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.

Abstract 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 Δ R 2 ∗ 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 = 194.5 T -1 s -1 ppm -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.