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.
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References
Rakesh K. Jain, Cancer Res. 48, 2641 (1988)
Peter Vaupel, Friedrich Kallinowski, Paul Okunieff, Cancer Res. 49, 6449 (1989)
Michael Hckel, Peter Vaupel, J. Natl. Cancer Inst. 93, 266 (2001)
L.H. Gray, A.D. Conger, M. Ebert, S. Hornsey, O.C.A. Scott, Brit. J. Radiol. 26, 638 (1953)
R.K. Jain, Cancer Res. 47, 3039 (1987)
R.K. Jain, L.T. Baxter, Cancer Res. 48, 7022 (1988)
R.K. Jain, Annu. Rev. Biomed. Eng. 1, 241 (1999)
C.H. Heldin, K. Rubin, K. Pietras, A. Ostman, Nat. Rev. Cancer 4, 806 (2004)
A.I. Minchinton, I.F. Tannock, Nat. Rev. Cancer 6, 583 (2006)
R.K. Jain, Science 307, 58 (2005)
Ricky T. Tong, Yves Boucher, Sergey V. Kozin, Frank Winkler, Daniel J. Hicklin, Rakesh K. Jain, Cancer Res. 64, 3731 (2004)
Rakesh K. Jain, Cancer Cell 26, 605 (2015)
Lee B. Rivera, Gabriele Bergers, Science 349, 694 (2015)
Mary Purcell Wiedeman, Ronald F. Tuma, Harvey Norman Mayrovitz, An Introduction to Microcirculation (New York, Academic Press, 1981)
Cecil D Murray, Proc. Natl. Acad. Sci. U.S.A. 12, 207 (1926)
T.F. Sherman, J. Gen. Physiol. 78, 431 (1981)
Fan Yuan, Hassan A. Salehi, Yves Boucher, Usha S. Vasthare, Ronald F. Tuma, Rakesh K. Jain, Cancer Res. 54, 4564 (1994)
E.N. Marieb, K. Hoehn, Human Anatomy and Physiology (Pearson, 2013)
A.R.A. Anderson, M.A.J. Chaplain, Bull. Math. Biol. 60, 857 (1998)
M.A. Gimbrone, R.S. Cotran, S.B. Leapman, J. Folkman, J. Natl. Cancer Inst. 52, 413 (1974)
S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, J.A. Sherratt, Bull. Math. Biol. 64, 673 (2002)
S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, J. Theor. Biol. 241, 564 (2006)
J. Wu, S. Xu, Q. Long, M.W. Collins, C.S. Konig, G. Zhao, Y. Jiang, A.R. Padhani, J. Biomech. 41, 996 (2008)
Jie Wu, Quan Long, Shixiong Xu, Anwar R. Padhani, J. Biomech. 42, 712 (2009)
B. Döme, S. Paku, B. Somlai, J. Tímár, J. Pathol. 197, 355 (2002)
J. Holash, P.C. Maisonpierre, D. Compton, P. Boland, C.R. Alexander, D. Zagzag, G.D. Yancopoulos, S.J. Wiegand, Science 284, 1994 (1999)
T. Alarcon, H.M. Byrne, P.K. Maini, J. Theor. Biol. 225, 257 (2003)
Helen M. Byrne, Markus R. Owen, Tomas Alarcon, James Murphy, Philip K. Maini, Math. Mod. Meth. Appl. Sci. 16, 1219 (2006)
M.R. Owen, T. Alarcn, P.K. Maini, H.M. Byrne, J. Math. Biol. 58, 689 (2009)
R. Weislo, W. Dzwinel, D.A. Yuen, A.Z. Dudek, J. Mol. Model. 15, 1517 (2009)
R. Betteridge, M.R. Owen, H.M. Byrne, T. Alarcon, P.K. Maini, Networks Heterogen. Media 1, 515 (2006)
Katalin Bartha, Heiko Rieger, J. Theor. Biol. 241, 903 (2006)
D.S. Lee, H. Rieger, K. Bartha, Phys. Rev. Lett. 96, 058104 (2006)
