THREE DIMENSIONAL KINEMATICS OF HUMAN METATARSOPHALANGEAL JOINT DURING LOCOMOTION

THREE DIMENSIONAL KINEMATICS OF HUMAN METATARSOPHALANGEAL JOINT DURING LOCOMOTION A thesis submitted to The University of Manchester for the degree of Master of Philosophy in the Faculty of Engineering and Physical Science 2014 Sivangi Raychoudhury School of Mechanical, Aerospace and Civil Engineering

2 Contents List of Tables... 5 List of Figures... 7 Acknowledgements... 14 Chapter 1: Introduction 1.1 Background... 15 1.2 Objectives... 16 1.3 Thesis Overview... 17 Chapter 2: Literature Review 2.1 Introduction... 19 2.2 Human Foot Anatomy... 19 2.3 Gait Cycle and Gait Analysis... 22 2.4 Kinematic analysis of the human foot... 26 2.5 Discussion... 30 Chapter 3: Theoretical Background 3.1 Human anatomical reference planes... 32 3.2 Human body model... 33 3.3 Segmental Kinematics... 34 3.3.1 Global Reference System (GRS)... 34 3.3.2 Local reference system (LRS)... 35 3.3.3 Technical and Anatomical Coordinate system (ACS)... 35

3 3.4 Joint Kinematics... 36 3.5 The Helical Axis Approach... 37 3.6 The Functional Method... 39 Chapter 4: Three-Dimensional Gait Measurement 4.1 Introduction... 42 4.2 The motion capture system... 43 4.3 Gait measurement... 44 4.3.1 Experimental protocol... 46 4.3.2 Force plate... 51 4.3.3 QTM Software... 52 4.3.4 Data analysis with GMAS... 55 4.4 Some Measurement Results... 58 4.5 Discussion... 59 Chapter 5: Three-Dimensional Kinematics of Human Metatarsophalangeal Joint during Level Walking 5.1 Background... 61 5.2 Method... 64 5.2.1 MP joint definition and parameters... 64 5.2.2 Data analysis... 65 5.3 Results... 69 5.4 Discussions... 77 5.5 Conclusion... 79

4 Chapter 6: Three-Dimensional Kinematics of Human Metatarsophalangeal joint during running 6.1 Background... 80 6.2 Method... 83 6.2.1 Data analysis... 83 6.3 Results... 89 6.4 Discussion... 100 6.5 Conclusion... 102 Chapter 7: Conclusion and Future Work 7.1 Conclusions... 103 7.2 Future Work... 105 Appendix Appendix A Anatomical landmarks used in 3D gait measurement... 107 Appendix B Cardan angles plots... 112 Appendix C Publication list... 115 Appendix D MATLAB codes... 116 References... 124 Words 31858

5 List of Tables Chapter 4 Table 4.1. Definitions of the anatomical coordinate system for the lower limb (see Appendix A, for details)....49 Table 4.2. Determination of the joint centre position (see Appendix A for details).51 Table 4.3. Anthropometric details of the six subjects 58 Chapter 5 Table 5.1. The data presenting the orientation and position of the functional axis (1) and anatomical axis (2), for all the six subjects during slow walk. 66 Table 5.2. The data presenting the orientation and position of the functional axis (1) and anatomical axis (2), for all the six subjects during normal walk. 67 Table 5.3. The data presenting the orientation and position of the functional axis (1) and anatomical axis (2), for all the six subjects during fast walk 68 Table 5.4. The result of the statistical analysis of the position and orientation difference between the functional axis (FA) and the anatomical axis (AA) of the MP joint.75 Table 5.5. The result of the statistical analysis of the effect of walking speed on the orientation and position of the functional axis (FA) of the MP joint 76 Table 5.6. The result of the statistical analysis of the effect of walking speed on the orientation and position of the anatomical axis (AA) of the MP joint.77 Chapter 6 Table 6.1. The data presenting the position and orientation of the FA (1) and AA (2), during slow run...84

6 Table 6.2. The data presenting the position and orientation of the FA and AA during normal run.85 Table 6.3. The data presenting the position and orientation information of the FA and AA during fast run...85 Table 6.4. The table presenting the position and orientation data of FA for all six speeds, from slow walking to fast running, as 1 to 6 respectively 87 Table 6.5. The results of the statistical analysis of the position and orientation difference between the functional axis (FA) and the anatomical axis (AA) of the MP joint while running..95 Table 6.6. The result of the statistical analysis of the effect of increase in speed from walking to running on the position and orientation of the functional axis (FA) of the MP joint.96

7 List of Figures Chapter 2 Figure 2.1. Dorsal and plantar view of the human foot bones... 21 Figure 2.2. Different bones and joints.... 22 Figure 2.3. The gait cycle... 23 Figure 2.4. (A) Heel rocker, (B) Ankle rocker and (C) MP joint rocker... 25 Chapter 3 Figure 3.1. Three anatomical planes... 32 Figure 3.2. A seven segment human model... 34 Figure 3.3. The foot coordinate system... 36 Chapter 4 Figure 4.1. The motion laboratory comprising of twelve-camera motion analysis system (Qualisys, Sweden) and six force plates (Kistler, Switzerland) mounted with the surface of the walking way.... 45 Figure 4.2. Marker clusters on each segment of the foot along with the hemispherical anatomical markers.... 46 Figure 4.3. (a) the pelvic marker cluster, (b) the other lower limb markers indicated, (c) the medial view of the foot attached with markers, (d) lateral view of the foot attached with markers.... 47 Figure 4.4. One of the static calibration trial after digitization in Qualisys.... 49 Figure 4.5. Force plate with the embedded sensors. (a) the coordinate system of the force plate, (b) vertical forces acting on the foot while on the force plate, (c) the reaction forces from the sensors on each corner of the force plate, (d) the ground reaction force acting under the foot. (open.nlm.nih.gov)... 52

8 Figure 4.6. The subject holding the calibration wand and moving across the measurement volume during calibration, while the L-shaped wand is placed on the force plates as a reference to set the global coordinate system.... 54 Figure 4.7. Trajectory information windows after digitization of the markers.... 55 Figure 4.8. (a) The coordinate system in Qualisys, (b) the coordinate system in GMAS.58 Figure 4.9. Plots showing the cardan angle alpha (α), made by the MP joint in XOZ plane, during slow walk, normal walk and fast walk respectively.... 59 Figure 4.10. Plots showing the cardan angle beta (β), made by the MP joint in XOY plane, during slow walk, normal walk and fast walk respectively.... 59 Figure 4.11. Plots showing the cardan angle gamma (γ), made by the MP joint in YOZ plane, during slow walking, normal walking and fast walking respectively.... 59 Chapter 5 Figure 5.1. (a) The functional axis (red) and anatomical axis (blue) of the metatarsophalangeal joint, where the anatomical axis is defined as the line connecting the 1 st and 5 th metatarsal heads. The origin of the foot local coordinate system situates on the upper ridge of the calcaneus bone. (b) The position of the functional axis is defined by its intersection point (xf, yf) with the XOY plane of the foot coordinate system, whereas the location of the anatomical axis is determined by its intersection point (xa, ya) with the XOY plane of the foot coordinate system. (c) Angle α made by the functional (or anatomical) axis with respect to the foot X axis when projected to the XOZ plane of the foot coordinate system. (d) Angle β made by the functional (or anatomical) axis with respect to the foot Y axis when projected to the XOY plane of the foot coordinate system.... 65 Figure 5.2. The x and y positions of the anatomical axis (blue) and functional axis (red) of the MP joint in the XOY plane of the foot coordinate system, for all the six

9 subjects (A to F) across all three walking speeds. The solid dots indicate the mean x and y positions, whereas the bars show the one standard deviation zones.... 71 Figure 5.3. The orientation angle made by the functional axis (red) and anatomical axis (blue) with respect to the foot X axis when projected to the XOZ plane of the foot coordinate system for all the six subjects across all three walking speeds. The solid lines indicate the mean value of the angle, whereas the dash lines show the one standard deviation zones.... 72 Figure 5.4. The orientation angle made by the functional axis (red) and anatomical axis (blue) with respect to the foot Y axis when projected to the XOY plane of the foot coordinate system for all the six subjects across all three walking speeds. The solid lines indicate the mean value of the angle, whereas the dash lines show the one standard deviation zones.... 74 Chapter 6 Figure 6.1. The x and y positions of the anatomical axis (blue) and the functional axis (red) of the MP joint in the XOY plane of the foot coordinate system, for all the six subjects (A-F) across all the three speeds of running (slow, normal, fast). The solid dots indicate the mean x and y positions, whereas the bars show the one standard deviation zones.... 91 Figure 6.2. The orientation angle α made by the functional axis (red) and anatomical axis (blue) with respect to the X axis, when projected to the XOZ plane of the foot coordinate system for all the six subjects (A-F) across all the three running speeds (slow, normal, fast). The solid lines indicate the mean value of the angle and the dashed lines show the one standard deviation zones.... 93 Figure 6.3. The orientation angle β made by the functional axis (red) and anatomical axis (blue) with respect to the foot Y axis when projected to the XOY plane of the foot coordinate system for all the six subjects (A-F) and across all the three speeds

