Modelling the gait of healthy and post-stroke individuals

Faculdade de Engenharia da Universidade do Porto Modelling the gait of healthy and post-stroke individuals Morgana Pires Afonso Master’s degree in Bioengineering Supervisor: Prof. João Manuel R.S. Tavares Mechanical Engineering Department, FEUP Co-supervisor: Prof. Andreia Sofia Pinheiro Sousa Physiotherapy Department, ESTSP September 2015 ii © Morgana Pires Afonso, 2015 iii Resumo A locomoção é uma tarefa de grande importância na vida das pessoas. Mesmo que todos os indivíduos saudáveis apresentem uma variabilidade natural nos padrões da marcha, é possível definir um padrão aceitável para “marcha normal”. Contudo, algumas patologias podem induzir padrões de marcha anormais que podem limitar a vida de uma pessoa, tornandoa dependente de outros e, consequentemente, reduzindo a sua qualidade de vida. O acidente vascular encefálico (AVE) afeta 15 milhões de pessoas em cada ano, das quais 50% sofrem alterações da marcha não permanentes, de acordo com a Organização Mundial de Saúde. A marcha na sequência de um AVE é uma combinação de várias anomalias que dependem do indivíduo, da severidade e da localização do dano e do tempo decorrido após a ocorrência. A aplicação de um tratamento adequado nestes pacientes pode melhorar com o conhecimento de como a patologia afeta os músculos e os controlos nervosos associados a eles, permitindo desenhar soluções específicas e personalizadas a cada paciente. A análise experimental da marcha é de grande utilidade na extração de parâmetros de marcha, todavia, apresenta algumas fragilidades. Simulações computacionais dinâmicas, por outro lado, têm um grande potencial neste tipo de investigação e, combinada com dados experimentais, permitem a realização de estudos causa-efeito, sobre como músculos específicos afetam o movimento, por exemplo, em indivíduos que tenham sofrido um AVE. Neste trabalho, duas simulações computacionais foram desenvolvidas usando o OpenSim, a partir de dados cinemáticos e cinéticos obtidos em ensaios de marcha realizados num indivíduo saudável e outro na sequência de um AVE. Os dados experimentais foram extraídos de um ficheiro com a extensão *.c3d e pré-processados. Cada simulação começou com um modelo musculosquelético, que foi adaptado de acordo com a massa e dimensões do individuo posteriormente foram determinados os ângulos e momentos nas articulações por cinemática e dinâmica inversa; as forças e momentos residuais foram reduzidos e finalmente foi usado o “Computed Muscle Control” para determinar a contribuição muscular dos principais flexores plantares (soleus e gastrocnémio medial), flexor dorsal (tibial anterior) e um músculo da coxa iv (semimembranoso). Os ângulos e momentos nas articulações relativos ao indivíduo saudável revelaram-se de acordo com a referência. No entanto, os músculos analisados mostraram diferenças nos padrões de ativação. Na simulação envolvendo ao indivíduo pós AVE, verificouse alguma redução do ângulo e momento no tornozelo do membro afetado, mas a ativação e potência dos flexores plantares só foi reduzida no gastrocnémio medial. Por outro lado, verificou-se ativação prolongada do semimembranoso durante a fase de apoio do membro afetado. Os atuadores musculares não foram capazes de gerar a cinemática pretendida sem recorrer a forças residuais e de reserva e ainda foi verificado um erro alto no ângulo do tornozelo direito. v Abstract Locomotion is a task with great importance in the life of a person. Even though every healthy individual shows natural variability in gait patterns, it is possible to define an acceptable pattern for “normal gait”. However, some pathologies can induce abnormal gait patterns that can limit the life of a person, making him/her dependent of others and consequently reducing his/hers quality of life. Treatments involving rehabilitation or surgical procedures can revert or diminished the impairments in gait, showing good improvements on the people’s life. Stroke or cerebrovascular accident (CVA) affects 15 million people each year, from which 50% suffer non-permanent gait impairments, according to the World Health Organization. Gait after stroke is a combination of several abnormalities that depend on the individual, the severity and the location of the injury and the time passed after its occurrence. The application of an adequate treatment in these patients can be improved with the understanding of how the pathology affects the muscles, and the neural controls associated with it and allow to design specific solutions for each patient. Experimental gait analysis is useful in measuring important gait parameters, but it has limited capabilities. Computational dynamic simulations, on the other hand, have great potential in this type of investigation and, combined with the experimental data, allow performing cause-effect studies, about how specific muscles influence the movement, for example, in individuals affected in the sequence of a stroke. In the present work, two computational dynamic simulations were developed using OpenSim, using kinematic and kinetic data collected from a gait trail performed on a healthy and a poststroke individual. The experimental data was extracted from a *.c3d file and processed. Each simulation started from a musculoskeletal model, scaled according to the mass and dimensions of each individual; followed the determination of the joint angles and moments by solving an inverse kinematics and dynamics problem; then the residual forces were reduced and finally Computed Muscle Control was used to determine the muscle contributions for the gait of the principal plantarflexors (soleus and medial gastrocnemius) and dorsiflexors (tibialis anterior) vi and one hamstring (semimembranosus). The joint angles and moments relative to the healthy individual showed to be in agreement with the reference values for normal gait. However, the muscles analysed showed differences in the activation patterns. In the simulation involving a post-stroke individual it was verified lower plantarflexor angle and moment but the activation and power of the plantarflexor muscles were only reduced in the medial gastrocnemius of the impaired limb. On the other hand it was verified early activation of the plantarflexors and prolonged activation of the semimembranosus from the impaired limb during its stance. The muscular actuators were not able to track the kinematics without the use of residual and reserve forces and the right ankle had a high error associated. vii Acknowledgments I would like to thank to my supervisor and co-supervisor, Professor Dr. João Tavares and Dra. Andreia Sousa, for their attention, guidance and advice during the development of this work. Also I would like to thank to the Eng. Pedro Fonseca from the LABIOMEP for the provision of the experimental data and for the attention in answering my questions and to Dra. Augusta Silva for her help analysing the results. I would like to express my sincere gratitude to my family and friends, for their constant support and care. Finally I want to thank to God for the opportunities and people that He put in my path. viii ix xvi xvii List of tables Table 2. 1. Common spacio-temporal, kinematic and kinetic/EMG abnormalities in gait of post-stroke patients. ................................................................................. 17 Table 5.1. General gait parameters obtained for the Study 2 and Study 1. ...................... 55 Table 5. 2 Marker error (RMS) and maximum error associated with the scaling process for the models in the Study 2 and Study 1 and the respective limit values recommended in [50]. .................................................................................................. 56 Table 5. 3 Marker error (RMS) and maximum error associated with the scaling process for the models in the Study 2 and Study 1 and the respective limit values recommended in [50]. .................................................................................................. 60 Table 5. 4 Maximum and RMS values of the residual forces and moments and rotational errors obtained for the RRA of the Study 2 and Study 1 and the recommended [50] optimal and maximum thresholds. ................................................................. 66 Table 5. 5 Maximum and RMS values of the residual forces and moments, reserve forces and translational and rotational errors obtained for the CMC of the Study 2 and Study 1 and the recommended [50] optimal and maximum thresholds. .................... 67 Table 6.1 Correspondence between the marker set used in the gait trial performed in the LABIOMEP and the default marker set used in OpenSim. The X indicates that a marker is not included in the respective configuration. ....................................... 85 xviii xix Abbreviations and Symbols BTK Biomechanical ToolKit CE Contractile Element CMC Computed Muscle Control COM Centre of Mass CONTRA Contralateral COP Centre of Pressure CPG Central Pattern Generator CVA Cerebrovascular Accident DOF Degree of Freedom EMG Electromyography GRF Ground Reaction Force ID Inverse Dynamics IK Inverse Kinematics IPSI Ipsilateral LED Light Emitting Diode MEDGAS Medial gastrocnemius PEE Parallel Elastic Element PWA Point of Wrench Application RRA Residual Reduction Algorithm SEE Series Elastic Element SEMEMB Semimembranosus SOL Soleus TA Tibialis Anterior xx i Chapter 1 Introduction to the dissertation and its structure 1.1 - Introduction Locomotion is present in almost every animal and it is learned in the beginning of life. Terrestrial locomotion in humans, or gait, is of great importance in their daily life, since it is the vehicle for many other tasks. Biomechanical gait analysis can be based in experimental methods that allows the determination of important gait parameters (kinematic, kinetic and electromyographic). However, using uniquely this approach it is difficult to establish cause-effect relations between a specific muscle’s action and its contribution for the overall movement. Dynamic simulations are able to fill this gap since it enables the access to the inputs that generate the outputs assessed experimentally: the forces that originated the motions measured. This is due to the fact that the system (model) is known and is described mathematically. The description of the model is, however, complex and, as consequence, it is necessary to use computational tools to solve these equations. OpenSim is an example of a software designed for this purpose and allows performing dynamical simulations, using experimental data. The application of gait analysis in the clinical field, for example, in the characterizations of the impact of a pathology in gait or even as a diagnostic tool is possible. Subjects with stroke present several gait impairments that are dependent of numerous factors: brain area affected, time after the injury, physical characteristics of the patient, etc. The study of the muscle forces in these individuals permits the identification of the source of the damages and allows the creation of suitable therapeutic and/or surgical solution for each patient. Moreover, taking into account studies performed in healthy individuals, it contributes to the increase of the knowledge about the outcomes of this pathology. Introduction to the dissertation and its structure 2 1.2 - Objectives The main objectives of this monograph were the following: 1. Explore the fundamentals of the human gait, taking into account: a. The musculoskeletal system of the lower limb involved in the process: anatomical constitution (bones, joints and muscles) and function; b. Understand the process of gait as a coordinated movement as result of a complex system of neuromuscular control and study the gait cycle, by decomposing it in the respective phases and subphases in order to understand the sequence of events. c. Explore the concepts of gait abnormality and pathological gait and determine the consequences of a stroke in the task of walking, considering previous studies. 