Coupling tumor growth and bio distribution models

A.R. Anderson, M.A. Chaplain, Bull. Math. Biol. 60, 857 (1998)

C.J.W. Breward, H.M. Byrne, C.E. Lewis, A multiphase model describing vascular tumour growth. Bull. Math. Biol. 65, 609–640 (2003). https://doi.org/10.1016/S0092-8240(03)00027-2

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)

S.C. Cowin, L. Cardoso, Mech. Mater. 44, 47 (2012)

M.W. Dewhirst, T.W. Secomb, Nat. Rev. Cancer 17, 738 (2017)

D.E. Discher, P. Janmey, Y.-L. Wang, Science 310, 1139 (2005)

S. Eikenberry, C. Thalhauser, Y. Kuang, PLoS Comput. Biol. 5, e1000362 (2009)

M. Ferrari, Trends Biotechnol. 28, 181 (2010)

M. Ferrari, Int. J. Non. Linear. Mech. 56, 3 (2013)

M. Fraldi, A.R. Carotenuto, J. Mech. Phys. Solids 112, 345 (2018)

G. Freyer, B. Ligneau, B. Tranchand, C. Ardiet, F. Serre-Debeauvais, V. Trillet-Lenoir, Cancer Treat. Rev. 23, 153 (1997)

W. Gray, C. Miller, Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems (Springer International Publinshing, Cham, 2014)

W. Gray, B. Schrefler, Int. J. Numer. Anal. Methods Geomech. 31, 541 (2007)

W.G. Gray, C.T. Miller, B.A. Schrefler, Adv. Water Resour. 51, 123 (2013)

A. Hawkins-Daarud, S. Prudhomme, K.G. van der Zee, J.T. Oden, J. Math. Biol. 67, 1457 (2013)

E.J. Koay, M. Ferrari, Phys. Biol. 11, 60201 (2014)

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). https://doi.org/10.1016/j.compbiomed.2018.05.022

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)

M. Kojic, M. Milosevic, V. Simic, E.J. Koay, N. Kojic, A. Ziemys, M. Ferrari, J. Serbian Soc. Comput. Mech. 11, 108 (2017b)

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)

J. Kremheller, A.T. Vuong, L. Yoshihara, W.A. Wall, B.A. Schrefler, Comput. Methods Appl. Mech. Eng. 340, 657 (2018)

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). https://doi.org/10.1002/num.21934

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)

F. Michor, J. Liphardt, M. Ferrari, J. Widom, hat does physics have to do with cancer? Nat. Rev. Cancer. 11, 657–670 (2011). https://doi.org/10.1038/nrc3092

M. Milosevic, V. Simic, B. Milicevic, E. Koay, M. Ferrari, A. Ziemys, M. Kojic, Comput. Methods Appl. Mech. Eng. 338, 97 (2018)

N.M. Moore, N. Kuhn, S.E. Hanlon, J.S.H. Lee, L.A. Nagahara, Phys. Biol. 8, 10302 (2011)

J.T. Oden, A. Hawkins, S. Prudhomme, Math. Model. Methods Appl. Sci. 20, 477 (2010)

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)

J.T. Oden, E.E. Prudencio, A. Hawkins-Daarud, Math. Model. Methods Appl. Sci. 23, 1309 (2013)

M.M. Rahman, Y. Feng, T. Yankeelov, J.T. Oden, Comput. Methods Appl. Mech. Eng. 320, 261 (2017)

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)

R. Santagiuliana, M. Ferrari, B.A. Schrefler, Comput. Methods Appl. Mech. Eng. 304, 197 (2016)

R. Santagiuliana, C. Stigliano, P. Mascheroni, M. Ferrari, P. Decuzzi, B.A. Schrefler, Adv. Model. Simul. Eng. Sci. 2, 19 (2015)

G. Sciumè, W.G. Gray, F. Hussain, M. Ferrari, P. Decuzzi, B.A. Schrefler, Comput. Mech. 53, 465 (2014a)

G. Sciumè, R. Santagiuliana, M. Ferrari, P. Decuzzi, B.A. Schrefler, Phys. Biol. 11, 65004 (2014b)

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)

G. Vilanova, M. Burés, I. Colominas, H. Gomez, J. R. Soc. Interface 15, 20180415 (2018)