Skip to main content

Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

  • Chapter
  • First Online:
Systems Biology of Tumor Microenvironment

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 936))

Abstract

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such as oxygen or glucose, is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature. Integrative models, based on detailed experimental data and physical laws, implement, in silico, the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. This chapter provides an overview over the current status of computer simulations of vascular remodeling during tumor growth including interstitial fluid flow, drug delivery, and oxygen supply within the tumor. The model predictions are compared with experimental and clinical data and a number of longstanding physiological paradigms about tumor vasculature and intratumoral solute transport are critically scrutinized.

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

  1. Aker E, JØrgen MÅlØy K, Hansen A, Batrouni G (1998) A two-dimensional network simulator for two-phase flow in porous media. Trans Porous Media 32(2):163–186. doi:10.1023/A:1006510106194

    Google Scholar 

  2. Alarcon T, Byrne H, Maini P (2003) A cellular automaton model for tumour growth in inhomogeneous environment. J Theor Biol 225:257–274

    Article  CAS  PubMed  Google Scholar 

  3. Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59(4):863–883

    Article  PubMed  PubMed Central  Google Scholar 

  4. Ambrosi D, Mollica F (2004) The role of stress in the growth of a multicell spheroid. J Math Biol 48(5):477–499

    Article  CAS  PubMed  Google Scholar 

  5. Ambrosi D, Preziosi L (2009) Cell adhesion mechanisms and stress relaxation in the mechanics of tumours. Biomech Model Mechanobiol 8(5):397–413

    Article  PubMed  Google Scholar 

  6. Anderson A, Chaplain MAJ (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 60(857–900):857–899

    Article  CAS  PubMed  Google Scholar 

  7. Ando J, Yamamoto K (2013) Flow detection and calcium signalling in vascular endothelial cells. Cardiovasc Res 99(2):260–268

    Article  CAS  PubMed  Google Scholar 

  8. Armstrong NJ, Painter KJ, Sherratt JA (2006) A continuum approach to modelling cell-cell adhesion. J Theor Biol 243(1):98–113

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Baish JW, Netti PA, Jain RK (1997) Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors. Microvasc Res 53:128–141

    Article  CAS  PubMed  Google Scholar 

  10. Baish JW, Stylianopoulos T, Lanning RM, Kamoun WS, Fukumura D, Munn LL, Jain RK (2011) Scaling rules for diffusive drug delivery in tumor and normal tissues. Proc Natl Acad Sci USA 108(5):1799–1803

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Bartha K, Rieger H (2006) Vascular network remodeling via vessel cooption, regression and growth in tumors. J Theor Biol 241:903–918. doi:http://dx.doi.org/10.1016/j.jtbi.2006.01.022. http://www.sciencedirect.com/science/article/pii/S0022519306000373

    Google Scholar 

  12. Basan M, Prost J, Joanny JF, Elgeti J (2011) Dissipative particle dynamics simulations for biological tissues: rheology and competition. Phys Biol 8(2):026,014

    Google Scholar 

  13. Baxter LT, Jain RK (1989) Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. Microvasc Res 37:77–104

    Article  CAS  PubMed  Google Scholar 

  14. Beard DA (2001) Computational framework for generating transport models from databases of microvascular anatomy. Ann Biomed Eng 29(10):837–843

    Article  CAS  PubMed  Google Scholar 

  15. Bentley K, Gerhardt H, Bates PA (2008) Agent-based simulation of notch-mediated tip cell selection in angiogenic sprout initialisation. J Theor Biol 250(1):25–36. doi:http://dx.doi.org/10.1016/j.jtbi.2007.09.015. http://www.sciencedirect.com/science/article/pii/S0022519307004432

    Google Scholar 

  16. Betteridge R, Owen MR, Byrne HM, Alarcon T, Maini PK (2006) The impact of cell crowding and active cell movement on vascular tumour growth. Netw Heterog Media 1(4):515–535

    Article  Google Scholar 

  17. Brackbill JU, Kothe DB, Zemach C.: A continuum method for modeling surface tension. J Comput Phys 100:335–354 (1992). doi:10.1016/0021-9991(92)90240-Y

    Article  CAS  Google Scholar 

  18. Breward CJ, Byrne HM, Lewis CE (2003) A multiphase model describing vascular tumour growth. Bull Math Biol 65(4):609–640

    Article  PubMed  Google Scholar 

  19. Brown JM, Wilson WR (2004) Exploiting tumour hypoxia in cancer treatment. Nat Rev Cancer 4(6):437–447

    Article  CAS  PubMed  Google Scholar 

  20. Bru A, Albertos S, Subiza JL, Lopez J, Garcia-Asenjo, Bru I (2003) The universal dynamics of tumor growth. Biophys J 85:2948–2961

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Buchanan CF, Verbridge SS, Vlachos PP, Rylander MN (2014) Flow shear stress regulates endothelial barrier function and expression of angiogenic factors in a 3D microfluidic tumor vascular model. Cell Adh Migr 8(5):517–524

