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A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. (English) Zbl 1402.92050

Summary: Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials.
We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls.
This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy.
This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

MSC:

92C15 Developmental biology, pattern formation
92C50 Medical applications (general)
92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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[1] Addison-Smith, B.; McElwain, D.L.S.; Maini, P.K., A simple mechanistic model of sprout spacing in tumour-associated angiogenesis, J. theor. biol., 250, 1, 1-15, (2008) · Zbl 1397.92307
[2] Ahmad, S.A.; Liu, W.; Jung, Y.D.; Fan, F.; Reinmuth, N.; Bucana, C.D.; Ellis, L.M., Differential expression of angiopoietin-1 and angiopoietin-2 in colon carcinoma. A possible mechanism for the initiation of angiogenesis, Cancer, 92, 5, 1138-1143, (2001)
[3] Alarcón, T.; Byrne, H.; Maini, P., A multiple scale model for tumor growth, Multiscale model simul., 3, 440-475, (2005) · Zbl 1107.92019
[4] Anderson, A.R.A.; Chaplain, M.A.J., Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. math. biol., 60, 5, 857-899, (1998) · Zbl 0923.92011
[5] Araujo, R.P.; McElwain, D.L.S., New insights into vascular collapse and growth dynamics in solid tumors, J. theor. biol., 228, 3, 335-346, (2004) · Zbl 1439.92062
[6] Araujo, R.P.; McElwain, D.L.S., A mixture theory for the genesis of residual stresses in growing tissues I: a general formulation, SIAM J. appl. math., 65, 1261-1284, (2005) · Zbl 1074.74043
[7] Araujo, R.P.; McElwain, D.L.S., A mixture theory for the genesis of residual stresses in growing tissues II: solutions to the biphasic equations for a multicell spheroid, SIAM J. appl. math., 66, 2, 447-467, (2005) · Zbl 1130.74311
[8] Araujo, R.P.; McElwain, D.L.S., The nature of the stresses induced during tissue growth, Appl. math. lett., 18, 1081-1088, (2005) · Zbl 1079.74515
[9] Araujo, R.P.; McElwain, D.L.S., The role of mechanical host – tumour interactions in the collapse of tumour blood vessels and tumour growth dynamics, J. theor. biol., 238, 4, 817-827, (2006) · Zbl 1445.92069
[10] Ausprunk, D.H.; Folkman, J., Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis, Microvasc. res., 14, 1, 53-65, (1977)
[11] Bartha, K.; Rieger, H., Vascular network remodeling via vessel cooption, regression and growth in tumors, J. theor. biol., 241, 4, 903-918, (2006) · Zbl 1447.92083
[12] Baxter, L.T.; Jain, R.K., Transport of fluid and macromolecules in tumors. I. role of interstitial pressure and convection, Microvasc. res., 37, 1, 77-104, (1989)
[13] Benjamin, L.E.; Keshet, E., Conditional switching of vascular endothelial growth factor (VEGF) expression in tumors: induction of endothelial cell shedding and regression of hemangioblastoma-like vessels by VEGF withdrawal, Proc. natl. acad. sci. USA, 94, 16, 8761-8766, (1997)
[14] Bergers, G.; Hanahan, D., Modes of resistance to anti-angiogenic therapy, Nat. rev. cancer, 8, 8, 592-603, (2008)
[15] Blagosklonny, M.V.; Pardee, A.B., The restriction point of the cell cycle, Cell cycle, 1, 2, 103-110, (2002)
[16] Boucher, Y.; Baxter, L.T.; Jain, R.K., Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: implications for therapy, Cancer res., 50, 15, 4478-4484, (1990)
