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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 1: 121-150. doi: 10.3934/mbe.2013.10.121
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A multiple time-scale computational model of a tumor and its micro environment

  • 1.
    University of California, Irvine, Dept. of Statistics, School of Information and Computer Science, 3019 Bren Hall, Irvine, CA 92617-5100
  • 2.
    Princeton University, Dept. of Computer Science, 35 Olden Street, Princeton, NJ 08540-5233
  • 3.
    Wesleyan University, Dept. of Mathematics and Computer Science, 265 Church St. Middletown, CT 06459
  • 4.
    Pomona College, Dept. of Mathematics, 610 N. College Ave., Claremont, CA 91711
  • Experimental evidence suggests that a tumor's environment may be criticalto designing successful therapeutic protocols: Modeling interactionsbetween a tumor and its environment could improve our understanding oftumor growth and inform approaches to treatment. This paper describes anefficient, flexible, hybrid cellular automaton-based implementation ofnumerical solutions to multiple time-scale reaction-diffusion equations,applied to a model of tumor proliferation. The growth and maintenance ofcells in our simulation depend on the rate of cellular energy (ATP)metabolized from nearby nutrients such as glucose and oxygen. Nutrientconsumption rates are functions of local pH as well as localconcentrations of oxygen and other fuels. The diffusion of these nutrientsis modeled using a novel variation of random-walk techniques.Furthermore, we detail the effects of three boundary updateruleson simulations, describing their effects on computationalefficiency and biological realism. Qualitative and quantitative resultsfrom simulations provide insight on how tumor growth is affected byvarious environmental changes such as micro-vessel density or lower pH,both of high interest in current cancer research.

    Citation: Christopher DuBois, Jesse Farnham, Eric Aaron, Ami Radunskaya. A multiple time-scale computational model of a tumor and its micro environment[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 121-150. doi: 10.3934/mbe.2013.10.121

    Related Papers:

  • Experimental evidence suggests that a tumor's environment may be criticalto designing successful therapeutic protocols: Modeling interactionsbetween a tumor and its environment could improve our understanding oftumor growth and inform approaches to treatment. This paper describes anefficient, flexible, hybrid cellular automaton-based implementation ofnumerical solutions to multiple time-scale reaction-diffusion equations,applied to a model of tumor proliferation. The growth and maintenance ofcells in our simulation depend on the rate of cellular energy (ATP)metabolized from nearby nutrients such as glucose and oxygen. Nutrientconsumption rates are functions of local pH as well as localconcentrations of oxygen and other fuels. The diffusion of these nutrientsis modeled using a novel variation of random-walk techniques.Furthermore, we detail the effects of three boundary updateruleson simulations, describing their effects on computationalefficiency and biological realism. Qualitative and quantitative resultsfrom simulations provide insight on how tumor growth is affected byvarious environmental changes such as micro-vessel density or lower pH,both of high interest in current cancer research.


