Editor,—The recent article by Muntinga and colleagues1 confirms, using non-invasive techniques, the findings obtained more directly by Brookes and colleagues2that beat to beat left ventricular performance in spontaneous atrial fibrillation depends on beat to beat variation in cycle length, left ventricular end diastolic volume (EDV), and contractility. Their contention that afterload is another independent determinant rests on their fig 5 in which ejection fraction is plotted against end systolic pressure/stroke volume (ESP/SV). However, ejection fraction is SV/EDV, so they have SV on both axes, which is invalid. A plot of a variable, in this case SV, against its reciprocal 1/SV will lead inevitably to an inverse hyperbolic relation as a mathematical necessity. In this case it is accompanied by a small amount of scatter caused by the other variables, but the main relation shown is a mathematical artefact and not an actual dependence of ejection fraction on afterload.

Figure 3 is also incorrect because SV/EDV is plotted against EDV (EDV appearing on both axes), but in this case a plot of SV against EDV would have resulted in a positive relation and the same conclusion.

In the study by Brookes and colleagues,2 the left ventricular systolic pressure (directly measured with catheter tip manometer) varied rather little during atrial fibrillation, which the authors attributed to clamping of the arterial systolic pressure by peripheral mechanisms. This finding and …