The basic flow equations of electrophysiology in the presence of chemical reactions: I. Development of the equations |
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Authors: | Peter B Bright |
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Institution: | 1. Committee on Mathematical Biology, University of Chicago, Chicago, USA
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Abstract: | Starting from the basic flux equation, it is possible to obtain an integral form relating the current componentsI i at an arbitrary pointr 2 to the distribution of mobilities and concentrationsc i, potential forces\(\bar \mu \), and chemical productivityp i without any restrictive assumptions such as constant mobilities, constant field, steady state, or electrical neutrality. The equation is$$\begin{gathered} I_i (r_2 ) = G_i (r_2 )\left {\Delta \bar \mu _i - \int_{r_1 }^{r_2 } {z_i } FA\left( {p_i - dc_i /dt} \right)\left( {\frac{1}{{G_i (r)}}} \right)dr} \right]; \hfill \\ G_i (r) = 1/\int_{r_1 }^r {\frac{{dr}}{{z_i^2 F^2 c_i u_i }}.} \hfill \\ \end{gathered} $$ |
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