Non-linear pulsatile blood flow through a permeable capillary controlled by distensibility effects

Abstract

Pulsatile blood flow in a distensible and permeable capillary is investigated through a nonlinear model that describes the coupled effects of wall elastic deformation and filtration through the wall. The governing equation is derived from mass and momentum balances using the Reynolds transport theorem and lubrication theory under low Womersley number conditions (Wo ≪ 1). The resulting nonlinear differential equation for pressure is rewritten in dimensionless form in terms of key parameters, including the permeability or filtration coefficient β , an osmotic parameter Γ, and an elastic parameter γ ₀ , which controls the transition between linear and nonlinear regimes. Analytical solutions are obtained using a regular perturbation technique for large values of γ ₀ , while numerical solutions are computed using a finite difference scheme for finite values of γ ₀ . The results show that the simultaneous increase in permeability and osmotic effects leads to a progressive rise in pressure along the capillary, which may be associated with pathological conditions. Furthermore, the volumetric flow rate exhibits nonlinear oscillations induced by the pulsatile boundary condition, with pronounced spatial variations associated with wall distensibility. These results provide insight into the role of pulsatile flow in the interaction between permeability and wall elasticity in microvascular systems, and establish a theoretical framework for analyzing capillary dynamics under physiologically relevant conditions.