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Background. Despite the routine prescription of rate control therapy foratrial fibrillation (AF), clinical evidence demonstrating a heart rate targetis lacking. Aim of the present study was to run a mathematical model simulatingAF episodes with a different heart rate (HR) to predict hemodynamic parametersfor each situation.  Methods. The lumped model, representing the pumping heart together withsystemic and pulmonary circuits, was run to simulate AF with HR of 50, 70, 90,110 and 130 bpm, respectively.  Results. Left ventricular pressure increased by 56.7%, from 33.92+-37.56 mmHgto 53.15+-47.56 mmHg, and mean systemic arterial pressure increased by 27.4%,from 82.66+-14.04 mmHg to 105.29+-7.63 mmHg, at the 50 and 130 bpm simulations,respectively. Stroke volume (from 77.45+-8.5 to 39.09+-8.08 mL), ejectionfraction (from 61.1+-4.4 to 39.32+-5.42%) and stroke work (SW, from 0.88+-0.04to 0.58+-0.09 J) decreased by 49.5, 35.6 and 34.2%, at the 50 and 130 bpmsimulations, respectively. In addition, oxygen consumption indexes (ratepressure product, RPP, tension time index per minute, TTI/min, and pressurevolume area per minute, PVA/min) increased from the 50 to the 130 bpmsimulation, respectively, by 185.7% (from 5598+-1939 to 15995+-3219 mmHg/min),55.5% (from 2094+-265 to 3257+-301 mmHg s/min) and 102.4% (from 57.99+-17.9 to117.37+-25.96 J/min). In fact, left ventricular efficiency (SW/PVA) decreasedfrom 80.91+-2.91% at 50 bpm to 66.43+-3.72% at the 130 bpm HR simulation.  Conclusion. Awaiting compulsory direct clinical evidences, the presentmathematical model suggests that lower HRs during permanent AF relates toimproved hemodynamic parameters, cardiac efficiency, and lower oxygenconsumption.

Rate Control Management of Atrial Fibrillation: May a Mathematical Model Suggest an Ideal Heart Rate?