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Cumulant Expansions for Measuring Water Exchange using Diffusion MRI

Institution:
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Publisher:
American Institute of Physics
Publication Date:
Feb-2018
Journal:
J Chem Phys
Volume Number:
148
Issue Number:
7
Pages:
074109
Citation:
J Chem Phys. 2018 Feb 21;148(7):074109.
PubMed ID:
29471656
PMCID:
PMC5821513
Appears in Collections:
NAC, LMI, SPL
Sponsors:
R21 MH115280/MH/NIMH NIH HHS/United States
R01 MH097979/MH/NIMH NIH HHS/United States
R01 MH074794/MH/NIMH NIH HHS/United States
R01 MH111917/MH/NIMH NIH HHS/United States
P41 EB015902/EB/NIBIB NIH HHS/United States
Generated Citation:
Ning L., Nilsson M., Lasič S., Westin C-F., Rathi Y. Cumulant Expansions for Measuring Water Exchange using Diffusion MRI. J Chem Phys. 2018 Feb 21;148(7):074109. PMID: 29471656. PMCID: PMC5821513.
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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.