................................ 21 Walking disability in the chronic phase................................................................... 22 Part 2: Asymmetry in Spatiotemporal St ep Characteristics and Ground Reaction Fo rces during Hemiparetic Walking............................................................................................... 22 Spatiotemporal Characteristics of Steps.......................................................................... 23 Temporal asymmetry................................................................................................ 24 Spatial asymmetry....................................................................................................25 Ground Reaction Forces in Hemiparetic Gait................................................................. 26 Relevance of the Reviewed Literature to Study One......................................................27 Part 3. Intra-Subject Vari ability during W alking................................................................... 28 Motor Control and Gait Variability................................................................................. 28 Significance of gait variabili ty: theoretical approach .............................................. 28 Role of variability during walking...........................................................................28 Step-by-Step Variability in Sp atiotemporal Characteristics ............................................ 29 Step Variability as Quantifiable Markers of Impaired Walking..................................... 30 Relevance of Reviewed Literature to Study Two............................................................32 Part 4. Foot Placement in a Body Reference Frame............................................................... 32 Defining Foot Placement Relative to Body..................................................................... 33 Control of Foot during Gait............................................................................................. 33 Body Center of Mass Position and Velocity : Pos tulated Link to Foot Placement.......... 33 Foot Placement Relative to Body and its Relation to W alking Sub-tasks...................... 34 Relevance of Reviewed Literature to Study Three..........................................................35 Part 5. Pre-Swing and Swing Ph ase during Hem iparetic Gait................................................ 36
7 Introduction to Pre-Swing and Swing Phase during Gait................................................36 Kinematic Characteristics duri ng Pre-Swing and Swing Phase ......................................37 Kinetic Characteristics duri ng Pre-Swing and Swing phase ...........................................38 Moments, Powers, Angular velocities......................................................................38 Interjoint coordinati on during swing phase .............................................................. 40 Muscle Activity during Pre-Swing and Swing Phase...................................................... 41 Relevance of Reviewed Literature to Study Four...........................................................42 3 RELATIONSHIP BETWEEN STEP LENGTH ASYMMETRY AND WALKING PERFORM ANCE IN SUBJECTS WI TH CHRONIC HEMIPARESIS................................ 49 Introduction................................................................................................................... ..........49 Methods..................................................................................................................................51 Participants......................................................................................................................51 Procedures..................................................................................................................... ..52 Data Analyses..................................................................................................................53 Statistical Analyses.......................................................................................................... 54 Results.....................................................................................................................................55 Relationship between Step Length Asymmetry (SLR) and GRFs.................................. 55 Relationship between Asymmetrical Step Lengths, He miparetic Severity and Walking Speed.............................................................................................................57 Relationship between Step Length Asym m etry, Time Spent in Pre-Swing and Swing Time..................................................................................................................57 Relationship between SLR, Change in Gait Speed and Parameters That C ontribute to Change in Speed......................................................................................................57 Discussion...............................................................................................................................58 Relationship between Step Length Asymm etry and Propulsive Forces during Hemiparetic Walking...................................................................................................58 Relationship between Step Length Asym m etry, Walking Speed and Hemiparetic Severity........................................................................................................................61 Relationship between Step Length Asym m etry, Paretic Pre-Swing Time and Vertical GRFs..............................................................................................................62 Conclusions.............................................................................................................................63 4 VARIABILITY IN SPATIOTEMPORAL ST EP CHARACTERISTICS AND ITS RELATIONSHIP TO WALKING PE RFORMANCE POST-STROKE...............................70 Introduction................................................................................................................... ..........70 Methods..................................................................................................................................71 Participants......................................................................................................................71 Procedures..................................................................................................................... ..72 Data Analyses..................................................................................................................73 Statistical Analyses.......................................................................................................... 74 Results.....................................................................................................................................75 Differences in Step Variability betw een Healthy and He miparetic Walking.................. 75 Association between Step Variability, C linical Assessm ents and Asymmetry Index..... 76 Discussion...............................................................................................................................77
8 Differences in Step Variability between Healthy and He miparetic Participants............ 77 Relationship between Hemiparetic Step Variability and Im paired Performance Post-Stroke...................................................................................................................78 Study Limitations............................................................................................................ 81 Conclusions.............................................................................................................................82 5 FOOT PLACEMENT IN A BODY RE FER ENCE FRAME DURING WALKING AND ITS RELATIONSHIP TO HEMIPA RETIC WALKING PERFORMANCE.............. 88 Introduction................................................................................................................... ..........88 Methods..................................................................................................................................90 Participants......................................................................................................................90 Procedures..................................................................................................................... ..91 Data Analyses..................................................................................................................92 Statistical Analyses.......................................................................................................... 94 Results.....................................................................................................................................95 Quantifying Foot Placement Relative to the Pelvis ......................................................... 95 Relationship between Anterior-Posterior F oot Pla cements Relative to Pelvis, Step Length Asymmetry and Paretic Propulsion................................................................. 96 Relationship between Medial-Lateral Foot Place ments Relative to Pelvis, Step Widths, Paretic Weight Support and Dynamic Stability Margin................................. 97 Discussion...............................................................................................................................98 Anterior-Posterior Foot Placement Relative to Pelvis and its Relation ship to Step Length Asymmetry and Forward Progression............................................................. 98 Medial-Lateral Foot Placement Relative to Pelv is and its Rela tionship to Weight Supported on Paretic Leg and Dynamic Stability Margin......................................... 101 Limitations.................................................................................................................... .103 Conclusions...........................................................................................................................104 6 EVALUATION OF STEP LENGTH GENERATION DURING POST-STROKE HEMIPARE TIC WALKING USING A NOVEL METHODOLOGY OF STEP-BYSTEP VARIABILITY IN GAIT DATA.............................................................................. 112 Introduction................................................................................................................... ........112 Methods................................................................................................................................115 Participants....................................................................................................................115 Procedures..................................................................................................................... 116 Data Analyses................................................................................................................117 Statistical Analyses........................................................................................................ 118 Results...................................................................................................................................120 Predictors of Step Length Variability a nd the Dif ferences in Selected Predictor Variables across the Asymmetrical Sub-Groups....................................................... 120 Shorter paretic group..............................................................................................120 Symmetric group.................................................................................................... 121 Longer paretic group.............................................................................................. 121 Discussion.............................................................................................................................122
9 Contralateral Stance Leg Ground Reaction Force (AP I mpulse during Ipsilateral Swing) is a Significant Predicto r of Step Length Variability.................................... 123 Ipsilateral Hip Impulse in Early Swing is a Sign ificant Predic tor of Step Length Variability in Persons taking Longer Paretic than Non-Paretic Steps.......................124 Ankle-Joint Center Velocity at Toe-Off is a Significant Predictor of Non-Paretic Step Length Variability .............................................................................................. 126 Leg Orientation at Toe-Off and Pelvis Ve locity at Toe-Off and their Contribution to Explaining Step Length Variability .......................................................................126 Within-Subjects Regression Models............................................................................. 127 Limitations.................................................................................................................... .128 Conclusions...........................................................................................................................129 7 CONCLUSIONS: INTEGRATING THE FINDINGS......................................................... 140 Step Length Asymmetry during Hem iparetic Walking........................................................ 140 Step Variability during Hemiparetic Walking...................................................................... 141 Asymmetrical Stepping in a B ody Reference Fram e Post-Stroke........................................ 142 Step Length Generation during Hem iparetic Walking......................................................... 142 Summary...............................................................................................................................143 APPENDIX A LOWER EXREMITY FUGL-MEYER SCALE.................................................................. 144 B DYNAMIC GAIT INDEX SCALE...................................................................................... 145 LIST OF REFERENCES.............................................................................................................147 BIOGRAPHICAL SKETCH.......................................................................................................163
10 LIST OF TABLES Table page 3-1. Correlation between SLR and walking variables............................................................... 644-1. Definitions of study variables........................................................................................... .824-2. Step variability (expressed as standard deviation) within the hemiparetic population sub-divided based on thei r performance measures............................................................ 835-1. Definition of study variables............................................................................................ 1056-1. Subject characteristics.................................................................................................. ....1306-2. Average gait characteristic s for individual participants................................................... 1316-3. Regression models for individual partic ipants to predict paretic step length variability.................................................................................................................... .....1326-4. Regression models for individual partic ipants predicting non-p aretic step length variability.................................................................................................................... .....133
11 LIST OF FIGURES Figure page 2-1. A simplified model demonstrating neural control of gait .................................................. 43 2-2. Division of a gait cycle into phases................................................................................... 44 2-3. Methodology for collection of spatiotemporal characteristics during walking using an instrum ented mat (GAITRite)............................................................................................ 45 2-4. Illustration of ground reaction forces exerted by the lim bs and typical force curves........ 46 2-5. Variability (in stride time) during walking and its relation to risk for falls ....................... 47 2-6. Power profiles in swing phase of a healthy gait cycle ....................................................... 48 3-1. Illustration of horizontal GRF i mpulses............................................................................65 3-2. Comparison of GRFs between the pareti c and non-paretic legs for subjects walking with differing SLR .............................................................................................................66 3-3. Relationship between st ep length ratio and Propulsion Paretic.............................................67 3-4. Relationship between step length as ymmetry, walking speed and hem iparetic severity....................................................................................................................... ........68 3-5. Change in speed, cadence and individual step lengths in subjects walking at different SLR [SLR > 1.1 (n = 21), 0.9 < SLR < 1.1 (n = 21), SLR < 0.9 (n = 4)].......................... 69 4-1. Differences in temporal variability betw een healthy (n = 22) and participants with hem iparesis (n = 94) at Self-selected (SS) walking speeds............................................... 84 4-2. Differences in spatial variability betw een healthy (n = 22) and participants with hem iparesis (n = 94) at Self-selected (SS) walking speeds............................................... 85 4-3. Differences in temporal variability in hem iparetic participants based on their performance on clinical assessments................................................................................. 86 4-4. Differences in spatial variability in hemiparetic participants based on their perform ance on clinical assessments................................................................................. 87 5-1. Illustration of marker positions for kinematic data collection and the SIMM model generated ..........................................................................................................................106 5-2. Calculation of ante rior-posterior and m edial-lateral foot placements relative to pelvis.. 107 5-3. Foot placement relative to pelvis during hemiparetic and healthy gait........................... 108
12 5-4. Relationship between anterior foot placem ent asymmetry relative to pelv is and step length asymmetry in participants with hemiparesis......................................................... 109 5-5. Relationship between step length asymmetry and anterior-posterior foot p lacement relative to pelvis in participants with hemiparesis........................................................... 110 5-6. Relationship between paretic and non-p are tic lateral foot placement asymmetry relative to pelvis and percent weig ht supported on the paretic leg.................................. 111 6-1. An individual participant walking on the split belt treadmill as kinematic, kinetic and EMG data were recorded ................................................................................................. 134 6-2. Illustration of vari ables used in the study ........................................................................135 6-3. Frequency distribution of step-tostep variability in step lengths. ................................... 136 6-4. Non-paretic AP impulse and Paretic hip im pulse during paretic stepping in the asymmetrical sub-groups................................................................................................. 137 6-5. Relationship between paretic hip impulse in early swing, non-pa retic AP impulse in early and late swing in an individual participant taking longer paretic steps than nonparetic ...............................................................................................................................139
13 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy QUANTIFICATION OF ASYMMETRICAL STEPPING POST-STROKE AND ITS RELATIONSHIP TO HEMIPARETI C WALKING PERFORMANCE By Chitra Lakshmi Kinatinkara Balasubramanian August 2008 Chair: Steven A. Kautz Major: Rehabilitation Science Asymmetrical stepping is a char acteristic feature of hemiparetic walking and a result of sensorimotor deficits post-stroke Asymmetry measures (that is, relative performa nce of paretic leg) may characterize hemiparetic gait better than overall gait performance measures (such as gait speed) and can provide insights into underl ying paretic leg impairments. Therefore, the major purpose of this dissertation was to quant ify the asymmetry in steps post-stroke and understand its relationship to hemiparetic walkin g performance. Overall, four studies were conducted. Persons with chronic hemiparesis and healthy controls walked overground and over a split-belt instrumented treadmill as spatiotemporal, kinematic and kinetic data were collected. Clinical assessments included lower-extremity Fugl-Meyer grading and Dynamic Gait Index assessments. In study one, step length asymmetry during wa lking was quantified. Results showed that step length asymmetry related to propulsive force generation during hemiparetic walking. Further, asymmetrical step lengths may not n ecessarily limit the self-selected walking speed likely due to other compensatory mechanisms. We suggest that step length asymmetry can be utilized as a clinical measure to evaluate asymmetrical stepping post-stroke.
14 In study two, step-by-step variability and its relation to asymmetrical stepping were investigated. Results showed that increased spa tiotemporal variability, asymmetry in swing and pre-swing time variability and re duced width variability were re lated to severe hemiparesis, asymmetrical stepping and poor balance. We suggest that step-by-step va riability measures are quantifiable markers of impaired walking performance post-stroke. In study three, asymmetrical stepping was evaluated in a body reference frame. Results showed that anterior-posterior and medial-lateral foot plac ements relative to body were asymmetrical and this foot plac ement asymmetry related to step length asymmetry but not step widths. Wider paretic foot placement relative to pelvis than non-paretic also related to reduced paretic leg weight support and late ral instability, suggesting the clin ical utility of medial-lateral foot placement relative to pelvis as an outcome to quantify weight support during hemiparetic walking. In study four, mechanisms underlying step le ngth generation were evaluated. Contralateral anterior-posterior and hip impul ses during swing explained the st ep length variability in the majority of participants. However, relationship of the predictors to step lengths differed in the asymmetrical sub-groups. This implies that mech anisms of step length generation were different across persons showing differing step length as ymmetry patterns. Based on these mechanisms, we have proposed specific impairments and th erapeutic strategies targeted towards these impairments underlying asymmetrical stepping.
15 CHAPTER 1 INTRODUCTION The Am erican Heart Association reports approximately 700,000 cases of stroke or cerebrovascular accident annually  Stroke is the number-one cause of long-term disability around the world  and is estimated to result in $30 billion in health care costs and lost productivity each year . As the most disablin g chronic disease, the cumulative consequences of stroke are often staggering for individuals, families, and the society [3, 4]. Hemiparesis (unilateral movement dysfuncti on or weakness of one-half of the body) is commonly seen in three-quarters of persons post-str oke . The residual sensorimoto r control deficits of a person with post-stroke hemiparesis involves multiple impairments such as muscle weakness, abnormal synergistic organization of movement, impair ed force regulation, abnormal muscle tone, impaired balance and sensory deficits [2, 5, 6]. Additionally, residual cognitive and visual deficits contribute to the reduced functi onal mobility in this population [7, 8]. Regaining independent walking is the most often-stated goal fo r rehabilitation in patients post-stroke . Walking deficits in those who have sustained a stroke range from complete immobility to independent mobility, with almost a third of stroke survivors showing severe walking impairments . Although post-stroke hemiparesis appears to reflect a single diagnostic category, there is immense heternogenity in the walking perfor mance post-stroke , warranting a systematic characterization of walking performance deficits and underlying impairments. Quantification of impairments th at limit functional walking performance and investigation of mechanisms underlying these impairm ents will directly assi st in development of targeted therapies to improve hemiparetic walking function. Asymmetrical performance between lower extremities is a characteristic hallmark that is unique to hemiparetic gait [12, 13] While the asymmetrical nature of hemiparetic walking is
16 well documented in the literature [12-15], there is insufficient understanding of the underlying mechanisms related to gait asymmetry. One of the primary reasons limiting an integrated understanding of gait asymmetry post-stroke is the heterogene ity in asymmetrical patterns among stroke patients primarily due to the dive rse motor recovery processes and compensatory mechanisms . Furthermore, the relationship of gait asymmetry to functional performance is unclear, primarily because functional performance has been traditionally evaluated using walking speed . Gait asymmetry is reported to show a weak relation to attained walking speed implying that asymmetry may not limit th e functional performance [5, 17-19]. However, faster walking speeds in some persons show ing severe asymmetry can be achieved by compensatory strategies from the non-paretic leg, limiting the specific understanding of the contribution of paretic leg performance to functio nal performance. While it can be argued that compensations post-stroke are central to the wa lking performance due to altered circuitry and limited ability after a neurological injury , it is essential to differentiate impairments from compensations such that therapeutic strategies can be specifically designed to improve the paretic leg performance. Furthermore, there is no clear consensus in the literature regarding the clinical relevance of evaluating gait asymmetry . As a clinical m easure, gait velocity reflects overall gait performance but is limited in its value to ev aluate post-stroke gait specific to paretic leg impairments . In turn, asymmetry measures (i .e., relative performance of the paretic leg) can provide insights on the paretic leg performance in relation to the non-pa retic leg. Therefore, asymmetry measures could be deve loped as outcomes that specifica lly reflect the contribution of the paretic leg towards functional walking. The ai m of this dissertation was to systematically quantify asymmetrical performance (specifical ly in stepping measures) during hemiparetic
17 walking, to explore underlying mechanisms and to understand how asymmetry might relate to walking performance post-stroke. In particular, th is dissertation will focus on stepping (spatialtemporal) asymmetry. A step during walking is the final outcome of all events occurring in the gait cycle . Therefore, spatial-temporal char acteristics of steps (such as step length, swing time, etc.) can be used as quantifiable measures of walking performance reflective of underlying gait processes . Furthermore, stepping parame ters can be easily recorded enhancing their clinical utility as gait performance measures. In this dissertation, four st udies were conducted to quantify asymmetrical stepping and understand its relationship to hemiparetic walkin g performance. In the first study, step length asymmetry during walking was qua ntified and the relationship between spatial asymmetries and hemiparetic walking performance was explained. In the second study, the st ep-by-step variability in selected spatial and temporal characteristics of steps was evaluated and their relation to stepping asymmetry and hemiparetic performa nce was explained. The third study of this dissertation evaluated asymmetri cal stepping in a body reference fr ame to gain insights regarding asymmetrical foot placement relative to the body during hemiparetic walking. Finally, in the fourth study of this dissertation, mechanisms related to initial conditions of the leg and swing phase were investigated to explain step length generation during hemiparetic walking. The overall purpose of studies in this dissertation was to provide a foundation for the development of a framework to use asymmetry measures to asse ss walking impairments post-stroke. Specificity in assessment of walking impairments will, in tu rn, facilitate the development of rehabilitation strategies that are cost -effective and efficient.
18 CHAPTER 2 LITERATURE REVIEW Introduction The following literature review is composed of six m ain pa rts and provides the background underlying specific aims of this dissertation study. Part one, is an overview of walking function and describes walking deficits of persons who have sustained a stroke In the second part, literature related to motor control mechanisms in hemiparetic walking is presented. This section presents background literature rele vant to Study One (Chapter 3). In the third part, intra-subject variability during walking is discussed in relevance to Study Two (Chapter 4) of this dissertation. Part four describes literature related to foot placement during walking and forms the basis for aims of Study Three (Chapter 5). In part five, pre-swing and swing phase control during walking is discussed and this part focuses on the literature relevant to Study Four (Chapter 6) of this dissertation. Part 1: Overview of Walking Function Neuromotor Control of Healthy Gait Walking is essentially an inter-lim b coordina ted movement in which the limbs move in a symmetrical alternating pattern such that the bod y can progress forward in a stable and efficient manner [22, 23]. Human walking is remarkable in that the healt hy locomotor system integrates input from the motor cortex, cerebellum, and the basal ganglia, as well as synchronizes feedback from visual, vestibular and proprioceptive sensors to produce carefully controlled motor commands that result in coordinated muscle firings and limb movements . Figure 2-1 demonstrates a model of walking from previ ous works [25, 26]. While the spinal pathways (central pattern generators) can generate the basic locomotor rhythm, sensory inputs from higher
19 centers (through descending pathways as cortic ospinal tracts) and feedback from peripheral mechanisms (afferent feedback) enable a rich variation in the basic locomotor rhythm. Furthermore, the three major requirements for successful locomotion are suggested to be a) progression, defined as the ability to generate a basic locomoto r pattern that can move the body in a desired direction; b) stab ility, defined as the ability to support and control the body against gravity; c) adaptability, defined as the ability to meet the indi viduals goals and the demands of the environment . Quantifying Gait: Phases in the Healthy Ga it Cycle Walking function is usually quan tified as a Gait cycle. A Gait (Stride) cycle is defined as the events occurring from foot stri ke of one limb to the foot strike of the ipsilateral limb [28, 29]. Each gait cycle is further divide d into a stance phase (as when ipsilateral limb is on the ground) and swing phase (as when ipsilateral limb is swinging with no contact on the ground) . Stance and Swing phases of a gait cycle can be fu rther sub-divided into different phases. Figure 2-2 presents these sub-divisi ons of a Gait cycle phase. Walking Capacity after a Stroke Stroke: incidence and consequences OSullivan et al. (2000) has de fined a stroke, o r cerebrovasc ular accident (CVA), as an acute onset of neurological dysfunction due to an abnormality in cerebral circulation with resultant signs and symptoms that correspond to i nvolvement of 19 focal areas of the brain . The American Heart Association reports stroke as a common neurologic al event occurring in 700,000 people annually. Over 4 million people currently live with residual deficits . Stroke is the primary cause of long-term disability and is classified as one of th e most disabling chronic diseases. It has been estimated that one in five stroke survivors need help walking and seven out of ten cannot return to th eir previous jobs . Fifty one perc ent of stroke surv ivors are unable to
20 return to any type of work . In particular; ability to return to work is primarily shown to relate to walki ng function [34, 35]. Pathophysiological basis of the locomotor disorder post-stroke The pathophysiological basis of walking disability after a stroke is dam age to motor neurons and pathways of the central nervous system caused by interruption of arterial blood supply because of a hemorrhage (hemorrhagic str oke) or thrombus (ischemic stroke) usually on one side of the brain . Consequently, paresis (or paralysis) is observed in opposite half of the body (hemiparesis) [36-38]. The types and degrees of disability that follow a stroke primarily depend upon multiple factors such as location and size of brain lesion, severity of the lesion, individual degree of spontaneous recovery, and the duration of st roke onset [39, 40]. Nonetheless, residual deficits ar e common after a stroke. Typical re sidual deficits after a stroke include sensorimotor, cognitive and visual deficits, all of which can independently or in combination result in reduced or impaired walking ability. Motor control impairments of weakness (paresis) , loss of volitional movements of the weaker or paretic side (opposite to lesion) or inappropriately gr aded muscle activations of the weaker side affect locomotor performance imme diately after a stroke [36, 39]. Impairments of spasticity and changes in the mechanical properties of muscles further contribute to walking disability, developing a few weeks after the initial insult . Nonetheless, damage to the motor control system and the re sidual impairments vary with the natu re and extent of brain lesion . Therefore, while there are some common moto r control impairments that affect walking performance after a stroke, several sub-groups within the population can be identified that present differing motor control impairments.
21 Nature and rate of walking recovery Mechanisms of recov ery: Recovery following a stroke is a complex process involving both spontaneous recovery and recovery due to the effects of a therapeutic intervention that are usually difficult to separate . In general, wh ile the mechanisms of lo comotor recovery after a stroke are largely unknown, it is suggested that co rtical and spinal reorganization , functional compensation from existing pathways , new ne uronal sprouting  a nd spinal and afferent reflex modulation [45, 46] are potential mechan isms that contribute to functional locomotor recovery. Furthermore, motor recovery processes that unde rlie walking recovery specifically can be explained (at least partially) by the step-wise reco very process earlier proposed by Twitchell and colleagues . Twitchell et al. (1951) argued that motor rec overy follows a step-wise and predictable sequence after an initi al stage of areflexia and flaccid paralysis. After this initial stage, reflexes return, become hyperactive, muscle tone increase s and spasticity develops. In the next stage, voluntary movement appears as part of stereotyped, reflexive flexor and extensor muscle synergies, after which voluntary m ovement may be achieved out of synergy. Finally, normalization of muscle tone and reflexes may occur. Rate of recovery: Only 23 37 % of persons who have su stained a stroke are able to walk independently during the first week , but th ere is a general agreem ent that 50 80 % of survivors can walk at 3 weeks or at discharg e , and by 6 months as many as 85 % of the population can walk . While it is generally assumed that walk ing function recovery plateaus after 3 months, there is some evidence that rec overy may continue up to 2 years (using gait speed as the outcome measure) [50, 51]. Nonetheless, residual walk ing impairments last several months to years after the acute onset. Further, these residual impairments limit walking performance .
