Model equations
| Equation type | Equation | Equation number |
| Membrane potential equation | ||
| Membrane potential | ψ = (RT/F) ln[(α + [K+]e)/(β +[K+]a)] | 1 |
| Flux equations | ||
| Potassium flux | JKa = PK(ψF/RT)([K+]a − [K+]eexp(−ψF/RT))/(1 − exp(-ψF/RT)) − JKapump | 2 |
| Potassium pump flux | JKapump = 2JKapump(0) [1 + [K+]e(0)/(Δ[K+] − Δ[K+](0) − 2[K+]e(0))] | 3 |
| Water flux | JVa = PfvW(Φe − Φa) | 4 |
| Differential equations for volume and concentration | ||
| ECS volume | d(de)/dt = JVa | 5 |
| Astrocyte volume | d(da)/dt = −JVa | 6 |
| ECS [K+] | d[K+]e/dt + (Jva/de)[K+] = JKa/de | 7 |
| Astrocyte [K+] | d[K+]a/dt − (Jva/da)[K+] = −JKa/da | 8 |
| Integral equations for osmolarity | ||
| ECS osmolarity | Φe = Φe(0)/de + 2(∫JKadt)/de | 9 |
| Astrocyte osmolarity | Φa = Φa(0)/da-2(∫JKadt)/da | 10 |
| Non-K+ osmolarity | [non-K+]a = Φa(t + Δt) − 2[K+]a | 11 |
| Diffusion equations | ||
| K+ diffusion | ∂[K+]/∂t = Da ∂2[K+]/∂x2 | 12 |
| Non-K+ diffusion | ∂[non-K+]/∂t = Da ∂2[non-K+]/∂x2 | 13 |
| Equation for flux through the moving membrane | ||
| Flux boundary condition | ∂[K+]a/∂t = −JKa /δ | 14 |
| Equation type | Equation | Equation number |
| Membrane potential equation | ||
| Membrane potential | ψ = (RT/F) ln[(α + [K+]e)/(β +[K+]a)] | 1 |
| Flux equations | ||
| Potassium flux | JKa = PK(ψF/RT)([K+]a − [K+]eexp(−ψF/RT))/(1 − exp(-ψF/RT)) − JKapump | 2 |
| Potassium pump flux | JKapump = 2JKapump(0) [1 + [K+]e(0)/(Δ[K+] − Δ[K+](0) − 2[K+]e(0))] | 3 |
| Water flux | JVa = PfvW(Φe − Φa) | 4 |
| Differential equations for volume and concentration | ||
| ECS volume | d(de)/dt = JVa | 5 |
| Astrocyte volume | d(da)/dt = −JVa | 6 |
| ECS [K+] | d[K+]e/dt + (Jva/de)[K+] = JKa/de | 7 |
| Astrocyte [K+] | d[K+]a/dt − (Jva/da)[K+] = −JKa/da | 8 |
| Integral equations for osmolarity | ||
| ECS osmolarity | Φe = Φe(0)/de + 2(∫JKadt)/de | 9 |
| Astrocyte osmolarity | Φa = Φa(0)/da-2(∫JKadt)/da | 10 |
| Non-K+ osmolarity | [non-K+]a = Φa(t + Δt) − 2[K+]a | 11 |
| Diffusion equations | ||
| K+ diffusion | ∂[K+]/∂t = Da ∂2[K+]/∂x2 | 12 |
| Non-K+ diffusion | ∂[non-K+]/∂t = Da ∂2[non-K+]/∂x2 | 13 |
| Equation for flux through the moving membrane | ||
| Flux boundary condition | ∂[K+]a/∂t = −JKa /δ | 14 |