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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.