Shape optimization of an Un-cemented Total Hip Replacement Prosthesis Considering Volumetric Wear

Abstract

In the present paper, optimization of a three dimensional parametric finite element model of an uncemented total hip replacement (THR) prosthesis is conducted considering volumetric wear as the objective function. Total hip replacement surgery is used to restore the mobility of hips affected by diseases such as arthritis, avascular necrosis and osteoporosis, and typically involves the surgical removal of the femoral head, reaming of the femoral canal and pelvis, and broaching of the femoral canal into the shape of the prosthesis. A semi-spherical acetabular component consisting of an ultra-high molecular weight polyethylene (UHMWPE) liner and titanium (Ti6Al4V) shell is inserted in the reamed pelvis, while a titanium femoral stem is inserted into the canal and a cobalt-chrome (CoCr) femoral head is press-fit onto the stem. One of the major causes of loosening and failure of un-cemented hip stems is periprosthetic osteolysis. Wear debris produced by the articulation of the femoral head and acetabulum can cause an inflammatory reaction in the bone tissue surrounding the implant, eventually leading to bone density degradation and loss of fixation. Shape optimization of a modular un-cemented THR prosthesis is considered in this study using volumetric wearing of the UHMWPE liner as an objective function. The volumetric wear objective function is formulated using a modified form of Archard’s wear law which states that volumetric wear is related to the normal contact pressure, sliding distance, and contact area on the UHMWPE liner articulating surface. A three dimensional parametric finite element model of the un-cemented THR components and femur are constructed in Hypermesh. Non-linear contact analysis is performed between the UHMWPE liner and CoCr femoral head, and the titanium femoral stem and bone using ANSYS. Eleven load steps are applied to the three-dimensional model with load and kinematic data for a typical gait cycle being taken from the ISO 14242-1 wear testing standard. Optimization is conducted using sequential quadratic programming in MATLAB through integration with Hypermesh and ANSYS in batch mode. Four design variables are chosen using a sensitivity analysis: femoral head radius, head-liner clearance, medial stem shape, and stem length. Significant reductions in the volumetric wear objective function are achieved in optimization showing that the size and shape of the THR components can be used to control volumetric wearing at the liner surface. The largest decrease in volumetric wear achieved is 47% with a minimum volumetric wear of 31.7 mm per million cycles, or one year of gait. A comparison is made between the initial and optimum designs in terms of wear and creep penetration distributions after one million cycles of gait using a MATLAB script.