Sports | Studies, essays, thesises » Laura Martin De Azcarate - Muscle contributions to body mass center acceleration during the first stance of sprint running

DEGREE PROJECT IN MECHANICS, SECOND LEVEL STOCKHOLM, SWEDEN 2019 Muscle contributions to body mass center acceleration during the first stance of sprint running LAURA MARTÍN DE AZCÁRATE K T H R O Y AL I N S T I T U T E O F TE C H N O L O G Y ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH Muscle contributions to body mass center acceleration during the first stance of sprint running Laura Martín de Azcárate 2019-02-07 Master’s Thesis Examiner and Academic adviser Elena M. Gutierrez-Farewik KTH Royal Institute of Technology School of Engineering Sciences in Chemistry, Biotechnology and Health (SCI) Department of Mechanics SE-100 44 Stockholm, Sweden Abstract | i Abstract The best results in a sprint running are based upon covering the distance in the shortest possible time, and therefore performance has to be maximized. To achieve the best performance, the sprinter has to develop the greatest forward acceleration, reach his/her maximal speed, and

keep it over the run. The greatest anteroposterior acceleration is generated in the first stance of a sprint due to the greatest propulsive force production. Thus, the first step was selected to study induced accelerations by the main muscles of the lower limb. Since a wider step width was founded out to help with force generation during long foot-ground contacts, an elite sprinter with a wide step width was selected. Ankle plantarflexors were the main contributors to body propulsion and support, while knee extensors decelerated forward propulsion but induced medial accelerations. Hip extensors and hip adductors did not offer a remarkable contribution to body COM acceleration in any direction. Keywords Sprinting biomechanics, first stance, forward dynamic simulation, induced acceleration analysis, individual muscle contribution, elite sprinter, step width Acknowledgments | iii Acknowledgments First, I would like to thank Professor Lanie Gutierrez-Farewik for giving me the

opportunity to develop a project in the Department of Mechanics. This project could not have been developed without the help of Paul Sandamas, who had the idea of analyzing the contributions of individual muscles to the acceleration of the body mass center at the beginning of a sprint for his PhD. Another person that I would like to thank is Ruoli Wang, who was always offering me advices and guidance. I am also grateful to all my family and friends, especially to those that have come to visit while I was away, giving me the needed support and some time to relax while exploring my new city. And last but not least, thanks to my new friends in Stockholm, for your friendship, your encouragement, and our multiple trips. Stockholm, February 2019 Laura Martín de Azcárate Table of contents | v Table of contents 1 2 Introduction . 1 Methods . 3 2.1 Participant 3 2.2 Materials 4 2.21 Marker placement protocol . 4 2.22 Electrode placement protocol . 4 2.23 Motion capture system . 5

2.24 Experimental biomechanics data . 5 2.3 Procedure 5 2.31 Model . 6 2.32 Data preprocessing . 6 2.33 OpenSim simulation . 7 3 Results. 13 4 Discussion . 21 5 Conclusions . 27 References . 29 Appendix A: State of the Art. 33 A.1 Sprinting biomechanics 33 A.11 Gait cycle . 33 A.12 Running and sprinting cycles . 35 A.13 Upper limb functions during running and sprinting . 36 A.14 Sprint phases . 37 A.15 Sprint techniques . 39 A.2 Musculoskeletal models and muscle-actuated simulations of running . 40 A.21 Models . 41 A.22 Simulations . 43 A.3 Biomechanical software tools 44 A.4 Summary 45 References (State of the Art) . 46 Appendix B: Marker placement protocol. 51 Appendix C: Electrode placement protocol . 55 List of figures | vii List of figures Figure 2-1: Different foot placements showing different step widths at the beginning of a sprint start . 3 Figure 2-2: Placement of the anatomical and tracking marker sets. 4 Figure 2-3: The arrangement of the GIH Motion

Analysis Laboratory . 5 Figure 2-4: Definitions of the degrees of freedom of all the joints included in the musculoskeletal model . 6 Figure 2-5: Overview of the MATLAB motion data elaboration toolbox for neuromusculoskeletal applications (MOtoNMS) . 7 Figure 2-6: Different steps that have to be followed in OpenSim in order to be able to analyze in a deeper level the simulation . 8 Figure 2-7: Possible types of a kinematic constraint in OpenSim between the foot and the ground . 11 Figure 3-1: Joint angles from IK, ground reaction forces, and joint moments from ID over the stance phase .13 Figure 3-2: Final joint moments from ID and RRA for the hip, knee, and ankle over the stance phase . 15 Figure 3-3: Residual forces and moments from ID and RRA .16 Figure 3-4: Activation of the main muscles of the lower limb computed with CMC and compared to processed EMG data .16 Figure 3-5: Ground reaction forces and induced constraint reaction forces at the foot . 17 Figure 3-6:

Horizontal and vertical contribution of the measured ground reaction forces, of all the muscles, and of the major lower-limb muscles . 18 Figure 3-7: Relative contribution to body propulsion and body support of the major lower-limb muscles .19 Figure 3-8: Mediolateral contribution of the major lower-limb muscles.19 List of tables | ix List of tables Table 3-1: Different possibilities of input data for the IK and ID tools when considering whether or not they are filtered .13 List of acronyms and abbreviations | xi List of acronyms and abbreviations .C3D Coordinate three-dimensional file format .MAT MATLAB data file format .MOT Motion file format .STO Storage file format .TRC Track row column file format .XML Extensible markup language file format C3D2MAT .C3D file format to MAT file format CFSQP C code for feasible sequential quadratic programming CMC Computed muscle control DOF Degree of freedom EMG Electromyography GIH Gymnastik- och

idrottshögskolan (The Swedish School of Sport and Health Sciences) IAA Induced acceleration analysis ID Inverse dynamics IK Inverse kinematics IPOPT Interior point optimizer ISB International Society of Biomechanics MOtoNMS MATLAB motion data elaboration toolbox for neuromusculoskeletal applications MVC Maximum voluntary contraction RRA Reduction residual algorithm SIMM Software for Interactive Musculoskeletal Modeling SO Static optimization Introduction | 1 1 Introduction A sprint is a type of run with quicker movements of the body segments, which is performed over shorter distances, and where the purpose is to cover the distance as fast as possible. Therefore, the speed is the variable to maximize in order to reduce the running time. The sprinting speed is defined by the product of step length and step frequency [1] and is a variable with high inter-subject dependency [2]. However, the relation between these terms is not directly proportional, since an

increment of step length usually leads to a reduction of step frequency, and vice versa. Some researchers [3] suggest that this inverse relation takes place especially at the beginning of the run and others [4] that it is during the constant velocity phase. In addition, both parameters are correlated and due to this fact, it is not possible to separate them and study their influence on the running time individually [5]. Each sprinter develops its own sprinting speed throughout the whole run, which can be divided into three phases: acceleration, constant velocity and deceleration phases. Moreover, the acceleration phase can be sub-divided into the initial acceleration phase, which takes place between the starting block clearance and the end of the second step, and the transition phase, which happens from the third step until the runner has a speed close to his/her maximal (Section A.14) Both the step length and step frequency have been studied only between the starting block clearance

and first step [6], during the whole acceleration phase [3][4][7] or during the constant velocity phase [8], but also during the whole sprint [5]. Indeed, step length rises from the initial acceleration phase to the final deceleration phase [9], while step frequency achieves its maximum value right after the sprinter leaves the starting blocks [3][7]. Furthermore, studies related to achieving a better performance while sprinting reported different results about the influence of step length and frequency. In [10], it was suggested that step length was the most important contributor, while in [9] and [11] it was proposed that the primary performance limit was due to step frequency, and even in [7] it was concluded that both step length and frequency were not the predominant variables. Nonetheless, all the mentioned studies focused only on step length and step frequency, and they did not analyze if step width was another variable that had to be taken into consideration as well. As stated

in [12], a wider step helped with force generation during the foot-floor interaction in the parts of the acceleration phase where the foot touched the ground for longer time, i.e, in the initial acceleration and beginning of the transition phases In addition, another parameter –apart from the running speed– that changes from one sprinter to other is the mediolateral force [13]. A ground reaction force can be divided into its vertical, horizontal (anteroposterior) and mediolateral components. Several studies, as shown in Fig. 21 in [14] (p 13), have analyzed both the vertical and horizontal ground reaction forces in the acceleration and constant velocity phases of a sprint: the vertical force offers support and lifts the body upwards, while the horizontal force propels the body forward. This latter force has been sub-divided into braking and propulsive forces [1] and the difference between them lies in the sign of the horizontal force. A negative value in the force generated by the

sprinter when touching the ground leads to a braking phase, in which the mass center velocity decreases. On the contrary, a positive value in the generated forces is linked with an increase in the mass center velocity as well as with a propulsive phase. However, since the sprinter only has one foot in contact with the ground, there will be a lateral shift toward the swinging lower limb that needs to be taken into consideration. Even though mediolateral forces are the smallest of the three components of ground reaction forces [15], it is possible that its effect can alter the body mass center acceleration 2 | Introduction in the case of runners that do not have a neutral step width, i.e, that follow the midline between the placement of both feet. Those sprinters present a cross-over –or negative base of gait– or a wide –or positive– base of gait, being the base of gait the mediolateral distance between feet placement (Section A.15) In the case of the latter sprinters, i.e,

the ones that run with a wide step width, they have shown the widest step width in the first contact between the foot and the floor and the step width has followed a downward trend until the end of the transition phase [12]. Although some studies have analyzed the muscle contribution to drive upward and forward the acceleration of the body mass center during running and sprinting (Section A.22), none of them included runners with a considerable wide step width. Based on having the widest step in the first foot-floor interaction, the aim of this study was to assess how every individual muscle from the lower limb contribute to the mass center acceleration during the first stance of sprint running when the runner presented a side-to-side movement at the beginning of a sprint start. Since it is not possible to measure muscle functions with a non-invasive procedure, a three-dimensional model would be used, and a forward dynamic simulation would be performed. The first hypothesis was that

soleus, gastrocnemius, and quadriceps (rectus femoris and vasti) were the major contributors to body support, that quadriceps were the primary contributors to body braking and that soleus and gastrocnemius were the principal contributors to body propulsion. A second hypothesis considered that most of the muscles contributed laterally. Methods | 3 2 Methods 2.1 Participant Data from a female professional elite sprinter (mass: 62.7 kg, height: 170 m) were collected She performed different trials using her own spiked shoes and her desired position for the starting blocks. She was selected from a group of ten sprinters (eight males and two females) because she had the widest side-to-side movement from the group, in which all the sprinters had a way of running with a considerable side-to-side movement. There were mainly two types of trials that were performed: static trials and dynamic trials. Dynamics trials were divided into two groups: those performed with the preferred step

width, i.e, with a wide step width, and those with a more neutral step width (narrower) In order to perform the narrower dynamic trials, two ropes were placed on the running track with the width of the starting blocks (0.3 m) and the participant was forced to run in between. Each participant had some time to practice before these trials were recorded, since it was not his/her preferred step width. The inclusion criterion for considering that the sprinter had a wider step width than average during the first stance was having a step width at least 30% bigger when running with their own style than when running with the ropes (Figure 2-1). In particular, the selected (widest) trial of the participant presented a step width of 0.33 m Figure 2-1: Different foot placements showing different step widths at the beginning of a sprint start: a neutral step width (left), where the distance between the heel and the midline of the body is inexistent, and a wider step width (right), where the

distance is considerable. For the group experiment, the participant has to meet an inclusion criterion during the first stance: having a preferred step width (wp) at least 30% bigger than his/her forced narrower step width (wf), which is still bigger that a neutral step width. The black footprint represents the foot placement when running with the preferred step width and the grey footprint, the foot placement when running with a forced step width. The blue dashed line represents the track of the midline of the center of mass of the body and the orange dashed line, the track of the center of the heel. The ropes are represented by two grey solid lines [16]. 4 | Methods 2.2 Materials Paul Sandamas, who is a PhD candidate in sports biomechanics at Gymnastik- och idrottshögskolan (The Swedish School of Sport and Health Sciences or GIH, Stockholm, Sweden), was the person in charge of developing the group experiment. 2.21 Marker placement protocol The experimental retroreflective