    [1] Journal of Theoretical Biology, 225 (2003), 257-274.
    [2] Seminars in Cancer Biology, 15 (2005), 84-96.
    [3] Bulletin of Mathematical Biology, 60 (1998), 857-900.
    [4] Computers in Biology and Medicine, 31 (2001), 303-331.
    [5] Bulletin of Mathematical Biology, 65 (2003), 903-931.
    [6] Mathematical Modelling of Natural Phenomena, 2 (2007), 30-46.
    [7] Journal of Theoretical Biology, 262 (2010), 142-150.
    [8] Cancer Cell, 4 (2003), 133-146.
    [9] in "The Basic Science of Oncology" (editors, I. Tannock and R. Hill), 295-321. McGraw Hill, New York, (1998).
    [10] Mathematical and Computational Modelling, 24 (1996), 1-17.
    [11] European Journal of Applied Mathematics, 8 (1997), 639-658.
    [12] Cancer Research, 64 March (2004), 2054-2061.
    [13] Radiat Res., 141 (1995), 28-36.
    [14] Journal of Cellular Physiology, 151 (1992), 386-394.
    [15] Lect. Notes Math., 1872 (2006), 131-183.
    [16] J Math Biol., 46 (2003), 191-224.
    [17] Journal of Theoretical Biology, 238 September (2005), 841-862.
    [18] Journal of Computational and Mathematical Models in Medicine, 7 June-September (2006), 159-276.
    [19] J Theor Med., 3 (2001), 79-100.
    [20] Math Comput Model. (Special Issues), 37 (2003), 1221-1244.
    [21] in "Computational Fluid and Solid Mechanics" (editor, K. Bathe), M.I.T., 2 (2003), 1661-1668.
    [22] Cancer Research, 65 September (2005), 7950-7958.
    [23] Semin Radiat Oncol., 8 (1998), 143-50.
    [24] In Silico Biology, 2 (2002), 0035.
    [25] Phyisca A-Statistical Mechanics and its Applications, 322 (2003), 546-554.
    [26] Journal of Statistical Physics, 107 (2002).
    [27] Phys Rev E, 65 (2002).
    [28] Cancer Growth and Progression, 3 (2004).
    [29] Nature Reviews Cancer, 4 (2004), 891-899.
    [30] in "19th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2007)" 1 36-43. IEEE Computer Society, (2007).
    [31] in "Seventh International Conference on Parallel and Distributed Systems Workshops (ICPADS'00 Workshops)", pages 181-187. IEEE Computer Society, (2000).
    [32] International Congress Series, 1240 (2003), 1113-1118.
    [33] Biochem. J., 364 (2002), 309-315.
    [34] Diseases Colon Rect., 44 (2001), 876-884.
    [35] 2002.
    [36] Clinical Cancer Research, 8 (2002), 1284-1291.
    [37] 2001.
    [38] Int J Cancer., 57 (1994), 532-537.
    [39] J Math Biol., 44 Mar.(2002), 201-226.
    [40] Cambridge University Press, Great Britain, 2nd edition, 2000.
    [41] Cancer Science, 97 (2006), 1056-1060.
    [42] Journal of Biological Chemistry, 278 (2003), 45651-45660.
    [43] in "16th International Conference on Artificial Reality and Telexistence-Workshops (ICAT'06)", 110-114. IEEE Computer Society, (2006).
    [44] Journal of Mathematical Biology, 58 (2009), 765-798.
    [45] Journal of Theoretical Biology, 239 (2006), 334-350.
    [46] Cancer Research, 63 (2003), 7232-7240.
    [47] Proc. Natl. Acad. Sci. USA, 89 December (1992), 11832-11836.
    [48] W. H. Freeman and Co., 4th edition, 2004.
    [49] Cancer Science, Epub ahead of print, October 2006.
    [50] Journal of Theoretical Biology, 226 (2004), 377-399.
    [51] Journal of Theoretical Biology, 213 (2001), 315-331.
    [52] Mathematical Biology and Medicine Series. Chapman & Hall/CRC, 2003.
    [53] Future Generation Computer Systems, 18 (2002), 961-972.
    [54] J. Math.Biol., 47 (2003), 270-294.
    [55] Journal of Theoretical Biology, 247 JUL 7 (2007), 186-204.
    [56] Wiley Interdisciplinary Reviews - Systems Biology and Medicine, 3 Jan-Feb (2011), 115-125.
    [57] Experimental Biology and Medicine, 235 April (2010), 411-423.
    [58] Int J Radiat Biol., 75 (1999), 1377-93.
    [59] NeuroImage, 37 (Supplement 1) (2007), S120 - S134. Proceedings of the International Brain Mapping & Intraoperative Surgical Planning Society Annual Meeting, (2006).
    [60] Neoplasia, 5 (2003), 135-145.
    [61] J. Biol. Chem., 281 (2006), 977-981.
    [62] Br J Cancer, 76 (1997), 421-428.
    [63] Journal of Theoretical Biology, 244 (2006), 703-713.
    [64] Journal of Theoretical Biology, 234 (2005), 476-484.
    [65] Anal Cell Pathol., 17 (1998), 71-82.
    [66] Anal Cell Pathol., 7 (1994), 91-106.
    [67] Clinical & Experimental Metastasis, 20 (2003), 237-250.
    [68] Cancer Letters, 123 (1998), 159-165.
    [69] Physical Review E, 71 (2005), pp.12. 041903.
    [70] Physical Review E, 69 (2004), 021910.
    [71] British Journal of Cancer, 89 (2003), 2254-2263.
    [72] Adv Exp Med Biol., 454 (1998), 591-602.
    [73] Journal of Theoretical Biology, 242 (2006), 440-453.
    [74] University of Illinois Press, 1966.
    [75] Mathematical and Computer Modelling, 53 January (2011), 1-20.
    [76] Biochemical and Biophysical Research Communications, 313 (2004), 459-465.

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