10 (slow, normal, fast). The solid lines represent the mean value of the angle and the dashed lines indicate the one standard deviation zones.... 94 Figure 6.4. The trend of x position (normalised by the foot length) of the functional axis of the MP joint when the normalised velocity increases from slow walk to fast run. The circle represents the mean x position, whereas the bars show the one standard deviation zones. Different colours are the representation of different speeds: red (slow walk), blue (normal walk), green (fast walk), magenta (slow run), cyan (normal run) and black (fast run).... 98 Figure 6.5. The trend of y position (normalised by the foot length) of the functional axis of the MP joint when the normalised velocity increases from slow walk to fast run. The circle represents the mean y position, whereas the bars show the one standard deviation zones. Different colours are the representation of different speeds: red (slow walk), blue (normal walk), green (fast walk), magenta (slow run), cyan (normal run) and black (fast run).... 99 Figure 6.6. The trend of the orientation angle α made by the functional axis of the MP joint in the transverse plane, with the increasing normalised velocity V, from slow walk to fast run. The circle represents the mean α angle, whereas the bars show the one standard deviation zones. Different colours are the representation of different speeds: red (slow walk), blue (normal walk), green (fast walk), magenta (slow run), cyan (normal run) and black (fast run).... 99 Figure 6.7. The trend of the orientation angle β made by the functional axis of the MP joint in the sagittal plane, with the increasing normalised velocity V, from slow walk to fast run. The circle represents the mean β angle, whereas the bars show the one standard deviation zones. Different colours are the representation of different speeds: red (slow walk), blue (normal walk), green (fast walk), magenta (slow run), cyan (normal run) and black (fast run).... 100

The University of Manchester, Mrs Sivangi Raychoudhury Degree: Master of Philosophy (MPhil) Title: Three dimensional kinematics of the human metatarsophalangeal joint during locomotion Date: December 27 th, 2014 Abstract As the only part of the human body in contact with the ground, the human foot plays various important roles in attenuating the ground impacts, generating the propulsive powers and moving the body forward as well as maintaining the stability during locomotion. However, our understanding of the biomechanical function of the human foot is yet very limited. Till now, little is known about the actual in vivo kinematics of the distal part of the human foot. The objective of this thesis is to investigate the three-dimensional kinematics of the functional rotation axis (FA) of the human metatarsophalangeal (MP) joint during walking and running at different speeds, and also to examine the effects of locomotor speed on the in vivo orientation and position of the functional joint axis, defined based on the relative motion between tarsometatarsi (hind-foot) and phalanges (fore-foot) segments. Firstly, the three-dimensional gait measurements during walking and running at three different self-selected speeds were conducted. A twelve infrared camera motion analysis system was used to capture the three-dimensional motion of the foot segments and a six force plate array was used to record the simultaneous ground reaction forces and moments. The data were processed using GMAS (Generalised Motion Analysis Software) and the results were statistically analysed using the SPSS 20.0 software. From the walking measurement and statistical results, it was found that the FA remains anterior to the anatomical axis (AA), defined as a line connecting the first and fifth metatarsal heads, with an average distance of about 16% of the foot length across all the walking speeds and is superior to AA with an average distance of about 2% of the foot length during normal and fast walking. On the other hand, the FA showed a higher obliquity than AA with anteriorly superior orientation across all walking speeds. From the running data analysis, it was found that the FA remains more anterior to AA with an average distance of about 19% of the foot length across all the running speeds. On the other hand, in the vertical direction the FA moves inferior to AA with an average distance of about 4.8% of the foot length during normal and fast running. Same as in walking, the FA showed higher obliquity than AA across all the running speeds with anteriorly inferior orientation. This suggests that using the AA to represent the MP joint may result in overestimated MP joint power and moment, and also underestimated muscle moment arms for the MP extensor muscles. Since the FA shifts forward towards the more anterior position with increasing speed from walking to running, this axis shift may help to increase the effective mechanical advantage of the MP extensor muscles, moderate the muscular effort, maximise the locomotor efficiency and also reduce the risk of injury. These results may further improve our understanding of the contribution of the intrinsic foot structure to the propulsive function of the human foot during locomotion at different speeds. 11

12 CANDIDATE DECLARATION Sivangi Raychoudhury Faculty of Engineering and Physical Sciences THREE DIMENSIONAL KINEMATICS OF HUMAN METATARSOPHALANGEAL JOINT DURING LOCOMOTION I declare that no portion of the work referred to this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. Signed Date

13 COPYRIGHT STATEMENT The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. The ownership of certain Copyright, patents, designs, trademarks and other intellectual property (the Intellectual Property ) and any reproductions of copyright works in the thesis, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://documents.manchester.ac.uk/docuinfo.aspx?docid=487), in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in The University s policy on Presentation of Theses.

14 Acknowledgements I would like to express my genuine gratitude to those who contributed for the successful completion of this thesis. I am extremely indebted to my supervisor, Dr. Lei Ren, who had the trust in me and gave me an opportunity to grow academically. I would like to thank him for his continuous guidance, supervision, suggestions and immense patience, without which this thesis would not have been possible. I would like to show my deepest appreciation to my colleague, Dan Hu for helping and guiding me throughout this thesis. And to all my other research mates, Mohammad Akrami, Manxu Zheng and Ali Jabran for their constant support and encouragement. I owe the credits and success of this thesis to my beloved husband for supporting my dreams and letting them come true. I would like to thank him from the bottom of my heart for being my strongest support. Last but not the least, a special thanks to my family and my parents for their endless sacrifices, love and support which has made me to reach this level.

15 Chapter 1 Introduction 1.1 Background The foot is the most intricate part of the human body, which has numerous bones, joints, sophisticated network of muscles and tendons. As the only part to be constantly in contact with the ground during locomotion, the foot plays a very important role in gait. During locomotion, the foot is solely responsible for carrying the body weight forward, generating the propulsive power, maintaining stability of the body as well as moderating the impact of the ground reaction forces. Moreover, the foot is the most functional part during both the double stance and single stance phase. The largest motion taking place in the foot during locomotion was found to be at hind-foot and fore-foot with minimal motion in the mid-tarsal joints (MacWilliams et al., 2003). Numerous investigations were done before to know the kinetics and kinematics of the ankle joint, since this joint is the first part to strike the ground and the first one to bear the load of the body. According to the author s opinion, because of the complexity of the fore-foot structure and joints, very few studies have been done till now to understand the biomechanical functioning of the distal parts of the human foot during gait. The metatarsophalangeal (MP) joint is a synovial condyloid joint present between the metatarsal head and the cavity of the proximal end of the phalanx, as shown in Figure 2.2 on page 23. This joint plays an important role in flexion and extension during the gait cycle, especially during the late stance phase, when the centre of pressure moves rapidly through the MP joint (Bojsen-Moller et al., 1979; Grundy et al., 1975; Mann et al., 1979). It was found that the MP joint dissipates large amount of energy, and in addition, it is a significant absorber of energy during sprinting and running (Stefanyshyn and Nigg, 1997). Furthermore, a considerable amount of energy absorption was found at the MP joint during 30-60% of the

16 gait cycle (Kim et al., 2012). Hence, the objective of this thesis work is to investigate the fore-foot joint kinematics to determine the in vivo position and orientation of the MP joint axis and the effect of the speed on the axis. This study is planned to provide a clear vision of the biomechanical functioning of the MP joint during different locomotor speeds. It can also improve our understanding of the intricate structure of the fore-foot. Furthermore, it may help in improvising the existing designs and innovating new designs of the therapeutic and sports footwear, robotic legs and prosthetic lower limbs. 1.2 Objectives The main objective of the work presented in this thesis is to investigate the three-dimensional (3D) kinematics of the functional rotation axis (FA) of the human MP joint during level walking and running at different speeds and compare it with the anatomical axis (AA). This primary objective is attained by the fulfilment of the following secondary objectives. To find the location of the FA in the sagittal plane during level walking at different speeds. To find out the orientation of FA with respect to the AA during different speeds of walking. To study the effect of the change in the speed of walking on FA. To find the 3D position and orientation of the FA while running with different speeds. To study the effect on FA when the speed is increased while running. To investigate the trend of the location and orientation change of the FA from slow walking to fast running.

