7_Conclusion

Transcription

1 Study of the dynamic model analysis of the human foot complex during gait and its applications Takamichi TAKASHIMA

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3 ( )= ()+ () Tt () = TFRF () t + TF () t I () θ t T t kθ t dθ t k d iii

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12 COW HORSE HUMAN DOG Fe:femar BARE T:tibia F:fibla Digitigrade type at running. :phalanx :calcaneus :metatarsal Plantigrade type at walking. Digitigrade type Ungurigrade type Plantigrade type Fig. 1-1 The skeletal structure of the human and animal leg, and change with locomotion type in human foot. (28) 5

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14 Hip J. moment Thigh segment Fig. 1-2 The theoretical rigid link model for the human gait analysis methods. There are three segments, thigh, shank, and foot, and three joints, hip, knee, and ankle joint. Each segment has its own mass and moment of inertia. FRF Knee J. moment Shank segment Ankle J. moment Foot segment 7

15 Flexible Structure Rigid Structure STJ CCJ TNJ Early stance Terminal stance STJ CCJ TNJ TTJ Low arch High arch TTJ Fig. 1-3 The changes of the foot conditions, rigid and flexible structures during a gait cycle. 8

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18 Fig. 1-4 The total design of this study. 11

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22 Fig. 2-1 The procedure of X-ray Digital Fluorscopy and Image Intensifier. Table. 2-1 Specifications of DRF system. A/D Converter sampling Image memory speed matrix D/A Converter 8 bit 10 MHz max 7.5 frame/sec 1024 x 1034 dot 8 bit Fig. 2-2 The situation of sampling. 15

23 Fig. 2-3 Digital radiographic images of human foot during stance phase of the gait by 7.5 flames per second. 16

24 y origin 50mm 100mm x Fig. 2-4 Calibration of the x-y coordinate system using the 1mm diameter lead balls placed on the sampling plane. 17

25 M1: Metatarsal# CN: Cuneiforms NV: Navicular 8 7 TL: Talus CC: Calcaneus M5: Metatarsal#5 CB: Cuboid a. The template and reference points for identification of bone in the foot. Template TR y M1 CN NV CC o x b. digitizing method. Fig. 2-5 Digitization of the positions of each foot bone using template method at the each frame. 18

26 frame#01 y o x frame#02 y o x frame#03 y o x y o x frame#04 Fig. 2-6 Videofluoroscopic pictures and to provide the stic pictures of each bones from digityzing X-Y coordinate data. (Subject::TT, male, 45, bodyweight::67 kg, footsize:: 26.5 cm) 19

27 frame#05 y o x frame#06 y o x frame#07 y o x frame#08 y o x 20

28 deg. 10 M1 - CC angle (6 trials) deg. 10 frame M1 - CC angle (Means + SD. of 6 trials) frame -2 Fig. 2-7 Medial arch transformation angle were approximated by CC-M1,M2 motions. 21

29 deg. deg TL - NV angle TL - CC angle deg. deg NV - CL angle CN - M1 angle Fig. 2-8 The results of angle changes of each major joints of foot during a stance phase. 22

30 deg. CC - CB angle deg. 10 CB - M5 angle Fig. 2-9 Lateral arch angle transformations were approximated by CC-M5 motion. 23

31 O ( ) + ( ) = ( ) + ( ) x x y y x x y y 2 P1 0 P1 0 P2 0 P ( Q1 0) + ( Q1 0) = ( Q2 0) + Q2 0 x x y y x x y y ( ) Q2 (x Q2, y Q2) y O (x 0, y 0) P2 (x P1, y P1) P P1 (x P2, y P2) Q o x a. Q1 (x Q1, y Q1) O b. Fig Instant centers determination method. 24

32 Instant Center of P:7 Q:9 Navicular y o x 1 st metarsal navicular Instant Center of P:5 Q:6 Talus talus 1 st metarsal Instant Center of P:3 Q:4 Calcaneus 1 st metarsal calcaneus Fig This picture shows the instant centers of motion between calcaneus and fixed 1 st metatarsal, and layers the ragiographic image of the foot for the references. 25

