Derive the cable equation for a uniform cylinder, with
optimal boundary conditions.
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Answer Posted / Rashmi Yadav
The cable equation is a partial differential equation that describes the voltage distribution along an axon (a uniform cylinder). It takes into account the capacitance, resistance, and leakage conductance of the membrane, as well as the ionic currents flowing through various channels. The optimal boundary conditions assume no current flows across the ends of the axon, which simplifies the equation to: dv/dt = (-r²/(2a²)) * d²(v - v_m) / dx² + I_ion(x,t), where a is the radius, r is the radial distance from the axis, and v_m is the membrane potential at infinity.
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