Coupling tumor growth and bio distribution models

  • Raffaella SantagiulianaEmail author
  • Miljan Milosevic
  • Bogdan Milicevic
  • Giuseppe Sciumè
  • Vladimir Simic
  • Arturas Ziemys
  • Milos Kojic
  • Bernhard A. Schrefler
Part of the following topical collections:
  1. Biomedical Micro-Nanotechnologies toward Translation


We couple a tumor growth model embedded in a microenvironment, with a bio distribution model able to simulate a whole organ. The growth model yields the evolution of tumor cell population, of the differential pressure between cell populations, of porosity of ECM, of consumption of nutrients due to tumor growth, of angiogenesis, and related growth factors as function of the locally available nutrient. The bio distribution model on the other hand operates on a frozen geometry but yields a much refined distribution of nutrient and other molecules. The combination of both models will enable simulating the growth of a tumor in a whole organ, including a realistic distribution of therapeutic agents and allow hence to evaluate the efficacy of these agents.


Modeling Multiphase Biodistribution Code coupling Angiogenesis Smearded finite element 



B.A.S. gratefully acknowledges the support of the Technische Universität München - Institute for Advanced Study, funded by the German Excellence Initiative and the TUV SÜD Foundation. The authors acknowledge CITO Award, Houston Methodist Research Institute, Houston, NCI U54 CA210181. The authors affiliated to Serbian institutions also acknowledge support from Ministry of Education and Science of Serbia, grants OI 174028 and III 41007, and City of Kragujevac.


