The Role of Dephasing in the Assessment of DMRI through Langevin Equation Approach

Introduction: Diffusion Weighted Magnetic Resonance Imaging (DWMRI) provides visual contrast, depends on Brownian motion of water molecules. The diffusive behavior of water in cells alters in many disease states. Dephasing is a factor of magnetic field inhomogeneity, heterogeneity of tissue and etc., which is associated with the signal amplitude. In a series of DWI acquisition, when diffusion sensitivity is increased, decay of the image intensity due to dephasing is observed. There are some formulas that fit the decay phase curve of the behavior of water molecules in human tissue. Thus, if a physical model found to fit the decay observed in DWI, it would be possible to increase the sensitivity of the technique for the observation of subtle changes. Random phase variables are described using Langevin equation and Gaussian random variables by Cooke [Jennie M. Cooke, Phys. Rev, 2009]. Materials and Methods: As a step toward, it is the purpose of us to simulate the normal phase diffusion problem and its treatment by Langevin equation which is solved in a random formalism via Stratonovich algorithm for the random variables, using only the properties of the characteristic of Gaussian random variables, the classical dephasing results of Carr and Purcell, Torrey, and Stejskal and Tanner for normal diffusion. This work is done with/without taking inertia of the nuclei into account, in which the statistics are governed by the Ornstein–Uhlenbeck process and to other more complicated situations where the nuclei move in a field of potential V(r). Moreover, signal amplitude has been analyzed in both cases. Results: In the non-inertia approach, the stochastic results are same as classical one, however, considering inertia, signal amplitude can be achieved with higher accuracy than before. For validation, simulation results will be compared with the results of Cooke. Conclusion: we have shown how the magnetization dephasing in DMRI may be determined by simply writing and simulating the Langevin equation for the phase random variable and then calculating its characteristic function. Hence, we have a microscopic explanation of the dephasing process in DMRI.