22 Walking disability in the chronic phase While, in general, 85% of stroke survivors can walk by 6 m onths of stroke, the quality of walking remains impaired amongst most patients. Wa lking after a stroke is characterized by slow walking speed , poor endurance  and impaired mu scle coordination [55, 56]. Specifically, the impaired muscle coordination after post-stroke hemiparesis results in the characteristic asymmetrical nature of walki ng commonly referred to as Hemiparetic Gait. Furthermore, impaired muscle coordination after a stroke significantly limits the walking ability of persons and restricts their independent mobilit y about the home and community . Further, difficulty in walking is associated with limited abili ty to return to work [ 58] and deterioration in the quality of life. Risk for falls while walking: Persons who have sustained a stroke are at a high risk for falling [59, 60]. Since gait and balance deficits are primary contributors to falls, risk for falling further increases significantly in those stroke survivors who are ambulatory and have balance deficits . Consequently, a fa ll after a stroke compounds to the post-stroke disability. For most patients with stroke, functional walking ability is rarely regained even at the end point of their rehabilitation and several therapeutic interven tions are aimed at maximizing walking recovery. Nevertheless, there is a lack of targeted interventions to improve walking ability. In part, the problem is because walking impairments are not specifically quantif ied . Therefore, quantification of walking impair ments is necessitated to assist in development of focused therapeutic strategies. Part 2: Asymmetry in Spatiotemporal Step Characteristics and Ground Reaction Forces during Hemiparetic Walking Inter and intra-limb  coordinati on deficits are com monly observed during poststroke hemiparetic walking. These coordination deficits along with sensorimotor and motor
23 control deficits result in the asymmetrical perf ormance after stroke. In fact, asymmetry in motor performance between the paretic and non-paretic le gs is a characteristic feature of hemiparetic gait [12, 65, 66]. In particular, spatiotemporal characteristics of steps and Ki netic (Ground Reaction Forces) parameters during walking are commonly used to characterize both overall walking performance and specifically asymmetrical performance. Spa tiotemporal step characteristics and kinetic parameters are most relevant to studies in this dissertation and therefore are reviewed below. Spatiotemporal Characteristics of Steps Spatial (i.e., length and width) a nd tem poral (i.e., timing of ev ents) characteristics of steps are commonly examined since they represent the final outcome of collective motions that contribute to walking [20, 67]. These parameters are also clinically releva nt since they are both easily observable and quantifiable. Figure 23 shows a common methodology for collecting spatiotemporal (ST) parameters during gait usi ng an instrumented walkway (GAITRite). Given the clinical relevance of the ST parameters of steps, characte rization of these parameters and quantification of underlying mechanisms during hemiparetic gait can provide useful insights regarding hemiparetic gait. The most consistently reported spatiotemporal parameter is slower walking speed. In 17 studies reporting gait speed, the average speeds ranged from 0.23 0.11 m/s  to 0.73 0.38 m/s . The attainable maximal speed is also limited by functional limitations imposed due to the pathology of stroke . Consistent with slower walking speeds, persons with hemiparesis take shorter stride leng ths and have lower cadence (number of steps taken per minute) compared to age-matched healthy adults [13, 68]. Slower gait speed after a stroke is also associated with a longer gait cycle duration [13, 68]. Further, the proportion of time spent in stance versus swing is
24 also altered on both paretic and non -paretic sides, when compared to healthy adults walking at normal speeds [5, 13, 16]. While, gait speed or other unilateral measures reflect overall gait pe rformance; asymmetry in ST parameters of steps can reveal deficits in motor coordi nation between the paretic and nonparetic legs and the performance of the paretic leg relative to the non-pare tic. Literature specific to spatiotemporal asymmetry during hemiparetic gait is reviewed in the following paragraphs. Temporal asymmetry Asymm etries in temporal parameters of steps in persons who have sustained a stroke are well documented [12, 13] and have been consis tently related to disturbances in motor coordination . In particular, it is reported that persons after a stroke spend longer time bearing weight on the stance phase of th e non-paretic leg than paretic  Further, stance phase of both paretic and non-paretic sides is l onger in duration and occupies a greater portion of the full gaitcycle  as compared to both age-matche d and speed-matched healthy adults . Similarly, it is reported that pe rsons after a stroke spend long er time swinging their paretic leg, likely because they spend longer time bear ing weight on the non-paretic leg (i.e., longer stance time) . This asymmetr y in swing time is reported to be a significant predictor of hemiparetic walking performance (since it strongly correlates with stag es of motor recovery, walking speed and falls) [13, 15]. Furthermore, a greater proportion of cycle time is spent in double support phase of the gait cycle during he miparetic gait. Particularly, of the two double support phases, relatively greater time is spent in the second double support of the paretic gait cycle (paretic pre-swing phase) than the nonparetic . Furt her, Dequervain et al. (1996) reported that the paretic pre-swing phase was markedly prolonged for those persons who had very slow gait velocities . Specifically, it is suggested that this prolonged paretic pre-swing duration indicates a poor progression of hip flexi on during swing phase of patients with slow gait
25 velocity [69, 70]. In summary, several aspects of temporal asymmetry are well characterized in the literature and temporal asym metry has been consistently rela ted to poor motor performance during hemiparetic walking. Spatial asymmetry W hile temporal asymmetry is well characte rized and the direction of asymmetry is consistently reported in the literature, direc tion of spatial asymmetry varies across studies. It has earlier been reported that, after a stroke, patients may walk with either relatively longer paretic steps or longer non-paretic st eps [19, 65, 69]. In a study by Kim et. al. (2003), considerable variability in step length asymmetry was observed in a sample of 28 chronic stroke survivors. While 14 of these 28 participants walked with longer paretic steps than non-paretic, 14 others walked with relatively longer nonparetic steps. Dettman et al (1987) and Hsu et al. (2003) reported that while, on an average persons with stroke walked with longer paretic than nonparetic steps, step length patterns were inconsis tent within sub-groups of the population [65, 71]. Thus, it is unclear whether person s within the hemipare tic population walk with one or the other pattern or both. Furthermore, reasons for the variability in step length asymmetry patterns and relationship of these variable patterns to walking performance are unexplain ed. For example, Kim et al. (2003) hypothesized that the variability in patterns of step length asymmetry may be due to compensatory strategies that increase or decrease the step length of either paretic or non-paretic limb . However, they were unable to advance the discussion since they found a nonsignificant relationship between step length symmetry and symmetr y in vertical ground reaction forces. Further, in a recent review article, Lamontagne and colleagues  suggest that an inconsistency in the direction of asymmetries between paretic and non-paretic legs is the result of differences in walking ability in the subjects, but they do not specifically report these differences.
26 Another reason for insufficient understanding of the affect of step length asymmetry on hemiparetic walking performance is that the relationship between step length asymmetry and walking speed is not well documented in the cu rrent literature. For instance, shorter stride lengths (bilaterally) have been related to slower walking speed and thereby poor walking performance , and yet a non-significant relationship has been suggested between step length asymmetry and walking speed  Since kinetic characteristics represent the underlying causes for the kinematic and spatiotemporal patterns , it might be useful to examine the kinetic characteristics to quantify the step length asymmetry. Ground Reaction Forces in Hemiparetic Gait Ground reaction forces (GRFs), as measured by f o rce platforms, reflect the net vertical and shear forces acting on the surface of the platform . Forces are exerted by the limbs (due to muscle activity) on the ground while a person walks and is recorded as the equal and opposite reaction force exerted by the for ce platforms in response (Figure 2-4). Mathematically, GRFs are the algebraic summation of the mass-acceleration products of all body segments while the foot is in contact with the platform [ 73]. The net GRF has three compone nts: Vertical, Horizontal and Mediolateral. The vertical force has a characte ristic double-hump (first related to weight acceptance and the second related to push-off), (F igure 2-4). The horizontal force has a negative phase in the first half of stance (indicating a net deceler ation or braking of the body) and a positive phase in the second half (indicati ng a net acceleration or propulsion of the body forward), (Figure 2-4). The vertical force curve is shown to be vari able across subjects and most commonly has an initial low peak. Carlsoo et al. (1974) reported three different patte rns of Vertical GRFs: 1) first peak during heel contact and s econd during push-off, 2) pattern showing continuous plateau, 3) pattern showing single peak in midstance  Kim et al (2003) further showed that the
27 symmetry in vertical GRFs is accompanied by symmetry in temporal parameters but not in the symmetry of distance variable . This is expect ed since the vertical GRFs primarily act on the vertical acceleration of the center of mass and symmetry in distance variables are likely related to a horizontal component of the GR F (i.e., Anterior-Posterior GRF). Conversely, Mediolateral GRFs during hemiparetic walking have not been systematically reported. Rogers and associates study on voluntary leg flexion movements in the hemi paretic persons provides some insight into the relevance of the M-L forces to stepping . The results of their study revealed asynchrony and reversals in usual directions of lateral for ces, suggesting the inter-lim b coordination deficits in this population. In a recent study, A-P GRFs during hemiparetic walking was quantified for the first time . Bowden et al. (2006) showed that anterior (propulsion) for ces by the paretic leg are reduced compared to the propulsive forces by the non-pare tic leg . In this st udy, a measure from the A-P forces was developed that quan tified the coordinated ou tput of the paretic limb to the task of body propulsion during walking. This measure was re ferred to as paretic propulsion (Pp), which represented the percentage of total propulsion generated by the paretic leg during walking. Pp was also found to correlate with both wa lking speed and hemiparetic severity. Relevance of the Reviewed Literature to Study One Overall, current evidence sugge sts that persons after a stroke walk with different patterns of step length asymm etry that may be unrelated to the attained walking speed. However, these spatial asymmetries are not quantified and it is un clear how the different asymmetrical patterns relate to post-stroke hemiparetic walking perf ormance and why asymmetr y in step lengths may not necessarily limit the attained walking speed. Therefore, study one of this dissertation aimed at quantifying the step length asymmetry and explaining its relation to hemiparetic walking performance.
28 Part 3. Intra-Subject Variability during Walking While variability during walking exists both be tween individuals (inter -subject) and within individuals (intra-subject), intr a-subject variability in the perform ance of tasks has received less attention . Intra-subject vari ability during walking is the vari ation observed in an individuals walking performance (i.e., variability in steps fo r individual participants ). No two steps during walking are exactly similar and there is some natu ral variability from step to step . Walking variability can be quantified usi ng spatiotemporal, kinematic, kinetic and EMG characteristics. Motor Control and Gait Variability Significance of gait variabil ity: theoretical app roach Walking is a rhythmical inter-limb coordina ted task and it is suggested that pattern generators located in the spinal cord generate the basic motor rhythm during walking . These pattern generators are considered to be closely coupled for walk ing movements, suggesting little variability (stability) in the pattern of walking. Nevertheless, walking movements are not strictly rhythmical and emerge as a consequence of th e interaction of neural and mechanical dynamic systems, pattern generators, modulation from supr aspinal neural system and afferent modulation [80, 81]. These multiple modulation in the neur omuscular system may induce variability in walking movements. Walking, specifically, is an ex ample of flexible coordination where stability co-exists with the abundant variability in m ovements [82-84]. Further, the degree of the variability has also been linked to the health of a biological sy stem [78, 85], suggesting that impairments in gait might alter the variabilit y. In summary, coordinati on patterns like walking are highly flexible, being simu ltaneously stable and variable. Role of variability during walking The trad itional approach in motor control is to consider intra-subject variability as an index of noise in the sensorimotor sy stem . More recently, positive aspects of movement variability
29 have been proposed [87-89]. Such perspectives s uggest that variability in movement constitutes a pattern of stimulation. This pattern of stimula tion provides task-relevant information about the dynamical interaction between a person and the envi ronment . There is also some indication that intra-subject motor variability can well predict performance of motor tasks and that variability is essential for many aspects of motor performance  Furthermore, stride-to-stride variability in gait parameters might reflect the in herent flexibility in the locomotor system  and therefore might be a re quisite for adaptability. Step-by-Step Variability in Spatiotemporal Characteristics Gait var iability is most commonly quantified as variability in spatiotemporal (ST) characteristics of steps. The concept of variabi lity within the ST parameters, its quantification and relation to falls risk is pres ented in Figure 2-5. Stride-to-stri de variability in stepping patterns during walking is consistently reported to be low in healthy persons [91, 92] during free unperturbed walking at natural walking speeds. Kinetic and EMG va riability is also reported to be low in healthy gait [93, 94], a lthough higher than variability in ST parameters of steps. The magnitude or degree of variability is commonly reported, using parameters like standard deviation (SD) [95, 96] and coefficien t of variation (CV) [97, 98]. However, recent studies suggest the use of measures that can qua ntify not only the magnit ude of variability, but also the structure of va riability (e.g. fractal dynamics of ga it rhythm) [99, 100]. In Study two of this dissertation, only the magnitude of variability will be evaluated. SD reflects the absolute varia tion of a parameter while CV, is the variability computed relative to the mean of the distribution [CV= standard deviation / m ean]. SD and CV are expected to correlate because they are mathematically derived similarly (i.e., CV is defined from SD). SD and CV are also reported to be correlat ed in patient populations . There is no clear
30 consensus in the literature regarding the measur e suited to quantify variability and there are few reports on reliability and validity of each of these measures. Advantages and disadvantages of gait variability measures: SD is reported to be unrelated to the mean of the parameter distribut ion  and therefore, might better quantify the absolute variation across parameters or when comparisons are made within variables across persons. In cases where comparis ons of variability are made acr oss parameters, CV might be more advantageous since it normalizes the variation in reference to the individual mean of each parameter distribution . However, extremel y low parameter means can drive the CVs to infinity and thereby, suggest spuriously large variations. Step Variability as Quantifiable Marke rs of Impaired Walking Increased or decreased variability is co mmonly reported in populations with gait abnormalities like elderly fallers [103, 104], older frail adults  and persons with neurodegenerative diseases (e.g, Parkinsons diseas e) [106, 107], suggesting that gait variability strongly associates with gait impairments. It is also suggested that alteration in ga it variability is specific to pathology and that healthy aging might not a lter gait variab ility . Step variability and its rel ation to gait impairments: Altered gait variability has been strongly related to walk ing impairments and is suggested to be a quantifiable biomechanical marker to evaluate impaired performance . Increased gait variability has been related to slower gait speed and poor c ognitive status in adult fallers [77, 96, 109]. Similarly, central nervous system impairments (like cognitive f unctioning and motor performance) have been related to increased stan ce time variability , while decreased step width variability has been related to sensory impairments and balan ce deficits during walking [104, 110, 111]. Gait variability is also suggested to predict mobility disability . Increa sed gait variability has also been related to risk for falls, implying that excess variability in steps might relate to balance
31 impairments . Further, there is a strong sugges tion in the literature that altered (increased or decreased) variability in steps is directly related to dynamic ba lance impairments since altered variability has consistently shown to predict the ri sk for both past and future falls and those falls specific to walking [77, 96, 101, 103]. Direction of alteration in gait variability: Motor control theories (like older hierarchical models and more recent dynamical systems theo ries) support both views of increased and decreased step variability as being beneficial to walking. While older motor control theories suggest that increased motor variability is reflective of decreased motor skill, more recently positive aspects of movement variability have been proposed . It is suggested that stride-tostride variability in gait parame ters might reflect the inherent abundance of the locomotor system and therefore might be a requis ite for adaptability . Variability in step characterist ics like step length, swing time, stride time and stance time is consistently reported to increase during impaired gait [96, 98, 103, 106, 112]. However, there is no clear consensus on the direct ion of alteration in step widt h variability and studies report both increase [91, 112] and decrease in step wi dth variability [96, 98, 113 ] in populations with altered gait patterns. For exam ple, while results of the st udy in healthy elderly population reported that step width variabil ity increased , Brach et al (2001) and Maki et al. (1997) reported that older adults with a history of falls show decreased step wi dth variability [96, 98]. Brach et al. (2005) also showed th at there is an optimal variability in step width that might be required and that either too little or too much vari ability might be related to falls risk . One of the reasons for the inconsistency in the literatur e regarding step width variability is due to the differences in the way step width is defined across studies, population groups tested and the testing environment  .
32 Relevance of Reviewed Literature to Study Two While alterations in step characteristics duri ng walking are frequently reported (as shorter step lengths, spatiotem poral asymmetries), characterization of gait variability may provide quantifiable measures to evaluate additional aspects of impaired performance (like dynamic balance and risk for falls) post-st roke. Further, in the stroke population, it is unclear whether there would be an asymmetry in step variab ility and how this might relate to walking performance. With the current s uggestion in literature regardi ng the association between step variability and walking impairments, it seems that characterization of variability in step characteristics will provide insights into moto r and balance control mechanisms in a stroke population. Further, investigation of the relati onship between stepping asymmetry and step variability would help determine those persons with asymmetry showing specific performance deficits (as evaluated by their step variability). Therefore, study two of this dissertation characterized the step-by-step va riability in ST characteristic s and explained its relation to hemiparetic walking performance. Part 4. Foot Placement in a Body Reference Frame One of the essential tasks during gait is appropriate positioning of the foot relative to the body . Especially, placement of the foot at the end of swing phase serves to establish a stable base of support such that the body can progress forward efficiently during walking. Therefore, foot placement is closely relate d to trunk/upper body move ments and vice versa. Biomechanical models of trunk movements and foot positions/placements during walking have been earlier presented [114, 116-119]. However, a ssumptions of these models are validated mainly in healthy young subjects and not in neurologically impaired popu lations. Investigation of foot placement in a body reference frame (i .e., relative to the body) in a hemiparetic population can directly assist in examination of parameters underlying generation of a step.
33 Defining Foot Placemen t Relative to Body Note that sp atiotemporal characteristics of step s that were discussed earlier in this literature review specifically refer to kine matics of one foot as defined rela tive to the other foot (e.g., the spatiotemporal parameter of step length is defined as anterior distance from the leading foot to the trailing foot). Specifically, F oot placement refers to the position of the foot in a step relative to the body. For example, anterior foot position at heel strike relative to the body indicates the instance at which foot was placed anterior to the body in a step. Control of Foot during Gait While basic lim b movements are primarily dete rmined by central pattern generators , animal studies suggest that movements of the foot during gait are further fine-tuned and regulated by cortical control [120, 121]. The cortical infl uences on foot during walking contribute to the adaptability of the gait pattern [122, 123]. It is widely accepted that the coordination of multiple degrees of freedom involved in locomotion is constrained by the central nervous system through a small number of be havioral units [79, 124-126]. In human walking, studies also indicate that while control of foot is implemented by ankle, knee and hip rotations, the dynamics of the foot are cen trally coded to generate the coordinated movements of stance and swing phase [127, 128]. David Winter proposed that foot kinematics is a precisely controlled sensorimotor task and is under the multisegmental motor control of both stance and swing phase [127, 128]. Control of the foot during gait can also be understood within the premise of the motor equivalence theory, where a given invariant ta sk goal (as foot cleara nce or foot trajectory) can be achieved through va riable means [129, 130]. Body Center of Mass Position and Velocity : P ostulated Link to Foot Placement Approximately two-thirds of our body mass (head, arm, trunk), which dominates the calculation of the center of mass position, is precar iously balanced over the two legs. Such a
34 postural state imposes critical demands on the ba lance control system . Unlike upright weight-bearing postures where balance is maintain ed when the vertical projection of body center of mass falls (COM) within the base of support (BOS), stability during locomotion is challenged because both BOS and COM are in motion [132, 133]. COM is within the BOS only during the two double support phases, which constitutes only 20% of a stride [132, 133]. During walking, COM is controlled by support forces generated from the legs [132, 133]. Di rection and point of application of support forces prov ided from the ground acts at the cen ters of pressure on the foot during the stride cycle. Foot placement at th e end of each swing phase provides the primary method of moving the COP in both sagittal a nd frontal plane [132, 133]. Thus, one of the essential functions of foot position relative to body is to maintain the position of COM with respect to the BOS such that dynamic bala nce during walking is maintained . COM velocity during walking: Townsend proposed, through simulation analyses, that stable gaits can be defined by foot placements which are a linear function of the position and velocity of body center of mass at the time of foot placement [ 117]. Especially during walking, the COM velocity, in addition to COM displacement, needs to be considered. Pai and group demonstrated that balance may be impossible if COM velocity is directed outward, even if the COM is above the BOS [135, 136]. As a refinement of this rule, Hof et al. (2007) recently showed that the COM position plus its velocity (extrapolated COM: xCOM ) should be within the base of support . They also suggested a measur e of stability the margi n of stability, which is the minimum distance from the xCOM to BOS . Foot Placement Relative to Body a nd its Relation to Walking Sub-tasks Appropriate foot kinem atics re lative to body is essential to maintain functional sub-tasks during gait. In the stance phase, body center of mass is propelled with in limits of the foot placed (to avoid falling). In the swing phase, trajectory of the foot needs to be appropriately controlled
35 such that foot positioning at the end of the sw ing phase is appropriately timed and placed. Foot placement relative to body is also related to minimization of energy, conservation of forward momentum or compensation for some musculos keletal deficit . Therefore, given the importance of appropriate kinema tics of the foot to maintain smooth and efficient locomotion, it seems that investigation of foot kinematics during hemiparetic walking will serve as a tool to investigate the unique impairments in this population. Balance during gait, involves controlling m ovement of the whole body COM relative to the BOS (often defined as the area enclosed between the foot placem ents) . Thus, as explained earlier, one of the esse ntial roles of foot placement dur ing gait is believed to be in determining a new base of support at each step and thereby, maintaining the dynamic balance during walking. Foot placements relative to the body and its rela tionship to the maintenance of walking balance have earlier been explained in healthy gait [116-119]. Redfern and Schuman in 1994 postulated that foot placement requires symmetry of the limbs with respect to the pelvis at heel cont act such that the body cen ter of mass is placed equidistant from both feet during double suppor t, creating a stable support base during the transition to the next step [ 118]. Mackinnon et al. (1993) and To wnsend MA (1981) showed that the most important factor affecting frontal whole body balance is the mediolateral foot placement relative to the center of mass established at initial contac t [116, 134]. Therefore, these studies suggest that foot placement relative to body is closely related to dynamic balance during gait. Relevance of Reviewed Literature to Study Three Post-stroke, quantifying where the fo ot is pl aced relative to body could provide a deeper understanding of the mechanisms of hemiparetic walking than is possible when foot kinematics alone are known (as when it is de fined relative to other foot). Fo r example, in persons who take asymmetrical step lengths (relative ly longer or shorter paretic step lengths), it is unclear whether
36 their foot placements relative to pelvis (or trunk) would also be asymmetrical. Further, since the above literature review suggested that foot placement relative to body is also related to motor and dynamic balance control mechanisms during walk ing, we expected that investigation of foot placement relative to body would provide insights into motor control impairments during hemiparetic walking. Therefore, st udy three of this dissertation quantified asymmetrical stepping post-stroke in a body reference frame and explained its relati onship to hemiparetic walking performance measures. Part 5. Pre-Swing and Swing Ph ase during He miparetic Gait During walking, pre-swing of gait precedes the generation of a step and swing phase occurs as the leg is stepping. Therefore, it is likely that several parameters (muscle activity, kinetics and kinematics) that determine the pre-swing and swing phase of walking directly affect where the foot is placed in the step. Conseque ntly, investigation of mechanisms underlying the generation of the pre-swing and swing phase during hemiparetic walking are likely to enable the evaluation of the underlying cause s of generation of stepping. Introduction to Pre-Swing and Swing Phase during Gait In healthy gait, pre-swing phase occupies 10% of the gait cycle and is more comm only referred to as the second double support . Swing phase occupi es 40% of the gait cycle and begins as the foot takes-off from the ground and ends when the foot strikes the ground again [20, 67]. Essential function of the pre-swing phase is to propel the trunk forward in preparation of leg swing initiation [138, 139]. Essential functions of the swing phase include limb clearance from the floor, advancement and forward progression of the leg and positioning the foot at the end of swing phase in preparation for st ance phase weight-bearing [20, 67]. Swinging motion of the leg is often like ned to the unforced swinging of a compound pendulum, suggesting that swing phase is a ra ther passive phenomenon [140, 141]. Furthermore,
37 activity in the leg muscles duri ng swing is low [142, 143] and join t torques in the hip, knee and ankle are also small in the swing phase relative to the stance of walking . Nevertheless, while joint torques are small in the swing phase they cannot be disregarded [145-147]. Furthermore, muscle activity is consistently reported during the swing phase of walking suggesting the active constraints during sw ing [139, 148, 149]. Most importantly, precise trajectory of the swinging limb and adequate cl earance of the limb need to be planned and optimized for efficient locomotion [128, 150]. It is also suggested that the swing phase of walking is under fine regulation by the higher corti cal centers in the central nervous system (that are mediated by spinal and in terneuronal networks) . Kinematic Characteristics during Pre-Swing and Swing Phase Pelvis ex cursions: Increased pelvic hiking during swing [ 152] to clear the paretic foot and large lateral pelvis displacements  related to impaired side-to-side balance  are most commonly reported in hemiparetic gait. Dequervain et al. (1996) also reported that the pelvis was retracted at terminal swing in eleven of the 12 particip ants with slow gait speed and posteriorly tilted throughout swing . Hip excursions: Decreased pre-swing hip extension (b ilaterally), decreased paretic hip flexion (attributed primarily to slower speed) in mid-swing and at terminal swing have been consistently observed in hemiparetic gait [16, 70] Dequervain et al. (199 6) also reported that there was a delay in initiation of paretic hip flexion at toe-o ff and progression of paretic hip flexion during swing, especially in those persons walking at extr emely slow walking speeds . Paretic hip circumduction to clear the foot is also commonly reported in pers ons with stroke . Paretic hip is also shown to be excessively a bducted and externally rotated during the swing phase .