    Article  PubMed  PubMed Central  Google Scholar 

  22. Byrne H, Preziosi L (2003) Modelling solid tumour growth using the theory of mixtures. Math Med Biol 20(4):341–366

    Article  PubMed  Google Scholar 

  23. Byrne HM, Owen MR, Alarcon T, Murphy J, Maini PK (2006) Modelling the response of vascular tumours to chemotherapy: a multiscale approach. Math Models Methods Appl Sci 16(Supp 01):1219–1241. doi:10.1142/S0218202506001522

    Article  CAS  Google Scholar 

  24. Cai Y, Xu S, Wu J, Long Q (2011) Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion. J Theor Biol 279(1):90–101. http://dx.doi.org/10.1016/j.jtbi.2011.02.017. http://www.sciencedirect.com/science/article/pii/S0022519311001196

    Google Scholar 

  25. Carmeliet P, Jain R (2000) Angiogenesis in cancer and other diseases. Nature 407:249–257

    Article  CAS  PubMed  Google Scholar 

  26. Carmeliet P, Jain RK (2011) Molecular mechanisms and clinical applications of angiogenesis. Nature 473(7347):298–307

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Cassot F, Lauwers F, Fouard C, Prohaska S, Lauwers-Cances V (2006) A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation 13(1):1–18

    Article  CAS  PubMed  Google Scholar 

  28. Cattaneo L, Zunino P (2014) A computational model of drug delivery through microcirculation to compare different tumor treatments. Int J Numer Method Biomed Eng 30(11):1347–1371

    Article  CAS  PubMed  Google Scholar 

  29. Chaplain MA, Graziano L, Preziosi L (2006) Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math Med Biol 23:197–229

    Article  CAS  PubMed  Google Scholar 

  30. Chauhan VP, Boucher Y, Ferrone CR, Roberge S, Martin JD, Stylianopoulos T, Bardeesy N, DePinho RA, Padera TP, Munn LL, Jain RK (2014) Compression of pancreatic tumor blood vessels by hyaluronan is caused by solid stress and not interstitial fluid pressure. Cancer Cell 26(1):14–15

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Chauhan VP, Martin JD, Liu H, Lacorre DA, Jain SR, Kozin SV, Stylianopoulos T, Mousa AS, Han X, Adstamongkonkul P, Popovi? Z, Huang P, Bawendi MG, Boucher Y, Jain RK (2013) Angiotensin inhibition enhances drug delivery and potentiates chemotherapy by decompressing tumour blood vessels. Nat Commun 4:2516

    Google Scholar 

  32. Ciarletta P, Ambrosi D, Maugin GA, Preziosi L (2013) Mechano-transduction in tumour growth modelling. Eur Phys J E Soft Matter 36(3):23

    Article  CAS  PubMed  Google Scholar 

  33. Da ̧su A, Toma-Da ̧su I, Karlsson M (2003) Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia. Phys Med Biol 48(17):2829–2842

    Google Scholar 

  34. D’Angelo C (2012) Finite element approximation of elliptic problems with dirac measure terms in weighted spaces: applications to one- and three-dimensional coupled problems. SIAM J Numer Anal 50(1):194–215

    Article  Google Scholar 

  35. Degond P, Mas-Gallic S (1989) The weighted particle method for convection-diffusion equations. Part 1: the case of an isotropic viscosity. Math Comput 53(188):485–507

    Google Scholar 

  36. DelGiorno KE, Carlson MA, Osgood R, Provenzano PP, Brockenbough JS, Thompson CB, Shepard HM, Frost GI, Potter JD, Hingorani SR (2014) Response to Chauhan et al.: interstitial pressure and vascular collapse in pancreas cancer-fluids and solids, measurement and meaning. Cancer Cell 26(1):16–17

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Döme B, Hendrix MJ, Paku S, Tovari J, Timar J (2007) Alternative vascularization mechanisms in cancer: pathology and therapeutic implications. Am J Pathol 170(1):1–15

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  38. Döme B, Paku S, Somlai B, Tímár J (2002) Vascularization of cutaneous melanoma involves vessel co-option and has clinical significance. J Pathol 197(3):355–362

    Article  PubMed  Google Scholar 

  39. Drasdo D, Höhme S (2005) A single-cell-based model of tumor growth in vitro: monolayers and sphereoids. Phys Biol 2:133–147

    Article  CAS  PubMed  Google Scholar 

  40. Du J, Li FH, Fang H, Xia JG, Zhu CX (2008) Microvascular architecture of breast lesions: evaluation with contrast-enhanced ultrasonographic micro flow imaging. J Ultrasound Med 27(6):833–842

    PubMed  Google Scholar 

  41. Enderling H, Anderson AR, Chaplain MA, Beheshti A, Hlatky L, Hahnfeldt P (2009) Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res 69(22):8814–8821

    Article  CAS  PubMed  Google Scholar 

  42. Enderling H, Hlatky L, Hahnfeldt P (2009) Migration rules: tumours are conglomerates of self-metastases. Br J Cancer 100(12):1917–1925

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Erber R, Eichelsbacher U, Powajbo V, Korn T, Djonov V, Lin J, Hammes HP, Grobholz R, Ullrich A, Vajkoczy P (2006) EphB4 controls blood vascular morphogenesis during postnatal angiogenesis. EMBO J 25(3):628–641

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Espinoza I, Peschke P, Karger CP (2013) A model to simulate the oxygen distribution in hypoxic tumors for different vascular architectures. Med Phys 40(8):081,703

