Henrik Lundell1 and Samo Lasič1,2
1Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark, 2Random Walk Imaging, Lund, Sweden
1Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark, 2Random Walk Imaging, Lund, Sweden
We propose an augmented 1D random walk model that within relevant limits mimics the time dependent diffusion in a 3D model of an axon with varying radius. The model provide fast and interpretable results.
A) Our test substrate is a straight cylinder with mean radius $$$R_m$$$ and a variation in radius in axial direction with the wavelength $$$L$$$ and relative amplitude $$$k_a$$$. B) A 3D rendering. C) Scaling of step probability in relation to area. Only a portion relative to the overlapping area can move into the smaller i+1 section (green) whereas the excess walkers (red area) remain stationary. D) The corresponding propagator for a time step from the central section, where the restricted direction (right direction) is scaled by the ratio of cross-sectional areas.
Time dependent diffusivity vs. time (units in µm2/ms and ms) over a range of varicosity wavelengths and amplitudes. The 1D model is shown in red and the 3D model is shown in different shades of gray for different radii.