Min Wu, Hermann B. Frieboes, Steven R. McDougall, Mark A.J. Chaplain, Vittorio Cristini, John Lowengrub, J. Theor. Biol. 320, 131 (2013)
J.L. Gevertz, Comput. Math. Methods Med. 2011, 830515 (2011)
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)
W. Schreiner, J. Biomed. Eng. 15, 148 (1993)
Ralf Gödde, Haymo Kurz, Dev. Dyn. 220, 387 (2001)
M. Welter, K. Bartha, H. Rieger, J. Theor. Biol. 259, 405 (2009)
M. Welter, H. Rieger, PLoS ONE 8, e70395 (2013)
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)
F. Cassot, F. Lauwers, C. Fouard, S. Prohaska, V. Lauwers-Cances, Microcirculation 13, 1 (2006)
Spyros K. Stamatelos, Eugene Kim, Arvind P. Pathak, Aleksander S. Popel, Microvasc. Res. 91, 8 (2014)
Romain Guibert, Caroline Fonta, Franck Plouraboue, J. Cereb. Blood Flow Metab. 30, 1860 (2010)
J. Lee, P. Beighley, E. Ritman, N. Smith, Med. Image Anal. 11, 630 (2007)
A.R. Pries, T.W. Secomb, T. Gessner, M.B. Sperandio, J.F. Gross, P. Gaehtgens, Circ. Res. 75, 904 (1994)
A.R. Pries, T.W. Secomb, Am. J. Physiol. - Heart Circulat. Physiol. 289, H2657 (2005)
A.R. Pries, T.W. Secomb, P. Gaehtgens, J.F. Gross, Circ. Res. 67, 826 (1990)
N. Safaeian, M. Sellier, T. David, J. Theor. Biol. 271, 145 (2011)
A.R. Pries, T.W. Secomb, P. Gaehtgens, J.F. Gross, Circ. Res. 67, 826 (1990)
Peter Carmeliet, Rakesh Jain, Nature 407, 249 (2000)
Peter Carmeliet, Rakesh K. Jain, Nature 473, 298 (2011)
J. Holash, S.J. Wiegand, G.D. Yancopoulos, Oncogene 18, 5356 (1999)
B. Döme, M. Hendrix, S. Paku, J. Tóvarí, Am. J. Path. 170, 1 (2007)
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)
M. Scianna, C.G. Bell, L. Preziosi, J. Theor. Biol. 333, 174 (2013)
Elizabeth A. Logsdon, Stacey D. Finley, Aleksander S. Popel, Feilim Mac Gabhann, J. Cell. Molec. Med. 18, 1491 (2014)
C.J. Breward, H.M. Byrne, C.E. Lewis, Bull. Math. Biol. 65, 609 (2003)
R.P. Araujo, D.L.S. McElwain, J. Math. Biol. 66, 1039 (2004)
N. Bellomo, E. De Angelis, L. Preziosi, J. Theor. Med. 5, 111 (2003)
T. Alarcn, M.R. Owen, H.M. Byrne, P.K. Maini, Comp. Math. Methods Med. 7, 85 (2006)
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 Control
A. Stephanou, S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, Math. Comput. Model. 44, 96 (2006)
M.A.J. Chaplain, S.R. McDougall, A.R.A. Anderson, Annu. Rev. Biomed. Eng. 8, 233 (2006)
Yan Cai, Shixiong Xu, Jie Wu, Quan Long, J. Theor. Biol. 279, 90 (2011)
Michael A. Gimbrone, Ramzi S. Cotran, Stephen B. Leapman, Judah Folkman, J. Natl. Cancer Inst. 52, 413 (1974)
M. Welter, H. Rieger, Eur. Phys. J. E 33, 149 (2010)
P. Tracqui, Rep. Prog. Phys. 72, 056701 (2009)
Katie Bentley, Holger Gerhardt, Paul A. Bates, J. Theor. Biol. 250, 25 (2008)