    Google Scholar 

  45. Folkman J (1971) Tumor angiogenesis: therapeutic implications. N Engl J Med 285(21):1182–1186

    Article  CAS  PubMed  Google Scholar 

  46. Fraser GM, Goldman D, Ellis CG (2013) Comparison of generated parallel capillary arrays to three-dimensional reconstructed capillary networks in modeling oxygen transport in discrete microvascular volumes. Microcirculation 20(8):748–763

    CAS  PubMed  PubMed Central  Google Scholar 

  47. Furuberg L, Feder J, Aharony A, Jossang T (1988) Dynamics of invasion percolation. Phys Rev Lett 61(18):2117–2120

    Article  CAS  PubMed  Google Scholar 

  48. Gazit Y, Berk DA, Michael Leunig LTB, Jain RK (1995) Scale-invariant behavior and vascular network formation in norma and tumor tissue. Phys Rev Lett 75(12):2428–2431

    Article  CAS  PubMed  Google Scholar 

  49. Gerhardt H, Golding M, Fruttinger M, Ruhrberg C, Lundkvist A, Abramsson A, Jeltsch M, Mitchell C, Alitalo K, Shima D, Betsholz C (2003) VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia. J Cell Biol 161(6):1163–1177

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Gevertz JL (2011) Computational modeling of tumor response to vascular-targeting therapies–part I: validation. Comput Math Methods Med 2011:830,515

    Google Scholar 

  51. Gimbrone M, Cotran R, Leapman S, Folkman J (1974) Tumor growth and neovascularization: an experiment model using the rabbit cornea. J Natl Cancer Inst 52:413–427

    PubMed  Google Scholar 

  52. Gödde R, Kurz H (2001) Structural and biophysical simulation of angiogenesis and vascular remodeling. Dev Dyn 220(4):387–401

    Article  PubMed  Google Scholar 

  53. Goettsch W, Gryczka C, Korff T, Ernst E, Goettsch C, Seebach J, Schnittler HJ, Augustin HG, Morawietz H (2008) Flow-dependent regulation of angiopoietin-2. J Cell Physiol 214(2):491–503

    Article  CAS  PubMed  Google Scholar 

  54. Goldman D (2008) Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15(8):795–811

    Article  PubMed  PubMed Central  Google Scholar 

  55. Goldman D, Bateman RM, Ellis CG (2004) Effect of sepsis on skeletal muscle oxygen consumption and tissue oxygenation: interpreting capillary oxygen transport data using a mathematical model. Am J Physiol Heart Circ Physiol 287(6):H2535–2544

    Article  CAS  PubMed  Google Scholar 

  56. Goldman D, Bateman RM, Ellis CG (2006) Effect of decreased O2 supply on skeletal muscle oxygenation and O2 consumption during sepsis: role of heterogeneous capillary spacing and blood flow. Am J Physiol Heart Circ Physiol 290(6):H2277–2285

    Article  CAS  PubMed  Google Scholar 

  57. Goldman D, Popel AS (2000) A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport. J Theor Biol 206(2):181–194

    Article  CAS  PubMed  Google Scholar 

  58. Gray LH, Conger AD, Ebert M, Hornsey S, Scott OCA (1953) The concentration of oxygen dissolved in tissues at the time of irradiation as a factor in radiotherapy. Br J Radiol 26(312):638–648. doi:10.1259/0007-1285-26-312-638. http://dx.doi.org/10.1259/0007-1285-26-312-638. PMID:13106296

    Google Scholar 

  59. Griffon-Etienne G, Boucher Y, Brekken C, Suit HD, Jain RK (1999) Taxane-induced apoptosis decompresses blood vessels and lowers interstitial fluid pressure in solid tumors: clinical implications. Cancer Res. 59(15):3776–3782

    CAS  PubMed  Google Scholar 

  60. Grosenick D, Wabnitz H, Moesta KT, Mucke J, Schlag PM, Rinneberg H (2005) Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas. Phys Med Biol 50(11):2451–2468

    Article  PubMed  Google Scholar 

  61. Guibert R, Fonta C, Plouraboue F (2010) Cerebral blood flow modeling in primate cortex. J Cereb Blood Flow Metab 30(11):1860–1873. doi:10.1038/jcbfm.2010.105

    Article  PubMed  PubMed Central  Google Scholar 

  62. Hanahan D, Weinberg RA (2011) Hallmarks of cancer: the next generation. Cell 144(5):646–674

    Article  CAS  PubMed  Google Scholar 

  63. Harris AL (2002) Hypoxia–a key regulatory factor in tumour growth. Nat Rev Cancer 2(1):38–47

    Article  CAS  PubMed  Google Scholar 

  64. Heldin CH, Rubin K, Pietras K, Ostman A (2004) High interstitial fluid pressure – an obstacle in cancer therapy. Nat Rev Cancer 4(10):806–813

    Article  CAS  PubMed  Google Scholar 

  65. Hellums JD, Nair PK, Huang NS, Ohshima N (1996) Simulation of intraluminal gas transport processes in the microcirculation. Ann Biomed Eng 24(1):1–24

