Fiber ball imaging

Abstract

By modeling axons as thin cylinders, it is shown that the inverse Funk transform of the diffusion MRI (dMRI) signal intensity obtained on a spherical shell in q-space gives an estimate for a fiber orientation density function (fODF), where the accuracy improves with increasing b-value provided the signal-to-noise ratio is sufficient. The method is similar to q-ball imaging, except that the Funk transform of q-ball imaging is replaced by its inverse. We call this new approach fiber ball imaging. The fiber ball method is demonstrated for healthy human brain, and fODF estimates are compared to diffusion orientation distribution function (dODF) approximations obtained with q-ball imaging. The fODFs are seen to have sharper features than the dODFs, reflecting an enhancement of the higher degree angular frequencies. The inverse Funk transform of the dMRI signal intensity data provides a simple and direct method of estimating a fODF. In addition, fiber ball imaging leads to an estimate for the ratio of the fraction of MRI visible water confined to the intra-axonal space divided by the square root of the intra-axonal diffusivity. This technique may be useful for white matter fiber tractography, as well as other types of microstructural modeling of brain tissue.

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

“…The exponent of approximately one-half for white matter is consistent with the large b-value limit predicted for a model of water confined to thin, impermeable cylindrical tubes [10,34], which is commonly used to describe the diffusion dynamics of intra-axonal water [34-37]. Our results support this as being a reasonable approximation for white matter (Table 1, Fig.…”

“…We also calculated the quantity $$\zeta =2\cdot \sqrt{\frac{b}{\pi }}\cdot \frac{\stackrel{‒}{S}}{S_0},$$ where b is the b-value, $\stackrel{‒}{S}$ is the direction-averaged DWI signal, and S 0 is the signal for b = 0. Recent work has argued that $$\zeta \approx \frac{f}{\sqrt{D_a}},$$ for white matter if the b-value is sufficiently large, where f is the fraction of MRI visible water inside axons and D a is the intrinsic intra-axonal diffusivity (i.e., the along-axis diffusivity of water inside axons) [10]. …”

“…Previously proposed models include bi-exponentials [3-7], stretched exponentials [8] and power laws [9,10]. Although each of these approaches can approximately fit DWI data over significant ranges of b-values, their precise mathematical forms are quite different, as is particularly evident for large b-values.…”

“…For stretched exponentials, the signal decay has the form exp[−( kb ) a ], where b is the b-value, k is a constant, and a < 1 parameterizes the degree of stretching. For the statistical model of Yablonskiy and coworkers [9], the signal decays as 1/ b for large b , while for the model considered by Jensen and coworkers [10] , the large b signal decays as $1∕\sqrt{b}$.…”

Mapping the Orientation of White Matter Fiber Bundles: A Comparative Study of Diffusion Tensor Imaging, Diffusional Kurtosis Imaging, and Diffusion Spectrum Imaging

“…Compared to several other dODF reconstructions, the kurtosis dODF has been shown to have a comparable or improved resolving power (48); however, numerical simulations indicate that the kurtosis dODF may sometimes have a greater angular error than other dODFs for larger fiber crossing angles (16,48). Fiber bundle orientations can also be estimated from directional diffusional kurtosis estimates provided by DKI without estimating the dODF directly (49), or the white matter fiber bundles may be modeled mathematically and used to estimate a model-dependent, fiber orientation distribution function, for example using fiber ball imaging (50) or constrained spherical deconvolution (51,52). Since none of these techniques is directly analogous to the dODF, they were not included in the present study.…”