Like a complex highway system, a network of vessels carries blood from the heart to all corners of your body and back again. This “distribution network” is not only complicated, it is also huge and astoundingly efficient. Even when one part of the body is injured, flow to and from the rest of the body is rarely interrupted.
Many living organisms exhibit networks like this, from animals to plants. Understanding why these networks are so efficient could help us design better, more reliable systems for distributing electrical power, telecommunications nodes, and even commercial products.
One common approach to exploring the efficiency of a network is to optimize the network with a mathematical model. However, this doesn’t work very well for complicated systems like ours—involving of thousands of veins and branches that work optimally both as a whole and when you zoom in on a particular area. You can’t start with a set of simple rules and come up with patterns that have these properties.
|Left: A leaf chemically processed and colored to better show the distribution network.|
Right: A sample of results obtained using a new method to simulate the structure.
Image Credit: Henrik Ronellenfitsch/PRL.
This question captured the attention of Henrik Ronellenfitsch, who started tackling it seriously after defending his Ph.D. in biophysics and before starting a postdoctoral position at the University of Pennsylvania. In an upcoming paper in the American Physical Society’s Physical Review Letters, Ronellenfitsch and Eleni Katifori from the University of Pennsylvania outline a simple physical mechanism that could explain how complicated, optimized networks develop.
It started with a hunch. After reading through the scientific literature on plant and animal networks, Ronellenfitsch realized that no one had really explored how the overall growth of an organism might affect its distribution network—the network develops, or “grows up,” right along with the embryo (or leaf bud, as the case may be). Could this be the key?
To explore this hunch, Ronellenfitsch and Katifori derived mathematical equations that describe the behavior of developing networks in growing tissue. Their model is valid for the early stages of growth, when cells divide rapidly. It shows the relationship between growth and the flow of blood (or nutrients) through a distribution network. They ran simulations based on these equations. It turns out that the equations incorporating growth led to dramatically more efficient systems than those that did not.
Their results indicate that the complicated, efficient layout of arteries, veins, and capillaries in our circulatory system (and the corresponding systems in leaves) is not prescribed. Instead, it seems to be the natural result of each vessel adapting to the flow of blood (or nutrients) passing through it during the early stages of development. In other words, as the tissue grows and an area needs more blood (or nutrients), the vessel and structure evolve to more efficiently serve that area.
Instead of solving a complex problem in detail and using a lot of space to store the solution, in this case nature gets around the problem with a simple, clever technique. “Sometimes, biology can exploit the laws of physics to make life easy!” said Ronellenfitsch. As we tackle large-scale problems like energy distribution, hopefully this work will inform and inspire our search for simple, responsive solutions to complicated problems.