    Article  CAS  PubMed  Google Scholar 

  66. Holash J, Maisonpierre PC, Compton D, Boland P, Alexander CR, Zagzag D, Yancopoulos GD, Wiegand SJ (1999) Vessel cooption, regression, and growth in tumors mediated by angiopoietins and VEGF. Science 284(5422):1994–1998

    Article  CAS  PubMed  Google Scholar 

  67. Holash J, Wiegand S, Yancopoulos G (1999) New model of tumor angiogenesis: dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF. Oncogene 18:5356–5362

    Article  CAS  PubMed  Google Scholar 

  68. Hopcroft J, Tarjan R (1973) Algorithm 447: efficient algorithms for graph manipulation. Commun ACM 16(6):372–378. doi:10.1145/362248.362272. http://doi.acm.org/10.1145/362248.362272

    Article  Google Scholar 

  69. Hsu R, Secomb TW (1989) A green’s function method for analysis of oxygen delivery to tissue by microvascular networks. Math Biosci 96(1):61–78

    Article  CAS  PubMed  Google Scholar 

  70. Hubbard M, Byrne H (2013) Multiphase modelling of vascular tumour growth in two spatial dimensions. J Theor Biol 316(0):70–89. http://dx.doi.org/10.1016/j.jtbi.2012.09.031. http://www.sciencedirect.com/science/article/pii/S0022519312005097

    Google Scholar 

  71. Höckel M, Vaupel P (2001) Tumor hypoxia: definitions and current clinical, biologic, and molecular aspects. J Natl Cancer Inst 93(4):266–276. doi:10.1093/jnci/93.4.266. http://jnci.oxfordjournals.org/content/93/4/266.abstract

    Article  PubMed  Google Scholar 

  72. Ito M, Lammertsma AA, Wise RJ, Bernardi S, Frackowiak RS, Heather JD, McKenzie CG, Thomas DG, Jones T (1982) Measurement of regional cerebral blood flow and oxygen utilisation in patients with cerebral tumours using 15O and positron emission tomography: analytical techniques and preliminary results. Neuroradiology 23(2):63–74

    Article  CAS  PubMed  Google Scholar 

  73. Jain RK (1987) Transport of molecules across tumor vasculature. Cancer Metastasis Rev 6(4):559–593

    Article  CAS  PubMed  Google Scholar 

  74. Jain RK (1987) Transport of molecules in the tumor interstitium: a review. Cancer Res 47(12):3039–3051

    CAS  PubMed  Google Scholar 

  75. Jain RK (1988) Determinants of tumor blood flow: a review. Cancer Res 48:2641–2658

    CAS  PubMed  Google Scholar 

  76. Jain RK (1999) Transport of molecules, particles, and cells in solid tumors. Annu Rev Biomed Eng 1:241–263

    Article  CAS  PubMed  Google Scholar 

  77. Jain RK (2005) Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. Science 307(5706):58–62

    Article  CAS  PubMed  Google Scholar 

  78. Jain RK (2013) Normalizing tumor microenvironment to treat cancer: bench to bedside to biomarkers. J Clin Oncol 31(17):2205–2218

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Jain RK (2014) An indirect way to tame cancer. Sci Am 310(2):46–53

    Article  PubMed  Google Scholar 

  80. Jain RK (2015) Antiangiogenesis strategies revisited: from starving tumors to alleviating hypoxia. Cancer Cell 26(5):605–622

    Article  CAS  Google Scholar 

  81. Jain RK, Baxter LT (1988) Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer Res 48(24 Pt 1):7022–7032

    CAS  PubMed  Google Scholar 

  82. Jain RK, Stylianopoulos T (2010) Delivering nanomedicine to solid tumors. Nat Rev Clin Oncol 7(11):653–664

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Jain RK, Tong RT, Munn LL (2007) Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model. Cancer Res. 67(6):2729–2735

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Kallinowski F, Schlenger KH, Kloes M, Stohrer M, Vaupel P (1989) Tumor blood flow: the principal modulator of oxidative and glycolytic metabolism, and of the metabolic micromilieu of human tumor xenografts in vivo. Int J Cancer 44(2):266–272

    Article  CAS  PubMed  Google Scholar 

  85. Karakashev SV, Reginato MJ (2015) Progress toward overcoming hypoxia-induced resistance to solid tumor therapy. Cancer Manag Res 7:253–264

    PubMed  PubMed Central  Google Scholar 

  86. Kelly CJ, Brady M (2006) A model to simulate tumour oxygenation and dynamic [18F]-Fmiso PET data. Phys Med Biol 51(22):5859–5873

    Article  CAS  PubMed  Google Scholar 

  87. Krogh A (1919) The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J Physiol (Lond) 52(6):409–415

    Article  CAS  Google Scholar 

  88. Lagerlöf JH, Kindblom J, Bernhardt P (2014) The impact of including spatially longitudinal heterogeneities of vessel oxygen content and vascular fraction in 3D tumor oxygenation models on predicted radiation sensitivity. Med Phys 41(4):044,101

    Google Scholar 

  89. Lagerlöf JH, Kindblom J, Cortez E, Pietras K, Bernhardt P (2013) Image-based 3D modeling study of the influence of vessel density and blood hemoglobin concentration on tumor oxygenation and response to irradiation. Med Phys 40(2):024,101

