Bifurcation is the division of something into two branches or parts. Anatomically, bifurcation is observed at the fork where the trachea divides into two bronchial tubes to divert air flow into each lung. Bronchial tubes are further bifurcated as they divide into smaller and smaller channels.
Blood vessels are another example of bifurcation in the human body. Arteries divide into smaller and smaller vessels, with flow diverted in different directions. The splitting does not need to be into equal amounts for bifurcation to apply. The aorta, the large vessel that delivers blood from the heart to the body, features several small bifurcations before the split of the abdominal aorta into the left and right iliac arteries, two equal channels that deliver blood to the legs.
Bifurcation can also occur in flow fields without a physical divider. High-velocity blood flow within the heart can cause portions of the flow to separate, resulting in vortexes and eddies. In addition, flow bifurcations can occur due to the curvature of a vessel or other discontinuities in the flow. The complexity of blood flow is an important area of medical research.
Bifurcation as mathematical phenomena is also present in dynamical systems analysis. A dynamical system may be described as any model whose state changes over time. This describes essentially all biological processes. Bifurcation occurs in dynamical systems when a small smooth change made to a parameter value of a system can cause a sudden change in system behavior.
To better understand this concept, consider the simple example of a swinging pendulum. At low velocities, the pendulum oscillates back and forth. Slowly increasing the velocity causes the pendulum to swing higher, but the behavior is qualitatively similar to previous behavior. However, as the height approaches the vertical upright position, the system is on the verge of a transition. Increasing the velocity slightly will result in a bifurcation and the behavior will switch from oscillating to orbiting. The new behavior of the trajectory will be around and around in the same direction. This is qualitatively different behavior than the oscillatory behavior observed prior to the bifurcation. Bifurcation principles have been used to characterize the nonlinear dynamics of cardiac arrhythmias, the firing of neurons, the switching on and off of gene expression, and the mutations associated with cancer.
