Dependence on b-value of the direction-averaged diffusion-weighted imaging signal in brain

Abstract

Purpose: The dependence of the direction-averaged diffusion-weighted imaging (DWI) signal in brain was studied as a function of b-value in order to help elucidate the relationship between diffusion weighting and brain microstructure.

Methods: High angular resolution diffusion imaging (HARDI) data were acquired from two human volunteers with 128 diffusion-encoding directions and six b-value shells ranging from 1000 to 6000s/mm² in increments of 1000s/mm². The direction-averaged signal was calculated for each shell by averaging over all diffusion-encoding directions, and the signal was plotted as a function of b-value for selected regions of interest. As a supplementary analysis, similar methods were also applied to retrospective DWI data obtained from the human connectome project (HCP), which includes b-values up to 10,000s/mm².

Results: For all regions of interest, a simple power law relationship accurately described the observed dependence of the direction-averaged signal as a function of the diffusion weighting. In white matter, the characteristic exponent was 0.56±0.05, while in gray matter it was 0.88±0.11. Comparable results were found with the HCP data.

Conclusion: The direction-averaged DWI signal varies, to a good approximation, as a power of the b-value, for b-values between 1000 and 6000s/mm². The exponents characterizing this power law behavior were markedly different for white and gray matter, indicative of sharply contrasting microstructural environments. These results may inform the construction of microstructural models used to interpret the DWI signal.

Keywords: B-value; Brain; Diffusion; HARDI; MRI; Microstructure.

Figure 1

Locations of the seven ROIs considered in the quantitative analysis superimposed on the average b0 image for one subject. Each ROI represents the core of a different anatomical region. Cerebellar peduncle (violet), splenium (cyan), internal capsule (blue) and frontal white matter (green) are all regarded as white matter regions, for the purposes of this study, while cerebellar gray matter (red), putamen (yellow) and thalamus (white) are classified as gray matter.

Figure 2

(a) Log-log plot showing the relationship between the direction-averaged DWI signal $\stackrel{‒}{S}$ from each ROI (normalized by dividing by the signal without diffusion weighting, S₀) and the six b-values (1000, 2000, 3000, 4000, 5000 and 6000 s/mm²) for all the ROIs of Subject 1. The reference b-value b₁ is set to 1000 s/mm². The error bars show the standard deviations of the measurements. The fits to Eq. (1) for white and gray matter regions are indicated by solid and dashed lines, respectively. (b) Linear scale plot showing the same data, but without normalization and error bars in order to better demonstrate the quality of the fits. WM = white matter; GM = gray matter.

Figure 3

Parametric maps of the exponent α for a single axial slice from each subject. For reference, the corresponding FA and a similar MPRAGE (T1) images are also shown. In white matter, α is close to 0.5, while for gray matter regions the exponent is consistently larger.

Figure 4

Axial maps of estimates for the quantity ζ, as given by Eq. (1), for a single human subject as a function of the b-value. From the theory of Ref. 10, the estimates in white matter are expected to converge, for large b-values, to a level that is characteristic of the tissue microstructure. The scale bar is in units of ms^1/2/μm.

Figure 5

(a) The quantity ζ for the four white matter ROIs as estimated with Eq. (1) and the HARDI data for b = 4000 s/mm². (b) Mean ζ values for all the white matter ROIs as a function of the b-value. The mean values for b = 4000, 5000, and 6000 s/mm² are all similar, in consistency with the theory of Ref. 10. All error bars indicate standard deviations. SP = splenium; CP = cerebellar peduncle; FWM = frontal white matter; IC = internal capsule.

Figure 6

(a) Log-log plot showing the relationship between the direction-averaged DWI signal $\stackrel{‒}{S}$ from each ROI (normalized by dividing by the signal without diffusion weighting, S₀) and the four b-values (1000, 3000, 5000, 10,000 s/mm²) for all the ROIs in the HCP dataset (Similar to Fig 2a). (b) The exponent α for each ROI and subject. The HCP estimates are similar to those from the primary dataset. (c) Parametric maps of the exponent α and FA for a single axial slice from the HCP dataset. A similar T1 slice is provided as an anatomical reference. All error bars indicate standard deviations. SP = splenium; CP = cerebellar peduncle; FWM = frontal white matter; IC = internal capsule, TH = thalamus, PU = putamen, CGM = cerebellar gray matter.