markers used during the different trials had mainly functions: defining all the body segments (anatomical markers) and computing the movement (tracking markers). Some markers included both functions Altogether, the participant had 74 markers on the body, which are shown in Figure 2-2. The meaning of the acronyms and the location of each marker is included in Appendix B: Marker placement protocol. Figure 2-2: Placement of the anatomical and tracking marker sets. The anatomical markers (blue) are placed on bony landmarks, while the tracking markers (green) are located on the arms, legs, and feet. Some anatomical markers are also used for tracking (red markers). The meaning of the acronyms and the location of each anatomical marker are included in Table B-1Appendix B: Marker placement protocol [17]. 2.22 Electrode placement protocol The surface electrodes were used in a bipolar configuration, so two electrodes were placed over the recommended location and a third electrode was needed

as a reference electrode. Electrodes were placed on the surface of the body over the following lower-limb muscles: soleus, gastrocnemius medialis, biceps femoris, vastus lateralis, gluteus medius, and gluteus maximus. Electrodes over these muscles were located bilaterally, ie, on both the right and left lower extremities, which made a total of 12 EMG measured signals. Recommendations from [18] were followed for the selected muscles (Appendix C: Electrode placement protocol). Methods | 5 2.23 Motion capture system The experiment took place at Rörelseanalyslaboratoriet (the Motion Analysis Laboratory) at GIH. A 12-camera motion capture system (Oqus 4, Qualisys AB, Göteborg, Sweden) was used in order to cover the starting blocks and the first step. The running track had 15 m of length and 1.22 m of width and was delimited by a tartan surface Each camera recorded marker positions at a frame rate of 250 Hz. EMG data (Noraxon USA, Inc, Scottsdale, Arizona, United States of America)

were recorded at the same time and were sampled at 1,500 Hz. The laboratory incorporated two Kistler 9281EA force platforms (Kistler Group, Winterthur, Switzerland) embedded on the floor and covered with the tartan surface, and two Kistler 9347B force transducers on the starting blocks. They both measured data at a rate of 1,500 Hz. The layout of the laboratory is shown in Figure 2-3 Figure 2-3: The arrangement of the GIH Motion Analysis Laboratory while the different static and dynamic trials were performed during the group experiment. 2.24 Experimental biomechanics data The global coordinate system used in the experiment followed the recommendation of the International Society of Biomechanics (ISB). Since the ground reaction forces were measured in the local coordinate system of the force platforms, which was different from the global system, a rotation matrix was needed to transform data collected. 2.3 Procedure The following software was used: OpenSim version 3.3 [19] as the

biomechanics software, MATLAB (version R2017b, The MathWorks, Inc., Natick, Massachusetts, United States of America) and Microsoft Excel (Microsoft Office 365, Microsoft Corporation, Redmond, Washington, United States of America) as computer systems, Mokka (Motion Kinematic and Kinetic Analyzer, Biomechanical ToolKit) as a .C3D file reader, MLSviewer (Motion Lab Systems, Inc., Baton Rouge, Luisiana, United States of America) as a C3D file viewer, and PSPad and Sublime Text as text editors. 6 | Methods 2.31 Model The model used in OpenSim was taken from [20] and was developed by Hamner, Seth, and Delp in 2010. It was divided into twelve segments and had 29 degrees of freedom (DOF) and 92 Hill-type musculotendon actuators (Section A.21) for the lower limbs and lumbar motions. Arms were driven by ideal torque actuators Figure 2-4 shows the different DOF for each joint. Figure 2-4: Definitions of the degrees of freedom (DOF) of all the joints included in the 12 segment, 29 DOF

musculoskeletal model. This model was created in the study of Hamner et al [21] (Appendix A Supporting information). 2.32 Data preprocessing Since OpenSim v.33 did not allow the user to input collected data directly into the program, these data had to be preprocessed. Data collected with the motion capture system were in .C3D file format, and had to be converted into marker and motion files (TRC and MOT file formats). The tool that was used for the conversion was MOtoNMS, which stands for MATLAB motion data elaboration toolbox for neuromusculoskeletal applications [22]. An overview schema of the tool is presented in Figure 2-5. The core of the toolbox was data elaboration, where data were processed in agreement with the user’s selections during the system configuration steps. The input and output files were loaded and stored, respectively, in the data management area. Methods | 7 Figure 2-5: Overview of the MATLAB motion data elaboration toolbox for neuromusculoskeletal

applications (MOtoNMS). On the one hand, data collected in C3D file format are converted to MAT files in the data management area. On the other hand, the user has to create three XML files related to data acquisition and static and dynamic trials using different interfaces in the system configuration area. With these three files, it is possible to obtain the desired output files in the data elaboration area, with dynamic and static trials, that can be opened in OpenSim after passing the data management area. Output files can also be used in the CEINMS software, which stands for Calibrated EMGInformed Neuromusculoskeletal Modeling Toolbox [22] (p 3) First,.C3D files were converted to MATLAB data files, ie, MAT files [22] Data in C3D files included marker trajectories, characteristics of the force platforms, ground reaction forces, and EMG signals. Next, data from dynamic trials were processed and TRC and MOT files were created. Then, data from static trials were processed and only TRC

files were generated, since there was no motion. After finishing with data preprocessing, three output files were created: one .MOT file and two .TRC files, one for the static trial and one for the dynamic trial In order to filter marker trajectories and ground reaction forces, a custom code in MATLAB was created using the butter and filtfilt functions, to design a Butterworth filter and to filter the input data, respectively. Both data were filtered with the same cut-off frequency to avoid the development of artificial peaks, which could have turned up into dynamic inconsistencies in the equations of motion [23]. Initially, the selected frequency was 12 Hz, but it finally was changed to 50 Hz because force data were distorted. EMG data was filtered using the MOtoNMS toolbox and the filtering technique involved a second-order band-pass Butterworth filter with two cut-off frequencies of 30 and 300 Hz, a linear envelope (a full-wave rectification followed by a second-order low-pass

Butterworth filter with a cut-off frequency of 6 Hz), and a normalization procedure. 2.33 OpenSim simulation As stated before, the software used to achieve the goal of the project was OpenSim and five different steps were performed: scaling, inverse kinematics (IK), inverse dynamics (ID), residual reduction algorithm (RRA), computed muscle control (CMC), and induced acceleration analysis (IAA). However, the third step was not mandatory to proceed, but it 8 | Methods was added since a common mistake after IK was the introduction of ground reaction forces. Figure 2-6 includes these different steps. Figure 2-6: Different steps that have to be followed in OpenSim in order to be able to analyze in a deeper level the simulation. The first step is scaling the generic model, the second step is running inverse kinematics (IK), the third step is executing the residual reduction algorithm (RRA), and lastly the fourth step is computing muscle control (CMC) [24]. The first tool in OpenSim

used during the project was the scaling tool. It allowed the model to accommodate the anthropometry of the specific subject that performed the trials in the best way that was possible [24]. First, the virtual markers had to be placed on the generic model by setting an approximate location of each marker. Next, the anatomical markers were weighted more heavily so that they were taken more into account. Then, experimental marker trajectories from collected data were compared to the virtual markers located on the model. Finally, the adjustment of both the mass properties (mass and inertia tensor) and the dimensions of the body segments was achieved. Therefore, two input files were required to scale the model: the initial generic model, which was described in Section 2.31, and the TRC file that included all the data from the positions of the experimental markers during the static trial. The output file was the new model that faithfully represented the participant. The second tool that was

used in OpenSim was inverse kinematics, which positioned the model in the posture that best matched experimental marker trajectories, i.e, when the sum of weighted squared marker error was as minimal as possible [24]. A marker error was the distance between an experimental marker and the corresponding virtual marker. The posture of the model was analyzed at each time frame of experimental data. As in scaling, markers had to be weighted. However, the markers that offered a better performance of the movement this time were tracking markers instead of anatomical markers. With the IK tool, the weighted squared problem was resolved as specified in (1) [24]: 2 min [∑ �� ‖����,� − ���,� ‖ ] ��� (1) � where ��� is the vector of generalized coordinates (or joint angles), �� is the marker weight, ���� is the experimental position of the marker � –which depends on the coordinate–, and ��� is the position of the corresponding

virtual marker on the model. Methods | 9 The input files were the scaled model and the .TRC file that included experimental markers trajectories data during the dynamic trial. The output file was the motion file that had all the information about the joint angles calculated with the IK solver. Later, the inverse dynamic tool was used in order to calculate joint net forces and moments. The ID tool used accelerations, generated from the differentiation of generalized coordinates twice, and external forces to generate joint moments [24]. The inverse dynamic approach started with the isolation of the most distal body segment, i.e, the foot, where ground reaction forces were applied and which allowed ankle joint moment computation, and then it continued with more proximal segments: the shank and the thigh, to get knee and hip joint moments, respectively. With the ID tool, an inverse dynamic analysis was carried out, and thus the equations of motion, as specified in (2), were solved at

each joint [24]: (2) �(�)�̈ + � (�, �̇ ) + � (�) = � where �, �̇ , �̈ are the vectors of generalized coordinates, velocities, and accelerations, respectively, � is the mass matrix, � is the vector of Coriolis and centrifugal forces, � is the vector of gravitational forces, and � is the unkown vector of generalized forces. The input files that were needed were the scaled model and two motion files: the one created with the IK tool and the one with the collection ground reaction forces data. As output, a storage file including net joint torques and forces was generated. This step helped with discovering that the ground reaction forces were properly rotated and applied, but it was found out that cut-off frequency for marker and force data was not appropriate and therefore it was changed from 12 to 50 Hz. Next, the residual reduction algorithm tool was used. It was run to minimize both the measurement errors in the motion capture data and the

inaccuracies of the musculoskeletal model and mass distribution [24]. These errors and inaccuracies would have cause a dynamic failure in the Newton's Second Law when the motion of the subject and the external force data were put together into the simulation algorithm [25]. In order to avoid the dynamic inconsistencies, non-physical compensatory forces (residuals, at the pelvis) were added to the equation and their value had to be as reduced as possible. Therefore, the performance criterion is shown in (3) [24]: �(�⃗��� ) = ∑ �� ( � ����,� ����,� 2 ( ) ( ) ��� ) + ∑ �� (�̈ ���,� � + � − �̈ ���,� � ) � 2 (3) with �⃗̈��� (� + �) = �⃗̈�� (� + �) + �� (�⃗̇�� (� ) − �⃗̇��� (�)) + �� (�⃗�� (� ) − �⃗��� (� )) where ����,� is the force of the actuator �, �� is the weight on the actuator stresses,

