The derivation of homogenized diffusion kurtosis models for diffusion MRI
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Updated: Feb 1, 2026

Role of Diffusion MRI Tractography in Endoscopic Endonasal Skull Base Surgery
Published on: July 5, 2021
Houssem Haddar1, Marwa Kchaou2, Maher Moakher2
1INRIA, Ecole Polytechnique, Université Paris Saclay, Route de Saclay, 91128 Palaiseau Cedex, France.
Abstract:
We use homogenization theory to establish a new macroscopic model for the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses in the case of biological tissue with impermeable membranes. In this model, new higher-order diffusion tensors emerge and offer more information about the structure of the biological tissues. We explicitly solve the macroscopic model to obtain an ordinary differential equation for the diffusion MRI signal that has similar structure as diffusional kurtosis imaging models. We finally present some validating numerical results on synthetic examples showing the accuracy of the model with respect to signals obtained by solving the Bloch-Torrey equation.
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