Vidhya sundhararaj 2115580 Supervisor Prof Mark Taylor

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

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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

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100Cumulative "Energy" per Principal Component Term

0 2 4 6 8 10 12 14 16 1840

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60

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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

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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

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Fx

fem

oral

leng

th (

func

tiona

l)

0 50 100 150 200 250 300 350 400 45018

19

20

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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

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0.5

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1.5

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2.5

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

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0.5

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1.5

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2.5

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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

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0.5

1

1.5

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2.5

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

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0.5

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1.5

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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

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500Principal Component 1

Data Point

For

ce

0 500 1000 1500 2000 2500 3000 35000

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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