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. 2020 Jun 22;10:10102. doi: 10.1038/s41598-020-66887-w

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Heartrate pulsations drive oscillatory, but not directional flow. Large non-physiological pulsations are required for appreciable peristaltic pumping. (a) Schematic of the axisymmetric peristatic pumping model. The arterial wall undergoes peristatic movement, while the outer wall of the PVS is fixed. The length of the PVS is taken as one wavelength of the peristaltic wave (λ) with periodic boundary conditions at the two axial ends. (b) Schematic of the fluid motion during periodic peristalsis. The fluid displaced by the moving wall should move with lower resistance along the direction of the peristaltic wave than in the opposite direction. This difference in flow resistance results in net forward pumping. (c) The magnitude of the axial velocity is denoted by color, with arrows showing the direction. The half-wave amplitude of the peristaltic wave is 0.8% of the vessel radius. The deformations are scaled by a factor of 50 in the figure to clearly show the arterial wall movement. (d) The plots show the relative phase between arterial wall velocity and the centerline fluid velocity at the same axial (z) location (midpoint, z = λ/2). There is a 270° phase difference between the wall velocity and fluid velocity. (e) The trajectory (in z) of a fluid particle at the center of the PVS, where the amplitude of the peristaltic wave is similar to heartbeat driven pulsation^6,7 (0.8% peak-to-peak change in arterial radius). The flow is mostly oscillatory with very little unidirectional movement. (f) The trajectory (in z) of a fluid particle at the center of the PVS, where the amplitude of the peristaltic wave is unrealistically large (50% peak-to-peak change in arterial radius). This trajectory with appreciable unidirectional movement looks similar to experimental results^6,7. (g) Plot showing the ratio of mean flow speed (average unidirectional flow velocity) to oscillatory velocity (peak velocity change in a cycle) as a function of the amplitude of the peristaltic wave. The shaded region shows the normal amplitude of pulsation cerebral arteries (1–4% of arterial radius peak-to-peak). Note that in this range, the oscillatory velocity is ~2 orders of magnitude higher than the pumping velocity (a–d). were generated with COMSOL Multiphysics 5.4(http://comsol.com). (e–g) were generated with MATLAB 2019b(https://www.mathworks.com/products/matlab.html).