- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 830515, 17 pages
Computational Modeling of Tumor Response to Vascular-Targeting Therapies—Part I: Validation
Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, P.O. Box 7718, Ewing, NJ 08628-0718, USA
Received 17 August 2010; Accepted 13 January 2011
Academic Editor: Henggui Zhang
Copyright © 2011 Jana L. Gevertz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Carmeliet and R. K. Jain, “Angiogenesis in cancer and other diseases,” Nature, vol. 407, no. 6801, pp. 249–257, 2000.
- J. Folkman, “Fundamental concepts of the angiogenic process,” Current Molecular Medicine, vol. 3, no. 7, pp. 643–651, 2003.
- D. W. Siemann, “Tumor vasculature: a target for anticancer therapies,” in Vascular-Targeted Therapies in Oncology, pp. 1–8, John Wiley & Sons, West Sussex, UK, 2006.
- P. E. Thorpe, “Vascular targeting agents as cancer therapeutics,” Clinical Cancer Research, vol. 10, no. 2, pp. 415–427, 2004.
- G. Bergers and D. Hanahan, “Modes of resistance to anti-angiogenic therapy,” Nature Reviews Cancer, vol. 8, no. 8, pp. 592–603, 2008.
- M. Dickson and J. P. Gagnon, “Key factors in the rising cost of new drug discovery and development,” Nature Reviews Drug Discovery, vol. 3, no. 5, pp. 417–429, 2004.
- C. P. Adams and V. Van Brantner, “Estimating the cost of new drug development: is it really $802 million?” Health Affairs, vol. 25, no. 2, pp. 420–428, 2006.
- J. Gabrielsson and D. Weiner, Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications, Swedish Pharmaceutical Press, Stockholm, Sweden, 3rd edition, 2000.
- A. Iliadis and D. Barbolosi, “Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model,” Computers and Biomedical Research, vol. 33, no. 3, pp. 211–226, 2000.
- K. R. Fister and J. C. Panetta, “Optimal control applied to cell-cycle-specific cancer chemotherapy,” SIAM Journal on Applied Mathematics, vol. 60, no. 3, pp. 1059–1072, 2000.
- D. Barbolosi and A. Iliadis, “Optimizing drug regimens in cancer chemotherapy: a simulation study using a PK-PD model,” Computers in Biology and Medicine, vol. 31, no. 3, pp. 157–172, 2001.
- K. R. Fister and J. C. Panetta, “Optimal control applied to competing chemotherapeutic cell-kill strategies,” SIAM Journal on Applied Mathematics, vol. 63, no. 6, pp. 1954–1971, 2003.
- A. Bertuzzi, A. D'Onofrio, A. Fasano, and A. Gandolfi, “Regression and regrowth of tumor cords following single-dose anticancer treatment,” Bulletin of Mathematical Biology, vol. 65, no. 5, pp. 903–931, 2003.
- B. Ribba, K. Marron, Z. Agur, T. Alarcón, and P. K. Maini, “A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results,” Bulletin of Mathematical Biology, vol. 67, no. 1, pp. 79–99, 2005.
- E. S. Norris, J. R. King, and H. M. Byrne, “Modelling the response of spatially structured tumors to chemotherapy: drug kinetics,” Mathematical and Computer Modelling, vol. 43, no. 7-8, pp. 820–837, 2006.
- L. G. De Pillis and A. Radunskaya, “A mathematical tumor model with immune resistance and drug therapy: an optimal control approach,” Journal of Theoretical Medicine, vol. 3, no. 2, pp. 79–100, 2001.
- H. B. Frieboes, M. E. Edgerton, J. P. Fruehauf et al., “Prediction of drug response in breast cancer using integrative experimental/computational modeling,” Cancer Research, vol. 69, no. 10, pp. 4484–4492, 2009.
- D. Y. Arifin, K. Y. T. Lee, and C. H. Wang, “Chemotherapeutic drug transport to brain tumor,” Journal of Controlled Release, vol. 33, pp. 211–226, 2000.
- J. Sinek, H. Frieboes, X. Zheng, and V. Cristini, “Two-dimensional chemotherapy simulations demonstrate fundamental transport and tumor response limitations involving nanoparticles,” Biomedical Microdevices, vol. 6, no. 4, pp. 297–309, 2004.
- M. Abundo and C. Rossi, “Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy,” Journal of Mathematical Biology, vol. 27, no. 1, pp. 81–90, 1989.
- M. I. S. Costa, J. L. Boldrini, and R. C. Bassanezi, “Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity,” Mathematical Biosciences, vol. 125, no. 2, pp. 211–228, 1995.
