Synthetic Birth: Emergent Behaviors in an Agent-Based Model of the Human Uterus

Mel L. Barclay
University of Michigan School of Medicine

The process of birth in humans is powered by the action of the uterus. The forces it generates propel the infant as it passes from the intrauterine to the external environment. The uterus has patterns of behavior which are dependent on the basic physiology of muscular contraction. Muscle fibers are stimulated, respond to stimulation with mechanical activity, enter a refractory or unresponsive period, and then contract again. >From a modeling point of view, the uterus is structurally and functionally simple. There is a single pumping chamber and the uterine contents are propelled along a single outflow path.

The uterus in labor has many properties which suggest it may be capable of generating complex dynamical patterns of activity. It has elasticity, elements of slip and stick, play and backlash, and possibly nonlinear electrical conduction with feedback.

We have designed a cellular automaton to model uterine function. A Turing-type matrix of cells is applied to a single-layered surface, which has the shape of human uteri, derived from historical anatomic descriptions as well as mathematically generated ellipsoids and paraboloids of revolution. Individual cells are capable of stimulation, impulse transmission, contraction, a resting or refractory period, and then reactivation. Rules for impulse transmission to neighboring cells are specific as are the activation, contraction, and refractory periods.  

Cells contract isovolumetrically generating one unit of pressure measured summatively at the center of the uterus according to Pascal's Law. This produces pressure waveforms similar to those observed in the uteri of laboring human females. Complicated emergent behaviors and patterns of depolarization including vortices have been observed which may provide additional insights into those factors that promote the initiation of premature and spontaneous labor.

Fig. 1 A phase-space diagram depicting the relationship between two cell states.  Two quite different areas are obvious. The upper region characterizes non-synchronous random or chaotic contractile activity that is not productive of organized uterine activity.  The lower region characterizes variable yet regular contractile activity, an emergent phenomenon.  A single pathway apparently connects the two domains.

Created by Mathematica  (April 20, 2004)