Efficient simulation of magnetic resonance imaging with Bloch–Torrey equations using intra-voxel magnetization gradients

Bloch simulations with intra-voxel spin dephasing

“…It should be noted that, using only a single isochromat per voxel without any account for IVD, the model is not capable to realistically simulate the effect of field perturbations and the results substantially deviate from the experimentally obtained data. In [9] it was estimated that in order to obtain reasonable simulation results, at least 8 isochromats per directions are necessary when the multiple isochromats summation strategy is used. The previous results indicate that usage of the IVD algorithm could be much more computationally efficient for the tracking of susceptibility-induced intravoxel dephasing compared to the summation of transverse magnetization from multiple voxels.…”

“…Another approach assumes a linear phase change across the voxel which determines the dephasing slope for the phase of the neighboring isochromats, and finally, integration of transverse magnetization is used to calculate the signal generated by each element [8]. An alternative approach is to calculate intra-voxel dephasing iteratively using an analytical formula for partial derivatives of the magnetization vectors [9].…”

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

“…Nevertheless, Blees' approach removed the need for the two-step process of simulating the propagator and then the echo attenuation. Jochimsen et al [49,50] performed isochromat summations of the BlochTorrey equations to simulate MRI, but only simulated free diffusion with their addition of the diffusion term.…”

Signal decay due to susceptibility-induced intravoxel dephasing on multiple air-filled cylinders: MRI simulations and experiments

“…They help to understand the complex MR phenomena and they can be used to investigate the causes and effects of artefacts, and for the optimization of MR sequences and validation of image analysis methods [24][25][26][27][28]. While Yoder et al [26] included field inhomogeneities due to magnetic susceptibility in their simulator; no quantitative comparison has been done with a long echo time exploration and various parameters.…”