Faculty Bibliography

A mathematical model using simple concepts of repeated games is proposed to model the course and prognosis of factitious disorders. Although simple, the model seems capable of explaining the yet unknown mechanisms underlying the variable course of factitious disorders. One of the notable results of this study is the significant effect of involved physicians in the treatment process on the course of the disease. Particularly, the doctor's error rate in realizing whether the symptoms are real or factitious can considerably affect the course of the disease. This is the first paper to apply a mathematical model to factitious disorders.

A nonlinear model of the atrioventricular (AV) node physiology in atrial fibrillation (AF) is proposed based on three assumptions: (1) normal distribution of atrial impulses, (2) right-skewed distribution of R-R intervals, (3) increase in the refractory period of the AV node due to rapid bombardment from the atria. Simulation resulted in the following conclusions, all of which are in agreement with previous experience: (1) the entry speed of atrial impulses into the AV node in AF is inversely proportional to the ventricular rate, (2) the autocorrelation function of R-R intervals is zero at all delays, (3) a newly introduced index, sign of first difference, has a negative autocorrelation function at the first delay and zero ones at all others. In spite of its simplicity, the model is able to explain what happens in atrial premature complexes, sinus tachycardia and sinus bradycardia. Different rhythms, some of which rarely seen clinically, can be reproduced by changing input patterns or by slightly manipulating the model parameters. In order to make possible a long irregular time series of R-R interval, aperiodic changes in atrial signals are shown to be necessary. In conclusion, we proposed a simple model for the AV node physiology capable of explaining the previously known facts about AF as well as predicting interesting properties of some other supraventricular arrhythmias.