17 1.3 Thesis Overview This thesis is divided into seven chapters. The first chapter briefly reviews the current state of the kinematics analysis of the human foot. It also introduces the objectives of the research work presented in this thesis and the methodology used. The remaining six chapters include: a chapter reviewing the literature on human foot kinematics, the overview of the theoretical background of the biomechanics used in this research work, three chapters describing the core work of the thesis and the concluding chapter that summarises the work presented in the thesis as a whole. Below is the breakdown of the thesis, previewing the content of each of the constituent chapters. In Chapter 2, a literature review of the relevant research on the kinematics of the human foot is presented. The 3D orientations and positions of the foot segments are presented. A comparison between different speeds, different pattern and footwear effects during gait are also given here. Finally, the effects on the human foot muscles are mentioned. In Chapter 3, the relevant theoretical concepts are defined, which will be helpful in understanding the work. Also, the biomechanical concepts used in this study are briefly described. Since the core work of this research is based only on the foot, the human foot anatomy, the gait cycle, gait analysis and kinematics of human locomotion are mentioned in this chapter. Moreover, we discussed the helical axis approach and the problems faced in this approach, which prompted us to use the functional approach for the work. In Chapter 4, the experimental protocol used and the process of 3D locomotion measurement is presented. Along with the designed protocol, a set of specially designed plastic plates carrying reflective marker clusters were adopted to capture the motion of the body segment we were interested in. Anatomical landmarks and local coordinate systems were defined to reconstruct the positions and orientations of the lower limb. Moreover, the software GMAS

(General Motion Analysis System) is used to analyse the 3D kinematics of human fore-foot while walking and running. At the end, results of our measurements are presented. 18 Chapter 5 describes one of the core works in this thesis, mainly the orientation and location of the fore-foot joint. The statistical differences between the AA and the FA while level walking are described. Moreover, the axis shift while increasing the speed of walking is also observed. This study helps in understanding the biomechanical property and functioning of the human fore-foot joint in depth. In Chapter 6, the orientation and position of the FA of human MP joint while running is shown. The effect on the axis due to the change in speed from walking to running is described along with the possible implications in the fields of sports science and rehabilitation. In continuation with the previous chapter, this study reveals many factors related to the distal end of the human foot complex and provides some ideas to improve the locomotion efficiently. Finally, Chapter 7 summarises the main results of our work and draws some general conclusions. The findings of this thesis give a broader vision of the in-vivo biomechanical functioning of the human MP joint as well as the adaptation of the propulsive function of the foot with different speeds of locomotion. This information may provide some guidance in clinical applications. Finally, some suggestions for possible future works are given. The thesis is accompanied by four appendices that contain relevant information used in this study. Anatomical and technical markers lists are given in Appendix A. The measurement result plots which could not be presented in the chapter 6 are given in Appendix B. A list of publications arising from this thesis is mentioned in Appendix C. Finally, the MATLAB codes used for the original research work reported in this thesis are presented in Appendix D.

19 Chapter 2 Literature Review 2.1 Introduction Biomechanics is the science that is concerned with the internal and external forces acting on the body of the living organisms and the effects produced by these forces. The word biomechanics is coined from the Greek words bios meaning life and mechanike meaning mechanics. Biomechanics provides the conceptual and mathematical tools that are necessary for understanding how living beings move. The application of biomechanics in human movement can be classified into two areas: improvement in the performance and the reduction or treatment of injury. As this thesis is based on the biomechanics of MP joints, we will mostly focus on this in the subsequent discussions. 2.2 Human Foot Anatomy Human foot is a very strong, complex and mechanical structure that supports the body weight and propels the body forward when one walks or runs. To understand the mechanics of the foot as described in the literature, it is important to know the anatomy of the human foot. Human foot consists of 26 bones, 33 joints and a number of muscles, ligaments and tendons. This primarily divided into three parts: hind-foot, mid-foot and fore-foot (Marieb et al., 2001; Martini et al., 2000). As shown in Figure 2.1, hind-foot is the most posterior part of the human foot. It comprises of two bones: talus (ankle bone) and calcaneus (heel bone). The two long bones from the lower leg, i.e. tibia and fibula, get connected to the top of talus to form the ankle. Talus transmits the weight of the body from tibia anteriorly towards the toes. The talus is the

20 second largest foot bone. Calcaneus is the largest bone of the foot and can be easily palpated. While standing normally, most of the body weight is transmitted from tibia to the talus, then to calcaneus, and then finally to ground. The mid-foot consists of five bones, named cuboid, navicular and 1 st, 2 nd, 3 rd cuneiforms. These are the irregular bones and form the arch of the foot. This arch helps to absorb the shocks that accompany sudden changes in weight-loading. The mid-foot is connected to hind- and fore-foot by muscles and plantar fascia. The bones from hind- and mid-foot are together called as the tarsal bones. The fore-foot is the distal end of the foot. It consists of metatarsus and phalanges. The metatarsal bones are five long bones that form the sole of the foot. These bones are numbered 1 to 5 beginning from medial to lateral foot. The first metatarsal at the base of the big toe is the largest and plays an important role in supporting the weight of the body. Distally, each metatarsal bone articulates with proximal phalanx. The fourteen phalanges of the toes have the same organization as those of the fingers. The great toe, or hallux, has two phalanges (proximal and distal) and the other four toes have three phalanges (proximal, medial and distal). Apart from these main bones, there are two sesamoid bones which are the accessory bones under the hallux that improve its function. It can be seen clearly in Figure 2.1 (plantar view). The presence of a number of bones and joints makes the foot structure more complex. Since this work is mainly focused on the MP joints, here is a glimpse of the foot joints. As can be seen in Figure 2.2, in the hind-foot, the joint where tibia articulates the dome of talus, forms a hinge joint known as the talocrural joint or ankle joint. This joint permits limited dorsiflexion and plantar flexion. The talus articulates with the calcaneus and forms synovial joint called the subtalar joint. Most of the movements in the ankle happen at this joint.

21 Figure 2.1. Dorsal and plantar view of the human foot bones Digital image http://vo2maxproductions.files.wordpress.com/2010/11/footanatomy.jpg In the mid-foot, the joint formed between cuboid and calcaneus is called the calcaneocuboid joint, and that formed between navicular and talus is called the talonavicular joint. Also, the tarsal bone to tarsal bone joint is called as the intertarsal joint. The joints formed by the tarsal bones and metatarsal bones are altogether called the tarsometatarsal joint. These articulations allow limited sliding and twisting movements. The first three metatarsal bones articulate with medial, intermediate and lateral cuneiforms. The fourth and fifth metatarsals articulate with the cuboid bone. In the fore-foot, the ellipsoidal joints formed by metatarsal bones and phalanges are called metatarsophalangeal joints. These joints permit flexion/extension and abduction/adduction. The phalanx to phalanx joint is the hinge joint, called the interphalangeal joint. These joints give permission for flexion and extension.

22 Figure 2.2. Different bones and joints. Digital image http://dailyanatomy.tumblr.com/page/3 2.3 Gait Cycle and Gait Analysis A systematic study of human walking is called gait analysis. More precisely, this is a detailed investigation of the motion patterns which can be helpful in measuring the body mechanics and muscle activities (Cappozzo, 1984, 1991). Gait analysis provides a proper tool for the treatment of the individuals with defective or diseased walking patterns. To carry out the measurements in this study, it is important to know about the gait cycle beforehand. Human gait is the process of locomotion in which the body is supported first by one leg and then by the other. The gait pattern depends on various factors, such as injury, disease, gender, age and footwear (Whittle, 2007). The gait cycle begins when one foot contacts the ground and ends when the same foot contacts the ground again. There are two phases of the gait cycle: stance and swing.

23 Figure 2.3. The gait cycle Digital image http://biometrics.derawi.com/wp-content/uploads/2011/01/gaitcycle.png The stance phase is the interval in the cycle when the foot is in contact with the ground and it covers almost 62% of the cycle (Figure 2.3). The stance phase is further sub- divided into five periods. (a) Initial contact phase where the heel touches the ground. (b) Loading response phase in which the heel contacts the ground till the foot is flat and the toes of the opposite foot leave the ground. Here, the shift of the weight occurs from one foot to the other. (c) Mid-stance phase where the foot is flat on the ground and the opposite foot leaves the ground completely. Herein, the centre of gravity is directly on the reference foot. (d) Terminal stance phase when the centre of gravity is on the reference foot and the heel rises off the ground. Also, the opposite foot touches the ground. (e) Pre-swing phase when, along with the heel, the toes leave the ground and the other foot takes the load of the body. This is the unloading phase. In the next period of the gait cycle, the foot is not in contact with the ground. This is the swing phase. Again, this phase is divided into three periods as shown in Figure 2.3.

24 (a) Initial swing when the toes leave the ground and the knee makes maximum flexion. (b) Mid-swing where the foot remains in the air until the tibia is vertical to the ground. (c) Terminal swing which is the period from vertical tibia till the heel touches the ground again. There is a phase in the gait cycle when both the feet are in contact with the ground. It is called double-limb support phase. The amount of time spent in double-limb support decreases as the speed of gait increases. The gait cycle time is defined as the duration taken for completing one full gait cycle. The stance phase is 62% of the cycle time and the swing phase contributes to the rest 38% of the cycle time (Rose et al., 2006). The gait cycle is a result of repetition of the above-mentioned eight processes in sequential order. The smooth transition of the body weight towards the direction of progression over the supporting foot depends on three functional rockers (Perry, 1992; Miyazaki et al., 1993). First, the heel rocker is active during the stance phase when the heel contacts the ground. The heel causes the ankle to planterflex. The heel and ankle absorb the shock and the foot becomes more flexible. Second, the ankle rocker is active from foot-flat until the heel leaves the ground. Here, the opposite leg starts to move forward and the ankle of the supporting foot dorsiflexes. Third, the fore-foot rocker or MP joint rocker is activated from heel-lift until the foot-ground contact is lost. Here, dorsiflexion occurs at the MP joint, as shown in Figure 2.4.

