Physics of the tumor vasculature: Theory and experiment

Review
Part of the following topical collections:
  1. Focus Point on the Physics of Cancer

Abstract.

Growing solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth and gain of metastatic potential. Consequently the tumor vasculature has been a major target of anti cancer therapies since four decades. The main underlying strategic concepts range from “starving a tumor to death” over “blood vessel normalization” to “blood vessel growth promotion” for improved drug delivery and oxygenation for increased success rates of radiation therapy. A mechanistic understanding of the these strategies is often elusive and call for a quantitative analysis of the underlying physics. Oxygen supply as well as drug delivery is determined by blood and interstitial fluid flow, for which reason such an analysis must focus on the relation between the intra- and extra-vascular transport characteristics and the tumor vasculature morphology. Here we review the current status of theoretical concepts and computational analysis of physical determinants of the tumor vasculature and the emerging predictions for blood flow, oxygen distribution, interstitial fluid pressure and efficiency of drug delivery.

Supplementary material

13360_2016_1017_MOESM1_ESM.pdf (262 kb)
Supplementary material

References

  1. 1.
    Rakesh K. Jain, Cancer Res. 48, 2641 (1988)Google Scholar
  2. 2.
    Peter Vaupel, Friedrich Kallinowski, Paul Okunieff, Cancer Res. 49, 6449 (1989)Google Scholar
  3. 3.
    Michael Hckel, Peter Vaupel, J. Natl. Cancer Inst. 93, 266 (2001)CrossRefGoogle Scholar
  4. 4.
    L.H. Gray, A.D. Conger, M. Ebert, S. Hornsey, O.C.A. Scott, Brit. J. Radiol. 26, 638 (1953)CrossRefGoogle Scholar
  5. 5.
    R.K. Jain, Cancer Res. 47, 3039 (1987)Google Scholar
  6. 6.
    R.K. Jain, L.T. Baxter, Cancer Res. 48, 7022 (1988)Google Scholar
  7. 7.
    R.K. Jain, Annu. Rev. Biomed. Eng. 1, 241 (1999)CrossRefGoogle Scholar
  8. 8.
    C.H. Heldin, K. Rubin, K. Pietras, A. Ostman, Nat. Rev. Cancer 4, 806 (2004)CrossRefGoogle Scholar
  9. 9.
    A.I. Minchinton, I.F. Tannock, Nat. Rev. Cancer 6, 583 (2006)CrossRefGoogle Scholar
  10. 10.
    R.K. Jain, Science 307, 58 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Ricky T. Tong, Yves Boucher, Sergey V. Kozin, Frank Winkler, Daniel J. Hicklin, Rakesh K. Jain, Cancer Res. 64, 3731 (2004)CrossRefGoogle Scholar
  12. 12.
    Rakesh K. Jain, Cancer Cell 26, 605 (2015)CrossRefGoogle Scholar
  13. 13.
    Lee B. Rivera, Gabriele Bergers, Science 349, 694 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Mary Purcell Wiedeman, Ronald F. Tuma, Harvey Norman Mayrovitz, An Introduction to Microcirculation (New York, Academic Press, 1981)Google Scholar
  15. 15.
    Cecil D Murray, Proc. Natl. Acad. Sci. U.S.A. 12, 207 (1926)ADSCrossRefGoogle Scholar
  16. 16.
    T.F. Sherman, J. Gen. Physiol. 78, 431 (1981)CrossRefGoogle Scholar
  17. 17.
    Fan Yuan, Hassan A. Salehi, Yves Boucher, Usha S. Vasthare, Ronald F. Tuma, Rakesh K. Jain, Cancer Res. 54, 4564 (1994)Google Scholar
  18. 18.
    E.N. Marieb, K. Hoehn, Human Anatomy and Physiology (Pearson, 2013)Google Scholar
  19. 19.
    A.R.A. Anderson, M.A.J. Chaplain, Bull. Math. Biol. 60, 857 (1998)MATHCrossRefGoogle Scholar
  20. 20.
    M.A. Gimbrone, R.S. Cotran, S.B. Leapman, J. Folkman, J. Natl. Cancer Inst. 52, 413 (1974)Google Scholar
  21. 21.
    S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, J.A. Sherratt, Bull. Math. Biol. 64, 673 (2002)CrossRefGoogle Scholar
  22. 22.