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37 z (y2, z2) t2 (ym, zm) m, I (f2, n2) t1 T+ (f1, n1) y Hip J. moment Thigh segment m (y1, z1) m x = f f m m y = n n m g m f = f m x 2 1 n = n m( g+ y ) 2 1 I θ = t2 t1+ n1( x1 xm)+ f1( ym y1) n2( xm x2) f2( y2 ym) t = t + I 2 1 θ n( x xm) f ym y + n 2 ( xm x 2 )+ f 2 ( y 2 ym) ( ) Knee J. moment Ankle J. moment Shank segment FRF Foot segment Fig. 3-1 Freebody dyagram of the rigid link using the Newton-Euler dynamics method. The joint moment T2 was solved by inverse dynamics algorism. Fig. 3-2 The theoretical rigid link model for the human gait analysis methods. 30

38 m i g my 1 m1 = f1 f12 m ( z + g)= n n 1 m I θ = T + T + T 1 1 ARC FRF1 F12 T ARC 31

39 θ + T N + z FRF2 (f2, n2) y FRF1 (f1, n1) (yn, zn) (y2, z2) m2, I2 (ym2, zm2) F1 (f1, n1) m1, I1 (ym1, zm1) (y1, z1) Fig. 3-3 The simple foot model in sagital plane. 32

40 Position Data Force 600 The simple foot model Force Plate 1 Force Plate 2 Mass & Moment of inertia Fig. 3-4 The diagram of this study. Using the simple model of foot. 33

41 Table 3-1. The weight of foot segment. Ig I MglT 2π 2 = ( ) = + I I Ml o 2 o g 2 34

42 a. the plaster model of the foot was sepalated. b. each point of mass c. swing test tool Fig. 3-5 Plaster model of the two foot parts. There are hanging at voluntary points for estimate the moment of inertia. Table 3-2 Pertial foot segmental mass and moment of inertia. mass moment of inertia m i [kg] I i [kgm 2 ] Fore Foot (i=1) BW* Hind Foot (i=2) BW* * BW: BodyWeight [kg] Reflective marker Hind Foot Fore Foot Force Platform 1 Force Platform 2 Fig. 3-6 Schematic illustration of the center of mass about the hindfoot and the forefoot segment, and relationship between the markers. 35

43 specification samplig rate: 60Hz CCD cameras: 12 Force Platforms: Fig. 3-7 The VICON 512 System using 8 force plates and 12 CCD-camera. infrared light grass beads lens marker skin surface Fig. 3-8 Video Tracking system to recognize the infrared markers. Fig. 3-9 The method of 3D Video Tracking system to recognize the infrared markers using the DLT (Direct Linear Transformation) method. 36

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45 Fig Picture of the subject foot with infrared rays reflective markers. 38

46 n s f Force Vertical Antero-Posterior Medio-Lateral Floor Reaction Force Specification of Force Platform KISTLER 9281C Range : kN (Fx,Fy) kN (Fz) Linearity : <+0.5 %FSO Hysteresis: < 0.5 %FSO Fig The floor reaction force vector. The force platform is able to measure the floor reaction forces, there are separated three direction forces, vertical compornent, antero-posterior compornent, and medio-lateral compornent. 39

47 l l1 f1 l2 f2 Fl = f l + f l F = f + f 1 2 Fig Calcuration method of the center of pressure at the force platform. 40

48 FRF 2 FRF 1 NV point Force Platform Fig The foot in midstance, placed the center of two force plates. (N) [cm] Force Plate 1 Force Plate 2 (a) Check system NV point at midstance after sampling. 0 gait cycle(100%) (b) Floor reaction force patterns of each segment. Fig The forefoot and hindfoot forces measurement system. (N) Fig General floor reaction force paterns of normal gait. 41

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51 [ ] = [ ] ( ) M M C x y z G G m Cm, 0 Cm, Cm [M ] G [M ] G0 C x, y, z = [ ] m Cm Cm Cm T θ = CmNV M1NV cos 1 CmNV M1NV 44

