On the Comparative Suitability of Strain Relaxation and Stress Relaxation Compression for Ultrasound Poroelastic Tissue Characterization

Poroelastic tissue strain imaging measures the time- and spatially-varying deformation of a soft-tissue matrix during compression, as tissue fluid escapes compartmental boundaries. With ultrasound, it has been carried out by observing the evolution of images of the echo strain over time, showing that during a stress relaxation experiment a front of negative dilatation propagates slowly from a sample’s boundaries towards its centre. The fitting of equations that predict this behaviour to experimental data has previously allowed the quantitative imaging of the product of a tissue phantom’s aggregate modulus and permeability, HAk, and its Poisson’s ratio, ν. An ability to image such novel tissue characteristics may benefit biomedical research and have various clinical applications, including lymphoedema assessment, cancer diagnosis, prediction of anticancer drug effectiveness and monitoring of response to treatments. This method is problematic, however, for application in vivo because the calculation of volumetric strain requires lateral and elevational strains, in addition to axial strain (along the direction of the sound beam), which are difficult to measure accurately with conventional ultrasound strain imaging. This paper investigates for the first time whether ultrasound observation during a strain relaxation experiment (constant applied uniaxial stress) could be used to observe the same mechanical behaviour and provide the same information about the properties of a poroelastic sample as the stress relaxation experiment. Analytical theory was used to demonstrate that the propagation of dilatation seen in stress relaxation should also be observable during strain relaxation, and that observation using axial strain alone should be sufficient, which is relatively easy to measure in vivo. Finite element modelling (FEM) was employed to simulate all strain components within a homogeneous poroelastic material, first during strain and then during stress relaxation. Fitting of the analytical model to the FEM results allowed inversion of time-varying volumetric strain, to recover images of HAk and ν. The strain relaxation configuration offers the potential to derive the same important quantitative poroelastic properties of tissue as stress relaxation, while avoiding the difficulties and errors associated with strain estimation along axes perpendicular to the imaging axis, thus offering opportunities for easier clinical translation.