Fig. 1
From: Blood osmolytes such as sugar can drive brain fluid flows in a poroelastic model
Schematic of the model domain consisting of a deformable porous tissue (soft yellow) with uniform vasculature. (a) Coronal MRI from reference9 in which the ventricles are enlarged due to 50 mOsm hypertonic stimulation of the blood (lower panel) compared to baseline ketamine/xylazine anesthesia (upper panel, reprinted with permission). (b) A coronal section of the mouse brain is simplified as a slice of a symmetrical tissue sphere (c) with an inner sphere representing the ventricles. (d, e) Our model considers the brain to be uniform (d) by averaging out volumes with arterioles, capillaries, and venules (e). (f) To get a rough intuition for why divergence should equal absorption, consider the one-dimensional example: If interstitial fluid enters a small cube (magnified red box from e) with side-lengths \(\Delta x\) at velocity \({v}_{1}\) and exits with velocity reduced to \({v}_{2}={v}_{1}-q\Delta x\) due to capillary absorption, then the divergence of the fluid velocity is \(\nabla \cdot {\varvec{v}}=\left({v}_{1}-{v}_{2}\right)/\Delta x=-q\). We use this proposition along with standard osmotic membrane flow and the Darcy law for porous fluid flow to find a screened Poisson equation for the interstitial fluid pressure (Eq. 3).
