Evren Özarslan1,2
1Department of Biomedical Engineering, Linköping University, Linköping, Sweden, 2Center for Image Science and Visualization, Linköping University, Linköping, Sweden
1Department of Biomedical Engineering, Linköping University, Linköping, Sweden, 2Center for Image Science and Visualization, Linköping University, Linköping, Sweden
A new diffusion-encoding and data analysis framework is introduced with which the true diffusion propagator can be measured. The technique is sensitive to the structural parameters of the pore space.
Fig. 3 Simulations for two compartments separated by a membrane of permeability $$${w}=0.6\,\mu m/ms$$$. Compartment sizes: $$$L_L=4.5\,\mu m$$$ (left), $$$L_R=5.5\,\mu m$$$ (right), diffusivities: $$$D_L=3\,\mu m^2/ms$$$, $$$D_R=2\,\mu m^2/ms$$$. Time-scales: $$$\tau_L=L_L^2/\pi^2D_L$$$, $$$\tau_R=L_R^2/\pi^2D_R$$$, $$$\tau_{ex}=\sqrt{D_L D_R}/{w}^2$$$. Top to bottom: true propagator, estimated propagator, EAP. Left three columns: near-ideal parameters. Last column: $$$\delta_1=200\,ms,\delta_{2,3}=1.2\,ms$$$, and $$$G_{max}=10\, T/m$$$.
Fig. 1 (a) Effective gradient waveform of the Stejskal-Tanner sequence [1]. The signal can be transformed into the ensemble average propagator [2]. (b) Effective gradient waveform of the sequence by Laun et al [3], which can be utilized to obtain the long-time form of the diffusion propagator. (c) Effective waveform for one realization of the experiment considered. Here, $$$-\mathbf q-\mathbf q’$$$, $$$\mathbf q$$$, and $$$\mathbf q’$$$ are the signed areas under the first, second, and third gradient pulses, respectively. The signal can be transformed into the actual propagator.
