Diffusion MRI of Brain Tissue: Importance of Axonal Trajectory

Obtaining microstructural information non-invasively on brain tissue remains a challenge. Diffusion magnetic resonance imaging (dMRI) is an imaging method that can provide such information. That includes geometrical considerations of nerve cells projections, axons, that are present in the white matter of the human brain. Axons carry information encoded into electrical impulses to other cells. The thesis deals with estimating parameters of the axonal trajectories, modeled as one-dimensional pathways, from the dMRI signal. That is achieved in two steps: constructing a forward model to predict the dMRI signal and, vice versa, estimating the tissue parameters from dMRI signal by solving the so-called inverse problem. The proposed forward model employs a spectral analysis of dMRI signal. This formulation enables signal prediction for any gradient waveform and helps to identify the physical characteristics of the underlying system that are preserved in the dMRI signal. The physical properties are represented in so-called diffusion spectra whereas gradient waveforms, that sensitizes the signal, are in the encoding spectra. To mimic biologically plausible axonal trajectories, axonal trajectories were modeled by a 1D-toy model that incorporates harmonic waves with variable degree of randomness. Different numerical methods for computation of diffusion spectra were compared, and the resulting spectra were characterized by a phenomenological model incorporating three parameters. It was not possible to estimate the exact parameters of the 1D-toy model from diffusion spectra. Nonetheless, it was possible to estimate their statistical descriptors, namely microscopic orientation dispersion and dispersion-weighted wavelength. Solving the inverse problem posed a major challenge. The phenomenological model of the diffusion spectra was incorporated in a forward model of the diffusion-weighted signal perpendicular to the trajectory and applied to a state-of-the-art data acquired in human brain white matter of a healthy volunteer. It was not possible to estimate all the parameters of the phenomenological model but by constraining the parameters to plausible values we could estimate the last that was within the range predicted by histology. Incorporating trajectory-parameters in the model of white matter diffusion yielded fit residuals as small as those obtained with current state-of-the-art models assuming parallel, straight, and cylindrical cylinders. However, the cylinder model predicted axon diameters far outside the range expected from histology. We conclude that neglecting the axonal trajectories leads to biased models of axons in brain white matter.