- J. R. Usher and D. Henderson, “Some drug-resistant models for cancer chemotherapy part 1: cycle-nonspecific drugs,” Journal of Mathemathics Applied in Medicine and Biology, vol. 13, no. 2, pp. 99–126, 1996.
- J. L. Boldrini and M. I. S. Costa, “Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy,” Journal of Mathemathics Applied in Medicine and Biology, vol. 17, no. 1, pp. 33–51, 2000.
- U. Ledzewicz and H. Schättler, “Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis,” Journal of Theoretical Biology, vol. 252, no. 2, pp. 295–312, 2008.
- J. P. Sinek, S. Sanga, X. Zheng, H. B. Frieboes, M. Ferrari, and V. Cristini, “Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation,” Journal of Mathematical Biology, vol. 58, no. 4-5, pp. 485–510, 2009.
- J. Panovska, H. M. Byrne, and P. K. Maini, “A theoretical study of the response of vascular tumors to different types of chemotherapy,” Mathematical and Computer Modelling, vol. 47, no. 5-6, pp. 560–579, 2008.
- P. Hinow, P. Gerlee, L. J. McCawley et al., “A spatial model of tumor-host interaction: application of chemotherapy,” Mathematical Biosciences and Engineering, vol. 6, no. 3, pp. 521–545, 2009.
- E. C. Holland, “Glioblastoma multiforme: the terminator,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 12, pp. 6242–6244, 2000.
- C. J. Wheeler, K. L. Black, G. Liu et al., “Vaccination elicits correlated immune and clinical responses in glioblastoma multiforme patients,” Cancer Research, vol. 68, no. 14, pp. 5955–5964, 2008.
- E. A. Maher, F. B. Furnari, R. M. Bachoo et al., “Malignant glioma: genetics and biology of a grave matter,” Genes and Development, vol. 15, no. 11, pp. 1311–1333, 2001.
- A. R. Kansal, S. Torquato, G. R. Harsh, E. A. Chiocca, and T. S. Deisboeck, “Simulated brain tumor growth dynamics using a three-dimensional cellular automaton,” Journal of Theoretical Biology, vol. 203, no. 4, pp. 367–382, 2000.
- J. L. Gevertz and S. Torquato, “Modeling the effects of vasculature evolution on early brain tumor growth,” Journal of Theoretical Biology, vol. 243, no. 4, pp. 517–531, 2006.
- J. Holash, P. C. Maisonpierre, D. Compton et al., “Vessel cooption, regression, and growth in tumors mediated by angiopoietins and VEGF,” Science, vol. 284, no. 5422, pp. 1994–1998, 1997.
- P. C. Maisonpierre, C. Suri, P. F. Jones et al., “Angiopoietin-2, a natural antagonist for Tie2 that disrupts in vivo angiogenesis,” Science, vol. 277, no. 5322, pp. 55–60, 1997.
- R. A. Brekken and P. E. Thorpe, “VEGF-VEGF receptor complexes as markers of tumor vascular endothelium,” Journal of Controlled Release, vol. 74, no. 1-3, pp. 173–181, 2001.
- W. C. Broaddus, P. J. Haar, and G. T. Gillies, “Nanoscale neurosurgery,” in Encyclopedia of Biomaterials and Biomedical Engineering, pp. 1035–1042, Marcel Dekker, New York, NY, USA, 3rd edition, 2004.
- J. E. Fletcher, “Mathematical modeling of the microcirculation,” Mathematical Biosciences, vol. 38, no. 3-4, pp. 159–202, 1978.
- V. Tse, L. Xu, Y. C. Yung et al., “The temporal-spatial expression of VEGF, angiopoietins-1 and 2, and Tie-2 during tumor angiogenesis and their functional correlation with tumor neovascular architecture,” Neurological Research, vol. 25, no. 7, pp. 729–738, 2003.
- X. Zheng, S. M. Wise, and V. Cristini, “Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method,” Bulletin of Mathematical Biology, vol. 67, no. 2, pp. 211–259, 2005.
- J. L. Gevertz, G. T. Gillies, and S. Torquato, “Simulating tumor growth in confined heterogeneous environments,” Physical Biology, vol. 5, no. 3, Article ID 036010, 2008.
- J. Gevertz and S. Torquato, “Growing heterogeneous tumors in silico,” Physical Review E, vol. 80, no. 5, Article ID 051910, 2009.
- D. J. Brat, B. Kaur, and E. G. Van Meir, “Genetic modulation of hypoxia induced gene expression and angiogenesis: relevance to brain tumors,” Frontiers in Bioscience, vol. 8, pp. 100–116, 2003.
