Poroelastography: Imaging the poroelastic properties of tissues

In the field of elastography, biological tissues are conveniently assumed to be purely elastic solids. However, several tissues, including brain, cartilage and edematous soft tissues, have long been known to be poroelastic. The objective of this study is to show the feasibility of imaging the poroelastic properties of tissue-like materials. A poroelastic material is a material saturated with fluid that flows relative to a deforming solid matrix. In this paper, we describe a method for estimating the poroelastic attributes of tissues. It has been analytically shown that during stress relaxation of a poroelastic material (i.e., sustained application of a constant applied strain over time), the lateral-to-axial strain ratio decreases exponentially with time toward the Poisson's ratio of the solid matrix. The time constant of this variation depends on the elastic modulus of the solid matrix, its permeability and its dimension along the direction of fluid flow. Recently, we described an elastographic method that can be used to map axial and lateral tissue strains. In this study, we use the same method in a stress relaxation case to measure the time-dependent lateral-to-axial strain ratio in poroelastic materials. The resulting time-sequenced images (poroelastograms) depict the spatial distribution of the fluid within the solid at each time instant, and help to differentiate poroelastic materials of distinct Poisson's ratios and permeabilities of the solid matrix. Results are shown from finite-element simulations.