We study the effects of interstitial fluid flow and interstitial fluid drainage on the spatio-temporal response of soft tissue strain. The motivation stems from the ability to measure in vivo strain distributions in soft tissue via elastography, and the desire to explore the possibility of using such techniques to investigate soft tissue fluid flow. Our study is based upon a mathematical model for soft tissue mechanics from the literature. It is a simple generalization of biphasic theory that includes coupling between the fluid and solid phases of the soft tissue, and crucially, fluid exchange between the interstitium and the local microvasculature. We solve the mathematical equations in two dimensions by the finite element method (FEM). The finite element implementation is validated against an exact analytical solution that is derived in the appendix. Realistic input tissue properties from the literature are used in conjunction with FEM modelling to conduct several computational experiments. The results of these lead to the following conclusions: (i) different hypothetical flow mechanisms lead to different patterns of strain relaxation with time; (ii) representative tissue properties show fluid drainage into the local microvasculature to be the dominant flow-related stress/strain relaxation mechanism; (iii) the relaxation time of strain in solid tumours due to drainage into the microvasculature is on the order of 5-10 s; (iv) under realistic applied pressure magnitudes, the magnitude of the strain relaxation can be as high as approximately 0.4% strain (4000 microstrains), which is well within the range of strains measurable by elastography.

We present an analytical-numerical method to simulate time-harmonic ultrasonic scattering from nonhomogeneous adhesive defects in anisotropic elastic laminates. To that end, we combine the quasistatic approximation (QSA) with a very high-order (tens or hundreds of terms) regular perturbation series to allow modeling of nonuniform interfacial flaws. To evaluate each term in the perturbation series, we use a recursive algorithm based on the invariant imbedding method. It is applicable to solve wave propagation problems in arbitrarily anisotropic layered plates and it is stable for high frequencies. We demonstrate examples of convergence and divergence of the perturbation series, and validate the method against the exact solution of plane wave reflection from a layered plate immersed in water. We present a further example of scattering of a Gaussian beam by an inhomogeneous interfacial flaw in the layered plate. We discuss how results of our simulations can be used to indicate the frequencies and angles of incidence where scattering from potential defects is strongest. These parameters, presumably, offer the best potential for flaw characterization.

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.

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