Thermodynamic theory of nonlinear ultrasound in soft biological tissue

Abstract

A new theoretical model of ultrasound propagation in soft biological media is presented based on an extended thermodynamics formalism. The long-standing experimental conjecture claiming that a continuous distribution of internal degrees of freedom can be used to model ultrasound in biological media is given theoretical justification. A strategy to derive a well-defined set of equations coupling the balance equations of mass, momentum, energy and entropy with relaxation kinetics of a medium characterized by a continuous distribution of internal states is presented. We demonstrate that new phenomenological coefficients of the proposed governing equations can be extracted directly from experimental data. Our theory successfully explains the anomalous attenuation law found in experiments with biological media that is inconsistent with the conventional models using a finite number of internal degrees of freedom. The results presented offer new possibilities for medical applications of high-intensity ultrasound and ultrasound emission methods to study matter with complex internal structure. These techniques include using pressure relaxation methods for accurate investigation of fast protein folding and a variety of other applications for media where irreversible thermodynamic simulations are essential.