52 z' x' z Cm x plantar coordinate system y' global coordinate system y Fig The plantar coordinate system was cariculated by coordinate transformation method from the global coordinate system. Arch Morment [Nm] dash::2d solid::3d Fig Comparative data of the angular change of foot arch, compare the global coordinate system and the plantar coordinate system. 45

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54 subject-a male 22, BW=64.5kgf means of 6 trials. subject-b male 23, BW=68kgf means of 7 trials. subject-c female 32, BW=48.3kgf means of 9 trials Arch Falling heel contact Arch Elevation stance phase toe off heel contact stance phase toe off heel contact stance phase toe off gait cycle gait cycle gait cycle Fig The determinant arch angle and moment in sagittal plane motion about 3 subjects Moment [Nm] Angle [deg.] 47

55 Fig Check of the movement between skin and bones. Five lead balls on the calcaneus, navicular, and 1 st metatarsal head were digitizesed. The effect of distances between each ball were almost similar. deg 10 Mi-Nv- Cl angle stance phase [60Hz] a. Arch angle from VICON data deg 10 calca-meta angle stance phase [8Hz] metatarsal 1 calcaneus b. Arch angle from videofluoroscopic data Fig This picture shows measured arch angles about two method, (a) 3D Video tracking method, and (b) videofluoroscopic analysis. The determined angle patterns by both method were similarly. 48

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59 TCJ Talus Calcaneus STJ Navicular TNJ CNJ TMJ TCJ MPJ Tibia Fibula STJ TCJ: taroclural joint axis STJ: subtalar joint axis STJ TCJ Arch MPJ TNJ: taronavicular joint axis CNJ: cuneonavicular joint axis TMJ: tarsometatarsal joint axis MPJ: metatarsopharangeal joint axis Fig. 4-1 The anatomical mechanism of human foot complex. This picture shows the axis of taroclural joint(tcj), subtalar joint(stj), taronavicular joint(tnj), and cuneonavicular joint(cnj). TCJ Axis STJ Axis x z y Global coordinate [M] G STJ Axis m 2 Arch Axis m 1 MPJ Axis Fig. 4-2 Human foot model include TCJ, STJ, MPJ, and Arch in global coordinate system. 52

60 [M ] G Cmx Clx NVx L Tbx Cmy Cly NVy L Tb y Cmz Clz NVz L Tb z [M ] PL [M ] STJ [M ] TCJ [M ] MPJ [R ] 1 2 FRF i COP i F ij 53

61 PL [ M] = [ R] [ M] PL G G my 1 m1 = f1 f12 m1( zm 1+ g)= n1 n12 I θ = T + T + T 1 1 ARCH FRF1 F12 FRF1 (f1, n1) z T ARC θ ARC Cm NV M1 y F12 (f12, n12) m1, I1 (a) definition of TCJ angle and marker position. (b) definition of TCJ moment. Fig. 4-3 The arch model in plantar coordinate system. 54

62 Fig. 4-4 The anatomical axis of ankle joint. 55

63 [M] PL [M] TCJ f21,n21 FRF2 FRF2 TCJ [ M] = [ R] [ M] TCJ PL PL my 2 m 2 = f2 + f21 f23 m2( zm 2 + g)= n2+ n21 n23 I θ = T T + T + T T 2 2 ARCH TCJ FRF 2 F 21 F 23 Tb z Am θ TCJ T TCJ Dm F23 (f23, n23) m2, I2 y F21 (f21, n21) FRF2 (f2, n2) T ARC (a) definition of TCJ angle and marker position. (b) definition of TCJ moment. Fig. 4-5 The Taroclural joint(tcj) model in TCJ coordinate system. 56

64 z Am A θ STJ T STJ Cm Cl FRF2 (s2, n2) m4, 4 x FRF1 (s1, n1) F43 (s43, n43) (a) definition of STJ angle and marker position. (b) definition of STJ moment. Fig. 4-6 The Subtalar joint(stj) model in STJ coordinate system. 57

