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Multiscale agent-based cancer modeling

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Abstract

Agent-based modeling (ABM) is an in silico technique that is being used in a variety of research areas such as in social sciences, economics and increasingly in biomedicine as an interdisciplinary tool to study the dynamics of complex systems. Here, we describe its applicability to integrative tumor biology research by introducing a multi-scale tumor modeling platform that understands brain cancer as a complex dynamic biosystem. We summarize significant findings of this work, and discuss both challenges and future directions for ABM in the field of cancer research.

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References

  1. Anderson AR, Weaver AM, Cummings PT, Quaranta V (2006) Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127: 905–915

    Article  Google Scholar 

  2. Swanson KR, Alvord EC Jr, Murray JD (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif 33: 317–329

    Article  Google Scholar 

  3. Swanson KR, Alvord EC Jr, Murray JD (2002) Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br J Cancer 86: 14–18

    Article  Google Scholar 

  4. Swanson KR, Alvord EC Jr, Murray JD (2002) Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery. Acta Biotheor 50: 223–237

    Article  Google Scholar 

  5. Swanson KR, Bridge C, Murray JD, Alvord EC Jr (2003) Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sci 216: 1–10

    Article  Google Scholar 

  6. Araujo RP, Petricoin EF, Liotta LA (2005) A mathematical model of combination therapy using the EGFR signaling network. Biosystems 80: 57–69

    Article  Google Scholar 

  7. Armstrong NJ, Painter KJ, Sherratt JA (2006) A continuum approach to modelling cell–cell adhesion. J Theor Biol 243: 98–113

    Article  MathSciNet  Google Scholar 

  8. Zhang L, Dai W, Nassar R (2005) A numerical method for optimizing laser power in the irradiation of a 3D triple layered cylindrical skin structure. Numer Heat Tr A 48: 21–41

    Article  Google Scholar 

  9. Zhang L, Dai W, Nassar R (2006) A numerical method for obtaining an optimal temperature distribution in a 3D triple-layered cylindrical skin structure embedded with a blood vessel. Numer Heat Tr A 49: 765–784

    Article  Google Scholar 

  10. Chaplain M, Lolas G (2005) Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system. Math Modell Methods Appl Sci 15: 1685–1734

    Article  MATH  MathSciNet  Google Scholar 

  11. Wolfram S (1994) Cellular automata and complexity: collected papers. Addison-Wesley, Reading, MA

    MATH  Google Scholar 

  12. Mansury Y, Deisboeck TS (2003) The impact of “search precision” in an agent-based tumor model. J Theor Biol 224: 325–337

    Article  MathSciNet  Google Scholar 

  13. Mansury Y, Deisboeck TS (2004) Simulating ‘structure-function’ patterns of malignant brain tumors. Physica A 331: 219–232

    Article  Google Scholar 

  14. Mansury Y, Deisboeck TS (2004) Simulating the time series of a selected gene expression profile in an agent-based tumor model. Physica D 196: 193–204

    Article  MATH  Google Scholar 

  15. Schofield P, Chaplain M, Hubbard S (2005) Evolution of searching and life history characteristics in individual-based models of host-parasitoid-microbe associations. J Theor Biol 237: 1–16

    Article  MathSciNet  Google Scholar 

  16. Orme ME, Chaplain MA (1997) Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. IMA J Math Appl Med Biol 14: 189–205

    Article  MATH  Google Scholar 

  17. Byrne HM, Alarcon T, Owen MR, Webb SD, Maini PK (2006) Modelling aspects of cancer dynamics: a review. Philos Transact A Math Phys Eng Sci 364: 1563–1578

    Article  MathSciNet  Google Scholar 

  18. Kansal AR, Torquato S, Harsh IG, Chiocca EA, Deisboeck TS (2000) Cellular automaton of idealized brain tumor growth dynamics. Biosystems 55: 119–127

    Article  Google Scholar 

  19. Anderson AR, Chaplain MA (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 60: 857–899

    Article  MATH  Google Scholar 

  20. Anderson AR, Chaplain M, NewMan EL, Stelle RJC, Thompson AM (2000) Mathematical modelling of tumor invasion and metastasis. J Theor Med 2: 129–154

