Three-dimensional tumor perfusion reconstruction using fractal interpolation functions

It has been shown that the perfusion of blood in tumor tissue can be approx imated 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-di mensional (2-D) tumor vessel network has a fractal structure and that the e volution of the perfusion front can be characterized using invasion percola tion. In this paper, the three-dimensional (3-D) tumor perfusion is reconst ructed from the 2-D slices using the method of fractal interpolation functi ons (FIF), i.e., the piecewise self-affine fractal interpolation model (PSA FIM) and the piecewise hidden variable fractal interpolation model (PHVFIM) . The fractal models are compared to classical interpolation techniques (li near, 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 da ta. Among the two FIF methods, PHVFIM conserves the 3-D fractality better d ue 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 resultin g 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 reconstruct ed 3-D perfusion has a percolation-like scaling, As the perfusion term from bio-heat equation is possibly better described by reconstruction via fract al interpolation, a more suitable computation of the temperature field indu ced during hyperthermia treatments is expected.