A biphasic modeling framework for arterial compressibility under steady axisymmetric deformation

Arterial walls contain large amounts of water and have conventionally been modeled as incompressible. However, recent experimental studies have reported non-negligible arterial compressibility, with volumetric changes on the order of 10% or larger depending on loading conditions. To clarify the mechanical origin and its implications, this study develops a biphasic modeling framework for arterial mechanics, in which apparent compressibility arises from interstitial fluid transfer within the arterial wall. The arterial wall is modeled as a saturated biphasic material consisting of a solid skeleton and interstitial fluid, in which the solid skeleton is modeled as an anisotropic, hyperelastic material with macroscopic volumetric deformability, and the fluid motion is governed by Darcy's law. Assuming steady, axisymmetric plane-strain deformation, the resulting nonlinear mechanical equilibrium is reduced to a one-dimensional radial boundary-value problem and solved numerically using a finite element method. Systematic parametric analyses demonstrate that radial and circumferential deformations, as well as the resulting volumetric changes, are consistent with experimentally observed mean values, with deviations within 2% under the same loading conditions. Such volumetric expansion, driven by the hydrostatic pressure of the interstitial fluid, induces tensile stress components in the radial direction within the solid skeleton, revealing a mechanical consequence of fluid-solid interactions that is not directly accessible from apparent deformation measures alone. These findings suggest that biphasic modeling provides a mechanically interpretable framework for examining arterial wall responses in regimes where fluid-solid interactions are relevant.