Proceedings of International Forum for Green Asia 2019
5th International Exchange and Innovation Conference on Engineering & Sciences (IEICES 2019)

GA15 / P27
Assessment of Vertebral Strength using CT-image Based Finite Element Method
1

Shun Wu1, Mitsugu Todo2
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University,
2
Research Institute for Applied Mechanics.
Email: Todo@riam.kyushu-u.ac.jp

Abstract: Traditional diagnosis criterion of osteoporosis is mainly based on single criterion, Young Adult Mean.
However, single Young Adult Mean method ignores the strength of vertebra itself, another dimension of osteoporosis.
This research developed a two-dimensional osteoporosis diagnosis criterion combining Young Adult Mean and bonestrength predicted by finite element analysis. It has been proven that it can reduce the misdiagnosis rate the simply using
Young Adult Mean value failed to detect fracture risk. In the other hand, assessment of vertebral strength via finite element
is a very complex processing, not clinically applicable. The study revealed that trabecular volumetric bone mineraldensity is more mechanically correlated with bone strength than Young Adult Mean. Then, the indicator to estimate bonestrength without finite element analysis also been studied. For healthy vertebrae without abnormality in shape, it may beachieved by measuring Logarithmic volume ratio of Extreme low density elements.
Keyword: Osteoporosis Diagnosis, Finite Element Analysis, Vertebral Strength.
1. Introduction

achieved, then, the BS can be estimated quickly but asaccurate as FEA.

Traditional diagnosis criterion of osteoporosis is mainly
based on Bone Mineral Density (BMD). Generally, there
are two approaches to indicate one’s BMD: areal BMD(aBMD)
measuredbyDual-Energy
X-ray
Absorptiometry (DEXA) and volumetric BMD (vBMD)
calculated from Quantitative Computer Tomography(QCT). The aBMD is a readily available indicator of
global bone mass (total bone mineral content) of a
specific site. Further, a percentage of one’s aBMD of five
lumbers divided by average of young lumbers aBMD
derives a value called Young Adult Mean (YAM). YAM
quantify the osteoporosis as YAM < 70% [1]. However,single YAM method ignores the strength of vertebra
itself, another dimension of osteoporosis. The vertebral
strength correlates with lumber aBMD (YAM) well (r2 =0.64) [2]. While this correlation is not based onmechanical principles. Although global bone mass isidentical, vertebral strength could change significantly
due to various densitometric inhomogeneities andvertebral geometry [3]. So far, assessment of vertebral
strength can be achieved by CT-image based Finite
Element Analysis (FEA) well [4]. The vertebral modelfor FEA is usually built from CT images. The voxels ofCT images can reflect the volumetric BMD (vBMD). Thematerial properties of elements in FEA can be transferredfrom vBMD of voxels. Hence, vBMD has a strong
mechanical correlation. According to this, this researchdeveloped a two-dimensional osteoporosis diagnosis
criterion based on both YAM and FEA-predicted BoneStrength (BS), in order to reduce the possibility ofmisdiagnosis.

Above all, this research aims to (1) develop a twodimensional criterion to diagnose osteoporosis
combining YAM and BS, and (2) discover factors ofvBMD inhomogeneities that correlate with BS strongly.
2. Method
2.1 Vertebral strength prediction by FEA
Department of neurosurgery, Inazawa Community
Hospital supplied CT images of 88 patients (23 males, 65females), aged from 42 to 96. YAM ranged from 32 to142. After eliminating vertebrae with surgical treatment
or fractures, total 247 vertebrae was analyzed, including
19 vertebrae of T11, 47 of T12, 51 of L1, 71 of L2 and
59 of L3. Then, a generic CT-based FEA software,
Mechanical Finder Clinic (MFC, RCCM), was used to
extract Region of Interest (ROI) of vertebral bodies
without pedicle and generate mesh. The vBMD ofelements was transferred from grey degree of voxels.
Material properties was determined automatically byvBMD [5]. The load of axial compression was applied by
MFC automatically, see Fig. 1. The vertebral BS wasdefined as the load when any element of vertebral body
started to generate damage.

