Frontiers of Physics

, 12:128902 | Cite as

Exponential distance distribution of connected neurons in simulations of two-dimensional in vitro neural network development

  • Zhi-Song Lv
  • Chen-Ping Zhu
  • Pei Nie
  • Jing Zhao
  • Hui-Jie Yang
  • Yan-Jun Wang
  • Chin-Kun Hu
Research Article


The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain’s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two-dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski’s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.


distance distribution connected neurons development exponential power-law neural networks complex systems 



The anonymous referees are appreciated for their patience to review the manuscript and for pertinent comments and suggestions for the revision. C. K. Chan is acknowledged for valuable discussion. The work was supported by Project No. 11175086 of the National Natural Science Foundation of China. C. K. Hu was supported by Grants MOST 104-2112-M-001 -002 and MOST 105-2112-M-001 -004.


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Zhi-Song Lv
    • 1
  • Chen-Ping Zhu
    • 1
    • 2
  • Pei Nie
    • 1
  • Jing Zhao
    • 3
  • Hui-Jie Yang
    • 2
  • Yan-Jun Wang
    • 4
  • Chin-Kun Hu
    • 5
    • 6
  1. 1.Department of Physics in Science CollegeNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Research Center of Complex Systems ScienceUniversity of Shanghai for Science and TechnologyShanghaiChina
  3. 3.Department of MathematicsCollege of Logistic Engineering of PLANanjingChina
  4. 4.College of Civil AviationNanjing University of Aeronautics and AstronauticsNanjingChina
  5. 5.Institute of PhysicsAcademia SinicaNankang, TaipeiTaiwan
  6. 6.National Center for Theoretical SciencesTsing Hua UniversityHsinchuChina

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