    Google Scholar 

  90. Lee D, Rieger H, Bartha K (2006) Flow correlated percolation during vascular remodeling in growing tumors. Phys Rev Lett 96(5):058,104–1–058,104–4. doi:10.1103/PhysRevLett.96.058104. http://link.aps.org/doi/10.1103/PhysRevLett.96.058104

  91. Lee J, Beighley P, Ritman E, Smith N (2007) Automatic segmentation of 3D micro-CT coronary vascular images. Med Image Anal 11(6):630–647

    Article  PubMed  Google Scholar 

  92. Leenders KL, Beaney RP, Brooks DJ, Lammertsma AA, Heather JD, McKenzie CG (1985) Dexamethasone treatment of brain tumor patients: effects on regional cerebral blood flow, blood volume, and oxygen utilization. Neurology 35(11):1610–1616

    Article  CAS  PubMed  Google Scholar 

  93. LeVeque RJ (2007) Finite difference methods for ordinary and partial differential equations – steady-state and time-dependent problems. SIAM

    Book  Google Scholar 

  94. Logsdon EA, Finley SD, Popel AS, Gabhann FM (2014) A systems biology view of blood vessel growth and remodelling. J Cell Mol Med 18(8):1491–1508

    Article  PubMed  Google Scholar 

  95. Lowengrub JS, Frieboes HB, Jin F, Chuang YL, Li X, Macklin P, Wise SM, Cristini V (2010) Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity 23(1):R1–R9

    Article  PubMed  PubMed Central  Google Scholar 

  96. Macklin P, Lowengrub J (2007) Nonlinear simulation of the effect of microenvironment on tumor growth. J Theor Biol 245:677–704

    Article  CAS  PubMed  Google Scholar 

  97. Macklin P, McDougall S, Anderson AR, Chaplain MA, Cristini V, Lowengrub J (2009) Multiscale modelling and nonlinear simulation of vascular tumour growth. J Math Biol 58:765–798

    Article  PubMed  Google Scholar 

  98. Mandelbrot BB (1983) The fractal geometry of nature. Freeman, San Francisco

    Google Scholar 

  99. Mankoff DA, Dunnwald LK, Gralow JR, Ellis GK, Charlop A, Lawton TJ, Schubert EK, Tseng J, Livingston RB (2002) Blood flow and metabolism in locally advanced breast cancer: relationship to response to therapy. J Nucl Med 43(4):500–509

    PubMed  Google Scholar 

  100. Marieb E, Hoehn K (2013) Human anatomy & physiology. Pearson, San Francisco

    Google Scholar 

  101. McDonald DM, Choyke PL (2003) Imaging of angiogenesis: from microscope to clinic. Nat Med 9(6):713–725

    Article  CAS  PubMed  Google Scholar 

  102. Minchinton AI, Tannock IF (2006) Drug penetration in solid tumours. Nat Rev Cancer 6(8):583–592

    Article  CAS  PubMed  Google Scholar 

  103. Mönnich D, Troost EG, Kaanders JH, Oyen WJ, Alber M, Thorwarth D (2011) Modelling and simulation of [18F]fluoromisonidazole dynamics based on histology-derived microvessel maps. Phys Med Biol 56(7):2045–2057

    Article  PubMed  Google Scholar 

  104. Moschandreou TE, Ellis CG, Goldman D (2011) Influence of tissue metabolism and capillary oxygen supply on arteriolar oxygen transport: a computational model. Math Biosci 232(1):1–10

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Murray C (1926) The physiological principle of minimum work: the vascular system and the cost of blood volume. Proc Natl Acad Sci USA 12:207–214

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  106. Nair PK, Hellums JD, Olson JS (1989) Prediction of oxygen transport rates in blood flowing in large capillaries. Microvasc Res 38(3):269–285

    Article  CAS  PubMed  Google Scholar 

  107. Nair PK, Huang NS, Hellums JD, Olson JS (1990) A simple model for prediction of oxygen transport rates by flowing blood in large capillaries. Microvasc Res 39(2):203–211

    Article  CAS  PubMed  Google Scholar 

  108. Nehls V, Herrmann R, Hühnken M (1998) Guided migration as a novel mechanism of capillary network remodeling is regulated by fibroblast growth factor. Histochem Cell Biol 109:319–329

    Article  CAS  PubMed  Google Scholar 

  109. Netti PA, Roberge S, Boucher Y, Baxter LT, Jain RK (1996) Effect of transvascular fluid exchange on pressure-flow relationship in tumors: a proposed mechanism for tumor blood flow heterogeneity. Microvasc Res 52(1):27–46

    Article  CAS  PubMed  Google Scholar 

  110. Nico B, Benagiano V, Mangieri D, Maruotti N, Vacca A, Ribatti D (2008) Evaluation of microvascular density in tumors: pro and contra. Histol Histopathol 23(5):601–607

    PubMed  Google Scholar 

  111. Owen MR, Alarcon T, Maini PK, Byrne HM (2009) Angiogenesis and vascular remodelling in normal and cancerous tissues. J Math Biol 58(4–5):689–721

    Article  PubMed  Google Scholar 

  112. Peirce SM, Van Gieson EJ, Skalak TC (2004) Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J 18(6):731–733

    CAS  PubMed  Google Scholar 

  113. Pennacchietti S, Michieli P, Galluzzo M, Mazzone M, Giordano S, Comoglio PM (2003) Hypoxia promotes invasive growth by transcriptional activation of the met protooncogene. Cancer Cell 3(4):347–361

