Shear wave elastography is a technique used to noninvasively estimate the mechanical properties of tissue from propagating mechanical waves. These mechanical properties can be used to noninvasively diagnose and help with the treatment of various diseases like cancer, and liver fibrosis. The mechanical properties can also be used to understand various biological processes like wound healing, and cell division. To compute the mechanical properties, one needs to solve an inverse problem governed by differential equation models. I will present several direct variational formulations that can be used to efficiently solve the inverse problem. I will discuss some of the mathematical properties of these variational formulations, and compare their performance on simulated data.

BIO: Olalekan Babaniyi is currently an assistant professor in the School of Mathematics and Statistics at Rochester Institute of Technology (RIT). Prior to joining RIT, he was a post-doctoral scholar at the University of California, Merced, working on developing computational tools to solve large scale ice sheet inverse problems. Prior to that, he was a postdoctoral associate at Duke University working on inverse problems in the medical imaging field. He earned his Bachelors, masters, and PhD degrees at Boston University where he began working on inverse problems in the elastography field.