Simulation of Double Pulsed Field Gradient Experiments

Introduction The assessment of local diffusion anisotropy in tissue using diffusion tensor imaging (DTI) is known to be problematic in regions that contain an admixture of tissue types or multiple fiber orientations. One approach to ameliorating this problem is to acquire high angular resolution qspace data, augmented with more sophisticated analysis schemes using higher order tensor models. However, this approach is still ultimately limited to tissues like white matter that exhibit highly anisotropic diffusion on both microscopic and voxel length scales. Recently, the ability to detect microscopic anisotropythrough the use of "multiple scattering" [1] that applies multiple q-space encoding gradients between successive refocusing pulses so that the net signal is sensitive to local variations in diffusion. The double pulsed field gradient (DPFG) is one such method of particular interest because it is sensitive to restricted diffusion at diffusion wavelengths long compared to the dimensions of the restrictions (and thus requires only modest diffusion gradients). Because the pulse sequence is simple it can be included in standard imaging sequences. Recently, a theory has been developed to quantify the effects of restricted diffusion in the general DPFG experiment [2]. Here we present an independent validation of this theory by simulating two key DPFG experiments for a cylindrical pore in [2] using a recently developed diffusion simulation environment DIFSIM [3]. We then extend the simulation to a physiologically more realistic model of packed cylinders in a water bath for which analytical models are more difficult to obtain. Theory The general theory of the NMR signal in restricted diffusion in a multiple PFG is presented in [2] and is an extension of the multiple correlation function method of Grebenkov [4] to arbitrary angular variations between the gradients, a critical feature for applications to diffusion weighted MRI. The method is applied to the general DPFG pulse sequence (Fig 1). Two important special cases are evaluated: (1) collinear gradients for a range of mixing times (the diffraction problem), and (2) angular variations between the two gradients for a fixed mixing time, both in a cylindrical pore. For the cylindrical pore and equal gradient widths (δ1=δ2), the signal attenuation is given by E=〈0|e +q )·Ao 1 2 |0〉 where Λ(D0,r0) is an operator that depends on the diffusion coefficient D0 and the cylinder radius r0, and A=(X,Y), X is an operator that depends on r0, and Y is a rotated version of X [2]. The theoretical curves for these two cases are shown as lines in Figs 3 and 4, respectively. In Fig 3, dashed lines represent negative values. Fig 1. DPFG pulse sequence.