����,� ��� is the optimal force of the actuator, �� is the weight on the acceleration errors, and �̈ ���,� (�) is the new acceleration of the coordinate �. The division of the actuator force divided by its optimal force represents the actuator control. This tool was not able to solve the performance criterion with the default optimizer (IPOPT, which stands for interior point optimizer) and therefore it had to be changed to the CFSQP optimizer (C code for feasible sequential quadratic programming). 10 | Methods The same files as the ones used in the ID tool were needed as input files: the scaled model, the motion file created with the IK tool and the file with the ground reaction forces data. As output files, a new adjusted model, with a new torso mass center, and a storage file with the new kinematics were generated. Then, the computed muscle control tool was used to calculate actuator controls, e.g, muscle excitations, that had to cause the

generalized coordinates of a dynamic musculoskeletal model to follow the desired kinematics [24]. Therefore, the performance criterion shown in (4) had to be minimized [24]: (4) � (� ⃗⃗) = ∑ �� 2 � �� = �̈ � ∗ − �̈ ���,� ∀� where � ⃗⃗ is the vector of muscle excitations, � is the number of actuators, �⃗ is the vector of constraints and � is the coordinate. In this case, the input files required were the adjusted model after running the RRA tool, the motion file with the ground reaction forces data, and the storage file with the new kinematics. The output files were XML files with controls for the actuators, muscle and reserve forces, and model and muscle states of the simulated movement. Finally, with the induced acceleration analysis tool the accelerations caused by individual forces acting on the model were calculated. To do this, a constraint to represent the footfloor contact was needed because the acceleration induced

by a muscle force contributor was divided into the acceleration induced by the force contributor itself and a partial acceleration induced by the contact between the foot and the ground (�� ), as shown in (5) [24] and both the induced acceleration and the partial contact force were unknown. �̈ � = [�]−1 {[�]�� + �� } (5) With the kinematic constraint, the constraint equations of motion and the kinematic constraint reaction forces were solved at the same time in (6) and (7) [24]: [�]�̈ + [�]� � = � (�) + � (�, �̇ ) + [�]�� [� ]�̈ = � (�, �, �̇ ) (6) (7) where � is the constraint matrix, � is the constraint reaction forces, � is the generalized force due to gravity, � is the force due to Coriolis and centrifugal effects, � and �̇ are the vectors of generalized coordinates and velocities, respectively, and � is a function that defines the conditions on accelerations. There were three possible

constraints: point, weld, and roll (Figure 2-7). A roll constraint, which limited penetration, slip, and twist, was chosen because it was the one that represented accurately the real interaction between the two bodies and it enabled the reproduction of experimentally measured ground reaction forces and moments. Methods | 11 y z y x z y x z x Figure 2-7: Possible types of a kinematic constraint in OpenSim between the foot and the ground: point, weld or roll (rolling on a surface) constraint. With a point constraint, the contact point has to remain in the same place, but different orientations between the bodies are allowed. With a weld constraint, the contact point has to remain in the same position and with the same orientation. With a roll constraint, the foot can be moved on the ground without penetrating the surface and the constraint has to be pure rolling, i.e, no twisting and no slipping [24] The conditions of the roll constraint are included in equations

(8)–(11) [21]: Roll constraint Equation Condition(s) Vertical, unilateral, non-penetrating �� (�) ≥ 0 �̂� > ��ℎ���ℎ��� (8) Non-penetrating and Fore-aft no-slip �̇ � (�, �̇ ) = 0 Mediolateral no-slip �̇ � (�, �̇ ) = 0 Vertical no-twist �� (�, �̇ ) = 0 �̂� · ��������� > √�� 2 + �� 2 (9) Non-penetrating and �̂� · ��������� > √�� 2 + �� 2 No-slip and �̂� · ��������� · �������� > �� (10) (11) where � and �̇ are the position and velocity of the point of contact on the foot segment with respect to the ground, � is the angular velocity of the foot segment with respect to the ground, �̂� is the measured vertical ground reaction force, ��ℎ���ℎ��� is a threshold for the vertical reaction force with a value of 10 N, ��������� is a friction

coefficient with a value of 0.65, �� and �� are the simulated fore-aft and mediolateral constraint reaction forces, respectively, �������� is a contact radius with a value of 0.01 m representing the size of the contact area between foot and ground, and �� is the simulated vertical constraint reaction moment. These four constraint equations were then differentiated in order to compute accelerations, so (7) was be reformulated as shown in (12) [21]: 12 | Methods [� ] = − [ ��� �� ��̇� ��̇ ��̇� ��̇ ��� ��̇ and [� ] = ] [ �2 �� 2 �̇ ��2 ��̇� �̇ �� ��̇� �̇ �� ��� �̇ �� (12) ] Therefore, (6) and (7) were only dependent on the constraint reaction forces and the vector of accelerations, and therefore the equations could have been resolved. In addition to the CMC input files, the storage files with the actuator controls and model states after running

the CMC tool were also needed. The output file included the induced accelerations generated by each force contributor. Results | 13 3 Results Figure 3-1 shows joint angles, ground reaction forces, and joint moments after running the IK and ID tools. Different cut-off frequencies are compared in the case of the latter two variables. In the four cases (Table 3-1), marker data were not filtered when running IK, but kinematics were later on filtered with OpenSim when running ID. Joints considered were the ankle, knee, and hip in the sagittal plane. Figure 3-1: Joint angles from IK (left), ground reaction forces (middle), and joint moments from ID (right) over the stance phase. Considered joints include the sagittal hip, knee, and ankle Marker data are filtered with OpenSim with cut-off frequencies of 12 (blue, orange, gray) and 50 Hz (yellow) and force data are unfiltered (blue) and filtered with 12 (orange) and 50 Hz (gray, yellow) with MATLAB. Table 3-1: Different possibilities of

input data for the IK and ID tools when considering whether or not they are filtered. Input data includes marker trajectory data and ground reaction force data The color of each case in the graph is also included. Combination 1 2 3 4 Marker data Initially unfiltered (for joint angles), but later filtered with OpenSim (for joint moments) 12 Hz 50 Hz Force data Color Unfiltered Blue 12 Hz-filtered Orange 50 Hz-filtered Gray Yellow First, marker trajectories were not filtered, and the output (joint angles) showed an initial dorsiflexed position of the ankle joint of -13.40º when the foot started the contact with the ground. Then, the ankle was dorsiflexed until it reached an almost constant value of approximately -34.00º during the majority of the stance phase After that, the ankle started 14 | Results to get plantarflexed until leaving the ground with a plantarflexed position of 23.93º Therefore, the ankle covered a great part of the entire range of motion of the

joint, which was defined between -40 and 30º, representing the negative value a dorsiflexion movement and the positive value plantarflexion movement. The knee started with an initial flexed position of 88.71º and it was slowly getting extended until reaching a position close to the vertical (totally extended knee) with a coordinate of 8.64º The hip joint at the sagittal plane experienced an extended trend as well, starting with a flexed position of 83.2º and finishing in an extended position of -500º Next, ground reaction forces measured with the force platform located on first place when the sprinter stepped on it included three force components, one moment component in the transverse plane and two center-of-pressure components in the same plane. However, due to the importance of the force against the other two, Figure 3-1 only includes this variable. When looking to the horizontal force, possibilities 1 and 3/4 had a similar trend, with smaller fluctuations in the case of the

second options due to some noise cancelation. The minimum value took place during the braking phase, at 3.77% of the stance phase, and had a value of -24.94 and -17483 N, respectively The maximum value happened during the propulsive phase, with values of 671.27 and 67149 N, respectively However, when comparing these two possibilities to combination 2, the horizontal was positive during the entire stance phase (minimum value was 80.53 N) In the case of the vertical force, the characteristic peak at the beginning of the stance phase totally disappeared in the case of combination 2 and the force had a value of 372.14 N when the foot left the force platform, a lot greater than 17.09 and 2003 N with combinations 1 and 3/4, respectively. Maximum values were 117793 and 117743 N, respectively, in these latter cases, compared to 118.56 N in the distorted signal When checking the mediolateral force, a really smooth signal was generated with possibility 2. Fluctuations in the first half of the

stance phase in combinations 1 and 3/4 disappeared in combination 2, even though minimum values were really close (-212.82, 21260, and -21202 N, respectively) Maximum values were pretty similar in the first two cases (61.92 and 5400 N, respectively) compared to the latter (783 N) Then, from the four possibilities for joint moments, combination 2 was excessively smooth when looking at the ankle, knee and hip joint moments in the sagittal plane. Ankle joint moment presented its first peak at 3.77% of the stance phase, ie, when the horizontal force had its minimum value (maximum absolute value of the braking phase), in combination 1 and at 5.67% in combinations 5 and 6, ie, one unit of time ahead The value in these peaks were of 68.91, 5982, and 6051 N·m, respectively In the case of combination 6, the maximum value for the moment took place at 58.49% while in the other two cases it was at 64.15%, three units of time ahead, having all a value of 14599 (3), 14346 (1), and 144.75 N·m (4)

Knee joint moment presented its first peak at 3.77% for the three combinations, with values of 118.24, 8214, and 8195 N·m, respecting numerical order In the case of combination 6, the maximum value for the moment took place at 56.60%, a while after (seven units of time) compared to combinations 3 and 5 (43.40%) Its value was also greater (180.29 N·m compared to 16918 and 16869 N·m, respectively) In the case of the hip joint, the moment presented its first peak at 3.77% for the three combinations, with values of -10.58, 1891, and 2964 N·m, respecting numerical order Results | 15 However, combination 4 started to follow a different trend with more smaller fluctuations compared to the other combinations. Joint moments were changed after running the RRA tool and new results showed that all the joint moments were smoothed while adjusting residuals, as it can be seen in Figure 3-2. In the sagittal plane, the ankle joint followed the same trend before and after RRA while the trend

got increasingly smoothed as a more proximal joint moment was compared to its previous result. In the case of the frontal and transverse planes, the moments were highly smoothed. Figure 3-2: Final joint moments from ID (yellow) and RRA (green) for the hip, knee, and ankle over the stance phase. The hip angle is shown in the three anatomical planes while the knee and ankle angles are only shown in the sagittal plane. The non-physical compensatory forces applied at the pelvis after performing ID had extremely great values (peaks of 1,234.70, 1,97563, and -1,96318 N in the anteroposterior, vertical, and mediolateral directions), but they were severely reduced after performing RRA (peaks of 7.75, -1492, and -1005 N, respectively) In the case of residual moments, peaks were cut down from -1272.76, -23159, and -47356 N·m to 775, -11875, and 10282 N·m, respectively. Results are shown in Figure 3-3 16 | Results Figure 3-3: Residual forces (top) and moments (bottom) from ID (green) and

RRA (blue). The latter case shows severely reduced values due to the reduction algorithm. Activations of right soleus, gastrocnemius medialis, biceps femoris long head, vastus lateralis, gluteus medius, and gluteus maximus were compared to processed EMG data over the stance phase in Figure 3-4. However, muscle activation from CMC did not compute the first 14.15% of the stance phase due to the definition of initial muscle states Figure 3-4: Activation of the main muscles of the lower limb computed with CMC (blue) and compared to processed EMG data (gray). Muscles selected are right soleus, gastrocnemius medialis, biceps femoris long head, vastus lateralis, gluteus medius, and gluteus maximus, since EMG was performed on them. Muscle activation from CMC started 1415% after toe-off Results | 17 Results show that there was a small delay between EMG data and computed activation, but the six muscles followed a trend close to the expected. Soleus, gastrocnemius medialis, and gluteus

medius were relaxed at the beginning of the computation (activations lower than 0.05) and reached their maximum activation at the end (090, 057, and 085, respectively) Biceps femoris, vastus lateralis, and gluteus maximus started the computation with some activation (0.67, 011, and 044, respectively) Biceps femoris was almost fully activated (0.94) right after and became more relaxed as the toe-off event was getting closer, finishing with an activation of 0.17 Vastus lateralis and gluteus maximus reached their maximum activation at toe-off (0.82 and 094, respectively) Induced constraint reactions were obtained after performing IAA and were compared to experimentally measured ground reaction forces in Figure 3-5. Induced forces started at 14.15% of the stance phase and matched adequately ground reaction forces until 7055%, where the x and z-components of the induced force dropped to zero and the y-component commenced to represent the y-component of the external force unsatisfactorily.

