Mathematical Model of Tumor Growth

Malignant tumors are the second leading cause of death in the world and have become one of the most funded fields of research in modern society. As cancer research has developed over time, the discovery of factors such as health habits, environmental conditions, and genetics that play a role in the growth and spread of malignant tumors has become well-known. However, it has become evident that predicting the growth of malignant tumors poses a challenge due to the diversity of conditions that arise between patients. Since the early 20th century, mathematical models have been derived to describe cancer growth and decay. Many equations are built upon preliminary constants that describe conditions for all patients, however, all models to date fall short of a comprehensive model. 

As the tumor grows larger in volume, the center of the mass is starved of oxygen and vital nutrients that continue its growth, and thus, becomes necrotic. Using this biological principle, we were successful in explicitly solving a first-order nonlinear differential equation in terms of volume as a function of time. 

We hope the model will be a preliminary step that all individual patient cases can utilize in the development of a comprehensive mathematical model to describe cancer cell growth and decay.