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Multiscale modeling of angiogenic tumor growth, progression, and therapy

  • Complex Systems Biophysics
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Abstract

A mathematical model of angiogenic tumor growth in tissue with account of bevacizumab therapy was developed. The model accounts for convective flows that occur in dense tissue under active division of tumor cells, as well as the migration and proliferation dichotomy of malignant cells, which depends on the concentrations of major metabolites, such as oxygen and glucose. Tumor cells wich are in a state of metabolic stress produce vascular endothelial growth factor, which stimulates angiogenesis. To establish the relationship between the capillary network density and oxygen supply, a separate model of stationary blood flow in the capillary network was developed and investigated. A numerical study of the tumor-growth model showed that antiangiogenic bevacizumab treatment of tumors of the diffuse type reduces the total number of their cells, but practically does not affect the rate of their invasion into normal tissues. At the same time, it was found that the growth of dense tumors may be non-monotonic in a rather wide range of parameters. It was shown that in this case bevacizumab therapy stabilizes and significantly inhibits tumor growth, while its local-in-time efficiency is sensitive to the time that it begins.

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Abbreviations

VEGF:

vascular endothelial growth factor

References

  1. J. Folkman, P. Cole, and S. Zimmerman, Ann. Surg. 164 (3), 491 (1966).

    Article  Google Scholar 

  2. M. Welter, K. Bartha and H. Rieger, J. Theor. Biol. 259 (3), 405 (2009).

    Article  Google Scholar 

  3. J. Folkman, New Engl. J. Med. 285 (21), 1182 (1971).

    Article  Google Scholar 

  4. T. H. Adair and J.-P. Montani, Angiogenesis (Morgan & Claypool Life Sciences, San Rafael, CA, 2010).

    Google Scholar 

  5. P. Carmeliet and R. K. Jain, Nature 407 (6801), 249 (2000).

    Article  Google Scholar 

  6. B. Drogat, P. Auguste, et al., Cancer Res. 67 (14), 6700 (2007).

    Article  Google Scholar 

  7. M. A. Konerding, C. van Ackern, and E. Fait, in Blood Perfusion and Microenvironment of Human Tumors: Implications for Clinical Radiooncology, Ed. by M. Molls and P. Vaupel (Springer, Berlin, 2002), pp. 5–17.

  8. S. K. Stamatelos, E. Kim, A. P. Pathak, and A. S. Popel, Microvasc. Res. 91, 8 (2014).

    Article  Google Scholar 

  9. J. E. Fletcher, Math. Biosci. 38 (3–4), 159 (1978).

    Article  MathSciNet  Google Scholar 

  10. J. B. Geddes, R. T. Carr, F. Wu, et al., Chaos 20 (4), 045123 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  11. A. S. Kholodov, A. V. Evdokimov, and S. S. Simakov, in Mathematical Biology: Recent Trends (Anamaya Publishers, New Delhi, 2006), pp. 22–29.

    Google Scholar 

  12. A. Eberhard, S. Kahlert, V. Goede, et al., Cancer Res. 60 (5) 1388 (2000).

    Google Scholar 

  13. K. R. Swanson, R. C. Rockne, J. Claridge, et al., Cancer Res. 71 (24), 7366 (2011).

    Article  Google Scholar 

  14. A. V. Kolobov and M. B. Kuznetsov, Russ. J. Numeric. Anal. Math. Model. 28 (5), 471 (2013).

    Google Scholar 

  15. N. V. Mantzaris, S. Webb, and H. G. Othmer, J. Math. Biol. 49 (2), 111 (2004).

    Article  MathSciNet  Google Scholar 

  16. F. Milde, M. Bergdorf, and P. Koumoutsakos, Biophys. J. 95 (7), 3146 (2008).

    Article  ADS  Google Scholar 

  17. Y. Cai, J. Wu, Z. Li, and Q. Long, PLOS ONE 11 (3), e0150296 (2016).

    Article  Google Scholar 

  18. B. Szomolay, T. D. Eubank, R. D. Roberts, et al., J. Theor. Biol. 303, 141 (2012).

    Article  Google Scholar 

  19. S. D. Finley and A. S. Popel, J. Natl. Cancer Inst., djt093 (2013).

    Google Scholar 

  20. L. Soto-Ortiz, J. Theor. Biol. 394, 197 (2016).

    Article  MathSciNet  Google Scholar 

  21. A. V. Kolobov and M. B. Kuznetsov, Biophysics (Moscow) 60 (3), 449 (2015).

    Article  Google Scholar 

  22. A. V. Kolobov, V. V. Gubernov, and M. B. Kuznetsov, Russ. J. Numeric. Anal. Math. Model. 30 (5), 289 (2015).

    Google Scholar 

  23. A. Giese, R. Bjerkvig, M. E. Berens, and M. Westphal, J. Clin. Oncol. 21, 1624 (2003).

    Article  Google Scholar 

  24. A. V. Gusev and A. A. Polezhaev, Kratk. Soobshch. Fiz. FIAN Nos. 11–12, 85 (1997).

    Google Scholar 

  25. M. A. Konerding, C. van Ackern, and E. Fait, in Blood Perfusion and M icroenvironment of Human Tumors: Implications for Clinical Radiooncology, Ed. by M. Molls and P. Vaupel (Springer, Berlin, 2002), pp. 5–17.