    S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, J. Theor. Biol. 241, 564 (2006)MathSciNetCrossRefGoogle Scholar
  23. 23.
    J. Wu, S. Xu, Q. Long, M.W. Collins, C.S. Konig, G. Zhao, Y. Jiang, A.R. Padhani, J. Biomech. 41, 996 (2008)CrossRefGoogle Scholar
  24. 24.
    Jie Wu, Quan Long, Shixiong Xu, Anwar R. Padhani, J. Biomech. 42, 712 (2009)CrossRefGoogle Scholar
  25. 25.
    B. Döme, S. Paku, B. Somlai, J. Tímár, J. Pathol. 197, 355 (2002)CrossRefGoogle Scholar
  26. 26.
    J. Holash, P.C. Maisonpierre, D. Compton, P. Boland, C.R. Alexander, D. Zagzag, G.D. Yancopoulos, S.J. Wiegand, Science 284, 1994 (1999)CrossRefGoogle Scholar
  27. 27.
    T. Alarcon, H.M. Byrne, P.K. Maini, J. Theor. Biol. 225, 257 (2003)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Helen M. Byrne, Markus R. Owen, Tomas Alarcon, James Murphy, Philip K. Maini, Math. Mod. Meth. Appl. Sci. 16, 1219 (2006)MATHCrossRefGoogle Scholar
  29. 29.
    M.R. Owen, T. Alarcn, P.K. Maini, H.M. Byrne, J. Math. Biol. 58, 689 (2009)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    R. Weislo, W. Dzwinel, D.A. Yuen, A.Z. Dudek, J. Mol. Model. 15, 1517 (2009)CrossRefGoogle Scholar
  31. 31.
    R. Betteridge, M.R. Owen, H.M. Byrne, T. Alarcon, P.K. Maini, Networks Heterogen. Media 1, 515 (2006)MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Katalin Bartha, Heiko Rieger, J. Theor. Biol. 241, 903 (2006)CrossRefGoogle Scholar
  33. 33.
    D.S. Lee, H. Rieger, K. Bartha, Phys. Rev. Lett. 96, 058104 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Min Wu, Hermann B. Frieboes, Steven R. McDougall, Mark A.J. Chaplain, Vittorio Cristini, John Lowengrub, J. Theor. Biol. 320, 131 (2013)CrossRefGoogle Scholar
  35. 35.
    J.L. Gevertz, Comput. Math. Methods Med. 2011, 830515 (2011)MathSciNetCrossRefGoogle Scholar
  36. 36.
    N. Safaeian, 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, New Zealand (University of Canterbury, 2012)Google Scholar
  37. 37.
    W. Schreiner, J. Biomed. Eng. 15, 148 (1993)CrossRefGoogle Scholar
  38. 38.
    Ralf Gödde, Haymo Kurz, Dev. Dyn. 220, 387 (2001)CrossRefGoogle Scholar
  39. 39.
    M. Welter, K. Bartha, H. Rieger, J. Theor. Biol. 259, 405 (2009)MathSciNetCrossRefGoogle Scholar
  40. 40.
    M. Welter, H. Rieger, PLoS ONE 8, e70395 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    M. Welter, T. Fredrich, H. Rinneberg, H. Rieger, Relation between tumor oxygenation, vascular remodeling, and blood flow: a computational model with applications to breast cancer, submitted to PLOS Comp. Biol. (2015)Google Scholar
  42. 42.
    F. Cassot, F. Lauwers, C. Fouard, S. Prohaska, V. Lauwers-Cances, Microcirculation 13, 1 (2006)CrossRefGoogle Scholar
  43. 43.
    Spyros K. Stamatelos, Eugene Kim, Arvind P. Pathak, Aleksander S. Popel, Microvasc. Res. 91, 8 (2014)CrossRefGoogle Scholar
  44. 44.
    Romain Guibert, Caroline Fonta, Franck Plouraboue, J. Cereb. Blood Flow Metab. 30, 1860 (2010)CrossRefGoogle Scholar
  45. 45.
    J. Lee, P. Beighley, E. Ritman, N. Smith, Med. Image Anal. 11, 630 (2007)CrossRefGoogle Scholar
  46. 46.
    A.R. Pries, T.W. Secomb, T. Gessner, M.B. Sperandio, J.F. Gross, P. Gaehtgens, Circ. Res. 75, 904 (1994)CrossRefGoogle Scholar
  47. 47.