25 Figure 2.4. (A) Heel rocker, (B) Ankle rocker and (C) MP joint rocker Digital image http://www.jaaos.org/content/15/3/178/f2.large.jpg In the gait cycle, the speed also plays a very important role. Different joint kinetics and kinematics results were found when the speed of the gait increases from walking to running, sprinting, galloping or trotting (Biewener, 2003; Biewener et al., 2004; Stefanyshyn et al., 1997; Pohl et al., 2007; Czerniecki, 1988). Many previous studies have been done to understand the difference between various gait patterns, like walking and running (Srinivasan et al., 2006; Mann et al., 1979; Lipfert et al., 2012). In one of the previous studies, it was suggested that the time of one complete gait cycle during running is approximately 60% of that of walking period (Adelaar, 1986) and the phases of gait in walking are important to understand the running cycle. Moreover, the first phase of the gait cycle is heel-strike, which takes about 15% of the stance phase. At this stage, the supporting foot or the ankle absorbs most of the shock from the ground and holds the whole body weight. As the locomotor speed increases, the heel-strike pattern was found to be different for different individuals. Some runners were found to be heel-to-toe runners, whereas some were found to be mid-foot and some as fore-foot runners. As the speed increases from walking to running, most of the subjects showed the heel-strike pattern as fore-foot running (Altman and Davis, 2012). Furthermore, the speed was found to be more when the subjects ran on their fore-foot (Ardigo et al., 1995). It may be because, running with rear-foot strike pattern results in an impact at ground contact that has high magnitude and high loading rate. Moreover, in running with fore-foot strike, the initial ground contact is shifted towards the

front of the foot, where it reduces the peak pressure under the heel and increases the pressure under the metatarsal heads, which helps in distributing the pressure. 26 2.4 Kinematic analysis of the human foot The foot-landing pattern during the locomotion affects the shape, amplitude and timing of the ground reaction force (GRF) in the vertical direction (Cavanagh et al., 1980; Nilsson et al., 1987, 1989). During the stance phase when the heel leaves the ground and the push-off phase comes, all the load is on the fore-foot, which exceeds the body weight by about 20% (Stokes et al., 1979; Bruening et al., 2010; Garcia-Aznar, 2009). The functional areas of the fore-foot where the load acts are at the five toes and five metatarsal heads. The forces acting on the metatarsals during push-off phase of walking were measured and it was found that around 40% of the body weight was imposed on the toes. The greatest load was observed in the first metatarsal joint, about 10% of the body weight was on the second metatarsal joint and the smallest load on the fifth. But there were some limitations in these studies. They had assumed in particular that the MP joints are frictionless, no extensor muscles act on the toes during the stance phase of walking and forces due to the accelerations of components were negligible. In other studies, it was stated that the second MP joint is as necessary as the first joint, and therefore, they had included the internal forces on the muscles of the MP joint. In this case, it was seen that the second metatarsal bone was also heavily loaded, but more in bending. Also, if the first ray (big toe) is deprived of its function during locomotion, then it is very likely that the second ray will also fail (Jacob, 2001; Arndt et al., 2002). During the whole gait cycle, the centre of pressure moves forward and the weight of the body shifts directly from heel to fore-foot, and the mid-foot plays a very little role in transferring the load (Grundy et al., 1975). The load-bearing function of the fore-foot was found to be three times that of the hind-foot.

27 With the change in the speed of locomotion, the activities of different muscles are also different (Adelaar, 1986). During walking, the intrinsic muscles of the foot are active, when the gait is at mid-stance and toe-off. Along with that, plantar flexors and peroneals are considered to be important for stabilising the foot during the mid-stance. In running, this group of muscles is much more active in completing about 70% of the running cycle. The gastrocsoleus muscle is active during the first 50% of the stance phase and during the late swing phase while running. During walking, the MP joint undergoes dorsiflexion in stance phase, when the plantar aponeurosis wraps itself around the metatarsal heads. It is mostly functional in the big toe and progressively less functional in the lesser toes. These intrinsic muscles may help to stabilise, maintain and elevate the longitudinal arch of the foot, along with the windlass mechanism of the plantar aponeurosis (Mann and Hagy, 1979; Bargas et al., 1998). Many of the gait analysis models were developed to study and analyse the motion between the foot joints. It was found that the largest motion takes place at the hind-foot and fore-foot during walking, with very less motion occurring at the mid-foot segment (MacWilliams et al., 2003). Moreover, it was noted that the fifth MP joint was the first joint that rotated negatively during the later stance phase, as a result of which the head of this metatarsal stayed on the ground and the MP joint extended significantly during this period (Scott and Winter, 1993). This study suggested that the joints involved in the longitudinal arch extend slightly when the fore-foot is loaded and flex during push-off when the MP joint extends. A consistent and repeatable pattern of rotation was observed in several joints of the foot, although the analysis was limited to the first ray of the foot (Leardini et al., 1999; Carson et al., 2001). On the other hand, it was verified that the MP angle was slightly dorsiflexed by approximately 7 at initial contact and then it reduced till foot-flat. At the end of the stance phase, it increased to about 35 to complete the push-off and stayed dorsiflexed (Leardini et al., 2007). Though the mid-foot was considered to be rigid, motions between the hind-foot

and fore-foot relative to mid-foot were also studied and a relative motion was found between these segments (Jenkyn et al., 2007, 2009). 28 To analyse the foot motion, the motion capture (Mocap) systems are used in the gait laboratories. The Mocap system records the movements digitally. The measurement data includes the camera, force plate and pressure plate data for different motion trials. During a 3D analysis of the data, it is important to recognise and eliminate the artefacts to get the proper results (Cappozzo, 1991; Chiari et al., 2005; Leardini et al., 2005). During these motion trials, different types of movements at different speeds are recorded to study the kinetics and kinematics of the joints, segments and muscles in more details. The applications of gait analysis and the experimental methods were described in some earlier papers, where the use of an effective method of description of 3D joint kinematics and kinetics applied to the lower limb joints during the normal walking was suggested (Cappozzo, 1984; Apkarian, et al., 1989). In these studies, the whole foot was considered as a single segment and only the ankle joint was considered as the distal joint of the foot. The methods for getting the information about the spatial positions, orientations and transformations of the body segments during locomotion were given (Apkarian et al., 1989; Kinzel et al., 1972; Cappozzo et al., 1995). The methodology used for the experiment in this thesis work was in accordance with these papers. The anatomical landmarks and the anatomical reference systems defined before (Cappozzo, 1995) are used in this study. Very recently, reviews were done that provided the theoretical background for the reconstruction of the segmental kinematics and joint kinematics, when the stereophotogrammetry was used to study the human movement (Cappozzo et al., 2005; Deschamps et al., 2011). During locomotion, foot plays a very distinguishing role. When the heel strikes the ground, the overall load acts on it, and as the gait progresses, the load bearing capacity of the foot is transferred to the toes, where it stays for a longer period. To reduce the risk of injuries,

29 comparisons were made between the subjects with barefoot and with shoes (Grundy et al., 1975; Wright et al., 1998; Wei et al., 2009; Krabak et al., 2011). It was revealed that the shoes reduce the load-bearing function in the fore-foot as the rigidity of the sole increases. Also low forces are transferred from mid-foot and toes. It was found that the shoe type also affects the gait pattern and is important in sports as well. Some important functions of MP joints with shoes were explored (Oleson et al., 2005; Bojsen-Moller et al., 1979). The literature revealed the dynamic nature of the fore-foot stiffness. It was suggested that wearing shoes is more beneficial for MP-dorsiflexion than the bare foot during walking as the stiffness of the shoes contributes to the improvement of the pedal against the ground (Wei et al., 2009). On the other hand, barefoot running was considered better than shod running (Krabak et al., 2011). It was suggested that barefoot or minimal footwear running reduces the injuries of the foot and knee. The MP joint at the distal end of the foot may have multiple functions during locomotion (Bojsen-Moller et al., 1979; Mann et al., 1979; Stefanyshyn et al., 1997). The MP joint plays a very significant role during rapid changes of various body movements, as the toes help in balancing the body (Mann and Hagy, 1979). In a previous study, it was found that the MP joint dissipates a large amount of energy and it is a significant absorber of energy during sprinting, which was approximately double the amount in running (Stefanyshyn et al., 1997). However, this consideration was only after the ground reaction force acted distal to the MP joint. On the other hand, a considerable amount of energy absorption was found at the MP joint for 30-60% of the gait cycle during normal walking (Kim et al., 2012). The results showed that the joint moments start from the beginning of the foot-flat phase. The maximum MP joint moment was found to be at the pre-swing phase. The MP joint was found to be a large energy absorber, and generated only a minimal amount of energy at take-off during the jumps (Stefanyshyn and Nigg, 1998). Because the moment acting at the joint must be balanced by the muscle force Fm, the magnitude of this force is determined by the muscle s