  1. A.R. Anderson, M.A. Chaplain, Bull. Math. Biol. 60, 857 (1998)CrossRefGoogle Scholar
  2. C.J.W. Breward, H.M. Byrne, C.E. Lewis, A multiphase model describing vascular tumour growth. Bull. Math. Biol. 65, 609–640 (2003). CrossRefGoogle Scholar
  3. A.R. Carotenuto, A. Cutolo, A. Petrillo, R. Fusco, C. Arra, M. Sansone, D. Larobina, L. Cardoso, M. Fraldi, J. Mech. Behav. Biomed. Mater. 86, 55 (2018)CrossRefGoogle Scholar
  4. S.C. Cowin, L. Cardoso, Mech. Mater. 44, 47 (2012)CrossRefGoogle Scholar
  5. M.W. Dewhirst, T.W. Secomb, Nat. Rev. Cancer 17, 738 (2017)CrossRefGoogle Scholar
  6. D.E. Discher, P. Janmey, Y.-L. Wang, Science 310, 1139 (2005)CrossRefGoogle Scholar
  7. S. Eikenberry, C. Thalhauser, Y. Kuang, PLoS Comput. Biol. 5, e1000362 (2009)CrossRefGoogle Scholar
  8. M. Ferrari, Trends Biotechnol. 28, 181 (2010)CrossRefGoogle Scholar
  9. M. Ferrari, Int. J. Non. Linear. Mech. 56, 3 (2013)CrossRefGoogle Scholar
  10. M. Fraldi, A.R. Carotenuto, J. Mech. Phys. Solids 112, 345 (2018)MathSciNetCrossRefGoogle Scholar
  11. G. Freyer, B. Ligneau, B. Tranchand, C. Ardiet, F. Serre-Debeauvais, V. Trillet-Lenoir, Cancer Treat. Rev. 23, 153 (1997)CrossRefGoogle Scholar
  12. W. Gray, C. Miller, Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems (Springer International Publinshing, Cham, 2014)CrossRefGoogle Scholar
  13. W. Gray, B. Schrefler, Int. J. Numer. Anal. Methods Geomech. 31, 541 (2007)CrossRefGoogle Scholar
  14. W.G. Gray, C.T. Miller, B.A. Schrefler, Adv. Water Resour. 51, 123 (2013)CrossRefGoogle Scholar
  15. A. Hawkins-Daarud, S. Prudhomme, K.G. van der Zee, J.T. Oden, J. Math. Biol. 67, 1457 (2013)MathSciNetCrossRefGoogle Scholar
  16. E.J. Koay, M. Ferrari, Phys. Biol. 11, 60201 (2014)CrossRefGoogle Scholar
  17. M. Kojic, M. Milosevic, V. Simic, E.J. Koay, N. Kojic, A. Ziemys, M. Ferrari, Multiscale smeared finite element model for mass transport in biological tissue: from blood vessels to cells and cellular organelles. Comput. Biol. Med. 99, 7–23 (2018). CrossRefGoogle Scholar
  18. M. Kojic, M. Milosevic, V. Simic, E.J. Koay, J.B. Fleming, S. Nizzero, N. Kojic, A. Ziemys, M. Ferrari, Comput. Methods Appl. Mech. Eng. 324, 413 (2017a)CrossRefGoogle Scholar
  19. M. Kojic, M. Milosevic, V. Simic, E.J. Koay, N. Kojic, A. Ziemys, M. Ferrari, J. Serbian Soc. Comput. Mech. 11, 108 (2017b)CrossRefGoogle Scholar
  20. M. Kojic, R. Slavkovic, M. Zivkovic, N. Grujovic, N. Filipovic, M. Milosevic, PAK-Finite element program for linear and nonlinear analysis; software patent. Univ Kragujevac and R&D Center for Bioengineering, Kragujevac, (2010)Google Scholar
  21. J. Kremheller, A.T. Vuong, L. Yoshihara, W.A. Wall, B.A. Schrefler, Comput. Methods Appl. Mech. Eng. 340, 657 (2018)CrossRefGoogle Scholar
  22. E.A.B.F. Lima, R.C. Almeida, J.T. Oden. Analysis and numerical solution of stochastic phase-field models of tumor growth. Numerical methods for partial differential equations. 31, 552–574 (2015). MathSciNetCrossRefGoogle Scholar
  23. E.A.B.F. Lima, J.T. Oden, D.A. Hormuth 2nd, T.E. Yankeelov, R.C. Almeida, Math. Models Methods Appl. Sci. 26, 2341 (2016)MathSciNetCrossRefGoogle Scholar
  24. F. Michor, J. Liphardt, M. Ferrari, J. Widom, hat does physics have to do with cancer? Nat. Rev. Cancer. 11, 657–670 (2011). CrossRefGoogle Scholar
  25. M. Milosevic, V. Simic, B. Milicevic, E. Koay, M. Ferrari, A. Ziemys, M. Kojic, Comput. Methods Appl. Mech. Eng. 338, 97 (2018)CrossRefGoogle Scholar
  26. N.M. Moore, N. Kuhn, S.E. Hanlon, J.S.H. Lee, L.A. Nagahara, Phys. Biol. 8, 10302 (2011)CrossRefGoogle Scholar
  27. J.T. Oden, A. Hawkins, S. Prudhomme, Math. Model. Methods Appl. Sci. 20, 477 (2010)CrossRefGoogle Scholar
  28. J.T. Oden, E.A.B.F. Lima, R.C. Almeida, Y. Feng, M.N. Rylander, D. Fuentes, D. Faghihi, M.M. Rahman, M. DeWitt, M. Gadde, J.C. Zhou, Arch. Comput. Methods Eng. 23, 735 (2016)MathSciNetCrossRefGoogle Scholar
  29. J.T. Oden, E.E. Prudencio, A. Hawkins-Daarud, Math. Model. Methods Appl. Sci. 23, 1309 (2013)CrossRefGoogle Scholar
  30. M.M. Rahman, Y. Feng, T. Yankeelov, J.T. Oden, Comput. Methods Appl. Mech. Eng. 320, 261 (2017)CrossRefGoogle Scholar
  31. H.L. Rocha, R.C. Almeida, E.A.B.F. Lima, A.C.M. Resende, J.T. Oden, T.E. Yankeelov, Math. Model. Methods Appl. Sci. 28, 61 (2018)CrossRefGoogle Scholar
  32. R. Santagiuliana, M. Ferrari, B.A. Schrefler, Comput. Methods Appl. Mech. Eng. 304, 197 (2016)CrossRefGoogle Scholar
  33. R. Santagiuliana, C. Stigliano, P. Mascheroni, M. Ferrari, P. Decuzzi, B.A. Schrefler, Adv. Model. Simul. Eng. Sci. 2, 19 (2015)Google Scholar
  34. G. Sciumè, W.G. Gray, F. Hussain, M. Ferrari, P. Decuzzi, B.A. Schrefler, Comput. Mech. 53, 465 (2014a)MathSciNetCrossRefGoogle Scholar
  35. G. Sciumè, R. Santagiuliana, M. Ferrari, P. Decuzzi, B.A. Schrefler, Phys. Biol. 11, 65004 (2014b)CrossRefGoogle Scholar
  36. G. Sciumè, S. Shelton, W.G. Gray, C.T. Miller, F. Hussain, M. Ferrari, P. Decuzzi, B.A. Schrefler, New J. Phys. 15, 15005 (2013)CrossRefGoogle Scholar
  37. G. Vilanova, M. Burés, I. Colominas, H. Gomez, J. R. Soc. Interface 15, 20180415 (2018)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Civil, Environmental and Architectural EngineeringUniversity of PadovaPadovaItaly
  2. 2.Bioengineering Research and Development Center BioIRC KragujevacKragujevacSerbia
  3. 3.Belgrade Metropolitan UniversityBelgradeSerbia
  4. 4.Institut de Mécanique et d’Ingénierie (I2M, CNRS UMR 5295)University of BordeauxBordeauxFrance
  5. 5.The Department of NanomedicineHouston Methodist Research InstituteHoustonUSA
  6. 6.Serbian Academy of Sciences and ArtsBelgradeSerbia
  7. 7.Institute for Advanced StudyTechnische Universität MünchenGarching b. MünchenGermany

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