IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010717.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010717
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111717?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Carmeliet & Rakesh K. Jain, 2000. "Angiogenesis in cancer and other diseases," Nature, Nature, vol. 407(6801), pages 249-257, September.
    2. 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.
    3. 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.
    4. Peter Carmeliet, 2005. "Angiogenesis in life, disease and medicine," Nature, Nature, vol. 438(7070), pages 932-936, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rocío Vega & Manuel Carretero & Rui D M Travasso & Luis L Bonilla, 2020. "Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-31, January.
    2. Bin Wu & Haixiang Wu & Xiaoyan Liu & Houwen Lin & Jin Li, 2014. "Ranibizumab versus Bevacizumab for Ophthalmic Diseases Related to Neovascularisation: A Meta-Analysis of Randomised Controlled Trials," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-8, July.
    3. Atsuya Yaguchi & Mio Oshikawa & Go Watanabe & Hirotsugu Hiramatsu & Noriyuki Uchida & Chikako Hara & Naoko Kaneko & Kazunobu Sawamoto & Takahiro Muraoka & Itsuki Ajioka, 2021. "Efficient protein incorporation and release by a jigsaw-shaped self-assembling peptide hydrogel for injured brain regeneration," Nature Communications, Nature, vol. 12(1), pages 1-12, December.
    4. Ze-Feng Zhang & Tao Wang & Li-Hua Liu & Hui-Qin Guo, 2014. "Risks of Proteinuria Associated with Vascular Endothelial Growth Factor Receptor Tyrosine Kinase Inhibitors in Cancer Patients: A Systematic Review and Meta-Analysis," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-10, March.
    5. Moritz Gerstung & Hani Nakhoul & Niko Beerenwinkel, 2011. "Evolutionary Games with Affine Fitness Functions: Applications to Cancer," Dynamic Games and Applications, Springer, vol. 1(3), pages 370-385, September.
    6. Yi Sun & Yao Wang & Shu Yuan & Jialing Wen & Weiyu Li & Liu Yang & Xiaoyan Huang & Yanmei Mo & Yingqi Zhao & Yuanming Lu, 2018. "Exposure to PM2.5 via vascular endothelial growth factor relationship: Meta-analysis," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-12, June.
    7. Yuping Li & Mengzhuo Hou & Guangyu Lu & Natalia Ciccone & Xingdong Wang & Hengzhu Zhang, 2016. "The Prognosis of Anti-Angiogenesis Treatments Combined with Standard Therapy for Newly Diagnosed Glioblastoma: A Meta-Analysis of Randomized Controlled Trials," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-16, December.
    8. Wenhua Liang & Xuan Wu & Shaodong Hong & Yaxiong Zhang & Shiyang Kang & Wenfeng Fang & Tao Qin & Yan Huang & Hongyun Zhao & Li Zhang, 2014. "Multi-Targeted Antiangiogenic Tyrosine Kinase Inhibitors in Advanced Non-Small Cell Lung Cancer: Meta-Analyses of 20 Randomized Controlled Trials and Subgroup Analyses," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-7, October.
    9. Hanlin Lu & Peidong Yuan & Xiaoping Ma & Xiuxin Jiang & Shaozhuang Liu & Chang Ma & Sjaak Philipsen & Qunye Zhang & Jianmin Yang & Feng Xu & Cheng Zhang & Yun Zhang & Wencheng Zhang, 2023. "Angiotensin-converting enzyme inhibitor promotes angiogenesis through Sp1/Sp3-mediated inhibition of notch signaling in male mice," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    10. Nikoleta E. Glynatsi & Vincent A. Knight, 2021. "A bibliometric study of research topics, collaboration, and centrality in the iterated prisoner’s dilemma," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    11. Hailong He & Christine Schönmann & Mathias Schwarz & Benedikt Hindelang & Andrei Berezhnoi & Susanne Annette Steimle-Grauer & Ulf Darsow & Juan Aguirre & Vasilis Ntziachristos, 2022. "Fast raster-scan optoacoustic mesoscopy enables assessment of human melanoma microvasculature in vivo," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    12. Kimio Takeuchi & Ryoji Yanai & Fumiaki Kumase & Yuki Morizane & Jun Suzuki & Maki Kayama & Katarzyna Brodowska & Mitsuru Nakazawa & Joan W Miller & Kip M Connor & Demetrios G Vavvas, 2014. "EGF-Like-Domain-7 Is Required for VEGF-Induced Akt/ERK Activation and Vascular Tube Formation in an Ex Vivo Angiogenesis Assay," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-7, March.
    13. Klaus Eickel & David Andrew Porter & Anika Söhner & Marc Maaß & Lutz Lüdemann & Matthias Günther, 2018. "Simultaneous multislice acquisition with multi-contrast segmented EPI for separation of signal contributions in dynamic contrast-enhanced imaging," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-22, August.
    14. Rui D M Travasso & Eugenia Corvera Poiré & Mario Castro & Juan Carlos Rodrguez-Manzaneque & A Hernández-Machado, 2011. "Tumor Angiogenesis and Vascular Patterning: A Mathematical Model," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-10, May.
    15. Harman Ghuman & Kyungsoo Kim & Sapeeda Barati & Karunesh Ganguly, 2023. "Emergence of task-related spatiotemporal population dynamics in transplanted neurons," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    16. S. Kaessmeyer & H. Huenigen & S. Al Masri & P. Dieckhoefer & K. Richardson & J. Plendl, 2016. "Corpus luteal angiogenesis in a high milk production dairy breed differs from that of cattle with lower milk production levels," Veterinární medicína, Czech Academy of Agricultural Sciences, vol. 61(9), pages 497-503.
    17. Zélia Velez & Marco A. Campinho & Ângela R. Guerra & Laura García & Patricia Ramos & Olinda Guerreiro & Laura Felício & Fernando Schmitt & Maria Duarte, 2012. "Biological Characterization of Cynara cardunculus L. Methanolic Extracts: Antioxidant, Anti-proliferative, Anti-migratory and Anti-angiogenic Activities," Agriculture, MDPI, vol. 2(4), pages 1-21, December.
    18. Sara G. Romeo & Ilaria Secco & Edoardo Schneider & Christina M. Reumiller & Celio X. C. Santos & Anna Zoccarato & Vishal Musale & Aman Pooni & Xiaoke Yin & Konstantinos Theofilatos & Silvia Cellone Tr, 2023. "Human blood vessel organoids reveal a critical role for CTGF in maintaining microvascular integrity," Nature Communications, Nature, vol. 14(1), pages 1-18, December.
    19. Sun Young Lee & Farhan Haq & Deokhoon Kim & Cui Jun & Hui-Jong Jo & Sung-Min Ahn & Won-Suk Lee, 2014. "Comparative Genomic Analysis of Primary and Synchronous Metastatic Colorectal Cancers," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-9, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010717. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.