Movement analysis with stereophotogrammetry: anatomical landmarks calibration

Transcription

1 Movement analysis with stereophotogrammetry: anatomical landmarks calibration Ugo Della Croce, Ph.D. Biomedical Sciences Department, University of Sassari, ITALY Motion Analysis Lab, Spaulding Rehabilitation Hospital, PM&R Department, Harvard Medical School, Boston, USA Motion Analysis Lab, PM&R Department, University of Virginia, Charlottesville, Va, USA 1

2 the geometry of the Euclidean 3-dimensional space as a function of time looking at the space around us and describe it with numbers to be able to reproduce it exactly as it was when observed, even if it may have changed meanwhile 2

3 this is the complicated reality we want to frame into a numerical structure t = t 3

4 let s focus on a single bone 4

5 a body may be thought of as made of particles we represent a particle using the dimensionless geometric entity (model) point P 5

6 point which lies on a known plane described with numbers v v v = x y v x v y = v cos = vsin φ φ y v y v φ v x P x ( ) v = v 2 2 x + v y 6

7 what happens if we change perspective? The numerical description of the position of P changes Can we set a relationship between v and v? y y v v P x x 7

8 change of perspective by simply sliding (translating) the cross-wire y y v v P Rule for coordinate transformation v v x y = = p p ox oy + v + v x' y' o p o o x x v = p + o v' 8

9 rule for coordinate transformation y y θ yx θ yx P θ xy x v v x y = = v v x' x' cosθ cosθ x' x x' y + + v v y' y' cosθ cosθ y' x y' y θ xx x v v x y = cosθ cosθ x' x x' y cosθ cosθ y' x y' y v v x' y' v = Av' 9

10 general change of perspective What is the relationship between v and v? y y v v P x x 10

11 change of perspective in two steps: translate and rotate it the cross-wire y y v = p + o v' y v P v x v ' = Av'' p o x x v = p + o Av'' 11

12 a point in the three-dimensional space y P v y v v = v x v y v z v z v x x z 12

13 change of perspective in the three-dimensional space y y A = cosθ cosθ cosθ x' x x' y x' z cosθ cosθ cosθ y' x y' y z' z cosθ cosθ cosθ z' x z' y z' z v v P x p o = p ox p oy p oz p o x v = p + o Av' z z 13

14 we are using stereophotogrammetry y BTS BTS P v y v v = v x v y v z v z z v x x 14

15 markers over a body segment y BTS BTS v v = v x v y v z z x 15

16 markers over a body segment: requirements BTS NO REPEATABLE BTS visible to the cameras fast, easy and safe mounting minimal disturbance to the subject applicability over prostheses, orthoses spread in space 16

17 body segment representation: repeatibility BTS BTS points related to the anatomy joint axes location inertia properties (CoM, axes of inertia) 17

18 body segment representation: Bone-embedded Frames BTS BTS Bone-embedded Technical Frame (BTF) 18

19 body segment representation: Bone-embedded Frames BTS P 1 BTS P 2 P 3 P 1, P 2, P 3 mathematical operator p 0, A 19

20 body segment representation: Bone-embedded Frames BTS BTS Bone-embedded Technical Frame Anatomical Landmarks 20

21 body segment representation: Bone-embedded Frames BTS BTS Bone-embedded Technical Frame Bone-embedded Anatomical Frame (BAF) 21

22 body segment representation: Bone-embedded Frames P 1 BTS BTS P 3 P 2 P 1, P 2, P 3 mathematical operator p 0, A 22

23 anatomical landmark calibration ASIS PSIS LE, ME, GT LM, MM, TT, HF 23

24 now the scene is in motion BTS BTS 24

25 in every instant of time we use two systems of axes global (fixed with the laboratory) Y y X z x Bone-embedded (fixed with the moving body) Z 25

26 movement reconstruction position and orientation of the moving BF relative to the global frame y Y p o o X z Z A A = x p o cosθ cosθ cosθ = x' x x' y x' z p position vector ox cosθ cosθ cosθ p z' z oy y' x y' y p oz orientation matrix cosθ cosθ cosθ z' x z' y z' z 26

27 in each sampled instant of time: 1. locate the BF relative to the global set of axes and 2. locate the body points in the BF in the global set of axes Y y x Z X z 27

28 movement reconstruction Y Z X 28

29 sources of errors BTS BTS P 1) instrumental errors v = v x v y v z 2) skin movement artifacts 3) anatomical landmark mislocation 29

