Fractal parameters and vascular networks: Facts & artifacts

Theoretical Biology and Medical Modelling

Volumn 5, Issue , 2008, Pages

  Mancardi, Daniele ^a   Varetto, Gianfranco ^b   Bucci, Enrico ^b   Maniero, Fabrizio ^c   Guiot, Caterina ^a  

^a UNIVERSITY OF TURIN   (Italy)

^b Bioindustry Park del Canavese   (Italy)

^c UNIVERSITY OF TURIN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ANGIOGENESIS; BLOOD VESSEL; CHICK EMBRYO; CHORIO ALLONTOIC MEMBRANE; EMBRYO; EMBRYOLOGY; FRACTAL ANALYSIS; INCUBATION TIME; MATHEMATICAL ANALYSIS; MEMBRANE; METHODOLOGY; NONHUMAN; NOTE; VALIDATION STUDY; ALGORITHM; ANIMAL; ARTICLE; ARTIFACT; BIOLOGICAL MODEL; CHORIOALLANTOIS; CHORION; IMAGE PROCESSING; METABOLISM; NEOVASCULARIZATION (PATHOLOGY); PATHOLOGY; PHYSIOLOGY; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; ARTIFACTS; BLOOD VESSELS; CHICK EMBRYO; CHORIOALLANTOIC MEMBRANE; CHORION; FRACTALS; IMAGE PROCESSING, COMPUTER-ASSISTED; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NEOVASCULARIZATION, PATHOLOGIC; NEOVASCULARIZATION, PHYSIOLOGIC;

EID: 48349119715     PISSN: None     EISSN: 17424682     Source Type: Journal    
DOI: 10.1186/1742-4682-5-12     Document Type: Note

References (36)

