Tumor proliferation and diffusion on percolation clusters.
We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.
School of Physics, Sun Yat-sen University, Guangzhou, 510275, China.|BGI-Research in Shenzhen, Shenzhen, 518083, China.
Chongming
C
Jiang
Department of Medical Imaging, State Key Laboratory of Oncology in South China, Sun Yat-sen University Cancer Center, Guangzhou, 510060, China.
Chunyan
C
Cui
Siyuan Laboratory, Guangzhou Key Laboratory of Vacuum Coating Technologies and New Energy Materials, Department of Physics, Jinan University, Guangzhou, 510632, China.
Weirong
W
Zhong
School of Physics, Sun Yat-sen University, Guangzhou, 510275, China.
Gang
G
Li
Department of Medical Imaging, State Key Laboratory of Oncology in South China, Sun Yat-sen University Cancer Center, Guangzhou, 510060, China.
Li
L
Li
School of Physics, Sun Yat-sen University, Guangzhou, 510275, China. stssyz@mail.sysu.edu.cn.
Yuanzhi
Y
Shao
D049109:Cell Proliferation; D003198:Computer Simulation; D004058:Diffusion; D008954:Models, Biological; D009010:Monte Carlo Method; D009361:Neoplasm Invasiveness; D009362:Neoplasm Metastasis; D009369:Neoplasms / Q000473:pathology*
Inhomogeneity; Invasive and metastatic diffusion; Percolation; Reaction–diffusion systems; Tumor
Clin Exp Metastasis. 2015 Jan;32(1):15-27
25391215
Cancer Cell. 2003 Sep;4(3):163-6
14522249
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):3425-8
11970164
Proc Natl Acad Sci U S A. 2011 Feb 1;108(5):1799-803
21224417
Pflugers Arch. 2014 Nov;466(11):2127-38
24531759
Cell. 2013 Dec 19;155(7):1639-51
24332913
Lung Cancer. 2014 Oct;86(1):78-84
25130083
J Theor Biol. 2006 Nov 7;243(1):98-113
16860344
Nat Cell Biol. 2015 May;17 (5):678-88
25893917
Nat Med. 2006 Aug;12(8):895-904
16892035
Math Biosci Eng. 2011 Apr;8(2):371-83
21631135
Dev Cell. 2008 Jun;14(6):818-29
18539112
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 1):011916
16907136
Microvasc Res. 2009 Mar;77(2):87-95
19013623
Cell. 2009 Nov 25;139(5):871-90
19945376
J Clin Invest. 2009 Jun;119(6):1420-8
19487818
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):010901
22400505
Cell Stem Cell. 2014 Mar 6;14(3):275-91
24607403
J Cell Biochem. 2004 Mar 1;91(4):686-705
14991761
Cell Prolif. 2001 Apr;34(2):115-34
11348426
PLoS One. 2014 Oct 13;9(10):e109784
25310134
Nat Rev Drug Discov. 2014 Jul;13(7):497-512
24981363
J Theor Biol. 2009 Oct 7;260(3):359-71
19596356
Cancer. 2006 Apr 1;106(7):1624-33
16518827
Cell. 2011 Nov 23;147(5):992-1009
22118458
Proc Natl Acad Sci U S A. 2012 Jan 17;109(3):911-6
22203958
Math Med Biol. 2005 Jun;22(2):163-86
15781426
Cell. 2006 Nov 17;127(4):679-95
17110329
J Pathol Bacteriol. 1959 Apr;77(2):321-39
13642181
PLoS One. 2009;4(2):e4632
19247489
Biophys J. 2014 Dec 2;107(11):2546-58
25468334
Cancer Metastasis Rev. 1989 Aug;8(2):98-101
2673568
South Med J. 1988 Sep;81(9):1109-12
3420442
Adv Cancer Res. 2003;89:35-67
14587870
Cancer. 1997 Oct 15;80(8 Suppl):1572-80
9362424
J Biol Phys. 2000 Sep;26(3):219-34
23345723
Mol Biol Cell. 1998 Nov;9(11):3179-93
9802905
Bull Math Biol. 2002 Jul;64(4):673-702
12216417
Cancer Res. 2005 Jul 15;65(14):5991-5; discussion 5995
16024595
Phys Rev Lett. 2006 Feb 10;96(5):058104
16486998
Nature. 2006 May 25;441(7092):444-50
16724056
J Biol Phys. 2016 Jan;42(1):107-32
26293211
Phys Rev Lett. 2013 Mar 29;110(13):138103
23581378
Nat Rev Cancer. 2009 Apr;9(4):274-84
19308067
Dev Cell. 2013 Dec 9;27(5):560-73
24331928
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 1):061911
15697406
Cancer Res. 2005 Jul 15;65(14):5996-6000; discussion 6000-1
16024596
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041138
23214560
J Cell Sci. 2007 Mar 1;120(Pt 5):876-84
17298977
Biophys J. 2014 Oct 21;107(8):1821-8
25418163
Phys Rev Lett. 2011 Oct 28;107(18):188102
22107677
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 1):051901
12513517
Toxicol Sci. 2011 Oct;123(2):305-32
21750349
PLoS One. 2013 Dec 03;8(12):e80447
24312473
Nat Commun. 2014 Sep 17;5:4944
25229256
Proc Natl Acad Sci U S A. 2013 Dec 10;110(50):20176-81
24248371
Eur Phys J E Soft Matter. 2010 Oct;33(2):149-63
20607341
Nature. 2015 Nov 19;527(7578):329-35
26524530
Invasion Metastasis. 1997;17(6):281-96
9949288
Med Hypotheses. 1996 Sep;47(3):235-41
8898325
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 1):031920
21517536
Cancer Cell. 2013 Oct 14;24(4):542-56
24135284
Oncogene. 2014 Mar 6;33(10):1265-73
23524582
J Cell Sci. 2005 Oct 1;118(Pt 19):4325-6
16179603
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 1):031904
21517522