title: Multiscale modelling and nonlinear simulation of vascular tumour growth.
abstract: In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the multi-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression. Consistent with clinical observations, the hydrostatic stress generated by tumour cell proliferation shuts down large portions of the vascular network dramatically affecting the flow, the subsequent network remodeling, the delivery of nutrients to the tumour and the subsequent tumour progression. In addition, extracellular matrix degradation by tumour cells is seen to have a dramatic affect on both the development of the vascular network and the growth response of the tumour. In particular, the newly developing vessels tend to encapsulate, rather than penetrate, the tumour and are thus less effective in delivering nutrients.
authors.affiliation: School of Health Information Sciences, University of Texas Health Science Center, Houston, TX, USA. paul.t.macklin@uth.tmc.edu
authors.forename: Paul
authors.initials: P
authors.lastname: Macklin
authors.forename: Steven
authors.initials: S
authors.lastname: McDougall
authors.forename: Alexander R A
authors.initials: AR
authors.lastname: Anderson
authors.forename: Mark A J
authors.initials: MA
authors.lastname: Chaplain
authors.forename: Vittorio
authors.initials: V
authors.lastname: Cristini
authors.forename: John
authors.initials: J
authors.lastname: Lowengrub
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D001783:Blood Flow Velocity; D002196:Capillaries / Q000473:pathology / Q000503:physiopathology; D002465:Cell Movement / Q000502:physiology; D005109:Extracellular Matrix / Q000473:pathology / Q000502:physiology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009361:Neoplasm Invasiveness / Q000473:pathology / Q000503:physiopathology; D009369:Neoplasms / Q000098:blood supply* / Q000473:pathology* / Q000503:physiopathology; D009389:Neovascularization, Pathologic; D017711:Nonlinear Dynamics; D018874:Spheroids, Cellular / Q000473:pathology / Q000502:physiology; D014407:Tumor Cells, Cultured
references.citation: Bull Math Biol. 1998 Sep;60(5):857-99
references.pmid: 9739618
references.citation: Curr Pharm Des. 2006;12(23):2875-90
references.pmid: 16918418
references.citation: Cell. 1996 Feb 9;84(3):359-69
references.pmid: 8608589
references.citation: Nature. 2006 Apr 27;440(7088):1222-6
references.pmid: 16642001
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):051911
references.pmid: 17677102
references.citation: Biophys J. 1991 Jul;60(1):15-37
references.pmid: 1883934
references.citation: Math Med Biol. 2003 Dec;20(4):341-66
references.pmid: 14969384
references.citation: J Theor Biol. 2008 Jan 21;250(2):257-80
references.pmid: 17996256
references.citation: Expert Rev Anticancer Ther. 2006 Oct;6(10):1361-76
references.pmid: 17069522
references.citation: Cancer Res. 2006 Feb 1;66(3):1597-604
references.pmid: 16452218
references.citation: Bull Math Biol. 2004 Sep;66(5):1039-91
references.pmid: 15294418
references.citation: Bull Math Biol. 2002 Jul;64(4):673-702
references.pmid: 12216417
references.citation: Cell. 2006 Dec 1;127(5):905-15
references.pmid: 17129778
references.citation: Circulation. 2001 Dec 11;104(24):2981-9
references.pmid: 11739316
references.citation: J Math Biol. 1993;31(6):563-600
references.pmid: 8376918
references.citation: Nat Rev Cancer. 2003 May;3(5):362-74
references.pmid: 12724734
references.citation: Neuroimage. 2007;37 Suppl 1:S59-70
references.pmid: 17475515
references.citation: Math Biosci. 1995 Dec;130(2):151-81
references.pmid: 8527869
references.citation: Biomed Microdevices. 2004 Dec;6(4):297-309
references.pmid: 15548877
references.citation: J Math Biol. 2004 Aug;49(2):111-87
references.pmid: 15293017
references.citation: Am J Physiol Heart Circ Physiol. 2001 Sep;281(3):H1015-25
references.pmid: 11514266
references.citation: Semin Cancer Biol. 2005 Oct;15(5):365-77
references.pmid: 15975824
references.citation: Oncogene. 1999 Sep 20;18(38):5356-62
references.pmid: 10498889
references.citation: Acta Biotheor. 1995 Dec;43(4):387-402
references.pmid: 8919350
references.citation: J Biomol Screen. 2004 Jun;9(4):273-85
references.pmid: 15191644
references.citation: Hypertension. 2001 Dec 1;38(6):1476-9
references.pmid: 11751739
references.citation: Math Med Biol. 2005 Jun;22(2):163-86
references.pmid: 15781426
references.citation: J Math Biol. 2003 Mar;46(3):191-224
references.pmid: 12728333
references.citation: Annu Rev Biomed Eng. 2006;8:233-57
references.pmid: 16834556
references.citation: Cardiovasc Res. 1996 Oct;32(4):654-67
references.pmid: 8915184
references.citation: Bull Math Biol. 2005 Mar;67(2):211-59
references.pmid: 15710180
references.citation: Math Biosci. 1996 Jul 15;135(2):187-216
references.pmid: 8768220
references.citation: Onkologie. 2007 Jul;30(7):388-94
references.pmid: 17596750
references.citation: J Theor Biol. 2006 Aug 21;241(4):903-18
references.pmid: 16545398
references.citation: Neuro Oncol. 2005 Apr;7(2):134-53
references.pmid: 15831232
references.citation: Nature. 2005 Dec 15;438(7070):932-6
references.pmid: 16355210
references.citation: J Math Biol. 2006 Jul;53(1):86-134
references.pmid: 16791651
references.citation: Phys Rev Lett. 2006 Feb 10;96(5):058104
references.pmid: 16486998
references.citation: J Sci Comput. 2008 Jun 1;35(2-3):266-299
references.pmid: 21331304
references.citation: Am J Physiol. 1998 Aug;275(2):H349-60
references.pmid: 9683420
references.citation: Circ Res. 1995 Nov;77(5):1017-23
references.pmid: 7554136
references.citation: Nature. 1997 Feb 6;385(6616):537-40
references.pmid: 9020360
references.citation: Clin Chim Acta. 2005 Jul 24;357(2):173-9
references.pmid: 15907826
references.citation: Philos Trans A Math Phys Eng Sci. 2006 Jun 15;364(1843):1563-78
references.pmid: 16766361
references.citation: Cell. 2000 Jan 7;100(1):57-70
references.pmid: 10647931
references.citation: Bull Math Biol. 2004 Nov;66(6):1785-819
references.pmid: 15522355
references.citation: J Theor Biol. 1985 May 7;114(1):53-73
references.pmid: 2409405
references.citation: Crit Rev Oncol Hematol. 1989;9(3):197-242
references.pmid: 2480145
references.citation: J Math Biol. 2009 Apr;58(4-5):723-63
references.pmid: 18787827
references.citation: J Theor Biol. 2007 Apr 21;245(4):677-704
references.pmid: 17239903
references.citation: J Theor Biol. 2006 Aug 7;241(3):564-89
references.pmid: 16487543
references.citation: J Theor Biol. 1976 Jan;56(1):229-42
references.pmid: 1263527
references.citation: Semin Cancer Biol. 1991 Apr;2(2):111-4
references.pmid: 1912521
references.citation: Clin Cancer Res. 2005 Oct 1;11(19 Pt 1):6772-9
references.pmid: 16203763
references.citation: Nature. 2006 May 25;441(7092):437-43
references.pmid: 16724055