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.