    Article  PubMed  Google Scholar 

  114. Penta R, Ambrosi D (2015) The role of the microvascular tortuosity in tumor transport phenomena. J Theor Biol 364(0):80–97

    Google Scholar 

  115. Perfahl H, Byrne HM, Chen T, Estrella V, Alarcon T, Lapin A, Gatenby RA, Gillies RJ, Lloyd MC, Maini PK, Reuss M, Owen MR (2011) Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions. PLoS One 6(4):e14,790

    Article  CAS  Google Scholar 

  116. Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517. doi:10.1017/S0962492902000077. http://dx.doi.org/10.1017/S0962492902000077

    Article  Google Scholar 

  117. Preziosi L, Tosin A (2009) Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications. J Math Biol 58:625–656

    Article  PubMed  Google Scholar 

  118. Pries A, Secomb T, Gaehtgens P, Gross J (1990) Blood flow in microvascular networks. Experiments and simulation. Circ Res 67:826–834

    Article  CAS  PubMed  Google Scholar 

  119. Pries AR, Reglin B, Secomb TW (2005) Remodeling of blood vessels: responses of diameter and wall thickness to hemodynamic and metabolic stimuli. Hypertension 46(4):725–731

    Article  CAS  PubMed  Google Scholar 

  120. Pries AR, Secomb TW, Gessner T, Sperandio MB, Gross JF, Gaehtgens P (1994) Resistance to blood flow in microvessels in vivo. Circ Res 75(5):904–915

    Article  CAS  PubMed  Google Scholar 

  121. Primeau AJ, Rendon A, Hedley D, Lilge L, Tannock IF (2005) The distribution of the anticancer drug Doxorubicin in relation to blood vessels in solid tumors. Clin Cancer Res 11(24 Pt 1):8782–8788

    Article  CAS  PubMed  Google Scholar 

  122. Raica M, Cimpean AM, Ribatti D (2009) Angiogenesis in pre-malignant conditions. Eur J Cancer 45(11):1924–1934

    Article  CAS  PubMed  Google Scholar 

  123. Rieger H, Thome C, Sadjadi Z (2015) Meniscus arrest dominated imbibition front roughening in porous media with elongated pores. J Phys Conf Ser 638(1):012,007. http://stacks.iop.org/1742-6596/638/i=1/a=012007

    Google Scholar 

  124. Rieger H, Welter M (2015) Integrative models of vascular remodeling during tumor growth. Wiley Interdiscip Rev Syst Biol Med 7(3):113–129. doi:10.1002/wsbm.1295. http://dx.doi.org/10.1002/wsbm.1295

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Roose T, Chapman S, Maini P (2007) Mathematical models of avascular tumor growth. SIAM Rev 49(2):179–208. doi:10.1137/S0036144504446291. http://epubs.siam.org/doi/abs/10.1137/S0036144504446291

    Article  Google Scholar 

  126. Safaeian N, David T (2013) A computational model of oxygen transport in the cerebrocapillary levels for normal and pathologic brain function. J Cereb Blood Flow Metab 33(10):1633–1641

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  127. Safaeian N, Sellier M, David T (2011) A computational model of hemodynamic parameters in cortical capillary networks. J Theor Biol 271(1):145–156

    Article  PubMed  Google Scholar 

  128. Safaeian N (2012) Computational modelling of capillaries in neuro-vascular coupling: A Thesis Presented for the Degree of Doctor of Philosophy in Mechanical Engineering at the University of Canterbury, Christchurch. University of Canterbury

    Google Scholar 

  129. Sahani DV, Kalva SP, Hamberg LM, Hahn PF, Willet CG, Saini S, Mueller PR, Lee TY (2005) Assessing tumor perfusion and treatment response in rectal cancer with multisection ct: initial observations. Radiology 234:785–792

    Article  PubMed  Google Scholar 

  130. Sainson RC, Harris AL (2007) Anti-Dll4 therapy: can we block tumour growth by increasing angiogenesis? Trends Mol Med 13(9):389–395

    Article  CAS  PubMed  Google Scholar 

  131. Sanga S, Sinek JP, Frieboes HB, Ferrari M, Fruehauf JP, Cristini V (2006) Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev Anticancer Ther 6(10):1361–1376

    Article  CAS  PubMed  Google Scholar 

  132. Schreiner W (1993) Computer generation of complex arterial tree models. J Biomed Eng 15(2):148–150

    Article  CAS  PubMed  Google Scholar 

  133. Schreiner W, Buxbaum P (1993) Computer-optimization of vascular trees. IEEE Trans Biomed Eng 40(5):482–491

    Article  CAS  PubMed  Google Scholar 

  134. Scianna M, Bell CG, Preziosi L (2013) A review of mathematical models for the formation of vascular networks. J Theor Biol 333:174–209

    Article  CAS  PubMed  Google Scholar 

  135. Sciume G, Shelton S, Gray W, Miller C, Hussain F, Ferrari M, Decuzzi P, Schrefler B (2013) A multiphase model for three-dimensional tumor growth. New J Phys 15:015,005