38 Knee excursions: Knee flexion at pre-swing and duri ng swing phase is crucial for toe clearance, which is the primary function of sw ing phase during gait . In hemiparetic gait, reduced paretic knee flexion during swing [ 16, 156, 157] is most commonly observed. Reduced paretic knee flexion at pre-swi ng  and slow progression of paretic knee flexion during the swing phase  have also been observed. Ankle excursions: In hemiparetic gait, paretic ankle plantarflexion during pre-swing and ankle dorsiflexion during swing [16, 70, 152, 156] are substantially reduced. Further, Kim et al. (2004) reported that the paretic ankle remains in a relatively plantarflexed position even during terminal swing . Paretic ankl e plantarflexion at toe-off is reported to be reduced, especially, in those persons with stroke walkin g at slower walking speeds . Kinetic Characteristics durin g Pre-Sw ing and Swing phase Moments, Powers, Angular velocities Even in healthy gait, m oments, joint torque s and powers are substantially reduced in the swing phase compared to the stance. Therefore, most studies on healt hy and hemiparetic gait report either peaks or averages in these kinetic characteristics. This limits the understanding of kinetic characteristics specifically in the swing phase of hemiparetic gait. There is general consensus that most moments and power bursts are reduced in amplitude throughout the gait cycle in persons with stroke compared to both age-matched  and speed-matched healthy adults [158, 159]. Further, the reductions are report ed to be greater on the paretic side than nonparetic [158, 159]. There is much variation in the kinetic (see appe ndix for definition of kinetics) profiles of persons with stroke . In general, different kinetic strategies can be used to achieve similar kinematic outcomes, increasing the challenge in th e quantification of sub-groups that might have specific strategies within the stroke population .
39 Hip, knee, ankle power bursts during swing: In healthy gait, power bursts in the swing phase involve the A2 ankle burst (by concentr ic plantarflexor activity ) during pre-swing and early swing, K3 knee burst (by concentric extensor activity) during pre-swing and early swing, K4 knee burst (by eccentric flexor activity) and H3 hip burst (by concentric flexor activity) occurring in pre-swing and ear ly swing [94, 131, 161]. See Figure 2-6 for explanation of these power profiles. In hemiparetic gait, it is observe d that A2 burst is subs tantially reduced on the paretic side in slow walkers . Whereas, for th ose who walk fast, K3 burst is reported to be even greater than normal on the non-paretic side . Similar to the A2 burst, H3 burst is reported to be considerably reduced on the paretic side . Therefore, the amplitude of these kinetic variables seems to be positively scaled to the gait speed or functional capacity of persons with stroke [158, 159, 162, 163]. Inter-compensations between hip and ankle powers: Slow walkers especially present with a marked reduction in pre-swing ankle pus h-off (A2) and early swing hip pull-off (H3)  on both paretic and non-paretic sides. Contra rily, persons walking at faster walking speeds or higher functional capacities show less reduction in these power bursts and even present with larger positive work by bilateral hip extensors in early stance (H1) and by early swing paretic hip flexors (H3) [158, 159]. The greater magnitude of hip bursts (H1 and H3) can assist in propulsion, compensating for the reduction in ankl e push-off (A2) in persons with stroke who walk fast [158, 159]. Similarly, larger K3 burst is reported in the fast walkers [158, 159]. Thus, several kinetic asymmetries are acc entuated between limbs in the fast walkers, suggesting that locomotor capacity is not necessarily recovered through normalization of kinetic profiles but may be directly related to compensatory mechanisms . In the literature, this result is usually interpreted to mean that symmetry should not be a primary focus for rehabilitation [5, 18, 53].
40 However, investigation and diffe rentiation of impairment from compensation is essential to retrain function maximally. Identification of impairment, on the other hand, will assist in normalization of some of the underlying kinetics (e.g., improving the paretic ankle plantarflexor force generation to improve paretic ankle power burst). Angular velocity of knee in pre-swing determines knee flexion during swing: With regards to angular velocity, dynami c simulations of swing phase in healthy gait performed in the absence of muscle joint torques approximated normal knee kinematics by selecting the initial angular velocities and positions alone [140, 164]. This suggests that the initia l angular velocity is an important determinant of normal knee kine matics during swing. Further, Piazza and Delp (1996) found that the amount of knee flexion ac hieved during swing is decreased by either increasing hip flexion velocity or decreasing kn ee flexion velocity at pre-swing . In hemiparetic gait, Chen et al. (2005) showed that persons with stroke showed impaired paretic swing initiation that they char acterized as inadequate paretic limb propulsion in pre-swing, reduced paretic knee flexion at toe-off and mid-swing . Interjoint coordination during swing phase She mmell and associates (2007) recently showed that dynamic torques generated across hip, knee and ankle are tightly coupled during swing phase of normal gait and that a single kinetic time series can describe the pattern of torque production at each joint during this phase . They proposed that such a flexible inter-joint coupling might serve to simplify the control of the swing phase by the CNS. Inter-joint coordination during swi ng is also revealed indirectly through studies, which report that an increase in hip flexor mome nt during swing also increases knee flexion . Some inter-joint coordination is also expected given that bi-articular muscles that span two joints are physiolo gically capable of affecting segm ents further distally. Further,
41 the complex inter-segmental dynamics of the body can also explain the in ter-joint coordination of kinetics in the swing phase [167, 168]. Muscle Activity during Pre-Swing and Swing Phase Pre-sw ing and swing phase muscle activity in healthy gait: Although low, muscle activity is consistently reported in swing phase of healthy gait. In general, hip flexors have shown to dominate swing phase [169-171]. Specifica lly, Nene et al. (1999) and Neptune et al. (2001) show that rectus femoris (RF) is respon sible for swing initiation [139, 148]. Furthermore, medial gastrocnemius (MG) is also suggested to aid in swing initiation . On the other hand, Gotschall and Kram (2005) based on their novel methodology of application of external forces during treadmill walking, showed that while both iliopsoas (IP) and RF initiate and propagate swing, ankle extensors do not di rectly contribute to swing init iation . Further, indirect evidence of specific contributions of muscular acti vity in swing phase is revealed in the study by Goldberg et al. (2003) where they evaluate musc les that influence knee flexion velocity in the pre-swing phase (knee flexion ve locity directly influences knee kinematics during swing) . Goldberg et al. (2003) in their study conclude that while MG and IP directly contribute to swing by increasing the knee flexion velocity in pre-swing, vastii, RF and soleus decrease knee flexion velocity thereby reducing knee flexion in swing . Further, Winter DA (1992) suggested that Tibialis anterior (ankle dorsiflexor) were specifically re quired during mid-swing for limb clearance, whereas biarticular hamstrings (long h ead of biceps femoris) decelerates the limb in terminal swing to prepare it for weight acceptance . Pre-swing and swing phase muscle activity in hemiparetic gait: There are much fewer reports on muscle activity in pre-swing and swing phase of hemiparetic gait. In general, large interindividual variability is observed in the EM G patterns that characterize muscle activity in individual patients. Den Otter et al. (2007) reports that paretic TA activity significantly increases
42 in the swing phase of persons with stroke comp ared to healthy persons . Further, since EMG activity can be observed as premature activation, abnormal coactivation or as compensatory or adaptive coactivation, it is diffi cult to suggest whether observed muscle activity is a sign of impaired motor control or adap tive behavior to prom ote functional walking. Nevertheless, association of EM G activity to walking performan ce might provide insights into the role of observed activity. Relevance of Reviewed Literature to Study Four Overall, the above literature review suggests that several studies ha ve reported kinem atic, kinetic characteristics and muscle activity durin g pre-swing and swing of hemiparetic gait. Nevertheless, a holistic picture of control strategies in hemipa retic pre-swing and swing phase are lacking, primarily because pre-swing and sw ing phase dynamics have not been correlated with walking performance after hemiparesis. It is likely that events during the pre-swing and swing phase determine where the foot is placed in the step. Thus, patterns observed in these phases during hemiparetic gait might explain th e underlying reasons for the variability in stepping asymmetry. Therefore, in study four of this disserta tion specific pre-swing and swing phase variables were used to e xplain step length variability. Speci fically, selected kinematic and kinetic variables corresponding to initial conditions of the leg, swing phase and contralateral stance phase (occurring at the same instance as swing phase) explained step length generation during hemiparetic gait.
43 Figure 2-1. A simplified model demons trating neural control of gait The central pattern generators in the spinal cord generates the locomotor rhythm that is modified by afferent information from the higher cente rs and the periphery. Abbreviations: CST Corticospinal Tract.
44 Figure 2-2.Division of a gait cycle into phases The gait cycle is divided into stance (0 60 %) and swing (60-100%) phase. The stance phase can be further sub-divided into two double support phases (10% each) and a single support phase (40%). Source: http://www.vard.org/mono/gait/gaitcov.htm
45 Figure 2-3.Methodology for collection of spatiotemporal characteristics during walking using an instrumented mat (GAITRite) GAITRite is an electronic walkway with sensors embedded within it that record the spatial and temporal characteristics of steps as a person walks over it. A sample walk that was recorded by GAITRite is presented in this Figure. Note the parameters generated by the software.
46 Figure 2-4. Illustration of ground re action forces exerted by the limbs and typical force curves This Figure illustrates the 3-D forces applied to the ground from the legs (Fx, Fy, Fz) and the measured Ground reaction forces (Rx, Ry, Rz). Th e plots on the bottom demonstrate these GRF curves from the right (red) and left (blue) legs normalized to the body weight of the person for the three force components [Vertic al GRF (Rz), AP Anterior-posterior GRF (Ry), MLMedialLateral GRF (Rx)].
47 Figure 2-5. Variability (i n stride time) during walking and its relation to risk for falls Source: Hausdorff, J. M. (2005), Gait va riability: methods, modeling and meaning. J Neuroengineering Rehabil, 2 19
48 Figure 2-6. Power profiles in swi ng phase of a healthy gait cycle The swing phase begins at appr oximately 60% of the gait cycl e. The arrows show the power bursts in hip (H3), knee (K3) and ankle (A2) during swing phase of healthy gait. Red is right leg and blue is left leg.
49 CHAPTER 3 RELATIONSHIP BETWEEN STEP LENGTH ASYMMETRY AND WALKING PERFORM ANCE IN SUBJECTS WITH CHRONIC HEMIPARESIS Introduction The asymmetrical nature of he miparetic walk ing is well documented in persons who have sustained a stroke, [12, 13, 175] with the asymmetr ies in spatiotemporal, kinematic and kinetic parameters of walking related to disturbances in motor coordination . Specifically, asymmetry in spatiotemporal parameters have been common ly used in the clinic to examine the walking patterns in patients who have experienced a stroke . Previous studies [13, 176] have reported that temporal (swing time) asymmetry is a si gnificant predictor of hemiparetic walking performance since it strongly correl ates with stages of motor r ecovery, walking speed and falls. However, the relationship between spatial (ste p length) asymmetry and hemiparetic walking performance is unclear. It has earlier been reported that, after a str oke, patients may walk with either relatively longer paretic steps or longer non-paretic steps [19, 65, 71]. Therefore, consiste nt patterns of step length asymmetry have not been observed. Moreove r, the reasons for the variability in step length asymmetry patterns and the relation of the variable patterns with walking performance have not yet been explained. For instance, in the study by Kim et al. (2003), considerable variability in step length asymmetry was observe d in a sample of 28 chronic stroke survivors . While 14 of these subjects walked with longer paretic steps than non-paretic, 14 others walked with relatively longer non-paretic steps. Consequentl y, they hypothesized that the variability in the patterns of step length asymme try may be due to compensatory strategies that increase or decrease the step le ngth of either the paretic or non -paretic leg. However, they were unable to advance the discussion since they f ound a non-significant rela tionship between step length symmetry and symmetry in vertical ground r eaction forces. Further, other studies indicate
50 that; on an average, individuals w ho have sustained a stroke walk with relatively longer paretic steps [65, 71]. Therefore, neither consistent pa tterns of step length asymmetry have been observed nor have the asymmetri cal patterns been characterize d. Further, the relationship between step length asymmetry and walking sp eed is not well documented in the current literature. This may be another reason for insufficient understanding of the affect of step length asymmetry on hemiparetic walking performance. Fo r instance, shorter stride lengths (bilaterally) have been related to slower walking speed and thereby poor walking performance , and yet a non-significant relationship has been suggested between step length asymmetry and walking speed . Overall, curr ent evidence suggests that persons afte r a stroke may walk with different patterns of step length asymmetry that may be unrelated to the attained walking speed. However, it is not clear how the different asymmetrical patterns relate to post-stroke hemiparetic walking performance and why asymmetry in step lengths may not necessarily limit the attained walking speed. We propose that correlating the asymmetry obs erved in step lengths with propulsive ground reaction forces (GRFs) during walking ca n provide a basis to evaluate different asymmetrical patterns and their effect on hemi paretic walking performance. Propulsive GRFs represent the net forces generated by the legs to accelerate (propel) the bodys center-of-mass forward. The propulsive GRFs quantify forward pr opulsion during walking, which is an essential requirement of locomotion along with body support . In our recent work, we have shown that the paretic leg propulsive GRFs can provide a quan titative measure of the coordinated output of the paretic leg during hemiparetic walking . Specifically, we found that the percentage of propulsive forces generated by the paretic leg (Propulsion Paretic) can quantify the contribution of the paretic leg to the coordina ted task of forward propulsion during walking. In our present
51 study, we hypothesized that the Propulsion Paretic would correlate with asymmetry observed in step lengths since generation of a step requires forces exerted by the legs to propel the bodys center-of-mass. Further, we suggest that correlating the asymmetry observed in step lengths with propulsive GRFs during walking can help understand the relations hip between spatial asymmetry and walking performance after a stroke. Therefore, the primary purpose of our study was to explore the correlation between step length asymmetry and propulsive forces in an attempt to quantify the affect of spatial asymmetry on post-stroke hemiparetic walking performance. Further, we investigat ed how asymmetrical step lengths may be related to hemiparetic se verity (as rated by Brunns trom staging), walking speed, vertical GRFs and other spatiotemporal walking parameters (walking speed, swing time, pre-swing time and ability to change speed) to gain a holistic understanding of the relationship between asymmetrical step lengths a nd hemiparetic walking performance. Methods Participants We recruited 49 subjects with chronic hem iparesis [42 men, 7 women; ages = 62.7 10.2 (SD) years; time since stroke = 4.25 3.67 (SD) years; affected side left = 25, right = 24] were recruited at the Palo Alto Depart ment of Veterans Affairs Medical Center. The data presented in this study were collected as part of a larger study that investigated the links between gait characteristics and bone density in chronic stroke survivors . Inclusion criteria were: at least 6-12 months post stroke, uni lateral weakness, and the ability to walk 10 meters in 50 seconds or less without manual assi stance. Subjects were allowed to use their assistive devices (AFO and/or Cane) during the te sting. Subjects were excluded fr om the study if they had any orthopedic or neurological conditio ns in addition to the stroke, had more than one CVA incident
52 and were unable to provide informed consent. Br unnstrom motor recovery stages were used to determine the severity of hemiparesis for the s ubjects . Subjects varied in their ability to perform voluntary movements within and outside of flexor and extensor synergy patterns (as assessed clinically by Brunnstrom staging). Base d on their Brunnstrom stage, three groups of subjects with differing hemiparetic severity were identified. Subjects in the Severe hemiparesis group (Brunnstrom stage 3, n=19) were limited to movements within the synergy patterns (e.g., only basic limb flexion or extension synergies can be performed voluntar ily). Subjects in the Moderate hemiparesis group (Brunnstrom stag es 4-5, n=20) were able to produce some movement combinations outside of the synergy patterns. Subjects in th e Mild hemiparesis group (Brunnstrom stage 6, n=10) were able to produce both isolated joint movements and movements in synergy patterns. All participants in the study si gned a written informed consent and the Stanford Administrative Panel on Huma n Subjects in Medical Research approved the protocol. Procedures The subjects walked separately over the GAI TRite and force platform s at their selfselected and fastest safe speeds to collect the spatiotemporal parameters and GRFs, respectively. GAITRite (CIR Systems, Inc) is a portable in strumented electronic walkway 4.3 meter long and is a valid and reliable system for measuring spatiotemporal pa rameters . Force platforms (Advanced Medical Technology, Inc) embedded acr oss a 10 m walkway were used to collect three-dimensional GRFs during the gait cycle. Be fore testing, clear expl anations were provided to the subjects regarding the importance of walk ing in their natural manne r during the testing and avoidance of targeting the force plates. Du ring GAITRite data collection, the GAITRite was placed over the force plates. However, the force pl ate data was not collected while subjects were walking on the GAITRite. Subjects started walki ng 5-6 steps before the GAITRite and stopped
53 5-6 steps after passing the GAITR ite to get constant speed data over the mat and avoid the effects of acceleration and deceleration. Subjects walked a total distance of 10 meters over the GAITRite. Three good walking trials, each at self-sel ected and fastest safe speeds, were collected over the GAITRite. Some subjects were asked to wa lk 1 or 2 more trials due to problems like tripping during walking. The number of trials collect ed for the force plate da ta were variable and depended on whether both or at l east one leg were determined by visual inspection to have had adequate contact on the force pl atforms. GRF data were acquire d at 200 Hz and the horizontal and vertical forces (normalized to the indi viduals body weight) were used for analyses. A therapist provided close supervision during the walk ing trials. Subjects were allowed to take rests between trials if they needed to. Walki ng speed was calculated by the GAITRite and no estimates of speed were used from the force plate trials. Data Analyses GAITRite data: W e analyzed all the collected trials (3 for each speed). The data from individual trials were averaged together to determine the spatiotemporal variables for each participant. Spatiotemporal vari ables included in this study were self-selected and fastest walking speed, step lengths, swing times and pre-swing ti mes (time spent in double support phase of gait cycle). Paretic and Non-paretic step length, swin g time and pre-swing time data were averaged only from the trials of self-selected walking sp eed. Subjects self-selected walking speed were categorized as: speed < 0.4 m/s (household ambul atory); 0.4 0.8 m/s (limited community); and speed > 0.8 m/s (community ambulatory) . St ep length asymmetry was quantified using a step length ratio (SLR), which was defined as the Paretic step length  divided by the Nonparetic step length . The fastest safe walkin g speed data were utilized to calculate the percentage change (from self-selected to fastes t safe speeds) in walking speed, cadence, paretic step lengths, and non-pare tic step lengths.
54 Force plate data: We collected a minimum of 4 tria ls and a maximum of 15 trials to assure adequate contact on the force platforms to determine the ground reaction force patterns for each participant. The GRF values that were analyzed for individual partic ipants were variable and depended on the number of trials with good f oot contacts on the force platforms. Good foot contacts were determined if both legs made c ontact with the force platforms in entirety. When possible, multiple good foot contacts were averag ed to generate ground re action force values, but in one participant, only one trial could be analyzed. Raw anterior posterior a nd vertical GRF data were normalized to body weight and processed using a custom Matlab program. Note th at anteriorly directed forces are propulsive (positive) and posteriorly direct ed forces are braking (negative) (Figure 3-1). The impulse for each leg was calculated as the time integral of the GRF (the area under the GRF curve) : Ixl = GRFxdt (Equation 1) where I = Impulse, force component x= v (vertical), p(propulsive) or b (braking) and leg l = p (paretic) or n (non-paretic). Paretic propulsion (Pp) was then calculated from the propulsive impulse: PP (%) = Ipp / (Ipp + Ipn) 100 Statistical Analyses A paired sa mple t-test was used to test wh ether the differences be tween the paretic and non-paretic step length were sta tistically significant. Relationships between the step length asymmetry (SLR), GRFs and walking speed we re characterized using Pearsons correlation coefficient (r) and that between SLR and he miparetic severity using the non-parametric Spearmans correlation coefficient ( ). For other walking variab les included in the study, descriptive analyses were conducted to understa nd their relationship with the asymmetrical patterns. All statistical analyses were performed with SPSS 12.0 software.
55 Results The walking variables were collected at the self-selected walking speeds for all subjects and at the fastest safe speeds for 46 subjects. Da ta were not collected for 3 subjects at their fastest speeds due to safety conc erns. Nineteen of the 49 subjects used a mobility aid [i.e., a cane or an ankle foot orthosis or both] to ambulate. Paired sample t-tests revealed that the paretic step lengths were significantly different from the non-pa retic step lengths (p = .0001). Therefore, step length asymmetry was characterized and three patte rns of step length asymmetry were identified. The symmetrical group were defined as subjec ts with SLR between 0.9 to 1.1 [SLR = 1 0.1 (10%) SD]. Asymmetrical groups were those with SLR > 1.1 (longer paretic steps than nonparetic) and SLR < 0.9 (longer non-pa retic steps than paretic). Relationship between Step Length Asymmetry (SLR) and GRFs Correlation analys is revealed a strong negative correlation between SLR and Pp with Pp explaining 62 % (r = 0.785, p < 0.001) of variance in step length asymmetry (Table 3-1). Subjects that demonstrated impaired paretic leg propulsion (Pp) and in creased non-paretic leg propulsion walked asymmetrically with longer paretic steps th an non-paretic [Figure 3-2, top tracing]. In contrast, subjects generating symmetrical GRFs with the two legs walked nearly symmetrically [Figure 3-2, middle tracing]. Subj ects generating rela tively proportionate or greater Pp walked asymmetrically with longer non-paretic steps than paretic. However, the greater Pp generated by these subjects walking with longer non-paretic steps was lesser in magnitude compared to those walking symmetric ally. Refer to Figure 3-2 and compare the Pp between GRF curves of the bottom and middle tracing. Asymmetrical group with longer paretic step lengths than non-paretic (n = 16): Subjects that generated the leas t paretic propulsion (Pp < 20%) walked with relatively longer
56 paretic step lengths. Five of these 16 subjects generated 5% or less Pp and walked with the longest paretic steps relativ e to the non-pare tic leg (SLR > 1.5) (Figure 3-3). Asymmetrical group with longer non-paretic step lengths than paretic (n = 4): There were only 4 subjects who were classified as asymmetric and walked with relatively longer nonparetic step lengths. Three of these four subjects generated substantial prop ulsive forces with the paretic leg (Pp > 55%; however one s ubject generated only 25% Pp). Symmetrical group (n = 23): Twenty-three subjects walked symmetrically. Seventeen of these 23 subjects generated almost symmetrical propulsive forces (Pp = 35 57 %) and the rest generated lesser paretic leg propulsion (Pp = 15 30%). Only 10 of 49 subjects in th e study population generated a ne t braking impulse in the preswing (normally propulsive) phase of the gait cy cle and these 10 subjects walked at SLR > 1.1, with 5/10 subjects walking at SLR > 1.5. Nine of these 10 subjects used a mobility aid for ambulation and only one subject walked independe ntly. We separately analyzed the data for subjects who used a mobility aid from those w ho did not to investigate whether the relationship between step length asymmetry and paretic leg propulsion changed by using a mobility aid. Subjects walking with a mobility aid generated less Pp in comparison to those who walked without one. However, the relationship between SL R and Pp was not different for those who did or did not use a mobility aid. With respect to the vertical GRF, all subject s (irrespective of their step length asymmetry pattern) supported a greater percentage of body we ight on the non-paretic le g than the paretic leg during the two double support phases in the gait cy cle. However, moderate correlations (r = 0.447, p < .001) were found only between SLR and pe rcentage of body wei ght supported on the paretic leg during the pre-swing phase of the paretic leg (Table 3-1).
