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Mathematical Biosciences and Engineering

2026, Volume 23, Issue 4: 940-986. doi: 10.3934/mbe.2026037
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Modeling neural dynamics with optical nonlinearity: From classical models to optogenetic approaches

  • 1.
    Institute of Information Technologies, Mathematics and Mechanics, Lobachevsky University, Nizhny Novgorod, Russia
  • 2.
    Scientific and Educational Mathematical Center ´Mathematics of Future Technologies´, Lobachevsky University, Nizhny Novgorod, Russia
  • 3.
    Center for Biological Technology, Universidad Politécnica de Madrid, Pozuelo de Alarcón, Madrid, Spain
  • Published: 03 March 2026

  • Optogenetic experiments in vivo face fundamental limitations in real-time optical stimulation and biophotonic signal processing, constraining the efficiency and adaptability of neural circuit interrogation. This review establishes how photonic neuromorphic systems, operating at ultrafast speeds and with high energy efficiency, can overcome these barriers by forming a closed-loop optically driven interface with neural tissue. We present a comprehensive analysis of mathematical and computational models that describe neural dynamics in optical neuromorphic devices, bridging classical neuronal frameworks with optogenetic control paradigms. Emphasis is placed on how nonlinear dynamical modeling and data-driven approaches enable the design of photonic neurons and synapses capable of seamless integration with tapered fibers, fiber photometry, and computational optical control systems. Such integration allows real-time signal processing and adaptive feedback within optogenetic experiments, thereby enhancing precision and bidirectionality in living neural circuit interactions. By converging mathematical theory, photonic hardware, and neurobiology, this work provides a roadmap for next-generation neural interfaces that leverage optical neuromorphic computing to advance both intelligent neuroengineering and biomedical diagnostics.

    Citation: Svetlana A. Gerasimova, Alexander N. Pisarchik. Modeling neural dynamics with optical nonlinearity: From classical models to optogenetic approaches[J]. Mathematical Biosciences and Engineering, 2026, 23(4): 940-986. doi: 10.3934/mbe.2026037

    Related Papers:

  • Optogenetic experiments in vivo face fundamental limitations in real-time optical stimulation and biophotonic signal processing, constraining the efficiency and adaptability of neural circuit interrogation. This review establishes how photonic neuromorphic systems, operating at ultrafast speeds and with high energy efficiency, can overcome these barriers by forming a closed-loop optically driven interface with neural tissue. We present a comprehensive analysis of mathematical and computational models that describe neural dynamics in optical neuromorphic devices, bridging classical neuronal frameworks with optogenetic control paradigms. Emphasis is placed on how nonlinear dynamical modeling and data-driven approaches enable the design of photonic neurons and synapses capable of seamless integration with tapered fibers, fiber photometry, and computational optical control systems. Such integration allows real-time signal processing and adaptive feedback within optogenetic experiments, thereby enhancing precision and bidirectionality in living neural circuit interactions. By converging mathematical theory, photonic hardware, and neurobiology, this work provides a roadmap for next-generation neural interfaces that leverage optical neuromorphic computing to advance both intelligent neuroengineering and biomedical diagnostics.



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