65 STJ [ M] = [ R] [ M] STJ G G mx 4 m = s1+ s2 s43 m4( zm + g)= n1+ n2 n43 I θ = T + T T + T 4 4 STJ FRF1 FRF 2 F 43 Fig. 4-7 The measurement system using the DIAGNOST 97 DXTV(PHILIPS). 58

66 Eversion Neutral Inversion marker deg deg bone deg deg Fig. 4-8 The ragiographic verification of the marker system corresponding to STJ axes. 59

67 case_1 (y case_2 (y mp mp > y1) TMPJ = 0 < y ) T = T 1 MPJ FRF1 T MPJ z FRF1 (f1, n1) Dm θ MPJ To y (a) definition of MPJ angle and marker position. (y1, z1) (b) definition of MPJ moment. Fig. 4-9 The MPJ model in plantar coordinate system. 60

68 I STJ TCJ MPJ STJ TCJ ARCH MPJ STJ Fig The marker system corresponding to anatomical axes. 61

69 P = ω T 62

70 P = ω T ARCH ARCH ARCH 10 Cm T ARC θ ARC M1 Arch power [W] Arch moment [Nm] Archangle [deg.] HC FF MS HO TO Fig The arch angle, moment, and power in a gait cycle. 63

71 T TCJ Am Dm Tb θ TCJ TCJ power [W] TCJ moment [Nm] TCJ angle [deg.] HC FF MS HO TO Fig The TCJ angle, moment, and power in a gait cycle. 64

72 Fig Motion of the tarocrural and subtalar joint(wright; 1964). 65

73 10 θ STJ Am Cm A Cl T STJ STJ power [W] STJ moment [Nm] STJ angle [deg.] HC FF MS HO TO Fig The STJ angle, moment, and power in a gait cycle. 66

74 angle [deg.] Fig Motion of the MP joint(fujita). Fig Windlass mechanism(hicks). 67

75 θ MPJ TMPJ MPJ power [W] MPJ moment [Nm] MPJ angle [deg.] HC FF MS HO TO Fig The MPJ angle, moment, and power in a gait cycle. 68

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77 (1) Arch angle and moment Arch Angle [deg] Arch Moment [%] (2) TCJ angle and moment TCJ Angle [deg] TCJ Moment [%] (3) STJ angle and moment STJ Angle [deg] STJ Moment [%] (4) MPJ angle and moment MPJ Angle [deg] stance phase swing phase Gait Time [%] MPJ Moment [%] stance phase swing phase Gait Time [%] Fig Results from 5 normal subjects during normal gait cycle. It s means of seven samplings. (1) Arch angle and moment, (2)TCJ angle and moment, (3)STJ angle and moment, and (4)MPJ angle and moment. Moment datas were standardyzed by body weight and foot length. 70

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79 Cm Dm NV θ MPJ θ ARC To M1 Arch Angle [deg.] MPJ Angle [deg.] a. Experimentation data of the MPJ angle. Windlass effect: x [mm] b. Calucuration of the windrass effect by the model simulation. c. Experimentation data of the Arch angle. Fig Graphical simulation of the windlass effect (1991) 72

80 EHL / EDL TA TA FHL PL FDL PB TP EHL/EDL TS TA Arch Moment + FHL FDL TP TS STJ Moment+ Muscles EHL EDL TCJ Moment PL PB + TCJ Moment TS FDL FHL TP STJ Moment PL / PB TA :Tibialis Anterior TP :Tibialis Posterior EHL :Extensor Hallucis Longus FHL :Flexor Hallucis Longus EDL :Extensor Digitorum Longus FDL :Flexor Digitorum Longus TS :Triceps Sulae PL/PB:Peroneus Longus/ Brevis reverse stance phase swing phase Fig Muscle activities effect to the TCJ and STJ moment 73

