Skip to main content
SpringerLink
Log in

Reduced order modeling of passive and quasi-active dendrites for nervous system simulation

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Accurate neuron models at the level of the single cell are composed of dendrites described by a large number of compartments. The network-level simulation of complex nervous systems requires highly compact yet accurate single neuron models. We present a systematic, numerically efficient and stable model order reduction approach to reduce the complexity of large dendrites by orders of magnitude. The resulting reduced dendrite models match the impedances of the full model within the frequency range of biological signals and reproduce the original action potential output waveforms.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  • Antoulas, A. C. (2005). Approximation of large-scale dynamical systems. Philadelphia: Society of Industrial and Applied Mathematics (SIAM).

    Book  Google Scholar 

  • Bai, Z., & Su, Y. (2005). Dimension reduction of large-scale second-order dynamical systems va a second-order Arnoldi method. SIAM Journal on Scientific Computing, 26(5), 1692–1709.

    Article  Google Scholar 

  • Bower, J. M., & Beeman, D. (1998). The book of GENESIS: Exploring realistic neural models with the GEneral NEural SImulation System. New York: Springer.

    Google Scholar 

  • Bush, P. C., & Sejnowski, T. J. (1993). Reduced compartmental models of neocortical pyramidal cells. Journal of Neuroscience Methods, 46, 159–166.

    Article  PubMed  CAS  Google Scholar 

  • Butts, D. A., Weng, C., Jin, J., Yeh, C., Lesica, N. A., Alonso, J., et al. (2007). Temporal precision in the neural code and the timescales of natural vision. Nature, 449, 92–95.

    Article  PubMed  CAS  Google Scholar 

  • Dayan, P., & Abbott, L. (2001), Theoretical neuroscience: Computational and mathematical modeling of neural system. Cambridge: MIT Press.

    Google Scholar 

  • Djurfeldt, M., Lundqvist, M., Johansson, C., Rehn, M., Ekeberg, Ö., & Lansner, A. (2007). Brain-scale simulation of the neocortex on the IBM blue Gene/L supercomputer. IBM Journal of Research and Development, 52(1/2), 31–40.

    Google Scholar 

  • Dyhrfjeld-Johnsen, J., Maier, J., Schubert, D., Staiger, J., Luhmann, H. J., Stephan, K. E., et al. (2005). CoCoDat: A database system for organizing and selecting quantitative data on single neurons and neuronal microcircuitry. Journal of Neuroscience Methods, 141, 291–308.

    Article  PubMed  CAS  Google Scholar 

  • Feldmann, P., & Freund, R. W. (1995), Efficient linear circuit analysis by Padė approximation via the Lanczos process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14, 639–649.

    Article  Google Scholar 

  • Gerstner, W., Kreiter, A. K., Markram, H., & Herz, A. V. M. (1997). Neural codes: Firing rates and beyond. Proceedings of the National Academy of Sciences of the United States of America, 94, 12740–12741.

    Article  PubMed  CAS  Google Scholar 

  • Glover, K. (1984). All optimal Hankel norm approximations of linear multivariable systems and their L  ∞  error bounds. International Journal of Control, 39(6), 1145–1193.

    Article  Google Scholar 

  • Grimme, E. J., Sorensen, D. C., & Van Dooren, P. (2005). Model reduction of state space systems via an implicitly restarted Lanczos method. Numerical Algorithms, 12(1), 1–31.

    Article  Google Scholar 

  • Gugercin, S., Antoulas, S., & Beattie, C. (2008). H 2 model reduction for large-scale linear dynamical systems. SIAM Journal on Matrix Analysis and Applications, 30, 609–638.

    Article  Google Scholar 

  • Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.

    PubMed  CAS  Google Scholar 

  • Izhikevich, E. M., & Edelman, G. M. (2007). Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Sciences of the United States of America, 105, 3593–3598.

    Article  Google Scholar 

  • Jack, J. J. B., Noble, D., & Tsien, R. W. (1975). Electric current flow in excitable cells. Oxford: Calderon Press.

    Google Scholar 

  • Kellems, A. R., Chaturantabut, S., Sorensen, D. C., & Cox, S. J. (2010). Morphologically accurate reduced order modeling of spiking neurons. Journal of Computational Neuroscience, 28, 477–494.

    Article  PubMed  Google Scholar 

  • Kellems, A. R., Roos, D., Xiao, N., & Cox, S. J. (2009). Low-dimensional, morphologically accurate models of subthreshold membrane potential. Journal of Computational Neuroscience, 27, 161–176.