2. Elaborate a literature review addressing the following issues: a. Methodologies used currently in experimental gait analysis; b. Mathematical and mechanical models able to simulate the musculoskeletal system, the muscles and muscular control, developed to be used in computational simulations of gait; 3. Developed dynamic simulations of healthy and pathological gait in OpenSim, taking the following steps: a. Extract and process experimental data from a gait trial of a post stroke individual and prepare it to use as input in OpenSim; b. Execute the OpenSim workflow (choice of a musculoskeletal model, scaling, inverse kinematics, inverse dynamics, reduction of residuals and computed muscle control); 4. Compare the results obtained from the healthy and post stroke simulation and with the literature. 1.3 - Organizational Structure This dissertation is divided in six chapters, each one containing the respective introduction and summary. Next, is presented a brief description of each remainder chapter. Chapter 2 – Fundaments of Human Gait In this chapter the anatomical structures composing the lower limb and the pelvis (bones, joints and muscles) are described with interest in understanding their role in the walking task. In a second part, it is described normal gait and from the neuromuscular control involved, following by the characteristic gait cycle and the respective phases and subphases. Organizational Structure 3 Finally, are introduced the concepts of gait abnormality and pathological gait. A specific type of pathological gait, post-stroke gait, is explored. Considering experimental studies done with post-stroke individuals, the characteristics of this type of gait are enumerated and grouped according to their spacio-temporal, kinematic, kinetic and EMG nature. Chapter 3 – Literature review The state of art comprises the experimental and computational approaches of current gait analysis. In the first topic, the assessment of important gait parameters by visual gait analysis and the use of technological tools to extract kinematic and kinetic data, and the electrical activity of the muscles (EMG) is explained. In the second topic, regarding the computational analysis of gait, the models designed to simulate mathematically and mechanically the musculoskeletal system, the muscle tension paths, the operation of the muscles and tendons as an actuator, the muscular activation and the neuromuscular control are described. Chapter 4 – Methodology In the first part of this chapter, the method used for extracting the kinetic and kinematic data from a *.c3d and the respective processing is presented. In the second part, the computational environment, OpenSim, and its capabilities are introduced. Then, each step of the implemented workflow is described: the choice of the musculoskeletal model, the scaling process, the inverse kinematics and dynamics step, the reduction of the residuals and, finally the computed muscle control. Chapter 5 – Results and discussion In this chapter, the experimental data extracted from the *.c3d file and processed is analysed and discussed, as well as the methods used. Following the errors and the results obtained from each step of the workflow are presented and discussed, comparing the simulations developed for the healthy and the post-stroke individual with the literature. Chapter 6 - Final conclusions and future developments Being this the final chapter, it presents the general conclusions of the present study, as well as the limitations of this study and possible future developments. Introduction to the dissertation and its structure 4 Annex In the annex, the data that complement the understanding of the study is presented: a. Annex 1 list of body markers used in the LABIOMEP and in OpenSim; b. Annex 2: plots of the ground reaction moments filtered using different cut-off frequencies; c. Annex 3: weights used for each marker in the scaling process; d. Annex 4: weights attributed to each marker in the inverse kinematics process. 1.4 - Main Contributions The present work increases the knowledge about the sequence of procedures necessary to model gait, using OpenSim, starting with the generation of the input files in the appropriate format from a *.c3d file, which is a standard format among the biomechanical community, until the study of the muscular behaviour. It also explores the influences in considering the horizontal moments as part of the external forces and moments in the simulations of gait, that usually are not taken into account in some gait studies. 5 Chapter 2 Fundaments of Human Gait 2.1 - Introduction The understanding of anatomical organization of the lower limb and pelvis is fundamental in gait studies. The bones are rigid structures able to support the body and move. The movement is only ensured because of the existence of joints connecting the bones. Each joint allows one or more degrees of freedom, depending on its conformation. The muscles involve the skeletal system, being linked to the bones in insertion points through tendons. Due to this configuration, muscular contraction is capable of generate movement of bones around the joints. When several muscles are contracting, coordinated by the neural controls, complex movements can be made, for example, walking. Normal gait is difficult to define since there is some variability between healthy subjects, depending on the on the person sex, age, body geometry. Thus, the term “normal” has several definitions, according to the characteristics of the individual under study [1]. Gait is a complex task that involves nervous control to activate muscles and create a coordinated movement. The muscles are activated by electric impulses arriving through the neurons and sent from the mechanism controls. The high controls of locomotion are located in the brain, consisting in the brain cortex, basal ganglia and the cerebellum, and are responsible for planned actions by the person. The spinal cord is also important and it is there were the rhythmic and “automatic” movements of walking are generated. Another important aspect is that the control of gait counts with feedback mechanisms that help modulating the muscle excitations, such as muscle spindles, Golgi organs and mechanoreceptors in the skin. In order to study the gait cycle, it is necessary to focus our attention in one leg, since gait is symmetrical, and follows its movements through the cycle. Then it is possible to divide it in a Fundaments of Human Gait 12 The anterior compartment is formed by the quadriceps femoris group of muscles that have insertion in the patellar tendon: rectus femoris, vastus lateralis, medialis and intermedius. The sartorius, the longest muscle of the body is also part of this compartment [2]. The medial compartment is formed by the adductor muscles (brevis, longus and magnus), the gracilis and the pectineus, while the posterior, also called hamstring muscles include the biceps femoris, the semimembranosus and the semitendinosus [2]. Lastly, the muscles located in the leg, responsible for the movements of the ankle, foot and toes are classified in extrinsic and intrinsic. The extrinsic are also divided into three groups [2], based on their location: Anterior compartment: includes the extensor digitorum longus and hallucis longus, tibialis anterior and fibularis tertius and is responsible for dorsiflexion and eversion or inversion of the foot and extension of the toes; Lateral compartment: formed by the fibularis brevis and longus and involved in eversion of the foot and also plantar flexion; Posterior compartment: has superficial muscles, the gastrocnemius and soleus, which join the plantaris and form the calcaneal tendon (commonly known as Achilles tendon) and that are involved in plantar flexion of the foot. The deep muscles (flexor digitorum longus and hallucis longus, popliteus and tibialis posterior) act in flexion and inversion the toes. The intrinsic muscles of the foot are located inside the foot, in a similar structure of the hand and are responsible for toe flexion, extension, adduction and abduction [2]. 2.3 - Normal Gait 2.3.1 - Neuromuscular control Skeletal muscles are well-organized complex structures, composed by hundreds of fascicles, which consist in hundreds of muscle fibbers [1]. These are, in turn, an arrangement of filaments actin and myosin, which cause muscular contraction when they slide relatively to each other [1]. A motor unit is considered to be the combination of a neuron, and the muscle fibbers enervated by it and its branches [1, 4]. The neuron transmits electrical signals (activation potential) to each muscle fibber, causing the release of calcium ions, which will trigger the muscle contraction and generate movement, with consumption of metabolic energy [1, 4]. Muscular contraction can be isometric, if the muscle generates tension, but does not change its length; isotonic if the length changes, but the tension generated does not; concentric if the contraction causes muscle shortening; and eccentric if it causes lengthening [1]. Normal Gait 13 The walking movement was described as a complex interaction between supraspinal, spinal and afferent feedback mechanisms [5]. The supraspinal mechanisms are associated with the “fine control” of walking [6] and include [1, 7]: Motor cortex, which generates voluntary movement; Basal ganglia, responsible for planning and controlling parallel sequences of movements to produce complex movements; Cerebellum, responsible for the timing of muscular activities, namely in the smooth and rapid transition from one movement to another, thus being involved in the equilibrium of the body. Also helps in the control of intensity of muscular contraction. The spinal cord is responsible for the creation of reflexes that are fast reactions to a stimulus, detected by the afferent feedback mechanisms [1, 6]. The afferent feedback mechanisms include: muscle spindles, sensorial receptors located in the muscles responsible for muscle length and velocity feedback; Golgi organs, in charge for force feedback; and mechanoreceptors in the joints and skin, which give cutaneous feedback [5]. These mechanisms allow the adaptation of gait to the environment stimuli [8]. In the spinal cord, there are also Central Pattern Generators (CPG), which consist in networks of nervous cells [1, 8, 9]. Associated with the afferent feedback mechanism, the CPG produce rhythmic movements like walking, without conscious effort [6]. Even though the existence of these in quadruped animals was already proved, the evidence of those in human stills indirect [6, 10]. 