Form follows function: estimation of CSF flow in the third ventricle-aqueduct-fourth ventricle complex modeled as a diffuser/nozzle pump.

Abstract

In the last 20 years, researchers have debated cerebrospinal fluid (CSF) dynamics theories, commonly based on the classic bulk flow perspective. New hypotheses do not consider a possible hydraulic impact of the ventricular morphology. The present study investigates, by means of a mathematical model, the eventual role played by the geometric shape of the "third ventricle-aqueduct-fourth ventricle" complex in CSF circulation under the assumption that the complex behaves like a diffuser/nozzle (DN) pump. DN pumps are quite recent devices introduced as valveless micropumps in various industrial applications given their property of driving net flow when subjected to rhythmic pulsations. A novel peculiar DN pump configuration was adopted in this study to mimic the ventricular complex, with two reservoirs (the ventricles) and one tube provided with a conical reach (the aqueduct-proximal fourth ventricle). The flow was modeled according to the classic equations of laminar flow, and the external rhythmic pulsations forcing the system were reproduced as a pulsatile pressure gradient between the chambers. Several physiological scenarios were implemented with the integration of data acquired by MRI in 10 patients with no known pathology of CSF dynamics, and a quantitative analysis of the effect of geometric and hydraulic parameters (diverging angle, sizes, frequency of pulsations) on the CSF net flow was performed. The results showed a craniocaudal net flow in all the given values, consistent with the findings of cine MRI studies. Moreover, the net flow estimated for the analyzed cohort of patients ranged from 0.221 to 0.505 ml/min, remarkably close to the values found on phase contrast cine MRI in healthy subjects. Sensitivity analysis underlines the pivotal role of the DN configuration, as well as of the frequency of forcing pressure, which promotes a relevant net flow considering both the heart and respiration rate. This work suggests that the geometry of the third ventricle-aqueduct-fourth ventricle complex, which resembles a diverter, appears to be functional in the generation of a net craniocaudal flow and potentially has an impact on CSF dynamics. These conclusions can be drawn by observing the analogies between the shape of the ventricles and the geometry of DN pumps and by recognizing the basis of the mathematical model of the simplified third ventricle-aqueduct-fourth ventricle complex proposed.