• quantitative susceptibility mapping
• QSM
• MRI
• magnetic resonance imaging
• human brain

The power of Magnetic Resonance Imaging (MRI) in diagnostic and medical research is unquestionable because of its flexibility, its safety and its non-invasiveness. Its sensitivity to a broad range of tissue properties allows the exploration of many biological markers which are crucial in disease diagnosis and follow-up. The introduction of MRI systems operating at Ultra-High Field (UHF) has enabled higher spatial resolution and signal-to-noise ratio and has allowed to differentiate the signals originating from different tissues based on new types of physical properties, hence to reveal unprecedented details and information. In particular, UHF MRI is exquisitely sensitive to the subtle small-scale variations in magnetic field across the human brain which are caused by differences in magnetic susceptibility of the tissues. Susceptibility-weighted imaging (SWI) was developed in order to emphasize this effect and it was followed by the formulation of several algorithms to quantitatively
estimate magnetic susceptibility.
Magnetic susceptibility is a tensor quantity and the attempt to describe it as a scalar property leads to an inaccurate estimation of the magnetic properties of tissues which do not only depend on the bulk contribution of paramagnetic and diamagnetic molecules but also on the orientation of the tissue itself with respect to the main magnetic field as well as its molecular structure.
The aim of this work is to describe and implement several different methods for Quantitative Susceptibility Mapping (QSM) proposed in the literature and to assess their performance and feasibility for in-vivo acquisitions. Moreover, this thesis provides an evaluation of the effect of tissue orientation with respect to the main magnetic field, by combining susceptibility maps with diffusion-weighted imaging (DWI), a technique which provides information on structure anisotropy of tissues. Repeatability and reliability of susceptibility measurements are also examined in order to suggest suitable procedures for clinical application.
The first part of this thesis (Chapters 1-3) presents the physical principles of Nuclear Magnetic Resonance (NMR) and MRI, especially focusing on ultra-high field systems and the phenomena related to magnetic susceptibility. In this framework, a description of Quantitative Susceptibility Mapping (QSM) is given: this technique requires the deconvolution of phase images with a magnetic dipole kernel to obtain susceptibility maps.
However, this deconvolution is not straightforward and it is practically demanding due to
the ill-posed nature of this inverse problem.
The second part (Chapters 4-6) describes the implemented algorithms and the experiments conducted to obtain quantitative maps of magnetic susceptilibty in the human brain using MRI. Several techniques for regularizing the ill-posed inverse problem are introduced, implemented and discussed. Such techniques can be classied into two categories: single orientation and multiple orientation methods, depending on how many acquisition at different orientations of patient's head are required. First, they were tested on a simulated numerical phantom to evaluate their performance considering both the accuracy of the
reconstruction of the simulated susceptibility and the level of artifacts they introduce in the image. Then, their feasibility for in-vivo experiment was evaluated on one healthy volunteer. Multi orientation method provides the most accurate estimate of magnetic susceptibility; however, this method is time consuming and not realistically applicable in a clinical setting. Instead, the most advanced single orientation method, called iLSQR, is a powerful algorithm that provides good quality images and it can be considered the best algorithm currently available for QSM in clinical practice.
The problem of the variability of the susceptibility measures due to the dependence on tissue orientation with respect to the main magnetic field is examined by combining susceptibility maps with diffusion-weighted imaging (DWI) whose reconstruction algorithm was implemented during this work. The effect of tissue orientation for different levels of anisotropy of each voxel is studied, showing that tissue orientation does not signicanlty affect QSM for low anisotropy.
Finally, since QSM does not provide absolute measures but rather relative differences in magnetic susceptibility among different tissues, additional experiments were performed to identify and discuss the most suitable region that should be used as a reference.
The work presented in this thesis was carried out at the Laboratory of Medical Physics
and Magnetic Resonance Biotechnologies of the IMAGO7 Foundation at the IRCCS Stella
Maris Foundation (Calambrone, Pisa).