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PURPOSE: To assess the validity of the superposition approximation for crossing fascicles, i.e., the assumption that the total diffusion-weighted MRI signal is the sum of the signals arising from each fascicle independently, even when the fascicles intermingle in a voxel. METHODS: Monte Carlo simulations were used to study the impact of the approximation on the diffusion-weighted MRI signal and to assess whether this approximate model allows microstructural features of interwoven fascicles to be accurately estimated, despite signal differences. RESULTS: Small normalized signal differences were observed, typically 10-3-10-2. The use of the approximation had little impact on the estimation of the crossing angle, the axonal density index, and the radius index in clinically realistic scenarios wherein the acquisition noise was the predominant source of errors. In the absence of noise, large systematic errors due to the superposition approximation only persisted for the radius index, mainly driven by a low sensitivity of diffusion-weighted MRI signals to small radii in general. CONCLUSION: The use of the superposition approximation rather than a model of interwoven fascicles does not adversely impact the estimation of microstructural features of interwoven fascicles in most current clinical settings. Magn Reson Med 79:2332-2345, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Original publication




Journal article


Magn Reson Med

Publication Date





2332 - 2345


Monte Carlo simulations, crossing fascicles, diffusion-weighted MRI, superposition approximation, tissue microstructure, Algorithms, Axons, Brain, Computer Simulation, Diffusion Magnetic Resonance Imaging, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Monte Carlo Method, Phantoms, Imaging, Reproducibility of Results, Signal-To-Noise Ratio