Microenvironment-Mediated Modeling of Tumor Response to Vascular-Targeting Drugs

  • Jana L. Gevertz
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 936)


The tumor-associated microvasculature is one of the key elements of the microenvironment that helps shape, and is shaped by, tumor progression. Given the important role of the vasculature in tumor progression, and the fact that tumor and normal vasculature are physiologically and molecularly distinct, much effort has gone into the development of vascular-targeting drugs that in theory should target tumors without significant risk to normal tissue. In this chapter, a multiscale hybrid mathematical model of tumor-vascular interactions is presented to provide a theoretical basis for assessing tumor response to vascular-targeting drugs. Model performance is calibrated to quantitative clinical data on tumor response to angiogenesis inhibitors (AIs), preclinical data on response to a cytotoxic chemotherapy, and qualitative preclinical data on response to vascular disrupting agents (VDAs). The calibrated model is then used to explore two questions of clinical interest. First, the hypothesis that AIs and VDAs are complementary treatments, rather than redundant, is explored. The model predicts a minimal increase in antitumor activity as a result of adding a VDA to an AI treatment regimen, and in fact at times the combination can exert less antitumor activity than stand-alone AI treatment. Second, the question of identifying an optimal dosing strategy for treating with an AI and a cytotoxic agent is addressed. Using a stochastic optimization scheme, an intermittent schedule for both chemotherapy and AI administration is identified that can eradicate the simulated tumors. We propose that this schedule may have increased clinical antitumor activity compared to currently used treatment protocols.


Tumor-vasculature interactions Hybrid cellular automaton model Angiogenesis inhibitors Vascular disrupting agents Cytotoxic chemotherapy 


