On the separation of susceptibility sources in quantitative susceptibility mapping: Theory and phantom validation with an in vivo application to multiple sclerosis lesions of different age

PURPOSE

In biological tissue, phase contrast is determined by multiple substances such as iron, myelin or calcifications. Often, these substances occur co-located within the same measurement volume. However, quantitative susceptibility mapping can solely measure the average susceptibility per voxel. To provide new insight in disease progression and mechanisms in neurological diseases, where multiple processes such as demyelination and iron accumulation occur simultaneously in the same location, a separation of susceptibility sources is desirable to disentangle the underlying susceptibility proportions.

METHODS

The basic concept of separating the susceptibility effects from sources with different sign within one voxel is to include information on relaxation rate ΔR₂^∗ in the quantitative susceptibility mapping reconstruction pipeline. The presented reconstruction algorithm is implemented as a constrained minimization problem and solved using conjugate gradients. The algorithm is evaluated using a software phantom and validated in MRI measurements with a phantom containing mixtures of microscopic positive and negative susceptibility sources. Data from three multiple sclerosis patients are used to show in vivo feasibility.

RESULTS

In numerical simulations, the feasibility of disentangling susceptibility sources within the same voxel was confirmed provided the critera of the static dephasing regime were fulfilled. In phantom experiments, the magnitude decay kernel, which is an essential reconstruction parameter of the algorithm, was determined to be D_m=194.5T^-1s^-1ppm^-1, and susceptibility sources could be separated in MRI measurement data.

CONCLUSIONS

In conclusion, in this study a detailed description of the implementation of an algorithm for the separation of positive and negative susceptibility sources within the same volume element as well as its limitations is presented and validated quantitatively in both simulation and phantom experiments for the first time. An application to multiple sclerosis lesions shows promising results for in vivo usability.

A novel phantom with dia- and paramagnetic substructure for quantitative susceptibility mapping and relaxometry

PURPOSE

A phantom is presented in this study that allows for an experimental evaluation of QSM reconstruction algorithms. The phantom contains susceptibility producing particles with dia- and paramagnetic properties embedded in an MRI visible medium and is suitable to assess the performance of algorithms that attempt to separate isotropic dia- and paramagnetic susceptibility at the sub-voxel level.

METHODS

The phantom was built from calcium carbonate (diamagnetic) and tungsten carbide particles (paramagnetic) embedded in gelatin and surrounded by agarose gel. Different mass fractions and mixing ratios of both susceptibility sources were used. Gradient echo data were acquired at 1.5 T, 3 T and 7 T. Susceptibility maps were calculated using the MEDI toolbox and relaxation rates ΔR₂^∗ were determined using exponential fitting.

RESULTS

Relaxation rates as well as susceptibility values generally coincide with the theoretical values for particles fulfilling the assumptions of the the static dephasing regime with stronger deviations for relaxation rates at higher field strength and for high susceptibility values. MRI raw data are available for free academic use as supplementary material.

CONCLUSIONS

In this study, a susceptibility phantom is presented that might find its application in the development and quantitative validation of current and future QSM reconstruction algorithms which aim to separate the influence of isotropic dia- and paramagnetic substructure in quantitative susceptibility mapping.

Spin dephasing around randomly distributed vessels

We analyze the gradient echo signal in the presence of blood vessel networks. Both, diffusion and susceptibility effects are analytically emphasized within the Bloch-Torrey equation. Solving this equation, we present the first exact description of the local magnetization around a single vessel. This allows us to deduce the gradient echo signal of parallel vessels randomly distributed in a plane, which is valid for arbitrary mean vessel diameters in the range of physiological relevant blood volume fractions. Thus, the results are potentially relevant for gradient echo measurements of blood vessel networks with arbitrary vessel size.

Assessment of mesoscopic properties of deep gray matter iron through a model-based simultaneous analysis of magnetic susceptibility and R2* - A pilot study in patients with multiple sclerosis and normal controls

Most studies of brain iron relied on the effect of the iron on magnetic resonance (MR) relaxation properties, such as R2∗, and bulk tissue magnetic susceptibility, as measured by quantitative susceptibility mapping (QSM). The present study exploited the dependence of R2∗ and magnetic susceptibility on physical interactions at different length-scales to retrieve information about the tissue microenvironment, rather than the iron concentration. We introduce a method for the simultaneous analysis of brain tissue magnetic susceptibility and R2∗ that aims to isolate those biophysical mechanisms of R2∗ -contrast that are associated with the micro- and mesoscopic distribution of iron, referred to as the Iron Microstructure Coefficient (IMC). The present study hypothesized that changes in the deep gray matter (DGM) magnetic microenvironment associated with aging and pathological mechanisms of multiple sclerosis (MS), such as changes of the distribution and chemical form of the iron, manifest in quantifiable contributions to the IMC. To validate this hypothesis, we analyzed the voxel-based association between R2∗ and magnetic susceptibility in different DGM regions of 26 patients with multiple sclerosis and 33 age- and sex-matched normal controls. Values of the IMC varied significantly between anatomical regions, were reduced in the dentate and increased in the caudate of patients compared to controls, and decreased with normal aging, most strongly in caudate, globus pallidus and putamen.