13 March 2009 A PDE approach for quantifying and visualizing tumor progression and regression
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Abstract
Quantification of changes in tumor shape and size allows physicians the ability to determine the effectiveness of various treatment options, adapt treatment, predict outcome, and map potential problem sites. Conventional methods are often based on metrics such as volume, diameter, or maximum cross sectional area. This work seeks to improve the visualization and analysis of tumor changes by simultaneously analyzing changes in the entire tumor volume. This method utilizes an elliptic partial differential equation (PDE) to provide a roadmap of boundary displacement that does not suffer from the discontinuities associated with other measures such as Euclidean distance. Streamline pathways defined by Laplace's equation (a commonly used PDE) are used to track tumor progression and regression at the tumor boundary. Laplace's equation is particularly useful because it provides a smooth, continuous solution that can be evaluated with sub-pixel precision on variable grid sizes. Several metrics are demonstrated including maximum, average, and total regression and progression. This method provides many advantages over conventional means of quantifying change in tumor shape because it is observer independent, stable for highly unusual geometries, and provides an analysis of the entire three-dimensional tumor volume.
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Benjamin J. Sintay, Benjamin J. Sintay, J. Daniel Bourland, J. Daniel Bourland, } "A PDE approach for quantifying and visualizing tumor progression and regression", Proc. SPIE 7261, Medical Imaging 2009: Visualization, Image-Guided Procedures, and Modeling, 72612F (13 March 2009); doi: 10.1117/12.813751; https://doi.org/10.1117/12.813751
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