Abstract

Quantitative susceptibility mapping (QSM) has only recently entered the ever increasing armamentarium of magnetic resonance imaging. It represent a novel quantitative contrast of an intrinsic physical tissue property that may be regarded as one of the most fundamental properties in the context of magnetic resonance imaging because it reflects the reaction of the tissue to the static main magnetic field. Despite its young age, QSM has already unfolded an enormous scientific and clinical potential, which will be certainly explored in detail in the coming years. In particular, since phase contrast can exceed the magnitude contrast by up to an order of magnitude with gradient-echo imaging (GRE) at high field, transforming the GRE phase information into quantitative susceptibility maps will become increasingly more attractive with increasing field strengths. Among the many potential future applications, susceptibility contrast and susceptibility mapping is foreseen to be applied for risk assessment and therapy monitoring by examining iron deposition, demyelination and connectivity disruption in neurodegenerative diseases, microhemorrhages in traumatic brain injury (TBI), stroke assessment, bone mineralization, as well as atherosclerotic plaque composition and vulnerability. QSM will also enable noninvasive measurements of oxygen saturation in vivo [1] and will offer new contrast for studying nerve bundles and white matter fibre tracts that is important for quantitative connectivity studies or biophysical studies in neuroimaging [2,3]. If changes in susceptibility can be measured reliably based on GRE-EPI data, it will become possible to predict changes in blood susceptibility not only in single, large macro vessels [4], but also in regions containing randomly orientated blood vessels. Future avenues of QSM will further encompass applications to tissues and organs other than the brain (e.g., abdominal or breast imaging), which will have clinical implications and will open possibilities for future research. QSM is a novel contrast mechanism in MRI compared to conventional hypointensity contrast in SWI or T2*-weighted images and employs small magnetic field variations to compute quantitative maps of the corresponding underlying magnetic susceptibility distribution. Although QSM has been successfully demonstrated by using conventional clinical GRE data of single-angle acquisition, the applied algorithms rely on strong numerical regularization either of generic type [5-8] or by inclusion of spatial a priori information derived from associated magnitude images [9-12]. Consequently, the resulting susceptibility maps may suffer from streaking artefacts [9], underestimation of the susceptibility values [7,10,12,13], over-smoothing [10], or artefacts due to inconsistency between a priori information and the actual susceptibility distribution [14]. We have recently developed an improved QSM algorithm, Homogeneity Enabled Incremental Dipole Inversion (HEIDI), which utilizes a sophisticated problem-specific incremental inversion procedure and a priori information on the homogeneity of the susceptibility distribution. This approach adopts the incremental inversion strategy by Li et al. [15] and Wu et al. [16], extends it by introducing transitional sub-domains, and exploits a priori information on the homogeneity of the susceptibility distribution for reconstructing the ill-conditioned sub-domain. Extracting a priori information is based on the assumption that a small spatial gradient of the background-field corrected GRE phase images φ coincides with a small gradient of the magnetic susceptibility χ, i.e.