Boundary conditions in quantitative elastic modulus imaging

Abstract

Quantitative elastic modulus imaging from quasistatic strain fields has several advantages over other approaches. It requires no specialized hardware, provides spatial resolution nearly commensurate with Bmode, and may be extended to quantitative nonlinear modulus imaging in a straightforward way. It has the drawback, however, of requiring the solution of a complex inverse problem with an ultrasound measured displacement field. The most common approach to solving the inverse problem is iterative optimization. To solve the inverse problem, the experimental configuration is simulated. Material property distributions in the simulated experiment are then varied until the simulated deformation field matches the observed deformation field. The weak link in this process is uncertainty in the experimental conditions. In the context of iterative inversion, this translates into uncertainty in the boundary conditions of the forward model. In this talk, we discuss how different choices of displacement and/or traction boundary conditions affect the inverse problem's solution using phantom and clinical breast data. We show that a Bayesian estimate of the displacement field in the face of uncertain boundary conditions can be implemented by spring finite elements on the domain boundary. [Authors gratefully acknowledge funding from NSF and NIH (NSF SI2 Grant No. 1148111; NIH NCI-R01CA140271).]