Skip to main content
SpringerLink
Log in

Control-Theoretic Approaches for Modeling, Analyzing, and Manipulating Neuronal (In)activity

  • Chapter
Dynamic Neuroscience

  • 1552 Accesses

Abstract

Understanding the mechanisms of brain inactivation, such as during administration of general anesthesia, has emerged as a key question in basic and clinical neuroscience. This chapter will examine this question through the lens of dynamical systems and control theory. We will survey existing methods and new formalisms to probe and assess the geometry of neural trajectories, i.e., neural activity patterns at multiple spatial scales. In particular, we will discuss connections between neural dynamics and control-theoretic notions such as reachability and controllability, focusing on how these latter notions may inform our understanding of inactivated brain states. Subsequently, we will discuss how these analyses may enable strategies for neurocontrol, whereby neuronal dynamics are systematically altered by extrinsic means such as pharmacological modulation or neurostimulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Brown, E. N., Lydic, R., & Schiff, N. D. (2010). General anesthesia, sleep, and coma. New England Journal of Medicine, 363, 2638–2650.

    Article  Google Scholar 

  • Chemali, J., Ching, S., Purdon, P. L., Solt, K., & Brown, E. N. (2013). Burst suppression probability algorithms: state-space methods for tracking EEG burst suppression. Journal of Neural Engineering, 10, 056017.

    Article  Google Scholar 

  • Chen, C.-T. (1995). Linear system theory and design. Oxford: Oxford University Press.

    Google Scholar 

  • Ching, S., & Brown, E. N. (2014). Modeling the dynamical effects of anesthesia on brain circuits. Current Opinion in Neurobiology, 25, 116–122.

    Article  Google Scholar 

  • Ching, S., Brown, E. N., & Kramer, M. A. (2012a). Distributed control in a mean-field cortical network model: implications for seizure suppression. Physical Review E, 86, 021920.

    Article  Google Scholar 

  • Ching, S., Cimenser, A., Purdon, P. L., Brown, E. N., & Kopell, N. J. (2010). Thalamocortical model for a propofol-induced alpha-rhythm associated with loss of consciousness. Proceedings of National Academy of Sciences USA, 107, 22665–22670.

    Google Scholar 

  • Ching, S., Liberman, M. Y., Chemali, J. J., Westover, M. B., Kenny, J. D., Solt, K., et al. (2013). Real-time closed-loop control in a rodent model of medically induced coma using burst suppression. Anesthesiology, 119, 848–860.

    Article  Google Scholar 

  • Ching, S., Purdon, P. L., Vijayan, S., Kopell, N. J., & Brown, E. N. (2012b). A neurophysiological-metabolic model for burst suppression. Proceedings of National Academy of Sciences USA, 109, 3095–3100.

    Google Scholar 

  • Ching, S., & Ritt, J. T. (2013). Control strategies for underactuated neural ensembles driven by optogenetic stimulation. Frontiers in Neural Circuits, 7, 54.

    Article  Google Scholar 

  • Cimenser, A., Purdon, P. L., Pierce, E. T., Walsh, J. L., Salazar-Gomez, A. F., Harrell, P. G., et al. (2011). Tracking brain states under general anesthesia by using global coherence analysis. Proceedings of National Academy of Sciences USA, 108, 8832–8837.

    Google Scholar 

  • Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S., & Bergstrom, C. T. (2012). Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS ONE, 7(6), e38398.

    Article  Google Scholar 

  • Eghbali, M., Gage, P. W., & Birnir, B. (2003). Effects of propofol on GABA A channel conductance in rat-cultured hippocampal neurons. European Journal of Pharmacology, 468(2), 75–82.

    Article  Google Scholar 

  • Ehrens, D., Sritharan, D., & Sarma, S. V. (2015). Closed-loop control of a fragile network: Application to seizure-like dynamics of an epilepsy model. Frontiers in Neuroscience, 9, 58.

    Article  Google Scholar 

  • Flores, F. J., Hartnack, K. E., Fath, A. B., Kim, S.-E., Wilson, M. A., Brown, E. N., et al. (2017). Thalamocortical synchronization during induction and emergence from propofol-induced unconsciousness. Proceedings of National Academy of Sciences USA, 114, E6660–E6668.