2.3.2 - Gait Cycle Gait cycle is defined as the interval between two successive occurrences in the process of walking. For example, if it is considered the contact of the right foot with the ground (“initial contact”) as the beginning of the cycle, then the cycle ends in the next contact between the right foot and the ground [1, 11]. This period is characterized by a stance phase, during which the foot is in contact with the ground, and a swing phase, where the limb swings in the air [1, 11]. When one leg is the stance phase, the opposite is in swing phase, excluding the moment of double contact, in which both are in stance phase (Figure 2.4). Fundaments of Human Gait 14 Figure 2.4. Diagram of the gait phases for left and right legs [1]. The stance phase lasts approximately 60% of the gait cycle [11] and begins with the initial contact and ends with the toe off of the same leg. It comprises four subphases (Figure 2.5) [1, 11]: 1. Initial contact: the initial stage of the loading response, when the heel of the right foot contacts with the ground. It is characterized by hip flexion, knee extension and neutral dorsiflexion of the ankle. The ground reaction force has upwards direction; 2. Loading response: occurs after the initial contact and before opposite toe-off, when both feet are in contact with the ground and the weight of the body is transferred from the left leg to the right one. In this phase the ankle presents plantarflexion and the ground reaction force increases its magnitude and direction from upwards to upwards and backwards; 3. Mid-stance: occurs after the opposite toe-off and before the heel rise. It corresponds to the moment when the left leg is in the swing phase and passes the right one. The hip increases the extension, which is achieved mainly because of the inertia and gravity, while the knee is reaches the highest flexion point of the stance phase before it starts to extend. The ankle, which was in plantarflexion changes to dorsiflexion. The ground reaction force moves forward along the foot, from the moment when the foot is in full contact with the ground [1]; 4. Terminal stance: corresponds to the moment when the heel of right foot starts to leave the ground, before the left foot toe contacts with it [11]. The heel rise is characterized by peaks of hip and knee extension and ankle dorsiflexion. In opposite initial contact, the hip reaches the highest extension angle, while the knee starts flexing and the ankle moves into plantarflexion. During this phase, the ground reaction force moves forward [1]; Normal Gait 15 5. Pre-swing: is characterized by double support, since the left foot contacts with the walking surface and the body weight is shared between the two legs and it lasts until the toe off moment, which separates the stance phase from the swing phase [1, 11]. The remaining 40% of the cycle consists in the swing phase (Figure 2.4), which is subdivided in: 1. Initial swing: occurs when the right foot leaves the ground. The hip is flexed as well as the knee, and the ankle reaches the peak of plantarflexion immediately after the toeoff. The ground reaction force is positioned behind the knee and becomes zero when the foot leaves ground [1]; 2. Mid-swing: starts with the feet adjacent, when the right and left legs are side by side and ends with the tibia vertical. In the first step, the hip continues to flex and the knee is also flexed, mostly as consequence of the hip flexion. The ankle moves to an attitude considered neutral or dorsiflexed. The ground reaction force is null, since the right foot is in the air [1]; 3. Terminal swing: begins with tibia vertical, consisting on the tibia of the right leg being in a vertical position. The flexion of the hip ends, the knee is passively extended, and the ankle is between slight plantarflexion and dorsiflexion. This phase ends with the initial contact, which marks the beginning of a new cycle [1]. Figure 2.5. Stance and swing phases diagram and the respective subphases [1]. Fundaments of Human Gait 16 2.4 - Gait Disturbance 2.4.1 - Abnormal and pathological gait Some gait characteristics vary from person to person; however, it is possible to quantify some variables that allow to define or acceptable range of values that characterize a normal gait pattern [1]. Gait is generally accomplished by four main tasks [1, 12]: - Maintenance of the balance of the trunk, arms and head either statically or dynamically; - The stance leg must be able to support the body weight; - The swinging leg must advance to a position in order to accept the body weight transference; - The energy supply must be enough to allow the forward movements. It is considered that if at least one of these requirements is not fulfilled or the individual can perform all the tasks, but with extra energy consumption or with the need of walking aids (for example, canes), has a gait abnormality [1]. It is important to distinguish the term gait abnormality from pathological gait. Gait abnormality is the description of some gait characteristics that can be visually identified or by using experimental gait analysis methods (discussed in the chapter 3) and can include, for example: trunk bending, circumduction, hip hiking, vaulting, abnormal hip rotation, excessive knee extension/flexion, inadequate dorsiflexion control, abnormal foot contact, insufficient pushoff, abnormal walking base, rhythmic disturbances, etc. [1] Pathological gait is related with a pathology, such as cerebral palsy, myelomeningocele, Parkinson’s disease, stroke, etc. [1]. The gait patterns associated can include a single abnormality or a combination of several, which can interact between them and may change with time and therapy and vary from person to person [1, 13]. In pathological gait, an abnormality may result directly from any muscular or neural impairment such as muscle weakness, some deformity or spasticity, or be the consequence of a compensation of an impairment, being named in this case as adaptation [1, 12]. 2.4.2 - Post-stroke gait Cerebrovascular accident (CVA), commonly referred as stroke, is the death of brain tissue as consequence of a disturbance of the arterial blood supply [2, 12]. There are two types of stroke: haemorrhagic stroke that results from artery bleeding inside the brain and ischemic stroke that is consequence of the blockage of brain arteries by a thrombus, a blood clot, a fat globule or a gas bubble [2]. The outcomes of a stroke are dependent on the area of the brain which suffers Gait Disturbance 17 the temporary privation of blood and can include loss of communication and vision capabilities and abnormalities in the motor system. The most frequent case is the one in which one of the sides of the territory irrigated by the middle cerebral artery is affected and some motor functions are damaged, causing motor control disorders in the opposite side of the body [14]. In addition, motor function can also be impaired if the midbrain is injured because this can block nerve conduction the pathways between the brain and spinal cord, affecting the sensorial and motor systems and, consequently, abnormal gait [7]. Post-stroke patients suffer neurological and motor sequels, but more than 85% of stroke survivors are able to walk with or without assistance [15]. There is some variability of gait abnormalities between individuals following stroke, and they depend on the time after the injury, as well if the patient received rehabilitation therapy [12, 13]. Hemiparesis, one of the most common impairments [16], is the affection of one side of the body due to defective muscle activation [17]. In several studies, muscle activity was measured by electromyography (EMG), showing alterations in the magnitude and phase of the muscular activity patterns, comparing to health individuals and abnormalities on both the contralesional (CONTRA) and ipsilesional (IPSI) sides, leading to bilateral differences [18, 19]. Pronounced asymmetry in gait pattern, due to hemiparesis, may change some temporal, spacial, kinetic and kinematic gait variables [16]. Table 2.1 is presents a list of gait common impairments associated to post-stroke gait. Table 2. 1. Common spacio-temporal, kinematic and kinetic/EMG abnormalities in gait of post-stroke patients. Gait modifications Spaciotemporal [12, 13] - Reduced walking velocity; - Shorter stride length; - Longer gait cycle duration; - Longer proportion of double-support phase and stance/swing phases of both legs. Kinematics [19] - General decrease of joint peak displacements at the hip, knee and ankle. Sagittal plane - Decreased hip extension during stance and decreased hip flexion during swing; - Higher ankle plantarflexion at initial contact [13]; - Knee hyperextension during weight acceptance; Fundaments of Human Gait 18 - Decrease of knee flexion and absence of dorsiflexion at swing phase. Horizontal plane - Larger external rotation of the paretic hip and knee; Frontal plane - Larger abduction of the hip and large inversion of the ankle in the paretic side; - Larger pelvic hiking and lateral displacement. EMG/Kinetics - Weakness of the paretic muscles, suggested by the overall decrease of EMG levels in the paretic side [12, 19]; - Reduction of the plantarflexion moment in both sides in the correspondent late stance phases [17]: - Paretic side: attributed to the early and reduced EMG activity of the paretic plantarflexors (namely medial gastrocnemius); - Ipsilesional side: related with excessive antagonist coactivation as an adaptation for postural instability caused by impaired gait; - Prolonged stance co-activation of hamstrings and the quadriceps muscles in both sides (acting as compensatory mechanism for the weakness of the plantarflexors, which have been found to have the largest contribution to support during the single leg stance phase [16, 20, 21] ; - Hyperactive stretch reflexes that may cause knee hyperextension and hinder dorsiflexion in late stance phase, interfering with push-off [17]. Besides, plantarflexors generate large part of the energy to move the limbs forward during the push-off phase. This group of muscles, specifically the soleus and the gastrocnemius, showed insufficient power generation in the contralesional side [22]; - Reduction of the dorsiflexion moment in the swing phase, in the contralesional side caused by weakness of ankle dorsiflexors, namely tibilalis anterior, combined with increased plantarflexor passive stiffness [15, 17]; Gait Disturbance 19 - Dynamic spasticity of the plantarflexors and weakness of the dorsiflexors during loading response are responsible for the increasing of the step length [15, 17, 23]. - Concerning the power it is verified differences between slow and fast walkers[17]: - Slow walkers: Lower late stance ankle pull-off (A2: second ankle power burst) and early swing hip pull-off (H3: third hip power burst) propulsive power bursts on both sides; - Fast walkers: Larger positive work by both hip extensors in early stance (H1: first hip power burst) and, in the contralesional side, by the H3 propulsive power burst. Spasticity is verified in 20-30% of the post-stroke patients [5, 12]. It is defined as a “motor disorder by velocity-dependent increase in tonic stretch reflexes (muscle tone) with exaggerated tendon jerks, resulting from hyper excitability of the tendon reflex” [5]. However, there is controversy between the authors about the contribution of the spasticity in post-stroke gait impairments [15, 21]. These impairments lead to a higher energetic cost, at the biological (metabolic) and mechanic levels [12, 13, 16]. The metabolic cost in hemiplegic gait was found to be 50% to 97% higher than in healthy subjects [18]. Lamontagne et al. [17] reported that this general higher energetic cost may be related to the excessive co-activation of antagonistic muscles. 