On the other hand, assessment of vertebral strength via
FEA is a very time-consuming processing, and requires
good understanding on mechanics. As a result, theclinical application of FEA was restricted seriously overtwo decades. This research is also trying to find out thosefactors that correlate with FEA-predicted BS well. More
importantly, these factors can be obtained from analyzing
CT images directly, such as spatial and number
distribution of vBMD and geometric features. If it can beFig. 1 load and constraint conditions. Red arrows
represent load and dots mean constraints.

- 39 -

2.2 Measurement of vBMD inhomogeneities

YAM cannot identify these vertebrae. But these has morepotential that vulnerable fracture happens. It will be very
dangerous if surgeries misdiagnose by the single
indicator. Combination of YAM and FEA-predicted BS
can reduce misdiagnosis effectively.

Mechanical Finder (RCCM) was used to study the furthervBMD distribution. MFC is a simplified version of MF.
It cannot obtain vBMD distribution and specification ofvertebral body. There were 26 vertebrae selected tocreate a more complex three-dimensional finite element
model of vertebral body in MF. Mesh size and shape wasdetermined as 1 mm and tetrahedron. The methodology
of material property arrangement was same as MFC.
Then, the capture tools in MF helped to calculate theaverage vBMD of cross-sections in transverse plane ofvertebrae 1 mm by 1mm from upper to bottom surface
along axial direction. Then, an axial vBMD distribution
curve obtained. The trabecular area was considered by anarea between local maximum values nearest to central
position for upper limit and the lowest value in the curvefor lower limit, as showed in Fig. 2. Trabecular vBMD
(Tr.vBMD) was calculated by the average vBMD value
in this trabecular area.

Fig. 3 Two-dimensional osteoporosis diagnosis based on
OPIYAM and OPIBS. Vertebrae in different positions
distinguish by marker colors.
3.2 vBMD inhomogeneities
To study the effect of vBMD inhomogeneities on BS, allvertebrae in Fig. 3 can be divided into 4 groups: Group A(Both YAMOPI and BSOPI >1), B (YAMOPI >1, BSOPI <1),C (YAMOPI <1, BSOPI >1) and D (both YAMOPI and BSOPI<1). The 26 vertebrae selected for the vBMD
measurement in MF were evenly distributed in 4 groups,
see Fig. 4(a).
Then, OPIBS-OPIYAM relations
corresponding to the 4 groups were retrieved from Figure
3 and redrawn in Figure 4 (a). The OPIBS-OPITr.vBMD
relations for the 4 groups are also shown in Figure 4(b).

Fig. 2 The definition of Trabecular area for vertebrae.
2.3 Osteoporosis indicators
The critical YAM is 70% for diagnosing osteoporosis [1],and the critical BS was assumed as 2500 N. Therefore,
two osteoporosis indicators such as the strength based
OPIBS and the YAM based OPIYAM are defined byEquations 1 and 2, respectively.
$%

𝑂𝑃𝐼$% = ()**
𝑂𝑃𝐼+,- =(1)+,-(2).*Furthermore, the Tr.vBMD based indicator OPITr.vBMD isalso defined by:

𝑂𝑃𝐼/0.2$-3 =/0.2$-3*.4((3)

where 0.12 is an osteoporotic Tr.vBMD value suggested
by American College of Radiology [6].
3. Result and Discussion
3.1 2D diagnosis method for osteoporosis
Fig. 3 illustrated the proposed two-dimensional diagnosis
method. Yellow area in Fig. 3 The YAM-based
traditional osteoporotic area was illustrated in yellow.
However, FEA displayed the existence of some vertebrae
with high YAM but low BS (orange area in Fig. 3). There
were 17 vertebrae and 14 patients in this area. The
incidence rate was 6.9% in total 247 vertebrae, and 15.9%
in total 88 patients, respectively. Only diagnosing by- 40 -Fig. 4 (a) OPIBS-OPIYAM two-dimensional method.
Vertebrae were divided into 4 groups. The red line
displayed the correlation between BSOPI and YAMOPI forgroup A. (b) OPIBS-OPITr.vBMD method. The red line
displayed the correlation between OPIBS and OPIYAM forgroup A.
Based on OPITr.vBMD and OPIBS, the new two-dimensional
diagnosis method revealed a considerable reduction onthe ratio of vertebra in orange zone from 23% to 7.7%,
see in Fig. 4(b). The yellow area in Fig. 4 (b) cover morevertebrae with low strength than Fig. 4 (a). Tr.vBMD ismore appropriate as a single indicator to diagnose
osteoporosis.

