A diffusion MRI model for random walks confined on cylindrical surfaces: Towards non-invasive quantification of myelin sheath radius

Erick Jorge Canales-Rodríguez ^1,2,3* Chantal M.W. Tax ^4,5 Elda Fischi-Gomez ^1,2,3 Derek Jones ⁵ Jean-Philippe Thiran ^1,2,3 Jonathan Rafael-Patiño ^1,3

• ¹ Centre Hospitalier Universitaire Vaudois (CHUV), Lausanne, Vaud, Switzerland
• ² Center for Biomedical Imaging (CIBM), Lausanne, Vaud, Switzerland
• ³ Swiss Federal Institute of Technology Lausanne, Lausanne, Vaud, Switzerland
• ⁴ Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands, Netherlands
• ⁵ Brain Research Imaging Center, School of Psychology, College of Biomedical and Life Sciences, Cardiff University, Cardiff, United Kingdom

Quantifying the myelin sheath radius of myelinated axons in vivo is important for understanding, diagnosing, and monitoring various neurological disorders. Despite advancements in diffusion MRI (dMRI) microstructure techniques, there are currently no models specifically designed to estimate myelin sheath radii. This proof-of-concept theoretical study presents two novel dMRI models that characterize the signal from water diffusion confined to cylindrical surfaces, approximating myelin water diffusion.We derive their spherical mean signals, eliminating fiber orientation and dispersion effects for convenience. These models are further extended to account for multiple concentric cylinders, mimicking the layered structure of myelin. Additionally, we introduce a method to convert histological distributions of axonal inner radii from the literature into myelin sheath radius distributions. We also derive analytical expressions to estimate the effective myelin sheath radius expected from these distributions. Monte Carlo (MC) simulations conducted in cylindrical and spiral geometries validate the models. These simulations demonstrate agreement with analytical predictions. Furthermore, we observe significant correlations between the effective radii derived from histological distributions and those obtained by fitting the dMRI signal to a single-cylinder model. These models may be integrated with existing multi-compartment dMRI techniques, opening the door to non-invasive in vivo assessments of myelin sheath radii. Such assessments would require MRI scanners equipped with strong diffusion gradients, allowing measurements with short echo times. Further work is required to validate the technique with real dMRI data and histological measurements.