# A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort; B. van der Sanden; A. Juhem; A. Popov; A. Stéphanou

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 1, page 49-77
- ISSN: 0973-5348

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topPons-Salort, M., et al. "A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours." Mathematical Modelling of Natural Phenomena 7.1 (2012): 49-77. <http://eudml.org/doc/222279>.

@article{Pons2012,

abstract = {A computational framework for testing the effects of cytotoxic molecules, specific to a
given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The
model is based on a cellular automaton to describe tumour cell states transitions from
proliferation to death. It is coupled with a model describing the tumour vasculature and
its adaptation to the blood rheological constraints when alterations are induced by VDAs
treatment. Several therapeutic protocols in two structurally different vascular networks
were tested by varying the duration of cytotoxic drug perfusion and the periodicity of
treatment cycles. The impact of VDAs were also tested both experimentally from intravital
microscopy through a dorsal skinfold chamber on a mouse and numerically. Simulation
results show that combining cytotoxic treatment with a post treatment of VDA through a
judicious timing could favour the rapid eradication of the tumour. The computational
framework thus gives some insights into the outcome of cytotoxic and VDAs treatments on a
qualitative basis. Future validation from our experimental setup could open up new
perspectives towards Computer-Assisted Therapeutic Strategies.},

author = {Pons-Salort, M., van der Sanden, B., Juhem, A., Popov, A., Stéphanou, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {computational modelling; cellular automaton; cytotoxic molecules; vascular disrupting agents; vascular tumour growth; therapeutic protocols},

language = {eng},

month = {1},

number = {1},

pages = {49-77},

publisher = {EDP Sciences},

title = {A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours},

url = {http://eudml.org/doc/222279},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Pons-Salort, M.

AU - van der Sanden, B.

AU - Juhem, A.

AU - Popov, A.

AU - Stéphanou, A.

TI - A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/1//

PB - EDP Sciences

VL - 7

IS - 1

SP - 49

EP - 77

AB - A computational framework for testing the effects of cytotoxic molecules, specific to a
given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The
model is based on a cellular automaton to describe tumour cell states transitions from
proliferation to death. It is coupled with a model describing the tumour vasculature and
its adaptation to the blood rheological constraints when alterations are induced by VDAs
treatment. Several therapeutic protocols in two structurally different vascular networks
were tested by varying the duration of cytotoxic drug perfusion and the periodicity of
treatment cycles. The impact of VDAs were also tested both experimentally from intravital
microscopy through a dorsal skinfold chamber on a mouse and numerically. Simulation
results show that combining cytotoxic treatment with a post treatment of VDA through a
judicious timing could favour the rapid eradication of the tumour. The computational
framework thus gives some insights into the outcome of cytotoxic and VDAs treatments on a
qualitative basis. Future validation from our experimental setup could open up new
perspectives towards Computer-Assisted Therapeutic Strategies.

LA - eng

KW - computational modelling; cellular automaton; cytotoxic molecules; vascular disrupting agents; vascular tumour growth; therapeutic protocols