30 or muscle group s moment arm r relative to the moment arm R of the ground reaction force G. Mathematically, it can be represented as Fm r = G R (Biewener, 2003), where R and r are the perpendicular distances to the joint centre. Rearranging the equation, the relation between the mechanical advantage and force can be defined as r/r = G/Fm. These moment arm and force ratios provide a measure of the Effective Mechanical Advantage (EMA) of the limb muscle (Biewener, 1989, 1990; Biewener et al., 2004). 2.5 Discussion Stefanyshyn and Nigg (1997) highlighted the importance of the MP joint motion in sprinting and found the MP joint to be a large dissipater of energy during stance phase. But they have considered the five MP joints of the foot as a single joint rotating about an axis perpendicular to the sagittal plane, originating from the fifth metatarsal head (Stefanyshyn and Nigg, 1997, 1998, 2000). This simplification of the MP joint axes may misrepresent the joint kinetic and kinematic data during sprinting as the oblique nature of the MP joint was not considered. However, in a recent study, the effect of different MP joint axes definition was investigated on the MP joint kinematics and kinetics during sprinting (Smith et al., 2012). It was found that the MP joint axis has a significant effect on the joint moment, power and energy. The oblique MP joint axis, defined as the line connecting the first and fifth metatarsal heads, resulted in less energy absorption than the axis perpendicular to the sagittal plane. So the proper representation of the MP joint was suggested to be very necessary for a better understanding of the MP joint biomechanics during locomotion. In the previous studies, the MP joint axis was defined based on the anatomical landmarks, and was set as a line connecting the first and fifth metatarsal heads (Bosjen-Moller et al., 1979; Smith et al., 2012; Graf et al., 2012; Boonpratatong et al., 2010). However, another study highlighted that the MP joint has two axes about which push-off with the toes can be performed (Bojsen-Moller, 1978). First, the axis passing through the first and second metatarsal heads, and second, the axis passing through the second and fifth metatarsal heads. The push-off at faster speed was

31 considered to be more efficient when the axis was from first to second metatarsal heads. But, till now a very little is known about the realistic in-vivo orientation and position of the MP joint axis during locomotion and the effect of varying speed on the axis. In this thesis, the 3D study of the human MP joint kinematics is studied during different locomotor speeds. The position and orientation of the MP functional rotation axis during the stance phase in walking and running is compared with the previously defined AA. Along with it, the speed effect on the FA is also investigated. This study may help us to provide some useful information about the in-vivo biomechanics of the human MP joint. It may further increase our understanding on the propulsive function of the foot and its behaviour at different speeds.

32 Chapter 3 Theoretical Background 3.1 Human anatomical reference planes A plane is a two-dimensional surface, having length and width. Since the human locomotion is a 3D motion, this includes three planes, i.e. Sagittal, Coronal and Transverse, as shown in Figure 3.1. These three planes intersect each other at right angles and are used to describe the location of a particular structure in the body and various relationships between different structures. Figure 3.1. Three anatomical planes Digital image: www.healthpages.org/anatomy-function/anatomy terms/ 1. Sagittal Plane is a vertical plane (top to bottom) that divides the body into equal halves of left and right sides. 2. Coronal Plane (frontal plane) is a vertical plane that divides the body into front (anterior) and back (posterior). 3. Transverse Plane (horizontal plane) is a plane parallel to the ground and divides the body into up (towards the head) and down (towards the feet).

33 Earlier, the study of human locomotion was purely based on two-dimensional models. Since the most important events occur in the sagittal plane, it was considered the most (Cappozzo et al., 1975; Davy et al., 1987; Glasoe et al., 2014). But this is only suitable for the healthy subjects. For pathological subjects, the other two planes are also important to observe in the gait events, along with the sagittal plane. Therefore, the 3D models were built later for knowing the conditions and complications of the patients. Since all the subjects of this project are healthy, the sagittal plane is our main focus, although the 3D model is used for this study. 3.2 Human body model There are a number of models which are used to represent the human whole body. These are the representations of the series of segments connected by joints. The multi-body musculoskeletal models help in the study of the motions, the joint torques, muscle forces and body segment coordination during locomotion. Earlier models used were having 17- segments (Hatze, 1976), 14-segments (Vaugham et al., 1982) or 8-segments (Koopman et al., 1995). But nowadays, 7-segment model is the most commonly used (Abdulrahman et al, 2014; Ren et al., 2006). As shown in Figure 3.2, the human body can be divided into seven segments. The head, neck, arm and torso is considered as one rigid segment and is called as HAT. The upper body segments are considered as one segment because they all act together to keep the body balanced. Furthermore, no significant bending is observed during gait in the upper body parts. The thighs, shanks and feet of both sides form other six segments. Since this thesis is based on the foot, the lower part of this model, consisting of pelvis, thigh, shank and foot, is

suitable for this project. While taking measurements, only the right foot is measured because both the feet are assumed to be of the same size and characteristics. 34 Figure 3.2. A seven segment human model (Abdulrahman et al., 2014) 3.3 Segmental Kinematics To get the information of a segment in the 3D space, a collection of data is required for the reconstruction of the body or any segment in the space for each sampled instant of time. For this purpose, two types of information are needed. First is the morphological information like shape, size, structure etc., and second is the information related to the movement (Cappozzo et al., 2005). For this, several different types of reference systems are also defined. These reference frames are explained in details below. 3.3.1 Global Reference System (GRS) This is the fixed coordinate system defined for the convenience in the measurement. According to the general recommendations from the International Society of Biomechanics (ISB), the directions of the axes for the GRS in the biomechanical movement analysis are

35 already fixed (Wu et al., 1995; Winter, 2005; Cappozzo et al., 1995, 2005). In the orthogonal coordinate system, X-axis is pointing forward in the direction of progression, Y-axis is pointing vertically upwards and Z-axis is pointing to the right-hand side. In the gait laboratories, the direction of the axes of GRS is same as the direction of the axes in the force plates. 3.3.2 Local reference system (LRS) The reference system that is very conveniently chosen is either the GRS or LRS. A moving reference frame LRS is defined if its point of origin and its orientation are defined with respect to the GRS. These local frames are also called as the technical frames (Cappozzo et al., 2005), when associated with the bony structures. These frames give the location in the space. 3.3.3 Technical and Anatomical Coordinate system (ACS) The GRS has axes X-Y-Z, which are fixed everywhere. There is a necessity to transform this coordinate to x-y-z marker coordinate and to anatomical axes of the segment whose motion is being analysed. The marker coordinate system is used to describe the movement of a segment. For the correct 3D analysis, there are a few important points that should be kept in mind while capturing the motion. First, there must be at least three independent markers on each body segment. Second, there should not be any common marker between two adjacent segments. Third, the markers on each segment should not be in a straight line. Last but not the least, the markers should form a plane in 3D space. The anatomical frames specifically meet the requirements of the intra- and inter-subject repeatability. Their planes normally approximate the frontal, sagittal and transverse anatomical planes.

36 Figure 3.3. The foot coordinate system The anatomical coordinate system for the MP joint of the right foot, as used in this thesis, is shown in Figure 3.3. The anatomical landmarks were at the first and fifth metatarsal heads and the second phalanx head. The point of origin was set as the middle point of the first and fifth metatarsal heads. The X-axis was obtained by the origin minus second phalanx head. Z-axis was obtained by the origin minus fifth metatarsal head. And the Y-axis was the perpendicular axis to X- and Z-axes. 3.4 Joint Kinematics The joint kinematics is the description of the relative moment between two adjacent segments: proximal (p) and distal (d). Let the orientation matrices of both the segments be g Rp and g Rd respectively, and g Pp and g Pd are the position vectors of the local frames associated with the proximal and distal segments respectively, with respect to the global frame. The relative rotation between the two segments can be expressed as: p Rd = g Rp T g Rd (3.1) Where p Rd defines the rotation matrix of the distal with respect to the proximal segment and T refers to the transpose matrix. The joint position vector t is expressed as: t = g Rp T ( g Pd - g Pp) (3.2)

