A Fast Constrained Nonlinear Elastography Technique: Polyvinyl Alcohol (PVA) Phantom Study Using the Veronda-Westman Model

Breast elastography has been proposed as a novel imaging modality for breast cancer detection and assessment. As pathologies are known to change tissue stiffness significantly, the idea behind elastography is using tissue stiffness as imaging contrast agent. Evidence in the literature suggests that various pathological tissues exhibit different mechanical stiffness characteristics. Therefore, in addition to the ability of detecting the presence of abnormalities, elastography is capable of pathological tissue classification. In this work, we propose a novel nonlinear (hyperelastic) breast elastography system which takes into account tissue large deformations resulting from mechanical stimulation. To idealize breast tissue, we use the well-known Veronda-Westman model as the forward problem solution in the hyperelastic parameter reconstruction process. This process involves tissue mechanical stimulation, displacement data acquisition followed by solving an inverse problem to find the hyperelastic parameters iteratively. These parameters are useful for in vivo tumor classification, image guided surgery and Virtual Reality systems development. Due to the exponential form of the Veronda-Westman function, however, this model cannot be solved using inverse-matrix techniques. Therefore, we have developed a novel technique to solve the corresponding nonlinear inverse problem. To validate the technique, we used an experimental breast tissue mimicking phantom that was made up of PVA-C (Polyvinyl Alcohol), which exhibits nonlinear mechanical behavior. Displacement data was acquired using a combination of Time Domain Cross-Correlation Estimation (TDE) and Horn-Schunck Optical Flow techniques.