On parameter estimation for neuron models
J.L. Madden, Zina Ben Miled, Raymond C. Y. Chin, John H. Schild · 2002
Membrane bound ion channels give rise to many of the electrical signal characteristics exhibited by neurons. Ion channel models of neural function such as that proposed by Hodgkin-Huxley can be represented as a set of differential equations. Solving these differential equations for a given neuron involves finding optimal values for the parameters that define the Hodgkin-Huxley equations. Most often, these parameters are evaluated using an optimization algorithm that takes as input ion channel current data recorded from a neuron using the voltage clamp technique. Real-valued optimization algorithms often fail to find a global optimum for the parameters of the Hodgkin-Huxley differential equations. Here, the authors show that interval analysis based optimization algorithm, a branch and bound algorithm, provides an accurate solution for the Hodgkin-Huxley model.