Apparent exchange rate imaging: On its applicability and the connection to the real exchange rate

Magn Reson Med. 2021 Aug;86(2):677-692. doi: 10.1002/mrm.28714. Epub 2021 Mar 10.


Purpose: Water exchange between the intracellular and extracellular space can be measured using apparent exchange rate (AXR) imaging. The aim of this study was to investigate the relationship between the measured AXR and the geometry of diffusion restrictions, membrane permeability, and the real exchange rate, as well as to explore the applicability of AXR for typical human measurement settings.

Methods: The AXR measurements and the underlying exchange rates were simulated using the Monte Carlo method with different geometries, size distributions, packing densities, and a broad range of membrane permeabilities. Furthermore, the influence of SNR and sequence parameters was analyzed.

Results: The estimated AXR values correspond to the simulated values and show the expected proportionality to membrane permeability, except for fast exchange (ie, AXR>20-30s-1 ) and small packing densities. Moreover, it was found that the duration of the filter gradient must be shorter than 2·AXR-1 . In cell size and permeability distributions, AXR depends on the average surface-to-volume ratio, permeability, and the packing density. Finally, AXR can be reliably determined in the presence of orientation dispersion in axon-like structures with sufficient gradient sampling (ie, 30 gradient directions).

Conclusion: Currently used experimental settings for in vivo human measurements are well suited for determining AXR, with the exception of single-voxel analysis, due to limited SNR. The detection of changes in membrane permeability in diseased tissue is nonetheless challenging because of the AXR dependence on further factors, such as packing density and geometry, which cannot be disentangled without further knowledge of the underlying cell structure.

Keywords: AXR; DWI; diffusion; exchange rate; membrane permeability.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cell Membrane Permeability
  • Diffusion
  • Diffusion Magnetic Resonance Imaging*
  • Humans
  • Monte Carlo Method
  • Water*


  • Water