57 Relationship between Asymmetrical Step Le ngths, Hemiparetic Severity and Walking Speed While SLR correlated weakly with walking speed (r = -0.351, p < .05), a stronger correlation existed between SLR and hem iparetic severity ( = -.526, p < .001) (Table 3-1). Eleven out of the 19 subjects with severe hemi paresis walked asymmetrically with relatively longer paretic steps than non-pare tic and yet walked at differing walking speeds (Figure 3-4). Note that 4 subjects with severe hemiparesis that walked asy mmetrically with longer paretic steps generated much less paretic leg propulsion (Pp < 25%) and yet walked at speeds greater than 0.8 m/s (community ambulatory) , (Figure 3-4). In contrast, the 3 subjects (Figure 3-4) with mild hemiparesis (Stage 6) who walked symmetrically or asymmetrically (with longer nonparetic steps) generated much greater paretic leg propulsion (Pp 45%) and yet walked at slower speeds between 0.4 0.8 m/s (limited community ambulatory) . Relationship between Step Length Asymmetry, Time Spent in Pre-Swing and Swing Time Only 8 of 49 subjects spent greater than 20% of cycle tim e during the paretic pre-swing phase (compared to 10-20% cycle time in their non-paretic pre-swing). These 8 subjects walked asymmetrically with longer paretic steps than non-paretic. With respect to swing time, only 2 of 49 subjects spent greater time sw inging their paretic than the nonparetic leg. Subjects walking at SLR > 1.1, on an average, spent the gr eatest time swingi ng their paretic leg. Relationship between SLR, Change in Gait Speed and Parameters That Contribute to Change in Speed Absolute m ean differences were evalua ted for these analyses. Subjects walking symmetrically increased paretic and non-paretic step lengths and cadence at faster walking speeds. In contrast, those walking asymmetrically at SLR > 1.1 had little increase in their paretic step length at the faster walking speeds even th ough they increased their cadence as much as the symmetrical group (Figure 3-5).
58 Discussion Relationship between Step Length Asymmetr y and Propulsive Forces during Hemiparetic Walking Step length asymm etry during wa lking is related to propulsive forces generated by persons with hemiparesis. Our data revealed that subject s generating relatively le sser propulsive forces with the paretic leg walked as ymmetrically with longer pareti c steps than non-paretic (SLR > 1.1) On the other hand, subjects walking symm etrically (0.9 < SLR < 1.1) generated near symmetrical propulsive forces with the two legs. In Figure 3-2 comparison of PP between subjects with SLR > 1.1, 0.9 < SLR < 1.1 and SLR < 0.9 indicates that there may be distinct differences in paretic leg propul sion between subjects with diffe rent patterns of step length asymmetry. To our knowledge, there is little direct evid ence for the mechanisms that control step length in normal and hemiparetic walking. However, indirect evidence for the control of step length during walking is provided by a few studi es. Varraine et al. (2000) suggests two potential controlling mechanisms for intentio nally lengthening a stride in he althy individual s: control of trunk progression and control of le g trajectory . In their study, subjects were able to lengthen their stride by generati ng greater propulsive forces. The increased propulsive forces enabled the trunk to progress further forward a nd thereby, generate a l onger step. Additionally, subjects took a longer step by holding the leg long er in the swing phase. Fu rther, recent studies have highlighted the causa l relationships between muscle activity in pre-swing and the resulting swing leg trajectory [148, 183, 184]. These studies indicate that kine matics of the leg in its preswing phase affect trajectory of the leg in its swing phase and thereby, magnitude of the step length. This implies that the le g producing greater forward propul sion in pre-swing might take the longer step length. However, the results from our study suggest the op posite. We showed that
59 persons generating impaired paretic leg propulsion walked with a relatively longer paretic step. These persons generating impaired paretic leg propulsion also generate d relatively greater nonparetic propulsion, likely to compensate for th e lesser paretic leg propu lsion. For example, in Figure 3-2, compare the relative contributions of non-paretic propulsion in the top and middle GRF tracings. These results suggest that a high SL R (i.e., paretic step le ngth > non-paretic step length) is in large part the re sult of the relatively greater non-paretic leg propulsion. For instance, greater forward propulsion by the non-paretic leg in its stance phase will cause the trunk, including the pelvis to move forward. This fo rward motion of the pelvis will increase with increased propulsion and can cause the swinging paretic leg to move forward relative to the ground even if it moves little rela tive to the pelvis. Therefore, greater non-paretic leg propulsion is one mechanism for the longer paretic steps (high SLR). Further, pers ons with high SLR also spent a longer time swinging thei r paretic leg than others who walked with symmetrical steps. Therefore, one might hypothesize either/both gr eater non-paretic leg propulsion or a longer paretic swing phase as potential candidates to explain the mechanisms underlying a relatively longer paretic step length. The strong relationship between the patterns of step length asymmetry and propulsive force asymmetry might suggest a mechanical relation between step length and propulsive force. For example, if the leg were to be an invert ed pendulum, the generation of horizontal forces would be directly related to the position of the foot relative to the bodys center-of-mass. Specifically, foot placement anterior to the cente r-of-mass (as during heel strike) would induce a braking force and foot placement posterior to the center-of-mass (as in pre-swing phase) would induce a propulsive force. In this sense, an asymmetry in the placement of the feet may induce asymmetrical propulsive forces when the foot is placed more anterior to the center-of-mass than
60 posterior. However, the inability to place th e foot further behind the center-of-mass than forwards (as with longer paretic steps than non-pa retic) suggests specific impairments underlying the asymmetrical step lengths. For example, the inability to achieve adeq uate hip extension may limit the propulsive forces exerte d during the terminal stance. Furthermore, during the terminal stance of the paretic stride the paretic foot is likely posterior to the body s center-of-mass and yet there is no propulsive force genera ted (see Figure 3-2, top tracing). Therefore, it is more likely that there may be an active reduction in pr opulsive force generation. The active reduction in propulsive force generated in the pre-swing may, in turn, suggest impaired uniarticular ankle plantarflexor activity . On the contrary, in the participants walking with relatively shorter paretic steps (SLR < 0.9), the greater paretic propulsive force generati on suggests that plantar flexors may be providing reas onable propulsion. Ste pping, however, depends not only on the ability of the plantarflexors to propel the body forward but also on the ability of the hip flexors to generate power to the swinging leg . Ther efore, having shorter paretic steps relative to non-paretic steps may indicate an inability to ad vance the paretic leg due to impaired swing initiation by the hip flexors. In addition to di rect mechanical effect s of foot placement on propulsive force generation, it is likely that the mechanisms underlying asymmetrical steps reflect distinct muscular impairments that de termine the observed patterns of step length asymmetry during hemiparetic walking. Future studi es targeted at inves tigating the underlying muscular impairments shall further determin e the underlying causes for high SLR. Yet, the strong relationship between SLR and propulsion can be utilized in the clinic as a tool to distinguish persons in their ab ility to generate propulsive forces. Beyond simply promoting symmetry, SLR can be utilized to develop indivi dual goals that train pr opulsive force production,
61 equalize bilateral biomechanical involvement by improving hip ex tension, or promote paretic step initiation. Relationship between Step Length Asymmetr y, Walking Speed and Hemiparetic Severity W e were also able to investigate the re lationship between walking speed, hemiparetic severity and asymmetry in step lengths. A weak relationship between step length asymmetry and walking speed was observed, indicating that asymme trical patterns need not necessarily limit the attained walking speed. However, hemiparetic se verity (as rated by Brunnstrom staging) seemed to predict step length asymmetry since the majority of subjects with severe hemiparesis walked asymmetrically at SLR > 1.1. Furthermore, differen ces in Pp between the persons with mild and severe hemiparesis were unrelated to the attain ed walking speed. For example, in Figure 3-4, four subjects with severe hemiparesis had impair ed Pp and yet they were walking at speeds > 0.8 m/s. In contrast, three subjects with mild hemiparesis generated greater Pp and yet walked at slower speeds between 0.4-0.8 m/s. The weak re lation between Pp and walking speed indicates that other compensatory mechanisms could help some persons to attain a relatively functional walking speed. Quantification of these compensatory mechanisms may be difficult when speed alone is the outcome measure since walking speed is the net outcome of the two legs. However, asymmetrical step lengths might indicate compensation in those persons walking with a high SLR and faster walking speeds compared to thos e walking with a high SLR and slower walking speeds. This is because subjects with relatively lo nger paretic steps would have lesser paretic leg propulsion, and if they continue to walk at faster speeds they mi ght accomplish these speeds via compensatory strategies. For example, one of the ways to attain a faster speed (i.e., acceleration of the bodys center-of-mass) would be to generate greater propulsive for ces with the non-paretic leg that serves to accelerate the center-of-mass fo rward. Other compensations can also arise from
62 the paretic leg itself or from the trunk (e.g., forwar d lean) to attain rela tively functional walking speeds despite decreased propulsive force with the paretic leg. Relationship between Step Length Asymmetry, Paretic Pre-Sw ing Time and Vertical GRFs Furthermore, we were able to determine th e relationship between step length asymmetry, other spatiotemporal parameters and vertical GRFs. The evidence that impaired paretic leg function prolongs the paretic pre-swing phase su pports our finding that persons walking at SLR > 1.1 supported less weight on the paretic leg duri ng the pre-swing phase. This finding thereby increases the need to develop compensatory st rategies to overcome these deficits . In particular, note that in our study we allowed partic ipants to walk naturally as they would in the community and 19 persons used some mobility aid for ambulation even during the testing. Although persons walking with a mobility aid generated less Pp in comparison to those who walked without one, the relati onship between SLR and PP did not change while analyzing only the data for those subjects who used an ai d or those who did not. This corroborated our hypothesis that a high SLR was related to specific problems in propelling the body forward with the paretic leg. However, the high SLR may neither necessarily limit the attained speed nor may substantially limit persons from changing their walking speeds. As revealed in Figure 3-5, compared to the symmetrical group persons with high SLR seemed to primarily increase their speed by increasing cadence with much less increase in the paretic step lengths. This indicates that persons walking with asymmetrical step leng ths may utilize different strategies to increase their walking speeds. Further, even though the subjects with SL R > 1.1 walked with relatively longer paretic steps than non-paretic at their self-selected walking speeds, they were unable to change the paretic step length as much as the non-paretic when changing their speed.
63 Conclusions We were able to provide som e insights into the relationship between asymmetrical step lengths and hemiparetic walking performance. Asym metry in step lengths strongly relates to the propulsive forces generated by the paretic leg. Greater non-paretic leg pr opulsion to offset the impaired paretic propulsion is likely one of the m echanisms for the high SLR (paretic step length > non-paretic step length). Despite mechanical relations between foot placement and force generation that are expected, we believe that there are additional muscular impairments underlying the asymmetrical patterns. However, further research is warranted to confirm this. Yet, the strong relationship betw een SLR and propulsion can be ut ilized in the clinic as a measure to evaluate the propulsive forces genera ted by the paretic leg. We were also able to provide a basis to evaluate the different asym metrical patterns by correlating the asymmetry observed in step lengths with propulsive GRFs during hemiparetic walking. Moreover, the relationship between SLR, speed and hemiparetic severity indicates that SLR, when used along with speed as an outcome measure, can help understand compensatory strategies that some persons (who are asymmetrical a nd yet walk at faster speeds) us e to offset the lesser propulsive force ability of the paretic leg. The relationship between SLR and other spatiotemporal walking parameters further reveals how asymmetrical st ep lengths may affect hemiparetic walking. In summary, we propose that SLR is a promising tool that rehabilitation th erapists might use to further the understanding of hemiparetic walking performance. Clinically, this would enable the identification of walking impairments in hemipare tic individuals and tailor locomotor retraining specifically to address the root causes of impaired ambulation for each individual.
64 Table 3-1. Correlation between SLR and walking variables
65 Figure 3-1. Illustration of horizontal GRF impulses Positive values (shaded area) represent propuls ion. Negative values (unshaded area) represent braking. Paretic leg is the bold curve and non-paretic leg is the light curve. Ipp Propulsive impulse by the paretic leg is th e shaded area under the bold cu rve; Ipn -Propulsive impulse by the non-paretic leg is the shaded area under the light curve; Ibp Braking impulse by the paretic leg is the unshaded area under the bold curve; Ibn Braking impul se by the non-paretic leg is the unshaded area under the light curve.
66 Figure 3-2. Comparison of GRFs between the pare tic and non-paretic legs for subjects walking with differing SLR Abbreviations: PHS = paretic heel strike, NT O = non-paretic toe off, NHS = non-paretic heel strike, and PTO = paretic toe off. Positive va lues (shaded area) represent propulsion, and the positive area under the curve is the propulsive impulse. Subject walking with SLR = 1.47 (i.e, SLR > 1.1) generates decreased paretic leg propulsion (PP). In contrast, the subject walking at SLR = 0.98 (i.e., 0.9 < SLR < 1.1) generates symme trical propulsive impulse and the subject walking with SLR = 0.68 (i.e., SLR < 0.9) genera tes relatively greater pa retic leg propulsion, PP (although low in magnitude). SLR = 1.47 Gait Speed = 0.71 m/s Severe hemiparesis SLR = 0.98 Gait Speed = 0.75 m/s Mild hemiparesis SLR = 0.68 Gait Speed = 0.52 m/s Mild hemiparesis
67 Figure 3-3. Relationship between step length ratio and Propulsion Paretic Abbreviations: Propulsion Paretic = paretic leg propulsion (in %), P = Paretic leg, NP = Nonparetic leg. Solid vertical line indi cates symmetric steps (SLR = 1), vertical dashed lines indicate the SLR subdivisions at SLR = 0.9 and SLR = 1. 1. Solid horizontal line indicates symmetric propulsive force generation by the paretic leg (PP = 50%), horizontal dashed lines indicate differing levels of paretic leg propulsion (10%, 30% and 70 % PP).
68 Figure 3-4. Relationship between step length asymmetry, walking speed and hemiparetic severity Abbreviations: P = Paretic leg, NP = Non-paretic leg. Solid vert ical line indicates symmetric steps (SLR = 1), vertical dashed lines indicate the SLR subdivi sions at SLR = 0.9 and SLR = 1.1. Horizontal dashed lines indicate sub-divisions of walking speeds (< 0.4 m/s household walkers, 0.4 0.8 m/s limited community walkers, > 0.8 m/s community walkers). Note that subjects with different SLR walk at all levels of walk ing speeds, yet majority of those with severe hemiparesis walk asymmetrically at SLR > 1.1.
69 Figure 3-5. Change in speed, cadence and individual step lengths in subjects walking at different SLR [SLR > 1.1 (n = 21), 0.9 < SLR < 1.1 (n = 21), SLR < 0.9 (n = 4)] Abbreviations: P = Paretic, N = Non-Paretic. Subjects walking with SLR > 1.1 increase their speed by primarily increasing their cadence, with little increase in the paretic step length.
70 CHAPTER 4 VARIABILITY IN SPATIOTEMPORAL ST EP CHARACTERISTICS AND ITS RELATIONSHIP TO WALKING PERFORMANCE POST-STROKE Introduction Gait variability, defined as fluctu a tions in gait characteristics from one step to the next, is reportedly low during walking . However, in creased or decreased va riability is commonly reported in populations with gait abnormalities li ke elderly fallers [103, 104], older frail adults  and persons with neuro-degenerative diseases (e.g, Parkins ons disease) [106, 107], suggesting that gait variability strongly asso ciates with gait impairments. Increased gait variability has been related to risk for falls, impl ying that excess variability in steps might relate to balance impairments . Similarly, central nervous system impairments (like cognitive functioning and motor performance) have been rela ted to increased stance time variability , while decreased step width variability has been related to sensory impairments and balance deficits during walking [104, 110, 111]. Gait variabil ity is also suggested to predict mobility disability . Therefore, curr ent evidence suggests that gait va riability is rela ted to walking impairments and can be used as quantifiable biomechanical markers to evaluate impaired performance. In persons with post-stroke hemiparesis, ne uromuscular and sensorimotor impairments can influence the generation of a smooth coordinated walking pattern resulting in gait and balance deficits that impair walking performance. Walking performance post-stroke is commonly characterized using average gait characteristics . However, measures of gait variability may provide a sensitive assessment of the motor control system performance reflective of additional aspects of impaired performance. Nonetheless, gait variability has not been evaluated as measures of walking performance in the post-stroke hemiparetic populati on. Specifically, it is unknown whether variability in paretic steps di ffers from non-paretic steps, whether the
71 variability in steps might relate to severity of hemiparesis, and how gait variab ility might be associated with measures of impaired hemiparetic performance suggesting that a systematic characterization of gait variability is warranted in this population. Therefore, the purpose of this study was 1) to evaluate whether gait variability differs in persons with post-stroke hemiparesis by compari ng their variability patterns with a similarlyaged healthy population and 2) to determine if measures of gait variability may be indicative of impaired walking performance by investigating the association between gait variability and clinical assessments that evaluate im paired hemiparetic performance. Methods Participants Ninety-four participants (A ge = 61.4 11.4 years, 69 m en, 51 left-side hemiparesis, Walking speed = 0.63 0.32 m/s) with chronic he miparesis and twenty-two similarly aged healthy subjects (Age = 66.2 10.0 years, 6 men, Walking speed = 1.29 0.21 m/s) participated in this study (refer to Table 1 for participants demographics). Seventy participants with hemiparesis and the healthy cont rol subjects were part of an ongoing study at the VA-UF Human Motor Performance Laboratory, Gainesville, FL. Tw enty-four participants with hemiparesis had participated in a larger gait study at the Palo A lto Medical Center and un reported data from these participants were retrospectivel y used for analyses. All particip ants signed a written informed consent. University of Florid a Institutional Review Board and Stanford Administrative Panel on Human Subjects in Medical Rese arch approved the protocols. Participants were at least 6 months post-stroke, had unilatera l weakness, could walk 10 m in 50 seconds or less without assistance from another person and had no severe perceptual, cognitive or cardiovascular impairments contrain dicative to walking. Subjects were excluded if they had other neurological conditions in addition to stroke, had more than one cerebrovascular
72 accident, or were unable to provide informed consent. Healthy participants (serving as similarlyaged controls) were excluded if they had orthope dic or neurological disorders that influenced their walking pattern. Procedures All par ticipants walked at their self-selected speeds over an instrumented walkway (GAITRite) to record spatiotemporal step charac teristics. GAITRite is valid and reliable for measuring spatiotemporal characteristics . All aspects of data collec tion at the two facilities were similar. Participants began walking 2m in front of the GAITRite, continued walking 2m after the mat (overall distance ~ 10m) to get consta nt speed data, and used their assistive devices (if any) during walking. All par ticipants completed at least tw o walking trials (average = 3.4, range = 2 5 trials). Number of trials vari ed across some participants because a) many participants with hemiparesis were unable to wa lk more than 2 trials due to fatigue and low functional performance, and b) some participants walking fast completed more number of trials (4 5 trials) so that the eff ective number of steps were increas ed for comparative analyses. Hemiparetic performance was evaluated using step length asymmetry index and clinical assessments. The asymmetry in step lengths durin g hemiparetic walking was evaluated using an asymmetry index called the Paretic step ratio (PSR ), which is calculated as Paretic step length/ (Paretic + Non-paretic step lengt h) and expressed as a percentage. Asymmetry in the hemiparetic participants was characterized based on symmetr y ranges calculated from the similarly-aged healthy participants in this study and the asym metric groups were defined as follows: Longer paretic steps than non-paretic (PSR > 0.525), Shor ter paretic steps than non-paretic (PSR < 0.475) and Symmetric step lengths (0.475 PSR 0.525).
73 Clinical assessments in sub-sets of the popul ation were available for analyses. Eighty-one study participants underwent Lower-extremity F ugl-Meyer (LE-FM) evaluations, which is a valid  and reliable  s cale to evaluate hemiparetic se verity. Only synergy items (22point) of LE-FM were utilized to grade hemipare tic severity similar to earlier st udies . Severity of hemiparesis was graded as: severe (0 14: perform only within-synergy movements), moderate (15 18: perform movements combin ing synergy) and mild (19 22: perform movements out of synergy). Dynamic gait index (DGI) evaluated dynamic balance in thirty-two study participants. DGI rates performance of 8 wa lking-related tasks on an ordinal scale (0-3) (e.g., the ability to change speed and direc tion while walking, obstacle negotiation during walking, etc.). DGI is valid and reliable to ev aluate dynamic balance in ambulatory persons with chronic stroke . Performance on DGI was graded as: DGI score 19 (poor balance performance), DGI score > 19 (good balance perfor mance) . Only subsets were available for LE-FM and DGI assessments since a) only partic ipants in the Gainesville facility underwent DGI assessments and b) since participants in th e Gainesville study were part of a larger gait study, some participants were unable to complete these clinical assessments due to insufficient time. Data Analyses All collected footfalls from all trials were analyzed. This methodology to evaluate gait variability in clinically imp aired populations is similar to earlier works [104, 110, 189-191]. Average number of footfalls collected and an alyzed per subject was 25 steps (range = 12 42 steps) for the hemiparetic population and 13 st eps (range = 9 20 steps) for the control population collected from all trials. Note that, for the same average number of trials, three hemiparetic participants took many more step s than other study participants (48, 50 and 65
74 steps). The results did not differ when these pa rticipants were removed from the analyses compared to when they were included in the analyses. Therefore, these participants data were included in the study. The number of steps collected and analyzed in this study is similar to that reported in earlier works [91, 92, 98, 104, 110, 111, 192] that have assessed step variability and the relationship of the spatiotem poral variability to falls risk, CNS impairments, gait speed and mobility disability [98, 104, 110, 193]. Swing time, pre-swing (double-suppo rt) time, stride time, step length and stride width were selected for analyses based on a) literature review th at suggests their importance in evaluating walking impairments post-stroke [70, 194], and b) evidence that the chosen variables have earlier revealed meaningful conclusions on walking impair ments in gait variability studies of clinically relevant populations [101, 189, 195]. Stance and step time were not calculated since the aim was also to select mutually independent variables for analyses. Refer to Table 4-1 for definitions of calculated variables. Both stance and step time s include variables that were independently calculated in the study [i.e., stance time is th e two-double support phases pl us single stance time (proportional to the contra lateral swing time) and step time is the swing time plus pre-swing time]. Variability was quantified using the standa rd deviation in spatiotemporal characteristics across steps. Statistical Analyses Kolom ogorov-Smirnov tests revealed departur es from normality for spatiotemporal characteristics in participants with hemiparesis. To allow for the use of parametric statistical processing, the data were log10 transformed to achieve normality. Dependent t-tests revealed that there was no difference in variability between right and left legs for health y participants in step length (p = .32), swing time (p = .51) and pre-sw ing time (p = .22) variability. Therefore, a oneway ANOVA tested differences in step length, swing and pre-swing time variability between
75 paretic, non-paretic and healthy (l eft) leg. Results did not differ wh en the right leg of the healthy participants were used in the an alyses. For stride time and stride width, independent t-tests were conducted to test differences between population groups (hemiparetic and healthy). Note that since stride time and stride widt h were calculated using both right and left steps, there was only one factor (population) and only paretic strides we re analyzed to avoid redundant steps in the analyses. To test differences in variability across se verity and PSR groups a 3 (group) x 2 (leg) Mixed ANOVA (repeated on leg factor) was conduc ted for step length, swing time, pre-swing time variability and a one-way ANOVA for stride tim e and width variability. To test differences across DGI groups a 2 (group) x 2 (leg), Mi xed ANOVA (repeated on the leg factor) was performed for step length, swing time, pre-swing time variability and an independent t-test for stride time and stride width variability. When significant effects were detected, post-hoc pairwise comparisons were performed using Bonferroni-adj usted t-tests. All statistical analyses were conducted in SPSS (version 13.0). Results Differences in Step Variability betw een Healthy and Hemiparetic Walking Variability in step length, swing, pre-swing a nd stride tim e was increased in participants with hemiparesis compared to he althy control subj ects, while stride width variability (p = .153) was not changed in hemiparetic walking (Figures 4-1 and 4-2). However, if only the slower walkers (speed < 0.4m/s) were compared to cont rols, then width variab ility was significantly reduced (p = .038). For between-leg comparisons, swing time variabil ity was greater in paretic steps than nonparetic and there was a trend fo r paretic pre-swing (PPS) time to show greate r variability
76 compared to non-paretic pre-swing (NPS) time (p = .065, Figure 4-1). There was no difference in the variability between paretic and nonparetic step lengths (Figure 4-2). Association between Step Variability, C linical Assessments and Asymmetry Index Differences in variability across the three g r oups (determined by the assessments) for each spatiotemporal characteristic are presented belo w. Additionally refer to Figure 4-3 and Figure 44 for presentation of differing patterns of spa tiotemporal variability within the severity, asymmetrical and DGI groups and Table 4-2 for the mean variability across-groups. Swing time variability Main effects (ME) of Group and Leg were significant across severity (p<.01), asymmetrical (p<.01) and DGI groups (p .02). Paretic steps showed greater variability than the non-paretic steps across all groups, with greatest betw een-leg differences in persons with severe and modera te hemiparesis, those taking L onger paretic steps and showing poor balance performance (DG1 19). Pre-swing time variability ME of both Group and Leg were significant across severity (p<.01) groups, ME of leg (p< .001) was significant across asymme trical groups and ME of group was significant across DGI. PPS show ed greater variability than N PS in the severe and moderate groups and across asymmetrical groups. Both PPS and NPS showed greater variability in persons showing poor balance performance compared to those showing good balance performance. Stride time variability differed across severity groups (p < .0001). Severe and moderate groups showed greater stride tim e variability than the mild group (p < .003), but did not differ from each other (p > .05, Table 4-2). Stride tim e variability differed across asymmetrical groups (p = .023) but post-hoc tests showed that asymme trical groups showed only a trend (of greater variability) to differ from the symmetrical group (p .109). Stride time variability (p = .007) was greater in persons showing poor balance performance (DGI 19), (Table 4-2, Figure 4-3).