30 1) instrumental errors (apparent marker movement) BTS BTS P 1 P 2 O mm O X (t) s Della Croce et al., Med. & Biol. Eng. & Comp.,

31 compensation of instrumental errors BTS BTS increase the number of cameras improve camera location good marker maintenance 31

32 2) skin movement artifacts (actual marker movement) 32

33 skin markers 33

34 how to measure skin movement artifacts Fluoroscopy, GT, LE, HF, LM voluntary flexion 6 frames/sec Angeloni et al., ESB

35 how to measure skin movement artifacts intracortical pins 60 flexion => 5.0 Ab/Ad and 9.4 Int/Ext 60 flexion => 3.4 Ab/Ad and 10.6 Int/Ext Lafortune and Cavanagh, Journal of Biomechanics 1992 Ishii et al., ClinOrtRelRes 1997 percutaneous pins vs 11diff.arrays, tib/fib, 7 subj, gait Manal et al., GaitPost

36 the challenge rigid body estimator anatomical landmark identification 36

37 rigid body model calibration in a given instant of time y BTF z Laboratory frame x Spoor and Veldpaus, 1980 Veldpaus et al., 1988 Söderkvist and Wedin, 1993 Challis, 1994 Challis, 1995 Cheze et al., 1995 Cappozzo et al.,

38 fitting the rigid body model calibration to the markers in each sampled instant of time during the movement y Laboratory frame x z 38

39 anatomical landmark calibration BTF BTF bone-embedded technical frame w i anatomical landmark position vectors 39

40 3) anatomical landmark mislocation rigid body estimator anatomical landmark identification 40

41 palpable anatomical landmarks precision [mm] landmark INTRA-OPERATOR INTER-OPERATOR r r PELVIS ASIS PSIS FEMUR GT r ME LE TIBIA and TT 5 12 FIBULA HF 6 12 MM 7 15 LM 9 17 FOOT CA FM 8 22 Della Croce et al., Medical & Biol. Eng. & Comp.,

42 Identification of the hip joint center location x y z METHOD Func. Bell Davis Func. Bell Davis Func. Bell Davis MEAN [mm] SD [mm] Func. Cappozzo, Human Movement Science, 1984 Bell Bell et al., Journal of Biomechanics, 1990 Davis Davis et al., Human Movement Science, 1991 Z Y X Leardini et al., Journal of Biomechanics,

43 anatomical reference frame precision determined BAF marker cluster BTF actual BAF r [deg] INTRA- OPERATOR INTER- OPERATOR PELVIS A-P V M-L FEMUR A-P V M-L TIBIA and A-P FIBULA V M-L FOOT A-P V M-L Della Croce et al., Medical & Biol. Eng. & Comp.,

44 joint kinematics precision upright posture r [deg] INTRA- OPERATOR INTER- OPERATOR HIP Fl/ex Int/ext Ab/add KNEE Fl/ex Int/ext Ab/add ANKLE Fl/ex Int/ext Ab/add Della Croce et al., Medical & Biol. Eng. & Comp.,

45 joint kinematics precision flexion-extension error [deg] flexion [deg] flexion ab/adduction int/extern Della Croce et al., Medical & Biol. Eng. & Comp.,

46 FLEXION-EXTENSION MUSCULAR MOMENT AT THE HIP Y FC FO FC Z X extension flexion %W *H -30 mm +30 mm % of walking cycle Stagni et al., Journal of Biomechanics,

47 additional anatomical landmarks LE and ME LC and MC LP and MP FH GT 47

48 Bone-embedded Anatomical Frame (BAF) LE and ME V FH (BAF1) LC and MC LP and MP M-L A-P 48

49 additional BAF (2) LE and ME V FH (BAF1) (BAF2) LC and MC LP and MP A-P M-L 49

50 additional BAF (3) LE and ME LC and MC V FH (BAF1) (BAF2) (BAF3) LP and MP M-L A-P 50

51 additional BAF (4) LE and ME LC and MC V FH (BAF1) (BAF2) (BAF3) (BAF4) LP and MP A-P M-L 51

52 additional BAF (5) LE and ME LC and MC LP and MP V FH (BAF1) (BAF2) (BAF3) (BAF4) (BAF5) M-L A-P 52

53 additional BAF (6) V LE and ME LC and MC LP and MP FH GT (BAF1) (BAF2) (BAF3) (BAF4) (BAF5) (BAF6) M-L A-P 53

