九州大学大学院総合理工学府報告第 36 巻 第 2 号 6-9 頁 平成 27 年 2 月

Engineering Sciences Reports, Kyushu University
Vol. 36, No. 2, pp. 6-9, FEB, 2015

Prediction of Damage Formation in Total Hip
Arthroplasty using Finite Element Method
Abdul Halim ABDULLAH*1,3 and Mitsugu TODO*2,†
E-mail of corresponding author: todo@riam.kyushu-u.ac.jp†(Received January 26, 2015, accepted January 27, 2015)
Total hip arthroplasty (THA) patients sometimes encounter periprosthetic fractures. Sudden andhigh impact loading during certain activities may contribute to the incident such as sideway falls andbending. In this study, damage formation in femoral bone with a hip prosthesis was predicted using
the CT-based nonlinear finite element method. 3D model of femoral shaft was developed from
CT-images of a 54 years old patient. The femoral head was then cut off and aligned with hipprosthesis stem to reconstruct THA model. Three different configurations of isometric loadings
were considered to demonstrate high and complex impact loading. The applied impact forces werenormalized to body weight (BW) and vary from 1BW to 5BW. The results showed that the patterns ofpredicted bone fractures were different for each configuration. Numbers of element failures were thehighest in the lateral bending condition. Indication of failure elements at the bone-implant interfaces
suggested possibility of prosthesis loosening and instability.
Key words: Hip Prosthesis, Damage Formation, Femoral Bone, Finite Element Analysis

1.

Introduction

Total hip arthroplasty (THA) is one of themost recognized treatments for osteoarthritis
and rheumatoid arthritis. Improvements ofsurgical techniques and femoral implantdesign are continuously developed to promotelong term performance and stability. However,
THA patients were always at risk of falls due
to imbalance, medication side effects anddifficulty of avoiding environmental hazards[1]. Presence of artificial hip joint hascontributed to the gait impairment andremodeling process of the bones. Bones areadapted to the new mechanical environmentand became weaker.
Sideways falls might involve sudden andhigh impact loading to the hip of a THA
patient, which is very dangerous to elder
patients. It may also lead to femoral bone
fractures, joint failures and other successive
*1

*2
*3

Department of Molecular and Material Sciences,
Interdisciplinary Graduate School of Engineering
Sciences, Graduate Student
Research Institute for Applied Mechanics
Faculty of Mechanical Engineering, UiTM Malaysia

injuries [2]. Periprosthetic fractures of the hip
were expected for high and complex loading
vectors acting upon the femur [3]. In
predicting the fracture mechanism of femur, alot of studies have been conducted by surgeon
and researchers to investigate the effects ofloading direction [4]. For instance, Pinilla et al.
[5] conducted a compression test of cadaveric
femora specimen while Keyak et al. [5]demonstrated simulation studies on theinfluence of load direction using the linear
finite element method. As an improvement ofcomputational prediction, Bessho et al [4]established nonlinear finite element method
for the respective purpose. However, thosestudies were only focus on intact femur. In thisstudy, a computational model of femur with
THA was develop using CT-based nonlinear
finite element method.
The purpose of this study was to investigate
the mechanisms of periprosthetic femoralfractures associated with THA. Damage
models were introduced into the finite element
method in order to predict damage formations
in a femoral model with hip prosthesis.

2Prediction of Bone Fractures in Total Hip Arthroplasty using a CT-based Nonlinear Finite Element Method

2.

Method2.1

3D inhomogeneous modeling

Table 1 Mechanical property of hip prosthesis [7]3D inhomogeneous model of a left femoral
shaft was constructed from computed
topography (CT-based) data of 54 years old,male patient. The models were developed andanalyzed using a commercial biomechanicalsoftware, Mechanical Finder version 6.1.
Material properties for each tetrahedron
element of the bone model were computed by
Hounsfield unit value and presenting different
scale of bone densities. Assignment of young
modulus and yield strength of the model were
calculated based on the theory of Keyak et al[6], as illustrated in Fig.1a.

(a)
Fig.1

Properties

Ti6Al4V

Alumina

Elastic Modulus (GPa)

114

370

Poisson Ratio

0.34

0.22

Critical Stress (GPa)

0.88

0.40

Yield Stress (GPa)

0.97

3.00

Density (g/cm3)

4.43

3.96

stance (SC) [4], torsion (TC) and lateral
bending (BC) [8]. Each configuration exhibits
different loading directions at angle α (withreference to the long axis of femur in thefrontal plane) and β (with reference to thefemoral neck axis in the horizontal plane) [4].
Fig.2 illustrates the loading and boundary
conditions for each configuration while Table 2
describes the orientation of loading direction.
Different loading magnitudes which range
from 1BW to 5BW are considered to predict
the stress behavior and potential of fracture
patterns. Finite element analyses combinedwith damage mechanics models are performed
to predict damage formations in both THA
model and intact femur [9].

