A mathematical model based on the Finite Element Method is developed to simulate the non-linear flow of acrylic bone cement through cancellous bone. The cancellous bone bed is modelled as a bed of parallel capillaries filled with equal spaced toroidal trabeculae. By manipulating the relative size of the torus and the capillary, the flow within bone of varying porosity is simulated. An apparent permeability based on the volume weighted average viscosity and Darcy's law is developed to describe the flow of the acrylic through the cancellous bone bed. The model predicts a cancellous bone permeability of 5.6 × 10-9-8.3 × 10-9 m2 for linear flow. The non-linear behavior of the acrylic cement results in an increase of apparent permeability when compared to the permeability computed for linear flow. Estimates of penetration are achieved by running the model in a quasi-steady state fashion with pressure applied over a fixed time increment. Close agreement is shown between model predictions of penetration depth and experimental results available in the literature.
ASJC Scopus subject areas
- Orthopedics and Sports Medicine
- Biomedical Engineering