Axon diameter index estimation independent of fiber orientation distribution using high-gradient diffusion MRI

Abstract

Axon diameter mapping using high-gradient diffusion MRI has generated great interest as a noninvasive tool for studying trends in axonal size in the human brain. One of the main barriers to mapping axon diameter across the whole brain is accounting for complex white matter fiber configurations (e.g., crossings and fanning), which are prevalent throughout the brain. Here, we present a framework for generalizing axon diameter index estimation to the whole brain independent of the underlying fiber orientation distribution using the spherical mean technique (SMT). This approach is shown to significantly benefit from the use of real-valued diffusion data with Gaussian noise, which reduces the systematic bias in the estimated parameters resulting from the elevation of the noise floor when using magnitude data with Rician noise. We demonstrate the feasibility of obtaining whole-brain orientationally invariant estimates of axon diameter index and relative volume fractions in six healthy human volunteers using real-valued diffusion data acquired on a dedicated high-gradient 3-Tesla human MRI scanner with 300 mT/m maximum gradient strength. The trends in axon diameter index are consistent with known variations in axon diameter from histology and demonstrate the potential of this generalized framework for revealing coherent patterns in axonal structure throughout the living human brain. The use of real-valued diffusion data provides a viable solution for eliminating the Rician noise floor and should be considered for all spherical mean approaches to microstructural parameter estimation.

Keywords: Axon diameter; Diffusion MRI; High b-value; Human Connectome Project (HCP); Human connectome scanner; Spherical mean technique (SMT); Tissue microstructure; White matter.

Figure 1.

Workflow for extracting real-valued diffusion MRI data. A 2D Fourier transformation was applied to the acquired magnitude and phase data to retrieve the complex k-space data. The k-space data was multiplied by a Hamming window to obtain the low-frequency components. The inverse Fourier transform was applied to the k-space data to obtain an estimated background phase φ_BG. The background phase was then subtracted from the originally acquired phase to create a complex-valued image without background phase contamination. The real part was extracted, which included diffusion-contrast and Gaussian noise, whereas the imaginary part contained only the imaginary part of the complex Gaussian noise and was discarded.

Figure 2.

Comparison of the effects of Gaussian and Rician noise on estimated cylinder diameter a and restricted volume fraction f_r for substrates with varying simulated diameters between 1 and 9 μm and fixed f_r = 0.7. The mean (dots) and standard deviation (error bars) across 200 voxels with Gaussian (A, B) and Rician (C, D) noise with SNR=20 are plotted against the simulated values (grey lines). Results for parallel fibers are shown on the left and crossing fibers are shown on the right. Diameters were sampled at an interval of 0.1μm between 1 and 9μm. The Rician noise floor resulted in an elevation of the spherical mean signal at high q, resulting in underestimation of cylinder diameter and overestimation of the restricted volume fraction.

Figure 3.

Spherical mean images for (upper panel) real-valued and (lower panel) magnitude diffusion MRI data in a representative healthy subject obtained using the b-values and diffusion times (Δ) sampled in the diffusion MRI protocol. The noise floor due to Rician noise was visually discernable in the magnitude data for b>3000 s/mm². The b-values labeled in the Figure are in units of s/mm².

Figure 4.

Exemplary in vivo maps in a healthy subject. The blue triangles on the FA map in the upper panel (A) highlight white matter regions in the corona radiata with decreased FA caused by crossing fiber bundles. The white arrow in the lower panel (B) marks the central sulcus in each subject.

Figure 5.

Group statistics and averaged maps across all subjects. Histograms of the estimated apparent axon diameter (A) and relaxation-weighted restricted volume fraction (B) in cerebral white matter in 6 healthy volunteers were calculated, with each curve representing a single subject. The group-averaged maps of apparent axon diameter obtained with real-valued (C) and magnitude data (D) were shown through the right corticospinal tract, with the triangle denoting the central sulcus. The tract-averaged apparent diameter was calculated for each subject, and results obtained with real-valued (E) and magnitude (F) data are reported in the accompanying box-and-whiskers plots, which depict the mean, interquartile range, and upper and lower fences of apparent axon diameter across the six subjects.