Fig. 6: Computational results from a finite element simulation of the flow induced by a squeeze of intensity p₀ = 20 mm Hg applied over the squeeze zone.

The duration of the squeeze pulse is 2 s. The duration of the simulation is 10 s. The simulation is based on equations (1)—(9). The boundary conditions are described in the Supplementary Information. The parameters used in the simulation are found in Supplementary Table 1. As mentioned in the main text, the geometry we consider includes a rostral outflow point corresponding to the cribriform plate and a compliant vascular portion in the brain corresponding to the bridging veins to buffer pressure changes. These two elements are accounted for in the simulation by resistance boundary conditions (see ‘Boundary conditions’ section in the Supplementary Information). These resistances have similar mathematical expressions (Supplementary Table 1) and differ in the value of two resistance scaling parameters, denoted by \({\alpha }_{{\rm{CS}}}\) (for the central sinus) and \({\alpha }_{{\rm{out}}}\) (for the rostral outflow). Here their values are \({\alpha }_{{\rm{CS}}}={10}^{6}\) and \({\alpha }_{{\rm{out}}}={6\times 10}^{8}\). a, Initial geometry (not to scale) detailing model domains and boundaries. \({\Omega }_{{\rm{BR}}}\): brain and spinal cord domain (tan); \({\Omega }_{{\rm{SAS}}}\): CSF-filled domain (cyan); \(\Gamma\): \({\Omega }_{{\rm{BR}}}-{\Omega }_{{\rm{SAS}}}\) interface (red); \({\Gamma }_{{\rm{ext}}}\): external boundary of meningeal layer (blue); \({\Gamma }_{{\rm{SZ}}}\): squeeze zone (orange); \({\Gamma }_{{\rm{out}}}\): outlet boundary representing the cribriform plate CSF outflow pathway (green); \({\Gamma }_{{\rm{CS}}}\): central sinus boundary (purple). b, Average of pore pressure (in mm Hg) over \({\Omega }_{{\rm{BR}}}\) excluding the spinal cord over time. c, Spatial distribution of pore pressure (in mm Hg) over \({\Omega }_{{\rm{BR}}}\cup {\Omega }_{{\rm{SAS}}}\) at \(t=1\,{\rm{s}}\) during the squeeze pulse. d, Streamlines of filtration velocity \({{\boldsymbol{v}}}_{{\rm{flt}}}\) (that is, curves tangent to filtration velocity field; red lines with direction indicated by arrow tips) within \({\Omega }_{{\rm{BR}}}\) excluding the spinal cord, at \(t=1\,{\rm{s}}\) (left, middle of the squeeze pulse) and \(t=3\,{\rm{s}}\) (right, a squeeze pulse time interval from \(t=1\,{\rm{s}}\)). The streamlines overlay the color plot of the filtration velocity magnitude (in \({\rm{nm}}/{\rm{s}}\)), computed as \(\left|{v}_{{\rm{flt}}}\right|=\sqrt{{v}_{{\rm{flt}},r}^{2}+{v}_{{\rm{flt}},z}^{2}}\). The colorbar range is limited to 10 nm s⁻¹ to emphasize the spatial variation of the field. The maximum and minimum values of the field are indicated next to the triangles at the top and bottom of the colorbar, respectively. Because the SAS is extremely thin, the streamlines in this region are not shown. e, Volumetric fluid exchange rate \({Q}_{{\rm{flt}}}\) (in nL s⁻¹) over time across: the brain shell surface \({\Gamma }_{{\rm{BR}}}\) (blue), spinal cord surface \({\Gamma }_{{\rm{SC}}}\) (green), ventricle surface \({\Gamma }_{{\rm{V}}}\) (red) and central canal surface \({\Gamma }_{{\rm{CC}}}\) (light blue). \({Q}_{{\rm{flt}}} > 0\): fluid flow from \({\Omega }_{{\rm{BR}}}\) into \({\Omega }_{{\rm{SAS}}}\). \({Q}_{{\rm{flt}}}\) is computed as the integral of the normal component of filtration velocity over the surfaces indicated. The plot displays four lines, two that are seen easily (blue and green lines), and two that overlap and appear as horizontal lines near zero (red and light blue lines). This is due to the different orders of magnitude of \({Q}_{{\rm{flt}}}\) across the different portions of \(\Gamma\). f, Rostro-caudal (ros-cau) (blue) and medio-lateral (med-lat) (green) motion of point \({P}_{{\rm{br}}}\) on the brain surface (inset) over time caused by the squeeze pulse.