An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Due to its high relevance for designing ball joints in mechanical engineering and (artificial) hip joints in biomechanics, the almost conformal elastic contact between a sphere and a spherical cup represents an important contact problem of current research. As no closed-form analytical solution to the problem has been found to date, full computational methods such as the finite element method are needed for analysis. However, they often require incredibly long, unacceptable calculation times, making parameter studies hardly practicable. For this reason, approximate analytical and semi-analytical models are applied, capable of predicting quantities of interest with sufficient accuracy. In the present work, a very simple model based on a radially directed Winkler foundation is presented, which provides (approximate) closed-form analytical solutions for both the pressure distribution and the dependencies between macroscopic contact quantities such as normal force and indentation depth. To ensure an optimal mapping of a specific contact problem, only the foundation modulus must be defined in a suitable way. As an example, the proposed model has been successfully adapted to adequately simulate the frictionless normal contact for hard-on-soft hip implants. For this purpose, the foundation modulus was approximated with the aid of a finite element analysis instead of adopting it from already well-established models, as the latter produce clearly erroneous results for large liner thicknesses and large Poisson’s ratios. By a comparison with extensive parameter studies of finite element simulations, it is demonstrated that the proposed model provides acceptable results for all commonly used hard-on-soft hip implants. On this basis, the influence of geometrical changes of the femoral head and the acetabular cup on the maximum pressure as well as the half-contact angle is discussed, and consequences on the wear behavior are deduced.

IRAK-4 in macrophages contributes to inflammatory osteolysis of wear particles around loosened hip implants

TLRs recognizing PAMPS play a role in local immunity and participate in implant-associated loosening. TLR-mediated signaling is primarily regulated by IL-1 receptor associated kinase-M (IRAK-M) negatively and IRAK-4 positively. Our previous studies have proved that wear particles promote endotoxin tolerance in macrophages by inducing IRAK-M. However, whether IRAK-4 is involved in inflammatory osteolysis of wear particles basically, and the specific mechanism of IRAK-4 around loosened hip implants, is still unclear. IRAK-4 was studied in the interface membranes from patients in vivo and in particle-stimulated macrophages to clarify its role. Also, IL-1β and TNF-α levels were measured after particle and LPS stimulation in macrophages with or without IRAK-4 silenced by siRNA. Our results showed that the interface membranes around aseptic and septic loosened prosthesis expressed more IRAK-4 compared with membranes from osteoarthritic patients. IRAK-4 in macrophages increased upon particle and LPS stimulation. In the former, IL-1β and TNF-α levels were lower compared with those of LPS stimulation, and IRAK-4 siRNA could suppress production of pro-inflammatory cytokines. These findings suggest that besides IRAK-M, IRAK-4 also plays an important role in the local inflammatory reaction and contributes to prosthesis loosening.