title: Rate control management of atrial fibrillation: may a mathematical model suggest an ideal heart rate?
abstract: 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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Division of Cardiology, Department of Medical Sciences, "Città della Salute e della Scienza" Hospital, University of Turin, Turin, Italy.
authors.forename: Matteo
authors.initials: M
authors.lastname: Anselmino
authors.affiliation: DIMEAS -Department of Mechanical and Aerospace Engineering-, Politecnico di Torino, Turin, Italy.
authors.forename: Stefania
authors.initials: S
authors.lastname: Scarsoglio
authors.affiliation: DIATI -Department of Environmental, Land and Infrastructure Engineering-, Politecnico di Torino, Turin, Italy.
authors.forename: Carlo
authors.initials: C
authors.lastname: Camporeale
authors.affiliation: Division of Cardiology, Department of Medical Sciences, "Città della Salute e della Scienza" Hospital, University of Turin, Turin, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Saglietto
authors.affiliation: Division of Cardiology, Department of Medical Sciences, "Città della Salute e della Scienza" Hospital, University of Turin, Turin, Italy.
authors.forename: Fiorenzo
authors.initials: F
authors.lastname: Gaita
authors.affiliation: DIATI -Department of Environmental, Land and Infrastructure Engineering-, Politecnico di Torino, Turin, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Ridolfi
mesh_terms: D001281:Atrial Fibrillation / Q000503:physiopathology*; D006339:Heart Rate / Q000502:physiology*; D006439:Hemodynamics; D006801:Humans; D008954:Models, Biological; D010101:Oxygen Consumption