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Automated numerical simulation of biological pattern formation based on visual feedback simulation framework

Author

Listed:
  • Mingzhu Sun
  • Hui Xu
  • Xingjuan Zeng
  • Xin Zhao

Abstract

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.

Suggested Citation

  • Mingzhu Sun & Hui Xu & Xingjuan Zeng & Xin Zhao, 2017. "Automated numerical simulation of biological pattern formation based on visual feedback simulation framework," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-16, February.
    • Handle: RePEc:plo:pone00:0172643
    DOI: 10.1371/journal.pone.0172643
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    References listed on IDEAS

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    1. Avigdor Eldar & Ruslan Dorfman & Daniel Weiss & Hilary Ashe & Ben-Zion Shilo & Naama Barkai, 2002. "Robustness of the BMP morphogen gradient in Drosophila embryonic patterning," Nature, Nature, vol. 419(6904), pages 304-308, September.
    2. Yina Guo & Mingzhu Sun & Alan Garfinkel & Xin Zhao, 2014. "Mechanisms of Side Branching and Tip Splitting in a Model of Branching Morphogenesis," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-14, July.
    3. Ross J. Metzger & Ophir D. Klein & Gail R. Martin & Mark A. Krasnow, 2008. "The branching programme of mouse lung development," Nature, Nature, vol. 453(7196), pages 745-750, June.
    4. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
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    Cited by:

    1. Christopher J Lynch & Saikou Y Diallo & Hamdi Kavak & Jose J Padilla, 2020. "A content analysis-based approach to explore simulation verification and identify its current challenges," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-33, May.

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