International Forum for Green Asia 2020

Clinical Application of CT-image Based Finite Element Method
Combined with Machine Learning to Assessment of Bone Fracture
Shun Wu1and Todo Mitsugu2
1

Interdisciplinary Graduate School of Engineering, Kyushu University
2Research Institute for Applied Mechanics, Kyushu University
Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan

Abstract
In order to approach clinical vertebral body strength (BS) prediction quickly, it is necessary tocombine empirical research with machine learning methods using multiple vertebral features todevelop a BS evaluation methodology with the high accuracy. This research simulated BS bycomputed tomography based finite element method (CT-FEM). Then, BS-related
morphological and material inhomogeneous features of vertebral bodies were collected to train
six prevalent machine learning models. An empirical model was given based upon previousresearch. Compared with empirical model, logistic regression preformed most applicable.
1. Introduction
With the development of computed
tomography based finite element method(CT-FEM), its accuracy of predicting
vertebral body strength (BS) has been provenby some researches. [1] In order to approach
the BS prediction quickly, it is useful toinvestigate the determinants that influence
the BS value prediction in CT-FEM.
According to our previous research, CTFEM predicted BS was mainly decided by
CALnVRlow-BMD, minimal vertebral crosssectionalarea(MinCSA)
adjustedlogarithmic low volumetirc bone mineraldensity (vBMD) volume ratio, especiallywhen vBMD<0.05 mg/mm3 (see Eq. 1).

vertebral morphological feature, MinCSA,
and the material inhomogeneity feature. The
high correlation has shown in Figure 1.
However, there are many other BS
related features in the view of bonemorphology and material homogeneities,
such as vertebral height and the second
lumber areal BMD (L2 aBMD). [2] It is very
hard to connect them with CALnVRlow-BMD
for improving BS predictor performance. The
prevalent data-analysis method, machinelearning (ML), has been widely used to look
for the inner connection within complex
features. Thus, the objective of this researchis to combine the empirical research withmachine learning methods using multiple
vertebral features to develop a BS evaluation
methodology with the high accuracy.

(CALn%&!"#$%&' = ()*+,-.) ∙ 123+ !"#$%&'24 (Eq. 1)(()*+),*-

2. Method
2.1. Vertebral Strength Simulation
Department of neurosurgery, Inazawa
Community Hospital supplied CT images of88 patients, aged from 42 to 96. YAM ranged
from 32 to 142. 100 vertebrae without
surgical treatment or fractures were selected.
All of them located from the eleventh
thoracic (T11) to the third lumber (L3).
Mechanical Finder Clinic (MFC, ResearchCenter of Computational Mechanics, RCCM),
was used to extract vertebral bodies without

Figure 1. CALnVRlow-BMD VS vertebral strength.

This empirical model incorporates a31

International Forum for Green Asia 2020
pedicle and to generate meshing elements.
Then, the vBMD of elements was transferredfrom CT-values from voxels. Material
properties was calculated according toKeyak’s formulae. [3] The load of axial
compression was applied by MFC
automatically. The BS was defined as theonset loading raising at least one solid
element damaged in MFC.
2.2. BS-related Features Collections
Mechanical Finder 10 (MF10, RCCM)
was used to study the BS-related
morphological features and material
inhomogeneous features of vertebral bodies
further. 100 vertebrae were selected toreproduce vertebral bodies in MF10. Meshsize and shape were determined as 1 mm andtetrahedron, respectively. The methodology
of material property arrangement was samewith that of MFC. The BS-related features
evaluated in MF10 were: total volume ofvertebral body, the MinCSA along the axialdirection, vertebral height in anterior end(Height-A), in central position (Height-C)
and in posterior end (Height-P), low-vBMD(0-0.05 mg/mm3) volume, low-vBMD
volume ratio (VR), logarithmic VR andCALnVRlow-BMD. Additionally, five featuresthat likely correlate to BS considered in thisresearch were gender, age, L2 aBMD, Young
Adult Mean of lumber (YAM lumber) andYAM femur. Overall, 14 features.
2.3. Empirical Model VS Machine Learning
The empirical model was given as Eq. 2.
BS = 8 ∙ CALn%&!"#$%&' + :For each model, the parameters has been
tuned finely to avoid overfitting. The
classification accuracy of empirical model
only and ML models were evaluated using
cross validation of 5 folds by ‘accuracy’scoring. Their mean accuracy percentage andstandard deviation were listed in Table 1.
Table 1. Accuracy of empirical model & ML models
Model name
Mean accuracy (%) Std accu(%)
83.83

0.06

Logistic Regression

85.78

0.07

Decision Tree

82.94

0.07

Linear SVM

79.72

0.09

Random Forest

79.98

0.04

Voting Classifier

77.72

0.10

3. Result & Discussion
Table 1 display the mean accuracy forevery model clearly. Our empirical model
only had a high prediction accuracy. LogisticRegression slightly improved the result,while other ML models no better thanempirical model only. Since empirical modeland logistic regression are typically linearclassifier, meanwhile decision tree, random
forest and voting are more common on nonlinear classification, it may suggest that BS
maybe a linear superposition within some
BS-related features. Next, the deep learning
will be applied to improve the accuracy. The
mis-predicted vertebra will be selected to dig
more BS-related features.
Acknowledgment
I appreciate Todo Mitsugu sensei giving
me such a chance to learn and apply ML in
the research.

(Eq. 2)

Where ‘a’ and ‘b’ are coefficient and bias
respectively.
This study defined BS prediction as a
univariate classification problem. A vertebra
was classified as healthy, when its strength
more than 2500N, otherwise as weak state.
We applied most common but vigorous MLmodels. They were logistic regression (LR),decision tree (DT), linear support vector
machine by soft margin classification (SVM),
random forest (RF) and voting classifier (VC).

Empirical Model Only

Reference[1] P.K. Zysset, E. Dall’Ara, P. Varga, D.H. Pahr,Bonekey. Rep. 2013, 2, 386.
[2] J.M. Buckley, K. Loo, J. Motherway, Bone.
2007, 40, 767.
[3] J.H. Keyak, S.A. Rossi, K.A. Jones, H.B.
Skinner, J. Biomech. 1997, 31, 125.
Email: wu.shun.393@s.kyushu-u.ac.jp32