NeuroBox: computational mathematics in multiscale neuroscience

  • M. Stepniewski
  • M. Breit
  • M. Hoffer
  • G. QueisserEmail author
Special Issue CS Symposium 2016


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.



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.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. Stepniewski
    • 2
  • M. Breit
    • 2
  • M. Hoffer
    • 2
  • G. Queisser
    • 1
    Email author
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA
  2. 2.G-CSCGoethe University FrankfurtFrankfurtGermany

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