Smoothed Particle Hydrodynamics Applied to Cartilage Deformation

Modelling of the cartilage within the acetabulum is necessary for determination of stresses in preoperative simulation of femoral acetabular impingement (FAI), a condition that is considered a primary cause of osteoarthritis. Presented is a previously proven method for elastic solid deformation using smoothed particle hydrodynamics (SPH). Smoothed particle hydrodynamics is a mesh-free method that has advantages in computational speed and accuracy over other graphical methods and as such is attractive for medical simulations that require high degrees of precision and real-time operability. A complete formulation of the method of polar decomposition as devised for smoothed particle hydrodynamics is outlined with the inclusion of a corotational formulation for accurate rotation handling. Modifications to the existing method include boundary and collision handling using an adapted virtual particle method, as well as an algorithm for parallel implementation on the GPU using NVIDIA’s CUDA framework. The method is verified through testing with a range of material parameters within the provided elastic solid framework. Employing CUDA for calculations is found to dramatically increase the computational speed of the simulation. The results of an indenter analysis of cartilage modelled as a purely elastic solid are presented and evaluated, with the conclusion that with further refinement the presented method is promising for use in cartilage simulations.