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Optimal phase control of biological oscillators using augmented phase reduction.

Bharat Monga1, Jeff Moehlis2

  • 1Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA. monga@ucsb.edu.

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We developed a new optimal control algorithm that minimizes energy use for oscillator phase control. This method effectively addresses cardiac alternans and neurological tremors, outperforming prior techniques.

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Area of Science:

  • * Dynamical systems and control theory.
  • * Computational neuroscience and physiology.

Background:

  • * Oscillators are fundamental in biological and physical systems, exhibiting periodic behavior.
  • * Controlling oscillator phase with minimal energy is crucial for applications like medicine and neuroscience.
  • * Existing methods struggle with large phase changes or specific system dynamics.

Purpose of the Study:

  • * To develop a novel optimal control algorithm for precise oscillator phase manipulation.
  • * To minimize energy input and preserve the oscillator's natural trajectory.
  • * To apply this algorithm to physiological problems like cardiac alternans and tremor.

Main Methods:

  • * Employed a two-dimensional reduction technique utilizing isochrons and isostables.
  • * Integrated the control algorithm with physiological models for cardiac alternans.
  • * Compared performance against standard phase reduction methods.

Main Results:

  • * The novel algorithm achieves minimal energy input and preserves the orbit.
  • * Successfully demonstrated application in eliminating cardiac alternans.
  • * Showed superior effectiveness over previous methods, especially for large phase shifts.

Conclusions:

  • * The developed optimal control algorithm offers a robust and efficient method for oscillator phase control.
  • * This technique has potential therapeutic applications for essential tremor, Parkinsonian tremor, and circadian rhythm disorders.
  • * The algorithm's efficacy is validated across diverse models, including cardiac, neuronal, and circadian systems.