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84 Foot Motion during Gait DLT Method Motion Capture Foot Segment Parameter Mass Position Arch Angle Floor Reaction Forces In Chapter 4. Foot Model Newton-Euler s Equation Experimental Arch Moment Theoretical Arch Moment T * () t = k θ () t + d ( θ t ) Newton-Euler s Equation Experimental Arch Moment Arch Angle Least Square Method 4 Phase of a Gait Cycle I II III IV k 1 k 2 k 3 k 4 elasticity d 1 d 2 d 3 d 4 viscosity Discussion of Functional Change of the Foot Support Mechanism Fig. 5-1 Experimental arch moment was determined from anthropometric sampling data of the foot during gait, which was fitted to theoretical arch moment using the Least Square Method. k: elasticity and d: viscosity in each phase of a gait cycle were recognized in this study. 77

85 TP PL PB FDL FHL Ext.M (k M1 ) TC TA TA: tibialis anterior TP: tibialis posterior PL: peroneus longus PB: peroneus brevis FDL: extensor digitorum longus FHL: extensor hallucis longus TN CN MT Lig (k L ) Int.M (k M2 ) MP PF (k PF ) (a) The arch support mechanisms are consist of any ligamentous stabirities(lig), extrinsic muscles(ext.m), intrinsic muscles(int.m), and plantar fascia(pf). k d θ m (b) The simple foot arch model including torsional spring-damper in the arch joint. Fig. 5-2 (a) The arch support elements, and (b) the foot model simplify the human foot highly complex. my m = f1 fa mz ( m + g)= n1 n I θ = T + T + T FRF a Fa 78

86 T * T * () t = k θ () t + d ( θ t ) n J = { T( t) k θ ( t) d ( θ t )} 2 t= 1 J k = 0 J d = 0 79

87 I III I II III IV IIIII III III k 3 IIIII k 1 <k 2 <k 3 k 3 k 3 k 3 80

88 Phase I Phase II Fig. 5-3 The biomechanical function of the foot is changing during gait. Phase I : Weight acceptance phase; Heel contact to foot flat. Phase II : All plantar contact phase; foot flat to heel off. Phase III: Push-Off phase; heel off to toe off. FRF Vertical [N] HC FF HOTO HC phase I II III IV Fig. 5-4 The floor reaction forces about hind foot and fore foot part. Two platform data identified heel contact(hc), foot flat(ff), heel off(ho), toe off(to), and HC in the next gait cycle. Accordingly phase I to IV was decided. Arch Moment [Nm] anti-gravity phase line :: experimentation dot :: simulation phase I II III IV k k k k d d d d Fig. 5-5 The elasticity: ki and viscosity:di in each phase are recognized by the least squre method. This picture shows a sample of subject A. 81

89 d [Nm/rad 2 ] * * * * * * k k [Nm/rad] k 2 k d 2 d Fig. 5-6 The experimental arch moment(line) fitted to simulation arch moment(dot), and determinant elasticity: ki (**p<.01) and viscosity:di in each phase. 600 (**p<.01) 60 * * * * * * * * (**p<.01) elasticity k [Nm/rad] viscosity d [Nm/rad 2 ] k 1 k 2 k 3 d 1 d 2 d3-20 Subject: KN TM NK SF RN YN Fig. 5-7 The viscoelasticity about 6 subjects in anti-gravity phase (**p<.01). II k 3 d 2 k 3 82

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92 Fig. 5-8 The stress-strain rate of ligament(woo; 1982). 85

93 Moment [Nm] Angle [deg.] Fig. 5-9 The sampling situation of back pack loading gait. Fig The arch moment and arch angle assuming over load append to body weight. 86

94 Distance Cross section area of Plantar Ligaments Plantar Ligaments Fig The model with plantar ligaments, sectional datas were corected from CT Scan. Fig The shematic illustration of ligamentus arch support 87

95 Extrinsic M. Plantar Flexor 40 HO Dorsi Flexor Intrinsic M. Fig The shame shows the timing of muscle activities in the general gait pattern. Windlass effect Int. Muscles Ext. Muscles 14%[Kim:1995] [Basmajian: 1963] Ligaments [Woo, Allard, Kitaoka] Phase II Phase III Fig The shame shows the effects of stiffness of foot arch support. 88