2.5 - Summary The lower limb is composed by several bones, joint and muscles, organized similarly to the upper limb in some aspects. The localization of the muscles as well as their insertion in the bones is directly linked with the movement they generate. Considering their action, muscles can also be grouped, for example, the group of the hip flexors, which are involved in flexion of the hip. The fact that the joints in lower limb (and also the upper limb) system are synovial is important considering that the relative movement of the limbs and the simultaneous task of supporting Fundaments of Human Gait 20 the body weight lead to a high friction between the bones that could increase the wear if the joint was not equipped with cartilage, synovial lubricant and other mechanisms. The hip, knee and ankle joints and associated bones and muscles must receive special attention since considerable amount of movement are generated there. On the other hand, the joints in the pelvis and in the foot are very restrictive of the motion, when compared to these joints. Human gait involves control by supraspinal and spinal mechanisms that transmit electric signals to the muscles in order to generate the desired movement. In the particular case of locomotion, there are indirect evidences of a control center in the spinal cord, responsible for the generation of unconscious stepping. The gait cycle is divided in the stance and swing phases, which in turn are divided into five and three subphases, respectively. This method allows the study of the sequential events in terms of moments of the segments, ground reaction forces and muscles involved to achieve the task of locomotion. Gait abnormalities following stroke are mostly the consequence of the weakness of the muscles of one side of the body. Spasticity, however, has a neural origin, but there is still disagreement between the studies performed, about the influence of it in post-stroke gait. In the sequence of these disabilities, the affected individual develops mechanisms of compensation, with the objective of allowing his locomotion. Nevertheless, these are also classified as gait abnormalities. In the sequence of a stroke, patients must receive rehabilitation therapy in order to minimize or eliminate its outcomes and improve their quality of life. 21 Chapter 3 Related Work 3.1 - Introduction Human gait can be studied using an experimental approach by measuring several parameters that characterize gait, with the aid of the latest technologies available for this purpose. Many research laboratories and specialized clinics can perform this studies for purposes of research or to help in the process of rehabilitation. With the development of new complex models simulating the human body and the development of the computers, it became possible to combine the data collected experimentally with computational models and make dynamic simulations, able to estimate, for example, the individual muscle contributions for the movement. Studies aiming to test hypothesis (“what if” studies), such as see what happens when a muscular excitation pattern is modified [24] are also possible using computational simulations, which is hard to implement experimentally. In this chapter, the experimental methodologies to assess kinematic, kinetic measurements and muscle activity are reviewed. Afterwards, the mathematical models currently used with the aim to represent the biological structures (muscles, bones, ligaments) and the respective control are analysed. Finally, an overview of OpenSim, the software to be used, is given. 3.2 - Experimental methods for gait analysis Gait analysis is defined as “the systematic measurement, description, and assessment of those quantities though to characterize human locomotion” [25]. The study of human locomotion has been increasingly used in the last decades in the fields of sports, rehabilitation [26] and in research [17]. Roy B. et al [25], in 1991, defined clinical gait analysis as the use of gait analysis in which the clinician quantitatively examines the outcomes of a certain disease or injury suffered for the Related Work 28 3.3.2 - Muscle paths The muscles and tendons are assumed to be inserted in a single point in the bones and muscles which insert in the bone through a large area are modeled using more than one portion with only two insertion extremities [35]. The forces generated by each muscle are applied to the segments through a tensile path [39]. This path can be considered as a simple straight line, though this method can lead to errors when the muscle wraps around another component like a bone or another muscle [35]. Another possibility is to represent the muscle’s path through its cross-sectional centroids. However, this method presents several problems because it is hard to determine these points for every joint configuration [40]. An alternative method consists in establishing specific points along the cross-sectional centroid’s path, which are fixed in the structures where the muscle wraps and are linked by straight lines or curved segments [35] (Figure 3.2). Figure 3.2. Three dimensional representation of the shank, foot and toes and the tensile path of the soleus muscle (single straight line) and of the peroneus longus, with a series of line segments and constrained “via points” [41]. Another option is the obstacle-set approach that allows does not constraint the muscle path in the contact with the other segments (bones and/or muscles), allowing it to move freely over the neighboring structures [40]. 3.3.3 - Muscle-tendon actuator model The Hill-type muscle-tendon actuator model was widely adopted in computational dynamical simulations since it is considered efficient and usable in several movements and has computational reduced cost [4, 20, 22, 38]. Originally, the model was developed by A. V. Hill and it was only composed by two elements [4], but since then it was improved and the version currently used is composed by a muscle with three elements and a tendon, as shown in Figure Computational modelling and simulation of the human gait 29 3.3. The CE is a contractile element, where the force is generated and able to model the forcelength-velocity property, and the SEE and the PEE are elastic elements (springs) positioned, respectively, in series and in parallel [38]. The first one is responsible for modelling the muscle active stiffness and the latter one models muscle passive stiffness [35]. In this model, the tendon is assumed to be an elastic element. However, it is known that the force associated varies non-linearly as the length of the tendon changes and that this simplification does not affect significantly the overall behavior [35]. Figure 3.3. Hill-type muscle-tendon actuator, composed by a tendon in series with the muscle. The muscle is modeled by a contractile element (CE) in series with an elastic element (SEE) and in parallel with another elastic element (PEE) [38]. The muscle-tendon dynamic behavior is governed by a single non-linear differential equation [38]: 𝐹󰇗𝑀𝑇=𝑓(𝐹𝑀𝑇,𝑙𝑀𝑇,𝑣𝑀𝑇,𝑎𝑚),0≤ 𝑎𝑚≤1 (3.2) where: 𝐹𝑀𝑇 is musculo-tendon force; 𝐹󰇗𝑀𝑇 is the rate of change of the muscle-tendon force; 𝑙𝑀𝑇 is the musculo-tendon length; 𝑣𝑀𝑇is the musculo-tendon shortening velocity and 𝑎𝑚 is the muscle activation. Related Work 30 3.3.4 - Muscle activation model The excitation-contraction coupling has two steps (Figure 3.4): activation dynamics, consisting in the transduction of the neural stimulus into activation of the contractile element, and contraction dynamics, the transformation of activation into muscle contraction [39]. Figure 3.4. Musculo-tendon actuator dynamics [38]. There is a delay in time between the neural signal (excitation) and the consequent muscle activation (activation), due to the kinetics of chemical processes involving the calcium molecules [35, 39]. Consequently, several studies concerning gait analysis take in consideration this process [39], which is modeled by first-order differential equation: 𝑎󰇗𝑚=(1 𝜏𝑟𝑖𝑠𝑒)(𝑢2−𝑢𝑎𝑚)+(1 𝜏𝑓𝑎𝑙𝑙)(𝑢−𝑎𝑚);𝑢=𝑢(𝑡); 𝑎𝑚=𝑎𝑚(𝑡) (3.3) where: 𝑎𝑚 and 𝑎󰇗𝑚 are the muscular activation and the rate of muscular activation, respectively; 𝑢 is the muscle excitation; 𝜏𝑟𝑖𝑠𝑒 and 𝜏𝑓𝑎𝑙𝑙 are the time constants for rise and fall, respectively. 3.3.5 - Neuromuscular control model Having a musculoskeletal model built, it is necessary to define the control of the muscle excitation, so that realistic movements are produced [38]. There are admitted two basic approaches to do this: a dynamic optimization and a tracking solution problem [33, 35, 38]. Using dynamic optimization, it is necessary to define clearly an objective task/function in order to find the muscle controls that permit to achieve that objective [33, 38]. In the sports field, this method could be applied in studies where the objective task was, for example, the maximum height jumping [42], maximum speed pedaling [43] and maximum distance throwing [44]. In walking, Anderson and Pandy assumed that the objective function is the minimization of the metabolic energy consumed per distance unit, and the results of their study showed that the muscle function can be well described by assuming this objective function [45]. However, when we are dealing with the human gait, the objective task can be ambiguous in some cases [35]. An alternative method consists in solving the optimal tracking problem, by guiding the muscular controls in order to obtain the minimal difference between the simulation data and the Computational modelling and simulation of the human gait 31 experimental data, by means of a least-squares approach [33, 38]. This solution is considered to be the suitable in simulations concerning subject-specific gait and pathological gait and to quantify the muscle contributions, identify joint loading and injuries [33, 38]. 3.3.6 - Assessment of the muscle forces The determination of muscle forces and the understanding of how a muscle affects the movement of the joints, and the segments can be done by using a musculoskeletal model as described in Figure 3.5, applying a forward or inverse dynamics strategy [35, 38]. Figure 3.5. Diagram of the forward dynamics (top) and the inverse dynamics (bottom) methods [46]. Inverse dynamics (Figure 3.5) uses as input the body motions, which are differentiated and used to compute the muscle forces, by using the ground reaction forces and the joint moments in the classical Newton-Euler equations of motion [47]: 𝐹=𝑚𝑎 (3.4) 𝑀 󰇍 󰇍  =𝐼𝛼 (3.5) where 𝐹 is the force; 𝑎 is the acceleration; 𝑀 󰇍 󰇍  is the moment and is the angular acceleration. The other approach is forward dynamics, in which the inputs of the system are the muscle excitations and when applied in the muscle-tendon model (taking into account the coupling Related Work 32 excitation-activation) it is possible to obtain the muscle forces (Figure 3.5). Using these forces and the other elements (musculoskeletal model and skeletal dynamics) it is possible to obtain the movements generated by the input excitations [35]. The number of muscles acting in one joint is greater than its number of DOF, consequently an optimization strategy is usually used when considering these two approaches. Using inverse dynamics, the muscle forces are determined using static optimization, which solves a different optimization problem at each instant of the movement, to determine the muscle forces from the joint kinematics. On the other hand, in the case of forward dynamics, if a goal or motor task is defined, it is possible to use dynamic optimization, in which a single optimization problem is solved for the complete cycle of the movement, being this approach more expensive computationally [35]. Therefore, dynamic optimization is used, for example, in studies related to sport performance, in which the objective or task desired is defined and the muscle activations are known [35]. 