    Article  PubMed  Google Scholar 

  • Koch, C. (1999). Biophysics of computation. Oxford: Oxford University Press.

    Google Scholar 

  • Markram, H. (2006). The blue brain project. Nature Reviews. Neuroscience, 7, 153–160.

    Article  PubMed  CAS  Google Scholar 

  • Moore, B. C. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26, 17–31.

    Article  Google Scholar 

  • Odabasioglu, A. (1998). Prima: Passive reduced-order interconnect macromodeling algorithm. IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, 17, 645–654.

    Article  Google Scholar 

  • Pillage, L. T., & Rohrer, R. A. (1990). Asymptic waveform evaluation for timing analysis. IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, 9, 352–366.

    Article  Google Scholar 

  • Rall, W. (1959). Branching dendritic trees and motoneuron membrane resistivity. Experimental Neurology, 1, 491–527.

    Article  PubMed  CAS  Google Scholar 

  • Rall, W. (1964). Theoretical significance of dendrite trees for neuronal input-output relations. In R. Reiss (Ed.), Neuronal theory and modeling (pp. 73–97). Stanford: Stanford University Press.

    Google Scholar 

  • Rall, W. (1967). Distinguishing theoretical synaptic potentials computed for different soma-dendritic distribution of synaptic inputs. Journal of Neurophysiology, 30, 1138–1168.

    PubMed  CAS  Google Scholar 

  • Rapp, Y., Koch, C., & Segev, I. (1992). The impact of parallel fiber background activity on the cable properties of cerebellar purkinje cells. Neural Computation, 4, 518–532.

    Article  Google Scholar 

  • Roberts, C. B., Best, J. A., & Suter, K. J. (2010). Dendritic processing of excitatory synaptic input in hypothalamic gonadotropin releasing-hormone neurons. Endocrinology, 147, 1545–1555.

    Article  Google Scholar 

  • Saad, Y. (2003). Iterative methods for sparse linear systems. Philadelphia: Society of Industrial and Applied Mathematic (SIAM).

    Book  Google Scholar 

  • Salimbahrami, B., & Lohmann, B. (2002). Krylov subspace methods in linear model order reduction: Introduction and invariance properties. Scientific Report, Institute of Automation, University of Bremen.

  • Segev, I. (1992). Single neurone models: Oversimple, complex and reduced. TINS 15, 414–421.

    PubMed  CAS  Google Scholar 

  • Single, S., & Borst, A. (1998). Dendritic integration and its role in computing image velocity. Science, 281, 1848–1850.

    Article  PubMed  CAS  Google Scholar 

  • Spruston, N. (2008). Pyramidal neurons: Dendritic structure and synaptic integration. Nature Reviews. Neuroscience, 9, 206–221.

    Article  PubMed  CAS  Google Scholar 

  • Stein, R., Gossen, E., & Jones, K. (2005). Neuronal variability: noise or part of the signal? Nature Reviews. Neuroscience, 6, 389–397.

    Article  PubMed  CAS  Google Scholar 

  • Stewart, G. W. (2001), Matrix algorithms: Eigensystems. Philadelphia: Society of Industrial and Applied Mathematic (SIAM).

    Book  Google Scholar 

  • Villemagne, C. D., & Skelton, R. E. (1987). Model reduction using a projection formulation. International Journal of Control, 46, 2141–2169.

    Article  Google Scholar 

  • Wilson, M. A., & Bower, J. M. (1989). The simulation of large scale neural networks. In C. Koch, & I. Segev (Eds.), Methods in neuronal modeling (pp. 291–333). Stanford: MIT Press.

    Google Scholar 

  • Yan, B., Zhou, L., Tan, S., Chen, J., & McGaughy, B. (2008). DeMOR: Decentralized model order reduction of linear networks with massive ports. In Proc. Design Automation Conf. (DAC) (pp. 409–414).

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, 77843, USA

    Boyuan Yan & Peng Li

Authors
  1. Boyuan Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boyuan Yan.

Additional information

Action Editor: James M. Bower

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yan, B., Li, P. Reduced order modeling of passive and quasi-active dendrites for nervous system simulation. J Comput Neurosci 31, 247–271 (2011). https://doi.org/10.1007/s10827-010-0309-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-010-0309-5

Keywords

Search

Navigation