In vivo efficacy of current stimuli computed by optimal tracking of neuron membrane voltage

We describe an application of optimal control theory to in vivo intracellular stimulation of pressure-sensitive mechanosensory (P-cell) neurons of the leech Hirudo verbana. The control objective seeks optimal stimuli that balance the minimization of stimulation current energy and the error of tracking an action potential evoked by a high-energy rectangular pulse. Tracking a known neuron response mitigates controllability and numerical solution issues and avoids the need to constrain stimulation currents. The reduced second-order neuron conductance model used in optimization was not fit to the target P-cell, but parameters were instead selected based on an assumed saddle-node on invariant circle bifurcation. Optimal stimuli that provided a range of tracking performance and energy minimization were computed prior to experimental work. Remarkably, simulated and biological neurons show the same tracking performance decrease at higher levels of stimulus current energy reduction. Numerical analysis of neuron model responses to optimal current perturbations revealed a phase space separatrix between regions with and without action potential trajectories, demonstrating high sensitivity to optimal current shape in a high-energy reduction case and verifying local optimality. This proof-of-concept study demonstrates that a control strategy based on reproducing action potential shapes can compute reduced-energy current stimulation waveforms that are effective in biological neurons. This effectiveness may extend to other biological neurons since the optimization method was applied to the same reduced-order model for other bifurcations and to a six-dimensional neuron. This method may be useful in research and future clinical applications, particularly as technological advances expand intracellular stimulation to applications previously limited to less effective extracellular methods. The high sensitivity of the neuron response to the optimal current waveform shapes could be useful in drug discovery, neuron disease diagnosis, toxin identification, and provide insights into neuron dynamics.