A complete theory able to assess the longitudinal dispersion of a passive solute injected into an annular cavity subject to a pulsatile flow and a porous medium is provided. The Aris-Taylor method of statistical moments is combined with the Brinkman approach for porous flows and morphological dispersion, in order to get an analytical relationship for the time-dependent enhanced dispersion coefficient. The application of intrathecal drug delivery in the cerebrospinal fluid contained in the subaracnoid space is discussed in detail. The main result of the theory and its assumptions are also numerically validated through the use of a finite-volume solver. The role of several physiological features, such as the geometry, temporal frequency, and wavelength, of the pressure forcing are analyzed. It turns out that the presence of delicate strands of connective tissue, called trabeculae, that fill the cavity and link the innermost layer of meninges plays a crucial role. They in fact induce extra terms of morphological dispersion and act synergistically with pulsation to produce realistic times of drug delivery in clinically significant conditions. The results have potential for the optimization of delivery protocols of drug therapies of the central nervous system.

• Received 23 January 2019
• Accepted 16 March 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.043102

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