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Diffusion01:12

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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Models and Methods to Evaluate Transport of Drug Delivery Systems Across Cellular Barriers
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Exploring diffusion across permeable barriers at high gradients. II. Localization regime.

Denis S Grebenkov1

  • 1Laboratoire de Physique de la Matière Condensée, CNRS - Ecole Polytechnique, F-91128 Palaiseau, France.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|October 1, 2014
PubMed
Summary

We solved the Bloch-Torrey equation for diffusion across semi-permeable barriers. This work extends previous findings on pulsed-gradient spin-echo (PGSE) signals, revealing how barrier permeability affects diffusion behavior.

Keywords:
Bloch–Torrey equationDiffusionExchangeLocalizationPermeability

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Area of Science:

  • Physics
  • Physical Chemistry
  • Biophysics

Background:

  • The Bloch-Torrey equation models diffusion in magnetic fields.
  • Previous work predicted non-Gaussian diffusion signals (PGSE) at high gradients.
  • Semi-permeable barriers influence diffusion dynamics.

Purpose of the Study:

  • To derive an analytical solution for diffusion across multiple semi-permeable barriers using the Bloch-Torrey equation.
  • To generalize existing theories on pulsed-gradient spin-echo (PGSE) signal behavior.
  • To investigate the impact of barrier permeability on diffusion regimes.

Main Methods:

  • Analytical solution of the one-dimensional Bloch-Torrey equation.
  • Analysis of pulsed-gradient spin-echo (PGSE) signal behavior.
  • Mathematical modeling of diffusive exchange across barriers.

Main Results:

  • An analytical solution was developed for diffusion across multiple semi-permeable barriers.
  • The study characterizes the transition between localization and Gaussian diffusion regimes based on permeability.
  • High gradients enhance PGSE signal sensitivity to barrier permeability.

Conclusions:

  • The derived solution extends understanding of diffusion in confined systems with barriers.
  • Barrier permeability significantly alters the asymptotic behavior of diffusion signals.
  • The findings have implications for studying diffusion in complex biological and synthetic systems.