A geometric model of anorexia and its treatment

Anorexia is a severe psychological disorder in which a person's dieting turns into compulsive fasting. Some victims develop, after a time, a bulimic phase; their fasting is interrupted at intervals by bouts of indiscriminate gorging. One successful treatment makes use of a naturally occurring trance state, in which the anorexic's obsession with food recedes temporarily, to offer reassurance and rebuild a personality free of the obsession. The proposed model is catastrophe-theoretic. It assumes (a) that the bifurcation of eating attitudes typical of anorexia can be modeled by a cusp whose controls are hunger and eating regimen; and (b) that the normal cycle of falling asleep and waking up can be modeled by a hysteresis loop controlled by alertness. Catastrophe theory predicts two additional controls, and a larger model organized by the E6 singularity. The new controls are identified with loss of self-control and insecurity, and anorexia is correlated with high insecurity. The model makes the following predictions. First, under moderate levels of self-control and eating regimen, an anorexic has access to balanced, nonobsessive attitudes toward food at a reduced level of wakefulness. This is the trance state. Second, a healthy individual has two distinct sleep modes, dominated by cerebral and somatic elements, respectively. Third, with increasing insecurity the distinct modes fuse together, so that an anorexic's sleep patterns are abnormal. The model is geometric because the connection between behavior and controlling factors is made by graphs of certain standard form.