1. Dimension und auβeres Maβ E Hausdorff, Mathematische Annalen 1919 79 157 179 10.1007/BF01457179
2. ε-entropy and ε-capacity of sets of functional spaces. A Kolmogorov V Tihomirov, American Mathematical Society Translations 1961 17 277 364
3. How long is the coast of britain? statistical self-similarity and fractional dimension. B Mandelbrot, Science 1967 156 636 638 10.1126/science.156.3775.636 17837158
4. A Bunde S Havlin, A Brief Introduction to Fractal Geometry Berlin: Springer 1994
5. The fractal nature of nature: power laws, ecological complexity and biodiversity. JH Brown VK Gupta BL Li BT Milne C Restrepo GB West, Philos Trans R Soc Lond B Biol Sci 2002 357 1421 619 626 10.1098/rstb.2001.0993 12079523
6. Branching design of the bronchial tree based on a diameter-flow relationship. H Kitaoka B Suki, J Appl Physiol 1997 82 968 976 9074989
7. Scaling properties of the placenta's arterial tree. DL Bergman U Ullberg, J Theor Biol 1998 193 731 738 10.1006/jtbi.1998.0741 9745763
8. M Kleiber, The fire of life: an introduction to animal energetics Huntington, NY: Robert E Krieger 1975
9. A general model for ontogenetic growth.[see comment]. GB West JH Brown BJ Enquist, Nature 2001 413 628 631 10.1038/35098076 11675785
10. The dynamic evolution of the power exponent in a universal growth model of tumors. C Guiot PP Delsanto A Carpinteri N Pugno Y Mansury TS Deisboeck, J Theor Biol 2006 240 459 463 10.1016/j.jtbi.2005.10.006 16324717
11. On fractal properties of arterial trees. M Zamir, J Theor Biol 1999 197 517 526 10.1006/jtbi.1998.0892 10196094
12. Modelling of vascular growth processes: a stochastic biophysical approach to embryonic angiogenesis. K Sandau H Kurz, J Microsc 1994 175 205 213 7966255
13. Measuring fractal dimension and complexity - an alternative approach with an application. K Sandau H Kurz, J Microsc 1997 186 164 176 10.1046/j.1365-2818.1997.1270685.x 9183853
14. A new image analysis method based on topological and fractal parameters to evaluate the angiostatic activity of docetaxel by using the Matrigel assay in vitro. D Guidolin A Vacca GG Nussdorfer D Ribatti, Microvasc Res 2004 67 117 124 10.1016/j.mvr.2003.11.002 15020202
15. Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model. JW Baish Y Gazit DA Berk M Nozue LT Baxter RK Jain, Microvasc Res 1996 51 327 346 10.1006/mvre.1996.0031 8992232
16. Allometric scaling law questions the traditional mechanical model for axillary lymph node involvement in breast cancer. R Demicheli E Biganzoli P Boracchi M Greco WJ Hrushesky MW Retsky, J Clin Oncol 2006 24 4391 4396 10.1200/JCO.2006.05.5988 16926222
17. Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. RK Jain, Science 2005 307 58 62 10.1126/science.1104819 15637262
18. Angiogenesis and tumor metastasis. BR Zetter, Annu Rev Med 1998 49 407 424 10.1146/annurev.med.49.1.407 9509272
19. Stable interaction between alpha5beta1 integrin and Tie2 tyrosine kinase receptor regulates endothelial cell response to Ang-1. I Cascone L Napione F Maniero G Serini F Bussolino, J Cell Biol 2005 170 993 1004 16157706 10.1083/jcb.200507082
20. The chick embryo and its chorioallantoic membrane (CAM) for the in vivo evaluation of drug delivery systems. A Vargas M Zeisser-Labouebe N Lange R Gurny F Delie, Advanced Drug Delivery Reviews 2007 59 1162 1176 10.1016/j.addr.2007. 04.019 17870202
21. Current methods for assaying angiogenesis in vitro and in vivo. CA Staton SM Stribbling S Tazzyman R Hughes NJ Brown CE Lewis, Int J Exp Pathol 2004 85 233 248 10.1111/j.0959-9673.2004.00396.x 15379956
22. A report on the validity of the rorschach prognostic rating scale. FJ Kirkner WW Wisham FH Giedt, Journal of Projective Techniques 1953 17 465 470 13118575
23. A novel assay of angiogenesis in the quail chorioallantoic membrane: stimulation by bFGF and inhibition by angiostatin according to fractal dimension and grid intersection. P Parsons-Wingerter B Lwai MC Yang KE Elliott A Milaninia A Redlitz JI Clark EH Sage, Microvasc Res 1998 55 201 214 10.1006/mvre.1998.2073 9657920
24. Fractal analysis of region-based vascular change in the normal and non-proliferative diabetic retina. A Avakian RE Kalina EH Sage AH Rambhia KE Elliott EL Chuang JI Clark JN Hwang P Parsons-Wingerter, Curr Eye Res 2002 24 274 280 10.1076/ceyr.24.4.274.8411 12324866
25. A VEGF165-induced phenotypic switch from increased vessel density to increased vessel diameter and increased endothelial NOS activity. P Parsons-Wingerter UM Chandrasekharan TL McKay K Radhakrishnan PE DiCorleto B Albarran AG Farr, Microvasc Res 2006 72 91 100 10.1016/j.mvr.2006.05.008 16872639
26. Coadministration of angiopoietin-1 and vascular endothelial growth factor enhances collateral vascularization. JK Chae I Kim ST Lim MJ Chung WH Kim HG Kim JK Ko GY Koh, Arterioscler Thromb Vasc Biol 2000 20 12 2573 2578 11116055
27. Systemically expressed soluble Tie2 inhibits intraocular neovascularization. M Hangai YS Moon N Kitaya CK Chan DY Wu KG Peters SJ Ryan DR Hinton, Hum Gene Ther 2001 12 1311 1321 10.1089/104303401750270968 11440624
28. Activation of the tie2 receptor by angiopoietin-1 enhances tumor vessel maturation and impairs squamous cell carcinoma growth. T Hawighorst M Skobe M Streit YK Hong P Velasco LF Brown L Riccardi B Lange-Asschenfeldt M Detmar, Am J Pathol 2002 160 1381 1392 11943723
29. Angiopoietin 1 promotes tumor angiogenesis and tumor vessel plasticity of human cervical cancer in mice. WS Shim M Teh A Bapna I Kim GY Koh PO Mack R Ge, Exp Cell Res 2002 279 299 309 10.1006/excr.2002.5597 12243755
30. Recombinant angiopoietin-1 restores higher-order architecture of growing blood vessels in mice in the absence of mural cells.[see comment]. A Uemura M Ogawa M Hirashima T Fujiwara S Koyama H Takagi Y Honda SJ Wiegand GD Yancopoulos S Nishikawa, J Clin Invest 2002 110 1619 1628 12464667
31. Angiopoietin-1 inhibits vascular permeability, angiogenesis, and growth of hepatic colon cancer tumors. O Stoeltzing SA Ahmad W Liu MF McCarty JS Wey AA Parikh F Fan N Reinmuth M Kawaguchi CD Bucana LM Ellis, Cancer Res 2003 63 3370 3377 12810673
32. A VEGF165-induced phenotypic switch from increased vessel density to increased vessel diameter and increased endothelial NOS activity. P Parsons-Wingerter UM Chandrasekharan TL McKay K Radhakrishnan PE DiCorleto B Albarran AG Farr, Microvasc Res 2006 72 91 100 10.1016/j.mvr.2006.05.008 16872639
33. Abnormal vascular network complexity: a new phenotypic marker in hereditary non-polyposis colorectal cancer syndrome.[see comment]. C De Felice G Latini G Bianciardi S Parrini GM Fadda M Marini RN Laurini RJ Kopotic, Gut 2003 52 1764 1767 14633958 10.1136/gut.52.12.1764
34. Fractal dimension as a prognostic factor for laryngeal carcinoma. A Delides I Panayiotides A Alegakis A Kyroudi C Banis A Pavlaki E Helidonis C Kittas, Anticancer Res 2005 25 2141 2144 16158956
35. Fractal dimension in endometrial carcinoma. P Dey L Rajesh, Anal Quant Cytol Histol 2004 26 113 116 15131900
36. Fractal tumor growth of ovarian cancer: sonographic evaluation.[see comment]. A Kikuchi S Kozuma K Sakamaki M Saito G Marumo T Yasugi Y Taketani, Gynecol Oncol 2002 87 295 302 10.1006/gyno.2002.6842 12468328