    A.R. Pries, T.W. Secomb, Am. J. Physiol. - Heart Circulat. Physiol. 289, H2657 (2005)CrossRefGoogle Scholar
  48. 48.
    A.R. Pries, T.W. Secomb, P. Gaehtgens, J.F. Gross, Circ. Res. 67, 826 (1990)CrossRefGoogle Scholar
  49. 49.
    N. Safaeian, M. Sellier, T. David, J. Theor. Biol. 271, 145 (2011)MathSciNetCrossRefGoogle Scholar
  50. 50.
    A.R. Pries, T.W. Secomb, P. Gaehtgens, J.F. Gross, Circ. Res. 67, 826 (1990)CrossRefGoogle Scholar
  51. 51.
    Peter Carmeliet, Rakesh Jain, Nature 407, 249 (2000)CrossRefGoogle Scholar
  52. 52.
    Peter Carmeliet, Rakesh K. Jain, Nature 473, 298 (2011)ADSCrossRefGoogle Scholar
  53. 53.
    J. Holash, S.J. Wiegand, G.D. Yancopoulos, Oncogene 18, 5356 (1999)CrossRefGoogle Scholar
  54. 54.
    B. Döme, M. Hendrix, S. Paku, J. Tóvarí, Am. J. Path. 170, 1 (2007)CrossRefGoogle Scholar
  55. 55.
    R. Erber, U. Eichelsbacher, V. Powajbo, T. Korn, V. Djonov, J. Lin, H.-P. Hammes, R. Grobholz, A. Ullrich, P. Vajkoczy, EMBO 25, 628 (2006)CrossRefGoogle Scholar
  56. 56.
    M. Scianna, C.G. Bell, L. Preziosi, J. Theor. Biol. 333, 174 (2013)MathSciNetCrossRefGoogle Scholar
  57. 57.
    Elizabeth A. Logsdon, Stacey D. Finley, Aleksander S. Popel, Feilim Mac Gabhann, J. Cell. Molec. Med. 18, 1491 (2014)CrossRefGoogle Scholar
  58. 58.
    C.J. Breward, H.M. Byrne, C.E. Lewis, Bull. Math. Biol. 65, 609 (2003)CrossRefGoogle Scholar
  59. 59.
    R.P. Araujo, D.L.S. McElwain, J. Math. Biol. 66, 1039 (2004)MathSciNetCrossRefGoogle Scholar
  60. 60.
    N. Bellomo, E. De Angelis, L. Preziosi, J. Theor. Med. 5, 111 (2003)MATHCrossRefGoogle Scholar
  61. 61.
    T. Alarcn, M.R. Owen, H.M. Byrne, P.K. Maini, Comp. Math. Methods Med. 7, 85 (2006)CrossRefGoogle Scholar
  62. 62.
    A. Stephanou, S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, Math. Comput. Modell. 41, 1137 (2005) Modelling Complex Systems in Molecular Biology and Tumor Dynamics and ControlMathSciNetMATHCrossRefGoogle Scholar
  63. 63.
    A. Stephanou, S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, Math. Comput. Model. 44, 96 (2006)MathSciNetMATHCrossRefGoogle Scholar
  64. 64.
    M.A.J. Chaplain, S.R. McDougall, A.R.A. Anderson, Annu. Rev. Biomed. Eng. 8, 233 (2006)CrossRefGoogle Scholar
  65. 65.
    Yan Cai, Shixiong Xu, Jie Wu, Quan Long, J. Theor. Biol. 279, 90 (2011)CrossRefGoogle Scholar
  66. 66.
    Michael A. Gimbrone, Ramzi S. Cotran, Stephen B. Leapman, Judah Folkman, J. Natl. Cancer Inst. 52, 413 (1974)Google Scholar
  67. 67.
    M. Welter, H. Rieger, Eur. Phys. J. E 33, 149 (2010)CrossRefGoogle Scholar
  68. 68.
    P. Tracqui, Rep. Prog. Phys. 72, 056701 (2009)ADSCrossRefGoogle Scholar
  69. 69.
    Katie Bentley, Holger Gerhardt, Paul A. Bates, J. Theor. Biol. 250, 25 (2008)CrossRefGoogle Scholar
  70. 70.
    Holger Gerhardt, Matthew Golding, Marcus Fruttinger, Christina Ruhrberg, Andrea Lundkvist, Alexandra Abramsson, Michael Jeltsch, Christopher Mitchell, Kari Alitalo, David Shima, Christer Betsholz, J. Cell Biol. 161, 1163 (2003)CrossRefGoogle Scholar
  71. 71.
