Abstract
Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.
Highlights
Microvascular perfusion in skeletal muscle is essential for nutrient supply and cellular metabolism [1]
The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that models the diffusion decay signal as a stretched exponential
The pseudo-diffusion coefficient (Dp ) and diffusion coefficient (D) show more scatter around the theoretical curve but largely follow the theoretical prediction. In both muscle groups displayed, these relationships were consistent under physiological conditions at rest and post-exercise hyperemia
Summary
Microvascular perfusion in skeletal muscle is essential for nutrient supply and cellular metabolism [1]. The consideration of appropriate signal models and DW-MRI acquisition schemes for quantifying physical properties of these tissue compartments is of particular interest for assessing perfusion in skeletal muscle. Compared with the classical single compartmental model which characterizes the random Brownian motion of all tissue water molecules as a monoexponential decay of MRI signal, the IVIM model uses a biexponential representation to differentiate the incoherent motion of intra-vascular blood perfusion and extra-vascular water proton diffusion. The FFD model is a parsimonious representation of anomalous superdiffusion that models the diffusion decay signal as a stretched exponential In this model, a single diffusion compartment is represented for an exponent value of 1 and superdiffusion is represented when the exponent decreases to values less than 1. An analytical framework that could transform the stretched exponential fit parameters to the intuitive picture of the two-compartment IVIM model could provide utility in comparing and interpreting experimental results
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