Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI

SUMMARYWe propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient‐specific collagen fiber network. The finite strain model focuses on the load‐bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain‐dependent pores of the collagen–proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra‐high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through‐thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367–378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569–577, 2003). For the tissue sample investigated, both through‐thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution. Copyright © 2012 John Wiley & Sons, Ltd. We propose a new 3D biphasic, finite strain constitutive model and show representative finite element results for an indentation experiment with an impermeable, plane‐ended cylinder of diameter 1 mm compressing a cartilage sample to 1% global strain in 150 s‐column 1: normal Green‐Lagrange strain in the axial (indentation) direction; column 2: interstitial fluid pressure; column 3: von Mises stress; row 1: constitutive model including patient‐specific collagen fiber network and inhomogeneous material properties; row 2: model without collagen fiber network and homogeneous material properties. For the tissue sample investigated, through‐thickness inhomogeneity of both th