# Preliminary Results Of Geometrization Of Tumor Modeling For Mri

## Location

SU 219

## Department

Mathematics

## Abstract

Mathematical methods were developed for shape analysis of Magnetic Resonance Imaging (MRI) tumor images. MRI images of brain tumors in mice were analyzed. The objective was to identify and track the irregular boundary of the tumor in two dimensions and to make predictions about tumor growth. This approach has several significant advantages over common methods of tumor image analysis. Current methods rely on the subjective interpretation of a radiologist, and often average values within the region of interest (ROI). This approach, on the other hand, allows for partitioning of the ROI into homogeneous segments comprising a heterogenous whole and provides an objective method for making predictions. MATLAB © code was written to obtain an ordered list of points on the tumor boundary for each transverse slice. The slice that contained the largest ROI was selected for each scan, and the ROI for that slice was divided into four quadrants. The growth of each quadrant was recorded at three time points and used to predict the location of the ROI boundary in each quadrant at a fourth time point, assuming a linear growth model. A method for modeling such a segmented circular region was developed and used to model the tumor growth based on ROI measurements and the observed tumor growth rate. Convex arcs that represented the new boundary of each region at discrete points in time were connected using third-degree polynomials to create a smooth and continuous curve that enclosed the entire ROI at each point in time. Results obtained thus far show a positive linear correlation between the predicted tumor radius and the actual tumor radius in each quadrant (R- square=0.6574). A linear growth model is a rough approximation and the correlation between actual radius and predicted radius should improve with use of a growth model that more accurately reflects the underlying biological process. Future modifications to the methods developed thus far will include replacing the observed tumor growth rate with a growth rate derived from cell line data or MRI parameters, revising the code to increase the number of sectors into which the ROI is divided, and replacing the circular tumor boundary with a boundary drawn by a shape-fitting algorithm which takes as its input the ordered list of boundary points.

Preliminary Results Of Geometrization Of Tumor Modeling For Mri

SU 219

Mathematical methods were developed for shape analysis of Magnetic Resonance Imaging (MRI) tumor images. MRI images of brain tumors in mice were analyzed. The objective was to identify and track the irregular boundary of the tumor in two dimensions and to make predictions about tumor growth. This approach has several significant advantages over common methods of tumor image analysis. Current methods rely on the subjective interpretation of a radiologist, and often average values within the region of interest (ROI). This approach, on the other hand, allows for partitioning of the ROI into homogeneous segments comprising a heterogenous whole and provides an objective method for making predictions. MATLAB © code was written to obtain an ordered list of points on the tumor boundary for each transverse slice. The slice that contained the largest ROI was selected for each scan, and the ROI for that slice was divided into four quadrants. The growth of each quadrant was recorded at three time points and used to predict the location of the ROI boundary in each quadrant at a fourth time point, assuming a linear growth model. A method for modeling such a segmented circular region was developed and used to model the tumor growth based on ROI measurements and the observed tumor growth rate. Convex arcs that represented the new boundary of each region at discrete points in time were connected using third-degree polynomials to create a smooth and continuous curve that enclosed the entire ROI at each point in time. Results obtained thus far show a positive linear correlation between the predicted tumor radius and the actual tumor radius in each quadrant (R- square=0.6574). A linear growth model is a rough approximation and the correlation between actual radius and predicted radius should improve with use of a growth model that more accurately reflects the underlying biological process. Future modifications to the methods developed thus far will include replacing the observed tumor growth rate with a growth rate derived from cell line data or MRI parameters, revising the code to increase the number of sectors into which the ROI is divided, and replacing the circular tumor boundary with a boundary drawn by a shape-fitting algorithm which takes as its input the ordered list of boundary points.

## Comments

Nabil Kahouadji and Daniele Procissi are the faculty sponsors of this project.