37 This position vector carries the information about the orientation and position of the distal segment relative to the proximal segment. Thus, to determine the relative position and orientation of two segments, the coordinate system for each segment involved is required. The position and orientation of a rigid body in space is defined by six degrees of freedom, among which three components are for translation and three for rotation. The number of bony segments and the constraints imposed by the joints contribute to the number of degrees of freedom of the model and its structural faithfulness. The relative position between two segments is defined by the position vector joining the origins of the two frames of the involved segments. For describing the orientation of a frame (distal) with respect to another frame (proximal), the frames undergo three successive rotations and the three obtained angles (α, β, γ) are used to represent the joint instantaneous orientation (Cappozzo et al., 2005). If the distal segment rotates with respect to the proximal segment about Z axis by an angle α, then about Y axis by an angle β and finally, about X axis by an angle γ, then the orientation representation of the distal segment relative to proximal segment is given as p R d (Z Y X ) = R Z (α)r Y (β)r X (γ) (3.3) cα sα 0 cβ 0 sβ 1 0 0 = [ sα cα 0] [ 0 1 0 ] [ 0 cγ sγ], (3.4) 0 0 1 sβ 0 cβ 0 sγ cγ where c stands for cos and s stands for sine functions. These three matrices are considered as the basic rotation matrices (Craig, 2005). 3.5 The Helical Axis Approach The helical axis or screw axis is defined as the instantaneous axis of rotation along which an object rotates and translates from one position to another. The helical axis helps to analyse the joint motions. The instantaneous axis of rotation of a joint can be viewed as a helical axis and the relative translation of the bones along the instantaneous axis of rotation can be

38 quantified along the line. The position and orientation of the helical axis can be determined as follows. {R0} = [(1- cosθ)i sinθ <n>] -1. {t - n}, (3.5) where R0 gives a unique solution since it is the positive vector perpendicular to the helical axis. This R0 helps in determining the position of the axis. In equation 3.5, I is the identity matrix and θ is the angle of rotation which is expressed as θ = cos 1 [ tr (H) 1 2 ], (0< θ < π) (3.6) where tr () stands for the trace of a matrix and is the sum of the diagonal terms. H is the helical rotation matrix and is expressed as H = (1- cosθ){n}{n} T + cosθ I + sinθ<n>. (3.7) Here, {} stands for the column matrix operator and n is the unit vector of the helical axis, that gives the direction and orientation of the axis in the 3D space. < > is the cross-product operator, and <n> is determined as below: 0 n z n y <n> =[ n z 0 n x ], (3.8) n y n x 0 where nx, ny and nz are the x,y,z components of the unit vector, n. If n1, n2 and n3 are parallel to the vector n, then 1 2 (H + HT )cosθi = (1 cosθ)nn T = [{n 1 } {n 2 } {n 3 }], (3.9) where {n1}, {n2} and {n3} are the three column matrices. We can compute n from any column of the matrix in equation 3.9, but we have to use the column that gives the maximum magnitude because it is the least error-prone. For this reason, the vector n can be determined from the following expression: n = 1 n max n max. (3.10)

39 In equation 3.5, t is the translation of the position vector from frame i to i+1, and can be expressed as {t} = {ri+1} H{ri}, (3.11) where ri and ri+1 are the mean position of the markers at i th and i+1 th frames and t is constant for all markers. Finally, in equation 3.5 can be determined as follows: = {n} t. {t} (3.12) The helical axis method has been used previously to represent the joint movements for shoulder, elbow, knee and ankle (Cattrysse et al., 2005; Chin et al., 2010; Bogert et al., 2008; Blankevoort et al., 1990; Tuijthof et al., 2009). But this method has not been used to determine the fore-foot-rearfoot motion, until recently (Graf et al., 2012). However, only the torsion axis (anterior-posterior axis) of the foot was considered, whereas the main motion of the fore-foot takes place along the medio-lateral axis. Therefore, the author s intention in this thesis was to use the helical axis approach to determine the position and orientation of the MP joint during locomotion at different speed. Validation work (Appendix D) was done by the author to check the authenticity of this method, and it was found that, this method is very sensitive to the measurement errors when the rotation angles are very small. Therefore, during the calculation, the angles with smaller values had to be ignored. This limitation restricts the use of this method for determining the kinematics of the MP joint, as the values for the flexion and extension angles are not high enough in the fore-foot during the gait (Graf et al., 2012). 3.6 The Functional Method The functional method is used to locate the centre of rotation of the ball-and-socket joint or the axis of rotation (AoR) of a hinge joint. In this thesis, the functional method suggested by Gamage and Lasenby (2001, 2002) is used to estimate the AoR of the MP joint, as this joint

40 is assumed to be a hinge type joint. The new least squares solutions are used to determine the AoR in closed form and the whole data set can be taken into consideration for the measurements. In this method, one point on the AoR and the unit vector defining the direction of the axis are used to estimate the AoR. The main equations used in this method are described below. Let us assume that a set of vectors on a body rotates around a fixed AoR. The tips of the vectors are on the circles, whose centres lie on the rotational axis. It is assumed that the minimum distances between the markers and the axis are fixed. If v p k represents the pth vector in the kth time instant, m p is a point on the plane (circle) traced out by the pth vector and n is the unit vector in the direction of the rotational axis, then a least squares type cost function is defined as P N k=1 C = [(v p p=1 k m p ). n] 2, (3.13) where P is the number of markers and N is the number of frames. Equation 3.13 is based on the fact that the vector components v p k m p should ideally be on the plane perpendicular to the rotational axis. In the case where more noise is present, the sum of the magnitudes of the components parallel to the AoR is minimised. We first differentiate the cost function with respect to n and set the result to zero to get N k=1 P {(v p k m p ). n}(v p p=1 k m p ) = 0. (3.14) Now, differentiating with respect to m p results in m p. n = ( 1 N N v p k=1 k ). n = v p. n. (3.15) From equations 3.14 and 3.15, substituting m p. n, we get P N {v p k. n v p. n}v p p=1 k = 0. (3.16) k=1

41 In order to define the AoR, a point on the axis is also required. Let the point be m at the distance of r p from the circular arc. A least squares cost function formed as P N k=1 C = [(v p k m) 2 p=1 (r p ) 2 ] 2. (3.17) The equation of the AoR is given as XAoR = m + τn, (3.18) which is a straight line passing through m in the direction of n, parameterised by a scalar τ. The advantages of using this method are that, no manual adjustments are needed and it can be applied directly to find the direction of the rotation axis. The skin artefacts and noise in the measurement data do not degrade the results. This method can estimate the AoR with at least three markers with right configuration. Lastly, this method can be used straightforwardly and automatically for biomedical purposes, e.g. in extracting the centre of rotation or axis of rotation data from optical motion capture system. Thus, this least square functional method was used for determining the orientation and position of the MP joint in this study. From the acquired unit vector and the point of the rotation axis, we get the position of the axis in the space. In our study, for the position of the axis, only the sagittal plane (XOY plane) was considered. We use the symmetric equation of the line: x x 0 a = y y 0 b = z z 0, (3.19) c where a 0, b 0 and c 0. Since only sagittal plane was considered, z = 0. Here, a, b and c are the x, y and z components of the unit vector. Also, x0, y0 and z0 are the x, y and z components of the point. By equation 3.19 and given values of the components, the position of the axis in the sagittal plane can be determined. Similarly, the orientation angles can be determined from the unit vector of the axis.

42 Chapter 4 Three-Dimensional Gait Measurement 4.1 Introduction In the previous studies, the stability while walking, kinetics and kinematics of the lower limbs with different locomotor speeds were the matter of concern which required both the mathematical models as well as measurement data. The mathematical model provided the insight of the human mechanical properties on the kinetics and kinematics during locomotion. On the other side, the kinetic and kinematic measurement data played a very crucial role in validating the mathematical models and improving the quality of walking. In this research work, the 3D walking measurement was conducted to validate the human walking model in order to improve the accuracy of the human walking model predictions and to better understand the biomechanical functioning of the human foot. In this chapter, the experimental protocol and the 3D whole-body walking measurements are explained. The measurements were conducted using a multi-camera motion capture system, from where the kinematic data were calculated, and an array of force plates which measured the ground reaction force for each subject. Six students participated in the experiment as subjects. A set of specially designed reflective marker clusters were used to record the 3D motions of the body segments. The orientation and position of each body segment were defined by the set of anatomical landmarks. A software package GMAS (Ren et al., 2005) was used to process the 3D kinetic and kinematic data, which was then used to measure the functional axis and anatomical axis of human foot.

