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Cumulant expansions for measuring water exchange using diffusion MRI.

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This study introduces a new stochastic model for water diffusion and exchange across cell membranes, measurable by diffusion magnetic resonance imaging (dMRI). The model generalizes dMRI signal expressions and offers insights into optimizing single and double diffusion encoding sequences.

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Area of Science:

  • Biophysics
  • Magnetic Resonance Imaging
  • Cellular Biology

Background:

  • Water exchange across cell membranes is crucial for biological processes.
  • Diffusion magnetic resonance imaging (dMRI) is a key technique for measuring this exchange.
  • Existing models for dMRI signal analysis have limitations in handling complex exchange dynamics.

Purpose of the Study:

  • To develop a generalized stochastic model for water diffusion and exchange in dMRI.
  • To derive a novel nth order cumulant expansion for dMRI signals with water exchange.
  • To provide theoretical guidelines for optimizing single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences.

Main Methods:

  • Developed a stochastic model for diffusion and exchange of water molecules.
  • Derived a general nth order cumulant expansion for dMRI signals.
  • Computed cumulant expansions for SDE and DDE sequences.
  • Validated the theoretical analysis using Monte Carlo simulations.

Main Results:

  • The model provides a general solution for temporal evolution of dMRI signal for arbitrary gradient waveforms.
  • The derived cumulant expansion offers a new analytical tool for dMRI signal analysis with water exchange.
  • DDE sequences show higher sensitivity to water exchange at short timescales compared to SDE.
  • SDE sequences provide greater signal attenuation at long timescales than DDE sequences.

Conclusions:

  • The developed stochastic model and cumulant expansion offer a robust theoretical framework for dMRI analysis of water exchange.
  • The findings provide practical guidelines for optimizing experimental parameters in SDE and DDE sequences.
  • This work advances the understanding of water transport dynamics in biological systems using dMRI.