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Fully implicit parallel simulation of single neurons

Abstract

When a multi-compartment neuron is divided into subtrees such that no subtree has more than two connection points to other subtrees, the subtrees can be on different processors and the entire system remains amenable to direct Gaussian elimination with only a modest increase in complexity. Accuracy is the same as with standard Gaussian elimination on a single processor. It is often feasible to divide a 3-D reconstructed neuron model onto a dozen or so processors and experience almost linear speedup. We have also used the method for purposes of load balance in network simulations when some cells are so large that their individual computation time is much longer than the average processor computation time or when there are many more processors than cells. The method is available in the standard distribution of the NEURON simulation program.

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References

  • Hayes, B. (2002). The easiest hard problem. American Scientist, 90(2), 113–117.

    Article  Google Scholar 

  • Heglund, M. (1991). On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization. Numerical Mathematics, 59, 453–472.

    Article  Google Scholar 

  • Hindmarsh. A., & Serban, R. (2002). User documentation for CVODES, An ODE solver with sensitiviy analysis capabilities. Tech. rep., Lawrence Livermore National Laboratory. http://www.llnl.gov/CASC/sundials/.

  • Hines, M. L. & Carnevale, N. T. (1997). The NEURON simulation environment. Neural Computation, 9, 1179–1209.

    PubMed  Article  CAS  Google Scholar 

  • Hines, M., Eichner, H., & Schürmann, F. (2008). Neuron splitting in compute-bound parallel network simulations enables runtime scaling with twice as many processors. Journal of Computational Neuroscience, [Epub ahead of print], PMID: 18214662, 23 Jan. doi:10.1007/s10827-007-0073-3.

  • Korf, R. E. (1998). A complete anytime algorithm for number partitioning. Artificial Intelligence, 106, 181–203.

    Article  Google Scholar 

  • Lazarewicz, M. T., Migliore, M., & Ascoli, G. A. (2002). A new bursting model of CA3 pyramidal cell physiology suggests multiple locations for spike initiation. Biosystems, 67, 129–137.

    PubMed  Article  CAS  Google Scholar 

  • Lytton, W. W., & Hines, M. L. (2005). Independent variable time-step integration of individual neurons for network simulations. Neural Computation, 17, 903–921.

    PubMed  Article  Google Scholar 

  • Mascagni, M. (1990). A parallelizing algorithm for computing solutions to arbitrarily branched cable neuron models. Journal of Neuroscience Methods, 36, 105–114.

    Article  Google Scholar 

  • Migliore, M., Cannia, C., Lytton, W. W., Markram, H., & Hines, M. L. (2006). Parallel network simulations with NEURON. Journal of Computational Neuroscience, 21, 119–129.

    PubMed  Article  CAS  Google Scholar 

  • Miyasho, T., Takagi, H., Suzuki, H., Watanabe, S., Inoue, M., Kudo, Y., et al. (2001). Low-threshold potassium channels and a low-threshold calcium channel regulate Ca2+ spike firing in the dendrites of cerebellar Purkinje neurons: A modeling study. Brain Research, 891, 106–115.

    PubMed  Article  CAS  Google Scholar 

  • Morrison, A., Mehring, C., Geisel, T., Aertsen, A. D., & Diesmann, M. (2005). Advancing the boundaries of high-connectivity network simulation with distributed computing. Neural Computation, 17, 1776–801.

    PubMed  Article  Google Scholar 

  • Plesser, H. E., Eppler, J. M., Morrison, A., Diesmann, M., & Gewaltig, M.-O. (2007). Efficient Parallel Simulation of Large-Scale Neuronal Networks on Clusters of Multiprocessor Computers. In: A.-M. Kermarrec, L. Bouge, & T. Priol (Eds.), Euro- Par 2007: Parallel processing, lecture notes in computer science, 4641. (pp. 672–681).

  • Poirazi, P., Brannon, T., & Mel, B. W. (2003). Pyramidal neuron as two-layer neural network. Neuron, 37, 989–999.

    PubMed  Article  CAS  Google Scholar 

  • Rempe, M. J., & Chopp, D. L. (2006). Predictor-corrector algorithm for reaction–diffusion equations associated with neural activity on branched structures. SIAM Journal of Scientific Computing, 28, 2139–2161.

    Article  Google Scholar 

  • Santhakumar, V., Aradi, I., & Soltesz, I. (2005). Role of mossy fiber sprouting and mossy cell loss in hyperexcitability: A network model of the dentate gyrus incorporating cell types and axonal topography. Journal of Neurophysiology, 93, 437–453.

    PubMed  Article  Google Scholar 

  • Traub, R. D., Contreras, D., Cunningham, M. O., Murray, H., LeBeau, F. E., Roopun, A., et al. (2005). Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. Journal of Neurophysiology, 93, 2194–2232.

    PubMed  Article  Google Scholar 

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Acknowledgements

Research supported by NIH grant NS11613 and the Blue Brain Project. We are grateful to Thomas Morse for his work on initial porting of the Fortran version of the Traub model into NEURON and to Rajnish Ranjan for incorporating the load balance and multisplit methods into the BlueBrain workflow.

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Correspondence to Michael L. Hines.

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Hines, M.L., Markram, H. & Schürmann, F. Fully implicit parallel simulation of single neurons. J Comput Neurosci 25, 439–448 (2008). https://doi.org/10.1007/s10827-008-0087-5

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  • DOI: https://doi.org/10.1007/s10827-008-0087-5

Keywords

  • Computer simulation
  • Computer modeling
  • Neuronal networks
  • Load balance
  • Parallel simulation