title: Minimum energy control for in vitro neurons.
abstract: OBJECTIVE
  To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats.
  
  
  METHODS
  The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron's biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron's phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential.
  
  
  RESULTS
  The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli.
  
  
  CONCLUSIONS
  The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments.
authors.affiliation: Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA. nabi@engineering.ucsb.edu
authors.forename: Ali
authors.initials: A
authors.lastname: Nabi
authors.forename: Tyler
authors.initials: T
authors.lastname: Stigen
authors.forename: Jeff
authors.initials: J
authors.lastname: Moehlis
authors.forename: Theoden
authors.initials: T
authors.lastname: Netoff
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D002478:Cells, Cultured; D003198:Computer Simulation; D004558:Electric Stimulation / Q000379:methods*; D004735:Energy Transfer / Q000502:physiology*; D025461:Feedback, Physiological / Q000502:physiology; D008959:Models, Neurological; D017966:Pyramidal Cells / Q000502:physiology*; D020318:Rats, Long-Evans