Wave Simulation in Biologic Media Based on the Kelvin-Voigt Fractional-Derivative Stress-Strain Relation

The acoustic behavior of biologic media can be described more realistically using a stress-strain relation based on fractional time derivatives of the strain, since the fractional exponent is an additional fitting parameter. We consider a generalization of the Kelvin-Voigt rheology to the case of rational orders of differentiation, the so-called Kelvin-Voigt fractional-derivative (KVFD) constitutive equation, and introduce a novel modeling method to solve the wave equation by means of the Grünwald-Letnikov approximation and the staggered Fourier pseudospectral method to compute the spatial derivatives. The algorithm can handle complex geometries and general material-property variability. We verify the results by comparison with the analytical solution obtained for wave propagation in homogeneous media. Moreover, we illustrate the use of the algorithm by simulation of wave propagation in normal and cancerous breast tissue.