Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: Validation and application to brain imaging

Abstract

The diagnosis of many neurologic diseases benefits from the ability to quantitatively assess iron in the brain. Paramagnetic iron modifies the magnetic susceptibility causing magnetic field inhomogeneity in MRI. The local field can be mapped using the MR signal phase, which is discarded in a typical image reconstruction. The calculation of the susceptibility from the measured magnetic field is an ill-posed inverse problem. In this work, a bayesian regularization approach that adds spatial priors from the MR magnitude image is formulated for susceptibility imaging. Priors include background regions of known zero susceptibility and edge information from the magnitude image. There is a growing scientific and clinical interest in quantitatively mapping magnetic biomaterials by measuring their susceptibilities using MRI. Quantifying endogenous paramagnetic iron would be useful for assessing blood oxygenation (1-3) and iron overloading in organs such as the liver (4) and the heart (5). The diagnosis and monitoring of vascular and neurodegenerative diseases in the brain would benefit directly from iron quantification (6). Susceptibility quantification may allow exploiting the strong diamagnetism of calciumbased structures to characterize osteoporosis (7,8) or calcifications in the breast and brain. Furthermore, quantitative susceptibility mapping (QSM) would allow robust quantification of paramagnetic and superparamagnetic contrast agents essential to molecular and cellular imaging (9-11) and also be valuable to the characterization of cardiovascular function (12)(13)(14). Recently, an MR reporter gene enabling iron accumulation within the cell was demonstrated (15), and quantifying the induced iron would be very important for investigating in vivo molecular biology.Quantifying the susceptibility from the magnetic field is an inverse problem similar to magnetoencephalography, in which magnetic sources inside the brain must be located and quantified from limited measurements of the field outside the head (16). While quantification based on geometrical models has long been used for specific applications (1,2,4,8,14,(17)(18)(19)(20), the reconstruction of susceptibility maps in which each voxel has an unknown susceptibility is a much more complex problem. While some approaches have been theoretically proposed (6,21,22), the ill-posedness due to limited measurements was dealt with recently by using regularization approaches (8,23) or acquisition strategies (24). Here, a bayesian regularized approach is presented that introduces priors derived from the MR magnitude image. It is shown that imposing values at given locations together with seeking a solution that shares edges with the MR magnitude image is more robust that the previously proposed methods (23). The technique is validated using simulations and phantom experiments. Additionally, in vivo brain susceptibility maps are obtained, introducing a new quantitative contrast that is directly linked to the amount of iron in the brain. MATERIALS AND METHODS Susceptibility an...

In vivo assessment of myelination by phase imaging at high magnetic field

“…The back calculation of susceptibility maps (de Rochefort et al, 2010;Liu et al, 2009) from the measured frequency shift maps would potentially allow the quantification of myelination. Although such techniques have been used with some success to quantify contrast agents, or the iron content of deep gray matter structures, its application should be made with care in the context of gray-white matter contrast.…”

“…Such property makes the contrast observed between two tissues dependent on their orientation relatively to the main magnetic field and to extend beyond their boundaries (Schafer et al, 2009). It is therefore not surprising that many groups have centered their attention on how to calculate the underlying magnetic susceptibility (Cheng et al, 2009;de Rochefort et al, 2008de Rochefort et al, , 2010Liu et al, 2009;Shmueli et al, 2009), based on the measured phase images. Recently two independent groups have observed that the susceptibility associated with white matter was anisotropic (Lee et al, 2010b;Liu, 2010), with Liu's work introducing the concept of susceptibility tensor imaging.…”

Functional quantitative susceptibility mapping (fQSM)

“…The reconstruction of QSM series for MO datasets was performed using the regularized COSMOS algorithm (Liu et al, 2009;, whilst for SO datasets a regularized iterative algorithm using edge information derived from the modulus data (RSO, (de Rochefort et al, 2010;) and the threshold-based k-space division approach (TKD, (Shmueli et al, 2009;) were used. QSM time-series were demeaned, concatenated to include scans acquired with the same functional paradigm and high-pass filtered in the temporal domain with a FWHM of 1.5 times the block repetition period of the stimulation paradigm.…”

“…In order to produce anatomical reference QSMs, whole-head FLASH phase data were first spatially unwrapped using a fast 3D algorithm (Abdul-Rahman et al, 2007) and then high-pass filtered, using two different methods: (i) SHARP using a kernel radius of 6 voxels (6 mm) and a regularization threshold parameter of 0.2 (Schweser et al, 2011); (ii) the combined application of a 2 nd order, 3D polynomial highpass filter and an iterative dipole deconvolution algorithm, based on L 2 -norm minimization (de Rochefort et al, 2010;. The use of SHARP with a large kernel radius yielded excellent filter performance at the cost of no filtering on the external part of the brain over a region whose extent was approximately equal to the kernel size.…”

“…Hence, filtered phase data results using SHARP and the dipole deconvolution filter were combined to produce full coverage of the brain by replacing voxel values set to zero by SHARP with values generated by the dipole deconvolution. This combined dataset was used as input to the QSM calculation, which was based on the same regularized approach that was used for the functional SO fMRI datasets (de Rochefort et al, 2010;.…”