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)
A.R. Pries, T.W. Secomb, P. Gaehtgens, Am. J. Physiol. 275, H349 (1994)
M. Welter, K. Bartha, H. Rieger, J. Theor. Biol. 250, 257 (2008)
Axel R. Pries, Michael Höpfner, Ferdinand le Noble, Mark W. Dewhirst, Timothy W. Secomb, Nat. Rev. Cancer 10, 587 (2010)
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)
J. Du, F.H. Li, H. Fang, J.G. Xia, C.X. Zhu, J. Ultrasound Med. 27, 833 (2008)
Yuval Gazit, David A. Berk, Laurence T. Baxter Michael Leunig, Rakesh K. Jain, Phys. Rev. Lett. 75, 2428 (1995)
Alessandro Taloni, Martine Ben Amar, Stefano Zapperi, Caterina A.M. La Porta, Eur. Phys. J. Plus 130, 224 (2015)
R.K. Jain, R.T. Tong, L.L. Munn, Cancer Res. 67, 2729 (2007)
J. Zhao, H. Salmon, M. Sarntinoranont, Microvasc. Res. 73, 224 (2007)
M. Sefidgar, M. Soltani, K. Raahemifar, H. Bazmara, S.M. Nayinian, M. Bazargan, J. Biol. Eng 8, 12 (2014)
M. Sefidgar, M. Soltani, K. Raahemifar, M. Sadeghi, H. Bazmara, M. Bazargan, M. Mousavi Naeenian, Microvasc. Res. 99, 43 (2015)
P. Knabner, L. Angermann, Numerik partieller Differentialgleichungen (Springer Verlag, 2000)
S.M. Wise, J.S. Lowengrub, H.B. Frieboes, V. Cristini, J. Theor. Biol. 253, 524 (2008)
J.P. Sinek, S. Sanga, X. Zheng, H.B. Frieboes, M. Ferrari, V. Cristini, J. Math. Biol. 58, 485 (2009)
A. Daşu, I. Toma-Daşu, M. Karlsson, Phys. Med. Biol. 48, 2829 (2003)
C.J. Kelly, M. Brady, Phys. Med. Biol. 51, 5859 (2006)
D. Monnich, E.G. Troost, J.H. Kaanders, W.J. Oyen, M. Alber, D. Thorwarth, Phys. Med. Biol. 56, 2045 (2011)
A.C. Skeldon, G. Chaffey, D.J. Lloyd, V. Mohan, D.A. Bradley, A. Nisbet, PLoS ONE 7, e38597 (2012)
I. Espinoza, P. Peschke, C.P. Karger, Med. Phys. 40, 081703 (2013)
Carlo D’Angelo, SIAM J. Numer. Anal. 50, 194 (2012)
L. Cattaneo, P. Zunino, Int. J. Numer. Method Biomed. Eng. 30, 1347 (2014)
R.K. Jain, T. Stylianopoulos, Nat. Rev. Clin. Oncol. 7, 653 (2010)
A.J. Primeau, A. Rendon, D. Hedley, L. Lilge, I.F. Tannock, Clin. Cancer Res. 11, 8782 (2005)
J.H. Zheng, C.T. Chen, J.L. Au, M.G. Wientjes, AAPS PharmSci. 3, E15 (2001)
R.K. Jain, J. Clin. Oncol. 31, 2205 (2013)
P.A. Netti, D.A. Berk, M.A. Swartz, A.J. Grodzinsky, R.K. Jain, Cancer Res. 60, 2497 (2000)
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)
Benjamin Diop-Frimpong, Vikash P. Chauhan, Stephen Krane, Yves Boucher, Rakesh K. Jain, Proc. Natl. Acad. Sci. U.S.A. 108, 2909 (2011)
Triantafyllos Stylianopoulos, Rakesh K. Jain, Proc. Natl. Acad. Sci. U.S.A. 110, 18632 (2013)
A.C. Shieh, M.A. Swartz, Phys. Biol. 8, 015012 (2011)
J.D. Hellums, P.K. Nair, N.S. Huang, N. Ohshima, Ann. Biomed. Eng. 24, 1 (1996)
D. Goldman, Microcirculation 15, 795 (2008)
