Adjoint-based Perfusion Estimation from Dynamic Contrast-Enhanced Ultrasound: Advection-Diffusion and Two-Compartment Models
For researchers in medical imaging, this work provides a computational framework for perfusion estimation, though it is an incremental application of existing adjoint methods to a specific imaging modality.
The paper compares two models for estimating tumor perfusion parameters from dynamic contrast-enhanced ultrasound, using adjoint-based optimization with Tikhonov regularization. Numerical experiments on synthetic and in vivo data demonstrate the feasibility of the approach, but no quantitative performance metrics are reported.
Tumor perfusion and vascular properties are important determinants of a cancer's response to therapy. In this paper, we discuss the estimation of spatially varying blood flow velocities and perfusion parameters from time-resolved contrast agent concentration data. We compare a standard parabolic advection-diffusion model against a two-compartment model governed by a coupled system of hyperbolic advection-reaction equations, which is physiologically more sound. To address the inherent ill-posedness of this parameter identification problem, we employ Tikhonov regularization and derive continuous adjoint equations necessary for efficient, gradient-based minimization. We discuss the numerical discretization of the state and adjoint systems using state-of-the-art schemes, and demonstrate the efficacy of the proposed reconstruction algorithms through numerical experiments on synthetic data and in vivo dynamic contrast-enhanced ultrasound measurements.