    Google Scholar 

  136. Secomb TW, Hsu R, Park EYH, Dewhirst MW (2004) Green’s function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng 32(11):1519–1529

    Article  PubMed  Google Scholar 

  137. Sefidgar M, Soltani M, Raahemifar K, Bazmara H, Nayinian SM, Bazargan M (2014) Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors. J Biol Eng 8:12

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  138. Sefidgar M, Soltani M, Raahemifar K, Sadeghi M, Bazmara H, Bazargan M, Naeenian MM (2015) Numerical modeling of drug delivery in a dynamic solid tumor microvasculature. Microvasc Res 99(0):43–56

    Google Scholar 

  139. Sethian JA, Smereka P (2003) Level set methods for fluid interfaces. Ann Rev Fluid Mech 35(1):341–372. http://www.annualreviews.org/doi/abs/10.1146/annurev.fluid.35.101101.161105

  140. Shieh AC, Swartz MA (2011) Regulation of tumor invasion by interstitial fluid flow. Phys Biol 8(1):015,012

    Google Scholar 

  141. Sinek JP, Sanga S, Zheng X, Frieboes HB, Ferrari M, Cristini V (2009) Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation. J Math Biol 58(4–5):485–510

    Article  PubMed  Google Scholar 

  142. Skeldon AC, Chaffey G, Lloyd DJ, Mohan V, Bradley DA, Nisbet A (2012) Modelling and detecting tumour oxygenation levels. PLoS ONE 7(6):e38,597

    Article  CAS  Google Scholar 

  143. Song JW, Munn LL (2011) Fluid forces control endothelial sprouting. Proc Natl Acad Sci USA 108(37):15,342–15,347

    Google Scholar 

  144. Spinelli L, Torricelli A, Pifferi A, Taroni P, Danesini G, Cubeddu R (2005) Characterization of female breast lesions from multi-wavelength time-resolved optical mammography. Phys Med Biol 50(11):2489–2502

    Article  PubMed  Google Scholar 

  145. McDougall SR, Anderson A, Chaplain MAJ (2006) Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J Theor Biol 241:564–589

    Article  PubMed  Google Scholar 

  146. McDougall SR, Anderson A, Chaplain MAJ, Sherratt J (2002) Mathematical modelling of flow through vascular networks: implications for tumor-induced angiogenesis and chemotherapy strategies. Bull Math Biol 64:673–702

    Article  CAS  PubMed  Google Scholar 

  147. Stamatelos SK, Kim E, Pathak AP, Popel AS (2014) A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions. Microvasc Res 91:8–21

    Article  PubMed  Google Scholar 

  148. Stamper IJ, Byrne HM, Owen MR, Maini PK (2007) Modelling the role of angiogenesis and vasculogenesis in solid tumour growth. Bull Math Biol 69(8):2737–2772

    Article  CAS  PubMed  Google Scholar 

  149. Stauffer D, Aharony A (1994) Introduction to percolation theory. CRC Press, London

    Google Scholar 

  150. Stylianopoulos T, Martin JD, Chauhan VP, Jain SR, Diop-Frimpong B, Bardeesy N, Smith BL, Ferrone CR, Hornicek FJ, Boucher Y, Munn LL, Jain RK (2012) Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proc Natl Acad Sci USA 109(38):15101–15108

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  151. Swanson KR, Rockne RC, Claridge J, Chaplain MA, Alvord EC, Anderson AR (2011) Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res 71(24):7366–7375

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  152. Swartz MA, Lund AW (2012) Lymphatic and interstitial flow in the tumour microenvironment: linking mechanobiology with immunity. Nat Rev Cancer 12(3):210–219

    Article  CAS  PubMed  Google Scholar 

  153. Tammela T, Alitalo K (2010) Lymphangiogenesis: molecular mechanisms and future promise. Cell 140(4):460–476

    Article  CAS  PubMed  Google Scholar 

  154. Taroni P (2012) Diffuse optical imaging and spectroscopy of the breast: a brief outline of history and perspectives. Photochem Photobiol Sci 11(2):241–250

    Article  CAS  PubMed  Google Scholar 

  155. Taroni P, Torricelli A, Spinelli L, Pifferi A, Arpaia F, Danesini G, Cubeddu R (2005) Time-resolved optical mammography between 637 and 985 nm: clinical study on the detection and identification of breast lesions. Phys Med Biol 50(11):2469–2488

    Article  PubMed  Google Scholar 

  156. Cormen TH, Leiserson CE, RLR, Stein C (2009) Introduction to algorithms, 3rd edn., chap. 22 MIT Press, Cambridge

    Google Scholar 

  157. Tong RT, Boucher Y, Kozin SV, Winkler F, Hicklin DJ, Jain RK (2004) Vascular normalization by vascular endothelial growth factor receptor 2 blockade induces a pressure gradient across the vasculature and improves drug penetration in tumors. Cancer Res 64(11):3731–3736. doi:10.1158/0008-5472.CAN-04-0074. http://cancerres.aacrjournals.org/content/64/11/3731.abstract