3.4 - Summary Experimental gait analysis techniques give useful information about the quantifiable characteristics of gait, but the use of this data in computational simulations is showing good results in assessing quantities not measurable experimentally. These simulations use mathematical/mechanical models, described by complex equations, which need to be treated and analyzed using computers. 33 Chapter 4 Methodology 4.1 - Introduction Biomechanical laboratories around the world use different 3-D motion capture systems and software to collect their data, making more complicated sharing the data between users due to problems of software compatibility [48]. The situation has changed with the introduction of the *.c3d file format, that began in 1987 and since then it has been gradually adopted by the community, becoming a standard. *.c3d is a public domain type of binary file format to record and store synchronized 3D, analog and EMG raw data, processed data (for example gait events) and general information about the trial (instrumentation and software used and characteristics of the subject) [48]. Computational simulations are useful to study human motion, which involves complex mechanisms of control and actuation and frequently start from experimental data. OpenSim is a relatively new software that can be used to perform this type of simulations since it permits the understanding of how muscle actuates to reproduce a specific movement [39, 49, 50]. Thanks to its versatility (it allows to create and change the models and add components), has been used not only to study healthy movements of the human body, but as well pathological motion [51, 52]. Typically, a simulation starts from choosing a model and the data, conveniently treated and stored in the appropriate file format, serves as input. An OpenSim simulation consists in a sequence of steps, where the outputs from the previous step are used as inputs in the following, making necessary to reduce the errors as possible to avoid its accumulation. OpenSim requires, however, that the experimental data used as input to be in a specific format: for the kinematic data uses the format *.trc (Track Row Column), created by Motion Analysis Corporation and for the kinetic data the format *.mot (Motion), created by the developers of SIMM (Software for Interactive Musculoskeletal Modelling) [50]. If the experimental data is stored in a *.c3d file, is possible to extract it using, for example, the Biomechanical Toolkit Methodology 34 (BTK), which is an open-source and cross-platform library of functions to read, write and modify acquisition files. These operations can be performed in Matlab, by using the Matlab wrapper [53] and writing the files in the adequate format to use as input. The experimental data relative to a post-stroke individual was collected in the LABIOMEP and saved in *.c3d format. Matlab was used to extract and process the data and to extract the gait events, necessary to obtain one gait cycle to perform the biomechanical simulation that will be described in the Chapter 4. In the second part of this chapter, it will be described the each step of the workflow of biomechanical simulation using OpenSim. A model of the head, torso and lower limbs was used to reproduce the data recorded from a post-stroke patient and a healthy individual. The kinematics and joint moments were determined, as well as the muscular activations and powers. 4.2 - Experimental data treatment and analysis 4.2.1 - Kinematic and kinetic data The kinematic and kinetic data relative to a post-stroke subject was previously collected in the LABIOMEP, performing a gait trail with a male subject of 55 years old, 1,75 m height and 96Kg. The patient has suffered a CVA and he was mainly affected in the upper limbs. Consequently, the lower limb performance in gait was not substantially impaired. The patient pathology historical was not detailed known, the only information available was that his treatment included the application of botulin toxin only in the upper limbs. The kinematic data was acquired using a motion capture system 3D Qualisys™ Oqus Camera Series system, operating at 200 Hz with 12 cameras retroreflectors of infrared light and 32 reflector (passive) body markers. The marker data was acquired using the native software, Qualisys Track Manager. The configuration of the markers of the torso and lower limbs is shown in the Figure 4.1. Experimental data treatment and analysis 35 Figure 4.1. Location of the markers used in the gait trial performed in the LABIOMEP in a post-stroke patient: RAC – right acromion; LAC – left acromion; C7 – vertebra C7; STERN – sternum; RASIS – right superior iliac spine; LASIS – left superior iliac spine; RPSIS – right posterior superior iliac spine; LPSIS – left posterior iliac spine; RMK – right medial knee; LMK – left medial knee; RLK – right lateral knee; LLK – left lateral knee; RMA – right medial ankle; LMA – left lateral ankle; RLA – right lateral ankle; LLA – left medial ankle; RFOOT1 – right foot proximal phalange 5; LFOOT1 – left foot proximal phalange 5; RFOOT4 – right foot proximal phalange 5; LFOOT4 – left foot proximal phalange 5; RBACKFOOT – right back foot; LBACKFOOT – left back foot. (Only the markers of the torso and lower limbs, used in this study, are represented. The 10 markers used in the lower limbs are not shown). During the trial, the subject walked over a set of six force platforms disposed as shown in the Figure 4.2, allowing the temporal synchronization between the kinematic and kinetic data. The platforms 1, 2 and 6 (Bertec FP4060) and 3, 4 (Bertec FP6090) were type 2 extensiometric. The platform 5 was piezoelectric, type 3 (Kistler 9281E). The subject stepped in the platforms 2, 3, 4 and 6 and the data was collected with a sampling frequency of 2000 Hz. Methodology 36 Figure 4.2. Force platform disposition in the floor during the gait trial in the LABIOMEP. The force platforms in which the subject stepped are shown in orange (2, 3, 4 and 6). Image obtained using the software Mokka. 4.2.2 - Data extracting and pre-processing The data resulting from the trial described above was stored in *.c3d format and, posteriorly, it was extracted and processed using Matlab ®. There are already available functions developed by the OpenSim community, developed for this purpose [54]. In this work, the toolbox “c3d2OpenSim” developed by James Dunne in 2015 was used and adapted to the data. This toolbox uses as basis the functions of the Biomechanical ToolKit (BTK). In the Figure 0.3 is shown the sequence of actions performed prepare to use as input in OpenSim. Experimental data treatment and analysis 37 Figure 4.3.Sequence of steps taken to obtain the OpenSim input files containing the kinematic and kinetic data (*.trc and *.mot files, respectively) relative to the post-stroke individual. The information contained in the *.c3d file was extracted and stored inside a Matlab struct using a sequence of functions from the BTK. The function btkGetMarkers extracts the positions of the makers, defined in the laboratory coordinate system. Then, this values were converted to the OpenSim coordinate system and finally, a *.trc file was printed with this information. Regarding the force platform data, there are two methods for extracting the data: the function Methodology 44 It was necessary to associate to each body one or more maker pair, so that the corresponding scale factor was applied to that body. In the case of using more than one marker pair, the scale factor is computed as the average between the factors computed for each one. In the Figure 4.9 it is shown the Marker Set of the Scaling Tool for the Study 2, showing each body and the corresponding marker pairs associated. Figure 4.9. Display of the Measurement Set of the Scaling Tool (Study 2). At the left is presented a list of the measurements, associated with the scale factors are computed using the marker pairs shown at the right. The torso and the pelvis are recommended to be scaled non-uniformly [50], this is, with different scale factors in the three directions. For that reason, x and z direction of the torso was associated with the marker pairs RAC/LAC and RASIS/LASIS and for the y direction (vertical) with C7/RPSIS and C7/LPSIS (Figure 4.10). Although the markers chosen to scale the vertical direction are not aligned in the vertical direction, they are better indicators of the torso’s vertical length. A sacral marker would be more suitable for this purpose. Computational Simulation 45 45 Figure 4.10. Markers used to calculate the vertical scale factor of the torso. The dashed line represents the distances between the pairs C7/LPSIS and C7/RPSIS. Concerning the weight, the Scaling Tool offers has two possible approaches: preserve the total mass of the subject of the experiment, maintaining the relative masses of the bodies in the model, or scaling each segment mass taking into account only the scale factors computed before. In the last approach the total mass might not match the subject's real mass. The first alternative was chosen, since mass modifications could lead to errors in the next steps, when the ground reaction forces measured are considered. It important to note that the Scaling tool adapts the mass distribution (inertia matrix) of each body, when changing its mass and dimensions and, using his option, the scale factors computed using the measurement set (Figure 4.9) are not used for the mass scaling [50]. It is also necessary to weight each marker relatively to the others. Larger weights mean that the marker is tracked more tightly and the tracking errors are more penalized. For this reason the markers representing bone landmarks and functional joint centres should have larger weights [50], which is the case of the markers at the hip, knee and ankle joint .The coordinates representing the subtalar and metatarsophalangeal joints were locked in the neutral position (angle set to zero) and weighted heavily, so that they remain in that position during the simulations. In the OpenSim guide this step is recommended [50] and the reason why this recommended is because the model does not possess enough muscles to control these joints. In the case of the Study 1, there was no need to change the default marker configuration of the OpenSim. It was used a static trial file for scaling and the Measurement Set was already Methodology 46 defined in a file that came with the data. The weighting process was done by attributing larger weights the markers located in functional joint centres and bone landmarks, similarly to the Study 2. The relative weights used in both studies can be found in annex. After defining the parameters described above in both studies, the position of the experimental markers was manually adjusted to match the virtual markers, making several iterations until the RMS and the maximum error were minimized. 