Design optimization of a prosthesis stem reinforcing shell in total hip arthroplasty

The use of a perforated, titanium funicular shell to support the proximal femoral cortex in total hip arthroplasty was evaluated with the aid of both analytical and numerical techniques. The principal interactions between the femoral cortex, the metal shell, the implant stem and the acrylic bone cement were modeled using beam on elastic foundations theory and two-dimensional elasticity theory. Subsequent formulation of this model as a nonlinear design optimization problem enabled the determination of the dimensions of the implant and reinforcing shell which minimized an objective function based on a simplified material failure criterion. Two cases were examined, each with two cervico-diaphyseal angles: case A: with a rigid contact between a proximal prosthesis collar and the calcar femorale and case B: no collar contact (a collarless prosthesis or post-operative loosening). Case A achieved an optimal solution at a stem diameter 11-23 percent of the cortex inner diameter, a stem length to diameter ratio of 12-40, shell diameter 22-53 percent and thickness 0.2-7.2 percent of the cortex inner diameter and thickness, respectively. Case B achieved an optimal solution at a stem diameter 67-92 percent of the cortex inner diameter, length to diameter ratio of 4-6, and no shell. In case A the collar support makes the type of internal fixation unimportant, while in the more realistic case B, the shell is not recommended.