Modeling cancer metastasis
Cancer is one of the most problematic and fear-inducing diseases in our world today. The main thing that makes cancer so deadly is its ability to metastasize, or spread from its original location in the body to other places. Cancer that metastasizes greatly decreases the patient’s chance of survival. Cancer is spread through three main ways, local spread, spread through the blood circulation and spread through the lymphatic system. The spreading of a cancer can be modeled by graphs.
Cancer that spreads locally is modeled by a different graph than one that spreads through the lymph system or blood. This is because the cancer can only reach nearby body parts. It does this by either growing and pushing into surrounding tissue or using enzymes that break down normal cells and tissue so it can grow. However, modeling the local spread of cancer through either of these methods is this same, since the cancer spread range is the same. When modeling this, the tissue or body part that the cancer originated from is a node in the center of the graph. All around it are nodes of nearby tissue/body parts. The edges are directed pointing from the node in the center out to each of the nodes of nearby body parts. The edges have to be directed because the cancer cannot spread from the surrounding body parts to the origin of the cancer. The graph may also have additional nodes connected to the surrounding nodes. These represent body parts/tissue that are further away from the cancer origin but in proximity to the tissue nearby the origin of the cancer. Since this graph only represents local spread, the length of any path shouldn’t be very long.
Cancer that spreads through the cardiovascular or lymph system can be modeled similarly to each other. Since both systems circulate through the body, the graph that models these systems are in the form of nodes connected by edges in a circle. These edges are directed because the presence of valves in both these systems prevents the flow from going in the other direction. When cancer spreads through the cardiovascular system, a part of the original cancer breaks off, moves through the wall of a blood vessel and gets swept along in the bloodstream. The cancer usually gets stuck in the nearest capillary because of the small diameter of these vessels. It then once again moves across the capillary wall and into the tissue of a nearby organ. Usually, the blood from most organs goes to the capillaries in the lungs, so that is the most common place for cancer to spread. Blood from of the digestive system however, flows to the capillaries of the liver before going to the lungs, so many digestive system cancers spread to the liver. When modeling this, the capillary networks near different organs would be placed in the nodes following the direction of blood flow. These nodes would be connected by edges that represent blood vessels. Similarly, when cancer spreads through the lymph system, cancer cells often get stuck in the lymph nodes closest to the tumor. These lymph nodes would be the nodes on the graph connected by directed edges that represent lymph vessels.
Ongoing research by Dr. Eric Sahai from London Research Institute reveals a genetic switch that determines whether or not the cancer spreads to other places in the body. This switch turns on the TGF beta signaling pathway. When this signaling pathway is blocked, the cells tend to move collectively rather than breaking off into the lymph or cardiovascular system. This greatly reduces the spread of cancer. Going back to our models, when this signaling pathway is blocked, the spread of cancer is only modeled by the first graph described. From comparing the descriptions of first graph and the second graph, we can see that the potential spread is much smaller in the first case because the cancer can only spread in one direction, and does not circulate through the whole body. The distance between nodes in the first graph (refers to distance between nearby tissue) is also much smaller compared to the distance in the second graph (refers to distance between organs near capillary networks). Learning how to manipulate this switch therefore will be a big breakthrough in decreasing the potential spread of cancers and ultimately reducing their severity.
http://www.cancerresearchuk.org/cancer-info/cancerandresearch/all-about-cancer/what-is-cancer/grow-and-spread/cancer-spread/spreading-around-the-body