The b ‐Value Dependence for Higher‐Degree Spherical Harmonic Powers of the Diffusion MRI Signal Follows Stick Model Predictions in White Matter

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Abstract
Purpose: To compare the dependence on b ‐value of the spherical harmonic powers for the diffusion MRI signal in white matter to theoretical predictions from the stick model of water diffusion within axons. Methods: Diffusion MRI data were acquired at 3 T in three healthy adults with 10 b ‐value shells ( b = 1000–10 000 s/mm 2 ) and 64 directions per shell. For every b ‐value, the signal was expanded in spherical harmonics for all even degrees l up to l = 6, and the harmonic power for each degree was calculated. These were compared in selected white matter regions of interest to the theoretical predictions of the stick model, which depend on just two adjustable parameters: the intra‐axonal diffusivity and an amplitude factor for each degree. The intra‐axonal diffusivity was estimated independently using triple diffusion encoding MRI, leaving the amplitude factor as the sole fitting parameter. Results: Close agreement between experiment and theory was found for b 4000 s/mm 2 , the threshold where extra‐axonal water signal is expected to be strongly suppressed, for total cerebral white matter as well as separately within the genu, body, and splenium of the corpus callosum. These findings extend prior studies that either considered only the l = 0 harmonic power or treated the intra‐axonal diffusivity as a fitting parameter. Conclusion: In white matter, the b ‐value dependence of the diffusion MRI signal's even degree spherical harmonic powers up to l = 6 are relatively well‐described by the stick model of axons for b 4000 s/mm 2 .
Funding Information
  • National Institutes of Health (R01AG054159)
  • National Institutes of Health (R01AG057602)

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