Bone Ingrowth. in a shoulder prosthesis E.M.van Aken, Applied Mathematics. Outline. Introduction to the problem Models: Model due to Bailon-Plaza: Fracture healing Model due to Prendergast: Prosthesis Numerical method: Finite Element Method Results
in a shoulder prosthesis
E.M.van Aken, Applied Mathematics
After 2.4 days: After 4 days:
After 8 days: After 20 days:
Proliferation and differentiation rates depend on stimulus S, which follows from the mechanical part of the model.
Bone density after 80 days, stimulus=1
Incompressible: Problem if
Finite Element Method leads to inconsistent or singular matrix
1. Quadratic elements to approximate displacements
2. Stabilization term
Arm abduction 30 ° Arm abduction 90 °
30 ° arm abduction, during 200 days
Simulation of 200 days: first 100 days: every 3rd day arm abd. 90°,
rest of the time 30 °.
100 days200 days