A. Krogh, J. Physiol. (London) 52, 409 (1919)
P.K. Nair, J.D. Hellums, J.S. Olson, Microvasc. Res. 38, 269 (1989)
P.K. Nair, N.S. Huang, J.D. Hellums, J.S. Olson, Microvasc. Res. 39, 203 (1990)
T.E. Moschandreou, C.G. Ellis, D. Goldman, Math. Biosci. 232, 1 (2011)
Richard Hsu, Timothy W. Secomb, Math. Biosci. 96, 61 (1989)
D. Goldman, A.S. Popel, J. Theor. Biol. 206, 181 (2000)
Timothy W. Secomb, Richard Hsu, Eric Y.H. Park, Mark W. Dewhirst, Ann. Biomed. Eng. 32, 1519 (2004)
D. Goldman, R.M. Bateman, C.G. Ellis, Am. J. Physiol. Heart Circ. Physiol. 287, H2535 (2004)
D. Goldman, R.M. Bateman, C.G. Ellis, Am. J. Physiol. Heart Circ. Physiol. 290, H2277 (2006)
N.M. Tsoukias, D. Goldman, A. Vadapalli, R.N. Pittman, A.S. Popel, J. Theor. Biol. 248, 657 (2007)
N. Safaeian, M. Sellier, T. David, J. Theor. Biol. 271, 145 (2011)
G.M. Fraser, D. Goldman, C.G. Ellis, Microcirculation 20, 748 (2013)
N. Safaeian, T. David, J. Cereb. Blood Flow Metab. 33, 1633 (2013)
D.A. Beard, Ann. Biomed. Eng. 29, 837 (2001)
Heiko Rieger, Michael Welter, WIREs Syst. Biol. Med. 7, 113 (2015)
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)
L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, G. Danesini, R. Cubeddu, Phys. Med. Biol. 50, 2489 (2005)
P. Taroni, A. Torricelli, L. Spinelli, A. Pifferi, F. Arpaia, G. Danesini, R. Cubeddu, Phys. Med. Biol. 50, 2469 (2005)
P. Taroni, Photochem. Photobiol. Sci. 11, 241 (2012)
P. Degond, S. Mas-Gallic, Math. Comput. 53, 485 (1989)
J.H. Lagerlf, J. Kindblom, E. Cortez, K. Pietras, P. Bernhardt, Med. Phys. 40, 024101 (2013)
J.H. Lagerlf, J. Kindblom, P. Bernhardt, Med. Phys. 41, 044101 (2014)
F. Kallinowski, K.H. Schlenger, M. Kloes, M. Stohrer, P. Vaupel, Int. J. Cancer 44, 266 (1989)
A.R. Pries, B. Reglin, T.W. Secomb, Hypertension 46, 725 (2005)
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)
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)
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)
G. Griffon-Etienne, Y. Boucher, C. Brekken, H.D. Suit, R.K. Jain, Cancer Res. 59, 3776 (1999)
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)
J.W. Baish, R.K. Jain, Nat. Med. 4, 984 (1998)
Min Wu, Hermann B. Frieboes, Mark A.J. Chaplain, Steven R. McDougall, Vittorio Cristini, John S. Lowengrub, J. Theor. Biol. 355, 194 (2014)
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)
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Rieger, H., Fredrich, T. & Welter, M. Physics of the tumor vasculature: Theory and experiment. Eur. Phys. J. Plus 131, 31 (2016). https://doi.org/10.1140/epjp/i2016-16031-9
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DOI: https://doi.org/10.1140/epjp/i2016-16031-9