    Article  CAS  PubMed  Google Scholar 

  158. Tracqui P (2009) Biophysical models of tumour growth. Rep Prog Phys 72(5):056,701

    Google Scholar 

  159. Tsai AG, Johnson PC, Intaglietta M (2003) Oxygen gradients in the microcirculation. Physiol Rev 83(3):933–963

    Article  CAS  PubMed  Google Scholar 

  160. Tsoukias NM, Goldman D, Vadapalli A, Pittman RN, Popel AS (2007) A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks. J Theor Biol 248(4):657–674

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  161. Vaupel P, Kallinowski F, Okunieff P (1989) Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review. Cancer Res 49(23):6449–6465. http://cancerres.aacrjournals.org/content/49/23/6449.abstract

    CAS  PubMed  Google Scholar 

  162. Verdier C, Etienne J, Duperray A, Preziosi L (2009) Review: rheological properties of biological materials. Comptes Rendus Physique 10(8):790–811. http://dx.doi.org/10.1016/j.crhy.2009.10.003. http://www.sciencedirect.com/science/article/pii/S1631070509001492. Complex and biofluidsFluides complexes et biologiques

    Google Scholar 

  163. Volokh KY (2006) Stresses in growing soft tissues. Acta Biomater 2(5):493–504

    Article  CAS  PubMed  Google Scholar 

  164. Weislo R, Dzwinel W, Yuen DA, Dudek AZ (2009) A 3-D model of tumor progression based on complex automata driven by particle dynamics. J Mol Model 15(12):1517–1539

    Article  CAS  Google Scholar 

  165. Welter M, Bartha K, Rieger H (2008) Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor. J Theor Biol 250(2):257–280. http://dx.doi.org/10.1016/j.jtbi.2007.09.031. http://www.sciencedirect.com/science/article/pii/S0022519307004584

    Google Scholar 

  166. Welter M, Bartha K, Rieger H (2009) Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth. J Theor Biol 259(3):405–422. http://dx.doi.org/10.1016/j.jtbi.2009.04.005. http://www.sciencedirect.com/science/article/pii/S0022519309001635

    Google Scholar 

  167. Welter M, Fredrich T, Rinneberg H, Rieger H (2015, Submitted) Relation between tumor oxygenation, vascular remodeling, and blood flow: a computational model with applications to breast cancer. PLOS Comp Biol [10pt]

    Google Scholar 

  168. Welter M, Rieger H (2010) Physical determinants of vascular network remodeling during tumor growth. Eur Phys J E Soft Matter 33(2):149–163

    Article  CAS  PubMed  Google Scholar 

  169. Welter M, Rieger H (2013) Interstitial fluid flow and drug delivery in vascularized tumors: a computational model. PLoS ONE 8(8):e70,395. doi:10.1371/journal.pone.0070395. http://dx.doi.org/10.1371%2Fjournal.pone.0070395

    Google Scholar 

  170. Wilson CB, Lammertsma AA, McKenzie CG, Sikora K, Jones T (1992) Measurements of blood flow and exchanging water space in breast tumors using positron emission tomography: a rapid and noninvasive dynamic method. Cancer Res 52(6):1592–1597

    CAS  PubMed  Google Scholar 

  171. Wise SM, Lowengrub JS, Frieboes HB, Cristini V (2008) Three-dimensional multispecies nonlinear tumor growth–I model and numerical method. J Theor Biol 253:524–543

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  172. Wu J, Long Q, Xu S, Padhani AR (2009) Study of tumor blood perfusion and its variation due to vascular normalization by anti-angiogenic therapy based on 3d angiogenic microvasculature. J Biomech 42(6):712–721. http://dx.doi.org/10.1016/j.jbiomech.2009.01.009. http://www.sciencedirect.com/science/article/pii/S0021929009000281

    Google Scholar 

  173. Wu J, Xu S, Long Q, Collins MW, Konig CS, Zhao G, Jiang Y, Padhani AR (2008) Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature. J Biomech 41(5):996–1004

    Article  PubMed  Google Scholar 

  174. Wu M, Frieboes HB, McDougall SR, Chaplain MA, Cristini V, Lowengrub J (2013) The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. J Theor Biol 320(0):131–151. doi:10.1016/j.jtbi.2012.11.031. http://www.sciencedirect.com/science/article/pii/S0022519312006200

    Google Scholar 

  175. Yuan F, Salehi HA, Boucher Y, Vasthare US, Tuma RF, Jain RK (1994) Vascular permeability and microcirculation of gliomas and mammary carcinomas transplanted in rat and mouse cranial windows. Cancer Res 54(17):4564–4568

    CAS  PubMed  Google Scholar 

  176. Zhao J, Salmon H, Sarntinoranont M (2007) Effect of heterogeneous vasculature on interstitial transport within a solid tumor. Microvasc Res 73:224–236

    Article  CAS  PubMed  Google Scholar 

  177. Zheng JH, Chen CT, Au JL, Wientjes MG (2001) Time- and concentration-dependent penetration of doxorubicin in prostate tumors. AAPS PharmSci 3(2):E15

    Article  CAS  PubMed  Google Scholar 

  178. 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 67:211–259

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heiko Rieger .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Welter, M., Rieger, H. (2016). Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply. In: Rejniak, K. (eds) Systems Biology of Tumor Microenvironment. Advances in Experimental Medicine and Biology, vol 936. Springer, Cham. https://doi.org/10.1007/978-3-319-42023-3_3

Download citation

Publish with us

Policies and ethics