Modeling the Effect of Tissue Displacement during Avascular Tumor Growth on Tumor Progression

Authors

  • Karafyllidis Ioannis Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Kimmeria, Xanthi, Greece
  • Dimitra Sasaroli Department of Molecular Biology and Genetics, Democritus University of Thrace, 68100, Alexandroupolis, Greece
  • Athanasios Karapetsas Department of Molecular Biology and Genetics, Democritus University of Thrace, 68100, Alexandroupolis, Greece
  • Raphael Sandaltzopoulos Department of Molecular Biology and Genetics, Democritus University of Thrace, 68100, Alexandroupolis, Greece

Keywords:

cellular automata, tissue displacement, tumor growth, oxygen diffusion, glucose diffusion, avascular growth

Abstract

We have developed a model for tissue displacement caused by early tumor growth (i.e. before the onset of angiogenesis) using cellular automata and solving diffusion equations on the cellular automaton lattice in order to compute the distribution of oxygen and glucose into the tumor. Tumor growth causes mechanical forces that displace the already existing vessels away from it, thus affecting the distribution of oxygen and glucose which in turn influence tumor growth. We simulated this growth process and we found that tissue displacement may affect tumor progression rate. We also found that the relative distance of the tumor initiation area from neighboring vessels influences its growth. The model and the simulation software we developed can be used to understand the dynamics of early tumor growth and to explore various hypotheses of tumor growth relevant to drug delivery in chemotherapy. Importantly, our approach highlights that vessel displacement should not be neglected in tumor growth models.

 

Author Biography

Raphael Sandaltzopoulos, Department of Molecular Biology and Genetics, Democritus University of Thrace, 68100, Alexandroupolis, Greece

Department of Molecular Biology and Genetics, Assoc. Professor

References

W.F. Ames, Numerical Methods for Partial Differential Equations, Boston: Academic Press, 1992

R.P. Araujo and L.S. Mcelwain, “A history of the study of solid tumour growth: The contribution of mathematical modellingâ€, Bulletin of Mathematical Biology, vol. 66, pp. 1039-1091, 2004

R. Axelrod, D.E. Axelrod and K.J. Pienta, “Evolution of cooperation among tumor cellsâ€, Proceedings of the National Academy of Sciences, vol. 103, pp. 13474-13479, 2006

M.I. Balaguera, J.C. Briceño and J.A. Glazier, “An object-oriented modelling framework for the arterial wallâ€, Computer methods in biomechanics and biomedical engineering, vol. 13, pp. 135-142, 2010

H.M. Byrne, “Modeling avascular tumor growthâ€, Cancer Modeling and Simulation, Ch. 4, ed. Preziosi L, NY: Chapman & Hall, 2003

S. Cui and J. Escher, “Asymptotic behaviour of solutions of a multidimensional moving boundary problem in modeling tumor growthâ€, Communications in Partial Differential Equations, vol. 33, pp. 636-655, 2008

H.B. Frieboes, M.E. Edgerton, J.P. Fruehauf, F.R.A.J. Rose, L.K. Worrall, R.A. Gatenby, M. Ferrari and V. Cristini, “Prediction of drug response in breast cancer using interactive experimental/computational modelingâ€, Cancer Research, vol. 69, pp. 4484-4492, 2009

A. Friedman, Cancer models and their mathematic analysis, in Tutorials in mathematical biosciences, pp. 223-246, ed. Friedman A. , Berlin: Springer-Verlag, 2006

D. Hanahan and R.A. Weinberg, “The hallmarks of cancerâ€, Cell, vol. 100, pp. 57-70, 2000

G. Koch, A. Waltz, G. Lahu and J. Schropp, “Modeling of tumor growth effects of combination therapyâ€, Journal of Pharmacokinetics and Pharmacodynamics, vol. 36, pp. 179-197, 2009

L.D. Landau and E.M. Lifshitz, Mechanics, Oxford: Pergamon Press,1976

J.S. Lowengrub, H.B. Frieboes, , F. Jin, Y.L. Chuang, X. Li, P. MacKlin, S.M. Wise and V. Cristini, “Nonlinear modelling of cancer: Bridging the gap between cells and tumoursâ€, Nonlinearity, vol. 23, pp. R1-R91, 2010

P. Macklin and J. Lowengrub, “Nonlinear simulation of the effect of microenvironment on tumor growthâ€, Journal of Theoretical Biology, vol. 245, pp. 677-704, 2007

J. Moreira and A. Deutsch, “Cellular automaton models of tumor developmentâ€, Advances in Complex Systems Communications in Partial Differential Equations, vol. 33, pp. 247-267, 2002

M.J. Piotrowska and S.D. Angus, “A quantitative cellular automaton model of in vitro multicellular spheroid tumor growthâ€, Journal of Theoretical Biology, vol. 258, pp. 165-178, 2009

B. Ribba, B. You, M. Tod, P. Girard, B. Tranchand, V. Trillet-Lenoir and G. Freyer, “Chemotherapy may be delivered based on an integrated view of tumor dynamicsâ€, IET Systems Biology, vol. 3, pp. 180-190, 2009

D. Sabine and A. Deutsch, “Modeling of self-organized avascular tumor growth with a hybrid cellular automatonâ€, In Silico Biology, , vol. 2, pp. 393-406, 2002

A.M. Shnerb, Y. Louzoun, E. Bettlheim and S. Solomon, “The importance of being discrete: Life always wins on the surfaceâ€, Proceedings of the National Academy of Sciences, vol. 97, pp. 10322-10324, 2000

I. Tannock, R. Hill, R. Bristow and L. Harrington, The Basic Science of Oncology, NY: McGraw-Hill Professional, 2004

P. Tracqui, “Biophysical models of tumour growthâ€, Reports on Progress in Physics, vol. 72, 056701 pp. 1-30, 2009

R.A. Weinberg, The biology of cancer, NY: Garland Science, 2007

D. Wodarz and N.L. Komarova, Computational biology of cancer, London: World Scientific, 2005

Downloads

Published

2014-03-08

How to Cite

Ioannis, K., Sasaroli, D., Karapetsas, A., & Sandaltzopoulos, R. (2014). Modeling the Effect of Tissue Displacement during Avascular Tumor Growth on Tumor Progression. Asian Journal of Fuzzy and Applied Mathematics, 2(1). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/1013

Issue

Vol. 2 No. 1 (2014): February 2014

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.