    A.R. Pries, T.W. Secomb, P. Gaehtgens, Am. J. Physiol. 275, H349 (1994)Google Scholar
  72. 72.
    M. Welter, K. Bartha, H. Rieger, J. Theor. Biol. 250, 257 (2008)MathSciNetCrossRefGoogle Scholar
  73. 73.
    Axel R. Pries, Michael Höpfner, Ferdinand le Noble, Mark W. Dewhirst, Timothy W. Secomb, Nat. Rev. Cancer 10, 587 (2010)CrossRefGoogle Scholar
  74. 74.
    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, PLoS ONE 6, e14790 (2011)ADSCrossRefGoogle Scholar
  75. 75.
    J. Du, F.H. Li, H. Fang, J.G. Xia, C.X. Zhu, J. Ultrasound Med. 27, 833 (2008)Google Scholar
  76. 76.
    Yuval Gazit, David A. Berk, Laurence T. Baxter Michael Leunig, Rakesh K. Jain, Phys. Rev. Lett. 75, 2428 (1995)ADSCrossRefGoogle Scholar
  77. 77.
    Alessandro Taloni, Martine Ben Amar, Stefano Zapperi, Caterina A.M. La Porta, Eur. Phys. J. Plus 130, 224 (2015)CrossRefGoogle Scholar
  78. 78.
    R.K. Jain, R.T. Tong, L.L. Munn, Cancer Res. 67, 2729 (2007)CrossRefGoogle Scholar
  79. 79.
    J. Zhao, H. Salmon, M. Sarntinoranont, Microvasc. Res. 73, 224 (2007)CrossRefGoogle Scholar
  80. 80.
    M. Sefidgar, M. Soltani, K. Raahemifar, H. Bazmara, S.M. Nayinian, M. Bazargan, J. Biol. Eng 8, 12 (2014)CrossRefGoogle Scholar
  81. 81.
    M. Sefidgar, M. Soltani, K. Raahemifar, M. Sadeghi, H. Bazmara, M. Bazargan, M. Mousavi Naeenian, Microvasc. Res. 99, 43 (2015)CrossRefGoogle Scholar
  82. 82.
    P. Knabner, L. Angermann, Numerik partieller Differentialgleichungen (Springer Verlag, 2000)Google Scholar
  83. 83.
    S.M. Wise, J.S. Lowengrub, H.B. Frieboes, V. Cristini, J. Theor. Biol. 253, 524 (2008)MathSciNetCrossRefGoogle Scholar
  84. 84.
    J.P. Sinek, S. Sanga, X. Zheng, H.B. Frieboes, M. Ferrari, V. Cristini, J. Math. Biol. 58, 485 (2009)MathSciNetMATHCrossRefGoogle Scholar
  85. 85.
    A. Daşu, I. Toma-Daşu, M. Karlsson, Phys. Med. Biol. 48, 2829 (2003)CrossRefGoogle Scholar
  86. 86.
    C.J. Kelly, M. Brady, Phys. Med. Biol. 51, 5859 (2006)CrossRefGoogle Scholar
  87. 87.
    D. Monnich, E.G. Troost, J.H. Kaanders, W.J. Oyen, M. Alber, D. Thorwarth, Phys. Med. Biol. 56, 2045 (2011)CrossRefGoogle Scholar
  88. 88.
    A.C. Skeldon, G. Chaffey, D.J. Lloyd, V. Mohan, D.A. Bradley, A. Nisbet, PLoS ONE 7, e38597 (2012)ADSCrossRefGoogle Scholar
  89. 89.
    I. Espinoza, P. Peschke, C.P. Karger, Med. Phys. 40, 081703 (2013)CrossRefGoogle Scholar
  90. 90.
    Carlo D’Angelo, SIAM J. Numer. Anal. 50, 194 (2012)MathSciNetMATHCrossRefGoogle Scholar
  91. 91.
    L. Cattaneo, P. Zunino, Int. J. Numer. Method Biomed. Eng. 30, 1347 (2014)MathSciNetCrossRefGoogle Scholar
  92. 92.
    R.K. Jain, T. Stylianopoulos, Nat. Rev. Clin. Oncol. 7, 653 (2010)CrossRefGoogle Scholar
  93. 93.
