Evaluation of the effect of exchange on the diffusion weighted MR-signal in brain white matter

Methods Software phantom construction: The diffusion is modeled in a raster with a square cross-section filled with infinitely long parallel aligned rigid cylinders. The diameters (10 μm ± 3.5 μm) and density (79.5%) of the cylinder packing were chosen similar to those observed in brain WM [1] (see Figure 1). Diffusion MR simulation: The diffusion process was modeled by Monte Carlo (MC) simulation of 3.0×10 random walkers as described in [2]. The trajectory of random walker was generated by moving the particle during each time step t of 0.07 ms over a distance (6Dt) in a randomly chosen radial direction. The diffusion coefficients D were chosen similar to those described in literature for the intraand extracellular space in brain white matter [3]: 1.0×10 m2/s inside the cylinders and 2.5×10 m/s outside the cylinders. Exchange between the intracellular and extracellular space has been enabled by the method described in [4]. The phase φ of the particle was updated during each time step t according to the current position and the presence of diffusion gradients. Varying diffusion gradients were applied during a time δ of 0.7 ms. The diffusion time Δ was chosen to be 50 ms with corresponding b-factors, defined by γδG(Δ−δ/3), ranging from 0 up to 2500 s/mm. The diffusion weighted MR-signal S was derived as the sum of the phases of all spins ∑e.