Abstract
This paper presents a method to reconstruct and to calculate geometric invariants on brain tumors. The geometric invariants considered in the paper are the volume, the area, the discrete Gauss curvature, and the discrete mean curvature. The volume of a tumor is an important aspect that helps doctors to make a medical diagnosis. And as doctors seek a stable calculation, we propose to prove the stability of some invariants. Finally, we study the evolution of brain tumor as a function of time in two or three years depending on patients with MR images every three or six months.
Highlights
Cancer is a disease that starts in our cells
Benign tumor cells stay in one place in the body and are not usually life-threatening
Series of 3 typical biopsy-proved low-grade gliomas followed with serial MRI every 6 months were first selected for the purpose of the study
Summary
Cancer is a disease that starts in our cells. Our bodies are made up of millions of cells grouped together to form tissues and organs such as muscles and bones, the lungs, and the liver. Our cells obey these orders, and we remain healthy. Sometimes the instructions get mixed up, causing the cells to form lumps or tumors, or spread through the bloodstream and lymphatic system to other parts of the body. Tumors can be either benign (noncancerous) or malignant (cancerous). Benign tumor cells stay in one place in the body and are not usually life-threatening. Malignant tumor cells are able to invade nearby tissues and spread to other parts of the body. Cancer cells that spread to other parts of the body are called metastases
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