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Time-dependent diffusion in undulating thin fibers: Impact on axon diameter estimation.

Jan Brabec¹, Samo Lasič², Markus Nilsson³

¹Department of Clinical Sciences Lund, Medical Radiation Physics, Lund University, Lund, Sweden.

NMR in Biomedicine

|December 24, 2019

Summary

Diffusion MRI can map brain microstructure, but assuming straight axons overestimates diameter. Non-straight axonal trajectories significantly impact diffusion MRI signal analysis and interpretation.

Keywords:

axon diameter axonal trajectories diffusion MRI diffusion spectrum low frequency restricted diffusion time dependence undulation

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Area of Science:

Neuroimaging
Biophysics
Medical Physics

Background:

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive technique for mapping axonal microstructure.
Current dMRI methods often model axons as straight cylinders to estimate axon diameter from time-dependent diffusion signals.
The impact of non-straight axonal trajectories on dMRI signal analysis and diameter estimation remains insufficiently explored.

Purpose of the Study:

To investigate the influence of undulating axonal trajectories on time-dependent diffusion MRI signals.
To analyze how microscopic orientation dispersion affects diffusion spectra characteristics.
To evaluate the accuracy of axon diameter estimation when assuming straight cylinders versus undulating fibers.

Main Methods:

Development and application of a toy model: the undulating thin fiber model.
Analysis of time-dependent diffusion in the frequency domain.
Characterization of diffusion spectra by height, width, and low-frequency power law exponent.

Main Results:

Microscopic orientation dispersion is the primary determinant of diffusion spectra characteristics.
At lower frequencies (longer diffusion times), spectra from straight cylinders and undulating fibers are similar.
Using a straight-cylinder model for undulating axons leads to overestimation of axon diameter, proportional to undulation amplitude and dispersion.
At higher frequencies (shorter diffusion times), spectra differ between cylinders and undulating fibers.
The low-frequency power law exponent can be below 2 for undulating fibers, differing from straight cylinders.

Conclusions:

The non-straight nature of axonal trajectories significantly influences diffusion MRI signal characteristics.
Overestimation of axon diameter occurs when assuming straight cylinders for undulating axons.
Accurate analysis and interpretation of diffusion MRI data require consideration of axonal trajectory complexity.