96 II III I III II III III II III II III I IV III III II k 2 k L k M ex III k 3 k L k M ex k M in k PF 89

97 k L k M ex k M in k PF III k 3 II III k 3 k 2 k 3 k 2 k phase II k 2 [Nm/rad] phase III k 3 [Nm/rad] 100 morning evening 100 morning evening Subject: KN TM NK SF RN YN Fig The contrast between morning and evening foot. 90

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102 a. normal foot. structure. b. flat foot. structure. c.reconstruction of the foot arch. a. normal foot b. without calcaneum pronation. c. with calcaneum pronation. d. the arch support Fig. 6-1 The normal and flat foot structure and the concept of orthotic treatment. Fig. 6-2 The grade of flat foot deformities with and without calcaneum pronation. 95

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104 Nm Arch Moment %Gait deg Arch Angle %Gait Fig. 6-3 The arch moment and angles in barefoot compared with arch support intact. 97

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106 TA muscle (a) At the early stanse. internal moment external moment FRF human foot heel cushion and shock absorption FRF prosthetic foot CALF muscle (b) At the terminal stanse push off toe spring FRF FRF human foot prosthetic foot Fig. 6-4 The functional schematic illustration in a; early stanse, and b; terminal stanse in the human foot versus prosthetic foot. 99

107 Fig. 6-5 The trajectry of center of gravity in the transverse plane and center of pressure in the plantar surface. 100

108 deg 10 Subject_A deg 10 Subject_D 0 100% of stance 0 100% of stance deg 10 Subject_B deg 10 Subject_E 0 100% of stance 0 100% of stance deg 10 Subject_C deg 10 Subject_F 0 100% of stance 0 100% of stance Fig. 6-6 The deformation of medial and lateral arch about 6 subject. Medial arch angle Lateral arch angle 101

109 Fig. 6-7 At the case of long stump below knee amputation. 102

110 stress (kgf) 0 50 lateral medial strain (mm) Fig. 6-8 The design of the keel in the new concept of outside rigid structure and the stiffness curve of the medial and lateral keel.. load cell:a&d LC lasor displacement meter:keyence LB-01 X-Yrecorder:GRAPHTECH WX4421 Fig. 6-9 The keel measurement system. 103

111 Fig The trial prosthesis and situation of sampling systems, the center of gravity of the trank to assumes the center point of both acromion and greater trochanters. conventional foot prototype foot Fig The center of pressure pattern of the conventional foot(left) and new concept prototype prosthetic foot(right). 104

112 [m] JF 03 conventional foot [m] NN [m] prototype foot [m] Fig COG trajectory of the conventional foot and new concept prototype prosthetic foot. subject A male 22 60kg, 165cm subject B male 24 61kg, 173cm subject C male 24 64kg, 170cm Conventional Foot Prototype Foot ** (p<.01) * (p<.05) ** (p<.01) mm Fig Comparison of COG sway between conventional foot and new prottype foot in three subjects. 105

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115 T * () t = k θ () t + d ( θ t ) 108

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119 j1 j8 j7 j5 j3 j2 hind foot mid foot fore foot j8 j7 j5 j3 j4 j2 hind foot mid foot fore foot j8 j7 j5 j3 j4 j2 j1 medial view over view lateral view Talus Calcaneus j1 Taroclural Joint [TCJ] Navicular Cuboid j2 Sabtalar Joint [STJ] Medial Cuneiform j3talonavicular joint [TN] Intermediate Cuneiform Lateral Cuneiform j4 calcaneocuboid joint [CC] 1st. Metatarsal 2nd. Metatarsal j5 cuneonavicular [CN] 3rd. Metatarsal 4th. Metatarsal j6 intertarsal joint 5th. Metatarsal Sesamoid Proximal Phalanx j7 tarsometatarsal joint Middle Phalanx Distal Phalanx j8 metatarsophalangeal joint [MPJ] Fig. A1-1 The skeletal structure and anatomical joints of the human foot. It s consist of 28 bones and over fifty joints in perticulary, but in this paper aimed at 16 bones and 8 joints. 112

