Quantitative Multi-Parameter Mapping in Magnetic Resonance Imaging

Scholand, Nick

by Nick Scholand

Doctoral thesis

Date of Examination:2023-06-27

Date of issue:2023-08-18

Advisor:Prof. Dr. Martin Uecker

Referee:Prof. Dr. Martin Uecker

Referee:Prof. Dr. Hans Christian Hofsäss

Persistent Address: http://dx.doi.org/10.53846/goediss-10028

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Reproducibility

All reconstructions of this work were implemented in the Berkeley Advanced Reconstruction Toolbox (BART). The developed tools were published freely on Github until commit f1192bc. A frozen state of the software was archived on Zenodo:

Version 0.9.00 includes all features, which are required to reproduce the results in this work.

Chapter 4

The figures of chapter 4 can be reproduced with the scripts uploaded to Github/bloch-moba. A frozen state of the scripts was archived on Zenodo:

Chapter 5

The figures of chapter 5 can be reproduced with the scripts uploaded to Github/bloch-moba-misc. A frozen state of the scripts was archived on Zenodo:

Data

The datasets of this work were archived on Zenodo:

Abstract

English

Magnetic resonance imaging (MRI) is a versatile imaging technology with a broad variety of biomedical and clinical applications. It provides an excellent soft tissue contrast without the need for ionizing radiation or radioactive materials as required in modalities like computed tomography (CT) and positron emission tomography (PET). In general, the image contrast in MRI depends on tissue properties and hardware characteristics as well as the measurement technique. Thus, conventional MRI provides only a qualitative image contrast where images are interpreted based on relative intensity differences. In contrast, in quantitative MRI (QMRI) physical properties such as relaxation constants, flow velocities, temperatures, or diffusion coefficients are determined in physical units. From a clinical perspective, QMRI is relevant for classification, detection, and monitoring of abnormal tissue. It can be used to detect subtle changes that are not observable using conventional MRI and has the potential to replace measurements which require the use of contrast agents, benefiting otherwise excluded patients. From a methodological perspective, measuring physical quantities adds robustness of the acquired data against variations in the scanner hardware, the operating personnel or the software. It improves the longitudinal and inter-site comparability of results and thereby increases the reproducibility of studies. Most existing techniques in QMRI rely on special sequences designed for high sensitivity to specific physical quantities, while being robust against other influences. They utilize analytical signal representations that are used in an additional fitting step to extract quantitative maps from conventionally reconstructed images. The focus on robust sequences makes conventional QMRI methods very accurate in measuring specific physical quantities such as the T1 and T2 relaxation constants. Yet, this comes with a severe downside: The requirement to first obtain a number of high quality intermediate images for pixel-wise fitting leads to long measurement protocols which are then not feasible in a clinical setting. By exploiting the data in a more efficient way, e.g., by incorporating prior knowledge, it is possible to reduce the amount of data required for reconstruction, and, consequently, shorten the measuring time. This can be achieved with model-based reconstructions that bypass the reconstruction of intermediate images completely by formulating the image estimation as an inverse problem and by incorporating the physical signal model directly into the image reconstruction. Thus, the acquisition of redundant information is avoided, which reduces the measurement time substantially. Model-based reconstruction methods rely on sequences with analytical signal models, which are convenient to use with numerical optimization algorithms applied in image reconstructions. These signal models are often derived using assumptions that limit their accuracy by excluding certain physical effects of the magnetization during the acquisition. Furthermore, the requirement of analytical models restricts the application of model-based reconstructions to specific MRI measurements. Several efficient sequences that are simultaneously sensitive to multiple parameters have complicated, often non-analytical signal expressions which prevent their use in established model-based reconstruction schemes. The acquisition of multiple parameter maps then requires multiple scans, which -even with shorter measurements- still presents a challenge in a clinical setting. The aim of this thesis is to develop a generic model-based reconstruction method for quantitative mapping of multiple parameters with arbitrary MRI sequences. Building on a previous proof-of-principle study, a complete framework for QMRI that uses model-based reconstruction with the Bloch equations is developed and validated. The Bloch equations describe the behavior of nuclear spins under the influence of external magnetic fields and can be used to describe most MRI experiments. To integrate this into a practical reconstruction framework, a generic technique for the solution of the Bloch equations is described that efficiently exploits repeated patterns of the MRI measurement by pre-computation of state-transition matrices. This is combined with a direct sensitivity analysis for the computation of the partial derivatives that are required for numerical optimization. These techniques were then integrated into a calibration-less model-based reconstruction framework, which establishes a versatile and generic tool for QMRI. The technique was validated using simulations, phantom scans, and in vivo experiments.

Keywords: model-based reconstruction; sensitivity analysis; state-transition matrix; nonlinear inversion; Bloch equations; quantitative MRI

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