43 4.2 The motion capture system The motion capture, also known as Mocap, is a technique of digitally recording movements for entertainment, sports and medical applications. It started as an analysis tool in the biomechanics research, but has now become increasingly important as a source of motion data for computer animations as well as education, training and sports, and very recently, for cinema and video games. A performer wears a set of one type of marker at each joint: LED, magnetic or reflective markers, or the combinations of these, to identify the motion of the joints and segments of the body. The motion capture involves measuring an object s position and orientation in the 3D space, and the information is stored into a computer-useable form. The motion capture computer program records the positions, angles, velocities, acceleration and impulses, providing an accurate digital representation of the motion. This can reduce the costs of animation, which otherwise requires the animator to draw each frame, or with more sophisticated software, to interpolated key frames. Motion capture system saves the time and creates more natural movements than manual animation. But it is limited to the motions that are anatomically possible. It is used to capture both the static and dynamic movements, which further improves our understanding about the complexity and behaviour of the structure/object. Generally, there are three types of motion capture system: mechanical, optical and electromagnetic. Among these three methods, the passive optical motion capture system is widely used in the biomechanical studies. In this method, the subject is asked to wear some reflective dots, known as markers (explained in Section 4.2). The motion is recorded using several cameras surrounding the motion of the subject. This method is specifically designed for the biomechanical applications, such as sports injuries, rehabilitation etc. The advantage of this method is that, there are no cables or electronic devices attached to the body of the subject. This gives the subject very natural and free movements. Besides that, since there is no limit to the number of markers, large volumes of segment or joint motion data can be

44 captured, with more detail, clean and precise movements. But the biggest problem with this method is the light interference and the skin movement (Leardini et al., 2005). For this, all the measurements should be done indoor, where the intensity of the light can be controlled. For the skin artefact, precautions can be taken or bone-pin markers can be used. Also, sometimes there are some technical errors while recording or processing the data which does not yield accurate results (Chiari et al., 2005). Moreover, the cost of the optical motion capture system is more than the other methods. There are many varieties of motion capture systems available in the market. For our research purpose, we have used the Qualisys motion analysis system which is explained in detail in Section 4.3. 4.3 Gait measurement The 3D walking measurements were conducted to capture the lower limb walking motion at different walking speeds. Six healthy male subjects (age: 26.67 ± 2.69 years; weight: 67.17 ± 10.29 kilograms; height: 175.0 ± 4.43 centimetres) participated in the measurement and were asked to walk at the self-selected speed for slow, normal and fast walking. All the six subjects were free of any previous foot or lower limb injuries. Before starting the experiment, the subjects were provided informed consent in accordance with the policies of local institute ethical advisory committee. The subjects were asked to walk minimum ten times at each self-selected speed, from which only those trials were processed in which all the markers were properly visible. The motion data were recorded at 150 Hz using a twelve-camera motion analysis system (Qualisys, Sweden). For capturing the maximum range of the gait cycle, twelve cameras were placed as eight in high and four in low heights, as shown in Figure 4.1. Generally, up to ten cameras had been used in the previous studies (Wolf & Stacoff, 2008). But in this study, more number of cameras were used to increase the precision of the recorded data. Six force plates (Kistler, Switzerland), mounted on the surface of the walking way, were used to measure the GRF and moments at 1000 Hz (see Figure 4.1).

45 Camera (Qualisys) Force plates (Kistler) Figure 4.1. The motion laboratory comprising of twelve-camera motion analysis system (Qualisys, Sweden) and six force plates (Kistler, Switzerland) mounted with the surface of the walking way. The Qualisys system and the force plates were controlled by the desktops/ laptops. The angle of each camera was adjusted in a way that it can capture most of the motion range of the lower limb, while focusing on the force plates. For taking the measurements, the subjects were asked to wear a set of spherical infra-red reflective markers and marker clusters, to get the idea of the position and orientation change of the segments and joints. A marker cluster consists of four anatomical markers, as shown in Figure 4.2. The marker s surface is covered with the light reflective material, which can be captured by the camera. In the in-vivo measurements, as done in this thesis, the marker clusters were attached on the desired place by double-sided adhesive tapes. Apart from these marker clusters, the anatomical markers (see Figure 4.2) were also used. These spherical or hemispherical markers have the diameter ranging from 3mm to 8mm, and used according to the anatomical shapes and sizes of the segments. These anatomical markers were also used to calibrate force plates and the static and dynamic motions.

46 Marker clusters Anatomical markers Figure 4.2. Marker clusters on each segment of the foot along with the hemispherical anatomical markers. 4.3.1 Experimental protocol For each subject, the movement of five rigid lower limb segments (pelvis, right thigh, right shank, tarsometatarsi and phalanges of the right foot) were recorded, as shown in Figure 4.3. A set of specifically designed thermoplastic plates, each carrying a cluster of four reflective markers, were attached to each segment (Ren et al., 2005, 2008). An elastic hip belt was used to firmly locate the plastic plate carrying the four reflective markers on the pelvis. In total, 57 reflective markers were used to capture the lower limb motion during the walking trials (see Figure 4.3), including the marker clusters. The use of the plastic plates eliminate the relative motion between the markers on a segment, thus increasing the accuracy of the recorded motion data (Ren et al., 2008(a)).

47 a b c Figure 4.3. (a) The pelvic marker cluster, (b) the other lower limb markers indicated, (c) the medial view of the foot attached with markers, and (d) lateral view of the foot attached with markers. d Before taking the measurements, we had to make sure that the cameras are set properly. The markers were placed on the corners of each force plate which defined the local coordinate of the force plate, and the cameras were adjusted in a way that ensures that all the cameras can cover all the six force plates. Since the ground reaction forces were recorded in the local coordinate system of the force plate, an additional force plate location trial was needed to determine its position in the global reference frame. For doing this, the calibration wand with markers was put in the middle of the force plates to define the position of the origin of the force plate coordinate system. The coordinate system transformation was conducted in the GMAS software to obtain the GRF in the global reference frame. After putting the L-shaped

48 wand, the camera calibration was done manually. Normally, during calibration, the subject holds a T-shaped wand/stick which has few markers on it, and waves the stick across the force plates, and covering the total range of the cameras. The cameras record the marker data. After calibration, each camera should have recorded enough amount of markers, which increases the precision of the data to be recorded later. Once the calibration process was done, the positions of the camera were set, then the measurement procedure was carried further. To check if everything is alright, few sample trials were captured. There may be some problems like flashing, missing markers or swapping overs in the recorded data. In this case, the camera system should be calibrated and adjusted again, until the marker data became stable and all the markers were seen. During the measurement, the subject was asked to walk on the force plates along the X-axis of the global coordinate system. However, only the data of the right foot was recorded throughout the trials. To describe the segment s positions and orientations, anatomical landmarks and boneembedded anatomical reference system are defined for each body segment. These anatomical landmarks and reference frames are based on the recommendations of the previous researchers (Cappozzo et al., 1995; Vanderhelm et al., 1995; Ren et al., 2008(a)). A detailed description of the anatomical coordinate system for each major segment is described in Appendix A. Before the walking trials, a set of static calibration procedure was carried out to locate the anatomical landmarks based on the CAST (Calibrated Anatomical System Technique) technique (Cappozzo et al., 1995), as shown in Figure 4.4. After the reflective markers had been captured by the cameras, they were then processed in the QTM software (explained in Section 4.3.3) accompanied with the global coordinate system. Each marker was identified accordingly. Before the walking trials, the calibration markers were removed according to the CAST technique.

49 Figure 4.4. One of the static calibration trial after digitization in Qualisys. The lower limb multi-segment model in this research, which consisted of five segments, had their own anatomical coordinate system (Cappozzo et al., 1995). Table 4.1 describes the detailed definition of the anatomical coordinate system of the lower limb. Table 4.1. Definitions of the anatomical coordinate system for the lower limb (see Appendix A, for details). PELVIS Origin z-axis x-axis y-axis THIGH Origin Midpoint of RASIS and LASIS This axis is oriented along the line passing through RASIS and LASIS with its positive direction pointing right This axis lies perpendicular to the z-axis, its positive direction is anterior This axis is mutually perpendicular to both the x-axis and z-axis and is pointing upwards Midpoint of RLEP and RMEP

50 y-axis x-axis z-axis SHANK Origin y-axis z-axis x-axis FOOT Origin y-axis z-axis x-axis This axis is oriented along the line passing through HJC and midpoint between RLEP and RMEP with its positive direction pointing upwards This axis lies perpendicular to the y-axis, its positive direction is anterior This axis is mutually perpendicular to both the x-axis and y-axis and is pointing right Midpoint of RLML and RMML This axis is defined by the intersection between the quasi-coronal and quasi-sagittal plane with its positive direction pointing upwards This axis lies is perpendicular to the y-axis, its positive direction is right This axis is mutually perpendicular to both the y-axis and z-axis and is pointing anterior Upper ridge of calcaneus (CAL) This axis is defined by the intersection between the quasi-coronal and quasi-sagittal plane with its positive direction pointing upwards This axis lies perpendicular to the y-axis, its positive direction is pointing right This axis is mutually perpendicular to both the y-axis and z-axis and is pointing anterior The dynamic calibration trials used the relative segment motions to estimate the anatomical landmarks. These anatomical landmarks were normally approximated by a joint-centre, which was considered as a point that coincides with the rotational centre of the two adjacent segments. This functional approach (Cappozzo, 1984) was used by the subject to establish the joint-centre. The subject was asked to move the relevant segment with respect to the proximal segment (trunk/pelvis) in a sequence of motions like flexion, extension, abduction, adduction and circumduction. Then in the GMAS software, a closed-form algorithm was used, which determined the joint-centre position (Gamage and Lasenby, 2002). This algorithm used the whole marker data sets and did not require any manual adjustment of optimisation parameters. The anatomical joints of the lower limb involved in this experiment

and the relevant anatomical landmarks used to estimate the joint centre positions are listed in Table 4.2. 51 Table 4.2. Determination of the joint centre position (see Appendix A for details) Joint Hip Knee Ankle Joint-Centre Definition Functional rotational centre Midpoint of RLEP and RMEP Midpoint of RMML and RLML In the walking trials, the technical marker clusters were used to capture the lower limb segment motions. Then the marker data from the static calibration trials and walking trials were processed by using the GMAS software to provide 3D segmental positions and orientations for each instant of time. 4.3.2 Force plate During human locomotion, there is a constant interaction between the body and the ground due to gravity. While standing, walking, running or jumping, the body exerts some force downwards as its weight. According to Newton s third law of motion, when there is a downward vertical force, there will be an equal and opposite upward reaction force, which is called as GRF. To measure this GRF, force plate is the tool that is generally used (Winter, 2005). This GRF vector, being 3D, consists of a vertical component along with two shear components acting along the force plate surface. These shear forces are resolved into anterior-posterior (Y-axis) and medial-lateral (X-axis) directions as shown in the Figure 4.5.