    MATH  Google Scholar 

  21. Athale C, Mansury Y, Deisboeck TS (2005) Simulating the impact of a molecular ‘decision-process’ on cellular phenotype and multicellular patterns in brain tumors. J Theor Biol 233: 469–481

    Article  Google Scholar 

  22. Athale CA, Deisboeck TS (2006) The effects of EGF-receptor density on multiscale tumor growth patterns. J Theor Biol 238: 771–779

    Article  MathSciNet  Google Scholar 

  23. Zhang L, Athale CA, Deisboeck TS (2007) Development of a three-dimensional multiscale agent-based tumor model: simulating gene–protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J Theor Biol 244: 96–107

    Article  MathSciNet  Google Scholar 

  24. Sanga S, Sinek JP, Frieboes HB, Ferrari M, Fruehauf JP, Cristini V (2006) Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev Anticancer Ther 6: 1361–1376

    Article  Google Scholar 

  25. Davidsson P (2002) Agent based social simulation: a computer science view. JASSS 5

  26. Bonabeau E (2002) Agent-based modeling: methods and techniques for simulating human systems. Proc Natl Acad Sci USA 99(Suppl 3): 7280–7287

    Article  Google Scholar 

  27. Moreira N (2006) In pixels and in health: computer modeling pushes the threshold of medical research. Sci News 169: 40–41

    Article  Google Scholar 

  28. Peirce SM, Van Gieson EJ, Skalak TC (2004) Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J 18: 731–733

    Google Scholar 

  29. Kirschner D, Panetta JC (1998) Modeling immunotherapy of the tumor–immune interaction. J Math Biol 37: 235–252

    Article  MATH  Google Scholar 

  30. Perrin D, Ruskin HJ, Crane M (2006) An agent-based approach to immune modelling: priming individual response. Trans Eng Comput Technol 17: 80–86

    Google Scholar 

  31. Segovia-Juarez JL, Ganguli S, Kirschner D (2004) Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model. J Theor Biol 231: 357–376

    Article  MathSciNet  Google Scholar 

  32. An G (2001) Agent-based computer simulation and sirs: building a bridge between basic science and clinical trials. Shock 16: 266–273

    Article  Google Scholar 

  33. An G (2004) In silico experiments of existing and hypothetical cytokine-directed clinical trials using agent-based modeling. Crit Care Med 32: 2050–2060

    Article  Google Scholar 

  34. Mansury Y, Kimura M, Lobo J, Deisboeck TS (2002) Emerging patterns in tumor systems: simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model. J Theor Biol 219: 343–370

    Article  MathSciNet  Google Scholar 

  35. Wodarz D, Komarova NL (2005) Computational biology of cancer. World Scientific Publishing Company, Singapore

    MATH  Google Scholar 

  36. Schaller G, Meyer-Hermann M (2005) Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys Rev E Stat Nonlin Soft Matter Phys 71: 051910

    MathSciNet  Google Scholar 

  37. Engelberg J, Ganguli S, Hunt CA (2006) Agent-based simulations of in vitro multicellular tumor spheroid growth. In: Proceedings of the agent-directed simulation symposium, pp 141–48

  38. Zhu JJ, Coakley S, Holcombe M, MacNeil S, Smallwood RH (2006) Individual cell-based simulation of 3D multicellular spheroid self-assembly. Eur Cells Mater 11(Suppl 3): 31

    Google Scholar 

  39. Spencer SL, Gerety RA, Pienta KJ, Forrest S (2006) Modeling somatic evolution in tumorigenesis. PLoS Comput Biol 2: e108

    Article  Google Scholar 

  40. Buldyrev SV, Goldberger AL, Havlin S, Peng CK, Stanley HE, Stanley MH, Simons M (1993) Fractal landscapes and molecular evolution: modeling the myosin heavy chain gene family. Biophys J 65: 2673–2679

    Article  Google Scholar 

  41. Hausdorff JM, Peng CK, Ladin Z, Wei JY, Goldberger AL (1995) Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol 78: 349–358

