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Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
O I Craciunescu1, S K Das, J M Poulson
1Department of Radiation Oncology, Duke University Medical Center, Durham, NC 27710, USA. oana@radonc.duke.edu
IEEE Transactions on Bio-Medical Engineering
|April 27, 2001
Summary
This study reconstructs 3D tumor perfusion using fractal interpolation, better preserving its fractal structure than classical methods. The piecewise hidden variable fractal interpolation model (PHVFIM) accurately captures percolation-like scaling in tumor perfusion.
Area of Science:
- Biomedical Engineering
- Medical Imaging
- Computational Biology
Background:
- Tumor blood perfusion is crucial for cancer growth and hyperthermia treatment efficacy.
- Previous studies identified fractal structures in 2D tumor vasculature and used invasion percolation to model perfusion fronts.
- Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) provides relative perfusion index for blood pool approximation.
Purpose of the Study:
- To reconstruct three-dimensional (3D) tumor perfusion from 2D slices using fractal interpolation functions (FIFs).
- To compare the efficacy of FIFs (PSAFIM, PHVFIM) against classical interpolation techniques (linear, spline, polynomial) in preserving fractal properties.
- To assess the fractal dimension and percolation-like scaling of reconstructed 3D tumor perfusion.
Main Methods:
- Reconstruction of 3D tumor perfusion from 2D DE-MRI slices using piecewise self-affine fractal interpolation model (PSAFIM) and piecewise hidden variable fractal interpolation model (PHVFIM).
- Comparison of FIFs with classical interpolation methods by calculating the 2D fractal dimension of reconstructed slices.
- Evaluation of 3D fractal dimension of reconstructed perfusion structures and comparison with literature values for 3D percolation.
Main Results:
- Fractal interpolation functions (FIFs) superiorly conserve the fractal-like structure of tumor perfusion data compared to classical interpolation.
- The piecewise hidden variable fractal interpolation model (PHVFIM) better preserves 3D fractality due to cross-correlation between 2D slices and the reconstructed direction.
- 3D structures reconstructed with PHVFIM exhibit a fractal dimension closely matching reported values for 3D percolation (within 3%-5%), indicating percolation-like scaling.
Conclusions:
- Reconstructed 3D tumor perfusion demonstrates percolation-like scaling, validating the use of FIFs, particularly PHVFIM.
- Fractal interpolation offers a more accurate representation of the perfusion term in the bio-heat equation.
- Improved reconstruction accuracy is expected to enhance the computation of temperature fields during hyperthermia treatments.