Therefore, results in the remain figures will only show data between 14.15 and 7055% of the stance phase. Figure 3-5: Ground reaction forces (green) and induced constraint reaction forces at the foot (blue). Their trend in each component is similar between 14.15 and 7055% of the stance phase Horizontal and vertical accelerations induced to body mass center by all the muscles were similar to measured accelerations, which were calculated with the experimental ground reaction forces divided into the mass of the subject (top-middle graph in Figure 3-6). Since data were only computed after 14.15% of the stance phase took place, the braking phase (first 6.60%) did not appeared in the results and it was not possible to determine major contributors during this phase. However, in the majority of the propulsive phase (graphs in rows 2-4 in Figure 3-6), gastrocnemius and soleus were the main muscles that contributed to propulsion and lift of the mass center. Their contribution to forward

acceleration was of 62.62 and 3743%, and to upward acceleration, 2708 and 5077% (Figure 3-7), respectively. The vasti group and rectus femoris also contributed considerably to upward acceleration with values of 17.19 and 1317 %, respectively, but they were driving the body mass center backwards (-7.09 and -593%, respectively) Gluteus maximus and medius contributed minimally to upward acceleration (0.48 and 003%, respectively) In contrast, the hamstrings group, specially the biceps femoris muscle, and tibialis anterior contributed to downward acceleration during the stance phase (-1.63% –biceps femoris– and -076%) Adductor group was also included, but its contribution to horizontal and vertical accelerations was almost neglected. 18 | Results Figure 3-6: Horizontal and vertical contribution of the measured ground reaction forces (GRF, top-left), of all the muscles (top-middle), and of the major lower-limb muscles (rest): soleus, gastrocnemius (medialis and lateralis combined),

rectus femoris, vasti (vastus intermedius, lateralis, and medialis combined), gluteus maximus, gluteus medius, biceps femoris long head, tibialis anterior, and adductor magnus. Each ray is the resultant vector of the horizontal and vertical components of the acceleration. Only accelerations between 14.15 and 7055% of the stance phase are shown Scale of the y-axis is not constant for every individual muscle contribution. Results | 19 Figure 3-7: Relative contribution to body propulsion (left) and body support (right) of the major lower-limb muscles considered in Figure 3-6. A positive value means forward and upward body mass center acceleration. Medial and lateral body mass center accelerations were also examined, and they are shown in Figure 3-8. Vasti and rectus femoris were the main contributors to medial acceleration, with contributions of 45.77 and 3024% (positive relative contributions as they were driving the body mass center in the same direction as the measured

acceleration, but negative overall contributions over the stance phase as they were generating a medial acceleration). Soleus and gastrocnemius muscles also contributed substantially to medial acceleration (17.21 and 1627%), while the biceps femoris and tibialis anterior were the major contributors to lateral acceleration (-6.50 and -427%) Figure 3-8: Mediolateral contribution of the major lower-limb muscles: soleus (light blue), gastrocnemius (medialis and lateralis combined; gas, dark blue), rectus femoris (rect fem, orange), vasti (vastus intermedius, lateralis, and medialis combined; brown), gluteus maximus (glut max,yellow), gluteus medius (glut med, gold), biceps femoris long head (bifemlh, green), tibialis anterior (tib ant, purple), and adductor magnus (add mag, pink). Total contribution of the ground reaction forces (GRF) are also included (gray area) A positive value drives the body mass center laterally. Only accelerations between 1415 and 7055% of the stance phase are

shown Discussion | 21 4 Discussion The most important findings were that the cut-off frequency was a parameter that had to be deeply studied when simulating a sprint running, since it was considerably dependent on data collected from the sprinters, that motion in the sagittal plane was tracked better than in the frontal and transverse planes, and that the main contributors to horizontal and vertical body mass center acceleration were the soleus and gastrocnemius muscles –assisted by the quadriceps in the case of body support, but hindered by them in the case of body propulsion– , while the quadriceps were the main contributors to lateral acceleration. The first findings were conceived while developing the project, while the latter findings supported the first hypothesis that expressed main contributors to forward, backward, and upward body mass center accelerations. The second hypothesis was found to be reversed First, the filtering technique of raw marker and force data

was analyzed during IK and ID. Regarding to joint angles, raw input marker data were used in order to get similar results to [26] and to Paul results when using Visual 3D. The beginning of the stance phase showed different dorsiflexion movements between using unfiltered and filtered marker data, being more gradual in the case of filtered data. However, the difference between both inputs was not that much significant when looking at the knee and hip joints. The filtering technique was more important in the case of force data, since using different cut-off frequencies led to outputs were the input signal was distorted when using a poor cutoff frequency. The ground reaction forces were misrepresented when using a filter with 12 Hz, a common frequency in walking and running studies, since the braking phase of the horizontal force totally disappeared. Therefore, a cut-off frequency of at least 50 Hz had to be used in order to avoid losing information about the contact between the foot and

the ground. However, the selection of the mentioned cut-off frequency had more to do with experimental data rather than the system used for data collection. Force data filtered with 50 Hz showed a similar trend to well-trained participants in [27] when looking at horizontal (anteroposterior) and vertical ground reaction forces of the first stance phase (stance phase of first step performed with the right leg). In both studies, the horizontal force had a small braking phase (in time and magnitude) followed by a great propulsive phase, and the vertical force had a peak impact at a percentage of the stance phase similar to the one where the maximum absolute horizontal-force value of the braking phase was achieved. The maximum value for the vertical force took place in the second half of the stance phase. However, when comparing the mediolateral force in both studies, the trend was found to be totally different. This finding made visible the individual dependence of this component of the

ground reaction force, as concluded in [13]. During this project, it was also checked that the impact peak on joint moments at the beginning of the stance phase was really dependent on the selected cut-off frequency for kinematic and kinetic data. For the ankle joint moment, the cut-off frequency had a small effect on the impact peak during the first 6% of the stance phase (braking phase), but this effect started to increase when looking to the knee and, especially, to the hip joint moments, i.e, when moving to more proximal body segments Since ground reaction forces were known, as they were measured with the force platform, and were applied at the foot segment, as the contact between the body and the ground took place on the foot body segment, the ankle joint net force and moment were calculated in first place using Newton’s second law. Then, from ankle joint reaction forces, the knee joint net force and moment were calculated, and consequently, it was possible to 22 |

Discussion generate the hip joint net force and moment. Since the ankle joint resultants included an impact peak, its magnitude was propagated when approaching more proximal body segments and this propagation involved an increment in the magnitude of the resultants at the knee and even greater at the hip joints. However, the magnitude of the joint resultants in the rest of the stance phase, i.e, around 94%, was not much affected by the filtering procedure. This finding was in line with Bezodis, Salo, and Trewartha’s in [28]. They studied how the filtering procedure affected the knee resultant joint moment by considering the same and different cut-off frequencies for marker and force data. As the cut-off frequency for force data was increasing, a biggest fluctuation was shown in the first 5% of the stance phase in the knee joint moment, since force data included more noise. In addition, in the case of the constant cut-off frequency for force data, a greater impact peak was found out

when the difference between the frequencies for marker and force data was bigger, i.e, the smallest peak happened when the cut-off frequency was the same for marker and force data. The reason of this trend had to do with removing the high-frequency content in the marker data and it caused inconsistencies in the frequency content of marker and force data, creating an abnormal high impact peak which did not represent what was actually happening. Since [28] only included the trend in the knee joint moment in the first stance of a sprint running, the trend in the ankle and hip joint moments were unable be checked. Therefore, the ankle, knee, and hip joint moments obtained with this study were also compared to [6] and [29]. The trend in the sagittal plane was similar, and the values were close when using normalized moments, i.e, in N·m/kg However, none of these studies included hip joint moments in the frontal and transverse plane, since it is in the sagittal plane where the most findings

of the movement are revealed. This fact is in line with graphs in , where it can be seen that OpenSim offers a reliable tracking system for the sagittal plane, but this system is weak when looking to the frontal and transverse planes and therefore joint moments in those planes are excessively smoothed. Next, residual forces and moments were reported in Figure 3-3 to ensure that their values were small enough so that they do not have a considerable effect on the calculations that followed. Forces were lower than 5% of the magnitude of the ground reaction forces in all the planes and moments were lower than 10% of the magnitude of the ground reaction forces times the height of the center of mass in the sagittal and frontal planes, as recommendations in [30], but not in the transverse plane, where the reduction was of approximately 25%. This finding might have shown the effect of having a wide step width, causing some trouble to OpenSim when reducing residuals. Then, muscle activations

measured with the EMG system during the experiment were compared to [31] as well as to different trials performed by the same sprinter. In the three cases, the trend of each muscle was similar. Therefore, muscle activations generated by the CMC tool had to have a strong correspondence with EMG data, as shown in Figure 3-4. However, a small delay between EMG and muscle activation was assessed. This delay was related to the electromechanical delay observed between the onsets of electrical signals and of muscle-force activities. Finally, ankle plantar flexors were the main group contributor to body propulsion and support, as indicated in [32]. The main contributor to body propulsion was the gastrocnemius (lateralis and medialis combined) muscle, followed by the soleus, while the main contributor to body support was the soleus, helped by the gastrocnemius. The importance of ankle plantar flexors during the first stance of a sprint running was in agreement with other studies ([26], [32]),

since the contraction of this muscle group and the Discussion | 23 advantage of having the mass center located ahead of the contact point in the first step enabled the sprinter to propel the body forward and upward. In addition, in the case of body propulsion, ankle plantar flexors were the only great contributors and had to face the intention of the vasti group (vastus intermedius, lateralis, and medialis) and rectus femoris, i.e, the quadriceps group, to drive the body mass center backwards. Meanwhile, in body support, both ankle plantar flexors and knee extensors contributed together to drive the body mass center upwards. Knee extensors helped the sprinter to acquire a more upright position, compared to the crouched position in the starting blocks. This last finding confirmed that the main function of knee extensors was propelling the body upward, as stated in [32]. Thus, the first hypothesis of this project was proved to be true for body propulsion, body braking, and body

support. However, these facts were only analyzed during the majority of the propulsive phase of the first stance (percentage interval considered in Figure 3-6). Furthermore, having a different main contributor to body propulsion and body support, even though they were from the same muscle group, was not in consonance with Debaere et al.’s findings in the first stance [32], since the soleus was the predominant contributor in both cases and the gastrocnemius followed, but its contribution was always smaller (31.70 versus 25.30% in the case of body propulsion and 3590 versus 1950% for body support) Still, the difference in relative contribution to body propulsion between soleus and gastrocnemius in this project and in [32] was not that large and perhaps the variance between both studies was due to having elite sprinters instead of well-trained sprinters as in [32]. As training level increases, muscles are further strengthened, and this could explain why gastrocnemius was found to be the

major contributor to body propulsion. Regarding to the medial and lateral drive of the body mass center acceleration, quadriceps was the main group contributor, specially the vasti, to medial acceleration, as shown in Figure 3-8. Soleus and gastrocnemius also contributed in this direction, but their contribution was not as remarkable as when driving the body forward and upward. Biceps femoris and tibialis anterior were the main contributors to lateral acceleration, but their contribution was minimal compared to medial contributors. This fact confirmed the second hypothesis, since most of the muscles contributed medially. Since the sprinter presented a wide step width, the mediolateral force was medial over the majority of the stance phase and therefore muscle contributions had to be greater in this direction. Indeed, from data collection of the group experiment data, sprinters generated a medial ground reaction force for at least the first 75% of the stance phase. There are limitations

with some aspects of this study. First, OpenSim has some limitations when using the RRA and CMC tools. In the case of the first tool, it needs 1 ms to finish working since it works one unit of time ahead, and therefore that time unit cannot be considered in the rest of the simulation. In the case of the CMC, the time penalty consists of 30 ms due to muscle activation and this number is significantly longer compared to the previous time. These time penalties, which sum a total of 31 ms, cause a lack of information of what is happening during that time in the measured locomotion. Therefore, it was impossible to get results for the entire gait cycle and it had a detrimental effect, since in a sprint running the different steps in the acceleration phase cannot be re-reproduced by performing several steps, as in walking, running, and even in the constant velocity phase of sprinting. In fact, in the particular case of the first step, all the information related to muscle activation and