    Google Scholar 

  • Freudenberg, J. S., Hollot, C. V., Middleton, R. H., & Toochinda, V. (2003). Fundamental design limitations of the general control configuration. IEEE Transactions on Automatic Control, 48(8), 1355–1370.

    Article  MathSciNet  Google Scholar 

  • Gu, S., Pasqualetti, F., Cieslak, M., Telesford, Q. K., Yu, A. B., Kahn, A. E., et al. (2015). Controllability of structural brain networks. Nature Communications, 6, 8414.

    Article  Google Scholar 

  • Haynes, G., & Hermes, H. (1970). Nonlinear controllability via lie theory. SIAM Journal on Control, 8(4), 450–460.

    Article  MathSciNet  Google Scholar 

  • Hermann, R., & Krener, A. J. (1977). Nonlinear controllability and observability. IEEE Transactions on Automatic Control, 22(5), 728–740.

    Article  MathSciNet  Google Scholar 

  • Jin, Y.-H., Zhang, Z., Mendelowitz, D., & Andresen, M. C. (2009). Presynaptic actions of propofol enhance inhibitory synaptic transmission in isolated solitary tract nucleus neurons. Brain Research, 1286, 75–83.

    Article  Google Scholar 

  • Kalman, R. (1959). On the general theory of control systems. IRE Transactions on Automatic Control, 4(3), 110–110.

    Article  Google Scholar 

  • Khalil, H. K., & Grizzle, J. (2002). Nonlinear systems (Vol. 3). Upper Saddle River: Prentice Hall

    Google Scholar 

  • Kumar, G., & Ching, S. (2016). The geometry of plasticity-induced sensitization in isoinhibitory rate motifs. Neural Computation, 28, 1889–1926.

    Article  Google Scholar 

  • Kumar, G., Kim, S. A., & Ching, S. (2016). A control-theoretic approach to neural pharmacology: Optimizing drug selection and dosing. Journal of Dynamic Systems, Measurement, and Control, 138(8), 084501.

    Article  Google Scholar 

  • Lepage, K. Q., Ching, S., & Kramer, M. A. (2013). Inferring evoked brain connectivity through adaptive perturbation. Journal of Computational Neuroscience, 34, 303–318.

    Article  MathSciNet  Google Scholar 

  • Lepage, K. Q., Kramer, M. A., & Ching, S. (2013). An active method for tracking connectivity in temporally changing brain networks. In Proceedings of IEEE Engineering in Medicine and Biology Conference (pp. 4374–4377).

    Google Scholar 

  • Li, J.-S., Dasanayake, I., & Ruths, J. (2013). Control and synchronization of neuron ensembles. IEEE Transactions on Automatic Control, 58(8), 1919–1930.

    Article  MathSciNet  Google Scholar 

  • Liberman, M. Y., Ching, S., Chemali, J., & Brown, E. N. (2013). A closed-loop anesthetic delivery system for real-time control of burst suppression. Journal of Neural Engineering, 10, 046004.

    Article  Google Scholar 

  • Liu, S., & Ching, S. (2017). Homeostatic dynamics, hysteresis and synchronization in a low-dimensional model of burst suppression. Journal of Mathematical Biology, 74, 1011–1035.

    Article  MathSciNet  Google Scholar 

  • Liu, Y.-Y., Slotine, J.-J., & Barabasi, A.-L. (2011). Controllability of complex networks. Nature, 473, 167–173.

    Article  Google Scholar 

  • McCarthy, M. M., Brown, E. N., & Kopell, N. (2008). Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofol-induced paradoxical excitation. Journal of Neuroscience, 28(50), 13488–13504.

    Article  Google Scholar 

  • McCarthy, M. M., Ching, S., Whittington, M. A., & Kopell, N. (2012). Dynamical changes in neurological diseases and anesthesia. Current Opinion in Neurobiology, 22, 693–703.

    Article  Google Scholar 

  • Menolascino, D., & Ching, S. (2017). Bispectral analysis for measuring energy-orientation tradeoffs in the control of linear systems. Systems & Control Letters, 102, 68–73.

