Current Research

Cancer Modeling and Tumor Growth

Cancer is an uncontrolled growth of cells that can occur in any tissue of the body. Tumors cannot grow beyond a certain size through simple diffusion of oxygen and other essential nutrients into the tumor. One important step in malignant tumor growth is angiogenesis, which is the process by which tumors develop their own blood supply. Research, in collaboration with clinician/scientists at Princess Margaret Hospital in Toronto and McMaster University, as well as with Scientists in the Departments of Biomedical Engineering and Physics at MIT, includes the following topics:

• Application of mathematical models to tumor growth and the process of angiogenesis, particularly to study the effects of both cytotoxic and anti-angiogenic therapies.

• Computational approaches for studying the effects of anti-cancer drugs using nanoscale delivery systems.

• Combining mathematical models and imaging techniques to study the effects of different treatment strategies for brain tumors.

• Application of mathematical modelling to unravel the details of the tumor stem cell hierarchy, as well as the interactions of these cells with various therapies

Biomechanics of Soft Biological Tissues

Mechanical properties of living soft tissues such as brain, liver, kidney, etc., are a central subject of biomechanics. Recent developments in technology and experiments as well as modern applications of technology to medicine have contributed much to our understanding of the biomechanics of these soft tissues. Study of mathematical models of soft tissues may find different applications. One example is hydrocephalus that is a serious structural brain condition, where the ventricles (spaces inside the brain) become enlarged. Other applications may be robotic surgery, where prediction of deformation is needed, surgical operation planning and surgeon training systems, where free feedback is needed. A further application of brain biomechanics is to traumatic brain injury (TBI), which constitutes a significant portion of all injuries occurring for example in automotive and sports related injuries. In order to gain inside into mechanisms of TBI, mathematical models are often used to estimate deformations during traumatic loading. We have worked on the biomechanics of the brain to obtain the constitutive equation and its mechanical parameters. We have also used the fractional viscoelastic models in order to describe the dynamic behavior of brain tissues.

Previous Research