contribution in the braking phase was lost. Also, OpenSim focuses more on the sagittal plane, since it is the main plane where human locomotion takes place, but a better tracking in the frontal and transverse planes 24 | Discussion would be more interesting when trying to integrate different variations in these other planes into the main movement, such as when analyzing the effect of the step width. Furthermore, the muscle-driven simulation has some restraints due to the use of a model. The designed model was tested for walking and running, but not for sprinting Therefore, some movements with an excessive knee and/or hip flexion could have been limited due to the range of motion of each joint. In the case of this analysis, neither the knee nor the hip exceeded their range of motion. However, this limitation problem was solved in the model developed in [33], as some muscle paths and properties were redefined. Yet, when this model was used to develop the project, it was not behaving

as expected in the last OpenSim steps (e.g only the medialis head of the gastrocnemius, and not the lateralis head, was included as ankle plantar flexors) and it had to be discarded. Another limitation of the model that was found, which also concerns to the second model, was that the MTP joint did not work at all when behind unlocked. Joint angles and moments were zero during the entire stance phase. As it was stated in [29], the MTP joint should not have been ignored in sprint running since it was found to cause an unnaturally high peak in the ankle joint moments. Therefore, the foot should have been defined as a twobody segment, comprising a rearfoot segment –from the ankle joint to MTP joint– and a forefoot segment –from the MTP joint to the distal hallux–, and the ground reaction forces should have been at the toes segment due to a forefoot contact. Finally, findings are based on the results when analyzing a sprint running of one sprinter with a wide step width during the

first stance phase. Thus, it is important to recall that these findings cannot be extrapolated to other sprinters with a neutral or cross-over step width, or even to wide step sprinters since only the subject with the widest step width was selected. Therefore, not even for this sprinter results can be hypothesized for other phases of the sprint, nor indeed the second step. As concluded in [32], some muscles that contribute the most to body mass center acceleration in the first step no longer are accounted in the second step. In addition to these limitations, further studies are needed in order to analyze movements with a remarkable motion out of the sagittal plane. First of all, the obviously follow-up project would be using all the trials from the different sprinters that performed the group experiment, instead of just the one with the widest step width. In addition, narrow trials could be interesting to consider since the same sprinter performed dynamic trials with his/her preferred

running style and with a forced narrower step width trying to simulate his/her neutral step width. Moreover, it might be worth analyzing how the mediolateral component of the force evolves when considering wide and narrow trials, to see if some conclusions regarding to this component could be made. According to Cavanagh and LaFortune [13], the mediolateral force included a high variability between subjects, but they did not take into account that some sprinters have a neutral step width while some others have a wide or cross-over step width. Considering only wide step width sprinters, it could be relevant as well to analyze the starting blocks clearance or more steps, not only the first step. In this case, new experiments in a different laboratory should be performed due to the need of more force platforms. An adaptation of moving the starting blocks backwards could also be contemplated, so that the sprinter would step in the platform in the second, third and so on step. However, this

second option would lead to an enormous amount of trials since only one step would be simulated at each trial and several trials of each step should be recorded to check for repeatability. Discussion | 25 As the evolution of the step width decreases as the sprinting moves forward [12], a comparison between neutral and wide step width sprinters in the different subsequent steps could also be interesting for a future study. Regarding to OpenSim limitations, a new model with reinforced muscles acting on the MTP joint could be designed and this way an accurate simulation of the sprint movement could be performed. Another improvement for model developers could be creating musculoskeletal models with different muscle properties according to the running experience, i.e, models representing elite, well-trained, trained, and non-trained (regular model). Conclusions | 27 5 Conclusions This project was the first study that considered muscle contribution to the body mass center

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validation of musculoskeletal References | 31 models and simulations of movement. Journal of Biomechanical Engineering, vol 137, no. 2, 020905 [31] Mero, A. and Komi, PV (1990) Reaction time and electromyographic activity during a sprint start. European Journal of Applied Physiology and Occupational Physiology, vol. 61, no 1-2, pp73-80 [32] Debaere, S., Delecluse, C, Aerenhouts, D, Hagman, F, and Jonkers, I (2015) Control of propulsion and body lift during the first two stances of sprint running: a simulation study. Journal of Sports Sciences, vol 33, no19, pp 2016-2024 [33] Lai, A.KM, Arnold, AS, and Wakeling, JM (2017) Why are antagonist muscles co-activated in my simulation? A musculoskeletal model for analysing human locomotor tasks. Annals of Biomedical Engineering, vol 45, no 12, pp 2762-2774 Appendix A | 33 A. Appendix A: State of the Art A.1 Sprinting biomechanics Biomechanics of human movement concerns a specific study and description of motion as well as an

analysis of external forces to be able to create this motion [1]. There is a particular field in biomechanics that is directly related to sprinting. This field is called sports biomechanics and it studies and analyzes human movement patterns in sports [2]. A.11 Gait cycle A gait cycle can be defined as the period of time when a foot makes contact with the ground until the same foot touches the ground again [3]. The gait cycle allows one to describe the continuous and repetitive pattern of the lower extremities, which represents how humans walk or run during locomotion [4]. Depending on the revised literature, a gait cycle represents only walking [4] or just the time between two strides, for any kind of locomotion [3]. In this report, the term gait cycle is going to be used like in the second case, and therefore the movement it represents will be included before this term. The gait cycle consists of steps and strides. A step can be defined as the period of time when one foot strikes the

ground until the other foot contacts the ground, while a stride represents two consecutive steps, i.e, a gait cycle [4] Furthermore, a gait cycle can be broadly divided into two phases: the stance phase and the swing phase. The stance phase is the part of the gait cycle where the foot is touching the ground, and therefore it lasts from the initial contact (IC) up to the toe-off (TO). The swing phase takes place when there is no contact between the foot considered for the stance phase and the ground, i.e, between toe-off and a new initial contact These two phases can be divided again into various stages. Depending on the kind of motion, stages of stance and swing phases are different. Differences between gait cycles The stance and swing phases for the human locomotion related to this project can be seen in Figure A-1, where there are three different gait cycles shown. The first gait cycle represents human walking, while the second and the third match the running and sprinting cycles. In

these last two cycles, there are two reversal points: the stance phase reversal point (StR) and the swing phase reversal point (SwR). 34 | Appendix A Figure A-1: Schematic representation of walking, running and sprinting gait cycles where IC stands for initial contact, LR for loading response, MSt for mid-stance, TSt for terminal stance, PSw for pre-swing, ISw for initial swing, TO for toe-off, MSw for mid-swing, TSw for terminal swing, StR for stance phase reversal point, and SwR for swing phase reversal point [3] (p. 79) The reversal points represent the change in energy absorption and generation that happen between the initial contact of the first and second strides [3]. The absorption period goes from SwR to StR, passing through the initial contact that begins the gait cycle–, while the generation period goes from StR and SwR. Hence, these two periods are out of phase, since they do not start at the beginning of the cycle. On the one hand, during the absorption period,

there is a drop in the position and velocity of the center of mass. On the other hand, during the generation period, the mass center is moved upwards, and its velocity is accelerated. This is followed by an increase in both kinetic and potential energy. Even though walking and running (including sprinting) have some similarities when concerning locomotion, there is a significant difference between the stance and swing phases in walking and running. During walking, there are two stages of double support, where both feet are touching the ground, at the beginning and the end of the stance phase. These two stages are loading response (LR) and pre-swing (PSw). On the contrary, during running, the two stages of double support are replaced by two stages of non-supportive double float, where either foot is in contact with the ground, i.e, both feet are airborne at the beginning and end of the swing phase [3]. The main reason which explains these two types of stages is that the stance phase

lasts more than 50% of the cycle during walking, while in running the toe-off happens usually before 50% of the total cycle [5][6]. In addition, shock absorption, ground reaction forces and velocity while running are much bigger than while walking [7]. Specifically, it was found that ground reaction forces can rise up to 250-275% of the body weight at the center of pressure during the running gait cycle, while in walking it does not usually even reach 120% of the body weight [8][9]. The difference between running and sprinting is due to the speed, which results in a change of the footstep in the initial contact. The first part of the foot contacting the ground during running is usually the rear part (hindfoot), while it is switched to a more frontal part (midfoot or forefoot) during sprinting, as speed increases. It is possible that the hindfoot never touches the ground during a sprint, as sprint runners are usually midfoot strikers [10]. Despite of this difference, running and

sprinting have the same stages during stance and swing phases. Table A-1 gathers together the main variables that distinguish walking, running and sprinting. Apart from the speed, those variables include stride length, duration of the whole gait cycle and the percentage of the cycle that corresponds to stance and swing phases. Appendix A | 35 Table A-1: A comparison of the stride characteristics between walking, running and sprinting. The main characteristics analyzed are the speed, stride length, cycle time, and the percentages of the stance and swing phases of the gait cycle [11][12][13]. Variables Walking Running Sprinting Speed (m/s) 0.67 – 132 1.65 – 400 8.00 – 900 Stride length (m) 1.03 – 135 1.51 – 300 4.60 – 450 Cycle time (s) 1.55 – 102 0.91 – 073 0.57 – 050 Stance phase (% of gait cycle) 60.00 – 6600 30.00 – 5900 20.00 – 2500 Swing phase (% of gait cycle) 40.00 – 3400 70.00 – 4100 80.00 – 7500 A.12 Running and

sprinting cycles Now that the difference between walking and running is clear, it is time to give the details of the distinct stages of both the stance and swing phases when running and sprinting. A brief outline of all the stages is included in Figure A-2. Figure A-2: The various stages in the running and sprinting gait cycles. The run can be divided into two different phases: the stance phase and the swing phase. During the stance phase, the stages that take place are initial contact, mid-stance stage, and terminal or propulsive stage. During the swing phase, those are initial swing, mid-swing, and terminal swing [14]. The stance phase As it was discussed earlier, the stance phase is the first part of the gait cycle and it is during this phase when the foot touches the ground for the first time. Therefore, all the body weight is supported by the leg in contact with the ground. The stance phase is further divided into three stages: initial contact, mid-stance and propulsion [15].

However, some other studies split the stance phase of running in four stages: initial contact, braking, mid-stance and propulsion [16]. The initial contact is the stage when the gait cycle starts. It represents the exact moment when the foot makes contact with the ground, right after having both feet off the ground. The contact can be accomplished with the hindfoot, midfoot or forefoot, depending on the speed of the run. At the initial contact, the foot is unlocked, which means that it is flexible and has a wide range of motion. It is during this stage where the shock is absorbed by both the leg and the foot in contact with the ground. The leg is internally rotated, the knee is flexed as well as the ankle, and the foot rolls in in order to get prepared for the impact. When considering four stages, the cushioning phase is included in the braking stage. During this stage, the absorption of the shock forces takes place while the body is landing on the foot. 36 | Appendix A The

mid-stance stage follows next. The foot flattens to provide support, and this support allows the body weight to get transferred from the hindfoot or midfoot to the forefoot and to get ready for toe-off. In the mid-stance, the foot moves from pronation (inversion movement) to supination (eversion movement). When all the body weight relies on the toes, the propulsion stage starts, and the foot is locked in order to push off the whole body forward. It finishes when the toe-off takes place, and the stance phase leads out to the swing phase. During this stage, the energy that was absorbed at the initial contact is released. The swing phase The stance phase is followed by the swing phase, which starts when the toes leave the ground. During this phase there is no contact between the foot and the ground. When the same foot strikes the ground again, the running gait cycle finishes and a new one begins. The swing phase starts with an initial swing stage, where neither of the feet are touching

the ground (double float or flight time). Then, the other foot strikes the ground and midswing stage takes place At the end, there is a terminal swing, which starts when the toes of the other foot are raised off the ground and which ends when the first foot touches the ground again. Between start and end points of the terminal swing, the second double float occurs. The swing phase is not that much studied with regard to running biomechanics because the foot is not making contact with the ground. In fact, it is being moved forward and getting ready for the next initial contact that will lead to a new gait cycle. Therefore, in this project, only the stance phase will be studied. A.13 Upper limb functions during running and sprinting Even though gait cycles are focused on the lower limb, one has to keep in mind that the upper extremities have to be taken into account because they provide balance to the body while running, stabilizing the trunk and the vertical push-off [17][18]. Both arms

