The Mechanics of Vascularised Tissue

Abstract

Biological tissues consist of a mixture of fluid and solid components, and the mechanical behaviour of a tissue can be influenced by the fluid within that tissue. This thesis investigated how fluid pressure affects tissue mechanics, and how this influence can be incorporated in continuum-level models of whole organs. Firstly, a physical phantom model of vascularised tissue was constructed using silicone gel. Mechanical experiments were performed on this phantom to determine how it responded to changes in fluid pressure. Replicating the nonlinear, strain-stiffening behaviour of some tissues was attempted by incorporating a strainstiffening wool-yarn into the gel. Following this, a representative volume element model of vascularised tissue was developed that explicitly modelled vessels within tissue. This model predicted that anisotropy in the constitutive behaviour of a tissue’s solid components causes anisotropic swelling and stiffening, and that anisotropic vascular structure also contributes to anisotropic swelling. It was demonstrated that poroelasticity can be used to model increases in stiffness with fluid pressure, provided that the poroelastic material’s constitutive relation is strain-stiffening, and the strain-stiffening terms are volume dependent. Approaches for incorporating anisotropic vascular structure in poroelastic models were then investigated and compared. A poroelastic model with anisotropic constitutive behaviour was used to model the effect of perfusion pressure on the passive mechanics of the left ventricle of the heart. This model could reproduce the swelling deformation of myocardium, but further development of constitutive relations is required to accurately reproduce anisotropy in stiffness changes. Finally, the effect of perfusion pressure on the mechanics of the rat tibialis anterior muscle was investigated. No significant change in muscle stiffness was observed between perfusion pressures of 5 kPa and 20 kPa, but a small swelling deformation was measured.