52 Figure 4.5. Force plate with the embedded sensors: (a) the coordinate system of the force plate, (b) vertical forces acting on the foot while on the force plate, (c) the reaction forces from the sensors on each corner of the force plate, (d) the ground reaction force acting under the foot. (open.nlm.nih.gov) Since each sensor gives its own reaction force, the GRF of the foot is equal to the sum of the four sensors: R = R1+R2+R3+R4. 4.3.3 QTM Software Qualisys Track Manager (QTM) is the software with interface which allows the user to capture 2D and 3D motions. This software provides the advanced features along with simple method of application. Together with Qualisys optical measurement hardware, the QTM can streamline the coordination of all the features in a sophisticated motion capture system and provides the possibility of rapid production of distinct and accurate 2D and 3D data. The data from the cameras are displayed on QTM in real-time, while capturing the 2D and 3D motions. It enables the user to confirm the accuracy of the data acquisition. In QTM system, there are three calibration steps. Two of them are used for measurement. The first step is wand calibration method. In this method, a calibration kit, having two

53 instruments: L-shaped reference structure/wand and a calibration wand, are used. During calibration, the L-shaped wand is placed as reference to set the desired global coordinate system. Meanwhile, it should be made sure that all the cameras can see the markers that are attached to the L-shaped wand. Then the calibration wand is moved inside the measurement volume in all the directions. This is to make sure that all the axes are properly scaled. During the calibration, this wand is expected to move in all the areas that can be covered by all the cameras, and allow the cameras to see the wand in as many orientations as possible. Thus, the cameras are calibrated. In Figure 4.6, this process is shown, where the subject is holding the calibration wand and the L-shaped wand is on the force plates. The second step is frame calibration. In this step, the reflective markers with known fixed positions are used. For example, during the gait measurement, markers were placed on the four corners of each force plate. A frame is then placed inside the measurement volume and a calibration is made on the stationary frame. The frame must have at least five markers. The third step is to fix the cameras. In this, the fixed locations of the cameras and reference markers are used to calibrate the camera system. By this method, the system can cover larger area as compared to the other two methods. However, there are some chances that all the cameras cannot see the whole measurement volume. But, it is always easy to repeat the calibration, as the positions of the cameras are fixed.

54 Figure 4.6. The subject holding the calibration wand and moving across the measurement volume during calibration, while the L-shaped wand is placed on the force plates as a reference to set the global coordinate system. After the calibration, data processing also takes several steps, like tracking the measurement, gap-filling process, applying the AIM model, calculating the degrees of freedom, calculating the force data, exporting the digitized data to TSV files, then processing the data using GMAS in MATLAB. 3D tracking is also used in the measurement. In this process, the 3D points are constructed from the 2D rays of the captured data and then it sorts these points into the trajectories. There are three trajectory information windows in QTM, as shown in Figure 4.7. The three windows are: labelled trajectories window, unidentified trajectories window and discarded trajectories window. After the measurement, all the markers trajectories appear in the unidentified trajectories window. After the markers name list is imported, the identification of the respective markers is done. In the captured data, there may be some ghosts, shadows or other invalid markers. After identifying the right markers, these unwanted markers are discarded. These discarded markers appear in the discarded trajectories window, and not deleted, in case they may be needed if any mistake is done

55 during identification. Hence, the raw data is protected completely and can be digitised again, if needed. When all the required trajectories are labelled in a proper way, it is then exported into analog data as TSV files for processing. Figure 4.7. Trajectory information windows after digitization of the markers. 4.3.4 Data analysis with GMAS The software package GMAS, which is an updated version of SMAS (Salford Motion Analysis Software), was developed in the MATLAB programming environment for analysing the body movement recorded from motion capture system and the force plates (Ren et al., 2008(a)). This software helps in data processing as well as 3D kinematic and kinetic analysis. It works on inverse dynamics approach. The trials with more than 10-15 consecutive missing frames are discarded. After the fill-gap processing, the data are filtered using a low-pass zero-lag fourth-order Butterworth filter, with cut-off frequency of 6.0 Hz. From the static calibration data, the relative position of the anatomical landmarks with respect to the technical markers were obtained. For some anatomical landmarks, functional

56 method was used. The joint-centre positions were described in the LRS of the adjacent segment. The transformation from the LRS to GRS was done in the GMAS. After that, the anatomical landmarks positions in the anatomical coordinate systems were obtained for each instant of time. For this study, the software had been adjusted to analyse the human lower limb motion. The lower limb was divided into five segments: pelvis, thigh, shank, hind-foot, fore-foot (phalanx). Three templates were employed to define the biomechanical system: the body template, the marker template and the force template, which defined the multi-segment joint system, the marker clusters and the external force systems respectively. For the body template, firstly the five lower limb segments were defined, followed by joints connecting the body segments (i.e hip, knee, ankle and metatarsal). Then, the proximal and distal body segments for each joint were defined, in the same sequence as the joint definition: pelvis, right_thigh, right_shank, right_foot, right_phalanx. At last, the local frame definition function list is in the same sequence as the segment definition. The marker template defined two sets of markers: technical and anatomical. The technical markers were attached to the body segments to record their changing positions and orientations. And the anatomical landmark markers were used to point out the bony landmarks or joint centres, which were used to define the local frames. For the marker template, first the anatomical landmarks for each body segments were defined, in the sequence same as the body segment definition. That is, for pelvis: RASIS, LASIS, RPSIS, LPSIS; for thigh: RLEP, RMEP, HJCR; for shank: RHFB, RTTB, RMML, RLML; for foot: RCALT, R1MHD, R5MHD; for phalanx: R1PHD, R2PHD, R5PHD (see Appendix A). Then the technical markers for each body segment were defined in the same sequence as the body segment definition. After that, the regression landmark in the same sequence as joint

57 definition were defined: {RLEP, RMEP}, {RMML, RLML}, {R1MHD, R5MHD}. The force template described the external force systems acting on the biomechanical system. The force sensors (force plates) were normally used to measure the external forces. For the force template, first the external forces exerting on the body system were defined. In this research, this is right_ground and pelvic. Then the body segments, on which the external forces were exerted, were defined in the same order as force definition. Followed by the definition of action position (x, y, z) of external forces in ISB coordinate system in same sequence as force definition. Depending on whether the external forces were measured or not, they were defined as known=1 or unknown=0. Thereafter, the definition of the external force evaluation function list and force plate local frame function list were done. The experimental trial data were processed after these templates were set. In Qualisys system, the GCS was defined differently than in the GMAS, as shown in Figure 6.8. Generally, according to the ISB definitions, the subject should walk along the positive direction of X-axis. But, in Qualisys the subject was walking against X-axis and other two axes were also different from that of the GMAS, as shown in Figure 4.8. Therefore, the coordinate system of Qualisys was modified according to the setting of the GMAS. The X, Y and Z axes were named as 1, 2 and 3, respectively. To fit the coordinate system of Qualisys into the GMAS, a new coordinate system was defined as [-1, 3, 2].

58 a b Figure 4.8. (a) The coordinate system in Qualisys, (b) the coordinate system in GMAS. For the kinematic study in this thesis, the anthropometric data of all the subjects were very necessary. The anthropometric details of all the six subjects are listed in Table 4.3. These six subjects are the same subjects, participated in this study. Table 4.3. Anthropometric details of the six subjects. Subject Gender Age (years) Weight (kgs) Height (cm) No. 1 Male 24 56 170 2 Male 28 78 174 3 Male 23 77 176 4 Male 26 75 184 5 Male 31 52 172 6 Male 28 65 174 4.4 Some Measurement Results Some results of the orientation made by the fore-foot segment with respect to the hind-foot segment while walking is displayed below. The Cardan angles presented below in Figures 4.9, 4.10 and 4.11 are the mean ± standard deviation of the whole stance phase for a representative subject. Plots for the other subjects are presented in Appendix B. The information from the force plates were taken to recognise the stance phase and the following figures were constructed.