Deriving the effective ultrasound equations for soft tissue interrogation

We are interested in the ultrasound interrogation of soft tissue. As soft tissue is a complicated material, we derive the effective acoustic equations using an averaging method known as homogenization to arrive at suitable constitutive equations. Soft tissue is composed of actin, elastin, collagen, and interstitial fluid. Collagen is packaged in parallel-fibered bundles, or fasciles, in the case of tendon and ligament and a meshwork of fibrils in the case of skin. The interstitial fluid is a hydrophillic gel. The purpose of this paper is to show that one may derive a general form for the constitutive equations for the aggregate soft tissue structure. Subsequent research will be directed on the estimation of the various coefficients and kernels appearing in the effective law.