The Spherical Design Algorithm in the Numerical Simulation of Fiber-Reinforced Biological Tissues

M. Carfagna [1], A. Grillo [1],
[1] Dipartimento di Scienze Matematiche, Politecnico di Torino, Italy
Published in 2016

The numerical results of the unconfined compression test on a sample of Articular Cartilage (AC) are discussed. AC is modelled as a load-bearing, deformable, fiber-reinforced material filled with an interstitial fluid and comprising statistically oriented collagen fibers, chondrocytes, and a matrix of proteoglycans. A strain energy is assigned to characterize the mechanical behavior of the system. As the fibers in the tissue are statistically arranged, a probability density distribution is needed as a weight for each fiber direction in the strain energy and in the permeability. Consequently, a suitable averaging procedure should be used. We implemented the Spherical Design Algorithm (SDA) into COMSOL Multiphysics® software. This could represent a useful tool in describing more accurately heterogeneous deformable tissues having complex internal structure.