IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i12p2283-2290.html
   My bibliography  Save this article

Cellular automata models of tumour natural shrinkage

Author

Listed:
  • Naumov, Lev
  • Hoekstra, Alfons
  • Sloot, Peter

Abstract

In this paper we present three dimensional cellular automata models for tumour growth, with a focus on the tumour’s natural shrinkage caused by the removal of the dead cells’ mortal remains. The significance of this phenomenon for the resulting volume of the in silico tumour is shown. Two algorithms are presented, one using the chain shifting approach for tumour expansion and shrinkage and another improving the performance of the chain shifting approach. Simulations are validated against the experimental results.

Suggested Citation

  • Naumov, Lev & Hoekstra, Alfons & Sloot, Peter, 2011. "Cellular automata models of tumour natural shrinkage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2283-2290.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:12:p:2283-2290
    DOI: 10.1016/j.physa.2011.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111001142
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2011.02.006?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. Mansury, Yuri & Deisboeck, Thomas S., 2004. "Simulating ‘structure–function’ patterns of malignant brain tumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 219-232.
    2. Junior, S.C.Ferreira & Martins, M.L. & Vilela, M.J., 1998. "A growth model for primary cancer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 569-580.
    3. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    4. Dirk Drasdo, 2005. "Coarse Graining In Simulated Cell Populations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 8(02n03), pages 319-363.
    Full references (including those not matched with items on IDEAS)

    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. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    2. Giorno, Virginia & Román-Román, Patricia & Spina, Serena & Torres-Ruiz, Francisco, 2017. "Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 18-31.
    3. Cabrales, Luis Enrique Bergues & Montijano, Juan I. & Schonbek, Maria & Castañeda, Antonio Rafael Selva, 2018. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 96-110.
    4. Brutovsky, B. & Horvath, D. & Lisy, V., 2008. "Inverse geometric approach for the simulation of close-to-circular growth. The case of multicellular tumor spheroids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 839-850.
    5. R. Gutiérrez & R. Gutiérrez‐Sánchez & A. Nafidi, 2009. "Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 385-405, May.
    6. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    7. Debashis Ghosh & Arul Chinnaiyan, 2004. "Semiparametric methods for identification of tumor progression genes from microarray data," The University of Michigan Department of Biostatistics Working Paper Series 1039, Berkeley Electronic Press.
    8. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2008. "Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 209-217.
    9. Lorenzo Trippa & Gary L. Rosner & Peter Müller, 2012. "Bayesian Enrichment Strategies for Randomized Discontinuation Trials," Biometrics, The International Biometric Society, vol. 68(1), pages 203-211, March.
    10. Cabrales, Luis Enrique Bergues & Aguilera, Andrés Ramírez & Jiménez, Rolando Placeres & Jarque, Manuel Verdecia & Ciria, Héctor Manuel Camué & Reyes, Juan Bory & Mateus, Miguel Angel O’Farril & Palenc, 2008. "Mathematical modeling of tumor growth in mice following low-level direct electric current," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 112-120.
    11. Castañeda, Antonio Rafael Selva & Pozo, Josue Mariño del & Ramirez-Torres, Erick Eduardo & Oria, Eduardo José Roca & Vaillant, Sorangel Bolaños & Montijano, Juan I. & Cabrales, Luis Enrique Bergues, 2023. "Spatio temporal dynamics of direct current in treated anisotropic tumors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 609-632.
    12. repec:dau:papers:123456789/11429 is not listed on IDEAS
    13. Moussa Kounta & Nathan J. Dawson, 2021. "Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1155-1172, September.
    14. Guiraldello, Rafael T. & Martins, Marcelo L. & Mancera, Paulo F.A., 2016. "Evaluating the efficacies of Maximum Tolerated Dose and metronomic chemotherapies: A mathematical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 145-156.
    15. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2006. "Electricity consumption in Morocco: Stochastic Gompertz diffusion analysis with exogenous factors," Applied Energy, Elsevier, vol. 83(10), pages 1139-1151, October.

    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:phsmap:v:390:y:2011:i:12:p:2283-2290. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.