Extended Poroelasticity: An Analytical Solution and Its Application to p-Wave Propagation in Cervical Tissues

This work presents a semianalytical solution based on Laplace transform to study the behaviour of poroelastic materials in the context of the Extended Nonequilibrium Thermodynamics. In this framework, the fluid phase incorporates a relaxation time and, consequently, a frequency-dependence appears. This rheological behaviour could explain the frequency-dependence experimentally observed in biological tissues, which has traditionally attributed to the solid phase of tissues. In particular, the analytical solution is applied to two cases, heaviside and sinusoidal inputs, of a semi-infinite domain, which is filled with a material such as the human cervix. From the results, it is observed that the frequency-dependence of the fluid phase could be relevant to high relaxation times while for null relaxation times the classical poroelastic theory is recovered. Finally, the present analytical solution could be used to validate future computational codes and experimental settings.