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BIOMECHANICAL MODELING OF TUMOR GROWTH : ITS RELEVANCE TO GLIOMA RESEARCH

In 2009 the US National Center for Health Statistics showed that cancer is close to becoming the deadliest disease of modern times. Recent years have seen unprecedented advancements in medicine that have contributed to a substantial decrease in the death rates of some serious diseases such as heart disease, stroke, influenza and pneumonia. However, with cancer, equivalent scientific and technological advances have yet to be achieved. Theoretical models capable of explaining the fundamental mechanisms of tumor growth and making reliable predictions are urgently needed. These models can contribute considerably to the design of optimal, personalized therapies that will not only maximize treatment outcomes but also reduce health care costs. Recently [25] we have proposed a non-invasive way of classifying gliomas, primary brain tumors, based on their stiffness. The model uses image mass spectra of proteins present in gliomas and shows that the Young’s modulus of a high grade glioma is at least 10kPa higher than the Young’s modulus of a low grade glioma. In this paper we will use this model to investigate the effect of mechanics on the growth of gliomas. The proposed mechano-growth model is a non-linear evolution differential equation which is solved analytically using the Adomian method. The time evolution is represented in two ways: (1) using a classical first-order derivative, and (2) using a fractional order derivative. Our results show that the fractional order model captures a very interesting temporal multi-scale effect of tumor transition from low grade (benign) to high grade (malignant) glioma when a certain threshold of mechanical strain is reached in the tissue. For comparison, we also reproduce the results we presented in [25] when linearization is used to solve the evolution equations analytically.