Multi-scale multi-physics model of brain interstitial water flux by transcranial Direct Current Stimulation

Abstract

Objective. Transcranial direct current stimulation (tDCS) generates sustained electric fields in the brain, that may be amplified when crossing capillary walls (across blood-brain barrier, BBB). Electric fields across the BBB may generate fluid flow by electroosmosis. We consider that tDCS may thus enhance interstitial fluid flow. Approach. We developed a modeling pipeline novel in both (1) spanning the mm (head), μm (capillary network), and then nm (down to BBB tight junction (TJ)) scales; and (2) coupling electric current flow to fluid current flow across these scales. Electroosmotic coupling was parametrized based on prior measures of fluid flow across isolated BBB layers. Electric field amplification across the BBB in a realistic capillary network was converted to volumetric fluid exchange. Main results. The ultrastructure of the BBB results in peak electric fields (per mA of applied current) of 32-63 V m − 1 across capillary wall and >1150 V m − 1 in TJs (contrasted with 0.3 V m − 1 in parenchyma). Based on an electroosmotic coupling of 1.0 × 10−9 - 5.6 × 10−10 m 3 s − 1 m 2 per V m − 1 , peak water fluxes across the BBB are 2.44 × 10−10 - 6.94 × 10−10 m 3 s − 1 m 2 , with a peak 1.5 × 10−4 - 5.6 × 10−4 m 3 mi n − 1 m 3 interstitial water exchange (per mA). Significance. Using this pipeline, the fluid exchange rate per each brain voxel can be predicted for any tDCS dose (electrode montage, current) or anatomy. Under experimentally constrained tissue properties, we predicted tDCS produces a fluid exchange rate comparable to endogenous flow, so doubling fluid exchange with further local flow rate hot spots (‘jets’). The validation and implication of such tDCS brain ‘flushing’ is important to establish.