[17] Bresch, D., Colin, T., Grenier, E., Ribba, B., Saut, O., 2009a. Computational modeling of solid tumor growth: the avascular stage. Submitted.; Bresch, D., Colin, T., Grenier, E., Ribba, B., Saut, O., 2009a. Computational modeling of solid tumor growth: the avascular stage. Submitted. · Zbl 1214.92039
[18] Bresch, D., Colin, T., Grenier, E., Ribba, B., Saut, O., 2009b. A viscoelastic model for avascular tumor growth. Submitted.; Bresch, D., Colin, T., Grenier, E., Ribba, B., Saut, O., 2009b. A viscoelastic model for avascular tumor growth. Submitted. · Zbl 1185.92059
[19] Byrne, H.M.; Chaplain, M.A., Growth of necrotic tumors in the presence and absence of inhibitors, Math. biosci., 135, 15, 187-216, (1996) · Zbl 0856.92010
[20] Davis, S.; Aldrich, T.H.; Jones, P.F.; Acheson, A.; Compton, D.L.; Jain, V.; Ryan, T.E.; Bruno, J.; Radziejewski, C.; Maisonpierre, P.C.; Yancopoulos, G.D., Isolation of angiopoietin-1, a ligand for the tie2 receptor, by secretion-trap expression cloning, Cell, 87, 7, 1161-1169, (1996)
[21] DeVita, V.T.; Hellman, S.; Rosenberg, S.A., Cancer—principles and practice of oncology, (2005), Lippincott Williams and Wilkins
[22] Ebos, J.M.L.; Lee, C.R.; Cruz-Munoz, W.; Bjarnason, G.A.; Christensen, J.G.; Kerbel, R.S., Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis, Cancer cell, 15, 3, 232-239, (2009)
[23] Etoh, T.; Inoue, H.; Tanaka, S.; Barnard, G.F.; Kitano, S.; Mori, M., Angiopoietin-2 is related to tumor angiogenesis in gastric carcinoma: possible in vivo regulation via induction of proteases, Cancer res., 61, 5, 2145-2153, (2001)
[24] Ferrara, N., Molecular and biological properties of vascular endothelial growth factor, J. mol. med., 77, 7, 527-543, (1999)
[25] Ferrara, N., Role of vascular endothelial growth factor in the regulation of angiogenesis, Kidney int., 56, 3, 794-814, (1999)
[26] Ferrara, N., VEGF and the quest for tumour angiogenesis factors, Nat. rev. cancer, 2, 10, 795-803, (2002)
[27] Folkman, J., What is the evidence that tumors are angiogenesis dependent?, J. natl. cancer inst., 82, 1, 4-6, (1990)
[28] Folkman, J., Role of angiogenesis in tumor growth and metastasis, Semin. oncol., 29, 6 Suppl. 16, 15-18, (2002)
[29] Folkman, J., Antiangiogenesis in cancer therapy—endostatin and its mechanisms of action, Exp. cell res., 312, 5, 594-607, (2006)
[30] Gabhann, F.M.; Popel, A.S., Differential binding of VEGF isoforms to VEGF receptor 2 in the presence of neuropilin-1: a computational model, Am. J. physiol. heart circ. physiol., 288, 6, H2851-H2860, (2005)
[31] Gerisch, A.; Chaplain, M.A.J., Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion, J. theor. biol., 250, 4, 684-704, (2008) · Zbl 1397.92326
[32] Goldacre, R.J.; Sylven, B., On the access of blood-borne dyes to various tumour regions, Br. J. cancer, 16, 306-322, (1962)
[33] Hanahan, D.; Folkman, J., Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis, Cell, 86, 3, 353-364, (1996)
[34] Hogea, C.S.; Murray, B.T.; Sethian, J.A., Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method, J. math. biol., 53, 1, 86-134, (2006) · Zbl 1100.92029
[35] Hu, B.; Guo, P.; Fang, Q.; Tao, H.-Q.; Wang, D.; Nagane, M.; Huang, H.-J.S.; Gunji, Y.; Nishikawa, R.; Alitalo, K.; Cavenee, W.K.; Cheng, S.-Y., Angiopoietin-2 induces human glioma invasion through the activation of matrix metalloprotease-2, Proc. natl. acad. sci. USA, 100, 15, 8904-8909, (2003)