120 subtalar joint axes in horizontal plane 23 (4~47 ) tarocrural joint axes in horizontal plane subtalar joint axes in sagittal plane 42 (20.5~68.5 ) tarocrural joint axes in frontal plane 82 (74~94 ) a. The anatomical axis of tarocrural joint and subtalar joint. b. Motion of the dorsi flection and plantar flection in the tarocrural joint. c. Motion of the pronation and supination in the subtalar joint. Fig. A1-2 The ankle joint is consists of tarocrural joint and sabtalar joint, this picture shows the oblique axis of the tarocrural and subtalar joints and schematic illustration in each joint motion. 113

121 Lateral view Posterior view medial view tarus and calcaneus conection Fig. A1-3 The all joints in human body are constraint by the ligamentous linkage system. This picture shows the ligamentous construction mechanisms of the taloclural and subtalar joints. 114

122 EHL EDL Ankle Joint Axis PL PB TS Sabtalar Joint Axis TA FHL FDL TP TA :Tibialis Anterior FHL :Flexor Hallucis Longus FDL :Flexor Digitorum Longus TP :Tibialis Posterior TS :Triceps Sulae PL :Peroneus Longus PB :Peroneus Brevis EHL :Extensor Hallucis Longus EDL :Extensor Digitorum Longus Fig. A1-4 Function of muscle activities to talocrural and subtalar joint motion. There are extrinsic muscles of the foot, and each muscles effect of the each joints simultaniously. 115

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124 Fig. A1-5 The ligamentous stability of midfoot poetion, it s to support the longitudinal foot arch. muscles TA :Tibialis Anterior FHL :Flexor Hallucis Longus FDL :Flexor Digitorum Longus TP :Tibialis Posterior PL :Peroneus Longus Abd H.:Abductor Hullux bones TAL :talus NV :navicular CC :calcaneus M1 :1 st metatarsal TAL FHL NV M1 CC TP FHL FDL FHL PL EHL TA Abd.H Fig. A1-6 The illustration shows the effect of musculer support in the human foot arch complex. 117

125 53.5 MP joint axis abduction - adduction flexion -extention Fig. A1-7 Joint axis of the metatarsophalangeal, (MP) joint, in the motion of abduction - adduction, and flexion -extension. 118

126 visual information vestibulo-equilibratory control RESPONSE COMMANDS INFORMATION golgi tendon organs plantar soft tissue Fig. A2-1 The feedback control system of the stability at standing posture. 119

127 acromion elector spine 1cm back of the hip joint gluteus maximus 1cm front of the knee joint soleus soleus front of the ankle joint a. The gravity line passes the 1cm back of the hip joint, 1cm front of the knee joint, and front of the ankle joint. Hip joint and Knee joint is stabled by ligamentous stability, but the ankle joint is necessary to act the soleus muscle. b. It is necessary to act the soleus muscle at the stability in standing posture. Fig. A2-2 The stability of standing posture. 120

128 Fig. A2-3 The weight distribution mechanism by talus bone and arch structure. 121

129 stride length stride width step length Left Stance 60% 20% double support Left Swing 40% Righit Stance single support Left Stance Heel Contact Foot Flat MidStance Heel Off Toe Off Acceration Mid Swing Deceleration Stance Phase Swing Phase Weight Acceptance Swing Limb Support Limb Advancement Initial Contact Loading Response Mid Stance Terminal Stance Pre Swing Initial Swing Mid Swing Terminal Swing Fig. A3-1 The terminology in a gait cycle. 122

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132 Ankle joint motion PF.20' 10' 90' (0) DF.10' Plantar Flexion HC FF MS HO TO HC Dorsiflexion Ankle joint moment and FRF (BWLL) Planter Flexion Mom. FF MS HO TO Dorsiflexion Mom. % of Gait Cycle Muscle activities TA.Group H.C. M.S. T.O. H.C. Calf. Group H.C. M.S. T.O. H.C. Fig. A3-2 The ankle joint motion, moment, and muscle activities during the gait cycle. 125