UR - http://eudml.org/doc/222279

ER -

## References

top- T. Alarcon, H. Byrne, P.K. Maini. A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol., 225 (2003), No. 2, 257–74.
- T. Alarcon, H. Byrne, P.K. Maini. A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells. J. Theor. Biol., 229 (2004), No. 3, 395–411.
- A. Altinok, D. Gonze, F. Lévi, A. Goldbeter. An automaton model for the cell cycle. Interface Focus, 1 (2011), 36–47.
- A.R.A. Anderson, K.A. Rejniak, P. Gerlee, V. Quaranta. Modelling of cancer growth, evolution and invasion : bridging scales and models. Math. Mod. Nat. Phenom., 2 (2007), No. 3, 1–29. Zbl1337.92020
- B.C. Baguley, D.W. Siemann. Temporal aspects of the action of ASA404 (vadimezan ; DMXAA). Expert Opin. Investig. Drugs., 19 (2010), No. 11, 1413–25.
- H.M. Byrne. Dissecting cancer through mathematics : from cell to the animal model. Nat. Rev. Cancer, 10 (2010), 221–30.
- P. Carmeliet. Angiogenesis in life, disease and medicine. Nature, 438 (2005), No. 7070, 932–6.
- J.J. Casciari, S.V. Sotirchos, R.M. Sutherland. Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular PH. J. Cell Physiol., 151 (1992), No. 2, 386–94.
- A. d’Onofrio, A. Gandolfi. Chemotherapy of vascularised tumours : role of vessel density and the effect of vascular "pruning". J. Theor. Biol., 264 (2010), 253–65.
- A. Eichholz, S. Merchant, A.M. Gaya. Anti-angiogenesis therapies : their potential in cancer management. OncoTragets and Therapy, 3 (2010), 69–82.
- J. Folkman. Tumor angiogenesis : therapeutic implications. N. Engl. J. Med., 285 (1971), No. 21, 1182–6.
- J.P. Freyer, E. Tustanoff, A.J. Franko, R.M. Sutherland. In situ oxygen consumption rates of cells in V-79 multicellular spheroids during growth. J. Cell Physiol., 118 (1984), 53–61.
- J.P. Freyer, R.M. Sutherland. Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. Cancer Res., 46 (1986), 3504–3512.
- J.L. Gevertz. Computational modeling of tumor response to vascular-targeting therapies - part I : validation. Comput. Math. Methods Med., (2011), 830515. Zbl1219.92039
- J. Grote, R. Süsskind, P. Vaupel. Oxygen diffusivity in tumor tissue (DS-carcinosarcoma) under temperature conditions within the range of 20-40 degrees C. Pflugers Arch., 372 (1977), No. 1, 37–42.
- C.A. Honstvet. Targeting tumour vasculature as a cancer treatment. Comp. Math. Meth. Med., 8 (2007), No. 1, 1–9. Zbl1120.92021
- T. Hoshino, C.B. Wilson, M.L. Rosenblum, M.J. Barker. Chemotherapeutic implications of growth fraction and cell cycle time in glioblastomas. Neurosurg., 43 (1975), 127–35.
- R.K. Jain. Normalizing tumor vasculature with anti-angiogenic therapy : a new paradigm for combination therapy. Nat. Med., 7 (2001), No. 9, 987–9.
- J.W. Lippert. Vascular disrupting agents. Bioorg. Med. Chem., 15 (2007), 2, 605–15.
- J.S. Lowengrub, H.B. Frieboes, F. Jin, Y.L. Chuang, X. Li, P. Macklin, S.M. Wise, V. Cristini. Nonlinear modelling of cancer : bridging the gap between cells and tumours. Nonlinearity, 23 (2010), R1–R91. Zbl1181.92046
- P. Macklin, S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, V. Cristini, J. Lowengrub. Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol., 58 (2009), No. 4-5, 765–98. Zbl1311.92040
- M. Maurin, O. Stéphan, J.C. Vial, S.R. Marder, B. van der Sanden. Deep in vivo Two-Photon Imaging of Blood Vessels with a new Dye encapsulated in Pluronic Nanomicelles. J. Biomed. Opt., 16 (2011), 036001.
- S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain. Mathematical modelling of dynamic adaptative tumour-induced angiogenesis : clinical implications and therapeutic targeting strategies. J. Theor. Biol., 241 (2006), 564–89.
- S.R. McDougall, M.A.J. Chaplain, A. Stéphanou, A.R.A Anderson. Modelling the impact of pericyte migration and coverage of vessels on the efficacy of vascular disrupting agents. Math. Mod. Nat. Phenom., 5 (2010), No. 1, 163–202. Zbl1190.35219
- T. Morimura. Prolongation of G1 phase in cultured glioma cells by cis-dichlorodiammineplatinum (II) (CDDP) : Analysis using bromodeoxyuridine (BrdU)-Hoechst technique. J. Neuro-Oncol., 7 (1989), 71–79.
- L.J. Nugent, R.K. Jain. Extravascular diffusion in normal and neoplastic tissues. Cancer Res., 44 (1984), No. 1, 238–44.
