A new theory of fluid-solid coupling in a porous medium for application to the ultrasonic evaluation of tissue remodeling using bioelastomers
Bioelastomers have demonstrated tremendous value and potential in the field of tissue repair due to increasing health demands. Improved non-invasive methods are required for monitoring tissue development assisted by bioelastomers. In this paper, we present a novel theory of fluid-solid coupling in a porous medium for application to the ultrasonic evaluation of tissue remodeling using bioelastomers. The common assumption of equal solid and liquid displacements used in the conventional description of a fluid-saturated porous solid cannot be applied to soft media, such as bioelastomers. We revise the geoacoustic theory of Biot to allow for relative motion between a fluid and a solid in an aggregate and derive an expression for a characteristic fluid-solid coupling parameter. Unlike the conventional method, the propagation speed of shear waves observed by ultrasound shear wave elastography is considered a known quantity in the novel theory, and the calculated value of the coupling parameter is used to evaluate the status of tissue repair. The model is validated by analyzing selected cases. The conditions under which the model can be applied are identified. However, further development of the theory is required to extract dynamic parameters that can be used to monitor the entire tissue remodeling process. In this paper, a theoretical approach is developed that can be used to analyze the mechanics of tissue repair. The theory has potential applications in the field of acellular in situ tissue engineering for non-invasive monitoring of the complex mechanical remodeling process of tissue regeneration and bioelastomer degradation.