Mathematical Standard-Parameters Dual Optimization for Metal Hip Arthroplasty Wear Modelling with Medical Physics Applications

Abstract

Total hip metal arthroplasty (THA) constitutes an important proportion of the standard clinical hip implant usage in Medical Physics and Biomedical Engineering. A computational nonlinear optimization is performed with two commonly metal materials in Metal-on-Metal (MoM) THA. Namely, Cast Co-Cr Alloy and Titanium. The principal result is the numerical determination of the K adimensional-constant parameter of the model. Results from a new more powerful algorithm than previous contributions, show significant improvements. Numerical standard figures for dual optimization give acceptable model-parameter values with low residuals. These results are demonstrated with 2D and 3D Graphical/Interior Optimization also. According to the findings/calculations, the standard optimized metal-model parameters are mathematically proven and verified. Mathematical consequences are obtained for model improvements and in vitro simulation methodology. The wear magnitude for in vitro determinations with these model parameter data constitute the innovation of the method. In consequence, the erosion prediction for laboratory experimental testing in THA adds valuable information to the literature. Applications lead to medical physics improvements for material/metal-THA designs.

Review of Wear Model Optimization for Ceramic and Metal Total Hip Arthroplasty with Medical Physics Applications

“…Total hip arthroplasty (THA) is defined as the surgical implantation of a medical device whose main parts are cup (for natural acetabular substitution), head (for natural femur head substitution), and leg (the mechanical support inserted along the femur metaphysis) [1][2][3][4]. THA has a number of important properties, usually interdependent, directly and inversely.…”

“…Head-cup material combinations could be even (CoC, MoM) or uneven (PoM, CoM, PoC). When a polyethylene/polymer cup forms at least one component of the THA, the bearing is considered soft, [1][2][3][4], otherwise the bearing is hard. The wear of the THA implant occurs in-between the head and cup, specifically as an erosion and abrasion bio tribological phenomena.…”

“…As an example, in previous spinal surgery modelling contributions, optimization for screw-insertion was mathematically presented [25]. THA biotribological wearinterface is based on complex biomechanical forces distribution and was presented in previous publications [1][2][3][4]. After the surgical setting of the THA, the biodynamics and biomechanics cannot result as equal to natural hip biomechanics.…”

“…Therefore, the THA is subject of wear, mainly erosion and abrasion of the implant . Statistically, [1][2][3][4], the pathogenesis of the hip fracture and/or hip articulation malfunction is caused mainly by the high incidence/prevalence of femur neck fracture due to osteoporosis. Equation 1 and (Figure 1) prove the clinical path biomechanics.…”

“…According to statistics in Europe, Germany and Switzerland are the countries where a higher number of THA are surgically implanted/fixed. Given a femur neck with osteoporosis, [1], the typical fracture happens because the neck unites the head and trochanter, which is the weakest and thinnest bone zone. In addition, the hip load over the femur head causes a mechanical torque, whose arm is along the neck and fixed on trochanter as follows,…”