diff --git a/docs/formulation.tex b/docs/formulation.tex index 1ecc9843e32627e7a05cb77986b85e12f41bce08..d44d8cff2efe28a163c9444c6b41b8c685d3bcfc 100644 --- a/docs/formulation.tex +++ b/docs/formulation.tex @@ -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 diff --git a/docs/symbols.tex b/docs/symbols.tex index 90ac0ac5a823652d0e42d97b2167ac9f2bd84ce0..19db4a374eb9a3697bcb8971ca2cca9e0b40877e 100644 --- a/docs/symbols.tex +++ b/docs/symbols.tex @@ -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}