Flow Induced Deformation of Poroelastic Tissues and Gels: A New Perspective on Equilibrium Pressure Flow Thickness Relations

Abstract

Hydrostatic pressuredriven flows through soft tissues and gels cause deformations of the solid network to occur, due to drag from the flowing fluid. This phenomenon occurs in many contexts including physiological flows and infusions through soft tissues, in mechanically stimulated engineered tissues, and in direct permeation measurements of hydraulic permeability. Existing theoretical descriptions are satisfactory in particular cases, but none provide a description which is easy to generalize for the design and interpretation of permeation experiments involving a range of different boundary conditions and gel properties. Here a theoretical description of flowinduced permeation is developed using a relatively simple approximate constitutive law for straindependent permeability and an assumed constant elastic modulus, using dimensionless parameters which emerge naturally. Analytical solutions are obtained for relationships between fundamental variables, such as flow rate and pressure drop, which were not previously available. Guidelines are provided for assuring that direct measurements of hydraulic permeability are performed accurately, and suggestions emerge for alternative measurement protocols. Insights obtained may be applied to interpretation of flowinduced deformation and related phenomena in many contexts.