77 Step length variability showed a trend to differ acro ss severity groups (p = .069) and asymmetrical groups (p = .094). However, ME of group and leg were significant for step length variability (group: p = .026, le g: p = .03) across DGI groups (p .03), with the non-paretic leg showing greater variabilit y than the paretic leg. Stride width variability showed a trend to differ across severity groups (p = .045) but did not differ across the asymmetri cal or DGI groups (p > .95). Discussion Differences in Step Variability between Healthy and Hemiparet ic Participants We found that, similar to other populations with gait deficits [111, 190, 196], variability in all spatiotemporal characteristics (except stride width) increased in pe rsons with post-stroke hemiparesis compared to healthy controls (Figur e 4-1, 4-2). While increased variability has been related to gait deficits in impaired populations [106, 111, 190, 196], our study is the first to report between-leg differences in step variabil ity. We found between-leg differences in swing and pre-swing time variability s uggesting a direct a ssociation between underlying paretic leg impairments and step variability. Paretic swing time variability was greater than the non-paretic leg and this difference in variability between -legs was greatest for persons showing most impaired performance (severe and moderate hemipa resis, asymmetrical steps and those at risk for falling as predicted by lower DGI scores) (Figure 4-3, 4-4). Increased step variability specifically in the paretic leg might relate to the neuromuscular impairme nts after a hemiparetic stroke, such as altered neural i nputs to the paretic spinal half-cen ters, altered effects of afferent feedback to the paretic leg and impaired inte r-limb coordination during walking. Furthermore, PPS variability showed a trend to be greater than NPS. Prolonged tim e in PPS has been related to impaired progression during hemiparetic walking . The increased variability in PPS relative to NPS suggests that the neurom otor deficits in this phase may limit hemiparetic walking
78 performance. Step length va riability did not differ between -legs but was greater during hemiparetic walking compared to h ealthy. It is likely that spatia l variables such as step length (that determine the base of suppor t during gait) are inhe rently more tightly coordinated betweenlegs than temporal variables su ch that step-to-step variation in one leg is counter-balanced by variation in the other leg to ma intain steady-state walking. Furthe rmore, stride time variability was also increased during hemiparetic walking compared to healthy. In creased stride time variability is reported to be st rongly related to falls risk [ 101, 103], suggesting that increased variability post-stroke might re late to poor dynamic balance. Relationship between Hemiparetic Step Variab ility and Impaired P erformance Post-Stroke To test the use of gait variability measures as markers of impaired performance, we wanted to investigate the relationship between step va riability and hemiparetic performance. This relationship also provided insi ghts on potential mechanisms underlying the variability patterns. For example, the ability to produce independent voluntary movements of the paretic leg is related to motor recovery of the paretic leg and is graded using the LE FM (higher score greater recovery). The inverse relation between hemiparetic severity and step variability suggests that variability might decrease as motor recove ry progresses. Similarl y, greater step length asymmetry (both Longer paretic and Shorter pare tic groups) has been related to motor control impairments . In support of this hypothesis, our results revealed th at both asymmetrical groups presented with greater swing time variabi lity compared to the symmetrical group but did not differ from each other. Moreover, the associ ation between step variability and hemiparetic performance is revealed in the relation between DGI scores and variab ility (Figure 4-3, 4-4). Since DGI has been used to evaluate dynamic ba lance  (lower score lower balance), the inverse relation between DGI scores and step variability suggests that persons showing greater step variability might have poor dynamic balance. Specifically, DGI scores less than equal to 19
79 are reported to identify persons at risk for falling  and participants wi th hemiparesis in our study with scores less than equal to 19 exhibited greater st ep variability. While the overall increased step variability was related to impaired performance (lower LE FM score, greater asymmetry and lower DGI sc ore), the pattern across the sub-groups was not consistent for all spatiotempor al parameters (e.g. between-leg differences in pre-swing time variability was observed across severity groups but not across DGI groups ). Since the stroke population is immensely heterogeneous, we expected the spatiotemporal step variability patterns would differ across sub-groups of participants sugge sting that specific sp atiotemporal measures are more strongly associated with particular as pects of hemiparetic performance. For instance, between-leg differences in swing time variab ility were significant ac ross all sub-groups of participants (severity, asymmetr y and DGI groups) suggesting that between-leg differences in swing time variability were most strongly related to impaired hemiparetic performance (as measured by severity, asymmetry and DGI). St ride time variability differed across all subgroups. In comparison, for step length variability there were no differences between-legs when considering the hemiparetic populati on as a group. However, in pers ons at risk for falling, paretic variability was increased relative to non-pare tic; suggesting that step length differences betweenlegs might be unmasked in the most impaired pers ons. Nonetheless, the relatively small sample size of the DGI subgroups could have pot entially influenced these results. While step variability in different spatiotem poral parameters varied across sub-groups of participants in combination, vari ability in the spatiotemporal parameters seemed to robustly predict impaired hemiparetic performance. For instance, a participant having markedly increased PPS variability (black-bold arrow in Figure 4-3), increased pareti c step length and reduced width variability (black-bold arrow in Figure 4-4) shows impaired he miparetic walking performance.
80 The inferences from other measures, however, were inconsistent (poor balance performance (DGI = 8), moderate hemiparetic severity, symm etric steps). Similarly, another participant had good balance performance (DGI = 22) but walked asymmetrically with much longer paretic steps, again indicating the contra sting inferences on performance as predicted by these measures. This person had markedly increased stride time variability and reduced width variability (red arrow in Figure 4-4). Overall, these examples exhi bit a marked increase of variability in one or other spatiotemporal characteristic and reduced variability in stride widths, suggesting that although poor hemiparetic performance was not consistently evident across all clinical assessments, gait variability robustly identified impaired walking performance. Unlike other spatiotemporal characteristics, stride width variability was reduced in the slower walkers when compared to controls. Stride width is calculated in the frontal plane unlike other spatiotemporal characteristi cs that are sagittal plane me asures, suggesting an inherent difference in control of this parameter. Furthe rmore, in population groups susceptible to falls (such as elderly fallers, persons with Parkin sons disease and commun ity dwelling elderly), width variability is reported to be reduced and th is reduction in variability is shown to predict falls [104, 107, 189]. In our study, we also observed that participants showing markedly reduced width variability walked with wide strides. A wider step provides a wider base of support for side-to-side motion of the center of mass and mi ght be accompanied by a reduction in variability of medio-lateral foot placement to ensure that st eps are consistently wide Therefore, it is likely that observed reduction in width variability is compensatory to maintain stability. Decreased width variability in comparison to increased variability in other spatiotemporal characteristics implies that altered variability might be speci fic to step characteristics and should not be generalized.
81 Study Limitations There were som e limitations in our study. Da ta was collected from a limited number of steps that could have influenced the accuracy of our results . However, a major strength of our methodology was the ability to measure spa tial variables as well. Methodologies that capture hundreds of steps are based on reco rding temporal charac teristics only . Furthermore, despite the fewer number of steps collected in our study, observed patterns of gait variability were consistent with those observed in other impaired populations [101, 106, 111]. Further, use of the GAITRite based protocol is cl inically relevant and th erefore, our study results have the potential to rapidly translate to the c linical settings. We also evaluated gait variability using coefficient-of-variation (CV = standard deviation/mean) in step characteristics. Using CV to evaluate variability may result in ques tionable conclusions of increased variability, specifically when the mean value is of low magnitude. It is also likely th at the differences in stride variability could be due to differences in st rategies (i.e., length-frequency combinations) employed to achieve a certain speed . Nonethel ess, several studies have shown that stride variability, could be independent of st ride length and frequency [91, 189]. Furthermore, it is likely that the trial-to-tri al variability in speed resulted in observed changes in the variability. However, the speed variability did not differ (p = 0.268) between hemiparetic and healthy participan ts, suggesting that the trial-to-trial speed variation did not contribute to the observed pattern s of gait variability. Slower walking speeds post-stroke are likely to be associated with greater alterations in step variability. Yet, observed patterns of gait variability cannot be solely attr ibuted to effects of speed beca use if healthy persons walk at slower speeds similar to persons with gait defici ts, gait variability is likely to remain relatively low during healthy gait even at the slower speed s . In addition, while persons walking with assistive devices showed overall greater step variability than th ose not using assistive devices,
82 the inverse relationship between variability a nd walking performance was apparent when we evaluated the data for those using assistive devices separately from others who did not. Conclusions In conclusion, results of this study suggest th at step variability is altered post-stroke com pared to healthy controls and relates to hemiparetic walking performance. Specifically, between-leg differences in swing time and pre-swing variability, in creased step length and stride time variability and reduced wi dth variability can be indica tive of underlying sensorimotor impairments post-stroke; suggesting these as quantifiable measures of impaired hemiparetic performance. Future studies s hould investigate the underlying cause s of altered variability and the effect of therapeutic interventions on gait va riability to further validate its use to assess hemiparetic performance. Table 4-1. Definitions of study variables STEP LENGTH (cm): measured along the line of progression, from the heel center of the current footprint to the heel center of the previous footprint on the opposite foot. PRE-SWING TIME (sec): Pre-swing (or double suppor t) time occurs from opposite footfall first contact to support footfall last contact. SWING TIME (sec): time elapsed between the Last Contact of the current footfall to the First Contact of the next foot fall of the same foot. STRIDE TIME (sec): time elapsed between the firs t contacts of two consecutive footfalls of the same foot. STRIDE WIDTH (cm): vertical distance from midline midpoint of one footprint to the line formed by midline midpoints of two footprints of the opposite foot.
83 Table 4-2. Step variability (expressed as standard deviation) within th e hemiparetic population sub-divided based on their performance measures
84 Figure 4-1. Differences in temporal variability between healthy (n = 22) and participants with hemiparesis (n = 94) at Self -selected (SS) walking speeds The box plots indicate the range in the data. The central horizon tal line is the median of the sample. The length of the box indicates the in ter-quartile range with the upper and lower boundaries of the box indicating the upper and lower quartile, resp ectively. Circles represent sample values that statistically indicate outlier or extreme values (by SPSS software). In impaired populations, these outlier values are true indicators of behavi or and represent those persons showing excessive variability. indica tes statistically signifi cant differences from healthy leg at p < .0001, # indicate s statistically significant differe nce from non-paretic leg at p < .0001. Note that the statistical significance is based on the mean of the logtransformed values of the respective temporal characteristics. Variability in all temporal characteristics was increased during hemiparetic walking. Abbreviations: P Pa retic leg, N Non-paretic leg, HC Healthy control leg, H Hemiparetic walking (v alue includes steps from both legs).
85 Figure 4-2. Differences in spatia l variability between healthy (n = 22) and participants with hemiparesis (n = 94) at Self -selected (SS) walking speeds The box plots indicate the range in the data similar to Figure1 indicates statistically significant differences from healt hy leg at p < .0001 and the statis tical significance is based on the mean of the log transformed values of the re spective temporal characteristics. Variability in step length characteristics was increased during hemiparetic walking and that in stride width showed a trend to decrease during hemiparetic walking. Abbreviations: P Paretic leg, N Nonparetic leg, HC Healthy control leg, H Hemi paretic walking (value includes steps from both legs).
86 Figure 4-3. Differences in tempor al variability in hemipareti c participants based on their performance on clinical assessments The box plots indicate the range in the data similar to Figures 1. Blue represents paretic leg and Green represents non-paretic leg for swing time a nd pre-swing time variabili ty. In general, poor performance is indicated by more severe hemipa resis (lower LE-FM scores), asymmetrical gait (longer or shorter paretic steps) and poorer balance performance (lower DGI scores)]. Note the between-leg differences in swi ng and pre-swing time in persons with moderate and severe hemiparesis, those walking asym metrically and in persons showing poor balance performance. Note that while stride time variability diffe rences were observed in sub-groups of the hemiparetic population, these have not been represented in the Figure.
87 Figure 4-4. Differences in spat ial variability in hemiparetic participants based on their performance on clinical assessments The box plots indicate the range in the data similar to Figures 1. Blue represents paretic leg and Green represents non-paretic leg fo r step length variability. Note that stride width variability does not show a consistent trend to differ acro ss the different sub-groups of the hemiparetic population.
88 CHAPTER 5 FOOT PLACEMENT IN A BODY REFERE NC E FRAME DURING WALKING AND ITS RELATIONSHIP TO HEMIPARETI C WALKING PERFORMANCE Introduction Foot placem ent during walking is commonly quantified using parameters that are determined relative to the other foot during a step (e.g., step lengt h and step width). Nonetheless, foot placement closely relates to body m ovements [117, 118]. For instance, forward body progression during walking requires controlling the movement of the bodys center-of-mass relative to where the foot is pl aced. Similarly, dynamic stability during walking is established by foot placement in a body reference frame (in re lation to body movement). Specifically, by foot placement in a body reference frame, we imply calcula tion of where the foot is placed relative to the body during walking (and not relative to the ot her foot). For instance, step length in a body reference frame can be calculated as the anteri or distance between the leading foot center-ofmass and the center-of-mass of the pelvis at heel st rike. Patterns of foot placement relative to the body are rarely investigated during gait. In some earlier studies, foot placement relative to body was investigated during healthy gait and rela ted to motor control during gait [116-119, 134]. However, foot placement relati ve to body has not been investig ated in neurologically impaired populations and specifically in an asymmetrical population such as stroke. The observations of asymmetric foot and trunk kinematics in isol ation [198, 199] suggests that foot placement relative to body likely are asymmetric post-stroke but it is unclear whether persons with specific motor control deficits would have particular patt erns of where they place their foot relative to body. Post-stroke, quantifying where the foot is pl aced relative to body could provide a deeper understanding of the mechanisms of hemiparetic walking than is possible when foot kinematics alone are known (as when it is de fined relative to other foot). Fo r example, in persons who take
89 asymmetrical step lengths (relative ly longer or shorter paretic step lengths), it is unclear whether their foot placements relative to pe lvis (or trunk) would also be asym metrical. It is possible that, in those persons who take longer paretic steps th an non-paretic, while the paretic step is longer relative to the other foot; relative to pelvis both feet are placed symmetrically. Furthermore, in persons taking asymmetrical longer or shorter paretic steps than non-paretic, paretic and nonparetic stride lengths are likely to be the same. This suggests that investigation of foot placement relative to pelvis can reveal differential pattern s of asymmetrical foot placement anterior or posterior to the pelvis and help understand the sp ecific motor control in such asymmetrical subgroups. Similarly, it is unclear whet her there is any asymmetry in la teral foot placements relative to pelvis and whether it relates to step width post-stroke. Therefore, in this study patterns of foot placement relative to body were compared to step length asymmetry and step width to investigate the relation between stepping in a body reference frame to stepping relative to the other foot. Furthermore, we expected that investigation of foot placement rela tive to body will provide insights into forward progre ssion, weight support and dynamic stability during hemiparetic walking. Accurate foot placement in relation to the body during walk ing establishes a stable base for the body to progress forward [118, 132]; impl ying that foot placement during walking is closely related to forward progression. Furtherm ore, lateral balance of the body depends on the mediolateral foot placement  suggesting that identification of persons with hemiparesis with specific patterns of mediolater al foot placement can help de termine their dynamic stability. Mediolateral foot placement rela tive to the body can also infl uence the weight shifted and supported on the legs since how far one places th eir foot relative to th e body at ground contact will influence the extent of body displacement. Th erefore, we also investigated the relation
90 between mediolateral foot placement relative to body and weight supported on the leg to identify persons with disturbances in weight shifting. Therefore, in this study, in addition to quantifying foot placement relative to body during hemipare tic walking, the relationship between foot placement relative to body and walking performance was explored. Walking performance was quantified using step length asymmetry patte rns, paretic propulsi on, weight support and a dynamic stability margin. In summary, the purpose of this study was 1) to evaluate where the foot is placed relative to the body during walking in a post-stroke population and, 2) to understand how foot placement in the body reference frame relates to walking pe rformance. Foot placement relative to body was calculated in the anterior-posterior and medial-l ateral directions during hemiparetic walking and compared to patterns of foot placement in a similarly-aged healthy population (serving as controls) walking at matched slow speeds. Inclusi on of control subjects was deemed necessary to compare the foot placement patterns in the he miparetic gait to that of healthy gait. We hypothesized that the measures of stepping performance (step lengths and step widths), forward progression, weight support and dynamic stability would relate to the asymmetry in foot placement relative to body such that investigat ion of foot placement in a body reference frame will provide insights into essential requireme nts of locomotion and help better evaluate asymmetric gait post-stroke. Methods Participants Data were collected from thirty-nine participants with chronic hem iparesis (Age = 60.21 12.32 years, 20 men, 19 left-side hemi paresis) and twenty age-matche d healthy participants (Age = 66.15 10.03 years, 4 men) at the VA-UF Huma n motor performance laboratory, VA Medical center at Gainesville Florida. Inclusion criteria for the participants with hemiparesis were:
91 hemiparesis secondary to a single onset unilateral stroke ; ability to ambulate independently with or without an assistive device over 10 m on a level surface; ability to walk on a regular basis at least at home; absence of significant lower extremity joint pain and major sensory deficits; absence of significant lower limb contractures a nd no significant cardiovasc ular or respiratory symptoms contraindicative to walking. Participants from the study were excluded if they had any orthopedic or neurologic conditions in addition to stroke, had signifi cant musculoskeletal problems other than stroke that limit hip and knee extension or ankle planta r flexion to neutral, or were unable to provide informed consent. All participants in the study signed a written informed consent and Institutional Review Board of University of Florida approved the protocol. Procedures Retro-reflective m arkers were attached to the pa rticipant to collect bilateral 3D kinematics using a 12 camera VICON motion analyses system. Markers were attached to the head, trunk, upper extremity, lower extremity and the feet. Clus ters of reflective mark ers attached to rigid bodies were also located on the pe lvis, bilateral thighs, shanks and feet (Figure 5-1). A fixed laboratory coordinate reference fr ame was created within the VIC ON system that was placed at the left corner of the laboratory. At the beginning of the test se ssion, controls and participants with hemiparesis walked for 2-3 trials across a 12 ft long instrumented mat (GaitRite) at their self-selected walking speeds to collect over ground spatiotemporal parameters of steps and estimate their overground walking speeds. Gaitrite is a valid instrument to m easure spatiotemporal parameters during walking . Subsequently, controls and participants with hemiparesis walked on an instrumented splitbelt treadmill (TECMACHINE) for three trials at their self-selected treadmill walking speed. In case of participants with hemiparesis, the treadmill self-selected speeds were 10 30% slower
92 than the over ground self-selecte d speeds. Participants with hemiparesis completed three 30second walking trials without use of an assistive device or ankle-foot orthosis. A safety harness mounted to the laboratory ceiling was worn across the shoulders and chest to protect the participants in the even t that they loose balance. Note, th at no bodyweight was offloaded by the harness. Additionally, a physical therapist closely guarded the participants as they walked over the treadmill (although no manual support was provided by the therap ist). For healthy participants, treadmill speeds closely appr oximated their over ground speeds. Healthy participants, in addition, walked at fixed slow speeds on the treadmill for a single trial at 0.3 m/s, 0.6 m/s, and 0.9 m/s to provide control data at speeds matched to the slower speeds of the hemiparetic participants. To optimize capture of steady state data on the treadmill, each subject walked for 10 s prior to each of the 30 s of data collection. Three-dimensional GRFs were measured from each half of the treadmill along with the kinematic data collection during the walking trials. Data Analyses Kinema tic data: Raw kinematic data was low-pass filter ed using a fourth-order zero-lag Butterworth filter with a 10 Hz cutoff frequency. Th e joint center and anatomical trajectories was fitted to an eight-segment musculoskeletal model generated using SIMM (MusculoGraphics, Inc.) consisting of a trunk (incl uding the mass of the torso, head and arms), pelvis and legs for each subject (Figure 5-1 presents the SIMM model fr om an individual participants walking trial). Each lower extremity consisted of a thigh, shank and foot. The anthropometrics and inertial properties were based on that of de Leva . Segmental center-of-mass (COM) calculations were used to calculate the whole body COM. In this study, specifically pelvis COM was used to reference the body.