  1. 1.
    Bergers G, Hanahan D (2008) Modes of resistance to antiangiogenic therapy. Nat Rev Cancer 8:592–603CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Blakey DC, Russell Westwood F, Walker M, Hughes GD, Davis PD, Aston SE, Ryan AJ (2002) Antitumor activity of the novel vascular targeting agent ZD6126 in a panel of tumor models. Clin Cancer Res 8:1974–1983PubMedGoogle Scholar
  3. 3.
    Brekken RA, Thorpe PE (2001) VEGF-VEGF receptor complexes as markers of tumor vascular endothelium. J Control Release 74:173–181CrossRefPubMedGoogle Scholar
  4. 4.
    Carmeliet P, Jain RK (2000) Angiogenesis in cancer and other diseases. Nature 407:249–257CrossRefPubMedGoogle Scholar
  5. 5.
    Cooney MM, Ortiz J, Bukowski RM, Remick SC (2005) Novel vascular targeting/disrupting agents: combretastatin A4 phosphate and related compounds. Curr Oncol Rep 7:90–95CrossRefPubMedGoogle Scholar
  6. 6.
    Desjardins A, Reardon DA, Coan A, Marcello J, Herndon JE, Bailey L, Peters KB, Friedman HS, Vredenburgh JJ (2012) Bevacizumab and daily temozolomide for recurrent glioblastoma. Cancer 118:1302–1312CrossRefPubMedGoogle Scholar
  7. 7.
    Dowlati A, Robertson K, Cooney M, Petros WP, Stratford M, Jesberger J, Rafie N, Overmoyer B, Makkar V, Stambler B, Taylor A, Waas J, Lewin JS, McCrae KR, Remick SC (2002) A phase I pharmacokinetic and translational study of the novel vascular targeting agent combretastatin a-4 phosphate on a single-dose intravenous schedule in patients with advanced cancer. Cancer Res 62:3408–3416PubMedGoogle Scholar
  8. 8.
    Gevertz JL (2011) Computational modeling of tumor response to vascular-targeting therapies – part I: validation. Comput Math Methods Med 2011:830515CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Gevertz JL (2012) Optimization of vascular-targeting drugs in a computational model of tumor growth. Phys Rev E 85:041914CrossRefGoogle Scholar
  10. 10.
    Gevertz JL, Torquato S (2006) Modeling the effects of vasculature evolution on early brain tumor growth. J Theor Biol 243:517–531CrossRefPubMedGoogle Scholar
  11. 11.
    Gevertz JL, Torquato S (2009) Growing heterogeneous tumors in silico. Phys Rev E 80:051910CrossRefGoogle Scholar
  12. 12.
    Holash P, Maisonpierre PC, Compton D, Boland P, Alexander CR, Zagzag D, Yancoupoulos GD, Wiegand SJ (1997) Vessel cooption, regression, and growth in tumors mediated by angiopoietins and VEGF. Science 284:1994–1998CrossRefGoogle Scholar
  13. 13.
    Hoshino T, Wilson CB (1979) Cell kinetic analyses of human malignant brain tumors (gliomas). Cancer 44:956–962CrossRefPubMedGoogle Scholar
  14. 14.
    LoRusso PM, Boerner SA (2011) Clinical development of vascular disrupting agents: what lessons can we learn from ASA404? J Clin Oncol 29:2952–2955CrossRefPubMedGoogle Scholar
  15. 15.
    Lu JF, Bruno R, Eppler S, Novotny W, Lum B, Gaudreault J (2008) Clinical pharmacokinetics of bevacizumab in patients with solid tumors. Cancer Chemother Pharmacol 62:779–786CrossRefPubMedGoogle Scholar
  16. 16.
    Maisonpierre PC, Suri C, Jones PF, Bartunkova S, Wiegand SJ, Radziejewski C, Compton D, McClain J, Aldrich TH, Papadopoulos N, Daly TJ, Davis S, Sato TN, Yancopoulos GD (1997) Angiopoietin-2, a natural antagonist for Tie2 that disrupts in vivo angiogenesis. Science 277:55–60CrossRefPubMedGoogle Scholar
  17. 17.
    Mason RP, Zhao D, Liu L, Trawick ML, Pinney KG (2011) A perspective on vascular disrupting agents that interact with tubulin: preclinical tumor imaging and biological assessment. Integr Biol 3:375–387CrossRefGoogle Scholar
  18. 18.
    McConville P, Hambardzumyan D, Moody JB, Leopold WR, Kreger AR, Woolliscroft MJ, Rehemtulla A, Ross BD, Holland EC (2007) Magnetic resonance imaging determination of tumor grade and early response to temozolomide in a genetically engineered mouse model of glioma. Clin Cancer Res 13:2897–2904CrossRefPubMedGoogle Scholar
  19. 19.
    Mita MM, Sargsyan L, Mita AC, Spear M (2013) Vascular-disrupting agents in oncology. Expert Opin Investig Drugs 22:317–328CrossRefPubMedGoogle Scholar
  20. 20.
    Motzer RJ, Hutson TE, Olsen MR, Hudes GR, Burke JM, Edenfield WJ, Wilding G, Agarwal N, Thompson JA, Cella D, Bello A, Korytowsky B, Yuan J, Valota O, Martell B, Hariharan S, Figlin RA (2012) Randomized phase II trial of sunitinib on an intermittent versus continuous dosing schedule as first-line therapy for advanced renal cell carcinoma. J Clin Oncol 30:1371–1377CrossRefPubMedGoogle Scholar
  21. 21.
    Najafi M, Soltanian-Zadeh H, Jafari-Khouzani K, Scarpace L, Mikkelson T (2012) Prediction of glioblastoma multiforme response to bevacizumab treatment using multi-parametric MRI. PLoS ONE 7:e29945CrossRefPubMedPubMedCentralGoogle Scholar
  22. 22.
    Nathan P, Zweifel M, Padhani AR, Koh D-M, Ng M, Collins DJ, Harris A, Carden C, Smythe J, Fisher N, Taylor NJ, Stirling JJ, Lu S-P, Leach MO, Rustin GJS, Judson I (2012) Phase I trial of combretastatin A4 phosphate (CA4P) in combination with bevacizumab in patients with advanced cancer. Clin Cancer Res 18:3428–3439CrossRefPubMedGoogle Scholar
  23. 23.
    Rudek MA, Donehower RC, Statkevich R, Batra VK, Cutler DL, Baker SD (2004) Temozolomide in patients with advanced cancer: phase I and pharmacokinetic study. Pharmacotherapy 24:16–25CrossRefPubMedGoogle Scholar
  24. 24.
    Siemann DW (2006) Tumor vasculature: a target for anticancer therapies. In: Seimann DW (ed) Vascular-targeted therapies in oncology. John Wiley, Chichester, pp 1–8CrossRefGoogle Scholar
  25. 25.
    Siemann DW, Shi W (2008) Dual targeting of tumor vasculature: combining Avastin and vascular disrupting agents (CA4P or OXi4503). Anticancer Res 28:2027–2031PubMedPubMedCentralGoogle Scholar
  26. 26.
    Stuff R, Dietrich PY, Kraljevic SO, Pica A, Maillard I, Maeder P, Meuli R, Janzer R, Pizzolato G, Mirabell R, Porchet F, Regli L, de Tribolet N, Mirimanoff RO, Leyvraz S (2002) Promising survival for patients with newly diagnosed glioblastoma multiforme treated with concomitant radiation plus temozolomide followed by adjuvant temozolomide. J Clin Oncol 20:1375–1382CrossRefGoogle Scholar
  27. 27.
    Thorpe PE (2004) Vascular targeting agents as cancer therapeutics. Clin Cancer Res 10:415–427CrossRefPubMedGoogle Scholar
  28. 28.
    Torquato S (2002) Random heterogeneous materials: microstructure and microscopic properties. Springer, New YorkCrossRefGoogle Scholar
  29. 29.
    Xing HR, Zhang Q (2012) Real-time visualization and characterization of tumor angiogenesis and vascular response to anticancer therapies. In: Hoffman RM (ed) In vivo cellular imaging using fluorescent proteins: methods and protocols, methods in molecular biology, vol 872. Springer, New York, pp 115–127CrossRefGoogle Scholar
  30. 30.
    Zheng X, Wise SM, Cristini V (2005) Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull Math Biol 67:211–259CrossRefPubMedGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsThe College of New JerseyEwingUSA

Personalised recommendations