Fractal Characteristics of Tumor Vascular Architecture During Tumor Growth and Regression YUVAL CUIT,* JAMES W. BAISH,* NINA SAFABAKHSH? MICHAEL LEUNIG,' LAURENCE T. BAXTER? AND RAKESH K. JAIN: zyx "Harvard-MIT Division of Health Sciences' and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts. USA 'Edwin L. Steele Laboratory. Department of Radiation Oncology. Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, USA *Department of Mechanical En,@neering, Bucknell University, Lewisburg, Pennsylvania, USA Objective: Tumor vascular networks are different from normal vascular net- works, but the mechanisms underlying these differences are not known. Under- standing these mechanisms may be the key to improving the efficacy of treat- ment of solid himors. Methods: We studied the fractal characteristics of two-dimensional normal and tumor vascular networks grown in a murine dorsal chamber preparation and imaged with an intravital microscopy station. Results: During tumor growth and regression, the vasculature in the tumor has scaling characteristics that reflect the chan,$ng state of the tissue. Growing tumors show vascular networks that progressively deviate from their normal pattern. in which they seem to follow diffusion-limited aggregation to a patho- logical condition in which they display scaling similar to percolation clusters near the percolation threshold. The percolation-like scaling indicates that the key determinants of tumor vascular architecture are local substrate properties rather than gradients of a diffusing substance, such as an angiogenic growth factor. During tumor regression, the fractal characteristics of the vasculature return to an intermediate between those of growing tumors and those of healthy tissues. Previous studies have shown that percolation-like scaling generally inhibits transport. Conclusions: In the present context, the percolation-like nature of tumor vas- culature implies that tumor vascular networks possess inherent architechiral obstacles to the delivery of diffusible substances such as oxygen and clrugs. KE) zyxwvutsrq \\ ORDS: tumor vasculntiue, fractals, angiogenesis, network analysis, perco- lation. INTRODUCTION zyxwv R.J. zyxwvutsrqpon received an Outstancling Investigator Grant zyxwvuts (No. R35CA- zyxwvu 56591) and J.B. receivetl Grants front NSF Po. CTS-90.57+22) and IVIH (Nv. R23-CA-T+366). Y.C. is a Hvunrd Hcighes Medi- cal Institute Preiloctoral Fellow (I 992-1 996). M.L. is (I Fevclor zyxwvut Lynen Fellow vf the tktmbolclt Foiintlation (1991-1993). For reprints of this article. contact DI-. Rakesh K. Juiri. Steeie Luborutory. Department of Radiation Oncology. h1a.ssachctsett.s General FIo.spitd, Boston. M-l 02 114. DSA. Sitbrriitted for pirblication: .Vvi~ember 19, 1996: ncwpted for publication: September 17. 199: 107.?-968S 0 199; Cliapiriari & Hiill The vascular architecture of tumors is known to be si,mificantly different fro=] that of normal tissue, Tumor vascular networks display tortuous vessels, loops, shunts, dramatically variable intervascular distances, and large avascular areas (1,16,2 1,22), all of which are generally absent from normal vas- cular nemorks. The for these differences 8re largely 1inkno.ct-n ancl are particularly puzzling be- 395