In a typical experiment in compression elastography a sample is compressed to an overall strain of about 1-5%, and then perturbed with a much smaller strain in the range of 0.05%-0.1%. The displacement field corresponding to this perturbative excitation is measured using phase-sensitive OCT. This three-dimensional perturbative displacement data carries within it a wealth of information regarding the volumetric distribution of linear elastic properties of tissue. In this talk we will describe a class of iterative algorithms that use this data input and generate volumetric maps of linear elastic properties of biological specimens. The main idea behind these algorithms is to pose this inverse problem as a constrained minimization problem and use adjoint equations, spatially adaptive resolution and domain decomposition techniques to solve this problem.
We will also consider the case when the overall compression and the perturbative excitation steps are repeated several times while increasing the overall strain. For example, a sequence wherein the overall strain varies as 2, 4, 6, 8, and 10%, and each increment is followed by a small perturbative excitation. The measured displacement field corresponding to this small excitation is sensitive to the nonlinear elastic properties of the specimen, which determine how its elastic modulus varies with increasing strain. We will extend the algorithms designed to infer the linear elastic properties of biological specimens to infer these non-linear elastic properties. We will demonstrate our ability to infer linear and nonlinear elastic properties on tissue-phantom, and ex-vivo and in-vivo tissue samples.