[36] Kevrekidis, P.G.; Whitaker, N.; Good, D.J.; Herring, G.J., Minimal model for tumor angiogenesis, Phys. rev. E stat. nonlin. soft matter phys., 73, 6 Pt 1, 061926, (2006) · Zbl 1244.92032
[37] Kim, Y.-M.; Hwang, S.; Kim, Y.-M.; Pyun, B.-J.; Kim, T.-Y.; Lee, S.-T.; Gho, Y.S.; Kwon, Y.-G., Endostatin blocks vascular endothelial growth factor-mediated signaling via direct interaction with kdr/flk-1, J. biol. chem., 277, 31, 27872-27879, (2002)
[38] Koga, K.; Todaka, T.; Morioka, M.; Hamada, J.; Kai, Y.; Yano, S.; Okamura, A.; Takakura, N.; Suda, T.; Ushio, Y., Expression of angiopoietin-2 in human glioma cells and its role for angiogenesis, Cancer res., 61, 16, 6248-6254, (2001)
[39] Kumar, S.; Weaver, V.M., Mechanics, malignancy, and metastasis: the force journey of a tumor cell, Cancer metastasis rev., 28, 1-2, 113-127, (2009)
[40] Lee, D.-S.; Rieger, H.; Bartha, K., Flow correlated percolation during vascular remodeling in growing tumors, Phys. rev. lett., 96, 5, 058104, (2006)
[41] Li, H.-L.; Li, S.; Shao, J.-Y.; Lin, X.-B.; Cao, Y.; Jiang, W.-Q.; Liu, R.-Y.; Zhao, P.; Zhu, X.-F.; Zeng, M.-S.; Guan, Z.-Z.; Huang, W., Pharmacokinetic and pharmacodynamic study of intratumoral injection of an adenovirus encoding endostatin in patients with advanced tumors, Gene ther., 15, 4, 247-256, (2008)
[42] Lin, X.; Huang, H.; Li, S.; Li, H.; Li, Y.; Cao, Y.; Zhang, D.; Xia, Y.; Guo, Y.; Huang, W.; Jiang, W., A phase 1 clinical trial of an adenovirus-mediated endostatin gene (e10a) in patients with solid tumors, Cancer biol. ther., 6, 5, 648-653, (2007)
[43] Macklin, P.; McDougall, S.; Anderson, A.R.A.; Chaplain, M.A.J.; Cristini, V.; Lowengrub, J., Multiscale modelling and nonlinear simulation of vascular tumour growth, J. math. biol., 58, 4-5, 765-798, (2009) · Zbl 1311.92040
[44] Maisonpierre, P.C.; Suri, C.; Jones, P.F.; Bartunkova, S.; Wiegand, S.J.; Radziejewski, C.; Compton, D.; McClain, J.; Aldrich, T.H.; Papadopoulos, N.; Daly, T.J.; Davis, S.; Sato, T.N.; Yancopoulos, G.D., Angiopoietin-2, a natural antagonist for tie2 that disrupts in vivo angiogenesis, Science, 277, 5322, 55-60, (1997)
[45] Mantzaris, N.V.; Webb, S.; Othmer, H.G., Mathematical modeling of tumor-induced angiogenesis, J. math. biol., 49, 2, 111-187, (2004) · Zbl 1109.92020
[46] McDougall, S.R.; Anderson, A.R.A.; Chaplain, M.A.J., Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies, J. theor. biol., 241, 3, 564-589, (2006) · Zbl 1447.92096
[47] Metheny-Barlow, L.J.; Li, L.Y., The enigmatic role of angiopoietin-1 in tumor angiogenesis, Cell res., 13, 5, 309-317, (2003)
[48] Moon, W.S.; Rhyu, K.H.; Kang, M.J.; Lee, D.G.; Yu, H.C.; Yeum, J.H.; Koh, G.Y.; Tarnawski, A.S., Overexpression of VEGF and angiopoietin 2: a key to high vascularity of hepatocellular carcinoma?, Mod. pathol., 16, 6, 552-557, (2003)
[49] O’Reilly, M.S.; Boehm, T.; Shing, Y.; Fukai, N.; Vasios, G.; Lane, W.S.; Flynn, E.; Birkhead, J.R.; Olsen, B.R.; Folkman, J., Endostatin: an endogenous inhibitor of angiogenesis and tumor growth, Cell, 88, 2, 277-285, (1997)
[50] Partanen, J.; Armstrong, E.; Mäkelä, T.P.; Korhonen, J.; Sandberg, M.; Renkonen, R.; Knuutila, S.; Huebner, K.; Alitalo, K., A novel endothelial cell surface receptor tyrosine kinase with extracellular epidermal growth factor homology domains, Mol. cell biol., 12, 4, 1698-1707, (1992)
