Poroelastic longitudinal wave equation for soft living tissues
  Making use of the poroelastic theory for hydrated polymeric matrices, the ultrasound (US) propagation in a gel medium filled by spherical cells is studied . The model describes the connection between the poroelastic structure of living means and the propagation behavior of the acoustic waves. The equation of fast compressional wave, its phase velocity and its attenuation as a function of the elasticity, porosity and concentration of the cells into the gel external matrix are investigated. The outcomes of the theory agree with the measurements done on PVA gel scaffolds inseminated by porcine liver cells at various concentrations. The model is promising in the quantitative non-invasive estimation of parameters that could asses the change in the tissue structure, composition and architecture. 
Piero Chiarelli, Bruna Vinci, Antonio Lanat\'a, Clara Lagomarsini,   Simone Chiarelli
cond-mat.soft physics.bio-ph