Retrospective measurement of the diffusion tensor eigenvalues from diffusion anisotropy and mean diffusivity in DTI

Abstract

A simple theoretical framework to compute the eigenvalues of a cylindrically symmetric prolate diffusion tensor (D) from one of the rotationally-invariant diffusion anisotropy indices and average diffusivity is presented and validated. Cylindrical or axial symmetry assumes a prolate ellipsoid shape ( ሻ ‫؍‬ 1 > Ќ ‫؍‬ ( 2 ؉ 3 )/2; 2 ‫؍‬ 3 ). A prolate ellipsoid with such symmetry is largely satisfied in a number of white matter (WM) structures, such as the spinal cord, corpus callosum, internal capsule, and corticospinal tract. The theoretical model presented is validated using in vivo DTI measurements of rat spinal cord and human brain, where eigenvalues were calculated from both the set of diffusion coefficients and a tensor analysis. This method was used to retrospectively analyze literature data that reported tensor-derived average diffusivity, anisotropy, and eigenvalues, and similar eigenvalue measurements were obtained. The method provides a means to retrospectively reanalyze literature data that do not report eigenvalues. Diffusion tensor imaging (DTI) is a sensitive, noninvasive method that is increasingly being used to follow subtle changes in tissue microstructural organization (1-5) due to development (6 -8), cortical maturation (9 -11), normal aging (12-15), traumatic and diffuse axonal injuries (16), neurodegenerative and neurovascular diseases (17-19), drug abuse (20), and therapeutic intervention (21). DTI provides important qualitative and rotationally-invariant quantitative information about the integrity of compact fiber bundles, and may provide more sensitive and specific surrogate markers of disease activity, therapy, and clinical outcomes (1,6,20 -22). DT anisotropy is expressed as a single scalar index, such as fractional anisotropy (FA) (23) or relative anisotropy (RA), which is also known as A (24). A has also been termed normalized relative anisotropy (RA n ϭ 1/͌2RA ϭ A ) (25). While reduced diffusion anisotropy is interpreted as an indication of compromised fiber integrity, its specificity is somewhat limited (3-5).For instance, reduced anisotropy can result from excessive partial volume averaging from differently oriented fibers (1-5), edema (12), cerebrospinal fluid (CSF) (13), compromised myelin structure, changes in axonal morphology, or altered interaxonal spacing of fiber bundles (4,6,(15)(16)(17)(18)(19)(20)(21).Normal tissue maturation and development (6,9 -11), aging (12-15), pathology, injury, and recovery (16 -28) involve specific directional changes to the axonal structure and myelination (1)(2)(3)(4)(5)15,22,25). Indeed, recent studies have accumulated considerable evidence that individual DT eigenvalues provide enhanced pathological specificity compared to anisotropy and mean diffusivity indices (23-29). Beaulieu (4) summarized a number of studies prior to 2002 that highlighted the pathological specificity of the individual diffusivities. More recent DTI investigations using animal models of human diseases concluded that the tensor eigenvalues are more specific markers of m...

High-resolution diffusion tensor imaging in the substantia nigra of de novo Parkinson disease

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“…The utility of this formula and its analogous extension to σ(RA n ) in DTI parameter optimization (selection of optimal b-factor, and optimal partition N ref /N T ) is discussed below. The axially symmetric tensor [21,22] has two independent eigenvalues with diagonal covariance matrix; hence, the error in the estimated mean diffusivity…”

Diffusion Tensor Imaging at 3 Hours after Traumatic Spinal Cord Injury Predicts Long-Term Locomotor Recovery

“…Due to respiratory gating, the repetition time (TR * 1.2 sec) was slightly varied among animals according to the period of individual breathing cycle (*270 msec), with fixed echo time (TE) at 38 msec. Images, three slices per breath, were obtained with diffusion-sensitizing gradients applied in six orientations: (Gx,Gy,Gz) ¼ (1,1,0), (1,0,1), (0,1,1), (-1,1,0) , represents optimal experimental conditions within the gradient performance of our system for diffusion imaging of rodent model spinal cord (Budde et al, 2008;Hasan and Narayana, 2006;Kim et al, 2006Kim et al, , 2007Loy et al, 2007;Madi et al, 2005). Eight scans were averaged per k-space line, with field of view 10Â10 mm 2 , and data matrix 128Â256 (zero filled to 256Â256).…”