93 Kinetic data: Three-dimensional GRFs were sampled at 2000 Hz. Ground reaction force data was low-pass filtered using a fourth-order zero-lag Butterworth filter with a 20 Hz cutoff frequency. The SIMM Motion Module (MusculoGraphi cs, Inc.) was used to perform a standard inverse dynamics analysis to determine the inter-segmental joint moments. Kinetic data (GRFs and joint moments) was normalized by subject b ody weight. Kinetic data was time normalized to 100% of the paretic leg gait cy cle (paretic heel strike to paretic heel strike). Calculation of study variables: All variables were calculated by averaging across all complete gait cycles of each of the three trials. The number of steps that ar e used to calculate the averages varied across subjects sinc e they walked at different speeds. Foot Placement and foot position variables: Anterior-Posterior (A P) and medial-lateral (ML) foot placement and position variables relative to pelvis were calculated for individual legs. The body was referenced at the pelvis COM (Figur e 5-2). Calculation of initial foot placement (calculated at ground contact in the 1st doubl e support phase) and terminal foot position (calculated as toe-off in the 2nd double support phas e) in AP and ML direction is presented in Table 5-1. The term foot position was used to di stinguish these variable s from foot placement variables since the foot position variables de scribe how the body movement progressed in a specific positioning of the foot relative to the body. Stepping relative to the other foot: Step length and step widths were calcul ated for individual legs at the same instant as the variables calculated in the body reference frame (Table 5-1). Stepping asymmetry, forward progression, weight support and Dynamic stability: Step length asymmetry was qua ntified using a Paretic step ratio , (Table5-1). Asymmetry in the hemipa retic participants was characterized based on symmetry ranges calculated from similarly-aged h ealthy participants walking on the treadmill, as follows: Longer paretic steps than non-paretic ( PSR > 55), Shorter pa retic steps than non-
94 paretic (PSR < 45) and Sym metric step lengths (45 PSR 55). Forward progression was quantified using paretic propulsion , (Table 5-1). Weight support was quantified by the average vertical force supporte d on individual legs during the stance phases (Table 5-1). Dynamic stability was evaluated by a Dynamic Stab ility Margin (DSM) similar to earlier studies [201, 202], (Table 5-1). Specifically, we used th e DSM that we calculated at the instance at which the xCOM reached its maximum value in 1st double-support (DSMmax). Statistical Analyses For contro l subjects, right-left foot placements and positions were similar at all speeds (i.e., no between-leg asymmetry), in both AP and ML direction relative to pelvis (p < .001). Therefore, only control (left) leg was used in the comparisons with par ticipants post-stroke. To compare foot placement and position relative to the body between controls and participants with hemiparesis, a 3 (leg: paretic, non-paretic, control) x 2 (phase: foot-strike, foot-off) Mixed ANOVA was conducted. Median foot placements of control particip ants at varying speeds were compared to participants with hemiparesis walki ng at similar range of speeds in the statistical analyses. Controls participants walked at 3 varying slow speeds: 0.3 m/s, 0.6 m/s and 0.9 m/s. Therefore, the comparisons of hemiparetic particip ants were made for those persons walking less than equal to these speed ranges. Note that each speed group consisted of different hemiparetic participants walking at their self -selected speeds. Since median foot placements were used in the analyses, number of controls was matched to that of the hemipareti c in each speed group. Pearson correlations were conducted to evaluate the relationships betw een foot placements, positions and walking performance measures. Quadratic relations were additionally explored for each of the relationships but it did not improve the explanatory power significantly in any relationship, therefore linear relationships have been presented.
95 Results Quantifying Foot Placement Rela tive to the Pelvis For control subjects, right-left foot placements and positions were similar at all speeds (i.e., no between-leg asymmetry), in both AP and ML direction relative to pelvis (p < .001). Therefore, the left leg was used as the contro l leg in the comparisons with participants poststroke. AP direction: In control participants, foot placement was anterior at ground contact (GC) and foot position posterior at toeoff (TO) relative to pelvis, with the anterior placement showing greater excursion than posterior at all the varying speeds (40 80 mm, p < .001), (Figure 5-3a). The greater anterior excursion of the foot at GC than posterior at TO relative to pelvis is operationally termed as between-phase asymmetry in this study to differen tiate from between-leg asymmetry. In participants with hemiparesis, the pattern of paretic and non-paretic foot placement varied with their walking speeds. Foot placement in slow walkers ( 0.3 m/s, n = 22) and cont rols walking at matchedspeeds: Both between-leg and between-phase asym metry was observed in those hemiparetic participants walking slowly. Median foot placemen ts were anterior at GC and posterior at TO, with the paretic foot be ing more anterior and less posterior than non-paretic (p=.003). There was increased inter-subject variability in posterior pare tic foot position at TO su ch that at least half the participants in this group never positioned their foot posterior to the pe lvis (Figure 5-3a). The control foot showed grea ter excursion than both th e paretic and non-paretic feet even at matched slow speed (p<.001). However, the difference in anterior foot placement between control and paretic feet was small (~30 mm). Foot placement in Moderate (> 0.3m/s 0.6 m/s, n = 12) and Fast walkers (> 0.6 m/s 0.9m/s, n = 5) and controls walking at matched-speeds: For participants walking at moderate
96 (0.3 0.6 m/s) and fast (0.6 0.9 m/s) speeds th ere was no between-leg asymmetry but betweenphase asymmetry was apparent (GC TO relative to pelvis = 6 10 cm), (p<.01), Figure 5-3a. Further, for the fast walkers foot placement excurs ions were similar to that of Controls (p<.001), excepting paretic anterior foot placement that was reduced. ML direction: There was no between-phase asymmetry in foot placements in controls and participants with hemiparesis (i .e., same ML distance at GC and TO). Therefore, lateral foot placement at GC is presented. In participants with hemiparesis walking slow and at moderate speeds, the paretic foot was placed lateral to pe lvis compared to both non-paretic (difference range = 30 70 mm) and speed-matched control (d ifference range = 49 74 mm) foot placement (p < .001), (Figure 5-3b). Additionally, Paretic foot was lateral most compared to non-paretic in the slow walkers. In the fast walkers (speed 0.6 0.9 m/s), paretic foot was significantly lateral to the body only relative to speed-matched cont rol foot placement and not non-paretic foot placement (p< .01), (Figure 5-3b). Relationship between Anterior-Posterior Foot Placements Relative to Pelvis, Step Length Asymmetry and Paretic Propulsion Betw een-leg asymmetry (anterior foot placem ent relative to pelvis) and step length asymmetry: Anterior foot placement asymmetry was a ssociated with step length asymmetry (r = .756, p< .001), suggesting that person s taking asymmetrical step le ngths also place their feet asymmetrically relative to pelvis (Figure 54). Nonetheless, asymme try ranges in the two reference frames differed. Note that persons seve rely asymmetric in the global reference frame (PSR > 90%) showed similar patterns in both th e reference frames, however persons showing mild to moderate step length asymmetry (PSR = 60 80%) placed their paretic and non-paretic feet more symmetrically with respect to the pe lvis (asymmetry range in body reference frame = 55 60%), (Figure 5-4).
97 Anterior-posterior foot placement relative to pelvis and step length asymmetry: Paretic foot placement at TO a nd non-paretic foot placement at GC strongly correlated with step length asymmetry (PSR) even after controlling fo r walking speed (Figure 5-5). Note in Figure 55, participants taking relatively long paretic st eps (PSR > 70%) positione d their paretic foot anterior (opposite to the expected pattern) at TO Similarly, participants taking relatively shorter paretic steps (PSR 40%) positioned their pareti c foot much less posteriorly at TO relative to the symmetric group. Between-leg asymmetry and paretic propulsion: Asymmetrical anterior foot placements relative to pelvis and step length asymmetry were each negatively associated to paretic propulsion (r = -.584 and r = -.520, resp ectively), suggesting that both between-leg anterior foot placement asymmetry in body reference frame and step length asymmetry related to percent propulsion genera ted by the paretic leg. Relationship between Medial-Lateral Foot Pla cements R elative to Pelvis, Step Widths, Paretic Weight Support and Dynamic Stability Margin Lateral foot placement asymme try relative to pelvis, step widths and percent weight supported on the paretic leg: There was no difference in paretic and non-paretic step widths during hemiparetic walking (p = .732) and no re lation between step width and either percent weight borne on the paretic leg (r = .244, p = .135) or lateral foot placements (r = .235, p = .150). However, lateral foot placement was asymmetric and was negatively associated to the percent weight supported on the pa retic leg (Figure 5-6). Lateral foot placement asymmetry relativ e to pelvis, step widths and dynamic stability margins: Pearson correlations control ling for walking speed revealed that Lateral foot placement asymmetry was positively associated to paretic DSMmax (r = .548, p < .001); suggesting that the wider paretic foot placemen t relative to pelvis than non-paretic foot
98 placement is related to the wider paretic stabil ity margin. Step width was positively associated with both paretic and non-paretic DSMmax (r = .520, p=.001 and r=.360, p= .024; respectively) suggesting that overall a wider step was related to greater stability margin on both paretic and non-paretic legs. Discussion The results of this study show that foot pl acem ent in a body reference frame is asymmetric in AP and ML directions during hemiparetic walk ing and this asymmetry related to hemiparetic walking performance. Anterior-Posterior Foot Placement Relative to Pelvis and its Relat ionship to Step Length Asymmetry and Forward Progression Between-phase asymmetry: Overall, relative to pelvis the foot was placed more anterior at GC and less posterior at TO in both controls and participants with hemiparesis at all speeds. Further, participants post-stroke showed greater between-phase asymmetry in the paretic leg than non-paretic legs and also greater asymmetry than controls walking at matched slow speeds. The excursions of the foot were also greater in AP direction for controls ev en at the matched slow speeds indicating that slower walking speeds alone cannot explain the AP asymmetry in the hemipaertic participants. Further, note that pa retic posterior foot position at TO specifically showed increased inter-subject variability (See Figure 5-3a, speeds 0.3 m/s) suggests that there were persons who never positioned their paretic foot posterior to the pelvis and others who positioned it posterior and yet these two groups were walking at similarly slow walking speeds. Further, we correlated the posterior foot position at TO to step length asymmetry because we hypothesized that the inter-subject variabi lity in posterior foot position would be well explained by relating the AP foot placements to step length asymmetry and could further help explain the motor control impairments in the asymmetrical groups. Redu ced posterior paretic
99 foot position at TO and anterior non-paretic foot placement at GC relative to pelvis strongly correlated with step length asym metry. Specifically, in persons taki ng Longer pareti c steps than non-paretic (PSR > 55%), the paretic posterior f oot position was either reduced or anterior relative to the pelvis suggesting that paretic leg orientation at pre-swing phase was opposite than that expected (posterior positioning) in this ph ase. Therefore, while these persons with Longer paretic steps had good stepping ability evidenced by the greater paretic anterior foot placement relative to pelvis than non-paretic (see Figure 5-4), an inability to achieve a more posterior paretic foot position at TO sugge sts impaired paretic leg extens ion in the Longer paretic group. A flexed leg orientation at TO versus extended in the paretic pre-swing phase can reduce the mechanical advantage of an extended extremity to propel the trunk forward. This observation is supported by the evidence that the Longer pa retic group shows reduced paretic propulsion . In support of our explanation, we would expe ct that in the Shor ter paretic group the posterior paretic foot position would be relatively greater compar ed to the Longer paretic group since these persons show good paretic propulsion. Wh ile all participants in the Shorter paretic group positioned their paretic foot posterior relati ve to pelvis (Figure 5-5), in the severely asymmetric (PSR < 40%), the poste rior foot position relative to pelvis was much reduced similar to some persons in the Longer paretic group. Ther efore, we additionally i nvestigated their foot position relative to the trunk COM to evaluate if compen satory trunk lean might be the mechanism utilized to propel th e body forward. Relative to the trunk, paretic foot position was much posterior at TO (showing similar excursion as anterior non-paretic foot placement at GC). Since the foot placement relative to trunk depends not only on wher e the foot is placed but where the trunk is positioned, it is possible that at least some of these persons in the Shorter paretic
100 group generate good body forward pr ogression during the paretic pr e-swing phase by flexing the trunk forward and thereby creati ng a mechanically advantageous position for the propulsive ground reaction forces generated from the paretic leg to propel the body forward. Therefore, by investigating the foot placement relative to the trunk (in additi on to pelvis), compensatory strategies could be diagnosed. Between-leg asymmetry in anterior foot placements: We also correlated anterior foot placement asymmetry to step length asymmetry (Fi gure 5-4) to understand the relation between foot placement in a body reference frame to steppi ng relative to the other foot. Overall, stepping asymmetry in the two reference frames were correlated (for example, persons taking Longer paretic steps relative to non-paretic were also placing their paretic f oot more anterior relative to pelvis). However, the symmetry range in the body reference frame was narrower than step length symmetry range and some persons who were asymme tric taking Longer paretic step lengths than non-paretic (PSR = 55 -65%) were symmetric in the body reference frame. Interestingly, others who were taking symmetrical step lengths were ac tually asymmetric relative to pelvis taking shorter paretic steps than non-paretic The ability to place the foot further anterior to the pelvis suggests good stepping ability and the observation that the borderli ne symmetric persons actually took shorter paretic steps relative to pelvis s uggests their impaired paretic stepping ability. Therefore, we suggest that since some persons [mildly asymmetric (longer paretic) and symmetric] step lengths changed their asymme try in a translating body reference frame, additional investigation of foot placement pattern re lative to pelvis might be necessary to classify them as symmetric or asymmetric. In summary, by relating the foot placement and position relative to the pelvis to step length asymmetry we are able to propose some unde rlying motor control mechanisms in the
101 asymmetrical groups. Longer paretic group sh owed poor forward body progression likely due to altered initial conditio ns of the leg in their pre-swing phase, whereas the Shorter paretic group showed poor stepping ability due to the inability to place the pa retic foot further anterior to the pelvis. Further, the good forward progression at least in some participants in the Shorter paretic group might be compensatory from lean ing the trunk forward in the pre-swing phase of their paretic gait cycle. Medial-Lateral Foot Placement Relative to Pelv is and its Relationship to Weight Supported on Paretic Leg and Dynamic Stability Margin There was no difference in ML foot placem ent at GC and TO (i.e. no between-phase asymmetry). However, between-legs, the pareti c foot was placed wider relative to pelvis compared to non-paretic and speed-matched control in participants with hemiparesis walking at slow and moderate speeds. Furthe r, this lateral foot placement asymmetry between-leg decreased with increasing walking speed dur ing hemiparetic walking (Figure 5-3b). Furthermore, we found that the lateral foot placement asymmetry was strongly correlated with both weight support and paretic dynamic stability margin. We quantified the percent weight supported on paretic leg as the percentage of Vertical Ground reaction force on the paretic leg during stance compared to the both legs. Overall paretic leg supported lesser we ight compared to non-paretic evidenced by the lower percentages than 50 (Figure 5-6). This we ight-bearing asymmetry is consistently reported in the post-stroke population [19, 154]. However, th e relationship between lateral foot placement and weight supported on the legs has not yet been reported in this population. While we expected that wei ght supported on the leg would be related to lateral foot placement, our results specifically show that the asymmetry in lateral foot placement relative to pelvis (i.e., wider paretic steps relative to pelv is than non-paretic) relate d to the weight supported on the paretic leg during stance. On the other han d, step widths were unr elated to the paretic
102 weight support suggesting that investigation of late ral foot placement as ymmetry relative to pelvis specifically revealed the impaired paretic leg weight support in persons taking wider paretic steps relative to body. Therefore, we sugg est that close observation of the lateral paretic foot placement relative to the body in comparis on to lateral non-paretic foot placement can provide useful insights to the clinicians rega rding the amount of weight supported on the paretic leg. Moreover, we found that the lateral foot pl acement asymmetry specifi cally related to the dynamic stability margin on the paretic side. We calculated the dynamic stability margin specifically for each foot (at init ial contact) as the ML distance between xCOM and foot COM at the instance when xCOM reached its maximum value in 1st double-support (Table 5-1). Foot placements at heel-strike have earlier shown to be a linear function of COM displacement and velocity and shown to be the most importa nt factor defining stable gaits [116, 117, 134] suggesting the importance of foot placement to dyna mic stability. Specifically, in this study we chose to use DSMmax since it physiologically rela tes to the point of maximum instability. We also calculated DSM at other in stances: first instance of groundcontact (DSM-GC) and at every 20% of 1st double-support. Evaluation of DSM at every 20% of the gait cycle revealed that there was no significant difference between DSM values as the 1st double-support phase progressed suggesting that the DSM doesnt change substa ntially across the double-support phase. Further, DSM-GC and DSMmax revealed the same pa ttern relative to foot placement, although correlations were stronger for DSMmax and foot pl acement. Note that, we did not use the entire area enclosed between foot placements (i.e., base of support) to define th e DSM since we wanted to investigate how foot placement on individual legs affected the margin established at each foot placement. We found that wider paretic foot pl acement relative to pelvis than non-paretic
103 specifically related to wider stab ility margin established on the pa retic side. However, there was no relation between the lateral foot placement asymmetry and th e non-paretic stability margin suggesting that the wider paretic foot placement relative to non-paretic may specifically establish a wider stability margin at paretic foot placement. As expected, step width related to both paretic and non-paretic stability margins indicating that a wider step in general related to a wider stability margin. A wider margin specifically on one side can predispose lateral instability since the COM was closer to the margin of the base of support on one side than other. Since there was no relation between step width a nd lateral foot placement asymme try, persons taking wider steps may have a wider or narrower margin on the pa retic side relative to non-paretic and it may be difficult to identify those persons with lateral in stability. Further, while the wider step on the paretic side related to decrease weight support it increased the stab ility margin on the paretic side indicating that ML asymmetry might be comp ensatory to increase the dynamic stability. Therefore, we suggest that latera l foot placement relative to pelv is is a useful outcome measure to quantify both paretic leg weight support and dynamic stability. Limitations There are som e limitations in this st udy. The current study was conducted over the treadmill and foot placement relative to body might differ overground. Nonetheless, it is expected that while absolute foot placement (in isolation) might be altered (i.e., longer versus shorter step lengths) while walking overground, its relation to the body movements remain consistent suggesting the functional relevan ce of foot placement relative to body. This hypothesis could be tested in future studies by ex ploring the step-by-step variability in foot placement relative to body and whether this changes from treadmill to overground walking. Hip and knee kinematics were not explored in th e current study. Since the foot is under multisegmental and end-point control, it is expected that the foot kinematics relative to body will be
104 the end result of different combinations of hi p and knee kinematics such that investigation of foot kinematics relative to body might be a relatively easy method to understand post-stroke walking from a control model viewpoint. Conclusions Post-stroke gait is asym metric when quantifying foot placement relative to pelvis in both AP and ML directions. We suggest that for the AP direction, ch aracterizing stepping relative to the other foot (i.e., step le ngth) was appropriate as outcomes to quantify asymmetrical performance and forward progression because stepping relative to the other foot and stepping in a body reference frame were associated. Nonethele ss, since some borderline asymmetrical (PSR = 55 65%) and other symmetrical persons show differing performance in the translating reference frame, it may be additionally useful to i nvestigate foot placement relative to pelvis in these persons. Further, we could understand motor control mechanisms in the asymmetrical subgroups (impaired initial conditions in the Longe r paretic group versus imp aired stepping ability in the Shorter paretic group) by investigating th e foot position patterns relative to pelvis. For the ML direction, we suggest using foot placem ent relative to pelvis as an outcome to characterize hemiparetic performance. A wider f oot placement of the pa retic foot relative to pelvis than non-paretic can quantify the reduced weight supported on the paretic leg and lateral instability. Overall, we were able to bette r evaluate asymmetrical performance during hemiparetic walking by investigating foot placemen t and position in a body reference frame that was not revealed when investiga ting stepping relative to other f oot. Therefore, we suggest that biomechanical analyses quantifying stepping pe rformance in impaired populations should investigate foot placement in a body reference frame (especially in the ML direction) to understand motor control during gait.
105 Table 5-1. Definition of study variables Foot placement and position relative to body Anterior-Posterior AP Foot placement relative to pelvis: Distance in AP direction from foot COM to pelvis COM at the initial foot placement (ground-contact in the 1st double-support). AP Foot position relative to pelvis: Distance in AP direction from foot COM to pelvis COM at the terminal foot position (toe-off in the 2nd double-support phase). Medial-Lateral ML Foot placement relative to pelvis: Distance in ML direction from foot COM to pelvis COM at the initial foot placement (ground-contact in the 1st double-support). ML Foot position relative to pelvis: Distance in AP direction from foot COM to pelvis COM at the terminal foot position (toe-off in the 2nd double-support phase). Stepping relative to the other foot Step length: Distance in AP direction from leading mid-foot to trailing mid-foot at the the initial foot placement (ground-contact in the 1st double-support). Step width: Distance in ML direction from leading mid-foot to trailing mid-foot at the the initial foot placement (ground-contact in the 1st double-support). Walking performance measures Step length asymmetry: calculated as a Paretic step ratio (PSR = Paretic step length / (Paretic + Nonparetic step length) and expressed as a percentage. Paretic propulsion: Paretic propulsive impulse / (Pare tic + Non-paretic propulsive impulse). Percent weight supported on the paretic leg: Paretic average vertical force / (Paretic + Non-paretic average vertical force) expressed as a percentage. Dynamic stability margin: ML Distance between the extrapolated COM (xCOM = COM displacement + COM velocity) and foot COM.
106 Figure 5-1. Illustration of marker positions for kinematic data collection and the SIMM model generated
107 Figure 5-2. Calculation of anterior-p osterior and medial-lateral foot placements relative to pelvis This figure presents the foot placement and positi on variables calculated relative to pelvis. These variables were calculated as th e AP and ML distance between foot COM and pelvis COM. Note, the yellow arrows present the step length and step width calculated relative to other foot. Anterior foot placement relative to pelvis Posterior foot position relative to pelvis Lateral foot placement relative to pelvis Anterior-Posterior Medial-Lateral
108 a. Anterior-Posterior foot pl acement relative to pelvis b. Medial-Lateral foot placement relative to pelvis Figure 5-3. Foot placement relative to pe lvis during hemiparetic and healthy gait Abbreviations: GC Ground contact at 1st double-s upport (initial foot placement), TO Toe-off at 2nd double-support (terminal foot position), PParetic foot, N-Non-paretic foot, C-Control foot. The box plots indicate the range in the data. The central horizontal line is the median of the sample. The length of the box indicates the in ter-quartile range with the upper and lower boundaries of the box indicating the upper and lower quartile, resp ectively. Circles represent sample values that statistically indicate outlier or extreme values (by SPSS software).
109 Figure 5-4. Relationship between anterior foot pl acement asymmetry relative to pelvis and step length asymmetry in participants with hemiparesis This figure shows the relationship between asymme try in foot placements relative to pelvis (body reference frame) and step length asymmetry (relative to the other foot). The vertical dashed lines indicate the st ep length symmetry ranges (45 PSR 55) and the horizontal dashed lines indicate symmetry ranges in the body reference frame (46 PSR 54) calculated similarly from healthy controls. Persons above the range take Longer paretic steps than non-paretic and those below the range take Shorter paretic steps than non-paretic. Note that, four persons (black arrow) taking longer paretic than non-pa retic step lengths placed their paretic and nonparetic feet symmetric with respect to the pelv is. On the other hand, three persons (red arrow) who were taking symmetric step leng ths place their paretic foot clos er to pelvis than non-paretic (i.e. shorter paretic steps in the body reference frame). Step length asymmetry % (PSR)
110 -300 -200 -100 0 100 200 300 400 3035404550556065707580859095100105110115120Ste p len g th as y mmetr y ( PSR % ) Posterior foot position Anterior foot placement (mm) Non-paretic foot placement (GC) Paretic foot position (TO) Figure 5-5. Relationship between step length asy mmetry and anterior-posterior foot placement relative to pelvis in participants with hemiparesis This figure shows the relationship between step length asymmetry and between-phase asymmetry in foot placements relative to pe lvis. The step length symmetry ranges (45 PSR 55) were calculated similarly fr om healthy controls. Note the pos terior paretic foot position in persons taking Longer paretic steps (PSR > 55). Some persons with severe asymmetry (PSR > 70%) never position their paretic foot posterior to the pelvis in th is phase of their gait cycle (2nd double support). Similarly, severely asymmetric persons taking Shorter paretic steps (PSR < 40%) place paretic foot much ante rior to pelvis than posterior at toe-off. Also, compare the paretic posterior and non-paretic anterior placemen t relative to pelvis between the symmetric and asymmetric persons. r = .607 r = -.467
111 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.530.40.450.50.550.60.650.70.75Lateral foot placement asymmetry Average weight supported on paretic leg Figure 5-6. Relationship between paretic and non-paretic latera l foot placement asymmetry relative to pelvis and percent weig ht supported on the paretic leg Note that greater lateral foot placement asymmetry (i.e., paretic foot placed wider relative to pelvis than non-paretic foot pl acement relative to pelvis) le sser the weight supported on the paretic leg during the stance phase. r = -0.560**
112 CHAPTER 6 EVALUATION OF STEP LENGTH GENERATION DURING POST-STROKE HEMIPARE TIC WALKING USING A NOV EL METHODOLOGY OF STEP-BY-STEP VARIABILITY IN GAIT DATA Introduction While hem iparetic walking is asymmetric, the underlying mechanisms responsible for step length generation during walking ar e not clearly understood in this population. Step lengths are reported to be shorter, asymmetric and variable from step to step during hemiparetic walking compared to healthy walking [5, 18, 69, 198]. Shor ter step lengths are co mmonly associated to the slower walking speeds post-str oke . Nonetheless, it is like ly that underlying sensorimotor and muscular impairments post-stroke directly influence the attained step lengths beyond changes due to the slower walking speeds. In part icular, step lengths are also asymmetric during hemiparetic walking with the direction of asym metry being inconsistent. Reports suggest that there are a greater number of persons taking longer paretic steps than no n-paretic and few take relatively shorter paretic steps than non-paretic [69, 194]. A subcategory of persons also walk with relatively symmetric steps . The inte r-subject variability in step length asymmetry suggests that the underlying neuromotor mechanisms controlling paretic st ep lengths could vary within these sub-groups of the hemiparetic population. Furthermore, there is considerable variability in step lengths on a step-by-step ba sis within individual str oke participants, with greater step-to-step variability reported in the mo re severe participants (unpublished data). This suggests that evaluation of the neuromotor mech anisms controlling step length generation needs to account for the subject-specific step-by-step variability in step length generation. Therefore, in this study, mechanisms of step length genera tion during hemiparetic walking were evaluated using a novel methodology that incorpor ates this within-subjects step -by-step variability in step lengths.