[51] Paweletz, N.; Knierim, M., Tumor-related angiogenesis, Crit. rev. oncol. hematol., 9, 3, 197-242, (1989)
[52] Pàez-Ribes, M.; Allen, E.; Hudock, J.; Takeda, T.; Okuyama, H.; Viñals, F.; Inoue, M.; Bergers, G.; Hanahan, D.; Casanovas, O., Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis, Cancer cell, 15, 3, 220-231, (2009)
[53] Plank, M.J.; Sleeman, B.D.; Jones, P.F., A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins, J. theor. biol., 229, 4, 435-454, (2004) · Zbl 1440.92014
[54] Relf, M.; LeJeune, S.; Scott, P.A.; Fox, S.; Smith, K.; Leek, R.; Moghaddam, A.; Whitehouse, R.; Bicknell, R.; Harris, A.L., Expression of the angiogenic factors vascular endothelial cell growth factor, acidic and basic fibroblast growth factor, tumor growth factor beta-1, platelet-derived endothelial cell growth factor, placenta growth factor, and pleiotrophin in human primary breast cancer and its relation to angiogenesis, Cancer res., 57, 5, 963-969, (1997)
[55] Ribba, B.; Colin, T.; Schnell, S., A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies, Theor. biol. med. model., 3, 7, (2006)
[56] Ribba, B.; Marron, K.; Agur, Z.; Alarcón, T.; Maini, P.K., A mathematical model of doxorubicin treatment efficacy for non-Hodgkin’s lymphoma: investigation of the current protocol through theoretical modelling results, Bull math. biol., 67, 1, 79-99, (2005) · Zbl 1334.92207
[57] Ribba, B.; Saut, O.; Colin, T.; Bresch, D.; Grenier, E.; Boissel, J.P., A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, J. theor. biol., 243, 4, 532-541, (2006) · Zbl 1447.92105
[58] Ribba, B.; You, B.; Tod, M.; Girard, P.; Tranchand, B.; Trillet-Lenoir, V.; Freyer, G., Chemotherapy may be delivered upon an integrated view of tumor dynamics, IET syst. biol, 3, 180-190, (2009)
[59] Sauter, B.V.; Martinet, O.; Zhang, W.J.; Mandeli, J.; Woo, S.L., Adenovirus-mediated gene transfer of endostatin in vivo results in high level of transgene expression and inhibition of tumor growth and metastases, Proc. natl. acad. sci. USA, 97, 9, 4802-4807, (2000)
[60] Sundberg, C.; Kowanetz, M.; Brown, L.F.; Detmar, M.; Dvorak, H.F., Stable expression of angiopoietin-1 and other markers by cultured pericytes: phenotypic similarities to a subpopulation of cells in maturing vessels during later stages of angiogenesis in vivo, Lab. invest., 82, 4, 387-401, (2002)
[61] Takahashi, G.H.; Fatt, I.; Goldstick, T.K., Oxygen consumption rate of tissue measured by a micropolarographic method, J. gen. physiol., 50, 2, 317-335, (1966)
[62] Tanaka, F.; Ishikawa, S.; Yanagihara, K.; Miyahara, R.; Kawano, Y.; Li, M.; Otake, Y.; Wada, H., Expression of angiopoietins and its clinical significance in non-small cell lung cancer, Cancer res., 62, 23, 7124-7129, (2002)
[63] Tosin, A.; Ambrosi, D.; Preziosi, L., Mechanics and chemotaxis in the morphogenesis of vascular networks, Bull math. biol., 68, 7, 1819-1836, (2006) · Zbl 1334.92066
[64] Welter, M.; Bartha, K.; Rieger, H., Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor, J. theor. biol., 250, 2, 257-280, (2008) · Zbl 1397.92379
[65] Zetter, B.R., Angiogenesis and tumor metastasis, Annu. rev. med., 49, 407-424, (1998)
[66] Zheng, X.; Wise, S.M.; Cristini, V., Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method, Bull. math. biol., 67, 2, 211-259, (2005) · Zbl 1334.92214
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