Shape optimal design of the stem of a cemented hip prosthesis to minimize stress concentration in the cement layer

An optimal shape of the metal stem of a cemented total hip prosthesis minimizing stress concentration in the cement layer was searched for. A gradient projection method of numerical optimization and a finite element method of stress analysis were employed. A two-dimensional model of the femoral part of a total hip prosthesis was derived equivalent to a simplified three-dimensional axisymmetric model. The result of the stress analysis of the two-dimensional model compared favorably with that of the three-dimensional axisymmetric model. Using this two-dimensional model, an optimal shape of the stem, minimizing stress concentration in the cement layer, was obtained by a gradient projection method and the shape was checked again by the three-dimensional finite element analysis. The resulting optimal shape of the stem profile was in good agreement with conventional ones, except in the proximal region where a significant amount of stress reduction in the cement layer was achieved by tapering the stem to the limit that the stem still could withstand the increased stem stress.