Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.


Journal Article

It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.

Full Text

Duke Authors

Cited Authors

  • Craciunescu, OI; Das, SK; Poulson, JM; Samulski, TV

Published Date

  • April 2001

Published In

Volume / Issue

  • 48 / 4

Start / End Page

  • 462 - 473

PubMed ID

  • 11322534

Pubmed Central ID

  • 11322534

International Standard Serial Number (ISSN)

  • 0018-9294

Digital Object Identifier (DOI)

  • 10.1109/10.915713


  • eng

Conference Location

  • United States