A new MRI-informed computational methodology for the characterization of drug dispersion in the spinal canal

Drug dispersion in intrathecal drug delivery processes, involving the injection of the drug into the cerebrospinal fluid (CSF) that fills the spinal canal, relies mainly on the slow Lagrangian drift stemming from the pulsatile motion induced by the cardiac and respiratory cycles. While MRI techniques can be successfully used to determine the spinal-canal anatomy and the pulsatile volumetric flow rate of CSF, they cannot describe with sufficient accuracy the slow Lagrangian drift, so that computational tools are needed to provide patient-specific predictions of drug dispersion. We present a new MRI-informed computational strategy that takes advantage of the slenderness of the canal and the existence of two different time scales, namely, the period of the CSF oscillatory motion and the much longer residence time associated with the Lagrangian drift. The development leads to a time-averaged, nonlinear integro-differential transport equation that describes the slow dispersion of the solute, thereby circumventing the need to describe the fast oscillatory motion. It is reasoned that the reduced-order description proposed here can provide accurate predictions of drug dispersion at a fraction of the computational cost associated with DNS computations.