Skip to main content

Particle Simulations of Growth: Application to Angiogenesis

  • Chapter
  • First Online:
Modeling Tumor Vasculature

Abstract

We apply the particle-based framework developed in the previous chapter to develop continuum and discrete-continuum models of sprouting angiogenesis under consideration of a detailed tumor microenvironment. We present results on the vessel development as a function of the extracellular matrix and different VEGF isoforms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alberts B, Bray D, Lewis J, Raff M, Roberts K, & Watson J. D (2002) Molecular Biology of the Cell Garland Science, New York, 4th edition

    Google Scholar 

  • Anderson A. R. A, & Chaplain M. A. J (1998) Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis Bull. Math. Biology, 60:857–900

    Article  CAS  Google Scholar 

  • Armstrong N. J, Painter K. J, & Sherratt J. A (2006) A continuum approach to modeling cell-cell adhesion J. Theor. Biol., 243(1):98–113

    Article  CAS  Google Scholar 

  • Axelson H, Fredlund E, Ovenberger M, Landberg G, & Pahlman S (2005) Hypoxia-induced dedifferentiation of tumor cells - A mechanism behind heterogeneity and aggressiveness of solid tumors; Biology of Hypoxia and Myogenesis and Muscle Disease Seminars in Cell & Developmental Biology, 16(4-5):554–563

    Google Scholar 

  • Bauer A. L, Jackson T. L, & Jiang Y (2007) A Cell-Based Model Exhibiting Branching and Anastomosis during Tumor-Induced Angiogenesis Biophys. J.,92(9):3105–3121

    CAS  Google Scholar 

  • Chaplain M. A (2000) Mathematical modeling of angiogenesis. J Neurooncol, 50(1-2):37–51

    Article  CAS  PubMed  Google Scholar 

  • Davis G. E, & Senger D. R (2005) Endothelial Extracellular Matrix: Biosynthesis, Remodeling, and Functions During Vascular Morphogenesis and Neovessel Stabilization Circulation Research, 97(11):1093–1107

    CAS  PubMed  Google Scholar 

  • Ferrara N, Gerber H.-P, & LeCouter J (2003) The biology of VEGF and its receptors Nat Med, 9:669–676

    Google Scholar 

  • Folkman J (2006) Angiogenesis Annual Review of Medicine, 57(1):1–18

    Article  CAS  PubMed  Google Scholar 

  • Folkman J (2007) Angiogenesis: an organizing principle for drug discovery? Nat Rev Drug Discov, 6(4):273–286

    Article  CAS  PubMed  Google Scholar 

  • Friedl P, & Bröcker E. B(2000) The biology of cell locomotion within three-dimensional extracellular matrix Cellular and Molecular Life Sciences (CMLS), 57(1):41–64

    Google Scholar 

  • Gerhardt H, Golding M, Fruttiger M, Ruhrberg C, Lundkvist A, Abramsson A, Jeltsch M, Mitchell C, Alitalo K, Shima D, & Betsholtz C (2003) VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia The Journal of Cell Biology, 161(6):1163–1177

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hanahan D, & Weinberg R. A (2000) The Hallmarks of Cancer Cell, 100(1):57–70

    CAS  Google Scholar 

  • Iruelaarispe M. L, Hasselaar P, & Sage H (1991) Differential expression of extracellular proteins is correlated with angiogenesis invitro Labratory Investigation,64(2):174–186

    Google Scholar 

  • Kearney J. B, Kappas N. C, Ellerstrom C, DiPaola F. W, & Bautch V. L (2004) The VEGF receptor flt-1 (VEGFR-1) is a positive modulator of vascular sprout formation and branching morphogenesis Blood, 103(12):4527–4535

    CAS  PubMed  Google Scholar 

  • Kirkpatrick N. D, Andreou S, Hoying J. B, & Utzinger U (2007) Live imaging of collagen remodeling during angiogenesis AJP - Heart and Circulatory Physiology, 292(6):H3298–H3206

