Stochastic Gradient Langevin dynamics for joint parameterization of tracer kinetic models, input functions, and T1 relaxation-times from undersampled k-space DCE-MRI

Abstract

Dynamic Contrast Enhanced (DCE) Magnetic Resonance Imaging (MRI) is an important diagnostic technique that can quantify the structure and function of microvasculature processes, using T1 relaxation times and tracer kinetic maps. However, a series of methodological limitations affect both the accuracy and standardisation of the quantified maps, and consequently their diagnostic ability. The main methodological challenge in the quantification of tracer kinetics is a multi-parameter optimization, with correlated parameters that have different scales, which results in local minima particularly when measurements are highly undersampled. This work suggests a novel data driven optimization scheme, based on a variation of the Stochastic Gradient Langevin dynamics (SGLD) Markov chain Monte Carlo algorithm, which combines stochastic gradient descent and Langevin dynamics. The proposed SGDL algorithm avoided local minima and accurately quantified proton density, T1 relaxation times and tracer kinetics. Joint direct parameterization significantly benefited the quantification of proton density, T1 relaxation times, and the selection of a suitable tracer kinetic model per tissue type. Model based arterial and portal vein input functions were automatically determined during the joint direct parameterization. Observations made on simulated fully and highly undersampled liver DCE MRI data were confirmed on acquired clinical data.