Pore-to-Pore Hopping Model for the Interpretation of the Pulsed Gradient Spin Echo Attenuation of Water Diffusion in Cell Suspension Systems

Abstract

A simplified pore-to-pore hopping model for the two-phase diffusion problem is developed for the analysis of the pulsed gradient spin echo (PGSE) attenuation of water diffusion in the condensed cell suspension systems. In this model, the two phases inside and outside the cells are treated as two different kinds of pores, and the spin-bearing molecules perform hopping diffusion between them. The size and the orientations of those two respective pores are considered, and then the diffraction pattern of the PGSE attenuation may be well simulated. Nevertheless, the intensity of the characteristic peak decreases with increasing membrane permeability, from which the exchange time may be estimated. We then analyze the experimental 1H PGSE results of the erythrocytes suspension system. The water-residence lifetime in the erythrocyte is obtained to be 10 ms, which is the same as that estimated from the two-region approximation. Furthermore, the PGSE attenuation curve of addition of p-Chloromercuribenzenesulfonate (p-CMBS) is also discussed. It predicts that the alignment of erythrocytes will become normal to the magnetic field direction after the addition of p-CMBS, and inspection using a light microscope confirms that result.

Pulsed-gradient spin-echo monitoring of restricted diffusion in multilayered structures

“…The role of permeable boundaries in diffusion-weighted experiments was studied by many authors [44][45][46][47][48][49][50][51][52][53][54]. In their seminal paper, Brownstein and Tarr used the spectral approach in order to investigate the signal attenuation due restricted diffusion inside a sphere subject to surface relaxation, which is also equivalent to one-way permeation of the spin-bearing particles outside the sphere [44].…”

“…In the framework of the narrow-pulse approximation (see Section 3.4), Kuchel and Durrant considered restricted diffusion inside two and four slabs separately by permeable membranes [50]. A simplified pore-to-pore hopping model for the twophase diffusion problem was developed by Jiang et al for the analysis of the pulsed-gradient spin-echo (PGSE) attenuation of water diffusion in the condensed cell suspension systems [51]. In this model, the two phases inside and outside the cells are treated as two different kinds of pores, and the spin-bearing molecules perform hopping diffusion between them.…”

Effects of permeable boundaries on the diffusion-attenuated MR signal: insights from a one-dimensional model

“…Numerous reports have been devoted to computer (Monte-Carlo) simulations or finite difference numerical solutions of the diffusion or Bloch-Torrey equations that make it possible to describe the MR signal in rather complicated multi-compartment structures [5,[14][15][16][17]. A phenomenological approach based on introducing residence or pre-exchange lifetimes of the magnetization in compartments (two-site K€ arger model and its three-and multi-site generalizations) has been developed in [18][19][20][21][22][23]. At long diffusion times, when a multi-compartment system can be characterized by a time-independent apparent diffusion coefficient (ADC), D, different theoretical models have been examined in [14,21,24].…”

The structural parameters of rigid matrix of saccharide-based gel described by short and long diffusion regime analysis

“…4-open circles). In the publication of [30], the pore size using pore-hopping model [34][35][36] was calculated as 64 lm for 2 wt% gel with toluene at 300 K, but this value strongly depends on the rate of temperature change during gelation process and even on the size of the tubes in which the process takes place. The results obtained in this work (the thick and length of rigid fibres of few and a dozen of lm, respectively) very well correspond with simulation of porosity-tortuosity relation which suggests small parallelepipeds shape of solid fibres [37].…”