Assessing exchange between multiple compartments using multi-directional double wave diffusion sequences

The Apparent Exchange Rate (AXR) has recently been suggested as a model free measure of water exchange between microstructural compartments using a double wave pulsed gradient spin echo (dPGSE) sequence [1][2]. The AXR value has been assumed to be independent upon measurement direction [3] but could potentially be affected by the local anisotropy of microscopic subspaces. In this study we evaluate the AXR measure in different directions in cortical gray matter (GM) of a fixed monkey brain. GM has a high cell density but is also characterized by anisotropic structures [4]. Furthermore we propose a novel pulse sequence for these experiments sharing some resemblance to a regular stimulated echo sequence, which utilizes a simpler design than the twice refocused dPGSE sequences used in previous studies. Our results demonstrate that AXR is indeed not a rotationally independent measure. This could be explained by variations in exchange rates between multiple sub compartments affected differently by measurement direction. We suggest that this rotationally dependent measure potentially could render more detailed information about water exchange in complex tissue. Method: The novel double bipolar stimulated echo (dSTE) sequence used for data acquisition can be seen in figure 1A) along with the dPGSE sequence, figure 1B). The dPGSE sequence offers in theory the possibility to overcome the loss of half the signal seen in stimulated echo sequences but B1-ihomogeneties prevent the echo stored between the 2 and 3 90° RF pulses to be perfectly recreated. Hence we propose a simpler and more robust design where the two 180° RF pulses are omitted resulting in a simpler signal pathway and also slightly higher SNR. The filter gradients selectively attenuate the fast diffusion signal components whereas the diffusion gradients encode with regular diffusion sensitivity. bf and bd denote the diffusion weighting from the filter and diffusion pair of gradients respectively. To estimate the AXR bf was kept fixed and bd varied between two different values yielding a regular ADC with bf≈0 and the mixing time(TM) at minimum(9ms) and ADC’(TM) with varying TM times. The AXR values can then be calculated as