Advances in Quantitative MRI: Acquisition, Estimation, and Application

Abstract

Quantitative magnetic resonance imaging (QMRI) produces images of potential MR biomarkers: measurable tissue properties related to physiological processes that characterize the onset and progression of specific disorders. Though QMRI has potential to be more diagnostic than conventional qualitative MRI, QMRI poses challenges beyond those of conventional MRI that limit its feasibility for routine clinical use. This thesis first seeks to address two of those challenges. It then applies these solutions to develop a new method for myelin water imaging, a challenging application that may be specifically indicative of certain white matter (WM) disorders.

One challenge that presently precludes widespread clinical adoption of QMRI involves long scan durations: to disentangle potential biomarkers from nuisance MR contrast mechanisms, QMRI typically requires more data than conventional MRI and thus longer scans. Even allowing for long scans, it has previously been unclear how to systematically tune the "knobs" of MR acquisitions to reliably enable precise biomarker estimation. Chapter 4 formalizes these challenges as a min-max optimal acquisition design problem and solves this problem to design three fast steady-state (SS) acquisitions for precise T1/T2 estimation, a popular QMRI application. The resulting optimized acquisition designs illustrate that acquisition design can enable new biomarker estimation techniques from established MR pulse sequences, a fact that subsequent chapters exploit.

Another QMRI challenge involves the typically nonlinear dependence of MR signal models on the underlying biomarkers: these nonlinearities cause conventional likelihood-based estimators to either scale very poorly with the number of unknowns or risk producing suboptimal estimates due to spurious local minima. Chapter 5 instead introduces a fast, general method for dictionary-free QMRI parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. Chapter 5 demonstrates PERK for T1/T2 estimation using one of the acquisitions optimized in Chapter 4. Simulations as well as single-slice phantom and in vivo experiments demonstrated that PERK and two well-suited maximum-likelihood (ML) estimators produce comparable T1/T2 estimates, but PERK is consistently at least 140x faster. Similar comparisons to an ML estimator in a more challenging problem (Chapter 6) suggest that this 140x acceleration factor will increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.

Chapter 6 applies ideas developed in previous chapters to design a new fast method for imaging myelin water content, a potential biomarker for healthy myelin. It first develops a two-compartment dual-echo steady-state (DESS) signal model and then uses a Bayesian variation of acquisition design (Chapter 4) to optimize a new DESS acquisition for precise myelin water imaging. The precision-optimized acquisition is as fast as conventional SS myelin water imaging acquisitions, but enables 2-3x better expected coefficients of variation in fast-relaxing fraction estimates. Simulations demonstrate that PERK (Chapter 5) and ML fast-relaxing fraction estimates from the proposed DESS acquisition exhibit comparable root mean-squared errors, but PERK is more than 500x faster. In vivo experiments are to our knowledge the first to demonstrate lateral WM myelin water content estimates from a fast (3m15s) SS acquisition that are similar to conventional estimates from a slower (32m4s) MESE acquisition.