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Using Poisson's Equation to Characterize Brain Tumor Shape

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abstract
The role that tumor shape plays in disease treatment, progression, and outcome is not well understood. This work investigates the quantification of shape information required for the statistical analysis of tumors. The statistical shape characterization method proposed by Haidar et al. 2006 that uses Poisson’s equation is adapted for tumor shape parameterization. An extensive algorithm using finite differences and a robust software toolset have been developed for efficient computation of the solution to Poisson’s equation for three-dimensional tumor volumes as well as general anatomic features. A characteristic plot that is unique to a given shape is generated. The statistical framework of this method utilizes a Monte-Carlo permutation test to establish significance between sets of characteristic plots. The method has been thoroughly tested for two-dimensional (2D) and three-dimensional (3D) test datasets that include simple geometric shapes as well as contoured anatomical volumes from images of the human brain. The shape characteristic curve is able to distinguish subtle differences in simple 2D and 3D phantoms as well as human brain anatomy. Such differences are difficult to quantify and often do not correlate to volume. Scale and translation insensitivity of the method are also proved. It is also shown that voxels can be upsampled, or resliced, to form images suitable for shape characterization for datasets with anisotropic data such as those acquired from magnetic resonance imaging (MRI) scans. The methods and software toolset have been applied in a retrospective, image-based clinical trial to examine the shape characteristic curves of pre-operative glioblastoma multiforme (GBM) tumors. This preliminary clinical trial shows that shape characteristics for these tumors can be predictive of outcome (survival) for a population of approximately 100 subjects up to one year following diagnosis.
subject
Geometry
Tumor shape
Malignant glioma
Biomedical engineering
Radiation oncology
Nuerosurgery
Partial differential equations
Poisson's equation
contributor
Sintay, Benjamin (author)
Plemmons, Robert (committee chair)
Bourland, Daniel J. (committee member)
Hampton, Carnell (committee member)
Munley, Michael (committee member)
Wyatt, Christopher (committee member)
date
2009-04-29T18:34:21Z (accessioned)
2010-06-18T18:59:14Z (accessioned)
2009-04-29T18:34:21Z (available)
2010-06-18T18:59:14Z (available)
2009-04-29T18:34:21Z (issued)
degree
Medical Engineering (discipline)
identifier
http://hdl.handle.net/10339/14840 (uri)
language
en_US (iso)
publisher
Wake Forest University
rights
Release the entire work for access only to the Wake Forest University system for one year from the date below. After one year, release the entire work for access worldwide. (accessRights)
title
Using Poisson's Equation to Characterize Brain Tumor Shape
type
Dissertation

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