usually swing when walking, running and sprinting. This motion is out of phase with the legs, since when the right leg moves forward, it is the left arm the one that moves along, and vice versa. The shoulders are the extremities in charge of driving the arms, moving them forward and backward, and producing the swing movement. It is common to flex the elbow while running and sprinting. With this configuration, it is possible to have the hand at the same height as the shoulder when the arm is moving forward, and at the same height as the hip when moving backward [19]. Indeed, a regular runner usually keeps the arms a little lower than the waist line and as relaxed as possible, while a sprint runner keeps them higher than the waist line. This difference lies in the need of a more powerful and repetitive movement while sprinting [18]. The balance given by the arms is with the aim of cancelling the lower extremities’ vertical moments about the body’s vertical axis due to the swinging

legs, and therefore arm swing acts as a counteracting mechanism [20]. Furthermore, the lack of this counteracting movement leads to greater vertical moments and higher metabolic cost of locomotion [21]. Apart from offering counterbalance, arm swing helps to avoid an unwanted rotation of the trunk as well as reducing the shock when the initial contact of the foot with the ground occurs [17]. In addition, it also helps to lift and drop the center of mass Therefore, it is important to consider the arms in the simulation. Appendix A | 37 A.14 Sprint phases During a sprint, there are three well-defined phases in the velocity-time curve: acceleration, constant velocity and deceleration [22]. However, it is possible to distinguish two sub-phases in the acceleration phase: the initial acceleration phase and the transition phase [23]. There are several studies that compare the different phases in sprinting and an agreement in the literature has not yet come, as it can be seen in Fig. 21 in

[24] (p 13) The distinct phases in this report were taken from [23]. The initial acceleration phase In this first phase, the sprinter is located on the starting block and adopts a crouched position, i.e, the sprinter has four points of contact to distribute the body weight uniformly: two contact points are the feet, touching the starting blocks, and the remaining two are the hands, touching the ground. In this forward lean position, the sprinter is located near the starting line and has a high center of mass (set position in Figure A-3) [25]. When the sprint begins, there is a strong and fast push off with both legs. The back leg moves forward while the front foot stays on the starting block. Even though the trunk is leaning forward, it forms almost a straight line with the front leg, which is extended (block clearing position in Figure A-3). Set position Block clearing position Figure A-3: The starting block clearance, where the sprinter moves from a crouched or set position (left)

to a forward lean or block clearing position (right) and steps on the floor for the first time of the run, starting with the first stride [26]. The rear leg produces 45% of the total force performed during the starting block phase [27]. At the same time, when the force is getting produced, there is an increase in knee and hip angles in both legs, but an initial decrease of ankle angles. Right after leaving the starting blocks, the sprinter is leaning forward and has the center of mass ahead of the point that offers support. This forward posture allows the center of mass to be lower and closer to the ground reaction force. During the first strides, this situation is reversed and by the end of the third stride, the center of mass is located behind [28]. Therefore, the initial acceleration phase covers the first two steps, apart from the starting block phase [23]. The reason of the change in position of the mass relies in a change in the mathematical sign of the horizontal ground

reaction forces. A forward lean offers a more horizontally guiding of the ground reaction forces, which are first negative and then positive during the contact period. Forces are negative during the braking phase, where the center of mass drops, and positive during the propulsive phase, where the center of mass rises and the force produced is greater [29] [30]. According to the literature, the braking phase lasts around 6.3-13% of the stance phase [31][32] and its peak force can drop down to -90% of the body weight [33]. Regarding to the 38 | Appendix A propulsive phase, the peak force can rise up to 128% of the body weight [33]. The vertical force can achieve 149% of the body weight [33]. The transition phase The transition phase starts when the sprinter touches down on the third step and lasts until the sprinter has reached 80% of the maximal velocity, which is supposed to happen right after the eleventh step [23]. During the transition phase the body of the sprinter decreases

its forward lean, reaching a more upright position (Figure A-4). The ground reaction forces no longer have to be driven horizontally, since the center of mass gets already behind after the third step. As speed increases, the braking phase becomes more important in the total contact: from 6.3-13% of the stance phase to 32.2% [34] However, the absolute value of the generated force in the propulsive phase is still greater: 90% of the body weight in the propulsive phase against 67% in the braking phase [34]. The vertical peak increases from 149% of the body weight to 333% [34], more than doubling its value. Figure A-4: The transition phase, where the sprinter moves from a forward lean position (left) to a more upright position (right) in order to develop a higher running speed [26]. It is during the whole acceleration phase, i.e, the initial acceleration and transition phases, where the greater force has to be generated and a high speed has to be produced. When comparing contact time, it

gets reduced as the sprinter takes off and running velocity increases [35]. This contact time will become even shorter during the constant velocity phase. As contact period decreases, impact forces increase their value The constant velocity phase After accelerating, there is a phase where running speed is constant until it is decreased again. The running velocity depends on both the stride length and stride frequency, and it is the latter parameter the one that has a greater influence on speed while sprinting [36]. In addition, the higher the speed, the lower the contact time and the higher the flight time. The constant velocity phase can be at submaximal, maximal or supramaximal speed. A submaximal speed is achieved when the sprinter is not running at the highest velocity, also called maximal velocity. A supramaximal speed can be reached with tail wind, running downhill or on a treadmill, and towing horizontally and/or vertically [25]. In the case of running at maximal (or

supramaximal) speed, two phases can be defined: the first phase is where the sprinter accelerates from the 80% of the maximal velocity to the 100% (or higher) of the maximal velocity and the second phase is where the sprinter keeps the maximal velocity [23]. As with the acceleration phase, the two phases of braking and propulsive are also occurring (Figure A-5). During the braking phase velocity decreases and the center of mass moves downwards while during the propulsive phase, speed increases and center of mass rises. However, the overall lowering and raising of the center of mass decreases in amplitude as speed increases [12]. Appendix A | 39 Figure A-5: The constant velocity phase, where each stride can be divided into stance and swing phases. Even though this phase is called constant velocity phase, the velocity during each stride fluctuates since the sprinter has to break and propel itself [26]. Even though this phase is called constant velocity, it changes within a single

step: the running velocity is lower when striking the ground than when pushing off. Therefore, to achieve a high velocity, the contact time has to be as small as possible. This contact time changes from 192 ms during the first step of initial acceleration phase [33] to 159 ms during the first step of the transition phase, i.e, the third step of the run [31], and to 94 ms during the constant velocity phase [25]. As speed increases, the braking phase lasts more during the maximal velocity phase than in the previous phases: around 39.5-495% of the stance phase [34] In the braking phase, the horizontal force generated during the first step of the initial acceleration phase represents the 44% of the produced force during the maximal velocity phase, and in the case of the vertical force, it represents only the 11% [25]. In the maximal velocity phase, the horizontal force during the braking phase is greater than the one produced during the propulsive phase: -130% of the body weight versus 88%

[34]. In the case of supramaximal speed, the horizontal peak forces correspond to -160 and 96%, respectively [25]. In the case of the vertical force, it is desired to have the total force as vertical as possible during the braking phase (490 and 587% of the body weight at maximal and supramaximal velocity, respectively) and as horizontal as possible during the propulsive phase (229 and 178%, respectively) [25]. Even though, during the propulsive phase, the force has a greater vertical component than the horizontal one, it is considerably lower than during the braking phase. The deceleration phase The last phase during a sprint run is the deceleration. In this phase, the stride rate decreases, although the stride length increases a little [35]. As well as the stride length, the contact time, braking distance and flight time also increase. However, running velocity decreases and center of mass gets lower [35]. There are no studies about ground reaction forces during the deceleration

phase, so no conclusions can be made. The lack of studies may be a result of the fact that the velocity-time curve is influenced by external factors as the distance of the sprint run increases. A.15 Sprint techniques There is a considerable amount of methods to develop an effective sprint and these methods are particularly related to the starting block and acceleration phases. It is in these two phases where the produced force has to be enhanced in order to get a higher running velocity. To obtain a greater force, all the major lower limb joints need to undergo a strong process of extensions [37]. 40 | Appendix A In the starting blocks, two possible methods can be highlighted. The first one consists of selecting an angle of the starting blocks of 40-65º, referred to the ground, because this tilt allows the greatest muscle-tendon length of the gastrocnemius and soleus muscles [38]. A larger initial muscle-tendon length is directly linked with a greater produced force. In addition,

since the gastrocnemius and the soleus are the main muscles of the ankle plantarflexors and help one with propulsion and stabilization during running and sprinting, it is relevant to have a greater initial muscle-tendon length in order to reduce the sprinting time. The second method related to the starting block phase has to do with applying a powerful pressure to the starting blocks while waiting for the gunshot because this motion pre-tenses the extensor muscles of the leg [38]. Again, as muscles are pre-tensed, a greater force will be generated. Moreover, when looking at the initial acceleration phase, there are there distinct positions: keeping the motion straight, with the heel on the midline of the body mass center of the body, or going side-to-side, with a mediolateral movement of the heel along the midline. In the first case the sprinter has a neutral step width, while in the latter case the sprinter can have a wide step width or a cross-over position depending on the sign of

the distance between the heel and the midline (positive or negative, respectively). Figure A-6 shows these three possible foot placements when touching the ground. Figure A-6: Different foot placements showing different step widths when contacting the ground: a neutral step width (left), a wide step width (middle), and a cross-over step width (right). In the case of the latter two positions, there is a side-to-side or mediolateral movement along the midline. When the placement of the foot is lateral (wide step width), the distance between the midline and the heel is positive, and when the placement is medial (cross-over step width), the distance is negative. The blue dashed line represents the track of the midline of the center of mass of the body and the orange dashed line, the track of the center of the heel [39]. In the case of going straight forward, there is a thought of wasting energy by the necessity of rotating the legs forwards and backwards at the hip joint [40]. The case

of going side-toside, which advocates the need of adducting the legs at the hip joint instead of rotating the legs, has not been extensively studied in the literature, especially in the case of cross-over sprinter. Both cross-over and wider positions have been considered as more metabolic-cost positions due to the need of keeping lateral balance [41], but also a wide step width facilitates the generation of the driving force [42]. A.2 Musculoskeletal models and muscle-actuated simulations of running Compared to walking, there is not a considerable amount of studies related to models and simulation of running. Hence, researches about sprinting are visibly lacking Therefore, in Appendix A | 41 this section, there will not be a distinction between running and sprinting, but a sprint will be considered as a type of running with a higher velocity and needing a greater force production. First, walking is the major motion that most people execute in their daily life which needs the

action of numerous muscles to support, propel, and balance human body. Therefore, the first studies related to gait analyses focused on this mode of locomotion. A likely fact that may affect the absence of running modeling and simulations as well could be the lack of knowledge of the main groups of muscles involved in forward propulsion. There are two different considerations: some studies proposed that knee extensors and ankle plantar flexors are the muscle groups that contribute to propulsion the most [3][5], while other studies indicate that those muscles are hip extensors [43]. This disparity could be caused by the incapacity of inverse dynamics and EMG analyses to recognize which are the main contributors. Another probable reason that justifies the insufficient investigation in running could be due to the need of a laboratory big enough to perform the run. If space is a problem when performing walking analysis, running observations are even harder. Indeed, a bigger capture motion

system is needed, with the involved cost. Therefore, it is common to use instrumented treadmills, even though there is not a direct connection between kinematics and ground reaction forces of the treadmill and a regular run [44]. Moreover, even though literature includes a deep study related to the dynamic joint properties, such as mass, inertias, length, and location of the mass center of the body segments, there is a lack of study in muscle properties. Therefore, some properties that perfectly work in walking studies may represent an obstacle to running, and specially to sprinting, simulations due to the higher range of motion, joint moments, and external forces [45]. In addition, one of the main difficulties that has to be faced with computational modeling is the muscle-moment redundancy problem [46]. Thus, several studies used torque-actuated muscles, i.e, models that have joints but no muscles, for both running and sprinting simulations (references in pp. 21-22 in [45]) A.21

