Magnetic resonance imaging shows orientation and asymmetry of white matter fiber tracts

Abstract

Apparent diffusion tensor maps of the human brain were acquired with a magnetic resonance imaging sequence (Gudbjartsson, H., Maier, S.E., Mulkern, R.V., Mórocz, I.A., Patz, S., Jolesz, F.A., Magn. Reson. Med. 36 (1996) 509–519). It was shown that the geometric nature of the apparent diffusion tensors can quantitatively characterize the tissue structure. Display of the orientation and directional uniformity of the water diffusion in the brain demonstrated most of the known major anatomical constituents of human white matter. A comparison of corresponding anatomic regions in the white matter of both hemispheres in 24 healthy volunteers revealed that fiber tracts within the anterior limb of the internal capsule have a significantly higher (P<0.01) measure of alignment in the right hemisphere. This method offers a unique tool for the in vivo demonstration of neural connectivity in healthy and diseased brain.

Introduction

With current conventional proton magnetic resonance imaging (MRI) techniques, the white matter of the brain appears to be a remarkably homogeneous tissue without any suggestion of the complex arrangement of fiber tracts. Although the individual axons and the surrounding myelin sheaths cannot be revealed with the limited spatial resolution of in vivo imaging, distinct bands of white matter fibers with parallel orientation may be distinguished from others running in different directions if MRI techniques are sensitized to water diffusion and the preferred direction of diffusion is determined. Here, we present a robust magnetic resonance diffusion tensor imaging method, a quantitative characterization of the geometric nature of the diffusion tensors, and a display method for showing clear and detailed in vivo images of human white matter tracts. The orientation and distribution of most of the known major fiber tracts are demonstrated and clear evidence of hemispheric laterality in the anterior limb of the internal capsule is shown.

Water diffusion in tissue due to Brownian motion is random but some structural characteristics of tissues may limit diffusion. In the white matter, the mobility of the water is restricted in the directions perpendicular to the axons which are oriented along the fiber tracts. This anisotropic diffusion is due to the presence of tightly packed multiple myelin membranes encompassing the axon. Myelination is not essential for diffusion anisotropy of nerves as shown in studies of nonmyelinated garfish olfactory nerves [2]and anisotropy exists in brains of neonates before the histological appearance of myelin [18]but myelin is widely assumed to be the major barrier to diffusion in myelinated fiber tracts. Therefore the demonstration of anisotropic diffusion in brain by magnetic resonance has opened the way to explore the structural anatomy of the white matter in vivo 10, 3, 1, 13.

In this work we applied a modified version of the recently proposed Line Scan Diffusion Imaging (LSDI) technique [8]. This method, like the commonly used diffusion-sensitized, ultrafast, echo-planar imaging (EPI) technique [15]is relatively insensitive to bulk motion and physiologic pulsations of vascular origin. But unlike EPI, LSDI exhibits minimal image distortion, does not require cardiac gating, head restraints or post-processing image correction, and can be implemented without specialized hardware on all standard MRI scanners.

Scalar measures of anisotropy or geometry can easily be displayed in two dimensions but the display of tensors or vectors poses more of a problem. Previous display methods have depicted octahedra or ellipsoids in each pixel 14, 1, but this does not really allow for high spatial resolution. Limited success was achieved by using different intensities of the three colors red, green and blue to indicate the size of the apparent diffusion coefficient in each of the three cartesian directions 4, 11. We propose a simple, intuitive solution to the problem using colors and lines.

In order to relate the measure of diffusion anisotropy to the structural geometry of the tissue a mathematical description of diffusion tensors and their quantitation is necessary 1, 17. First, a complete diffusion tensor, D, is calculated for each voxel (see Section 2.2). Using the symmetry properties of the diffusion ellipsoid we decomposed the diffusion tensor, and from the tensor basis assigned scalar measures, describing the linearity and the anisotropy, to each voxel.

