The diffusion propagator fully characterizes the diffusion process, which is highly sensitive to the confining boundaries and the structure within enclosed pores. While magnetic resonance has extensively been used to observe various features of the diffusion process, its full characterization has been elusive. Here, we address this challenge by employing a special sequence of magnetic field gradient pulses for measuring the diffusion propagator, which allows for “listening to the drum,” mapping structural dispersity, and determining not only the pore’s shape but also diffusive dynamics within it.
The distribution of net displacements, commonly referred to as the ensemble average propagator, has been measured using Stejskal-Tanner experiments. Here, a recently introduced diffusion sensitization method is employed in a similar manner to obtain the distribution of mean positions. By utilizing the two schemes synergistically, low b-value measurements are employed to decouple dynamic second moments from static ones. We illustrate our findings on an excised mouse spinal cord imaged using a benchtop MRI scanner.
We demonstrate the experimental determination of the diffusion propagator, indicating a conditional probability density function with two spatial arguments. To this end, a recently introduced method was implemented on a benchtop MR scanner and incorporated into imaging sequences. The data involving two independent wavenumbers were transformed from the measurement domain to the spatial domain, yielding an apparent diffusion propagator. Experiments on freely diffusing water provides accurate determination of the diffusion propagator while apparent propagators measured in mouse spinal cord reveal significant differences between white and gray matter regions.
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