Models Since it is not possible to measure individual muscle forces in vivo or with a non-invasive procedure, muscle forces have to be predicted with the use of a musculoskeletal model [47]. A computer-based musculoskeletal model is an instrument that allows one to visualize human movement, analyze the functional capacity of muscles, and design improved surgical procedures [48]. Therefore, this musculoskeletal model has to include models of the skeleton, muscle paths, muscle-tendon actuation, muscle excitation-contraction coupling, and body motion [49]. A computer-based musculoskeletal model allows one to obtain muscle-actuated simulations. The human body is represented by a multi-element mechanism that can be divided into bones, as elements of the mechanism, articulations, as joints of the mechanism, and muscles, as actuators that drive the mechanism [50]. However, these musculoskeletal models include some simplifications, such as considering the bones as infinitely rigid bodies and

articulations as ideal joints without including the cartilage, menisci, ligaments, and capsule structures [50]. Indeed, some models only have two dimensions instead of three when they focus on the flexion and extension movements of the sagittal plane. The insertion of the muscle tendons occurs at single points on the bones and there are two possible methods to model muscle paths: with a straight-line connecting the centroids of the muscle attachment sites or with a centroid-line connecting the position of crosssectional centroids of the muscle [49]. 42 | Appendix A Muscles are mechanically described with the Hill-type model in series with an elastic tendon. Therefore, the musculotendon unit consists of three components: the contractile – active– element and two elastic elements (parallel –passive– and series –elastic–). Muscle properties are defined by the peak isometric force, fiber length, pennation angle, and the shortening velocity. Furthermore, muscles need some

time to be activated or relaxed. This delay between muscle excitation and muscle activation is modeled as shown in (A.1) [51]: �̇ = � − �̂ � (A.1) where �̇ is the time change rate of muscle activation, � is muscle excitation, �̂ is the computed activation expressed in (A.2) [52], and � is the time constant expressed in (A3) [52]: • �̂ = �−���� (A.2) 1−���� where � is muscle activation and ���� is an adjustable lower bound. • �={ ���� · (0.5 + 15 · �̂) � > �̂ (A.3) ������ 0.5+15·�̂ � ≤ �̂ where ���� and ������ are muscle activation and deactivation time constants with a default value of 10 and 40 ms respectively. Once the model is designed, it can be used to compute muscle forces, which cannot be measured with a non-invasive procedure. To be able to obtain muscle forces from marker trajectories and external forces data, an inverse or forward

dynamic simulation has to be performed. From the existing models in the literature, the three-dimensional musculoskeletal model more complete and that has been used in most of the studies of walking, running, and sprinting is the one developed by Hamner et al. in 2010 [44] This model divided the human body into 12 body segments: head and torso, pelvis, and right and left thigh, shank, foot, upper arm, and lower arm. Then, joint kinematics were defined by 29 DOF: 6 at the pelvis, 5 in each leg, and 13 in the upper body. Finally, the lower limbs and lumbar motions were actuated by 92 Hill-type musculotendon actuators, and the upper limbs were driven by ideal torque actuators. Another widely-used model is the one from Rajagopal et al., created in 2015 and tested for walking and running [53]. This model divided the human body into 22 body segments: head and torso, pelvis, and right and left femur, patella, tibia and fibula, talus, calcaneus, humerus, ulna, radius, and hand. Joint

kinematics were defined by 37 DOF: 6 at the pelvis, 7 in each leg, and 17 in the upper body. The lower limbs were actuated by 80 Hill-type musculotendon actuators, and the upper body were driven by 17 ideal torque actuators. This model was improved in 2017 by Lai, Arnold, and Wakeling by increasing the range of motion of the knee from 120º to 140º of flexion, by renovating the paths of the muscles affected, and by correcting properties related to force generation of eleven muscles [54]. Apart from enabling walking and running simulations, the model was also tested for sprinting and cycling. Appendix A | 43 A.22 Simulations There are only a few studies that include a musculoskeletal model to estimate muscle forces from experimental data. These investigations were mainly performed from runs on instrumented treadmills ([44] and Thelen et al., 2005; Chumanov et al, 2007; Gazendam and Hof, 2007 references in [45]), and they are not equivalent to regular runs (Nelson et al., 1972;

Elliott and Blanksby, 1976; Frishberg, 1983; Nigg et al., 1995; Riley et al, 2008 references in [45]). There are only some studies that have taken a deeper look at muscle function during running and those studies are going to be presented in this review of the state of the art. However, the speed limit is 500 m/s, considerably lower than the limit for sprinting (9.00 m/s [12]) One of those deeper studies was performed in 2006 by Sasaki and Neptune. They simulated a forward dynamic running simulation at a speed of 1.96 m/s using a twodimensional musculoskeletal model, apart from a walking simulation [55] The selected speed was the preferred transition speed, i.e, the speed at where the person voluntarily switches from walking to running. The study suggested that, during the stance phase of running, the muscles that mainly contributed to body support were the vastus (VAS), gluteus maximus (GMAX) and soleus (SOL) muscles. In the case of forward propulsion, principal contributors were GMAX

at the braking phase and the SOL, gastrocnemius (GAS), and hamstrings (HAM) at the propulsive phase. However, this study had some limitations, since it considered only a two-dimensional model and it did not include the upper limb. In 2010, Pandy and Andriacchi used a three-dimensional muscle-actuated model to analyze how muscle function of the lower extremities was in a slow run at a preferred transition speed of 2.10 m/s and a run at the preferred speed of 340 m/s, apart from walking simulations [47]. The muscles that were analyzed were GMAX, gluteus medius (GMED), VAS, SOL, and GAS at the stance phase of a running cycle. At the preferred transition speed, VAS and SOL developed higher forces when compared to walking at the same speed. At the preferred speed, equivalent results as in Sasaki and Neptune study were achieved: GMAX, VAS, and SOL were the main contributors to body support. In the case of forward propulsion at the preferred speed, GMAX and GMED were the primarily

contributors at the braking phase and SOL and GAS at the propulsive phase. GMED was not analyzed in Sasaki and Neptune study. This study also considered the transverse plane, where GMED was the only muscle that contributed accelerating the center of mass medially, i.e, the rest of the muscles contributed laterally. Also in 2010, Hamner et al. simulated a running cycle at a higher speed of 396 m/s using a three-dimensional musculoskeletal model which included the upper extremities [44]. The whole model included 76 muscles of the lower extremities and torso. They found out that the quadriceps muscle group was the main contributor to both body support and forward propulsion during the braking phase of stance, without including GMAX and SOL as in previous studies. During the propulsive phase of stance, SOL and GAS were the main contributors. Unlike earlier studies, the results displayed the resultant acceleration of each individual muscle, calculated as the sum of the vertical and

horizontal acceleration, instead of the contribution to the ground reaction forces. In 2011, Lin et al. used a three-dimensional musculoskeletal model to calculate the muscle forces of the lower extremities during a running gait cycle with a speed of 3.48 m/s [56]. The selected muscles in this study were: SOL, GAS, VAS, rectus femoris (RF), GMAX, GMED, HAM, and iliacus and psoas combined (ILPSO). The main contributors to body support and forward propulsion were similar. 44 | Appendix A However, instead of analyzing the contribution of each lower-limb muscle, the aim of the study was to compare the results obtained from an inverse dynamic and a forward dynamic simulation. The main difference between forward dynamics and inverse dynamics is that the first simulation needs muscle excitation to calculate motion and ground reaction forces, while inverse dynamics can obtain both ground reaction forces and muscle excitation. In the inverse dynamic simulation, static optimization (SO) was

used. SO can be considered as a continuation of inverse dynamics that solves individual muscle forces at each time instant [45]. Inverse dynamics uses experimental joint kinematics and ground reaction forces and generates the net joint moments that are applied around each joint. These net joint moments are then used by SO to solve the individual muscle forces by minimizing the sum of squares of muscle activations at each instant. However, SO does not include timedependent muscle properties, nor does it include time-dependent performance criteria and explain muscle coordination principles [57]. In the forward dynamic simulation, computed muscle control (CMC) and neuromusculoskeletal tracking (NMT) were used. Forward dynamics uses neural excitation signals to generate the joint motion. They both use a feedback controller and include timedependent muscle properties, such as muscle activation dynamics However, they solve the muscle-moment redundancy problem in two different ways: CMC uses

static optimization at each instant and NMT minimizes a time-dependent performance criterion, such as minimum muscular effort or minimum metabolic energy consumption, over the whole cycle [56]. Therefore, while CMC only minimizes the sum of the squares of all muscle activations, NMT also minimizes the sum of squares of the joint torque tracking errors. Also, in 2011, Dorn, Lin, and Pandy analyzed how muscles contributed to the vertical, horizontal, and mediolateral components of the ground reaction forces considering six different models of possible interaction between the foot and the floor: ball, universal, hinge, weld, single-point and multi-point [58]. The first five ground contact models contemplate one single contact point at the center of pressure, while the last one considered five contact points. In addition, the first four models had time-independent constraints, while the last two had time-dependent constraints. In a later study in 2013, Hamner and Delp used the model that

Hamner et al. created in 2010, but they analyzed muscle contributions to support and propulsion when running at four different speeds: 2.00, 300, 400, and 500 m/s [59] Comparing the results of both studies, the latter with a speed of 4.00 m/s, no major differences were found in the trend of the corresponding muscle contributions. The study also included peak contributions to mass center acceleration. In 2015, Debaere et al. studied the contribution of both lower-limb joint moments and individual muscle forces to the vertical and horizontal mass center acceleration during the first two steps of a sprint [60]. This was the first study that introduce muscle contributions during sprinting and that linked both joint and muscle functions. The ankle was predominant joint contributor to support and propulsion the body in the first step, with the soleus and gastrocnemius as the main muscle contributors. The knee and the hip offered an auxiliary help in the first step, while only the knee helped

in the second step. A.3 Biomechanical software tools There is not a standard software tool to produce dynamic simulations of movement. These movements include walking, running, sprinting, jumping, and cycling, among others. Many laboratories build up their own simulation system, but they do not share their system and they do not allow another evaluation of their results [61]. This represents a significant constraint when talking about simulations of movement which could be avoided. Appendix A | 45 Having many different simulation systems involves that a new researcher has to dedicate a big amount of time developing, analyzing and controlling methods that already exist but are not open for researchers. These methods include the evaluation of musculoskeletal geometry, muscle-tendon parameters, and joint kinematics. In 1994, Delp and Loan created SIMM (Software for Interactive Musculoskeletal Modeling), which is a software package that offers a general tool to develop, modify, and

evaluate different musculoskeletal models without the need of programming [62]. However, SIMM has some limitations: it does not allow the user to compute muscle excitations, nor does it include enough tools for analyzing dynamic simulations [61]. On top of that, since the code is not accessible, it is not extensible, and no more features can be added. At the beginning of the twenty-first century, AnyBody Modeling System was created within AnyBody Technology. This musculoskeletal modeling system allows the user to analyze the interaction between the human body and the environment, which can be both modelled [63]. The environment can be within the body, attached to it, or interacting with it [64]. In 2006, another modeling tool called OpenSim was released. Unlike AnyBody, OpenSim is an open-source and freely available software that allows the user to model human body and analyze simulations of movement [63]. There is a community behind the system that shares several musculoskeletal

models, examples, tutorials, and the code of the program itself. It also offers support with a user’s and developer’s guide, and with an active forum. A.4 Summary There are several studies associated with the analysis of human walking, since walking is the most common locomotion mode. Some of those studies focus on the similarities and differences between walking and running, since running is an inherent prolongation of walking which usually needs a greater speed as well as a higher motion range and ground reaction forces, among other capabilities. However, the number of studies that examine sprinting biomechanics is quite restricted, and they mainly focus on different phases (acceleration as a whole, constant velocity), speeds (submaximal, maximal and supramaximal), or the distance travelled. Using OpenSim, an analysis of muscle contributions similar to [44] and [59], but performed at the beginning of a start sprint will be executed, as in [60]. This study differs from [60]

