[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

NeuroBox: computational mathematics in multiscale neuroscience

  • Special Issue CS Symposium 2016
  • Published:
Computing and Visualization in Science

Abstract

The brain is a complex organ operating on multiple scales. From molecular events that inform electrical and biochemical cellular responses, the brain interconnects processes all the way up to the massive network size of billions of brain cells. This strongly coupled, nonlinear, system has been subject to research that has turned increasingly multidisciplinary. The seminal work of Hodgkin and Huxley in the 1950s made use of experimental data to derive a coherent physical model of electrical signaling in neurons, which can be solved using mathematical and computational methods, thus bringing together neuroscience, physics, mathematics, and computer science. Over the last decades numerous projects have been dedicated to modeling and simulation of specific parts of molecular dynamics, neuronal signaling, and neural network behavior. Simulators have been developed around a specific objective and scale, in order to cope with the underlying computational complexity. Often times a dimension reduction approach allows larger scale simulations, this however has the inherent drawback of losing insight into structure-function interplay at the cellular level. This paper gives an overview of the project NeuroBox that has the objective of integrating multiple brain scales and associated physical models into one unified framework. NeuroBox hosts geometry and anatomical reconstruction methods, such that detailed three-dimensional domains can be integrated into numerical simulations of models based on partial differential equations. The project further focusses on deriving numerical methods for handling complex computational domains, and to couple multiple spatial dimensions. The latter allows the user to specify in which parts of the biological problem high-dimensional representations are necessary and where low-dimensional approximations are acceptable. NeuroBox offers workflow user interfaces that are automatically generated with VRL-Studio and can be controlled by non-experts. The project further uses uG4 as the numerical backend, and therefore accesses highly advanced discretization methods as well as hierarchical and scalable numerical solvers for very large neurobiological problems.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Afif, M., Bergam, A., Mghazli, Z., Verfürth, R.: A posteriori error estimators for the finite volume discretization of an elliptic problem. Numer. Algorithms 34 (2003)

  2. Agouzal, A., Oudin, F.: A posteriori error estimator for finite volume methods. Appl. Math. Comput. 100 (2000)

  3. Ahrens, J., Geveci, B., Law, C.: ParaView: an end-user tool for large data visualization. Visualization Handbook (2005)

  4. Ascoli, G.A.: Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat. Rev. Neurosci. 7, 318–324 (2006)

    Article  Google Scholar 

  5. Ayachit, U.: The ParaView Guide: A Parallel Visualization Application. Kitware, Clifton Park (2015)

    Google Scholar 

  6. Babuska, I., Aziz, A.: On the angle condition in the finite element method. SIAM J. Numer. Anal. 13, 214–226 (1976)

    Article  MathSciNet  Google Scholar 

  7. Bower, J., Beeman, D.: The Book of GENESIS: Exploring Realistic Neural Models with the General Neural Simulation System. Springer, New York (1997)

    MATH  Google Scholar 

  8. Breit, M., Kessler, M., Stepniewski, M., Vlachos, A., Queisser, G.: Spine-to-dendrite calcium modeling discloses relevance for precise positioning of ryanodine receptor-containing endoplasmic reticulum in neurons, in revision (2018)

  9. Breit, M., Stepniewski, M., Grein, S., Gottmann, P., Reinhardt, L., Queisser, G.: Anatomically detailed and large-scale simulations studying synapse loss and synchrony using neurobox. Front. Neuroanat. 10, 8 (2016)

    Article  Google Scholar 

  10. Broser, P.J., Schulte, R., Lang, S., Roth, A., Helmchen, F., Waters, J., Sakmann, B., Wittum, G.: Nonlinear anisotropic diffusion filtering of three-dimensional image data from two-photon microscopy. J. Biomed. Opt. 9, 1253–1264 (2004)

    Article  Google Scholar 

  11. Catmull, E., Clark, J.: Recursivley generated b-spline surfaces on arbitrary topological meshes. Comput. Aided Des. 10, 350–355 (1978)

    Article  Google Scholar 

  12. Doo, D., Sabin, M.: Analysis of the behaviour of recursive division surfaces near extraordinary points. Comput. Aided Des. 10, 356–360 (1978)

