Parsimonious modeling of skeletal muscle perfusion: Connecting the stretched exponential and fractional Fickian diffusion

Reiter, David A., Adelnia, Fatemeh, Cameron, Donnie, Spencer, Richard G. and Ferrucci, Luigi (2021) Parsimonious modeling of skeletal muscle perfusion: Connecting the stretched exponential and fractional Fickian diffusion. Magnetic Resonance in Medicine, 86 (2). pp. 1045-1057. ISSN 0740-3194

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Abstract

PURPOSE: To develop an anomalous (non-Gaussian) diffusion model for characterizing skeletal muscle perfusion using multi-b-value DWI. THEORY AND METHODS: Fick's first law was extended for describing tissue perfusion as anomalous superdiffusion, which is non-Gaussian diffusion exhibiting greater particle spread than that of the Gaussian case. This was accomplished using a space-fractional derivative that gives rise to a power-law relationship between mean squared displacement and time, and produces a stretched exponential signal decay as a function of b-value. Numerical simulations were used to estimate parameter errors under in vivo conditions, and examine the effect of limited SNR and residual fat signal. Stretched exponential DWI parameters, α and D , were measured in thigh muscles of 4 healthy volunteers at rest and following in-magnet exercise. These parameters were related to a stable distribution of jump-length probabilities and used to estimate microvascular volume fractions. RESULTS: Numerical simulations showed low dispersion in parameter estimates within 1.5% and 1%, and bias errors within 3% and 10%, for α and D , respectively. Superdiffusion was observed in resting muscle, and to a greater degree following exercise. Resting microvascular volume fraction was between 0.0067 and 0.0139 and increased between 2.2-fold and 4.7-fold following exercise. CONCLUSIONS: This model captures superdiffusive molecular motions consistent with perfusion, using a parsimonious representation of the DWI signal, providing approximations of microvascular volume fraction comparable with histological estimates. This signal model demonstrates low parameter-estimation errors, and therefore holds potential for a wide range of applications in skeletal muscle and elsewhere in the body.

Item Type: Article
Additional Information: © 2021 International Society for Magnetic Resonance in Medicine.
Uncontrolled Keywords: anomalous diffusion,fractional calculus,hyperemia,intravoxel incoherent motion,microvascular volume,superdiffusion,radiology nuclear medicine and imaging ,/dk/atira/pure/subjectarea/asjc/2700/2741
Faculty \ School: Faculty of Medicine and Health Sciences > Norwich Medical School
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Depositing User: LivePure Connector
Date Deposited: 14 Apr 2021 23:53
Last Modified: 30 Sep 2021 16:21
URI: https://ueaeprints.uea.ac.uk/id/eprint/79760
DOI: 10.1002/mrm.28766

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