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Melbourne [46] Crowninshield, R.D (1978) Use of optimization techniques to predict muscle forces. Journal of Biomechanical Engineering, vol 100, no 2, pp 88-92 [47] Pandy, M.G and Andriacchi, TP (2010) Muscle and joint function in human locomotion. Annual Review of Biomedical Engineering, vol 12, pp 401-433 [48] OpenSim Documentation. [online] Available from: https://simtkconfluence.stanfordedu/display/OpenSim/OpenSim+Documentation [Accessed February 2018] [49] Pandy, M.G (2001) Computer modeling and simulation of human movement Annual Review of Biomedical Engineering, vol. 3, pp 245-273 [50] Viceconti, M., Testi, D, Taddei, F, Martelli, S, Clapworthy, GJ, and Jan, SVS (2006). Biomechanics modeling of the musculoskeletal apparatus: status and key issues. Proceedings of the IEEE, vol 94, no 4, pp 725-739 Appendix A | 49 [51] Millard, M., Uchida, T, Seth, A, and Delp, SL (2013) Flexing computational muscle: modeling and simulation of musculotendon dynamics. Journal of Biomechanical

Engineering, vol. 153, no 2, 21005 – 11 pages [52] Thelen, D.G (2003) Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. Journal of Biomechanical Engineering, vol. 125, no 1, pp 70-77 [53] Rajagopal, A., Dembia, CL, DeMers, MS, Delp, DD, Hicks, JL, and Delp, SL (2016). Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Transactions on Biomedical Engineering, vol 63, no 10, pp 2068-2079 [54] Lai, A.KM, Arnold, AS, and Wakeling, JM (2017) Why are antagonist muscles co-activated in my simulation? A musculoskeletal model for analysing human locomotor tasks. Annals of Biomedical Engineering, vol 45, no 12, pp 2762-2774 [55] Sasaki, K. and Neptune, RR (2006) Differences in muscle function during walking and running at the same speed. Journal of Biomechanics, vol 39, no 11, pp. 2005-2013 [56] Lin, Y.C, Dorn, TW, Schache, AG and Pandy, MG (2012) Comparison of different methods for estimating muscle forces in human

movement. Proceedings of the Institution of Mechanical Engineers, vol. 226, no 2, pp 103-112 [57] Anderson, F.C and Pandy, MG (2001) Static and dynamic optimization solutions for gait are practically equivalent. Journal of Biomechanics, vol 34, pp 153-161 [58] Dorn, T.W, Lin, YC, and Pandy, MG (2012) Estimates of muscle function in human gait depend on how foot-ground contact is modelled. Computer Methods in Biomechanics and Biomedical Engineering, vol. 15, no 6, pp 657-668 [59] Hamner, S.R and Delp, SL (2013) Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds. Journal of Biomechanics, vol. 46, pp 780–787 [60] Debaere, S., Delecluse, C, Aerenhouts, D, Hagman, F, and Jonkers, I (2015) Control of propulsion and body lift during the first two stances of sprint running: a simulation study. Journal of Sports Sciences, vol 33, no19, pp 2016-2024 [61] Delp, S.L, Anderson, F C, Arnold, AS, Loan, P, Habib, A, John, CT, Guendelman, E.,

and Thelen, DG (2007) OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Transactions on Biomedical Engineering, vol. 54, no 11, pp 1940–1950 [62] Delp, S.L, and Loan, JP (1995) A graphics-based software system to develop and analyze models of musculoskeletal structures. Computers in Biology and Medicine, vol. 25, no 1, pp 21-34 [63] Langholza, J.B, Westmana, G, and Karlsteena, M (2016) Musculoskeletal modelling in sports - Evaluation of different software tools with focus on swimming. Procedia Engineering, vol 147, pp 281–287 [64] General description of AnyBody. [online] Available from: https://github.com/AnyBody/support/wiki/General-description-of-AnyBody [Accessed March 2018] Appendix B | 51 B. Appendix B: Marker placement protocol Table B-1: Description of all the experimental markers used during the experiment Torso (and head) RFHD Right front head marker, located over the right temple LFHD Left front head marker, located over

the left temple RBHD Right back head marker, located at the same height as the right front head marker but on the back of the head LBHD Left back head marker, located at the same height as the left front head marker but on the back of the head RSHO Right shoulder marker, located on the right acromioclavicular joint LSHO Left shoulder marker, located on the left acromioclavicular joint CLAV Clavicle marker, located on the jugular notch C7 Seventh cervical vertebra marker, located on the spinous process of the seventh cervical vertebra STRN Sternum marker, located on the xiphoid process of the sternum L1 First lumbar vertebra marker, located on the spinous process of the first lumbar vertebra Pelvis RILC Right ILC (iliac crest), located over the right iliac crest LILC Left ILC, located over the left iliac crest RASI Right ASIS (anterior superior iliac spine), located over the right anterior superior iliac spine LASI Left ASIS, located over the left anterior

superior iliac spine RPSI Right PSIS (posterior superior iliac spine), located over the right posterior superior iliac spine LPSI Left PSIS, located over the left posterior superior iliac spine Right thigh RKNE Right lateral knee marker, located on the lateral epicondyle of the right femur RMKN Right medial knee marker, located on the medial epicondyle of the right femur r thigh1 r thigh2 r thigh3 r thigh4 Right thigh markers, located on the thigh between the hip and the right knee 52 | Appendix B Table B-1 (continued) Left thigh LKNE Left lateral knee marker, located on the lateral epicondyle of the left femur LMKN Left medial knee marker, located on the medial epicondyle of the left femur l thigh1 l thigh2 l thigh3 l thigh4 Left thigh markers, located on the thigh between the hip and the left knee Right shank RANK Right lateral ankle marker, located on the lateral malleolus of the right fibula along an imaginary line that passes through the transmalleolar axis

RMAN Right medial ankle marker, located on the medial malleolus of the right tibia along an imaginary line that passes through the transmalleolar axis r shank1 r shank2 r shank4 Right shank markers, located on the shank between the right knee and the right ankle Left shank LANK Left lateral ankle marker, located on the lateral malleolus of the left fibula along an imaginary line that passes through the transmalleolar axis LMAN Left medial ankle marker, located on the medial malleolus of the left tibia along an imaginary line that passes through the transmalleolar axis l shank1 l shank2 l shank3 l shank4 Left shank markers, located on the shank between the left knee and the left ankle Right foot RHEE Right heel marker, located on the distal aspect of bisection of the right posterior calcaneal surface RTOE Right toe marker, located on the head of the second metatarsal of the right foot RLFT Right lateral midfoot marker, located close to the floor between the tuberosity of

the fifth metatarsal bone of the right foot and the right cuboid bone RMT1 Right first metatarsal marker, located on the head of the first metatarsal of the right foot RMT5 Right fifth metatarsal marker, located on the head of the fifth metatarsal of the right foot Appendix B | 53 Table B-1 (continued) Left foot LHEE Left heel marker, located on the distal aspect of bisection of the left posterior calcaneal surface LTOE Left toe marker, located on the head of the second metatarsal of the left foot LLFT Left lateral midfoot marker, located close to the floor between the tuberosity of the fifth metatarsal bone of the left foot and the left cuboid bone LMT1 Left first metatarsal marker, located on the head of the first metatarsal of the left foot LMT5 Left fifth metatarsal marker, located on the head of the fifth metatarsal of the left foot Right upper arm RELB Right lateral elbow marker, located on the lateral epicondyle of the right humerus RMEL Right medial

elbow marker, located on the medial epicondyle of the right humerus r u arm1 r u arm2 r u arm3 Right upper arm markers, located on the upper arm between the right shoulder and the right elbow Left upper arm LELB Left lateral elbow marker, located on the lateral epicondyle of the left humerus LMEL Left medial elbow marker, located on the medial epicondyle of the left humerus l u arm1 l u arm2 l u arm3 Left upper arm markers, located on the upper arm between the left shoulder and the left elbow Right lower arm (and hand) RLWR Right lateral wrist marker, located on the styloid process of the right radius RMWR Right medial wrist marker, located on the styloid process of the right ulna r farm1 r farm2 r farm3 Right lower arm markers, located on the lower arm between the right elbow and the right wrist RFIN2 Right second metacarpal marker, located on the head of the second metacarpal of the right hand RFIN5 Right fifth metacarpal marker, located on the head of the fifth

metacarpal of the right hand 54 | Appendix B Table B-1 (continued) Left lower arm (and hand) LLWR Left lateral wrist marker, located on the styloid process of the left radius LMWR Left medial wrist marker, located on the styloid process of the left ulna l farm1 l farm2 l farm3 Left lower arm markers, located on the lower arm between the left elbow and the left wrist LFIN2 Left second metacarpal marker, located on the head of the second metacarpal of the left hand LFIN5 Left fifth metacarpal marker, located on the head of the fifth metacarpal of the left hand Appendix C | 55 C. Appendix C: Electrode placement protocol Table C-1: Description of the recommendations for the location of electrodes used during the experiment on the selected muscles [18]. These muscles are the soleus, gastrocnemius medialis, biceps femoris, vastus lateralis, gluteus medius, and gluteus maximus. Soleus Starting posture Sitting with the knee flexed 90º and having the foot in contact with

the table Location of the electrodes At 2/3 on the line between the medial condyle of the femur and the medial malleolus Orientation of the electrodes In the direction of the line between the medial condyle and the medial malleolus Clinical test Keeping or pushing the knee downward with manual resistance on the knee while the subject tries to lift the heel from the table Gastrocnemius medialis Starting posture Lying down with the knee extended and the foot projecting over the end of the table Location of the electrodes On the most prominent bulge of the muscle Orientation of the electrodes In the direction of the shank Clinical test Pulling the heel upward causing plantarflexion of the foot by applying pressure against the calcaneus and the forefoot Biceps femoris Starting posture Lying down with the thigh on the table and the knees flexed. The thigh should be in slight lateral rotation and the shank in slight lateral rotation with respect to the thigh Location of the

electrodes At 1/2 on the line between the ischial tuberosity and the lateral epicondyle of the tibia Orientation of the electrodes In the direction of the line between the ischial tuberosity and the lateral epicondyle of the tibia Clinical test Pressing against the shank, proximal to the ankle, in the direction of knee extension 56 | Appendix C Table C-1 (continued) Vastus lateralis Starting posture Sitting on a table with the knees in slight flexion and the upper body in slight bend backward Location of the electrodes At 2/3 on the line between the anterior superior iliac spine and the lateral side of the patella Orientation of the electrodes In the direction of the muscle fibers Clinical test Extending the knee –without rotation of the thigh– while applying pressure against the shank, above the ankle, in the direction of flexion Gluteus medius Starting posture Lying on the side on a table Location of the electrodes At 1/2 on the line between the iliac crest

and the greater trochanter Orientation of the electrodes In the direction of the line between the iliac crest and the greater trochanter Clinical test Lying on the side with the legs spread against manual resistance on the ankles Gluteus maximus Starting posture Lying down on a table Location of the electrodes At 1/2 on the line between the sacral vertebrae and the greater trochanter, i.e, on the greatest prominence of the middle of the buttocks Orientation of the electrodes In the direction of the line between the posterior superior iliac spine and the middle of the posterior aspect of the thigh Clinical test Lifting the resistance complete leg against manual www.kthse