A mathematical model of left ventricular function in atrial fibrillation

Sixty patients with atrial fibrillation (AF) have been studied with Doppler ultrasound to establish the relationship between the duration of R-R intervals and subsequent left ventricular stroke outputs, assessed as stroke distance. Using multiple regression analysis, most of the beat-to-beat variation of stroke distance could be explained in terms of the two preceding R-R intervals (Mean R = 0.82). The relative contribution of these two intervals to the variation of stroke distance was assessed in each patient. In all patients there was a positive correlation between stroke distance and the preceding R-R interval, largely due to the influence of this interval on diastolic filling or preload. In all but one patient the correlation with the second previous R-R interval was negative, the mechanism being changing contractility due to operation of the force-frequency effect. On average, 58% of the variance in stroke distance could be explained by alteration of the previous R-R interval and 10% by alteration of the second previous R-R interval. The relative contribution of the previous R-R interval (preload) falls as left ventricular function declines, and also as mean ventricular rate rises. However, there is a wide individual variation in the pattern of left ventricular function, which may be represented graphically as the haemodynamic profile.