    A.J. Primeau, A. Rendon, D. Hedley, L. Lilge, I.F. Tannock, Clin. Cancer Res. 11, 8782 (2005)CrossRefGoogle Scholar
  94. 94.
    J.H. Zheng, C.T. Chen, J.L. Au, M.G. Wientjes, AAPS PharmSci. 3, E15 (2001)CrossRefGoogle Scholar
  95. 95.
    R.K. Jain, J. Clin. Oncol. 31, 2205 (2013)CrossRefGoogle Scholar
  96. 96.
    P.A. Netti, D.A. Berk, M.A. Swartz, A.J. Grodzinsky, R.K. Jain, Cancer Res. 60, 2497 (2000)Google Scholar
  97. 97.
    Trevor D. McKee, Paola Grandi, Wilson Mok, George Alexandrakis, Numpon Insin, John P. Zimmer, Moungi G. Bawendi, Yves Boucher, Xandra O. Breakefield, Rakesh K. Jain, Cancer Res. 66, 2509 (2006)CrossRefGoogle Scholar
  98. 98.
    Benjamin Diop-Frimpong, Vikash P. Chauhan, Stephen Krane, Yves Boucher, Rakesh K. Jain, Proc. Natl. Acad. Sci. U.S.A. 108, 2909 (2011)ADSCrossRefGoogle Scholar
  99. 99.
    Triantafyllos Stylianopoulos, Rakesh K. Jain, Proc. Natl. Acad. Sci. U.S.A. 110, 18632 (2013)ADSCrossRefGoogle Scholar
  100. 100.
    A.C. Shieh, M.A. Swartz, Phys. Biol. 8, 015012 (2011)ADSCrossRefGoogle Scholar
  101. 101.
    J.D. Hellums, P.K. Nair, N.S. Huang, N. Ohshima, Ann. Biomed. Eng. 24, 1 (1996)CrossRefGoogle Scholar
  102. 102.
    D. Goldman, Microcirculation 15, 795 (2008)CrossRefGoogle Scholar
  103. 103.
    A. Krogh, J. Physiol. (London) 52, 409 (1919)CrossRefGoogle Scholar
  104. 104.
    P.K. Nair, J.D. Hellums, J.S. Olson, Microvasc. Res. 38, 269 (1989)CrossRefGoogle Scholar
  105. 105.
    P.K. Nair, N.S. Huang, J.D. Hellums, J.S. Olson, Microvasc. Res. 39, 203 (1990)CrossRefGoogle Scholar
  106. 106.
    T.E. Moschandreou, C.G. Ellis, D. Goldman, Math. Biosci. 232, 1 (2011)MathSciNetMATHCrossRefGoogle Scholar
  107. 107.
    Richard Hsu, Timothy W. Secomb, Math. Biosci. 96, 61 (1989)MATHCrossRefGoogle Scholar
  108. 108.
    D. Goldman, A.S. Popel, J. Theor. Biol. 206, 181 (2000)CrossRefGoogle Scholar
  109. 109.
    Timothy W. Secomb, Richard Hsu, Eric Y.H. Park, Mark W. Dewhirst, Ann. Biomed. Eng. 32, 1519 (2004)CrossRefGoogle Scholar
  110. 110.
    D. Goldman, R.M. Bateman, C.G. Ellis, Am. J. Physiol. Heart Circ. Physiol. 287, H2535 (2004)CrossRefGoogle Scholar
  111. 111.
    D. Goldman, R.M. Bateman, C.G. Ellis, Am. J. Physiol. Heart Circ. Physiol. 290, H2277 (2006)CrossRefGoogle Scholar
  112. 112.
    N.M. Tsoukias, D. Goldman, A. Vadapalli, R.N. Pittman, A.S. Popel, J. Theor. Biol. 248, 657 (2007)MathSciNetCrossRefGoogle Scholar
  113. 113.
    N. Safaeian, M. Sellier, T. David, J. Theor. Biol. 271, 145 (2011)MathSciNetCrossRefGoogle Scholar
  114. 114.
    G.M. Fraser, D. Goldman, C.G. Ellis, Microcirculation 20, 748 (2013)Google Scholar
  115. 115.
    N. Safaeian, T. David, J. Cereb. Blood Flow Metab. 33, 1633 (2013)CrossRefGoogle Scholar
  116. 116.
    D.A. Beard, Ann. Biomed. Eng. 29, 837 (2001)CrossRefGoogle Scholar
  117. 117.
