Discrete element analysis in musculoskeletal biomechanics

This paper is written to honor Professor Y. C. Fung, the applied mechanician who has made seminal contributions in biomechanics. His work has generated great spin-off utility in the field of musculoskeletal biomechanics. Following the concept of the Rigid Body-Spring Model theory by T. Kawai (1978) for non-linear analysis of beam, plate, and shell structures and the soil-gravel mixture foundation, we have derived a generalized Discrete Element Analysis (DEA) method to determine human articular joint contact pressure, constraining ligament tension and bone-implant interface stresses. The basic formulation of DEA to solve linear problems is reviewed. The derivation of non-linear springs for the cartilage in normal diarthrodial joint contact problem was briefly summarized. Numerical implementation of the DEA method for both linear and non-linear springs is presented. This method was able to generate comparable results to the classic contact stress problem (the Hertzian solution) and the use of Finite Element Modeling (FEM) technique on selected models. Selected applications in human knee and hip joints are demonstrated. In addition, the femoral joint prosthesis stem/bone interface stresses in a non-cemented fixation were analyzed using a 2D plane-strain approach. The DEA method has the advantages of ease in creating the model and reducing computational time for joints of irregular geometry. However, for the analysis of joint tissue stresses, the FEA technique remains the method of choice.