    Article  Google Scholar 

  • Lee S, Jilani S. M, Nikolova G. V, Carpizo D, & Iruela-Arispe M. L (2005) Processing of VEGF-A by matrix metalloproteinases regulates bioavailability and vascular patterning in tumors J. Cell Biol., 169(4):681–691

    Article  CAS  Google Scholar 

  • Levine H. A, Sleeman B. D, & Nilsen-Hamilton M (2001) Mathematical modeling of the onset of capillary formation initiating angiogenesis Journal of Mathematical Biology, V42(3):195–238

    Article  Google Scholar 

  • McDougall S. R, Anderson A. R. A, & Chaplain M. A. J (2006) Mathematical modeling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies Journal of Theoretical Biology, 241(3):564–589

    Google Scholar 

  • Mignatti P, & Rifkin D. B (1993) Biology and biochemistry of proteinases in tumor invasion Physiological Reviews, 73(1):161–195

    Google Scholar 

  • Milde F, Bergdorf M, & Koumoutsakos P (2008) A Hybrid Model for Three-Dimensional Simulations of Sprouting Angiogenesis Biophysical Journal, 95(7):3146–3160

    Google Scholar 

  • Paweletz N, & Knierim M (1989) Tumor-related angiogenesis; Critical Reviews in Oncology/ Hematology, 9(3):197–242

    Article  CAS  PubMed  Google Scholar 

  • Pennacchietti S, Michieli P, Galluzzo M, Mazzone M, Giordano S, & Comoglio P. M (2003) Hypoxia promotes invasive growth by transcriptional activation of the met protooncogene Cancer Cell, 3:347–361

    PubMed  Google Scholar 

  • Plank M, & Sleeman B(2004) Lattice and non-lattice models of tumour angiogenesis Bulletin of Mathematical Biology, 66(6):1785–1819

    Google Scholar 

  • Ruhrberg C, Gerhardt H, Golding M, Watson R, Ioannidou S, Fujisawa H, Betsholtz C, & Shima D. T(2002) Spatially restricted patterning cues provided by heparin-binding VEGF-A control blood vessel branching morphogenesis Genes Dev., 16(20):2684–2698

    Google Scholar 

  • Saharinen P, & Alitalo K (2003) Double target for tumor mass destruction Journal of Clinical Investigation, 111(9):1277–1280

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Serini G, Valdembri D, & Bussolino F (2006) Integrins and angiogenesis: A sticky business Experimental Cell Research, 312(5):651–658

    Google Scholar 

  • Steinberg M, & Takeichi M (1994) Experimental Specification of Cell Sorting, Tissue Spreading, and Specific Spatial Patterning by Quantitative Differences in Cadherin Expression Proceedings of the National Academy of Sciences, 91(1):206–209

    CAS  Google Scholar 

  • Steinberg M. S (2007) Differential adhesion in morphogenesis: a modern view Curr. Opin. Genet. Dev., 17(4):281–286

    Article  CAS  Google Scholar 

  • Sun S, Wheeler M. F, Obeyesekere M, & Patrick C. W, Jr. (2005) A deterministic model of growth factor-induced angiogenesis Bulletin of Mathematical Biology, 67:313–337

    Article  CAS  PubMed  Google Scholar 

  • Taraboletti G, D’Ascenzo S, Dolo V, Giusti I, Marchetti D, Borsotti P, Millimaggi D, Giavazzi R, Pavan A, & Dolo V (February 2006) Bioavailability of VEGF in Tumor-Shed Vesicles Depends on Vesicle Burst Induced by Acidic pH Neoplasia, 8:96–103(8)

    Google Scholar 

  • Weinkauf T, & Theisel H (2002) Curvature Measures of 3D Vector Fields and their Applications In Skala V (ed), Journal of WSCG, volume 10, pages 507–514

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Petros Koumoutsakos .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Milde, F., Bergdorf, M., Koumoutsakos, P. (2012). Particle Simulations of Growth: Application to Angiogenesis. In: Jackson, T.L. (eds) Modeling Tumor Vasculature. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0052-3_12

Download citation

Publish with us

Policies and ethics