Modeling Cancer Growth

Author : Anupama Paul  

Cancer is a highly dangerous disease which diffuses death in the whole world. The death rate increases day by day and experts predict that death rate continually rising and in 2015 approximately 9 million people will be dying due to cancer.

Cancer causes dreadful and painful situation for the patient. It can affect any part of the body. It’s very difficult to find out. Malignant tumours and neoplasm are used as the synonyms of cancer. The characteristic of cancer is the unregulated cell growth. Cells divide and grow uncontrollably, forming malignant tumours and then it is spread to more distant part of body through the lymphatic system or blood stream.

Determine the reason for the cancer is very tough. Many things are there which increases the risk of cancer like tobacco use, certain infections, and radiations, lack of physical activity, poor diet, obesity and environmental pollutants. These can damage genes and it causes the disease. Cancer is very difficult to find out in the starting stages. It can be detected in a number of ways, including the presence of certain signs and symptoms, screening tests or medical imaging. Chemotherapy, radiation therapy and surgery are the commonly using treatment methods.

Mathematical models of tumour growth give more effective knowledge about cancer. There are several modelling methods which help for effective treatment plans. A good or effective mathematical model should be satisfied some criteria’s:

• The number of parameters used in the model should be minimum
• The model should be matched with the reality.
• The model predictions should be accurate and matched with experimental result.

Different types cancers are there so several different mathematical models are used for effective treatment. Mathematical models can be divided into 3 groups they are:

• Functional Models :- based on cell kinetics
• Structural models   :- developed specifically for spheroid growth
• Empirical Models: - based on the fundamental empirical growth      results from the increasing and decreasing      size of the tumour.

Two sets of empirical models are developed for finding the growth of tumour. First set contains the Generalized two-parameter model, Gompertz model, and Logistic and Bertalanffy equations. Another set contains Generic model, Hyper-Gompertz, Hyper-Logistic and Bertalanffy-Richards models.

References

1. MILJENKO MARUSIC, Mathematical models of tumor growth, 1996, 175-191.
2. MICHAEL OLINICK, Tumor Growth Models, 2009, 1-48.
3. KATIE HOGAN, Modeling Tumor Growth, 2006.
4. ESMAEIL MEHRARA, Quantitative Analysis of Tumor Growth and Response Therapy,  Department of Radiation Physics, University of Gothenburg, Sweden , Goteborg, 2010.