Let λ₁≥λ₂≥λ₃≥0 be the eigenvalues of the symmetric tensor D, and let ê_i be the normalized eigenvector corresponding to λ_i. Diffusion can be divided into three basic cases depending on the rank of the representation tensor:

(1) Linear case (λ₁≫λ₂≃λ₃): diffusion is mainly in the direction corresponding to the largest eigenvalue,

$$\text{D}\text{≃λ}{}_1\text{D}{}_{\mathrm{l}}\text{=λ}{}_1\text{e}\text{̂}{}_1\text{e}\text{̂}{}^{\mathrm{T}}{}_1\text{.}$$

(2) Planar case (λ₁≃λ₂≫λ₃): diffusion is restricted to a plane spanned by the two eigenvectors corresponding to the two largest eigenvalues,

$$\text{D}\text{≃2λ}{}_1\text{D}{}_{\mathrm{p}}\text{=λ}{}_1\text{(}\text{e}\text{̂}{}_1\text{e}\text{̂}{}^{\mathrm{T}}{}_1\text{+}\text{e}\text{̂}{}_2\text{e}\text{̂}{}^{\mathrm{T}}{}_2\text{)}$$

(3) Spherical case (λ₁≃λ₂≃λ₃): isotropic diffusion,

$$\text{D}\text{≃3λ}{}_1\text{D}{}_{\mathrm{s}}\text{=λ}{}_1\text{(}\text{e}\text{̂}{}_1\text{e}\text{̂}{}^{\mathrm{T}}{}_1\text{+}\text{e}\text{̂}{}_2\text{e}\text{̂}{}^{\mathrm{T}}{}_2\text{+}\text{e}\text{̂}{}_3\text{e}\text{̂}{}^{\mathrm{T}}{}_3\text{)}$$

The coordinates of D in the trace-normalized tensor basis {D_l, D_p, D_s} are measures of how close the diffusion is to the generic cases line, plane and sphere. A similar tensor shape analysis has proven to be useful in a number of computer vision applications 16, 7. Since only the shape of the diffusion tensor is of interest, the coordinates derived should be normalized. For example, normalization using Tr{D} gives for the linear, planar and spherical measures:

$$\text{C}{}_{\mathrm{l}}\text{=}\text{λ}{}_1\text{−λ}{}_2\text{λ}{}_1\text{+λ}{}_2\text{+λ}{}_3\text{,}\text{C}{}_{\mathrm{p}}\text{=}\text{2(λ}{}_2\text{−λ}{}_3\text{)}\text{λ}{}_1\text{+λ}{}_2\text{+λ}{}_3\text{,}\text{C}{}_{\mathrm{s}}\text{=}\text{3λ}{}_3\text{λ}{}_1\text{+λ}{}_2\text{+λ}{}_3$$

Each of these measures lies in the range from zero to one, and their sum is one. An anisotropy measure describing the deviation from the spherical case is achieved as follows:

$$\text{C}{}_{\mathrm{a}}\text{=C}{}_{\mathrm{l}}\text{+C}{}_{\mathrm{p}}\text{=1−C}{}_{\mathrm{s}}\text{=}\text{λ}{}_1\text{+λ}{}_2\text{−2λ}{}_3\text{λ}{}_1\text{+λ}{}_2\text{+λ}{}_3$$

When applied to white matter, the linear measure, C_l, reflects the uniformity of tract direction within a voxel because it will be high only if the diffusion is restricted in two orthogonal directions. The anisotropy measure, C_a, indicates the relative restriction of the diffusion in the most restricted direction and will emphasize white matter tracts which within a voxel exhibit at least one direction of relatively restricted diffusion. Fig. 2A and B show coronal images of the geometrical measures C_l and C_a.

We applied the MRI technique, together with our mathematical description of the diffusion and the new display method, for the demonstration of major fiber tracts in the human brain using axial slices which include the corpus callosum, the internal capsule and the corticospinal tract. In addition we used the quantitative diffusion measures to investigate asymmetry in relation to sex and handedness. A comparison of anatomy between the right and left hemispheres of the brain derives its importance from the relationship between anatomical and functional asymmetry. Left hemispheric dominance for language skills is hypothesized to be associated with the average larger size of the left planum temporale found in 100 post-mortem adult brains [6]. Handedness has been found to affect hemispheric asymmetry, for example, in white right-handed individuals the anterior portion of the right hemisphere is generally wider and protrudes further anteriorly than the left, and the posterior portion of the left hemisphere is commonly wider and protrudes further posteriorly than the right. Although numerous investigations report cortical asymmetry, very few relate to white matter 20, 5, 19, 9.