    Google Scholar 

  42. Ossadnik SM, Buldyrev SV, Goldberger AL, Havlin S, Mantegna RN, Peng CK, Simons M, Stanley HE (1994) Correlation approach to identify coding regions in DNA sequences. Biophys J 67: 64–70

    Article  Google Scholar 

  43. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49: 1685–1689

    Google Scholar 

  44. Peng CK, Havlin S, Stanley HE, Goldberger AL (1995) Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5: 82–87

    Article  Google Scholar 

  45. Barabasi AL, Stanley HE (1995) Fractal concepts in surface growth. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  46. Giese A, Loo MA, Tran N, Haskett D, Coons SW, Berens ME (1996) Dichotomy of astrocytoma migration and proliferation. Int J Cancer 67: 275–282

    Article  Google Scholar 

  47. Lund-Johansen M, Bjerkvig R, Humphrey PA, Bigner SH, Bigner DD, Laerum OD (1990) Effect of epidermal growth factor on glioma cell growth, migration, and invasion in vitro. Cancer Res 50: 6039–6044

    Google Scholar 

  48. Lund-Johansen M, Forsberg K, Bjerkvig R, Laerum OD (1992) Effects of growth factors on a human glioma cell line during invasion into rat brain aggregates in culture. Acta Neuropathol 84: 190–197

    Article  Google Scholar 

  49. Schlegel J, Merdes A, Stumm G, Albert FK, Forsting M, Hynes N, Kiessling M (1994) Amplification of the epidermal-growth-factor-receptor gene correlates with different growth behaviour in human glioblastoma. Int J Cancer 56: 72–77

    Article  Google Scholar 

  50. Westermark B, Magnusson A, Heldin CH (1982) Effect of epidermal growth factor on membrane motility and cell locomotion in cultures of human clonal glioma cells. J Neurosci Res 8: 491–507

    Article  Google Scholar 

  51. Alarcon T, Byrne HM, Maini PK (2004) A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells. J Theor Biol 229: 395–411

    Article  MathSciNet  Google Scholar 

  52. Zhang L, Wang Z, Sagotsky JA, Deisboeck TS (2008) Simulating brain tumor heterogeneity with a multiscale agent-based model: linking molecular signatures, phenotypes and expansion rate. Math Comput Model. doi:10.1016/j.mcm.2008.05.011

  53. Kleihues P, Ohgaki H (1999) Primary and secondary glioblastomas: from concept to clinical diagnosis. Neuro Oncol 1: 44–51

    Article  Google Scholar 

  54. Lang FF, Miller DC, Koslow M, Newcomb EW (1994) Pathways leading to glioblastoma multiforme: a molecular analysis of genetic alterations in 65 astrocytic tumors. J Neurosurg 81: 427–436

    Article  Google Scholar 

  55. Ohgaki H, Dessen P, Jourde B, Horstmann S, Nishikawa T, Di Patre PL, Burkhard C, Schuler D, Probst-Hensch NM, Maiorka PC, Baeza N, Pisani P, Yonekawa Y, Yasargil MG, Lutolf UM, Kleihues P (2004) Genetic pathways to glioblastoma: a population-based study. Cancer Res 64: 6892–6899

    Article  Google Scholar 

  56. Bankes SC (2002) Agent-based modeling: a revolution. Proc Natl Acad Sci USA 99(Suppl 3): 7199–7200

    Article  Google Scholar 

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Author notes

  1. Le Zhang

    Present address: Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA

Authors and Affiliations

  1. Complex Biosystems Modeling Laboratory, Harvard-MIT (HST) Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital-East 2301, Bldg. 149, 13th Street, Charlestown, MA, 02129, USA

    Le Zhang, Zhihui Wang, Jonathan A. Sagotsky & Thomas S. Deisboeck

Authors
  1. Le Zhang
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  2. Zhihui Wang
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  3. Jonathan A. Sagotsky
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  4. Thomas S. Deisboeck
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Corresponding author

Correspondence to Thomas S. Deisboeck.

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Zhang, L., Wang, Z., Sagotsky, J. et al. Multiscale agent-based cancer modeling. J. Math. Biol. 58, 545–559 (2009). https://doi.org/10.1007/s00285-008-0211-1

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  • DOI: https://doi.org/10.1007/s00285-008-0211-1

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