Biomechanical imaging is a promising new technology that enables monitoring of and predicting disease progression and the identification of cancerous and fibrotic tissue. The dynamic data that is input for our work is movies of propagating or harmonic waves; the movies are created from sets of MR or sets of ultrasound data that is acquired while the tissue is moving in response to a pulse or an oscillating force. The main characteristics of the movies are: either (1) there is a wave propagating with a front; or (2) there is a traveling wave created by two sources oscillating at different but nearly the same frequencies; or (3) there is multifrequency harmonic oscillation.
We will briefly show some of our recent work in cancer identification created from data with the characteristics (1) or (2) above. The remaining talk will concentrate on the mathematical model, algorithms and reconstructions from movie data acquired when the tissue is undergoing response to a single or multifrequency harmonic oscillation. We discuss viscoelastic and elastic models, our current choice for viscoelastic model and its properties. We discuss approximations to the mathematical model, estimates of the error made by the approximation, the algorithms inspired by the full model and the approximate model and their stability and accuracy properties, why some biomechanical parameters cannot be reliably recovered, and current questions about biomechanical parameters that inspire our work. We present images created by our algorithms both from synthetic, in vivo and in vitro data.