Biomechanical Analysis of Hip Joint Arthroplasties using CT-Image Based Finite Element Method

In the present study, medical CT images were utilized to develop 3D-computational models of hip joints and femoral bones. The finite element analysis was then performed to characterize the biomechanical problems associated with the bone models. The FEA results clearly exhibited dramatic changes of stress and SED profiles due to osteoarthritis and hip arthroplasty. Furthermore, a damage modelling was also introduced into the FEA to characterize the fracture problems of femoral bone with prostheses under a downstairs step and sideways fall conditions. Micro-damage formations are well predicted in the vicinity of the prostheses for bone cases. It is thus confirmed that CT-FEA can be very useful to understand the biomechanical problems in the field of orthopaedics.


Introduction
Computed tomography (CT) scan makes use of X-ray images to produce cross-sectional images of specific areas of human body.These sliced images can be utilized to construct the 3D structure of the area by layering each images in the direction perpendicular to the slicing.For example, 3D structures of skeleton can be developed by selecting bone parts from the CT images.The intensity of each image is directly related to the bone mineral density (BMD) distribution and a bright region usually corresponds to a higher BMD.It has been established that a simple linear relationship can be assumed between the CT values (Hounsfield unit) and BMD; therefore, it is possible to easily estimate the BMD distribution on each image.Furthermore, it is also possible to construct a 3D computational model of the bone with BMD distribution for finite element analysis (FEA) [1,2].Such CT-image based EFA (CT-FEA) has widely been utilized to characterize biomechanical problems associated with orthopaedic [2][3][4][5][6] and dental sciences [7,8], in which diseases related to bones are mainly treated.Bones mainly consist of organic and inorganic mineral components such as collagen and carbonate apatite.It has been believed that the apatite determines the stiffness and strength of the bone structures, and therefore, the bone mineral density (BMD) can be a controlling parameter in the biomechanical analysis of skeletal structures.Interactive problems between bone structures and metal implants have also been investigated by CT-FEA since such problems are strongly related to mismatching of elastic modulus between the material and bone tissue and/or stiffness between the implant and bone structure.
In this paper, two different biomechanical problems associated with hip arthroplasty are presented.One is biomechanical analysis of stress shielding, which is one of the most important mechanical problems associated with orthopaedic metal implants (Figure 1a).In this problem, bone tissue surrounding the metal implant such as a stem of hip prosthesis is gradually absorbed due to the mismatching of stiffness between the bone and stem.The reason is thought to be the reduction of mechanical stimulus to the bone due to the small deformation of stem with high stiffness.Another problem is fracture of bone associated with hip prostheses as shown in Figure 1b.CT-FEA was applied to analyse those two kinds of problems.

Three dimensional modelling of hip joint
An example of 3D hip joint model constructed from CT images of 52 years old patient is shown in Figure 2. The CT images were provided by Kyushu University Hospital.This female patient has been suffered by osteoarthritis of right hip joint.The computational modelling was conducted by using Mechanical Finder software (RCCM, Inc.).
Distribution of bone mineral densities (BMD) were estimated from CT values of each of the images by assuming a linear relation between the CT values and BMD.Then, the elastic modulus of a finite element was evaluated from the average value of BMD of the element on the basis of Keyak's model [1].The elastic modulus distributions of the right and left hip joints are shown in Figure 3.It is worth noting that inhomogeneous realistic distributions of modulus were clearly reproduced in the 3D finite element models.
A virtual model of total hip arthroplasty (THA) can be developed by using the current hip joint model and CAD images of hip prosthesis.Osteotomy was applied to the hip joint model so that the hip prosthesis can properly be inserted and placed into the femur and pelvis.The schematic procedure of the 3D THA modelling is shown in

Journal of Surgery and Research 37
In order to analyse bone fracture associated with hip arthroplasties, a whole femoral model was also developed from CT images of a 54 years old male.Resurface hip arthroplasty (RHA) and THA were then treated to the femoral model as shown in Figure 5.As the boundary conditions, two different situations such as downstairs step and sideway fall were assumed and simplified conditions were applied to the model as shown in Figure 6.A damage model was also introduced into the FEA code in order to predict bone fracture by damage accumulation.It was assumed that each of the finite elements could be damaged under both tensile and compressive situations.Under tensile condition, the bone tissue was assumed to be a linear elastic and brittle so that the maximum principal stress controlled the tensile fracture.The tensile fracture took place when the maximum principal stress reached its critical value.On the other hand, the bone tissue was assumed to be an elastic-plastic body under compression, and therefore, the equivalent stress controlled the yielding behaviour, while the compressive fracture occurred when the minimum principal strain reached its critical value.The elastic modulus of the tensile and compressive fractured elements was set to be the minimum value of the elastic moduli in the model.

Figure 4a .
Figure 4a.A simple boundary condition corresponding to a stance situation was introduced into the THA model as shown in Figure 4b.Distributed load of 1800 N was applied to the top of the pelvis.

Figure 2 :
Figure 2: 3D hip joint model constructed from CT images.

Figure 5 :
Figure 5: RHA and THA model for bone fracture analysis.

Figure 6 :
Figure 6: Boundary conditions for bone fracture analysis.

Figure 7 :
Figure 7: SED distribution on the cross-sections of femoral models.