4.3.4 - Inverse kinematic (IK) The Inverse Kinematics Tool allows to determine the joint angles and translations that best reproduce the experimental position of the markers. For each frame, it is solved a least-squares problem, in order to minimize the weighted error for each coordinate [49]: 𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑟𝑟𝑜𝑟= ∑𝑤𝑖(𝑥𝑖𝑠𝑢𝑏𝑗𝑒𝑐𝑡−𝑥𝑖𝑚𝑜𝑑𝑒𝑙)2 𝑚𝑎𝑟𝑘𝑒𝑟𝑠 𝑖=1 +∑𝑤𝑗(𝜃𝑗𝑠𝑢𝑏𝑗𝑒𝑐𝑡−𝜃𝑗𝑚𝑜𝑑𝑒𝑙)2 𝑗𝑜𝑖𝑛𝑡 𝑎𝑛𝑔𝑙𝑒 𝑗=1 (4.6) Where 𝑥𝑖𝑠𝑢𝑏𝑗𝑒𝑐𝑡 and 𝑥𝑖𝑚𝑜𝑑𝑒𝑙 are the three-dimensional positions of the ith marker, for the subject and the model; 𝜃𝑗𝑠𝑢𝑏𝑗𝑒𝑐𝑡 and 𝜃𝑗𝑚𝑜𝑑𝑒𝑙 are the angles of the jth joint, for the subject and the model; and 𝑤𝑖 and 𝑤𝑗 are the corresponding weights of the markers and the joints. This tool uses as input the makers positions stored in the *.trc file. The weighting of the markers was done by attributing larger weights to markers less susceptible to movements due to skin and soft tissue during gait [50]. The weights used in both simulations can be consulted in the annex 3. 4.3.5 - Inverse dynamics (ID) The Inverse Dynamics Tool calculates the joint moments necessary to make the model perform the desired kinematics, according to the basic equations of motion (Equations 3.4 and 3.5). Although, the following steps are not dependent on the ID results, this step was done to analyse the joint moments and the forces acting in the pelvis, before the reduction of the residuals. The output *.mot file of the Inverse Kinematics step was used as input, as well as the *.mot file containing the ground reaction forces, moments and the PWA/COP. The Inverse Dynamics Tool allows the possibility to consider the interaction with the ground as a body force, which acts in the centre of mass of a body or as a point force that acts in the PWA/COP and produces a torque. The second option was used in both simulations. During this and the following steps, the subtalar and the metatarsophalangeal joint were locked in the Coordinates Editor, so that the model was consistent with the kinematics obtained through the Inverse Kinematics step Computational Simulation 47 47 4.3.6 - Residual reduction algorithm (RRA) With the purpose of reducing the residual forces and moments acting in the model, which are assumed to solve the dynamic inconsistency between the experimental data and the model, the Residual Reduction Algorithm Tool was used. The residual forces are determined as described in the Equation 4.7, and the errors associated are obtained by the Equation 4.8. 𝐹𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙=∑𝑚𝑖𝑎𝑖−𝐹𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 𝑖=1 (4.7) Where 𝐹𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 is the external force acting on the model; 𝑚𝑖 and 𝑎𝑖 are the masse and acceleration of the ith segment and 𝐹𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 is the residual force. 𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑟𝑟𝑜𝑟= ∑Ω𝑖(𝑞󰇘𝑗𝑑𝑒𝑠𝑖𝑟𝑒𝑑−𝑞󰇘𝑗𝑚𝑜𝑑𝑒𝑙)2 𝑗𝑜𝑖𝑛𝑡𝑠 𝑗=1 (4.8) Where 𝑞󰇘𝑗𝑑𝑒𝑠𝑖𝑟𝑒𝑑 and 𝑞󰇘𝑗𝑚𝑜𝑑𝑒𝑙 are, respectively, the desired and the effective acceleration of the jth joint and Ω𝑖 is the weight associated to that joint. This algorithm replaces the muscles of the model by ideal actuators acting in each coordinate, and each one has an optimal force and an excitation control associated. The force produced by the ideal actuator is then given by the Equation 4.9. 𝐹𝑜𝑟𝑐𝑒𝑖𝑑𝑒𝑎𝑙 𝑎𝑐𝑡𝑢𝑎𝑡𝑜𝑟=𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝐹𝑜𝑟𝑐𝑒× 𝐸𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 (4.9) The tool uses as inputs the files containing the kinematics and the ground reaction forces and two XML files: - Actuators file, where are described the ideal actuators and their properties: optimal force, point of application (for point actuators), bodies (in the case of torque actuators) and the minimum and maximum excitation; - Tasks file, which specifies the relative weight attributed to each joint. Initially it was done an initial pass to verify if the model was strong enough to reproduce the kinematics. Actuators that require lower controls to generate force are less expensive for the algorithm and, consequently, it relies in these actuators. Thus, in the initial pass, high optimal forces were attributed to residual point actuators (Fx, Fy and Fz) and to residual torque actuators (Mx, My and Mz) and the weights were the same to each actuator. The results were analysed and the optimal forces of residual actuators were decreased to force the algorithm to use the coordinate actuators (joint actuators) instead of the residual ones. For each iteration Methodology 48 the error associated to each coordinate was verified and the weights of the coordinates with high error were increased to improve their tracking. This was done until an optimal solution was found, in which the RMS and the maximum values of the residuals and the errors were considered acceptable, according to [50]. It is important to refer that, since the subtalar and the metatarsophalangeal joints were kept locked, there were not include in the tasks file, because they were not tracked. And the actuators acting in these joints were removed. At the end of the process, OpenSim automatically adjusts the COM (Centre of Mass) of the torso and suggests mass adjustments to each one of the bodies, in order to reduce the residual forces, which were applied to the model before the next step. 4.3.7 - Computed muscle control (CMC) Computed Muscle Control Tool was used to determine how the muscles of the model actuates to produce the movement. This algorithm uses a combination of a proportional-derivative (PD) control and static optimization, as shown in the scheme of the Figure 4.11. Figure 4. 11. Scheme of the CMC algorithm used in gait [59]. Static optimization distributes the load to the muscles, which are synergistic actuators, for each time instant. This process uses a performance criterion that is intended to be minimized, with two possible formulations: slow and fast target (Equation 4.10). The fast target approach, generally recommended by producing better tracking [50], was used in both simulations. 𝐽=∑𝑥𝑖2𝑛𝑥 𝑖=1 ;𝐶𝑗=𝑞󰇘𝑗∗−𝑞󰇘𝑗∀𝑗 (4.10) Where 𝐽 is the performance criterion; 𝑥𝑖 is the excitation of the ith actuator; 𝑞󰇘𝑗∗ and 𝑞󰇘𝑗 are the desired and the obtained accelerations of the jth joint; and 𝐶𝑗 is the equality constraint (C=0), that requires the difference between the desired and obtained acceleration to be within the tolerance value, in this case was used 0,00001. Summary 49 The file inputs of CMC are: - *.mot file describing the kinematics, obtained with the RRA; - *.mot file with ground reaction forces (the same used in ID); - *.xml files containing: - model actuators: muscles, the reserve and residual actuators and their properties. The reserve actuators are ideal actuators that - control constraints, where are specified the maximum and minimum excitation for the actuators described in the model actuators file; - tasks which contains the relative weights for each coordinate, similarly to the tasks file from RRA. Similarly to the RRA step, it was made an initial pass with large optimal forces for residual and reserve actuators and the same weights for each coordinate. In the following iterations the optimal forces for reserves and residuals were reduced and the controls constrains increased, so that the controller choose to rely on muscles instead of residual and reserve forces. The iterations were stopped when the residuals, reserves and errors associated were reduced enough to acceptable values. 4.4 - Summary The data from a gait trial performed with post-stroke individual was extracted from a *.c3d file and processed using the BTK in Matlab and a *.trc and a *.mot file were obtained. The first one stores the marker trajectory data (kinematic) and the second one stores the ground reaction force data (kinetic). These two files were used as inputs in the OpenSim simulation described in the next chapter. Two gait simulations were performed using OpenSim, one with a subject considered healthy and the other with a post-stroke individual. From the correspondent experimental data, it was determined the joint angles and torques, using inverse kinematics and inverse dynamics, respectively, the residual forces and moments acting in the model were reduced (through RRA) and finally, the muscular behaviour was determined using CMC. 50 51 Chapter 5 Results and discussion 5.1 - Introduction In this chapter the results are presented and discussed. In the first part, the results from the extraction from a *.c3d file and the processing of the experimental data used in the Study 2 are presented. Secondly, the results obtained in each step of the workflow of the OpenSim are shown and analysed. In the case of the Study 1, since it consists in a simulation of a healthy individual, the values of the joint angles and moments and the muscle activations and powers were compared with the available reference values in the literature. For the Study 2, these parameters were also compared with the literature about post-stroke gait. In both cases, an analysis of the muscular activation and powers of the principal plantarflexor muscles (soleus and medial gastrocnemius), the main dorsiflexor (tibialis anterior) and one hamstring (semimembranosus) was done and analysed together with the results of the kinematics. 5.2 - Experimental data The data representing the 3D position of the markers was not subjected to processing, since it was not corrupted with noise. The software used in the data collection (Qualisys Track Manager) includes post-processing of the marker data, eliminating the need of filtering to remove the noise [60]. Using the software MLSViewer, a Motion Lab Systems Software © to display the Results and discussion 52 contents stored in a *.c3d file [61], it is possible to visualize the recorded trajectory of the markers. In the Figure 5.1 it is shown the trajectory of the marker placed in the heel of left foot (LBACKFOOT) in the three directions (x, y and z of the laboratory coordinate system), using MLSViewer, where is possible to see that the data is clean. Besides, this data was automatically filtered in OpenSim when using the IK, ID and RRA Tools, as recommended in the OpenSim guide [50]. Figure 5.1. Visualization of the position, in the three directions x, y and z (laboratory coordinate system) of the marker RBACKFOOT of the post-stroke individual, in MLSViewer. The force platforms used in the experimental trial and considered in this study were of type 2, meaning that each one has six output channels for analog data of the three components of the force and of the moments acting in the origin of the force platform [48]. This data was stored in a *.c3d, which contained also the scale factors and the calibration matrixes necessary to convert the raw data (electric output) into force data. This operation has been done by using the BTK, which has two distinct functions, both used in this work. Since the code of the functions is not available, it is not possible to analyse the each step of the operations performed. The output of the function btkGetForcePlatformWrenches is the value of the forces and moments in the origin of the force platform, consequently this function only needs to transform the electrical signal of the force plate, using the scale and calibration information, into force and moment data. On the other hand, according to the informative webpage of the BTK [62], the function btkGetGroundReactionWrenches, which gives the forces, location of the PWA and the moments defined in that point, in addition to this transformation, determines the PWA and the moments on it, by using the formula developed by Shimba [63] which also was described in Zatsiorsky [55]. Experimental data 53 Regarding the location of the COP and the PWA, all three components of the position did not show considerable differences, suggesting that the distance