- J. F. Lu, R. Bruno, S. Eppler, W. Novotny, B. Lum, and J. Gaudreault, “Clinical pharmacokinetics of bevacizumab in patients with solid tumors,” Cancer Chemotherapy and Pharmacology, vol. 62, no. 5, pp. 779–786, 2008.
- M. A. Rudek, R. C. Donehower, P. Statkevich, V. K. Batra, D. L. Cutler, and S. D. Baker, “Temozolomide in patients with advanced cancer: phase 1 and pharmacokinetic study,” Pharmacotherapy, vol. 24, no. 1, pp. 16–25, 2004.
- M. M. Cooney, J. Ortiz, R. M. Bukowski, and S. C. Remick, “Novel vascular targeting/disrupting agents: combretastatin A4 phosphate and related compounds,” Current Oncology Reports, vol. 7, no. 2, pp. 90–95, 2005.
- A. Narayana, P. Kelly, J. Golfinos et al., “Antiangiogenic therapy using bevacizumab in recurrent high-grade glioma: impact on local control and patient survival: clinical article,” Journal of Neurosurgery, vol. 110, no. 1, pp. 173–180, 2009.
- A. D. Norden, G. S. Young, K. Setayesh et al., “Bevacizumab for recurrent malignant gliomas: efficacy, toxicity, and patterns of recurrence,” Neurology, vol. 70, no. 10, pp. 779–787, 2008.
- R. V. Snowden, “Avastin approved for glioblastoma,” http://www.cancer.org/cancer/news/news/avastin-approved-for-glioblastoma.
- J. L. Gevertz and S. Torquato, “A novel three-phase model of brain tissue microstructure,” PLoS Computational Biology, vol. 4, no. 8, Article ID e1000152, 2008.
- R. Stupp, P. Y. Dietrich, S. O. Kraljevic et al., “Promising survival for patients with newly diagnosed glioblastoma multiforme treated with concomitant radiation plus temozolomide followed by adjuvant temozolomide,” Journal of Clinical Oncology, vol. 20, no. 5, pp. 1375–1382, 2002.
- P. McConville, D. Hambardzumyan, J. B. Moody et al., “Magnetic resonance imaging determination of tumor grade and early response to temozolomide in a genetically engineered mouse model of glioma,” Clinical Cancer Research, vol. 13, no. 10, pp. 2897–2904, 2007.
- M. C. Berenbaum, “In vivo determination of the fractional kill of human tumor cells by chemotherapeutic agents,” Cancer Chemotherapy Reports, vol. 56, no. 5, pp. 563–571, 1972.
- G. G. Dark, S. A. Hill, V. E. Prise, G. M. Tozer, G. R. Pettit, and D. J. Chaplin, “Combretastatin A-4, an agent that displays potent and selective toxicity toward tumor vasculature,” Cancer Research, vol. 57, no. 10, pp. 1829–1834, 1997.
- M. S. Gordon, K. Margolin, M. Talpaz et al., “Phase I safety and pharmacokinetic study of recombinant human anti-vascular endothelial growth factor in patients with advanced cancer,” Journal of Clinical Oncology, vol. 19, no. 3, pp. 843–850, 2001.
- P. D. Nathan, I. Judson, A. Padhani, et al., “A phase I study of combretastatin A4 phosphate (CA4P) and bevacizumabin subjects with advanced solid tumors,” Journal of Clinical Oncology, vol. 26, supplement, p. 3550, 2008.
- R. A. Gatenby, “A change of strategy in the war on cancer,” Nature, vol. 459, no. 7246, pp. 508–509, 2009.
- R. A. Gatenby, A. S. Silva, R. J. Gillies, and B. R. Frieden, “Adaptive therapy,” Cancer Research, vol. 69, no. 11, pp. 4894–4903, 2009.
- T. Alarcón, H. M. Byrne, and P. K. Maini, “A multiple scale model for tumor growth,” Multiscale Modeling and Simulation, vol. 3, no. 2, pp. 440–475, 2005.
- S. R. McDougall, A. R. A. Anderson, M. A. J. Chaplain, and J. A. Sherratt, “Mathematical modelling of flow through vascular networks: implications for tumor-induced angiogenesis and chemotherapy strategies,” Bulletin of Mathematical Biology, vol. 64, no. 4, pp. 673–702, 2002.
- S. R. McDougall, A. R. A. Anderson, and M. A. J. Chaplain, “Mathematical modelling of dynamic adaptive tumor-induced angiogenesis: clinical implications and therapeutic targeting strategies,” Journal of Theoretical Biology, vol. 241, no. 3, pp. 564–589, 2006.