Page 343 - Advances in Biomechanics and Tissue Regeneration

REFERENCES 341

[38] K.A. Rejniak, Systems Biology of Tumor Microenvironment, vol. 936, Springer, New York, NY, 2016.
[39] J.M. Ayuso, R. Monge, A. Martínez-González, M. Virumbrales-Muñoz, G.A. Llamazares, J. Berganzo, A. Hernández-
Laín, J. Santolaria, M. Doblar e, C. Hubert, et al., Glioblastoma on a microfluidic chip: generating pseudopalisades and enhancing aggressiveness
through blood vessel obstruction events, Neurooncology 19 (4) (2017) 503–513.
[40] J.M. Ayuso, M. Virumbrales-Muñoz, A. Lacueva, P.M. Lanuza, E. Checa-Chavarria, P. Botella, E. Fernández, M. Doblare, S.J. Allison,
R.M. Phillips, et al., Development and characterization of a microfluidic model of the tumour microenvironment, Sci. Rep. 6 (2016) 36086.
[41] F. Morfoisse, A. Kuchnio, C. Frainay, A. Gomez-Brouchet, M.-B. Delisle, S. Marzi, A.-C. Helfer, F. Hantelys, F. Pujol, J. Guillermet-Guibert, et al.,
Hypoxia induces VEGF-C expression in metastatic tumor cells via a HIF-1α-independent translation-mediated mechanism, Cell Rep. 6 (1) (2014)
155–167.
[42] Y. Kim, H. Jeon, H. Othmer, The role of the tumor microenvironment in glioblastoma: a mathematical model, IEEE Trans. Biomed. Eng. 64 (3)
(2017) 519–527, https://doi.org/10.1109/TBME.2016.2637828.
[43] J.R. Dormand, P.J. Prince, A family of embedded Runge-Kutta formulae, J. Comput. Appl. Math. 6 (1) (1980) 19–26.
[44] P. Bogacki, L.F. Shampine, A 3 (2) pair of Runge-Kutta formulas, Appl. Math. Lett. 2 (4) (1989) 321–325.
[45] C.G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comput. 19 (92) (1965) 577–593.
[46] J. Sherman, W.J. Morrison, Adjustment of an inverse matrix corresponding to a change in one element of a given matrix, Ann. Math. Stat. 21 (1)
(1950) 124–127.
[47] R.D. Skeel, M. Berzins, A method for the spatial discretization of parabolic equations in one space variable, SIAM J. Sci. Stat. Comput. 11 (1)
(1990) 1–32.
[48] L.F. Shampine, M.W. Reichelt, J.A. Kierzenka, Solving index-1 DAEs in MATLAB and Simulink, SIAM Rev. 41 (3) (1999) 538–552.
[49] A. Krogh, The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the
tissue, J. Physiol. 52 (6) (1919) 409–415.
[50] I.F. Tannock, Oxygen diffusion and the distribution of cellular radiosensitivity in tumours, Br. J. Radiol. 45 (535) (1972) 515–524.
[51] B.W. Pogue, J.A. O’Hara, C.M. Wilmot, K.D. Paulsen, H.M. Swartz, Estimation of oxygen distribution in RIF-1 tumors by diffusion model-based
interpretation of pimonidazole hypoxia and Eppendorf measurements, Radiat. Res. 155 (1) (2001) 15–25.
[52] T.W. Secomb, R. Hsu, M.W. Dewhirst, B. Klitzman, J.F. Gross, Analysis of oxygen transport to tumor tissue by microvascular networks, Int. J.
Radiat. Oncol. Biol. Phys. 25 (3) (1993) 481–489.
[53] A.A. Patel, E.T. Gawlinski, S.K. Lemieux, R.A. Gatenby, A cellular automaton model of early tumor growth and invasion: the effects of native
tissue vascularity and increased anaerobic tumor metabolism, J. Theor. Biol. 213 (3) (2001) 315–331.
[54] A. Martínez-González, G.F. Calvo, L.A. P erez Romasanta, V.M. P erez-García, Hypoxic cell waves around necrotic cores in glioblastoma: a bio-
mathematical model and its therapeutic implications, Bull. Math. Biol. 74 (12) (2012) 2875–2896, https://doi.org/10.1007/s11538-012-9786-1.
[55] P.-S. Tang, On the rate of oxygen consumption by tissues and lower organisms as a function of oxygen tension, Q. Rev. Biol. 8 (3) (1933) 260–274.
[56] A. Daşu, I. Toma-Daşu, M. Karlsson, Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia, Phys. Med. Biol.
48 (17) (2003) 2829.
[57] L. Hathout, B. Ellingson, W. Pope, Modeling the efficacy of the extent of surgical resection in the setting of radiation therapy for glioblastoma,
Cancer Sci. 107 (8) (2016) 1110–1116.
[58] A. Agosti, C. Giverso, E. Faggiano, A. Stamm, P. Ciarletta, A personalized mathematical tool for neuro-oncology: a clinical case study, Int. J.
Nonlinear Mech. 107 (2018) 170–181.
[59] H.B. Frieboes, J.S. Lowengrub, S. Wise, X. Zheng, P. Macklin, E.L. Bearer, V. Cristini, Computer simulation of glioma growth and morphology,
Neuroimage 37 (2007) S59–S70.
[60] C.E. Griguer, C.R. Oliva, E. Gobin, P. Marcorelles, D.J. Benos, J.R. Lancaster Jr, G.Y. Gillespie, CD133 is a marker of bioenergetic stress in human
glioma, PLoS ONE 3 (11) (2008) e3655.

II. MECHANOBIOLOGY AND TISSUE REGENERATION