113 Several potential contributing factors are likely to affect attained step lengths. Current evidence indicates that step length generation can be influenced primarily by the: 1) initial conditions at the initiation of sw ing phase of the ipsilateral leg, 2) biomechanics of the early (primarily accelerating) and late swing phase (pri marily decelerating) of the ipsilateral leg, and 3) contralateral stance leg ground reaction forces during its early and late single-support phase (usually braking and propulsive respectively, in healthy subject s), occurring simultaneously with the ipsilateral swing phase. Initial conditions of the leg (e .g. kinematics, kinetics and musc le activity in the pre-swing phase) are suggested to define the resulting sw ing leg trajectory . For instance, dynamic simulations of swing phase in healthy gait performed in the ab sence of muscle joint torques approximated normal knee kinematics by selecting th e initial angular velocities and positions alone [164, 203], implying that the initial angula r velocity is an important determinant of kinematics during swing. Initial conditions prior to swing also provide the energy to the swinging leg [204, 205]. Therefore, the strong influence of initial conditions on th e ipsilateral swing phase of the gait cycle, can indirectly affect where the leg is placed at the end of the swing phase. Nonetheless, while the init ial conditions of the leg prior to swing phase should be partially predictive of swing phase characteristics, swing phase muscle activity is likely to either augment the leg flexion during swing (presumably by leg fl exors) or decelerate the leg to terminate the swing (e.g., hamstrings muscle activity). Therefor e, events occurring spec ifically during swing phase of the gait cycle can independently control the eventual step length. In support, Varraine et al. (2003) showed that when healthy participants were asked to voluntarily modulate their step lengths, they lengthened the time the leg was held in the swing phase [ 182]. Consequently, they proposed that controlling the swinging leg trajectory by alteri ng the swing phase parameters
114 enabled the healthy participants to step longer. Therefore, while initial conditions prior to swing phase can indirectly control step lengths (by its influence on the swing phase), events during the swing phase present pote ntially direct mechanisms that can control step lengths. Lastly, contralateral stance leg ground reaction forces occu rring at the same instan ce as ipsilateral swing phase can influence step length generation. Recen t work showed a strong negative relationship between propulsive force asymmetry and step length asymmetry that highlights the causal relationships between ground reactio n forces and step lengths [ 194]. In particular, the finding that persons who take longer pare tic steps than non-pa retic generate lesser paretic leg propulsion; suggests that the greater compensatory non-pareti c leg propulsion might be causing the trunk to progress further forward as the paretic leg is st epping, thereby resulting in the relatively longer paretic steps. Overall, current li terature suggests several potential indirect and direct mechanisms related to the initial conditions of the leg, swi ng phase and contralateral stance phase that might influence step length generation. In this study, we selected kinematic and kineti c measures that independently describe each of these phases of the hemiparetic gait cycle. Leg or ientation at toe-off, pelvis velocity at toe-off and ankle joint center velocity at toe-off determin ed the initial state of the leg and body before the leg begins to swing. Hip Impulse in early and late swing and corre sponding contralateral Anterior-posterior (AP) ground reaction force (G RF) impulses were chosen to represent the events in the ipsilateral swing phase and corr esponding contralateral st ance phase, respectively. We hypothesized that the kinematic and kinetic measures that desc ribe each of these phases of the hemiparetic gait cycle would relate to step le ngths and explain step length variability withinsubjects. In particular, we hypot hesized that contralateral AP GRF impulses would be a strong predictor of step length variability in majority of persons. Whereas, hip impulse in ipsilateral
115 swing will be a strong predictor of step length va riability in persons taking longer paretic steps than non-paretic. Regression models were built for individual subjects using gait data from each step because we wanted to evaluate the kinematic and kinetic parameters that best predicted the step length variability within-subjects. In summary, the purpose of this study was to comprehensively evaluate the underlying mechanisms of step length generation during hemiparetic gait by determining the predictors that explain the step length (step-by-step) variability within-subjects. Methods Participants Participan ts were a convenience sample of th irty-eight persons with chronic hemiparesis (Average Age = 60.21 12.32 years, 20 men, 19 left -side hemiparesis) and twenty similarlyaged healthy participants (Age = 66.15 10.03 ye ars, 4 men) evaluated at the VA-UF Human motor performance laboratory, VA Medical center at Gainesville Florida. Table 6-1 presents the individual subject characteristics for the hemiparetic participants. Healthy subjects data were used to calculate the step length symmetry ranges for the hemiparetic participants. Inclusion criteria for the participants were: hemiparesis se condary to a single onset unilateral stroke; ability to ambulate independently with or without an assistive device over 10 m on a level surface; ability to walk on a regular basis at least at home; absence of significant lower extremity joint pain and major sensory deficits; absence of signi ficant lower limb contractures and no significant cardiovascular or respiratory symptoms contrai ndicative to walking. Participants from the study were excluded if they had any orthopedic or neurologic conditions in addition to stroke, had significant musculoskeletal problems other than stroke that limit hip and knee extension or ankle plantar flexion to neutral, or were unable to pr ovide informed consent. All participants in the
116 study signed a written informed consent and Institutional Review Board of University of Florida approved the protocol. Procedures Retro-reflective m arkers were attached to the pa rticipant to collect bilateral 3D kinematics using a 12 camera VICON motion an alyses system. Markers were at tached to the head (top, left, right, front and back), trunk (C7, T10, clavicle sternum and right scapula), upper extremity (bilateral shoulders, elbows and wrists), lower extremity (bilateral knees and ankles) and the feet (tip of the toes, left and right side of forefoot, midpoint of forefoot and calcaneus). Clusters of reflective markers attached to rigid bodies were also located on the pelvis, bilateral thighs, shanks and feet. A fixed laborat ory coordinate reference frame was created within the VICON system that was placed at the le ft corner of the laboratory. At the beginning of the test se ssion, controls and participants with hemiparesis walked for 2-3 trials across a 12 ft long instrumented mat (GaitRite) at their self-selected walking speeds to collect over ground spatiotemporal parameters of steps and estimate their overground walking speeds. Subsequently, participants with hemiparesis walked on an instrumented split-belt treadmill (TECMACHINE) for three trials at their self -selected treadmill walking speed. The treadmill self-selected speeds were 10 30% slower than that over gr ound for participants with hemiparesis. All partic ipants completed three 30-second walking trials without use of an assistive device or ankle-foot or thosis. A safety harness mounted to the laboratory ceiling was worn across the shoulders and chest to protect th e participants in the event that they loose balance. Note, that no bodyweight was offloaded by the harness. Additionally, a physical therapist closely guarded the participants as they walked over the treadmill (although no manual support was provided by the therapist). To optimize capture of steady state data on the treadmill,
117 each subject walked for 10 s prio r to each of the 30 s of data collection. Three-dimensional Ground Reaction Forces (GRFs) were measured from each half of th e treadmill along with kinematic data that were colle cted during the walking trials. Refer to Figure 6-1 showing a participant walking on the treadmill as kine matic and kinetic data were collected. Data Analyses Kinema tic data: Raw kinematic data was low-pass filt ered using a fourth-order zero-lag Butterworth filter with a 10 Hz cutoff frequency. Th e joint center and anatomical trajectories was fitted to an eight-segment musculoskeletal model generated using SIMM (MusculoGraphics, Inc.) consisting of a trunk (incl uding the mass of the torso, head and arms), pelvis and legs for each subject. Each lower extremity consisted of a thigh, shank and foot. The anthropometrics and inertial properties were based on that of de Leva . Joint positions and velocities were calculated within the SIMM Motion Module. The ki nematic variable calc ulated in this study included the Leg orientation at to e-off that was defined as the a ngle between the vector from the pelvis COM to the foot COM and ve rtical. Leg orientation is negati ve when the foot is posterior to the pelvis (Figure 6-2). Kinetic data: Three-dimensional GRFs were sampled at 2000 Hz. Ground reaction force data was low-pass filtered using a fourth-order zero-lag Butterworth filter with a 20 Hz cutoff frequency. The SIMM Motion Module (MusculoGraphi cs, Inc.) was used to perform a standard inverse dynamics analysis to determine the inter-segmental joint moments. Kinetic data (GRFs and joint moments) were normalized by subject b ody weight and to 100% of the paretic leg gait cycle (paretic heel strike to pare tic heel strike). Kinetic data included the pelvis velocity at toeoff, ankle joint center velocity at toe-off, Hip impulse and AP impulse (Figure 6-2). Hip impulse was calculated as the time integral of the hip mo ment during early swing and late swing. Positive moment indicated flex or moments and negativ e moments indicated extensor moments. AP
118 impulse was calculated as the time integral of the AP GRF during the si ngle-support phase of the contralateral leg occurring at the same instan ce as the ipsilateral sw ing phase (Figure 6-2). Positive impulses denoted propulsive (anterior) impulse and negative impulses denoted braking (posterior) impulse. Sub-division of the gait cycle: The stance phase of the gait cycle was subdivided into Bins to correspond with: the first double support phase following heel strike (Bin1), the first 50% of single leg stance (Bin 2), the second 50% of single leg stance (Bin 3) and the second double support phase during paretic pre-swing (Bin 4) Bins 1 through 4 were defined from GRF records. Additionally, the swing phase was sub-di vided into two phases: the first 50% of swing phase (Bin 5) and the second 50% of swing phase (Bin 6). The last instance of Bin 4 of stance phase was toe-off and the initial condition variables were calculated at this instance. The early and late hip impulses were calculated in Bin 5 and Bin 6 of swing pha se. The early and late contralateral AP impulses were calculated in Bin 2 and Bin 3 of stance phase. Statistical Analyses Stepwise Regression: Stepwise m odel-buildi ng techniques for regre ssion designs with a single dependent variable are described elsewhere . The basic procedures involve (1) identifying an initial model, (2) iteratively steppi ng, that is, repeatedly altering the model at the previous step by adding or removing a predictor variable in accordance with the stepping criteria, and (3) terminating the search when stepping is no longer po ssible given the stepping criteria, or when a specified maximu m number of steps has been reached. In this study, step length was the dependent variable and the selected kinematic and kinetic variables were the independent vari ables. A stepwise regression mode l was used to select critical predictors (from the 7 hypothesized variables) that could account for the variability in step lengths for individual part icipants and indicate how much variance in step length was explained
119 by these predictors (indicated by the R2 values ). Two regression models were built for each participants data to predict paretic and non-pa retic step length variability each. Therefore, overall 76 regression models were built for the 38 study participants. The step-wise regression was conducted by pooling individual steps from all trials together for individual participants. Note that for each participant different numbers of steps were analyzed (see Table 6-2 for the minimum number of steps analyzed) since each part icipant walked at their self-selected speed at a specific cadence. Only data from good steps of the participant were utilized (i.e., in the event that there was a crossover of a step these data were deleted for this step and the corresponding step). For some participants, there was a difference of 2-3 steps between paretic and non-paretic legs that depended on which leg took the first and last step. The stepping criteria for th is study was a significant relatio nship between the predictor variable and step length at p < .05. The chosen pr edictors could best expl ain the generated step lengths since they covaried (relat ed) with step lengths on a step-by-step basis. That is; greater or lesser value of the critical predictor variable th at was chosen related to longer or shorter step length in an individual partic ipant and therefore explained th e variability in step length generation in an individual participant. Entry p value for the stepwise regression model was set at less than 0.05 and removal p valu e was set at less than 0.10. Determination of step length asymmetry: St ep length asymmetry groups were determined based on the overground asymmetrical patterns in healthy control participants using a Paretic step ratio [PSR = Paretic step length/(Paretic + Non-paretic step length)] and expressed as a percentage . Asymmetry in the hemiparetic participants was characterized based on symmetry ranges calculated from similarly-aged healthy partic ipants, as follows: Longer
120 paretic steps than non-paretic (PSR > 52.5), Shorter paretic steps than non-paretic (PSR < 47.5) and Symmetric step lengths (47.5 PSR 52.5). Results Average gait characteris tics for individual part icipants with hemiparesis are presented in Table 6-2. There was no difference in step-by-step variability be tween paretic and non-paretic step lengths (p = .752). Majority of particip ants had paretic and nonparetic step length variability less than 5 cm (Figure 6-3). In general, greater variability was explained for the non-paretic step lengths than paretic for individual participants (com pare the difference in R2 values for individual participants in Tables 6-3 and 6-4). The explanat ory power of the models was also unrelated to the absolute magnitude of step-by-step variabil ity (standard deviation) in pare tic and non-paretic step lengths (p = .233). There were 2 participants for whom no predictor variables co uld explain the paretic step length variability at p < .05. In comparis on, there was no particip ant with unexplained nonparetic step length variability. Predictors of Step Length Variability and th e Differences in Selected Predictor V ariables across the Asymmetrical Sub-Groups Shorter paretic group For the paretic step length m odels, non-paretic AP impulse in late swing (APImp LS) was the most commonly selected variable related to paretic step lengths (Tab le 6-3). Further, it showed a positive association with step lengt hs wherever it was chosen. However, the nonparetic APImp LS occurring during paretic stepping were braking forces for several participants in this group (see Figure 6-4). Note that Pare tic Hip Impulse in early and late swing was not selected as a predictor variable related to paretic step lengt h variability in this group of participants.
121 For the non-paretic step length models, pa retic APImp LS was the most commonly selected variable related to non-paretic step le ngths (Table 6-4). The paretic APImp LS occurring during non-paretic stepping was propulsive in this phase. Unlik e for the paretic step length models, non-paretic Hip Impulse in early and late swing showed a significant posi tive relation to non-paretic step lengths in 3/6 pa rticipants. Specifically, the nonparetic hip impulse was flexor in these participants. Symmetric group For the paretic step length m odels, non-paretic APImp LS (in 7/10 participants) and paretic leg orientation at toe-off (in 6/10 participants ) were the most commonly selected variables related to variability in i ndividual participants. While non-paretic APImp LS was positively related to paretic step lengths (Table 6-3), pa retic LO was negatively related to step lengths. Further, non-paretic APImp LS was propulsive in all but one pa rticipant (H12) and paretic leg orientation was extension in all participants. For the non-paretic step length models, non-pareti c ankle joint center (A JC) velocity at toeoff (7/10 participants), non-paretic Hip Impulse in early swing and paretic APImp LS (6/10 participants) were most commonly selected vari ables that related to non-paretic step length variability. Further, all these variables were positively relate d to non-paretic step lengths. Specifically, hip impulse was flexor in early swing and paretic AP impulse was primarily propulsive in late swing. Longer paretic group For the paretic step length m odels, paretic hip impulse in early swing and non-paretic AP impulse in early swing (APImp ES) were the most commonly selected variables that related to paretic step length variability (1 2/22 participants selected these variables). Note that, APImp in this group was more commonly selected in the early swing than late compared to the Shorter and
122 Symmetric persons where APImp LS was more commonly selected (Table 6-3). However, paretic hip impulse in early sw ing showed a stronger relation with paretic step length in participants in this group compar ed to those selectively in the S horter paretic group (indicated in Table 6-3 by significant relations between, also refer to Figure 6-5). Both paretic hip impulse in early swing and non-paretic APImp ES were positively related to paretic step lengths (Figure 65). Note that paretic hip impulse in early swing was flexor in all participants. Non-paretic APImp ES was primarily propulsive in this phas e in majority of the participants (only 2/22 showed en tirely braking in this phase comp ared to most participants in Shorter paretic group who showed braking forces, Figure 6-4). For the non-paretic step length models, pareti c APImp LS and non-paretic hip impulse in early swing were most commonly se lected as predictors that related to non-paretic step length variability (15/22 participants showed significant relations for both of these variables). Both predictors were positively rela ted to non-paretic step lengths Non-paretic hip impulse was primarily flexor. Paretic APImp LS was primaril y braking in 10/22 partic ipants where it showed a significant relationship. Non-paretic AJC velocity at toe-of f (14/22 participants) was also among the commonly selected predic tors that related to non-paret ic step length variability. Discussion The purpose of this study was to comprehe nsively evaluate the m echanisms underlying step length generation during hemipa retic gait by determining those va riables that strongly relate to step length variability within -subjects. While recent work suggests potential mechanisms that might be related to step lengt hs during hemiparetic gait , there has been no systematic investigation to understand mechanisms underlyi ng step length generation during hemiparetic walking at a self-selected pace. To improve walking outcomes after a hemiparetic stroke, rehabilitation therapists commonly focus on incr easing the step lengths. Determining the most
123 significant predictors that relate to step-by-st ep variability in step lengths post-stroke, can provide insights on those parameters that can be ta rgeted to change step lengths (i.e., increase step lengths or even redu ce step length asymmetry). Overall, the range of variance explained by the regression models suggested that our hypotheses that the events occurring during a) th e initial conditions prio r to ipsilateral swing phase, b) ipsilateral swin g phase, and c) contralateral stance phase relates to step lengths. Our current methodology (of individual subject regression models) enabled us to determine several mechanisms underlying step length generation and also helped us to delineate differential mechanisms in sub-groups of this asymmetrical population. Specifically, w ithin-subject analyses as used in our study is specific to our study quest ion where we want to understand kinematic and kinetic variables that relate to step lengths in individual participants. Contralateral Stance Leg Ground Reaction Force (AP Impulse during Ipsilateral Sw ing) is a Significant Predictor of Step Length Variability In majority of participants contralateral AP impulse (pr opulsion mostly) occurring at the same instance as ipsilateral swing was the most commonly selected variable that was related positively to step length variability, suggesting that an increase in the contralateral AP impulse resulted in a longer ipsilateral step length in in dividual participants (Table 6-3, 6-4). However, sub-groups showing asymmetrical performance s howed a difference in selection of either contralateral AP impulse during its early versus late phase. In persons taking Symmetric and Shorter paretic steps, non-pare tic AP impulse during late no n-paretic single-support phase related strongly to paretic step lengths. Contrarily, in persons taking Longer paretic steps several persons showed a strong relation between non-paretic AP im pulse in the early phase and paretic step lengths (Figure 6-5). Further, since compared to the Shorter paretic and Symmetric group, persons in this group primarily showed non-paretic leg propulsion in its
124 early stance phase, it is likely that persons taking longer pareti c steps show additional increased non-paretic propulsive impulse that begins sooner in the gait cy cle (Figure 6-4). This greater non-paretic leg propulsive impulse might be propelling the tru nk further forward early during paretic leg swing phase resulting in the pare tic leg stepping longer than the non-paretic. Specifically, since impaired pare tic leg propulsion can be compen sated by increased non-paretic leg propulsion, persons in the L onger paretic group show greater compensatory non-paretic leg propulsion to offset the reduced paretic leg propulsion . Therefore, while increased nonparetic leg propulsion in general related to a longer step le ngth; greater compensatory nonparetic leg propulsion that begins sooner resulted in a rela tively longer paretic step than nonparetic in the Longer paretic group. Further, note that comp ared to the non-paretic leg propulsion being selected more in early stance than la te; the paretic leg pr opulsion is selected more in late stance than early and is also primarily braking in nature suggesting the reduced paretic leg propulsion in th e Longer paretic group. Ipsilateral Hip Impulse in Early Swing is a Significant P redictor of Step Length Variability in Persons taking Longer Paretic than Non-Paretic Steps Hip impulse during initial swing showed a str ong relationship to step lengths. It was selected as a significant predictor explaining paretic step length variability specifically in the Longer paretic group of participants and as an important predictor expl aining non-paretic step length variability in majority of participants. No te that in participants taking Shorter paretic steps, paretic hip impulse did not significantly ex plain paretic step length variability (Table 6-3). Whereas, in participants taking Longer paretic steps and Symmertic steps, hip impulse in initial swing was one of the important variab les (Longer paretic > Symmetric) chosen by the regression models. Furthermore, the hip impulse was primarily flexor during early swing (Figure
125 6-4) suggesting that this flexor moment during early swing was pivotal to accelerating the leg in this phase such that the step is longer. In particular, the weak relation between pare tic flexor moment in early swing and step length suggests that persons taki ng Shorter paretic step s might be at the limit of their paretic hip flexor moment generation ( due to impaired hip flexor ac tivity) such that it no longer correlates with step length on a st ep-by-step basis. Impaired pareti c flexor activity shortens the paretic steps relative to non-pare tic in the Shorter paretic gro up. Note that, the non-paretic hip impulse during early swing showed a significant re lationship to non-paretic step lengths in 3/6 participants further indicating the specific abse nce of relationship between paretic hip impulse and paretic step lengths in the Shorter paretic group (refer to Table 6-4) Therefore, we propose that the impaired paretic hip moment in early sw ing shortens the paretic step length resulting in asymmetrical shorter paretic steps than non-pa retic in this sub-group of participants. Note that while hip flexor moment in initia l swing was consistently positively related to step lengths, direction of relationship between hi p moments in late swing and step lengths was inconsistent. Hip moments during late swing can both accelerate and dece lerate the leg swing Flexor moments (from uniarticular hip flexors) during late swing can hold the leg longer in swing such that the leg steps longer, whereas ex tensor moments (often from biarticular muscles like hamstrings and gluteus maximus ) during late swing can terminate the swing phase such that the leg steps shorter. Inte restingly, most participants taki ng Shorter paretic steps showed paretic hip extensor moments, whereas 19/22 (H4 showed flexor activity) taking Longer paretic steps primarily showed hip flexor moments ev en in late swing phase (Figure 6-4). This observation further suggests the greater flexor related activity in the Longer paretic group compared to the Shorter paretic group. Furt her evaluation of EMG activity in individual
126 participants and similar model bu ilding using EMG activity to expl ain step length variability can help implicate the specific muscles responsible for these observed kinetic relationships. Ankle-Joint Center Velocity at Toe-Off is a Significant Predictor of Non-Paretic Step Length Variability Ankle joint center veloc ity at toe-off was significantly pos itively related to non-paretic step length variability in majority of participants, suggesting that greater AJC velocity at toe-off accelerates the foot forward into swing. Contrari ly, AJC velocity was not as commonly selected to explain paretic step length variability. AJC velocity at toe-off will be affected by ankle excursion (plantarflexion) at toe-off, ankle mu scle paresis, spasticit y, increased antagonist coactivation and increased passive stiffness . This indicate s that the paretic impairments commonly observed in majority of participants post-stroke can aff ect the AJC angular velocity at toe-off. Therefore, paretic AJC velocity at toeoff was not as strongly related to step lengths since majority of hemiparetic par ticipants might be at the limit of their paretic AJC velocity (due to impaired capacity). It is also possible that while there is little variation in AJC velocity withinsubjects, there would be considerable vari ation between-subjects and would contribute significantly to betw een-subject variation in step lengths. Leg Orientation at Toe-Off and Pelvis Velo city at Toe-Off and their Contributio n to Explaining Step Length Variability Leg orientation at toe-off was the second most commonly selected pred ictor variable that was significantly related to paretic step lengths in participants taking Symmetric steps. Note that, while it is expected that leg orientation would be negative at toe-off, there were seven hemiparetic participants (all taking Longer pareti c steps than non-paretic) with the leg oriented anterior to pelvis in this phase (i.e., showing positive values fo r paretic leg orientation for all steps that they walked) and four others who showed positive values for at least half of the steps that they took. Posterior leg orientation implies an extended leg at toe-off. Selection of paretic
127 leg orientation specifically in the symmetric gro up suggests that these persons might be attaining appropriate leg extension that would acts to direct the ground r eaction forces appropriately to propel the trunk forward at the term inal stance phase. Pelvis veloci ty at toe-off was significantly related to step lengths only in few participants; suggesting that the velocity of the body during the initial conditions prior to ipsilateral swing was not a strong predictor of step lengths. Within-Subjects Regression Models The within-subjects regression methodology as used in our study is different from conventionally used methodology where average data for individual subjects are used to build one regression model. Within-subject analyses as used in our study are specific to our study question where we want to determine parameters that influence the step length variability in individual participants. Since each participant wa lks at their self-selected speed and at a predetermined cadence that differs across participants grouping all subjects data would confound the results if we want to determine those predictors that significantly relate to step-by-step variability in step lengths. For instance, when we averaged the data for individual subjects and ran one regression model to understand paretic st ep length generation between-participants, the predictor variable that related to between-subj ects were leg orientati on at toe-off that was negatively related to step length and hip impulse in early swing that was positively related to step lengths. This result suggests th at longer or shorter paretic step length between-participants related to how their leg was or iented at toe-off and hip impulse in early swing. While this information is valuable to understand why some pe rsons take longer steps than others, in order to effect changes in individual patients' perfor mances, it would be more essential to understand which predictor variables resulted in an increase or decrease in step length. Such an approach of individual-subject anal yses has been highlighted in earlier work . Olney et al. (1994) in thei r attempt to understand the most cr itical variable s that predict
128 walking speed suggested that the regression analysis done on the subjects deviations from their averages (i.e., the within-subject analyses) is mo re appropriate if the aim were to understand what variables can affect individual persons pe rformance. They suggested that their withinsubjects regression analyses were appropriate because it shows that the walking speed of a subject increases with appropria te changes in the chosen pred ictor variables. They also acknowledged that on the other hand between-subject analyses were more appropriate if the aim were to determine those variables that predict the walking speeds of different subjects. The individual-subject regre ssion analyses as used in our st udy accounted for the step-by-step variability in the initial conditions, swing phase and contralateral stance phase mechanisms that control step lengths and theref ore, provide strong evidence fo r mechanisms of step length generation. Limitations Gait variables are expected to be correlated. This quality of the variables is described as "m ulticollinearity." Although multicollinearity can be a problem in some regression modeling, it does not interfere in our study because 1) we tried to select relati vely independent variables; 2) we only had 7 predictor variables, and 3) Step wise procedures mitigate against the retention of highly correlated predictor variables. It is possible that the step-bystep variability in step lengths was directly related to the e xplanatory power of the models; suggesting that increased or decreased model variance could be simply due to increased or decrea sed step variability. Nonetheless, we found that there was no signifi cant relationship betw een the step-by-step variability in step lengths and the varian ce explained by both the paretic and non-paretic regression models indicating the m odels specificity in selecting those variables that best related to paretic step lengths. Further, extrinsic s ources of error might ha ve increased the step variability (i.e., differences in marker placement from subject to subject). However, since we
129 used a within-subjects design these sources of variation were minimal. It is possible that there are other predictors that relate to step length va riability (e.g. knee and ankl e moments during initial conditions and during swing, pelvic displacements sp ecifically at the initial conditions prior to swing). Studies are warranted to systematically cons ider other predictors that might relate to step length variability. Conclusions Use of an individual-subjects design incorporat ing step-by-step variability in gait data helped us to determ ine the specific mechanisms that relate to step length generation. Based on chosen predictors that relate to step lengths, we are able to propose specific mechanisms that affect step length generation. Knowledge of thes e mechanisms, in turn, highlights rehabilitation strategies that can be targeted specifically to affect step le ngths and improve walking outcomes post-stroke. In the sub-group of persons taki ng Longer paretic step s than non-paretic, we suggest that improving paretic leg propulsion would increase the non-paretic step length that would reduce their asymmetry. On the other hand, in the sub-group taking Shorter paretic steps than non-paretic, improving the paretic hip flexor activity could lengthen the paretic steps and reduce their asymmetry. Future st udies should evaluate EMG muscle activity and its relation to step length variability to support and furthe r explain the current proposed mechanisms underlying step length generati on during hemiparetic walking.
