Optimized Quantification of Spin Relaxation Times in the Hybrid State

Purpose: The analysis of optimized spin ensemble trajectories for relaxometry in the hybrid state. Methods: First, we constructed visual representations to elucidate the differential equation that governs spin dynamics in hybrid state. Subsequently, numerical optimizations were performed to find spin ensemble trajectories that minimize the Cram\'er-Rao bound for $T_1$-encoding, $T_2$-encoding, and their weighted sum, respectively, followed by a comparison of the Cram\'er-Rao bounds obtained with our optimized spin-trajectories, as well as Look-Locker and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. Results: After a nonrecurring inversion segment on the southern hemisphere of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern half of the sphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and $T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus, the second parameter can be encoded at virtually no extra cost. Conclusion: We provide insights regarding the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.Comment: 10 pages, 5 figure

Cram\'er-Rao bound-informed training of neural networks for quantitative MRI

Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their immunity to the non-convexity of many fitting problems. We find, however, that in heterogeneous parameter spaces, i.e. in spaces in which the variance of the estimated parameters varies considerably, good performance is hard to achieve and requires arduous tweaking of the loss function, hyper parameters, and the distribution of the training data in parameter space. Here, we address these issues with a theoretically well-founded loss function: the Cram\'er-Rao bound (CRB) provides a theoretical lower bound for the variance of an unbiased estimator and we propose to normalize the squared error with respective CRB. With this normalization, we balance the contributions of hard-to-estimate and not-so-hard-to-estimate parameters and areas in parameter space, and avoid a dominance of the former in the overall training loss. Further, the CRB-based loss function equals one for a maximally-efficient unbiased estimator, which we consider the ideal estimator. Hence, the proposed CRB-based loss function provides an absolute evaluation metric. We compare a network trained with the CRB-based loss with a network trained with the commonly used means squared error loss and demonstrate the advantages of the former in numerical, phantom, and in vivo experiments.Comment: Xiaoxia Zhang, Quentin Duchemin, and Kangning Liu contributed equally to this wor

Hybrid-State Free Precession in Nuclear Magnetic Resonance

The dynamics of large spin-1/2 ensembles in the presence of a varying magnetic field are commonly described by the Bloch equation. Most magnetic field variations result in unintuitive spin dynamics, which are sensitive to small deviations in the driving field. Although simplistic field variations can produce robust dynamics, the captured information content is impoverished. Here, we identify adiabaticity conditions that span a rich experiment design space with tractable dynamics. These adiabaticity conditions trap the spin dynamics in a one-dimensional subspace. Namely, the dynamics is captured by the absolute value of the magnetization, which is in a transient state, while its direction adiabatically follows the steady state. We define the hybrid state as the co-existence of these two states and identify the polar angle as the effective driving force of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain

Advances in Quantitative MRI: Acquisition, Estimation, and Application

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.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147486/1/gnataraj_1.pd

Cerebral blood flow estimation from Arterial Spin Labeling MRI with Look-Locker readout: a bayesian approach

Arterial Spin Labeling (ASL) è una tecnica MRI che permette di misurare la perfusione in maniera completamente non invasiva. Diversi modelli sono stati proposti in letteratura per la quantificazione della perfusione (CBF) da acquisizioni ASL. In questo lavoro viene proposto un approccio bayesiano alla quantificazione, in grado di indirizzare al meglio le conoscenze disponibili sui parametri inclusi nel modello. Il modello standard, conosciuto anche come modello di Buxton, è stato consideratoopenEmbargo per motivi di priorità nella ricerca previo accordo con terze part