  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.
