Extended Data Fig. 7: Ancillary results to those presented in Fig. 6 from the same finite element simulation of the flow induced by a squeeze of intensity p₀ = 20 mmHg applied over the SZ.

The duration of the squeeze pulse is \(2\,{\rm{s}}\). The duration of the simulation is \(10\,{\rm{s}}\). The simulation is based on Equations (1)—(9). The boundary conditions are described in the Supplementary Material. 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 (cf. the Boundary conditions section in the Supplementary Information). These resistances have similar mathematical expressions (cf. 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. Average of normal filtration velocity (in \({\rm{\mu }}{\rm{m}}/{\rm{s}})\) over each of the cranial and spinal SAS sections (shown in the inset) over time. The plot displays 4 lines, with the blue one appearing as horizontal line near zero –due to the different orders of magnitude of the filtration velocity across the different SAS sections. The unit normal vector to the sections points in the rostral direction. b. Average of normal filtration velocity (in \({\rm{nm}}/{\rm{s}})\) over each of the brain and spinal cord sections (shown in the inset) over time. The plot displays 3 lines, with the orange one appearing as horizontal line near zero –due to the different orders of magnitude of the filtration velocity across \({\Omega }_{{\rm{BR}}}\). The unit normal vector to the sections points in the rostral direction. c. Average of normal filtration velocity (in \({\rm{\mu }}{\rm{m}}/{\rm{s}})\) over each of the central canal sections (shown in the inset) over time. The unit normal vector to the sections points in the rostral direction. d. Trajectories of points P1–P6 (shown in the inset) on the surface of the brain: traces of the points indicated in the inset over the time interval \(0 < t < 10\,{\rm{s}}\). e. Volumetric fluid outflow \({Q}_{{\rm{out}}}\) (in \({\rm{nL}}/{\rm{s}})\) through the outlet boundary \({\Gamma }_{{\rm{out}}}\) over time. \({Q}_{{\rm{out}}} > 0\): fluid flow out of \({\Omega }_{{\rm{SAS}}}\). \({Q}_{{\rm{out}}}\) is computed as the integral of the normal component of filtration velocity over the surface indicated. f. Average force \(F\) (in \({\rm{N}}\)) exerted by CSF over time onto brain and spinal cord during the squeeze. \(F(t)\) is computed as the integral average of \(({\boldsymbol{m}}\cdot {\bf{T}}{\boldsymbol{m}})\) over the surface \({\Gamma }_{{\rm{BR}}}\cup {\Gamma }_{{\rm{SC}}}\), where \({\bf{T}}\) is the total Cauchy stress acting on the mixture in the SAS and \({\boldsymbol{m}}\) is the outward unit normal to the surface indicated.