    Heiko Rieger, Michael Welter, WIREs Syst. Biol. Med. 7, 113 (2015)CrossRefGoogle Scholar
  118. 118.
    D. Grosenick, K.T. Moesta, M. Moller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P.M. Schlag, H. Rinneberg, Phys. Med. Biol. 50, 2429 (2005)CrossRefGoogle Scholar
  119. 119.
    L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, G. Danesini, R. Cubeddu, Phys. Med. Biol. 50, 2489 (2005)CrossRefGoogle Scholar
  120. 120.
    P. Taroni, A. Torricelli, L. Spinelli, A. Pifferi, F. Arpaia, G. Danesini, R. Cubeddu, Phys. Med. Biol. 50, 2469 (2005)CrossRefGoogle Scholar
  121. 121.
    P. Taroni, Photochem. Photobiol. Sci. 11, 241 (2012)CrossRefGoogle Scholar
  122. 122.
    P. Degond, S. Mas-Gallic, Math. Comput. 53, 485 (1989)ADSMathSciNetMATHGoogle Scholar
  123. 123.
    J.H. Lagerlf, J. Kindblom, E. Cortez, K. Pietras, P. Bernhardt, Med. Phys. 40, 024101 (2013)CrossRefGoogle Scholar
  124. 124.
    J.H. Lagerlf, J. Kindblom, P. Bernhardt, Med. Phys. 41, 044101 (2014)CrossRefGoogle Scholar
  125. 125.
    F. Kallinowski, K.H. Schlenger, M. Kloes, M. Stohrer, P. Vaupel, Int. J. Cancer 44, 266 (1989)CrossRefGoogle Scholar
  126. 126.
    A.R. Pries, B. Reglin, T.W. Secomb, Hypertension 46, 725 (2005)CrossRefGoogle Scholar
  127. 127.
    V.P. Chauhan, J.D. Martin, H. Liu, D.A. Lacorre, S.R. Jain, S.V. Kozin, T. Stylianopoulos, A.S. Mousa, X. Han, P. Adstamongkonkul, Z. Popović, P. Huang, M.G. Bawendi, Y. Boucher, R.K. Jain, Nat. Commun. 4, 2516 (2013)ADSCrossRefGoogle Scholar
  128. 128.
    T. Stylianopoulos, J.D. Martin, V.P. Chauhan, S.R. Jain, B. Diop-Frimpong, N. Bardeesy, B.L. Smith, C.R. Ferrone, F.J. Hornicek, Y. Boucher, L.L. Munn, R.K. Jain, Proc. Natl. Acad. Sci. U.S.A. 109, 15101 (2012)ADSCrossRefGoogle Scholar
  129. 129.
    V.P. Chauhan, Y. Boucher, C.R. Ferrone, S. Roberge, J.D. Martin, T. Stylianopoulos, N. Bardeesy, R.A. DePinho, T.P. Padera, L.L. Munn, R.K. Jain, Cancer Cell 26, 14 (2014)CrossRefGoogle Scholar
  130. 130.
    G. Griffon-Etienne, Y. Boucher, C. Brekken, H.D. Suit, R.K. Jain, Cancer Res. 59, 3776 (1999)Google Scholar
  131. 131.
    K.E. DelGiorno, M.A. Carlson, R. Osgood, P.P. Provenzano, J.S. Brockenbough, C.B. Thompson, H.M. Shepard, G.I. Frost, J.D. Potter, S.R. Hingorani, Cancer Cell 26, 16 (2014)CrossRefGoogle Scholar
  132. 132.
    J.W. Baish, R.K. Jain, Nat. Med. 4, 984 (1998)CrossRefGoogle Scholar
  133. 133.
    Min Wu, Hermann B. Frieboes, Mark A.J. Chaplain, Steven R. McDougall, Vittorio Cristini, John S. Lowengrub, J. Theor. Biol. 355, 194 (2014)CrossRefGoogle Scholar
  134. 134.
    J.W. Baish, T. Stylianopoulos, R.M. Lanning, W.S. Kamoun, D. Fukumura, L.L. Munn, R.K. Jain, Proc. Natl. Acad. Sci. U.S.A. 108, 1799 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Heiko Rieger
    • 1
  • Thierry Fredrich
    • 1
  • Michael Welter
    • 1
  1. 1.Theoretical PhysicsSaarland UniversitySaarbrückenGermany

Personalised recommendations