The Bloch - Torrey Equation & Diffusion Imaging ( DWI , DTI , q - Space Imaging )

Here, M is the magnetization of an excited sample placed in a static magnetic field B0, γ is the gyromagnetic ratio, Mx, My, Mz are the components of magnetization in the x, y and z directions, M0 is the magnetization at thermal equilibrium, T1 and T2 are the longitudinal and transverse relaxation times and D is the diffusion coefficient. The first two terms of Equation 1 are the original Bloch Equation [4]. The third term of Equation 1 was added by Torrey. The solution to the Bloch-Torrey equation (Equation 1) for magnetization in the transverse plane ( Mxy = Mx + iMy ) following a 90◦ pulse is given by,