Initially solid tumors are avascular, i.e., they do not have their own blood supply, and rely on diffusion from the surrounding vasculature to supply oxygen and nutrients. When the tumor becomes too large diffusion is too slow, growth in the core stops, and can resume only if the tumor becomes vascularized i.e. if it becomes permeated with a network of capillaries. Avascular tumors release growth factors into their environment to induce nearby blood vessels to grow new capillaries to vascularize the tumor through a process called angiogenesis. This results in the creation of a new capillary network that extends from a primary vessel into the growth-factor-secreting tumor, thereby bringing essential nutrients to the tumor and providing a shorter route for the spread of cancer cells to other parts of the body.
Metastasis is the process by which tumor cells detach from a primary tumor and migrate to nearby blood vessels or the lymph system, and are thereby able to spread to other organs in the host. Cancer cells invade the surrounding tissue either as individuals or as small groups of cells, and may secrete enzymes that degrade the ECM to facilitate passage of cells.
This workshop will address the mathematical and computational issues that arise from models of angiogenesis and metastasis. Such models are frequently hybrid models, that describe cells (either those building the vessel or those involved in metastasis) at a detailed level that treats their biochemical and mechanical responses to their environment, and couple this cell-based description with partial differential equations that describe the mechanics of the surrounding tissue and the reaction and transport of growth factors and chemotactic signals. Major topics to be treated are how to model the movement of single cells through the extracellular matrix, how to describe in sufficient detail the process by which new vessels grow toward a tumor, how to cope with the computational problems raised by such hybrid models, and what the implications are for our understanding of the underlying basic science and how that understanding can be translated into improved therapeutic regimens.