133 Fig. A3-3 The trajectry of the center of gravity in a gait cycle. The trajectry describes the sinusoidal curve in horizontal and sagittal plane (32). 126

134 P 2πfT ρ 2 Pole zero 2πf c T ρ 1 Pole ρ 2 Pole Fig. A4-1 The singularity in the Z plane. Hz ()= 3 ( z + 1) gz ρ 2 z 2ρ zcos2πft ρ 2 1 ( 2 c 2 ) ( ) + g 8 = 1 ρ 1 2ρ cos2πft ρ 2 1 ( 2 c 2 ) ( ) + yn ( )= yn ( 1) ( ρ1+ 2ρ2cos2πfT c ) 2 yn 2 ρ 2ρρ cos2πft ( ) + ( ) ( c ) 2 + yn 3ρρ xn ( )+ 3xn ( 1)+ 3xn ( 2)+ xn 3 g { ( )} 127

135 i x = i u jy jv = jy jv cosφ = cosφ j k = j k cos( 90 o + φ) = sinφ y w y w y O j y R x = cosφ sinφ Fig. A5-1 A definition of the rotation angle. 0 sinφ cosφ x w u k w z i x = i u k z j v v R = z cosψ sinψ 0 sinψ cosψ cosθ 0 sinθ R = y sinθ 0 cosθ 128

136 T T [ R] [ xyz] = R R R [ xyz] G T x z y G cψ sψ 0 cθ 0 sθ = 0 cφ sφ sψ cψ T 0 [ xyz] 0 sφ cφ sθ 0 cθ cθ cψ sψ cψ sθ = sθ sφ+ cθ cφ sψ cφ cψ cθ sφ+ cφ sθ sψ [ xyz] T cψ sθ+ cθ sφ sψ cψ sφ cθ cφ+ sθ sφ sψ 129

137 subject KN TM NK SF RN YN sex / age f / 27 m / 30 f / 26 f / 23 f / 26 m / 30 foot length body weight foot angle stride stiffness (k3)

138 Sampling code::0806kn{a02, a03, a05, a06, a07, a11}aug Morning BodyWeight::61.8 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

139 Sampling code::0806tm{a05, a06, a07, a08, a09, a10, a11, a12}aug Morning BodyWeight::69.2 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

140 Sampling code::0806nk{a02, a06, a08, a11}aug Morning BodyWeight::43.7 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

141 Sampling code::0730fj{a04, a05, a06, a07, a09}aug Morning BodyWeight::48.1 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

142 Sampling code::0730nr{a03, a07, a09, a11}aug Morning BodyWeight::51.1 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

143 Sampling code::0521nk{a19, a20, a21, a22, a23, a24, a25, a26, a27}mar Evening BodyWeight::82.4 kg Step Length = m Foot Angle = deg Elasticity Arch Elasticity Viscosity Arch Viscocity k-> d-> deg Arch Angle Nm Arch Moment W Arch Power deg TCJ Angle Nm TCJ Moment 100 W TCJ Power -100 deg 10 STJ Angle Nm 100 STJ Moment 100 W STJ Power deg MPJ Angle Nm -50 MPJ Moment W MPJ Power deg Lateral Arch Angle mm Arch Length 10 mm Ball Width

144 Fig. A7-1 The design of the new prosthetic foot by the concept of outside rigid structure. 137

145 138

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153 146

154 Cpp X C, pp DR, (3), pp Wing Foot 4, pp Orthosis , pp

155 S, pp S, pp S, pp S, pp WBC S, pp WBC S, pp (2), pp.73

156 (6), pp Possibility of orthotic gait as a tool for locomotor training in patients with spinal cord injury: New Horizons putting the science into rehabilitation- Abstracts Spinal Injury : New Horizons putting the science into rehabilitation- H. Yano K. Nakazawa T. Kikuchi H. Seki (s), pp (2), pp (s), pp , 4., (2) (S), pp (1), pp

157 4., (7), pp (3), pp (1), pp (11), pp (2), pp (1), pp CAPOD (s), pp CAPOD CAD-CAM SYSTEM (s), pp (3), pp