with BS than YAM. Tr.vBMD can diagnose osteoporosis
better than YAM, if as a single indicator. The indicator
to estimate BS directly also been studied. Logarithmic
volume ratio of vertebral EL element shows a great
potential. The further vBMD-related factors, such as
spatial distribution, will be considered next. Following,
the investigation will focus on quantifying the effect ofgeometric features on BS. If so, the strength of abnormalvertebrae with LO or SD can also be estimated accurately.
The vertebral cases should also increase to verify theeffectiveness further.

For group A, YAM had no correlation with BScompletely. Tr.vBMD linearly correlate with BS well,although such good correlation did not appear in othergroups. Tr. vBMD has been proven that has a bettermechanical correlation with BS. Generally, vBMD canbe separated into several 4 intervals, see in Table 1. The
ratio of EL can represent the degree of osteoporosis.

5. REFERENCES[1] Orimo H, Nakamura T, Hosoi T, Iki M, Uenishi K,
Endo N, Ohta H, Shiraki M, Sugimoto T, Suzuki T.
Japanese 2011 guidelines for prevention andtreatment of osteoporosis—executive summary.
Arch. Osteoporos. 7(2012)3-20.
[2] Cheng XG, Lowet G, Boonen S, Nicholson PH, Van
Der Perre G, Dequeker J. Prediction of vertebral andfemoral strength in vitro by bone mineral density
measured at different skeletal sites. J. Bone. Miner.
Res. 13(1998)1439-1443.
[3] Ferretti JL, Cointry GR, Capozza RF, Frost HM.
Bone mass, bone strength, muscle–boneinteractions, osteopenias and osteoporosis. Mech.
Ageing. Dev. 124(2003)269-279.
[4] Crawford RP, Cann CE, Keaveny TM. Finite
element models predict in vitro vertebral bodycompressive strength better than quantitative
computed tomography. Bone. 33(2003)744-750.
[5] Keyak JH, Rossi SA, Jones KA, Skinner HB.
Prediction of femoral fracture load using automatedfinite element modeling. J Biomech. 31(1998)12533.
[6] Radiology ACO. ACR–SPR–SSR practiceparameter for the performance of musculoskeletal
quantitative computed tomography (QCT).
American College of Radiology, Reston.

Table 1. Category of vBMD range
Category ofvBMD range (mg/mm3)

Extreme Low Density, ELD
Low Density, LD
Middle Density, MD
High Density, HD
Extreme High, EH

0 – 0.05
0.05 – 0.1
0.1 – 0.2
0.2 – 0.3
> 0.3

On the other hand, the strength may change considerably
due to the irregular geometry. The most common
abnormality
arisesfromLigament
Ossification (LO) and Spondylosis Deformans (SD), seein Fig. 5 (a) and (b). The existence of these abnormalities
may introduce too variables for strength estimation fromvBMD indicators. The orange points in Fig. 5 (c)displayed such deviation.
Therefore, excluding abnormal vertebral bodies help tounderstand the correlation between BS and vBMD
inhomogeneities. The results revealed that a significantly
linear correlation between BS and log scale of volume
ratio of EL elements in vertebrae without LO and SD.
Compared with FEA, the vBMD measurement in CT
images could be more operative and accessible clinically.
Hence, the logarithmic volume ratio of vertebral EL
element show a great potential to estimate BS.

Fig. 5 (a) vertebral body with LO and (b) SD. (c) The
correlation between BS and log scale of volume ratio ofvertebral ELD elements. Blue and orange markers meanvertebral body without and with LO or SD respectively.
4. Conclusion
This research first developed a two-dimensional
osteoporosis based on YAM and FEA-predicted BS. It
helped to reduce the misdiagnosis rate that simply using
YAM value failed to detect fracture risk. Then, the study
revealed that Tr.vBMD is more mechanically correlated- 41 -