STATISTICAL MODELING OF HUMAN FEMUR WITH FORCE AND GEOMETRY Vidhya sundhararaj 2115580 Supervisor Prof Mark Taylor
Dec 29, 2015
STATISTICAL MODELING OF HUMAN FEMUR WITH FORCE AND GEOMETRY
Vidhya sundhararaj 2115580
SupervisorProf Mark Taylor
BACKGROUND
Population based studies are important for implant study, risk assessment for fracture, pre-clinical studies.
Modelling of single femur or limited number of femur excludes inter-patient variability and extrapolation to population makes less sensible. Also creating multiple models is time consuming.
Statistical modelling overcomes this issue of model generation.
AIM
To statistically model femur that represents maximum variation in femur population in terms of bone geometry, material property and forces and analysing if force can predict geometry and material property.
METHOD
1
•PCA on Forces
2
•PCA on simple geometry
3
•PCA on registered geometry
5• PCA with Density
1
•Regression on force and simple geometry
2
•Regression on force and registered geometry
3
•Regression on force and density
4 PCA on surface nodes
PRINCIPAL COMPONENT ANALYSIS (PCA)
A data reduction method that accounts for most of the variation in the original
data. The obtained variables are Called principal components & are uncorrelated to each other.
STANCE AND SWING PHASE Time for stance was obtained from musculoskeletal models in OpenSim.
Muscolo skeletal models developed by Saulo martelli
FORCES INCLUDED
26 muscle forcesOn femur and hip joint Forces.
PCA RESULT ON FORCE
0 2 4 6 8 10 12 14 16 1830
40
50
60
70
80
90
100Cumulative "Energy" per Principal Component Term
9 modes36.118514248235049.015173414759060.927597028736269.004074290068475.637573685511081.413655458357385.324858658514389.067971476558791.4560197304632
MESH MORPHING
Surface matching – deforms the baseline surface to match the given target surface. Volume morphing- creates the internal mesh points based on surface nodes.
PCA ON SIMPLE AND REGISTERED GEOMETRY
0 2 4 6 8 10 12 14 16 1840
50
60
70
80
90
100Cumulative "Energy" per Principal Component Term
0 2 4 6 8 10 12 14 16 1840
50
60
70
80
90
100Cumulative "Energy" per Principal Component Term
6 modes 49.172285873789473.502202492446282.487924741789989.633120317722192.582191950889795.388699332539
6 modes46.09552352784672.06344842933580.677256697321688.115140418427592.294027859745795.0421274638311
PCA ON 3D REGISTERED SURFACE
0 2 4 6 8 10 12 14 16 1820
30
40
50
60
70
80
90
100
110Cumulative "Energy" per Principal Component Term
9 modes29.558117867815448.286686834721661.559853954134071.825252391178580.940328944958788.295586378784391.971669866844793.711239535665995.2916843891132
ANALYSIS
Analysis was performed on force and shape data to know if shape can predict force.
Scatter plots of force and shape
0 100 200 300 400 500 600 700360
370
380
390
400
410
420
430
440
Fx
fem
oral
leng
th (
func
tiona
l)
0 50 100 150 200 250 300 350 400 45018
19
20
21
22
23
24
Fy (N)
fem
oral
hea
d ra
dius
in (
m)
ANALYSIS
Regression – a measure of relationship between variable. Has independent variable as predictors and dependent variable as outcome or response variable.
Multiple regression analysis – more than one predictor to predict outcome.
Stepwise regression – shows significant variables that can predict outcome.
REGRESSION RESULT
Coeff. t-stat p-val
46344.8 1.2069 0.2450
-3612.61 -0.1881 0.8531
123926 2.6334 0.0174
1 2 3 4 5 6200
220
240
260Model History
RM
SE
-5 0 5 10 15 20
x 104
X1
X2
X3
Coefficients with Error Bars
X1- Head radiusX2- neck major radiusX3- neck minor radiusy- mean peak forces Fx
REGRESSION ON PCA MODES
Regstat function – performs multiple regression by fitting model to the data.
‘linear‘ - Includes constant and linear terms (default).'interaction‘-Includes constant, linear, and cross product terms.
Mode 1 force represented by shape modes Mode 2 force represented by shape modes
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
REGRESSION ON PCA MODES
Interaction model Mode 1 of force Mode 2 of force
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
REGRESSION ON REGISTERED FEMUR MODELS
MODE 1 FORCE REPRESENTED BY SHAPE MODES
MODE 2 FORCE REPRESENTED BY SHAPE MODES
0 2 4 6 8 10 12 14 16 18-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10 12 14 16 18-2
-1.5
-1
-0.5
0
0.5
1
1.5
REGRESSION- STEPWISELM TERMS ADDED TERMS REMOVED
RECONSTRUCTION RESULT FOR FORCE
0 500 1000 1500 2000 2500 3000 35000
50
100
150
200
250
300
350
400
450
500Principal Component 1
Data Point
For
ce
0 500 1000 1500 2000 2500 3000 35000
50
100
150
200
250
300
350
400
450
500
Data Point
For
ce
Principal Component 1
Reconstructed
FUTURE WORKS
Interpretation of force and shape modes Volume morphing. Density extraction from CT scans and assigning it to
meshes. PCA and Regression analysis
Questions