  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 56.7%, from 33.92+-37.56 mmHg
to 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), ejection
fraction (from 61.1+-4.4 to 39.32+-5.42%) and stroke work (SW, from 0.88+-0.04
to 0.58+-0.09 J) decreased by 49.5, 35.6 and 34.2%, 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 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 to
117.37+-25.96 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.