    Article  MathSciNet  Google Scholar 

  • Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002). Network motifs: simple building blocks of complex networks. Science, 298(5594), 824–827.

    Article  Google Scholar 

  • Nandi, A., Kafashan, M., & Ching, S. (2017a). Control analysis and design for statistical models of spiking networks. IEEE Transactions on Control of Network Systems. doi: 10.1109/TCNS.2017.2687824

    Article  Google Scholar 

  • Nandi, A., Schättler, H., & Ching, S. (2017b). Selective spiking in neuronal populations. In Proceedings of American Control Conference (pp. 2811–2816). New York: IEEE.

    Google Scholar 

  • Pasqualetti, F., Zampieri, S., & Bullo, F. (2014). Controllability metrics, limitations and algorithms for complex networks. IEEE Transactions on Control of Network Systems, 1(1), 40–52.

    Article  MathSciNet  Google Scholar 

  • Purdon, P. L., Pierce, E. T., Mukamel, E. A., Prerau, M. J., Walsh, J. L., Wong, K. F. K., et al. (2013). Electroencephalogram signatures of loss and recovery of consciousness from propofol. Proceedings of National Academy of Sciences USA, 110, E1142–E1151.

    Google Scholar 

  • Ritt, J. T., & Ching, S. (2015). Neurocontrol: Methods, models and technologies for manipulating dynamics in the brain. In Proceedings of American Control Conference (pp. 3765–3780). New York: IEEE

    Google Scholar 

  • Santaniello, S., McCarthy, M. M., Montgomery, E. B., Gale, J. T., Kopell, N., & Sarma, S. V. (2015). Therapeutic mechanisms of high-frequency stimulation in Parkinson’s disease and neural restoration via loop-based reinforcement. Proceedings of National Academy of Sciences USA, 112, E586–E595.

    Google Scholar 

  • Sontag, E. D. (2013). Mathematical control theory: Deterministic finite dimensional systems. New York: Springer.

    Google Scholar 

  • Truccolo, W., Eden, U. T., Fellows, M. R., Donoghue, J. P., & Brown, E. N. (2005). A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. Journal of Neurophysiology, 93, 1074–1089.

    Article  Google Scholar 

  • Vijayan, S., Ching, S., Purdon, P. L., Brown, E. N., & Kopell, N. J. (2013). Thalamocortical mechanisms for the anteriorization of α rhythms during propofol-induced unconsciousness. Journal of Neuroscience, 33, 11070–11075.

    Article  Google Scholar 

  • Whalen, A. J., Brennan, S. N., Sauer, T. D., & Schiff, S. J. (2015). Observability and controllability of nonlinear networks: The role of symmetry. Physical Review X, 5(1), 011005.

    Article  Google Scholar 

Download references

Acknowledgements

My career has been immeasurably enriched by the training I received from Professor Emery N. Brown, to whom this monograph is dedicated. Thank you Emery, for the opportunity to pursue research at the interface of engineering and neuroscience.

This chapter brings together several ideas and results from the past several years and I would like to acknowledge the important contributions of students and collaborators who were involved in published work. I would also like to acknowledge the Burroughs-Wellcome Fund Career Award at the Scientific Interface; Awards ECCS 1509342, CMMI 1537015 and CMMI 1653589 from the National Science Foundation; Awards R21NS096590, R21EY027590 from the National Institutes of Health; and Award 15RT0189 from the Air Force Office of Scientific Research, for support related to the research discussed in this chapter.

Author information

Authors and Affiliations

  1. Washington University at St Louis, St Louis, MO, USA

    ShiNung Ching

Authors
  1. ShiNung Ching
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ShiNung Ching .

Editor information

Editors and Affiliations

  1. School of Medicine, New York University, New York, NY, USA

    Zhe Chen

  2. Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, USA

    Sridevi V. Sarma

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Ching, S. (2018). Control-Theoretic Approaches for Modeling, Analyzing, and Manipulating Neuronal (In)activity. In: Chen, Z., Sarma, S.V. (eds) Dynamic Neuroscience. Springer, Cham. https://doi.org/10.1007/978-3-319-71976-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71976-4_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71975-7

  • Online ISBN: 978-3-319-71976-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation