The K\"arger vs bi-exponential model: theoretical insights and experimental validations

TL;DR

This paper compares three water exchange models in pulsed-gradient spin-echo measurements, providing theoretical insights and experimental validation, and introduces a new modality for estimating water exchange time.

Contribution

It offers a comparative analysis of the K"arger, modified K"arger, and bi-exponential models, highlighting their differences, similarities, and practical applications in experimental data fitting.

Findings

K"arger and modified K"arger models fit experimental data closely.

Bi-exponential model offers a physical interpretation and new measurement modality.

All models effectively describe water exchange in yeast cell suspensions.

Abstract

We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the K\"arger model, and a modified K\"arger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The K\"arger model and the modified K\"arger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.