Angular homeostasis II: Pursuit of a moving target in a plane and some implications for cardiac teratology

A model of cardiac ontogenesis is analyzed. It is cast in terms of the geometry of the pursuit of a linearly moving target by the growth of a chain of cells in the same plane, the pursuer, which at each step adjusts its direction of growth towards the current position of the target. The endpoint is the fusion between them, which can occur in 2 modes: either by the leading cell of the pursuer catching up with the target (pursuer-mediated fusion, or PMF) or by the target running into the preformed side of the pursuer (target-mediated fusion, or TMF). The causal specifications are the step size, the speed of the pursuer, the speed of the target, the restoration constant, and the initial direction of the pursuer; the outcome variables are the number of steps to fusion and the mode of fusion. The pattern of behavior is complicated, being more-or-less regular over large tracts of values, interspersed with abrupt, threshold-like changes that may generate a dichotomous pattern of inheritance despite a continuous gradation of genetic or other causes. The temporary abolition of the correction process (a change introduced to simulate the pattern of the effect of a teratogen) may delay fusion and suggest how a septum may fail to fuse, the ductus arteriosus to close, or an endocardial cushion to form. But the model also predicts that under certain plausible conditions, the "teratogen" would speed up fusion and hence perhaps offset a genetic predisposition to a congenital defect.