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Commit 2dc6633c authored by Benjamin Cumming's avatar Benjamin Cumming
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small corrections to FVM docs

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......@@ -47,7 +47,7 @@ where
\item $V$ is the potential relative to the ECM $[mV]$
\item $a$ is the cable radius $(mm)$, and can vary with $x$
\item $c_m$ is the {specific membrane capacitance}, approximately the same for all neurons $\approx 10~nF/mm^2$. Related to \emph{membrane capacitance} $C_m$ by the relationship $C_m=c_{m}A$, where $A$ is the surface area of the cell.
\item $i_m$ is the membrane current $[A]$. The total contribution from ion and synaptic channels is expressed as a the product of current per unit area $i_m$ and the surface area.
\item $i_m$ is the membrane current $[A\cdot/mm^{2}]$ per unit area. The total contribution from ion and synaptic channels is expressed as a the product of current per unit area $i_m$ and the surface area.
\item $i_e$ is the electrode current flowing into the cell, divided by surface area, i.e. $i_e=I_e/A$.
\item $r_L$ is intracellular resistivity, typical value $1~k\Omega \text{cm}$
\end{itemize}
......@@ -230,7 +230,7 @@ The equations can be rearranged to have all unknown voltage values on the lhs, a
\begin{align}
& V_i^{k+1} + \sum_{j\in\mathcal{N}_i} {\frac{\alpha_{ij}}{\sigma_i} (V_i^{k+1}-V_j^{k+1})}
\nonumber \\
= & V_i^k - \frac{2\Delta t}{ac_m}(i_m^{k} - i_e),
= & V_i^k - \frac{\Delta t}{c_m}(i_m^{k} - i_e),
\label{eq:ode_linsys}
\end{align}
where the value
......
......@@ -11,7 +11,7 @@
voltage & $V$ & volt $V$ & potential work per unit charge \\
resistance & $R$ & ohm $\Omega$ & recall Ohm's law $V=IR$ \\
capacitance& $C$ & farad $F$ & $C=\frac{q}{V}$, $[J\cdot C^{2}]$\\
conductance& $g$ & siemens $S$ & \\
conductance& $g$ & siemens $S$ & $g=1/R$ i.e. inverse of resistance \\
\hline
\end{tabular}
......
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