Related Experiment Video
Updated: Jul 15, 2026

Quantification of Breast Cancer Cell Invasiveness Using a Three-dimensional (3D) Model
Published on: June 11, 2014
Mathematical modeling of the malignancy of cancer using graph evolution
1Department of Computer Engineering, Bilkent University, Ankara TR-06800, Turkey. gunduz@cs.bilkent.edu.tr
Abstract:
We report a novel computational method based on graph evolution process to model the malignancy of brain cancer called glioma. In this work, we analyze the phases that a graph passes through during its evolution and demonstrate strong relation between the malignancy of cancer and the phase of its graph. From the photomicrographs of tissues, which are diagnosed as normal, low-grade cancerous and high-grade cancerous, we construct cell-graphs based on the locations of cells; we probabilistically generate an edge between every pair of cells depending on the Euclidean distance between them. For a cell-graph, we extract connectivity information including the properties of its connected components in order to analyze the phase of the cell-graph. Working with brain tissue samples surgically removed from 12 patients, we demonstrate that cell-graphs generated for different tissue types evolve differently and that they exhibit different phase properties, which distinguish a tissue type from another.
Related Concept Videos
Cancer Survival Analysis
Tumor Progression
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
Tumor Progression
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
Exponential Equations for Modeling Growth
Modeling with Differential Equations
Survival Curves
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...