- J.M. Osborne, A. Walter, S.K. Kershaw, G.R. Mirams, A.G. Fletcher, P. Pathmanathan, D. Gavaghan, O.E. Jensen, P.K. Maini, H.M. Byrne. A hybrid approach to multi-scale modelling of cancer. Philos. Transact. A Math. Phys. Eng., 368 (2010), No. 1930, 5013–28. Zbl1211.37113
- M.R. Owen, I.J. Stamper, M. Muthana, G.W. Richardson, J. Dobson, C.E. Lewis, H.M. ByrneMathematical modeling predicts synergistic antitumour effects of comibining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy. Cancer. Res., 71 (2011), No. 8, 2826–37.
- M. Pàez-Ribes, E. Allen, J. Hudock, T. Takeda, H. Okuyama, F. Viñals, M. Inoue, G. Bergers, D. Hanahan, O. Casanovas. Antiangogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis. Cancer Cell., 15 (2009), No. 3, 220–31.
- J. Panovska, H.M. Byrne, P.K. Maini. A theoretical study of the response of vascular tumours to different types of chemotherapy. Math. Comp. Mod., 47 (2008), 560–79. Zbl1148.92020
- H. Perfahl, H.M. Byrne, T. Chen, V. Estrella, T. Alarcon, A. Lapin, R.A. Gatenby, R.J. Gillies, M.C. Lloyd, P.K. Maini, M. Reuss, M.R. Owen. Multiscale modelling of vascular tumour growth in 3D : the roles of the domain size and boundary conditions. PLoS ONE, 6 (2011), No. 4, e14790.
- B. Pertuiset, D. Dougherty, C. Cromeyer, T. Hoshino, M. Berger, M.L. J Rosenblum. Stem cell studies of human malignant brain tumours. Part 2 : proliferation kinetics of brain-tumour cells in vitro in early-passage cultures. Neurosurg., 63 (1985), 426–32.
- F. Rehman, G. Rustin. ASA404 : update on drug development. Expert Opin. Investig. Drugs, 17 (2008), No. No. 10, 1547–1551.
- R. Rockne, J.K. Rockhill, M. Mrugula, A.M. Spence, I. Kalet, K. Hendrickson, A. Lai, T. Cloughesy, E.C. AlvordJr, K.R. Swanson. Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo : a mathematical modeling approach. Phys. Med. Biol., 55 (2010), 3271–85.
- R.J. Shipley, S.J. Chapman. Multiscale modelling of fluid and drug transport in vascular tumours. Bull. Math. Biol., 72 (2010), No. 6, 1464–91. Zbl1198.92028
- D.W. Siemann, E. Mercer, S. Lepler, A.M. Rojiani. Vascular targeting agents enhance chemotherapeutic agent activities in solid tumor therapy. Int. J. Cancer, 99 (2002), 1–6.
- D.W. Siemann, M.R. Horsman. Enhancement of radiation therapy by vascular targeting agents. Curr. Opin. Investig. Drugs, 3 (2002), 1660–5.
- D.W. Siemann, M.R. Horsman. Vascular targeted therapies in oncology. Cell Tissue Res.335 (2009), No. 1, 241–248.
- G.S. Stamatakos, V.P. Antipas, N.K. Uzunoglu, R.G. Dale. A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme : studies on the effect of clonogenic cell density. The British Journal of Radiology, 79 (2006), 389–400.
- A. Stéphanou, S.R. McDougall, A.R.A Anderson, M.A.J. Chaplain. Mathematical modelling of flow in 2d and 3d vascular networks : applications to anti-angiogenic and chemotherapeutic drug strategies. Math. Comp. Mod., 41 (2005), No. 10, 1137–56. Zbl1080.92050
- A. Stéphanou, S.R. McDougall, A.R.A Anderson, M.A.J. Chaplain. Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis. Math. Comp. Mod., 44 (2006), No. 1-2, 96–123. Zbl1130.92036
- E.A. Swabb, J. Wei, P.M. Gullino. Diffusion and convection in normal and neoplastic tissues. Cancer Res., 34 (1974), No. 10, 2814–22.
- K.R. Swanson, E.C. Alvord, J.D. Murray. Quantifying efficacy of chemotherapy of brain tumours with homogeneous and heterogeneous drug delivery. Acta. Biotheor., 50 (2002), No. 4, 223–37.
- G. Tanaka, Y. Hirata, S.L. Goldenberg, N. Bruchovsky, K. Aihara. Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil. Trans. R. Soc. A, 368 (2010), 5029–44. Zbl1211.37118
- G.M. Tozer, C. Kanthou, B.C. Baguley. Disrupting tumour blood vessels. Nat. rev. Cancer, 5 (2005), No. 6, 423–35.
- P. Tracqui. Biophysical models of tumour growth. Rep. Prog. Phys., 72 (2009), No. 5, 056701.
- J.T. Tyson, B. Novak. Temporal organization of the cell cycle. Curr. Biol., 18 (2008), No. 17, R759–R768.
- B. Wang, J.M. Rosano, R. Cheheltani, M.P. Achary, M.F. Kiani. Towards a targeted multi-drug delivery approach to improve therapeutic efficacy in breast cancer. Expert Opin. Drug Deliv., 7 (2010), No. 10, 1159–73.

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