Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico

Abstract

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

“…The shear module achieved by reconstructing the biological soft tissue, based on common MRE, cannot be descriptive of the distribution of true solid matrix parameters (Perriñez et al, 2008 ). Furthermore, tumors tend to have shear moduli between one and two orders of magnitude higher than surrounding tissue, which can be interpreted as poroelastic material rather than viscoelastic material (Sowinski et al, 2020 ). Magnetic resonance poroelastography (MRPE) allows the analysis of tissue-poroelastic behavior by distinguishing the mechanical response of the solid matrix from the free extracellular fluid (Perriñez et al, 2008 ).…”

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model

“…As initial range of values for the liquid phase dynamic viscosity µ l , we keep different estimation provided in [47] for cerebral fluid, between 0.7 • 10 −3 Pa • s and 1 • 10 −3 Pa • s. For the rheology of the glial phase, as we do not have experimental data, we choose a value close to literature used for generic cells (see [34] and [37]) µ g ≈ 30 Pa • s.…”

“…The important difficulty to design experiment on living tissue and the preferential use of single phase solid mechanics rather than poromechanics are probably partly responsible for this problem. In 2021, Sowinski et al [47] reported ranges of values for hydraulic conductivity K, using in silico magnetic resonance elastography. They reported hydraulic conductivity values from 2 • 10 −11 ms −1 to 2 • 10 −10 ms −1 .…”

“…Applying the ratio on hydraulic conductivity, a dynamic viscosity µ with the order of 1 • 10 −3 Pa • s will lead to an intrinsic permeability k s int between 2 • 10 −14 m 2 and 2 • 10 −13 m 2 , which is two orders higher than [48]. In [47], Sowinski et al hypothesise that in vitro experiments tend to lead to smaller values, due to pore collapse in sampled tissue. In [48], Jamal et al claim that these microstructural changes become significant after 6h post-mortem, hence they perform their experiments within these 6h.…”

Non-operable glioblastoma: proposition of patient-specific forecasting by image-informed poromechanical model

“…All the details are provided in [41]. This article allows for reducing the range the mechanical parameters of cortex tissue provided in the literature [61, 62, 63], and more specifically in the poromechanical literature [64, 56]. Although individual variation could be considered, these parameters are related the general mechanical behavior of healthy tissue.…”