Derivation of a suitable exchange fraction expression to model diffusion-driven exchange with MR measurements.

Motivation: Transmembrane water exchange in brain tissue is a process often modelled via the first order kinetics reaction (1OKR) expression. However, this expression does not account for diffusion dynamics, suggesting it is not suitable to describe diffusion-driven exchange. Goal(s): Assess the difference between the 1OKR expression and the exchange fraction derived from a generally defined system. Approach: The exchange fraction was derived considering geometry, and compartment-specific relaxation processes of a system via the diffusion-reaction equation. Results: The derived exchange fraction features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the 1OKR expression. Impact: The two additional features of the exchange fraction found in this work provide additional insight on a system’s microstructure and properties. This expression can therefore be the basis of new biophysical models which more accurately describe the water exchange process.