    Article  Google Scholar 

  13. Feiner, A.-S., McEvoy, A.: The nernst equation. J. Chem. Educ. 493, 493 (1994)

    Article  Google Scholar 

  14. Gewaltig, M.O., Diesmann, M.: Nest (neural simulation tool). Scholarpedia 2, 1430 (2007)

    Article  Google Scholar 

  15. Grein, S., Stepniewski, M., Reiter, S., Knodel, M.M., Queisser, G.: 1D–3D hybrid modelling—from multi-compartment models to full resolution models in space and time. Front. Neuroinform. 8, 1–13 (2014)

    Article  Google Scholar 

  16. Halavi, M., Hamilton, K.A., Parekh, R., Ascoli, G.A.: Digital reconstructions of neuronal morphology: three decades of research trends. Front. Neurosci. 48 (2012)

  17. Hayashi, Y., Majewska, A.K.: Dendritic spine geometry: functional implication and regulation. Neuron 46, 529–532 (2005)

    Article  Google Scholar 

  18. Hines, M.L., Carnevale, N.T.: The NEURON simulation environment. Neural Comput. 9, 1179–1209 (1997)

    Article  Google Scholar 

  19. Hodgkin, A.L., Huxley, A.F.: The components of membrane conductance in the giant axon of loligo. J. Physiol. 116, 473–496 (1952)

    Article  Google Scholar 

  20. Hodgkin, A.L., Huxley, A.F.: Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. J. Physiol. 116, 449–472 (1952)

    Article  Google Scholar 

  21. Hodgkin, A.L., Huxley, A.F.: The dual effect of membrane potential on sodium conductance in the giant axon of loligo. J. Physiol. 116, 497–506 (1952)

    Article  Google Scholar 

  22. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)

    Article  Google Scholar 

  23. Hodgkin, A.L., Huxley, A.F., Katz, B.: Measurement of current–voltage relations in the membrane of the giant axon of loligo. J. Physiol. 116, 424–448 (1952)

    Article  Google Scholar 

  24. Hoffer, M., Poliwoda, C., Wittum, G.: Visual reflection library: a framework for declarative gui programming on the java platform. Comput. Vis. Sci. 16, 181–192 (2013)

    Article  Google Scholar 

  25. Ippen, T., Eppler, J.M., Plesser, H.E., Diesmann, M.: Constructing neuronal network models in massively parallel environments. Front. Neuroinform. 11, 30 (2017)

    Article  Google Scholar 

  26. Kapitein, L., Hoogenraad, C.: Building the neuronal microtubule cytoskeleton. Neuron 87, 492–506 (2015)

    Article  Google Scholar 

  27. Knodel, M., Geiger, R., Ge, L., Bucher, D., Grillo, A., Wittum, G., Schuster, C., Queisser, G.: Synaptic bouton properties are tuned to best fit the prevailing firing pattern. Front. Comput. Neurosci. (2014). https://doi.org/10.3389/fncom.2014.00101

    Article  Google Scholar 

  28. Loew, L.M., Schaff, J.C.: The virtual cell: a software environment for computational cell biology. Trends Biotechnol. 19, 401–406 (2001)

    Article  Google Scholar 

  29. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. SIGGRAPH Comput. Graph. 4, 163–169 (1987)

    Article  Google Scholar 

  30. Malossi, A.C.I., Blanco, P.J., Deparis, S., Quarteroni, A.: Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows. Int. J. Numer. Methods Biomed. Eng. 27, 2035–2057 (2011)

    Article  MathSciNet  Google Scholar 

  31. Mörschel, K., Breit, M., Queisser, G.: Generating neuron geometries for detailed three-dimensional simulations using anamorph. Neuroinformatics 1–23 (2017)

  32. Muller, D., Nikonenko, I., Jourdain, P., Alberi, S.: Memory and structural plasticity. Curr. Mol. Med. 2, 605–611 (2002)

    Article  Google Scholar 

  33. Nernst, W.: Zur kinetik der in lösung befindlicher körper. erst abhandlung. Theorie der diffusion. Z. Phys. Chem. 2(9), 613–637 (1888)

    Google Scholar 

  34. Queisser, G., Wittmann, M., Bading, H., Wittum, G.: Filtering, reconstruction, and measurement of the geometry of nuclei from hippocampal neurons based on confocal microscopy data. J. Biomed. Opt. 13, 014009-1–014009-11 (2008)

    Article  Google Scholar 

  35. Reiter, S., Vogel, A., Heppner, I., Rupp, M., Wittum, G.: A massively parallel geometric multigrid solver on hierarchically distributed grids. Comput. Vis. Sci. 14, 151–164 (2013)

