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The notion of fractals in tumour angiogenic sprout initiation model based on cellular automata

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  • Sadhukhan, Sounak
  • Mishra, P.K.

Abstract

Tumour growth is considered chaotic, poorly controlled growth as its cells and vasculatures are irregular in shape. The vascular system of tumour is a complex network and its architectural complexity and geometrical characteristics cannot be defined with Euclidian geometry as it is only capable of expressing regular or smooth objects whereas, fractal geometry describes an object with irregularities and it is therefore well suited to quantify those morphological characteristics. In this paper, we develop a cellular automata (CA) based discrete model that tries to mimic all the features and make useful predictions of tumour angiogenesis with computer-coded rules. From the interactions of several species in 2-D tissue space, we study the effects of these various biological factors on the formation of the capillary sprouts. The model also captures anastomoses and branching phenomena in capillary blood vessels. It is observed that chemotaxis and randomness are the essential components for the capillary sprout motility whereas, haptotaxis works as an add-on feature. The model is also validated with partial sensitivity analysis. The fractal properties of the growing capillary sprouts in the model are investigated. The characterization of these fractal objects (capillary sprouts) is provided by the box-counting method. The model shows, the morphological change in the early stages of the vascularization process where the capillary sprouts are formed from the surrounding blood vessels. The model successfully simulates the morphological aspects of capillary vessel growth during tumour angiogenesis. The estimated fractal dimension is very close to the previously measured range. This is established our hypothesis about the fractal nature of vascular network pattern and our CA-based discrete model for capillary sprout initiation during tumour angiogenesis.

Suggested Citation

  • Sadhukhan, Sounak & Mishra, P.K., 2022. "The notion of fractals in tumour angiogenic sprout initiation model based on cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010717
    DOI: 10.1016/j.chaos.2021.111717
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    References listed on IDEAS

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    1. Lagarias Apostolos, 2010. "Urban Growth Simulation Through Cellular Automata: A Way to Explore the Fractal Nature of Cities," SCIENZE REGIONALI, FrancoAngeli Editore, vol. 9(2), pages 5-23.
    2. Peter Carmeliet & Rakesh K. Jain, 2000. "Angiogenesis in cancer and other diseases," Nature, Nature, vol. 407(6801), pages 249-257, September.
    3. Peter Carmeliet, 2005. "Angiogenesis in life, disease and medicine," Nature, Nature, vol. 438(7070), pages 932-936, December.
    4. Javad Salimi Sartakhti & Mohammad Hossein Manshaei & David Basanta & Mehdi Sadeghi, 2017. "Evolutionary emergence of angiogenesis in avascular tumors using a spatial public goods game," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-17, April.
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    Cited by:

    1. Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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