Magnetic Resonance Simulation of Effective Transverse Relaxation (T2*)

Purpose: To simulate effective transverse relaxation ($T_2^*$) as a part of MR simulation. $T_2^*$ consists of reversible ($T_2^{\prime}$) and irreversible ($T_2$) components. Whereas simulations of $T_2$ are easy, $T_2^{\prime}$ is not easily simulated if only magnetizations of individual isochromats are simulated. Theory and Methods: Efficient methods for simulating $T_2^{\prime}$ were proposed. To approximate the Lorentzian function of $T_2^{\prime}$ realistically, conventional simulators require 100+ isochromats. This approximation can be avoided by utilizing a linear phase model for simulating an entire Lorentzian function directly. To represent the linear phase model, the partial derivatives of the magnetizations with respect to the frequency axis were also simulated. To accelerate the simulations with these partial derivatives, the proposed methods introduced two techniques: analytic solutions, and combined transitions. For understanding the fundamental mechanism of the proposed method, a simple one-isochromat simulation was performed. For evaluating realistic cases, several pulse sequences were simulated using two phantoms with and without $T_2^{\prime}$ simulations. Results: The one-isochromat simulation demonstrated that $T_2^{\prime}$ simulations were possible. In the realistic cases, $T_2^{\prime}$ was recovered as expected without using 100+ isochromats for each point. The computational times with $T_2^{\prime}$ simulations were only 2.0 to 2.7 times longer than those without $T_2^{\prime}$ simulations. When the above-mentioned two techniques were utilized, the analytic solutions accelerated 19 times, and the combined transitions accelerated up to 17 times. Conclusion: Both theory and results showed that the proposed methods simulated $T_2^{\prime}$ efficiently by utilizing a linear model with a Lorentzian function, analytic solutions, and combined transitions.

A Fast and Precise Method for Searching Rectangular Tumor Regions in Brain MR Images

Purpose: To develop a fast and precise method for searching rectangular regions in brain tumor images. Methods: The authors propose a new method for searching rectangular tumor regions in brain MR images. The proposed method consisted of a segmentation network and a fast search method with a user-controllable search metric. As the segmentation network, the U-Net whose encoder was replaced by the EfficientNet was used. In the fast search method, summed-area tables were used for accelerating sums of voxels in rectangular regions. Use of the summed-area tables enabled exhaustive search of the 3D offset (3D full search). The search metric was designed for giving priority to cubes over oblongs, and assigning better values for higher tumor fractions even if they exceeded target tumor fractions. The proposed computation and metric were compared with those used in a conventional method using the Brain Tumor Image Segmentation dataset. Results: When the 3D full search was used, the proposed computation (8 seconds) was 100-500 times faster than the conventional computation (11-40 minutes). When the user-controllable parts of the search metrics were changed variously, the tumor fractions of the proposed metric were higher than those of the conventional metric. In addition, the conventional metric preferred oblongs whereas the proposed metric preferred cubes. Conclusion: The proposed method is promising for implementing fast and precise search of rectangular tumor regions, which is useful for brain tumor diagnosis using MRI systems. The proposed computation reduced processing times of the 3D full search, and the proposed metric improved the quality of the assigned rectangular tumor regions.

Fast Magnetic Resonance Simulation Using Combined Update with Grouped Isochromats

This work aims to overcome an assumption of conventional MR simulators: Individual isochromats should be simulated individually. To reduce the computational times of MR simulation, a new simulation method using grouped isochromats is proposed. When multiple isochromats are grouped before simulations, some parts of the simulation can be shared in each group. For a certain gradient type, the isochromats in the group can be easily chosen for ensuring that they behave the same. For example, the group can be defined as the isochromats whose locations along x-axis, T1, T2 and magnetic field inhomogeneity values are the same values. In such groups, simulations can be combined when a pulse sequence with the magnetic field gradient along x-axis only are processed. The processing times of the conventional and proposed methods were evaluated with several sequences including fast spin echo (FSE) and echo-planar imaging (EPI) sequences. The simulation times of the proposed method were 3 to 72 times faster than those of the conventional methods. In the cases of 27.5 million isochromats using single instruction multiple data (SIMD) instructions and multi-threading, the conventional method simulated FSE and EPI sequences in 208.4 and 66.4 seconds, respectively. In the same cases, the proposed method simulated these sequences in 38.1 and 7.1 seconds, respectively.

Development of MR spectral analysis method robust against static magnetic field inhomogeneity

Purpose:To develop a method that enhances the accuracy of spectral analysis in the presence of static magnetic field B0 inhomogeneity. Methods:The authors proposed a new spectral analysis method utilizing a deep learning model trained on modeled spectra that consistently represent the spectral variations induced by B0 inhomogeneity. These modeled spectra were generated from the B0 map and metabolite ratios of the healthy human brain. The B0 map was divided into a patch size of subregions, and the separately estimated metabolites and baseline components were averaged and then integrated. The quality of the modeled spectra was visually and quantitatively evaluated against the measured spectra. The analysis models were trained using measured, simulated, and modeled spectra. The performance of the proposed method was assessed using mean squared errors (MSEs) of metabolite ratios. The mean absolute percentage errors (MAPEs) of the metabolite ratios were also compared to LCModel when analyzing the phantom spectra acquired under two types of B0 inhomogeneity. Results:The modeled spectra exhibited broadened and narrowed spectral peaks depending on the B0 inhomogeneity and were quantitatively close to the measured spectra. The analysis model trained using measured spectra with modeled spectra improved MSEs by 49.89% compared to that trained using measured spectra alone, and by 26.66% compared to that trained using measured spectra with simulated spectra. The performance improved as the number of modeled spectra increased from 0 to 1,000. This model showed significantly lower MAPEs than LCModel under both types of B0 inhomogeneity. Conclusion:A new spectral analysis-trained deep learning model using the modeled spectra was developed. The results suggest that the proposed method has the potential to improve the accuracy of spectral analysis by increasing the training samples of spectra.