    Article  Google Scholar 

  36. Sekine, S., Miura, M., Chihara, T.: Organelles in developing neurons: essential regulators of neuronal morphogenesis and function. Int. J. Dev. Biol. 53, 19–27 (2009)

    Article  Google Scholar 

  37. Shewchuk, J.: What is a good linear element? Interpolation, conditioning, and quality measures, in Eleventh International Meshing Roundtable, pp. 115–126 (2002)

  38. Si, H.: Tetgen, a delauny-based quality tetrahedral mesh generator. ACM Trans. Math. Softw. 41(9) (2015)

    Article  MathSciNet  Google Scholar 

  39. Stepniewski, M., Queisser, G.: A subdivision based geometric multigrid method, under review (2018)

  40. Tada, T., Sheng, M.: Molecular mechanisms of dendritic spine morphogenesis. Curr. Opin. Neurobiol. 16, 95–101 (2006)

    Article  Google Scholar 

  41. van Aelst, L., Cline, H.T.: Rho GTPases and activity-dependent dendrite developement. Curr. Opin. Neurobiol. 14, 297–304 (2004)

    Article  Google Scholar 

  42. Vogel, A., Reiter, S., Rupp, M., Nägel, A., Wittum, G.: UG 4: a novel flexible software system for simulating PDE based models on high performance computers. Comput. Vis. Sci. 16, 165–179 (2013)

    Article  Google Scholar 

  43. Wittmann, M., Queisser, G., Eder, A., Wiegert, J., Bengtson, C., Hellwig, A., Wittum, G., Bading, H.: Synaptic activity induces dramatic changes in the geometry of the cell nucleus: interplay between nuclear structure, histone H3 phosphorylation, and nuclear calcium signaling. J. Neurosci. 29, 14687–14700 (2009)

    Article  Google Scholar 

  44. Wolf, S., Grein, S., Queisser, G.: Employing NeuGen 2.0 to automatically generate realistic morphologies of hippocampal neurons and neural networks in 3D. Neuroinformatics 11, 137–148 (2013)

    Article  Google Scholar 

  45. Xu, J., Zikatanov, L.: A monotone finite element scheme for convection-diffusion equations. Math. Comput. 68, 1429–1446 (1999)

    Article  MathSciNet  Google Scholar 

  46. Xylouris, K., Queisser, G., Wittum, G.: A three-dimensional mathematical model of active signal processing in axons. Comput. Visual. Sci. 13, 409–418 (2008)

    Article  MathSciNet  Google Scholar 

  47. Xylouris, K., Wittum, G.: A three-dimensional mathematical model for the signal propagation on a neuron’s membrane. Front. Comput. Neurosci. 94 (2015)

Download references

Acknowledgements

In alphabetical order I want to express by gratitude to Markus Breit, Michael Hoffer, Sebastian Reiter, Martin Stepniewski, Andreas Vogel, and Gabriel Wittum. Markus Breit and Martin Stepniewski have been most dedicated to developing the numerical methods and tools that lead to the development of NeuroBox. I thank them for there never-waning enthusiasm and effort to drive this project towards success. I thank Michael Hoffer for his stunning work in developing VRL and VRL-Studio, which has become a central platform of our tool development, and his time for discussions that have shaped many parts of our joint work. I thank Sebastian Reiter for his support in form of developing the grid library in uG4, the grid management tool ProMesh, and productive discussions along the way. I thank Andreas Vogel for his support around everything related to uG4. He has always been supportive when problems arose and needed to be solved. Finally, I thank Gabriel Wittum, to whom I dedicate this paper in honor of his 60th birthday. Gabriel gave me the scientific platform to grow my career, and has been a patient and supportive mentor over the many past years.

Author information

Authors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, PA, USA

    G. Queisser

  2. G-CSC, Goethe University Frankfurt, Frankfurt, Germany

    M. Stepniewski, M. Breit & M. Hoffer

Authors
  1. M. Stepniewski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Breit
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Hoffer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Queisser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Queisser.

Additional information

Communicated by Alfio Grillo.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

M. Stepniewski and M. Breit have equally contributed to this work.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepniewski, M., Breit, M., Hoffer, M. et al. NeuroBox: computational mathematics in multiscale neuroscience. Comput. Visual Sci. 20, 111–124 (2019). https://doi.org/10.1007/s00791-019-00314-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-019-00314-0