Three-dimensional MR reconstruction of high-contrast magnetic susceptibility by the variational born iterative method based on the magnetic field volume integral equation

Purpose To provide high-quality and high-contrast magnetic susceptibility mapping, a 3D MR reconstruction method for magnetic susceptibility based on the magnetic field volume integral equation with the variational Born iterative method (VBIM) is developed. Methods Three-dimensional magnetic susceptibility is reconstructed from the positive rotating magnetic field component H1+ of the radiofrequency field acquired by B1 mapping. The stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is implemented in the forward problem to solve for the magnetic field, and the conjugate gradient fast Fourier transform method is implemented in the inverse problem to reconstruct the magnetic susceptibility distribution. Results Numerical results demonstrated that good effectiveness and high accuracy can be achieved for both the forward solver of the stabilized biconjugate gradient fast Fourier transform method and the inverse solver of the VBIM method. The method proved to be robust under noise contamination. Moreover, the magnetic susceptibilities with much higher contrasts than that of the non–full wave methods can also be efficiently reconstructed. Conclusions The proposed method can reconstruct the magnetic susceptibility of not only human head, but also other human tissues or materials such as magnetic contrast agents with high magnetic susceptibilities. It has promising applications in high-contrast magnetic susceptibility mapping. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine.