In this paper, the authors suggest a potential mechanism for magnetoreception in birds: as the Earth's magnetic field (taken to be homogeneous over sufficiently small spatial scales) passes through the loops of the semicircular canals of the inner ear, a voltage is induced in those canals according to Lenz's law, stimulating nearby sensory neurons.
I'm trying to figure out how to model the stimulation of an individual neuron by the induced voltage. If, as in the paper, we take the induced voltage to be oscillating as the bird rotates its head, then I think the most simple method is to work in a conductance-based modeling framework and treat the induced voltage as an oscillating voltage source $U(t)$ in the equivalent circuit of the neuron. The corresponding circuit diagram is shown below:
Then, the only modification to make to the original Hodgkin-Huxley formalism is that the ionic current $I_j$ for ion channel species $j$ with voltage-dependent conductance $g_j(V_m)$ and reversal potential $E_j$ is now expressed as
$$I_j = g_j(V_m) [V_m - E_j - U(t)]$$
where $V_m$ is the membrane potential of the neuron. Is there anything wrong with this approach (e.g. do I need to account for more complex aspects of the system such as separate neuronal compartments, have I gotten any aspect of the circuit wrong, etc.)?