  26. A. G. Kamkin and A. A. Kamensky, Fundamental and Clinical Physiology (Akademiya, Moscow, 2004) [in Russian].

    Google Scholar 

  27. R. N. Pittman, in Colloquium Series on Integrated Systems Physiology: From Molecule to Function (Morgan & Claypool Life Sciences, 2011), Vol. 3 (3), pp. 1–100.

    Google Scholar 

  28. L. Garby and J. Meldon, in The Respiratory Functions of Blood (Springer New York, 1977), pp. 35–110.

    Book  Google Scholar 

  29. J. R. Levick, An Introduction to Cardiovascular Physiology (Butterworth-Heinemann, Oxford, 2013).

    Google Scholar 

  30. S. Simakov, I. Ispolatov, S. Maslov, and A. Nikitin, in Pathway Analysis for Drug Discovery, Ed. by A. Yuryev (Wiley, 2008), Chap. 4, pp. 67–102.

  31. A. T. Falk, J. Barriere, E. Francois, and P. Follana, Critical Rev. Oncol. Hematol. 94 (3), 311 (2015).

    Article  Google Scholar 

  32. O. N. Pyaskovskaya, D. L. Kolesnik, A. V. Kolobov, et al., Exp. Oncol. 30, 269 (2008).

    Google Scholar 

  33. K. Groebe, S. Erz, and W. Mueller-Klieser, Adv. Experim. Med. Biol. 361, 619 (1994).

    Article  Google Scholar 

  34. J. J. Casciari, S. V. Sotirchos, and R. M. Sutherland, Cell Prolif. 25 (1), 1 (1992).

    Article  Google Scholar 

  35. C. Androjna, J. E. Gatica, J. M. Belovich, and K. A. Derwin, Tissue Eng. A 14 (4), 559 (2008).

    Article  Google Scholar 

  36. A. Carreau, B. E. Hafny-Rahbi, A. Matejuket, et al., J. Cell. Mol. Med. 15 (6), 1239 (2011).

    Article  Google Scholar 

  37. J. M. Kelm, C. D. Sanchez-Bustamante, E. Ehler, et al., J. Biotechnol. 118 (2), 213 (2005).

    Article  Google Scholar 

  38. K. J. Kim, B. Li, J. Winer, et al., Nature 362, 841 (1993).

    Article  ADS  Google Scholar 

  39. J. Kleinheinz, S. Jung, K. Wermker, et al., Head Face Med. 6 (1), 17 (2010).

    Article  Google Scholar 

  40. N. Papadopoulos, J. Martin, Q. Ruan, et al., Angiogenesis 15, 171 (2012).

    Article  Google Scholar 

  41. Genentech Inc., Avastin Full Prescribing Information. http://www.gene.com/download/pdf/avastinprescribing.pdf (2015).

  42. I. B. Petrov and A. I. Lobanov, Lectures in Computational Mathematics (Internet Univ. Inform Techol., Moscow, 2006) [in Russian].

    Google Scholar 

  43. J. P. Boris and D. L. Book, J. Comput. Phys. 11 (1), 38 (1973).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskiy pr. 53, Moscow, 119991, Russia

    M. B. Kuznetsov & A. V. Kolobov

  2. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia

    N. O. Gorodnova, S. S. Simakov & A. V. Kolobov

  3. Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow oblast, 141701, Russia

    S. S. Simakov

Authors
  1. M. B. Kuznetsov
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  2. N. O. Gorodnova
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  3. S. S. Simakov
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  4. A. V. Kolobov
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Correspondence to A. V. Kolobov.

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Original Russian Text © M.B. Kuznetsov, N.O. Gorodnova, S.S. Simakov, A.V. Kolobov, 2016, published in Biofizika, 2016, Vol. 61, No. 5, pp. 1029–1039.

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Kuznetsov, M.B., Gorodnova, N.O., Simakov, S.S. et al. Multiscale modeling of angiogenic tumor growth, progression, and therapy. BIOPHYSICS 61, 1042–1051 (2016). https://doi.org/10.1134/S0006350916050183

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