between this two points is not relevant. It was verified that the values of the forces obtained with the two functions were the same, as expected. The vertical moments showed small dissimilarities which mean once more that the location of the PWA and the COP is very small. In fact, these difference of positions is explained by the horizontal moments about the PWA that, in this case, are very small (Figure 5.2). Figure 5.2. Ground reaction moment in the vertical direction (My, considering the OpenSim coordinate system) in the PWA, obtained using the function btkGetGroundReactionWrenches (PWA Right My and PWA Left My) and the free-moment acting in the COP, for the right and left legs of the post-stroke individual. Regarding the horizontal moments in the PWA (Figure 5.3), it were verified abnormal peaks in the beginning and the end of the contact phases. By analysing directly the data of the horizontal moments obtained with the function btkGetGroundReactionWrenches, it was noticed that the time of the beginning and of the end of the contact, assumed to be where the vertical force is higher than zero, it does not coincide with the delimitation of the contact in the horizontal moments. The found peaks could be smoothed by interpolating the data at the initial and final moments of contact. However, it is important to notice that the value of the horizontal moments is very R_IC L_TO L_IC R_TO R_IC L_TO L_IC R_TO -6 -4 -2 0 2 4 6 1,0 1,1 1,3 1,4 1,5 1,6 1,8 1,9 2,0 2,1 2,3 2,4 2,5 2,7 2,8 2,9 3,0 3,2 3,3 3,4 3,6 3,7 3,8 3,9 Moment (N.m) Time (s) Events PWA Right My PWA Left MY COP Right My COP left My Results and discussion 60 The errors associated with the tracking of the markers during the inverse kinematics process were satisfactory for the Study 2, but exceeded the recommended limits in the Study 1 (Table 5.3). The maximum error registered in this study is associated with the marker R.Acromium, which had associated a lower tracking weight. The IK process is very dependent of the scaling process [50] and consequently, the high errors registered in the IK for the Study 1 might be related with the errors obtained in the corresponding scaling process. Table 5. 3 Marker error (RMS) and maximum error associated with the scaling process for the models in the Study 2 and Study 1 and the respective limit values recommended in [50]. Study 1 Study 2 Recommended limits Marker error: RMS (cm) 2.25 1.19 < 2 Max error (cm) 8.56 (R.Acromium) 3.98 (RMK) < 2-4 5.3.3Inverse dynamics Using inverse dynamics, the model tried to reproduce the movement determined by inverse kinematics in the previous step while subjected to the external forces and moments contained in the *.mot files created. Making a first analysis of the force that acts in the pelvis, higher peaks in the vertical force (Fy) are observed in the instants of initial contact of the two limbs (Figure 5.6). If the vertical ground reaction forces are plotted in the same graph as the forces acting in the pelvis, from ID, (Figure 5.7) there is a coincidence with decrease of the peaks and the beginning of the contact. Indeed, the vertical force acting in the pelvis appears to be compensating the inexistence of a force in the instants before Fy becomes different from zero. This force is the major force component and accounts for the vertical acceleration of the centre of mass and the characteristic curve of this force includes a quick increase after heel strike [67]. However the vertical force obtained has an abrupt increase, verified in these instants, which rise from zero to 130 N (in the left initial contact) and 125 N (right initial contact) in a small interval of time. To minimize the errors originated from this, smoothing the data could be done in the processing step. OpenSim Simulation 61 Figure 5. 6. Forces acting in the pelvis, obtained using ID, before reducing the residuals. The blue line represent the vertical residual force, the red and the green represent the horizontal residual forces (Fx and Fy). Figure 5. 7. Plot of the vertical GRF acting on the left (red) and right (blue) legs and the force acting in the pelvis (green). Considering the differences between individuals in the size and weight of the segments, in order to compare the joint moments with the literature is necessary to scale these values in newton-meters per kilogram body mass. Results and discussion 62 Figure 5. 8. Reference internal joint moments for the hip, knee and ankle according to [1], in N.m/Kg, for one gait cycle. The gait events are represented as: IC – initial contact; OT – opposite toe-off; HR – heel rise; OI – opposite initial contact; TO – toe-off; FA – feet-adjacent; TV – tibia vertical Comparing the results of hip joint moments obtained in the healthy subject from the Study 1 (Figure 5.9) with the values found in the literature (Figure 5.8), the moment curve has a similar shape, however, the two legs show different range values: -0.8/ 0.5 N.m/Kg for the right leg and -0.6/0.6 N.m/Kg for the left leg. Also the knee moment obtained in this simulation is in agreement with the reference, though there were found differences between the two legs in the maximum hip flexion, at initial contact: the right leg reached a moment of -0.7 N.m/Kg and the left -0.6 N.m/Kg. Relatively to the ankle, the maximum plantarflexor moment it was higher than the reference values (approximately -1 N.m/Kg) in both limbs and the right leg registered a higher value (- 1.77 N.m/Kg) than the left (1.50 N.m/Kg). Normal gait is assumed to be symmetric, even though it is accepted a small degree of asymmetry, which is negligible in healthy subjects [68]. The results do not show considerable differences between both sides. Relatively to the Study 2, ID was performed using the external force data considering the COP and the PWA. Analysing the results obtained, there was not found considerable differences between them. The curves show the similar shape and maximum and minimum moment values. In the Figure 5.9 the joint moments obtained using the PWA are shown. The maximum hip flexion moment was higher for the IPSI limb (0.52 N.m/Kg) comparing to the CONTRA limb (0.45 OpenSim Simulation 63 N.m/Kg), while the maximum hip extension moment for the IPSI limb was -0.80 N.m/Kg and for the CONTRA limb -0.70 N.m/Kg. Regarding the knee moment, it was found a lower knee flexor moment in the CONTRA limb (- 0.16 N.m/Kg) before the initial contact, comparing to the IPSI limb in the correspondent initial contact (-0.32 N.m/Kg). However, it is observed high abnormal peaks happening during the initial contact, in both sides, that also occur in the hip moment data, higher than the ones that appear in the inverse dynamics results from the Study 1. The ankle plantarflexor maximum moment differ slightly from one limb to the other (-1.47 N.m/Kg in the IPSI limb and -1.40 N.m/Kg in the CONTRA limb). In both limbs it was not found the dorsiflexor moment after initial contact as expected, by looking at the curve found in the literature. An abnormal peak appeared in the IPSI limb during its initial contact. Results and discussion 64 Figure 5. 9. Hip, knee and ankle joint moments obtained with inverse kinematics, for the Study 1 (first row) and the Study 2 (second row). The blue line refers to the right limb (IPSI limb in the Study 2) and the red line to the left limb (CONTRA limb in the Study 2). -1 -0,5 0 0,5 1 0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100 Moment (N.m.Kg) Gait cycle (%) Hip flexion moment -1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100 Moment (N.m.Kg) Gait cycle (%) Knee extension moment -2 -1,5 -1 -0,5 0 0,5 0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100 Moment (N.m.Kg) Gait cycle (%) Ankle dorsiflexion moment -1 -0,5 0 0,5 1 014 28 43 57 71 85 99 Moment (N.m.Kg) Gait cycle (%) Hip flexion moment -0,5 -0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 014 28 43 57 71 85 99 Moment (N.m.Kg) Gait cycle (%) Knee extension moment -2 -1,5 -1 -0,5 0 0,5 1 014 28 43 57 71 85 99 Moment (N.m.Kg) Gait cycle (%) Ankle dorsiflexion moment OpenSim Simulation 65 5.3.4Residual reduction algorithm The reduction of the residuals was successfully accomplished in both studies 1 and 2, according to the recommended in the OpenSim guide [50], as it is possible to verify by analysing the Table 5.4 . The best results were obtained for the Study 1, in which the values of maximum and RMS residuals and errors were inside the optimal limit. In the Study 2, th e residuals overpassed the optimal threshold, however, decreasing residuals would increase the errors associated with the kinematics beyond the acceptable values. Analysing the plot of the residual forces in the Study 2 (considering the PWA), it is possible to see peaks in the vertical force (Fy), in the point of the right and left initial contact, also verified in the internal moments from ID. However, it is verified a decrease of the magnitude of these peaks, after the reduction of the residuals (Figure 5.10). Figure 5. 10. Residuals forces obtained in RRA for the Study 1, using PWA. The blue line represent the vertical residual force, the red and the green represent the horizontal residual forces (Fx and Fy). In ID, the action of external forces (GRF) is balanced only with the body forces, while in RRA the residuals that are the forces and moments acting in the pelvis are reduced and, consequently, this reduction is compensated by changes in the actuation of the other joint actuators. There are no reference values to evaluate the dimension of the total mass adjustment recommended by after the RRA step. In both cases it was less than 1%, being lower for the healthy model (Study 1). This might not be related with the pathology, but with the experimental data itself, since the RRA intends to compensate for dynamic inconsistencies. Results and discussion 66 Table 5. 4 Maximum and RMS values of the residual forces and moments and rotational errors obtained for the RRA of the Study 2 and Study 1 and the recommended [50] optimal and maximum thresholds. Relatively to the Study 2, the RRA was also performed having the GRF considering the COP and the PWA, to verify the influence mainly the influence of the horizontal moments in the simulation. In both cases it was used the same settings for the actuators and tasks. Small differences were detected in what concerns to the internal joint moments an the residuals obtained. The highest difference verified between the two analysis was found in the maximum rotational error associated with the right ankle, which was 1,57º when the PWA is considered and -3,00º for the analysis using the COP. The weight associated with the right ankle was increased to attempt to diminish the error in tracking this joint, however, the error was not diminished. This means that the model cannot track the motion completely without the action Study 1 Study 2 Absolute optimal threshold Absolute max threshold COP PWA Max Residual Forces (N) -7,21 (Fx) -19,00 (Fz) -17,27 (Fz) < 10 < 25 RMS Residual Forces (N) 3,26 6,98 7,10 < 5 < 10 Max Residual moments (Nm) -22,80 (Mz) -62,13 (Mx) -58,66 (Mx) < 50 < 75 RMS Residual Moments (Nm) 9,08 15,17 16,32 < 30 < 50 Max translational error (cm) -1,09 (Pelvis x) -2,89 (Pelvis z) -2,83 (Pelvis z) < 2 < 5 RMS translational error (cm) 0,61 1,31 1,35 < 2 < 4 Max rotational error (deg) -0,40 (Right hip flexion) -3,00 (Right ankle angle) -1,57 (Right ankle angle) < 2 < 5 RMS rotational error (deg) 0,16 0,64 0.58 < 2 < 5 Total mass adjustment (Kg) -0,05 -0,43 -0,56 - - Total mass adjustment (%) -0,07% -0,45% -0,58% - - OpenSim Simulation 67 of the residual forces and its decrease, particularly in the instants were the peaks exist, caused errors in tracking the kinematics. In the next step (CMC) it was used the PWA approach for the external forces, since the maximum error associated was lower and it will decrease the accumulation of errors in kinematics in the final result. 