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

Background: Despite the routine prescription of rate control therapy for atrial fibrillation (AF), clinical evidence demonstrating a heart rate target is lacking. Aim of the present study was to run a mathematical model simulating AF episodes with a different heart rate (HR) to predict hemodynamic parameters for each situation. Methods: The lumped model, representing the pumping heart together with systemic 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 57%, from 33.92±37.56 mmHg to 53.15±47.56 mmHg, and mean systemic arterial pressure increased by 27%, from 82.66±14.04 mmHg to 105.3±7.6 mmHg, at the 50 and 130 bpm simulations, respectively. Stroke volume (from 77.45±8.50 to 39.09±8.08 mL), ejection fraction (from 61.10±4.40 to 39.32±5.42%) and stroke work (SW, from 0.88±0.04 to 0.58±0.09 J) decreased by 50, 36 and 34%, at the 50 and 130 bpm simulations, respectively. In addition, oxygen consumption indexes (rate pressure product – RPP, tension time index per minute – TTI/min, and pressure volume area per minute – PVA/min) increased from the 50 to the 130 bpm simulation, respectively, by 186% (from 5598±1939 to 15995±3219 mmHg/min), 56% (from 2094±265 to 3257±301 mmHg s/min) and 102% (from 57.99±17.90 to 117.4±26.0 J/min). In fact, left ventricular efficiency (SW/PVA) decreased from 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 present mathematical model suggests that lower HRs during permanent AF relates to improved hemodynamic parameters, cardiac efficiency, and lower oxygen consumption.