130 Table 6-1. Subject characteristics Note that Fugl-meyer grading is based on scores from lower-exremity fugl-meyer scale (synergy portion only maximum score = 22). Severe 14, Moderate = 15 18, Mild 19.
131 Table 6-2. Average gait characterist ics for individual participants Note that min # of steps indicates the minimum number of good (paretic or non-paretic) steps that were used for data analyses for each participant pooling all trials together. Abbreviations: P Paretic; N Nonparetic; Cad Cadence; SL Step length; SwT Swing time.
132 Table 6-3. Regression models for individual particip ants to predict paretic step length variability Numbering (1, 2 ,3) indicates the order in which the predictors were chosen for the individual participants. nr indicates no result.Blue represents participants taking S horter paretic steps, Green repr esents participants taking Symmetric steps and Red represents participants taking Longer paretic steps (PSR > 52.5). Abbreviations: Sub ID Subject; PSR Paretic Step ratio; LO Leg orientation at toe-off; PV Pelvis velocity at toe-off; AJC Ankle joint center velocity at toe-off; Hip Imp ES Hip Impulse during Early (1st 50%) swing; Hip Imp LS Hip Impulse during late (2nd 50%) swing; cAPImp ES Cont ralateral AP impulse during ipsilateral early swing; cAPImp LS Contralateral AP impulse during ipsilateral late swing.
133 Table 6-4. Regression models for individual pa rticipants predicting non-paretic step length variability Numbering (1, 2 ,3) indicates the order in which the predictors were chosen for the individual participants. nr indicates no result.Blue represents participants taking S horter paretic steps, Green repr esents participants taking Symmetric steps and Red represents participants taking Longer paretic steps (PSR > 52.5). Abbreviations: Sub ID Subject; PSR Paretic Step ratio; LO Leg orientation at toe-off; PV Pelvis velocity at toe-off; AJC Ankle joint center velocity at toe-off; Hip Imp ES Hip Impulse during Early (1st 50%) swing; Hip Imp LS Hip Impulse during late (2nd 50%) swing; cAPImp ES Cont ralateral AP impulse during ipsilateral early swing; cAPImp LS Contralateral AP impulse during ipsilateral late swing.
134 Figure 6-1.An individual participant walking on the split belt treadmill as kinematic, kinetic and EMG data were recorded
135 Figure 6-2. Illustration of variables used in the study Kinematic and Kinetic profile is illustrated from one step duri ng walking for an individual participant. Note that all variables are normalized to the gait cycle. Red line indicates toe-off. Leg orientation, Pelvis velocity and Ankle joint center velocity calculated at toe-off were the initial condition variables. Hip impulse and Contralateral AP impulse during initial (1st 50%) and late (2nd 50%) swing were the swing phase variables calculated. Note that the impulse is calculated as the area under force curve. Raw profile for the Hip moment and AP GRF are not presented. The AP impulse presented in the figure is from the contralateral leg that is occurring at the same instance as the ipsilateral swing phase.
136 1.20 1.00 0.80 0.60 0.40 0.20 Paretic step length standard deviation (m) 20 15 10 5 0 Number of subjects MEAN = 0.36 m 1.20 1.00 0.80 0.60 0.40 0.20 Non-paretic step length standard deviation (m) 20 15 10 5 0 Number of subjects MEAN = 0.40 m Figure 6-3. Frequency distribut ion of step-to-step variab ility in step lengths.
137 A. Non-paretic AP Impulse Figure 6-4. Non-paretic AP impul se and Paretic hip impulse dur ing paretic stepping in the asymmetrical sub-groups
138 B. Hip Impulse Figure 6-4. Continued. This figure presents the non-paretic AP impulse and hi p impulse from individual steps for the asymmetrical subgroups (n = 28; 22 taking longer paretic steps and 6 taking shorter paretic steps). Each row of data is a simple dot plot of the AP impulse or hip impulse for individual participants. The participants are lined based on the ascending order of the asymmetry (note that symmetric persons have not been presented here). For AP impulse, positive values on the right represent propulsive forces and negative values on the left represent braking forces. For Hip impulse, positive values on the right represent flexor moment and negative values represent positive moments. Note that the non-paretic AP impulse in early swing is pr imarily propulsive for the Longer paretic persons compared to several shorter paretic persons showing braking forces. Similarly, the non-paretic AP impulse in late swing is propulsive for most participants taking longer paretic step s compared to 3 participants in the Shorter paretic group showing more braking. Paretic hip impulse was flexor in early swing for most participants. Conversely, hip impulse was extensor for at least some participants in the late swing. Participants taking shorter paretic steps showed extensor moments (4/6) while the most asymmetric longer paretic persons (bottom rows) showed primarily flexor moments.
139 0 0.5 1 1.5 2 2.5 3 3.5 4 0.220.270.320.37Paretic step length (m)Paretic Hip impulse in early swing 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.220.270.320.37Paretic step lengths (m)Non-paretic AP impulse Early swing Late swing Figure 6-5. Relationship between paretic hip impul se in early swing, non-pa retic AP impulse in early and late swing in an individual participant taking longer paretic steps than nonparetic PSR 69.8 Speed 0.30 m/s
140 CHAPTER 7 CONCLUSIONS: INTEGRATING THE FINDINGS The asymmetr ical nature of hemiparetic gait is extensively documented [12-15]. Yet, there is considerable disagreement in the literature regarding the clinical relevance of evaluating asymmetrical gait post-stroke. This disagreemen t stems from two conflicting suggestions in the literature. Some authors report that gait symmetry should be an ideal objective in walking rehabilitation post-stroke due to the apparently asymmetrical na ture of hemiparetic walking [12, 208, 209]. While others highlight that since compensatory strategies can promote functional performance, normalization of movement patte rns should not be the primary focus of gait rehabilitation [5, 18]. We suggest that, while gait symmetry need not be the primary focus for walking rehabilitation, gait asymmetry should be evaluated to identify the unique paretic leg motor deficits and to understand how the pareti c leg impairments might limit functional walking performance. This dissertation aimed at quantifying gait asymmetry, understanding its relationship to walking performance and investigating mech anisms underlying gait asymmetry. Specifically, stepping asymmetry was investigated since spatiotemporal characte ristics of steps are the final outcomes of all events occurring in the gait cycl e. Further, since the stepping measures can be easily recorded, transition of our results to clinical settings can be easily facilitated. Step Length Asymmetry during Hemiparetic Walking While tem poral asymmetry is well understood , step length asymmetry is not well quantified and its relation to hemiparetic walking performance is unclear. Therefore, in study one of this dissertation, we prim arily quantified the step lengt h asymmetry patterns during hemiparetic walking and proposed some underl ying mechanisms in the asymmetrical subgroups. We were able to quantify the step le ngth asymmetry patterns using a step length
141 asymmetry ratio and by relating the step length asymmetry to propulsive forces asymmetry. Our results also showed that while step length asymme try related to hemiparetic severity, it did not limit the attained walking speed highlighting ot her compensatory strategies to achieve the functional walking speeds. Our findings also sugg ested differing motor control mechanisms (i.e., ability to change speeds, weight supported on paretic leg) in persons showing different step length asymmetry patterns. Future work is encouraged to understand th e specific sensorimotor impairments related to the step length asym metry patterns and evaluate whether walking rehabilitation directed at these impairme nts can improve walking outcomes post-stroke. Step Variability during Hemiparetic Walking Study two of this dissertation investigated step variability to determ ine how gait variability m ight relate to asymmetrical walking post-stroke and whether measures of variability can be used as markers of impaired performance. Gait variability is shown to be strongly associated with motor and balance control during walking a nd suggested to be a quantifiable biomechanical marker to evaluates walking impairments . Our results revealed that increased variability in most spatiotemporal characteristics and reduced width variability related to poor performance outcomes (severe hemiparesis, asymmetrical gait and poor balance). Specif ically, results showed an asymmetry in swing and pre-swing time step vari ability in participants with the most impaired performance. There was no difference in step length variability between paretic and non-paretic steps, suggesting that the step length asymmetry patterns are relativ ely consistent from step to step during hemiparetic walking. Specifically since step variability is shown to strongly predict the risk for falling [98, 103], the finding that the asymmetrical groups showed greater step variability than the symmetrical persons sugge sts the dynamic balance impairments in these persons. Future research is warra nted to determine specific thres holds of step variability to further validate the use of variability measures as performance markers.
142 Asymmetrical Stepping in a Body Reference Frame Post-Stroke In study three of this dissertation, stepping asymm etry was quantified in a body reference frame. Literature shows that asymmetry in steps and asymmetry in body movements are investigated in isolation [11, 199] Nonetheless, since foot pla cement (during stepping) closely relates to body movements, it mi ght be essential to investigat e asymmetry in foot placement relative to body (rather th an in isolation). Our results showed that post-stroke anterior-posterior and medial-lateral foot placements were asymmetr ical relative to body and that this asymmetry related to step length asymmetry but not step widths. Wider pare tic foot placement relative to pelvis than non-paretic also re lated to reduced paretic leg weig ht support and lateral instability, encouraging the clinical utility of medial-lateral foot placement relative to pelvis. Since foot placement relative to body can be associated to forward progression and dynamic balance [132, 133], investigation of stepping asymmetry in a body reference frame also helped us propose underlying mechanisms of stepping asymmetry. Futu re studies are encouraged to evaluate the underlying kinematics of hip and knee to develop an integrated understanding of stepping in the asymmetrical groups. Step Length Generation during Hemiparetic Walking In study four of this dissertation, m echanisms of step length generation during hemiparetic walking were evaluated using a novel methodology that incorporated the step-by-step variability in step lengths. Literature sugge sts several potential i ndirect and direct mechanisms relates to step length [173, 182, 194] but there is no clear consen sus on predictors that relate to step length generation. Results revealed that contralateral anterior-posteri or and hip impulses during swing explained the step length variability in majority of participants. Relation of these predictors to step lengths differed based on st ep length asymmetry patterns, im plying differential mechanisms of step length generation across the sub-groups of persons showing differing step length
143 asymmetries. Compared to persons taking shorte r paretic steps or symmetric steps, persons taking longer paretic steps showed early stan ce phase non-paretic leg propulsion, suggesting increased non-paretic propulsive impulse beginning sooner in the gait cycle. In participants taking shorter paretic steps, paretic hip impulse in initial swing was not st rongly related to paretic step lengths unlike persons in other groups for whom hip flexor impulse was a strong predictor of paretic step lengths. Based on these observations, we suggest that in persons taking longer paretic steps than non-paretic, improving paretic leg propulsion would in crease the non-paretic step length and reduce their asymmetry. While in persons taking shorter paretic steps than nonparetic, improving the paretic hip flexor activity could lengthen the pareti c steps and reduce their asymmetry. Future studies should evaluate EMG muscle activity and its relation to step length variability to support and furt her explain the current propose d mechanisms underlying step length generation in the step length asymmetry groups. Summary Our findings suggest that steppi ng asymm etry is a clin ically relevant measure to evaluate paretic leg performance post-st roke. We propose step length as ymmetry, asymmetry in swing and pre-swing time step variability and medial-lateral f oot placement relative to the pelvis as outcomes of asymmetrical walking performance. Our findings also suggest differential motor control mechanisms in persons walking with differing step length asymmetry patterns. Results of this dissertation highlight the need to evaluate gait asym metry post-stroke which would, in turn, enable us to differentiate physiological restitution from compensation during walking. Clinically, specificity in evaluati on would help to tailor locomotor retraining specifically to address the root causes of impaired ambulation for each individual.
144 APPENDIX A LOWER EXREMITY FUGL-MEYER SCALE TEST ITEM SCOR ING CRITERIA Achilles 1. Reflex activity Patellar (KNEE FLEXION) 0-No reflex activity can be elicited 2-Reflex activity can be elicited 2. Within synergy Hip flexion (FLEXOR SYN HIP FLEX) Knee flexion (FLEXOR SYN KNEE FLEX) a. Flexor synergy (in supine) (FLEXOR SYN) Ankle dorsiflexion (FLEXOR SYN ANKLE DF) 0-cannot be performed at all 1-partial motion 2-full motion Hip extension (EXTENSOR SYN HIP EXT) Hip adduction (EXTENSOR SYN HIP ADD) Knee extension (EXTENSOR SYN KNEE EXT) b. Extensor synergy (in sidelying) (EXTENSOR SYN) Ankle plantarflexion (EXTR SYN ANKLE PF) 0-no motion 1-weak motion 2-almost full strength comapred to normal Knee flexion beyond 90 (COMBINE SYN KNEE FLEX) 0-no active motion 1-from slightly extended position, knee can be flexed, but not beyond 90 2-knee flexion beyond 90 3. Movement combining synergies (in sitting: knees free of chair) (COMBINE SYN) Ankle dorsiflexion (COMBINE SYN ANKLE DF) 0-no active flexion 1-incomplete active flexion 2-normal dorsiflexion Knee flexion (OUT OF SYN KNEE FLEX) 0-knee cnnot flex without hip flexion 1-knee begins flexion without hip flexion, but does not reach to 90, or hip flexes during motion 2-full motion as described 4. Movement out of synergy (in standing, hip at 0) (OUT OF SYN) Ankle dorsiflexion (OUT OF SYN ANKLE DF) 0-active motion 1-partial motion 2-full motion 5. Normal reflexes (sitting) Knee flexors Patellar Achilles 0-at least 2 of the 3 phasic reflexes are markedly hyperactive 1-one reflex is hyperactive, or at least 2 reflexes are lively 2-no more than one reflex is lively and none are hyperactive Tremor 0-marked tremor 1-slight tremor 2-no tremor Dysmetria 0-pronounced or unsystematic dysmetria 1-slight or systematic dysmetria 2-no dysmetria 6. Coordination/speed (supine : heel to opposite knee; 5 repititions in rapid succession) Speed 0-acticity is more than 6 seconds longer than unaffected side 1-(2-5) seconds longer than unaffected side 2-less than 2 seconds difference
145 APPENDIX B DYNAMIC GAIT INDEX SCALE Gait level surface _____ Instructions: Walk at your normal speed from here to the next mark (20) Grading: Mark the lowest category that applies. (3) Normal: Walks 20, no assistive devices, good sped, no evidence for imbalance, normal gait pattern (2) Mild Impairment: Walks 20, uses assistive devices, slower speed, mild gait deviations. (1) Moderate Impairment: Walks 20, slow speed, abnormal gait pattern, evidence for imbalance. (0) Severe Impairment: Cannot walk 20 without a ssistance, severe gait deviations or imbalance. Change in gait speed _____ Instructions: Begin walking at your normal pace (for 5), when I tell you go, walk as fast as you can (for 5). When I tell you slow, walk as slowly as you can (for 5). Grading: Mark the lowest category that applies. (3) Normal: Able to smoothly change walking speed without loss of balance or gait deviation. Shows a significant difference in walking speeds between normal, fast and slow speeds. (2) Mild Impairment: Is able to change speed but dem onstrates mild gait deviations, or not gait deviations but unable to achieve a significant change in velocity, or uses an assistive device. (1) Moderate Impairment: Makes only minor adjustments to walking speed, or accomplishes a change in speed with significant gait deviations, or changes speed but has significant gait deviations, or changes speed but loses balance but is able to recover and continue walking. (0) Severe Impairment: Cannot change speeds, or lo ses balance and has to reach for wall or be caught. Gait with horizontal head turns _____ Instructions: Begin walking at your normal pace. When I tell y ou to look right, keep wa lking straight, but turn your head to the right. Keep looking to the right until I tell you, look left, then keep walking straight and turn your head to the left. Keep your head to the left until I tell you look straight, then keep walking straight, but return your head to the center. Grading: Mark the lowest category that applies. (3) Normal: Performs head turns smoothly with no change in gait. (2) Mild Impairment: Performs head turns smoothly with slight change in gait velocity, i.e., minor disruption to smooth gait path or uses walking aid. (1) Moderate Impairment: Performs head turns with moderate change in gait velocity, slows down, staggers but recovers, can continue to walk. (0) Severe Impairment: Performs task with severe disruption of gait, i.e., staggers outside 15 path, loses balance, stops, reaches for wall. Gait with vertical head turns _____ Instructions: Begin walking at your normal pace. When I tell y ou to look up, keep walking straight, but tip your head up. Keep looking up until I tell you, look down, then keep walking straight and tip your head down. Keep your head down until I tell you look straight, then keep walking straight, but return your head to the center. Grading: Mark the lowest category that applies. (3) Normal: Performs head turns smoothly with no change in gait. (2) Mild Impairment: Performs head turns smoothly with slight change in gait velocity, i.e., minor disruption to smooth gait path or uses walking aid. (1) Moderate Impairment: Performs head turns with moderate change in gait velocity, slows down, staggers but recovers, can continue to walk. (0) Severe Impairment: Performs task with severe disruption of gait, i.e., staggers outside 15 path, loses balance, stops, reaches for wall.
146 Dynamic Gait Index continued. Gait and pivot turn _____ Instructions: Begin walking at your normal pace. When I tell you, turn and stop, turn as quickly as you can to face the opposite direction and stop. Grading: Mark the lowest category that applies. (3) Normal: Pivot turns safely within 3 seconds and stops quickly with no loss of balance. (2) Mild Impairment: Pivot turns safely in > 3 seconds and stops with no loss of balance. (1) Moderate Impairment: Turns slowly, requires verbal cueing, requires several small steps to catch balance following turn and stop. (0) Severe Impairment: Cannot turn safely requires assistance to turn and stop. Step over obstacle ____ Instructions: Begin walking at your normal speed. When you come to the shoebox, step over it, not around it, and keep walking. Grading: Mark the lowest category that applies. (3) Normal: Is able to step over the box without changing gait speed, no evidence of imbalance. (2) Mild Impairment: Is able to step over box, but must slow down and adjust steps to clear box safely. (1) Moderate Impairment: Is able to step over box but must stop, then step over. May require verbal cueing. (0) Severe Impairment: Cannot perform without assistance. Step around obstacles _____ Instructions: Begin walking at normal speed. When you come to the first cone (about 6 away), walk around the right side of it. When you come to the second cone (6 past first cone), walk around it to the left. Grading: Mark the lowest category that applies. (3) Normal: Is able to walk around cones safely without changing gait speed; no evidence of imbalance. (2) Mild Impairment: Is able to step around both cones, but must slow down and adjust steps to clear cones. (1) Moderate Impairment: Is able to clear cones but must significantly slow, speed to accomplish task, or requires verbal cueing. (0) Severe Impairment: Unable to clear cones, walks into one or both cones, or requires physical assistance. Steps _____ Instructions: Walk up these stairs as you would at home, i.e., using the railing if necessary. At the top, turn around and walk down. Grading: Mark the lowest category that applies. (3) Normal: Alternating feet, no rail. (2) Mild Impairment: Alternating feet, must use rail. (1) Moderate Impairment: Two feet to a stair, must use rail. (0) Severe Impairment: Cannot do safely. TOTAL SCORE: ___ / 24 Adapted from: Herdman SJ. Vestibular Rehabilitation. 2nd ed. Philadelphia, PA: F.A.Davis Co; 20
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163 BIOGRAPHICAL SKETCH Chitra Laks hmi K.Balasubramanian received her Bachelor in Phys ical Therapy from College of Allied Health Sciences, Manipal A cademy of Higher Education, Karnataka, India. She worked for one year imparting physical thera py to adults and children with disabilities in New Delhi, India. Her strong interest in an inte rdisciplinary approach to rehabilitation encouraged her to pursue the Rehabilitation Science Doctoral progra m at University of Florida. She was funded by the Alumni fellowship for four years of her graduate education and from an National Institutes of Health research grant for the final eight m onths of her doctoral education. Her research employed biomechanical measures to understand asym metrical nature of walking in persons who have had a stroke and she was guided under th e expert tutelage of Dr. Steve Kautz. In the near future, Chitra plans to use her doctoral education to actively pursue teaching and research in neurologically im paired populations. She is specifi cally interested in developing a scientific framework that will aid in designing efficient rehab ilitation strategies to improve walking function. In the long-term, she plans to re turn to India and aims to establish a strong foundation for rehabilitation education and relate d research and facilita te development of a common academic structure in rehabilitation.