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

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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.

ABBREVIATIONS CSF = cerebrospinal fluid; DN = diffuser/nozzle; PR = pumping or pulsation rate; RC = reference case.

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Article Information

Correspondence Alessandro Fiorindi: Neurosurgical Unit, Treviso Hospital, University of Padova, Treviso, Italy.

INCLUDE WHEN CITING Published online August 16, 2019; DOI: 10.3171/2019.5.JNS19276.

Disclosures The authors report no conflict of interest concerning the materials or methods used in this study or the findings specified in this paper.

© AANS, except where prohibited by US copyright law.



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    Schematic of DN pump driven by a rhythmic pressure: pumping mode (A) and supplying mode (B). Red arrows indicate pressure solicitation; blue arrows, the resulting flow rate (arrow length indicates the flow intensity). Figure is available in color online only.

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    The DN pump configuration proposed as a hydraulic model of the third ventricle–aqueduct–fourth ventricle complex given the peculiar shape of the complex. A: Thanks to flow reversal between the systolic and diastolic phases, the aqueduct behaves like a diffuser and a nozzle, respectively, and a craniocaudal net flow is generated (arrow length indicates flow intensity). B: Conceptual schematic of the proposed DN pump, with adopted notations for the flow rate, positive direction, and driving pressure. aq = aqueduct; p1 = pressure 1; p2 = pressure 2; Q12 = flow rate from chamber 1 to chamber 2; Q21 = flow rate from chamber 2 to chamber 1. Figure is available in color online only.

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    Pressure in the reservoirs and instantaneous flow rate through the DN (one cycle is shown). The red area represents the fluid volume going from chamber 1 to chamber 2 during the diffuser phase. The blue area is the volume going from chamber 2 to chamber 1 during the nozzle phase. The dotted area is the difference between red and blue areas; that is, it corresponds to the net volume pumped toward chamber 2 in one cycle. p = pressure; Q = flow rate; t = period. Figure is available in color online only.

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    A: Sagittal T1-weighted MR image outlining the supposed DN pump (green area with black contour). B: Magnification of box in panel A also showing diameters and lengths of the system (see text for further explanation). d and D = diameter; l and L = length. Figure is available in color online only.

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    Geometry of the aqueduct of Sylvius–fourth ventricle as extracted from the MR images for 10 subjects. We also show the geometry of the average patient (black outline). The patients in cases 9 and 10 (blue and light blue dotted lines) clearly appear as outliers and were excluded from the calculation of average data. Figure is available in color online only.

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    CSF flow in the aqueduct of Sylvius for the RC, with T = 1 second (A) and T = 5 seconds (B). In the remaining graphs, the behavior of CSF net flow in the aqueduct is shown as a function of various parameters. The gray area corresponds to the range of physiological flow. Graphs show dependence of Qnet on the PR and on period T of the ventricular pressure wave (C; the RC was adopted for the aqueduct), dependence of Qnet on the length L of the DN element for a fixed value of the diameter D (D), and dependence of Qnet on the diameter D of the DN element for L = 13 mm (E; a sketch of the examined configurations is also shown). T = 1 second was assumed in the computations reported in panels D and E. Figure is available in color online only.




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