Cumulant expansions for measuring water exchange using diffusion MRI

The Journal of Chemical Physics
Lipeng NingYogesh Rathi

Abstract

The rate of water exchange across cell membranes is a parameter of biological interest and can be measured by diffusion magnetic resonance imaging (dMRI). In this work, we investigate a stochastic model for the diffusion-and-exchange of water molecules. This model provides a general solution for the temporal evolution of dMRI signal using any type of gradient waveform, thereby generalizing the signal expressions for the Kärger model. Moreover, we also derive a general nth order cumulant expansion of the dMRI signal accounting for water exchange, which has not been explored in earlier studies. Based on this analytical expression, we compute the cumulant expansion for dMRI signals for the special case of single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences. Our results provide a theoretical guideline on optimizing experimental parameters for SDE and DDE sequences, respectively. Moreover, we show that DDE signals are more sensitive to water exchange at short-time scale but provide less attenuation at long-time scale than SDE signals. Our theoretical analysis is also validated using Monte Carlo simulations on synthetic structures.

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Citations

Sep 14, 2019·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Markus NilssonPia C Sundgren
Oct 14, 2020·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Filip SzczepankiewiczCarl-Fredrik Westin
Nov 5, 2020·Journal of Neuroscience Methods·Rafael N HenriquesAndrada Ianuş
Nov 27, 2020·Journal of Neuroscience Methods·Filip SzczepankiewiczMarkus Nilsson
Mar 24, 2021·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Björn LampinenMarkus Nilsson
Jul 31, 2021·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Rafael Neto HenriquesNoam Shemesh

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