A hybrid model of tumor spheroid growth
Yangjin Kim (Mathematical Biosciences Institute (MBI), The Ohio State University)
(November 30, 2006 10:30 AM - 11:30 AM)
Multicellular tumor spheroids (MCTS) have been used as a model system because of their remarkable ability of reproducing the properties of tumors in vivo. MCTS are made of three layers with different mechanical properties, i.e. proliferating outer layer, quiescent middle zone, and necrotic zone. Helmlinger et al (1997) were able to measure the residual stress generated by tumor growth in agarose gel. These results showed that tumor growth can be regulated by stress and that mechanical properties of extracellular matrix (ECM), such as stiffness, can inhibit the tumor growth in vitro. These authors also found that MCTS grew in ellipsoidal shape rather than spherical shape when grown in a long cylinder, which indicates that stress was a controling factor in MCTS growth. The residual stress caused by uncontrolled cell proliferation is believed as possible cause of localized blood vessel collapse in the tumor, thereby causing malfunction of vital organs.
For the proliferating zone, I consider force balance equation to get the evolution of cell movement where each cell is considered as a growing viscoelastic ellipse with two major axes. The discretely modeled cells can divide, push each other, and find the right path to move. These cells keep dividing as long as they get the necessary nutrients. As cells proliferate, cells in the center do not have enough nutrient and start to die, a process called necrosis. Cells in outer part of spheroid continue to proliferate, which produces residual stresses. Increased stresses surrounding the spheroid then inhibit MCTS growth and increase the cell density in the proliferating zone. By considering that the gel, quiescent zone, and necrotic region are viscoelastic materials, I use continuum model in these regions and couple the continuum model to the discrete cell model. Reaction-diffusion equations for nutrients are considered to describe the evolution of concentration of nutrients.
I discuss the stress effect on tumor growth and growth behavior of active tumor cells. I will also discuss a possible mechanism for reduction of cell volume. My future work includes the incorporation of a shedding effect, which is when tumor cells detach from the primary tumor and shed into the suspension medium. I will discuss how I plan to incorporate this effect, which is an important issue in cancer such as certain brain cancers. Another aspect of my future work is the inclusion of internal cell dynamics. I will discuss this as well.