5.3.5Computer muscle control The results of the kinematics computed in the previous step were used as the motion to track during CMC. For both studies it was performed several iterations in order to try to find the optimal solution, in which the residuals, reserves and errors were inside the optimal, or at least, the acceptable limits. In the Table 5.5 are shown the results for these parameters. The results relative to the Study 1 are satisfactory since all the parameters are inside the optimal threshold. In the case of the Study 2, the maximum values of residual moments, rotational error and reserve force surpassed this optimal limit, but still acceptable. However, it was obtained a peak of 130,60N of residual vertical force (Fz) in the simulation using the PWA, in the right initial contact (Figure5.11). Table 5. 5 Maximum and RMS values of the residual forces and moments, reserve forces and translational and rotational errors obtained for the CMC of the Study 2 and Study 1 and the recommended [50] optimal and maximum thresholds. Study 1 Study 2 (PWA) Optimal threshold Max threshold Max Residual Forces (N) -8,83 (Fx) 130,66 (Fz) < 10 < 25 RMS Residual Forces (N) 3,37 12,85 < 10 < 25 Max Residual moments (Nm) -22,39 (Mz) 59,31 (Mx) < 50 < 75 RMS Residual Moments (Nm) 9,43 15,76 < 30 < 50 Max translational error (cm) -0,01 (Pelvis z) 0,10 (Pelvis z) < 1 < 2 RMS translational error (cm) 5,31E-3 0,02 < 1 < 2 Max rotational error (deg) -0,38 (Left knee angle) -6,54 (Right ankle angle) < 2 < 5 Results and discussion 68 RMS rotational error (deg) 0,09 0,46 < 2 < 5 Max Reserve (N.m) 3.12 (Left ankle angle) -64,61 (Right knee angle reserve) < 25 < 50 RMS Reserve (N.m) 0,12 2,96 < 10 < 25 Figure 5. 11. Graph showing the value of the residual forces Fx (red), Fy (blue) and Fz (green) acting in the pelvis, resulting from CMC. The right ankle had the highest tracking error associated (-6,54º). Looking at the curve of the right ankle kinematics after RRA and after CMC (Figure5.12, it is possible to see that the error starts from the right initial contact, the instant where the large residuals were obtained, suggesting a relation between this occurrences. Similarly, in the previous step (RRA) the largest tracking error was associated with the right ankle angle, even though was inside the acceptable limits. Also in the instant of right initial contact it were verified high reserve moments in the right side: the right knee reserve actuator reached the maximum reserve value (-64,61 N.m) and also the right ankle registered 50,20 N.m. Decreasing the optimal force of this reserve actuators, so that the model would not use them, leads to interruption of CMC process, meaning that the model needs the action of these actuators to follow the kinematics. It could be hypothesized that the locking of the subtalar and metatarsophalangeal joints could influence the errors in tracking the ankle movement, but it was not verified the same problem in the left ankle, which was satisfactorily tracked in the CMC (0.69º), making this hypothesis less plausible. OpenSim Simulation 69 Figure 5. 12. Right ankle angle error. The red line corresponds to the right ankle angle obtained after RRA and the blue line represents the right ankle angle after CMC. 5.3.6Muscle action The output files of the CMC include: - Joint kinematics (position and angular velocity and acceleration) and in the case of the pelvis also the linear velocity and acceleration; - Tracking errors of the kinematics; - Actuator (muscle and reserves) forces and powers; - Actuator (muscle and reserves) powers; - Controls: excitation patterns of each actuator; - States: muscle activation and fibber length. The activation pattern of each reserve and residual actuator is directly linked to the respective excitation, since the activation is the result of the product of the excitation by the optimal force [50]. In the case of the muscles, the activation is obtained through the excitationactivation dynamics (Figure 3.4), described by the differential equation 3.3, resulting in some time delay between excitation and activation. The analysis of the muscle force through time is not enough to a better understanding of the behaviour of the muscles. Since a muscle can produce force isometrically (no fibber length changing), concentrically (produces force by contracting in the same direction of the movement) and eccentrically produces force by lengthening in the direction of the movement) and also can change its length and not exert force [1, 4]. Consequently, to do a more complete analysis is necessary to study the muscle activation together with the kinematics in the respective time, to verify the activation and the direction of the movement. When a muscle contracts concentrically, it produces energy, meaning that it generates positive power, while eccentric contraction leads to energy absorbing and, consequently negative power [1]. Since power is the variation of energy (joule) with time, its units are joule per second (J/s) watt (W). Results and discussion 76 Figure 5. 15. Activation and power associated with the muscles SOL, MEDGAS, TA, SMEMB, obtained in CMC (Study 2). The red line refers to the CONTRA limb and the blue line refers to the IPSI limb. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 011 24 37 47 55 63 76 89 98 Activation Gait cycle (%) TA activation 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 011 24 37 47 55 63 76 89 98 Activation Gait cycle (%) SMEMB activation -300 -250 -200 -150 -100 -50 0 50 100 150 011 24 37 48 55 64 77 89 98 Power( W) Gait cycle (%) TA power -40 -30 -20 -10 0 10 20 30 40 50 60 011 24 37 48 55 64 77 89 98 Power (W) Gait cycle (%) SMEMB Power Summary 77 5.4 - Summary Two simulations of gait were developed, one using normal gait and other using post-stroke gait. The experimental data used to simulate post-stroke gait was extracted from a *.cd3 file and the respective force platform data was used to compute the forces and moments that act in the PWA and in the COP. The results showed not relevant differences between the location of these points and the moments in the horizontal plane were small comparing to the vertical moment. The kinematics and joint moments obtained for the healthy model revealed to be in accordance with the reference. However, the muscular activations showed some asymmetry and, in the case of the TA and the SMEMB, these muscles were activated in instants of the cycle where it doesn’t happen in the reference. The kinematics of the post-stroke model, however, showed only low plantarflexion as the main impairment and the results from CMC for the plantarflexor muscles showed early activation, but not diminished in the paretic side. These muscles appeared to be able to generate the necessary power before propulsion. The hamstring muscle (SMEMB) from the CONTRA limb, showed prolonged activation during stance phase, which it is usually reported in the literature as a compensatory mechanism for plantarflexor weakness. This model had associated high tracking error for the right ankle and high magnitude residuals and reserves at the instant of right initial contact, suggesting that it was not able to reproduce its kinematics relying mainly in the muscular actuators. 78 79 Chapter 6 Final conclusions and future developments 6.1Final conclusions The aim of this dissertation consisted in simulate healthy and a pathological gait, specifically post-stroke gait, using computational methods, starting from experimental data. Firstly, the fundamentals of human gait were explored, regarding the anatomy and the neuromuscular controls involved. After that, gait impairments in the sequence of a stroke were studied and described. The experimental methodologies used to collect kinetic and kinematic data and the mathematical models that serve as fundamentals of the computational tools for biomechanical modelling were reviewed and described. The procedure for obtain the experimental kinematic and kinetic data from a *.c3d file was described, as well as its processing and conversion into *.trc and *.mot files to use as input in OpenSim. Following, the implementation of the OpenSim workflow described for each step of both simulations. The results obtained for the model of the healthy individual were in accordance with the literature, when the joint angles and moments were compared, despite small asymmetries, accepted in healthy subjects. The muscular actuators were activated according to the reference, however the TA and SMEMB actuators were also activated in other unpredicted instants. Regarding the post-stroke model, the kinematics associated revealed low plantarflexion in the CONTRA limb, characteristic from the post-stroke gait. The hamstring muscle SMEMB also Final conclusions and future developments 80 showed prolonged activation during CONTRA limb stance, which might be associated with the gradual decrease of hip flexion. However, the muscle activations of the plantarflexors only showed diminished activation in the medial gastrocnemius and in both plantarflexors, SOL and MEDGAS, showed early activation, as it is described in post-stroke gait literature. It is important to consider that the model was not able to completely reproduce the kinematics and even though tracking errors were expected, the right ankle angle had associated an error that overpassed the acceptable limits. Indeed, it was verified that the model had to use the residual and reserve actuators, even though these actuators were more expensive for the controller. 6.1Limitations The limitations of the present work are mainly related with the experimental data used. Less was known about the individuals and the conditions of collection of experimental data. Concerning the post-stroke patient, important information about the pathology historical was unknown: severity and affected brain area, time past after the accident and if he had received physiotherapy. Also the post-stroke individual used in the present work did not show accentuated impairments in gait, since he was mainly affected in the upper limbs. 6.2Future work As future work it is proposed to perform gait evaluations of a healthy and a post-stroke individuals with similar age, body height and weight, in the same conditions (use of the same number of markers, perform a static trial for scaling, making measurements of body segments and total height and body mass) and use EMG to assess the muscular activation experimentally. Taking pictures of the individual and record in video the gait trial would help to find subjectspecific characteristics and to identify sources of error related to it. 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Thigh.Rear RLK R.Knee.Lat LLK L.Knee.Lat RMK R.Knee.Med LMK L.Knee.Med X R.Shank.Upper X L.Shank.Upper X R.Shank.Front X L.Shank.Front X R.Shank.Rear X L.Shank.Rear RLA R.Ankle.Lat LLA L.Ankle.Lat RMA R.Ankle.Med LMA L.Ankle.Med RFOOT1 X LFOOT1 X RFOOT4 X LFOOT4 X X R.Midfoot.Sup X L.Midfoot.Sup X R.Midfoot.Lat X L.Midfoot.Lat X R.Toe.Lat X L.Toe.Lat X R.Toe.Med X L.Toe.Med X R.Toe.Tip X L.Toe.Tip RBACKFOOT R.Heel LBACKFOOT L.Heel