Vascularized biological tissue has been shown to increase in stiffness with increased perfusion pressure. The interaction between blood in the vasculature and other tissue components can be modeled with a poroelastic, biphasic approach. The ability of this model to reproduce the pressure-driven stiffening behavior exhibited by some tissues depends on the choice of the mechanical constitutive relation, defined by the Helmholtz free energy density of the skeleton. We analyzed the behavior of a number of isotropic poroelastic constitutive relations by applying a swelling pressure, followed by homogeneous uniaxial or simple-shear deformation. Our results demonstrate that a strain-stiffening constitutive relation is required for a material to show pressure-driven stiffening, and that the strain-stiffening terms must be volume-dependent.
Constitutive Relations for Pressure-Driven Stiffening in Poroelastic Tissues
Manuscript received November 18, 2013; final manuscript received April 2, 2014; accepted manuscript posted May 14, 2014; published online June 13, 2014. Assoc. Editor: Guy M. Genin.
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Reeve, A. M., Nash, M. P., Taberner, A. J., and Nielsen, P. M. F. (June 13, 2014). "Constitutive Relations for Pressure-Driven Stiffening in Poroelastic Tissues." ASME. J Biomech Eng. August 2014; 136(8): 081011. https://doi.org/10.1115/1.4027666
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