(b)(a) Distribution of young modulus in femoral
shaft, (b) 3D model of Total Hip Arthroplasty

2.2 THA modeling
A commercial model of hip implant wasimported and aligned in the femoral bone toconstruct THA model. The femoral ball was cut
off and inserted with a prosthesis stem topresent artificial ball and socket joint asshown in Fig.1b.
Material of the prosthesis stem is modeled
as titanium alloy while femoral ball asalumina. The respective properties weresummarized in Table 1 [7]. Interconnection
between both implants and bone was assumed
to be perfectly bonded at the interface.
2.3 Loading and Boundary Conditions
Three types of loading and boundary
conditions were considered in the analysis todemonstrate different configurations, namely

(a)
Fig.2

(b)

(c)

Description of loading and boundary condition
for different configurations: (a) stance, (b)torsion and (c) lateral bending

Table 2 Different angle of loading direction

Configuration

αβSC [4]TC [8]BC [8]1600900900平成 23 年度

九州大学大学院総合理工学報告

3.

Results & Discussion

3.1

Damage accumulation

Prediction of tensile and compressive
damages in the models was performed
computationally with use of failure and yield
criterions. The different fracture models are
installed in Mechanical Finder software. The
load bearing strain under compression was set
to 3000 micron which representing boneloading that leads to bone formation. The
tensile strength was set to 80% of the yieldstrength determined from the CT images[9,10]
Increment of failure and yielding elements
by increasing body weight (BW) loading arepresented in Fig. 3 for different configurations.
Failure elements were differentiated into
tensile and compressive criterion. Different
findings of isometric loadings were presentedin Fig.3a till Fig. 3c for stance, torsion andlateral bending configuration, respectively.
Both tensile and compressive failures werepredicted to increase rapidly from 3BW to5BW in SC configuration. However, themagnitude of them was much lower at 1300 ofFig.3

第 33 巻第3号

3configurations. Tensile failures were dominant
in TC and BC cases as compared tocompressive failures. The direction of loading
applied to the hip reflects to the findings.
Numbers of element failures were high in bothcases at smaller BW loading and exceed
extremely at 5BW magnitude. The total offailures was predicted about 15,000 and
30,000 elements for TC and BC configurations.
Hiploadingwith
lateralbending
configurations was predicted to demonstrate
the highest of element failures as compared toother configurations.
3.2 Locations of damage formation
Distribution patterns of different damages,
tensile and compressive failures and yielding,are shown in Fig.4. Different types of loading
configuration conducted in this study
suggested different type and location ofelement failure. Element of failure in tensile
direction was indicated as white, while yellow
and red color presenting compressive yielding
and failure elements, respectively.
Bending effects from prosthesis stem

Increment of element failures by increasing body weight (BW) loading for different configurations:(a) SC, (b) TC and (c) BC.

total elements, as compared to TC and BC

during stance lead to elements failure at thedistal end of femoral shaft as shown in Fig.4a.

4Prediction of Bone Fractures in Total Hip Arthroplasty using a CT-based Nonlinear Finite Element Method

4.

(a)Fig.4(b)(c)

Damage distribution patterns: (a) SC, (b) TC and(c) BC.

Failure of elements was also projected at thedistal stem which may initiate to stem
loosening. Configuration of TC and BC
presented extreme numbers of element failure
in high impact loading. Results of predicted
fracture location at 5BW loading were shownin Fig.4b and Fig.4c for TC and BC,respectively. Both cases estimated bone
fractures at the middle of femoral shaft andaround the distal prosthesis. Besides,
indication of element failures interfaces
between implant and bones suggested forunstable prosthesis and inadequate bone stock.
Extreme and high impact loading (5BW)
applied in the analysis might overestimate thereal magnitude during respective activity. But,
the current findings suggested that both
torsion and lateral bending configurations
produced greater consequences at lower
impact loading.

Conclusions

Computational analysis using the CT-image
based finite element method was performed topredict damage formulation of bone implantedwith prosthesis. The conclusions wereobtained as follows:(1)
Introduction of different types ofloading condition was capable to consider
different types of damage formation in femoral
model with hip prosthesis.
(2)
Introduction of different kinds ofdamage formation, namely, tensile failure,tensile yielding and compressive failure, wasenable us to predict different types of fracture
behavior associated with hip prosthesis.
(3)
Bending effects from prosthesis stem
during stance lead to element failure at thedistal end of femoral shaft. Failure of elements
was also projected at the distal stem which
may initiate to stem loosening.
(4)
For the TC and BC conditions, bone
fractures were predicted at the middle offemoral shaft and around the distal prosthesis.
Besides, indication of element failuresinterfaces between implant and bones
suggested for unstable prosthesis.
References
1) L.C Brunner et al, Am Fam Physician. 67-3 (2003)
537.
2) D.A. Winter, Gait & Posture, 3 (1995) 193.
3) S. Noor et al., Injury (2012), in press.
4) M. Bessho et al., Bone, 45 (2009), 226.
5) T.P. Pinilla et al., Calcif Tissue Int, 58 (1996) 231.
6) J.H. Keyak et al., J Biomech, 31 (1998) 125.
7) J.H. Keyak et al., J Orthop Res, 19 (2001) 539
8) R. Zdero et al., J Bone & Joint Surg (2008) 1068.
9) T.S. Kaneko et al., Med Eng & Phy, 25 (2003) 445.
10) D. Taylor et al., J Theo Bio, 225 (2003) 65.