On random walks and entropy in diffusion‐weighted magnetic resonance imaging studies of neural tissue. Issue 2 (February 2014)

• Record Type: Journal Article
• Authors: Ingo, Carson; Magin, Richard L.; Colon‐Perez, Luis; Triplett, William; Mareci, Thomas H.
• Is Part Of: Magnetic resonance in medicine. Volume 71:Issue 2(2014:Feb.)
• Page Start: spcone
• Page End: spcone
• Publication Date: 2014-02
• Subjects: Nuclear magnetic resonance -- Periodicals; Electron paramagnetic resonance -- Periodicals; 616.07548
• DOI: 10.1002/mrm.25153
• Languages: English
• ISSNs: 0740-3194

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <sec id="mrm25153-sec-0001" sec-type="section"> <title>Purpose</title> <p>In diffusion‐weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay. However, there have been numerous reports of signal decays that are not monoexponential, particularly in the white matter.</p> </sec> <sec id="mrm25153-sec-0002" sec-type="section"> <title>Theory</title> <p>We modeled diffusion in neural tissue from the perspective of the continuous time random walk. The characteristic diffusion decay is represented by the Mittag‐Leffler function, which relaxes a priori assumptions about the governing statistics. We then used entropy as a measure of the anomalous features for the characteristic function.</p> </sec> <sec id="mrm25153-sec-0003" sec-type="section"> <title>Methods</title> <p>Diffusion‐weighted MRI experiments were performed on a fixed rat brain using an imaging spectrometer at 17.6 T with <italic>b</italic>‐values arrayed up to 25, 000 s/mm<sup>2</sup>. Additionally, we examined the impact of varying either the gradient strength, <italic>q</italic>, or mixing time, Δ, on the observed diffusion dynamics.</p> </sec> <sec id="mrm25153-sec-0004" sec-type="section"> <title>Results</title> <p>In white and gray matter regions, the Mittag‐Leffler and entropy parameters demonstrated new information regarding subdiffusion and produced different image contrast from that of the classical diffusion coefficient. The choice of weighting on <italic>q</italic> and Δ produced different image contrast within the regions of interest.</p> </sec> <sec id="mrm25153-sec-0005" sec-type="section"> <title>Conclusion</title> <p>We propose these parameters have the potential as biomarkers for morphology in neural tissue. Magn Reson Med 71:617–627, 2014. © 2013 Wiley Periodicals, Inc.</p> </sec> </abstract>