Liver Tissue Engineering

Fluids Alter Elasticity Measurements: Porous Wave Propagation Accounts for Shear Wave Dispersion in Elastography

“…Liver diseases do not only alter the elasticity of the cellular matrix of the liver but are known to affect the porous parameters, notably porosity and permeability, as well. These insights led different groups to numerically model the liver as a poro-elastic or poro-visco-elastic material in the last decade [1,9,[13][14][15][16][17][18][19]. However, albeit early realization of interstitial fluid flow as an dissipative mechanism for acoustic waves [20], few attempts to link the shear wave dispersion in the liver to its porous and fluid properties have been made to our knowledge.…”

“…At very high frequencies, when ω → ∞ Hz, which is conceptually similar to the case when the porous material is saturated by a superfluid, the shear wave velocity reaches its maximum value. Because of the lack of viscosity, the fluid is not dragged along by viscous coupling and rests on average 1 . The fluid and solid displacements are thus out-of-phase and the shear wave experiences a different effective density: the solid frame density plus an apparent density due to the remaining added mass effect of the fluid.…”

“…The added mass effect stems from the fact that the fluid is considered to be at rest on average, while there is relative movement between the accelerating solid and the fluid phase (see [38] I, 11). Ignoring the inertial coupling described in 1 , the expression for the effective density is then: ρ eff (1 − ϕ)ρ s + ρ a . The higher the porosity of the medium, the lower the solid frame density and consequently due to v s μ ρ eff , the higher the shear wave speed in the high-frequency limit.…”

“…Linear elastic or viscoelastic theory is commonly assumed for the elasticity inversion. However, the order of magnitude of the shear modulus retrieved from elastography and other measurement methods, such as dynamic mechanical analysis (DMA), differs [1]. Furthermore, ex vivo and in vivo elastography measurements vary, making a standardization difficult [2,3].…”