Reliably quantifying longitudinal relaxation in heterogenous systems like white matter is challenging because measured parameters are sensitive to details of the measurement technique. In particular, cross-relaxation/magnetization exchange between aqueous and non-aqueous tissue components may lead to multi-exponential relaxation during inversion recovery, depending on the difference in the pools’ initial magnetizations. We use a generalization of the Bloch equations to fractional order to show that the additional component stemming from this exchange is better described by a stretched Mittag-Leffler function than a standard exponential in heterogenous systems. This approach may provide additional information about the material structure.
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