54 additional BAF (7) SVD (BAF1) (BAF2) (BAF3) (BAF4) (BAF5) (BAF6) (BAF7) a X a a a a a a a a = xgt x LE x ME x LP x MP x LC x MC x FH 54

55 results % A-P V M-L BAF BAF BAF BAF BAF BAF

56 recent advances optimization of functional methods for joint modelling augmented anatomical landmark identification i u m su provided in part by Department of Human Movement and Sport Sciences University Institute for Movement Science Rome, Italy 56

57 optimization of functional methods for joint modelling hip : spherical joint i u m su 57

58 optimization of functional methods for joint modelling functional approach HJC: m su relative rotation center between pelvis and femur u i 58

59 optimization of functional methods for joint modelling best algorithm hip : spherical joint more suitable movement criteria for marker cluster design Cereatti et al. (2004) Camomilla et al. (2006) 59

60 optimization of functional methods for joint modelling ankle : universal joint 2 degrees of freedom 3 angular rotations 3 linear displacements 60

61 optimization of functional methods for joint modelling functional approach axes positions and orientations 61

62 recent advances optimization of functional methods for joint modelling anatomical landmark identification 62

63 anatomical calibration: traditional approach y c superficial anatomical landmarks are identified by palpation y g x c z c x g z g c a c c c [ a a a ], i = 1,..., r i = xi yi zi lateral epicondyle 63

64 anatomical calibration: traditional approach selected anatomical landmarks y c ai = axi ayi azi, i = i c c c c unlabelled points selected in areas of the bone covered by a thin layer of soft tissues, so that the skin surface may be considered to coincide with the bone surface z c x c ui = uxi uyi u zi, i = 1,...,r c c c c 64

65 anatomical calibration: novel approach i u m su = u u u, i = 1,...,r g u g g g i xi yi zi Rozumalski A, Schwartz MH. Gait & Posture

66 global position of unlabelled points of the bone surface a wand carrying three non-aligned markers i u m su 66

67 points on the subject s bone surface as reconstructed using stereophotogrammetry GT y c femoral condyle z c x c marker-cluster frame 67

68 bone digital model* (template from database) morphological frame * Provided by Laboratorio di Tecnologie Biomediche at I.O.R - Bologna 68

69 the distal portion of the bone is isolated morphological frame 69

70 construction of the midepicondyle-gt line GT morphological frame 70

71 first approximation registration y c z c x c 71

72 registration: iterative method matching Minimization of mean direct Hausdorff distance Minimization was performed using a genetic algorithm Michalewicz, Z. (1996). Genetic Algorithm + Data Structures = Evolution Programs. Springer-Verlag: New York 72

73 first approximation registration y c z c x c f( P, U) =

74 iterations y c z c x c f( P, U) =

79 iterations y c z c x c f( P, U) = 53 79

83 solution b anatomical parameters = b b b, i = 1,..., n c c c c i xi yi zi y c z c x c f( P, U) = 10 83

84 solution b anatomical parameters = b b b, i = 1,..., n c c c c i xi yi zi y c z c x c f( P, U) = 10 84

85 ME MP LP LE repeatability assessment MC LC sd [mm] landmark LE ME LP MP LC MC Method # 3* Intra-operator Method # 3* Inter-operator Method # 4** Intra-operator Method # 4** Inter-operator * Della Croce U, Cappozzo A, Kerrigan C. Medical & Biol Engng & Comp 1999 ** Donati et al (2007) 85

86 ME MP LP LE repeatability assessment MC LC sd [mm] landmark LE ME LP MP LC MC Method # 3* Intra-operator Method # 3* Inter-operator Expert physiotherapists Method # 4** Intra-operator Method # 4** Inter-operator Bioengineers * Della Croce U, Cappozzo A, Kerrigan C. Medical & Biol Engng & Comp 1999 ** Donati et al (2007) 86

87 anatomical calibration: method # 4 Morphology data: High resolution non subject-specific data y m GT FH [ ] r m m m m âi = âxi âyi âzi, i = 1,..., Precise and economic LE m ˆb m m m = [ ], i = 1,..., n z i bˆ xi bˆ yi bˆ (no skilled professional zi required) m ME x m Registration data: unlabelled and labelled points of the bone surface y c GT c u i c c c [ u u u ], i = 1,..., r = xi yi zi z c x c c a c c c [ a a a ] i = i i = xi yi zi, 87

88 conclusions BTS BTS anatomical landmark mislocation can be reduced by: increasing the number of anatomical landmarks using the least sensitive BAF definition rules defining and determining anatomical landmark areas 88

89 Thank you 89