A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments

Abstract

The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young's modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500 N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.

p-FEMs in biomechanics: Bones and arteries

“…Determination of E(x, y, z) at each integration point (Gauss points), in the FE model is performed as follows. First a moving average algorithm is applied to average the HU data in each voxel based on a pre-defined cubic volume of 3 × 3 × 3 mm 3 surrounding it (cubic volumes of 27,125,343 mm 3 showed similar results in [28]). HU averaged data is subsequently converted to an equivalent mineral density ρ EQM by (2) which is determined by the calibration phantom -see for details [29,28].…”

“…Constant Poisson ratio ν = 0.3 was assigned to the entire bone. According to a sensitivity analysis in [28,21] the influence of ν on the results is very small. Determination of E(x, y, z) at each integration point (Gauss points), in the FE model is performed as follows.…”

Biomechanical properties of hip implant with ceramics coating

“…The step of tomographic slices is 1 mm. A similar approach was used in [3,4] and [14], during development of the three-dimensional solid model of the femur bone. For modeling the hip replacement femoral head and neck were removed from the model.…”

Experimental validation of finite element predicted bone strain in the human metatarsal

“…The elastic moduli for early isotropic models have been homogeneous (171)(172)(173), but more recent studies have used inhomogeneous materials (8,164,165,170,174-178) as they have been found to be more accurate than the models using homogeneous material properties (9,179,180). For inhomogeneous material properties, the elastic modulus is typically estimated using empirical equations that relate the bone density to modulus.…”

“…As CT attenuations only provide a scalar value at each point, many studies assume isotropic elasticity (164)(165)(166)(167)(168)(169), although anisotropic material properties have also been implemented using information within the voxel (170). The elastic moduli for early isotropic models have been homogeneous (171)(172)(173), but more recent studies have used inhomogeneous materials (8,164,165,170,174-178) as they have been found to be more accurate than the models using homogeneous material properties (9,179,180).…”