A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS.

Secretory diarrheas such as cholera are a major cause of morbidity and mortality in developing countries. We previously introduced the concept of antisecretory therapy for diarrhea using chloride channel inhibitors targeting the cystic fibrosis transmembrane conductance regulator channel pore on the extracellular surface of enterocytes. However, a concern with this strategy is that rapid fluid secretion could cause convective drug washout that would limit the efficacy of extracellularly targeted inhibitors. Here, we developed a convection–diffusion model of washout in an anatomically accurate three-dimensional model of human intestine comprising cylindrical crypts and villi secreting fluid into a central lumen. Input parameters included initial lumen flow and inhibitor concentration, inhibitor dissociation constant ( K d ), crypt/villus secretion, and inhibitor diffusion. We modeled both membrane-impermeant and permeable inhibitors. The model predicted greatly reduced inhibitor efficacy for high crypt fluid secretion as occurs in cholera. We conclude that the antisecretory efficacy of an orally administered membrane-impermeant, surface-targeted inhibitor requires both (a) high inhibitor affinity (low nanomolar K d ) to obtain sufficiently high luminal inhibitor concentration (>100-fold K d ), and (b) sustained high luminal inhibitor concentration or slow inhibitor dissociation compared with oral administration frequency. Efficacy of a surface-targeted permeable inhibitor delivered from the blood requires high inhibitor permeability and blood concentration (relative to K d ).

Potassium (K + ) ions released into brain extracellular space (ECS) during neuroexcitation are efficiently taken up by astrocytes. Deletion of astrocyte water channel aquaporin-4 (AQP4) in mice alters neuroexcitation by reducing ECS [K + ] accumulation and slowing K + reuptake. These effects could involve AQP4-dependent: (a) K + permeability, (b) resting ECS volume, (c) ECS contraction during K + reuptake, and (d) diffusion-limited water/K + transport coupling. To investigate the role of these mechanisms, we compared experimental data to predictions of a model of K + and water uptake into astrocytes after neuronal release of K + into the ECS. The model computed the kinetics of ECS [K + ] and volume, with input parameters including initial ECS volume, astrocyte K + conductance and water permeability, and diffusion in astrocyte cytoplasm. Numerical methods were developed to compute transport and diffusion for a nonstationary astrocyte–ECS interface. The modeling showed that mechanisms b–d, together, can predict experimentally observed impairment in K + reuptake from the ECS in AQP4 deficiency, as well as altered K + accumulation in the ECS after neuroexcitation, provided that astrocyte water permeability is sufficiently reduced in AQP4 deficiency and that solute diffusion in astrocyte cytoplasm is sufficiently low. The modeling thus provides a potential explanation for AQP4-dependent K + /water coupling in the ECS without requiring AQP4-dependent astrocyte K + permeability. Our model links the physical and ion/water transport properties of brain cells with the dynamics of neuroexcitation, and supports the conclusion that reduced AQP4-dependent water transport is responsible for defective neuroexcitation in AQP4 deficiency.