  Background. Different mechanisms have been proposed to relate atrial
fibrillation (AF) and coronary flow impairment, even in absence of relevant
coronary artery disease (CAD). However, the underlying hemodynamics remains
unclear. Aim of the present work is to computationally explore whether and to
what extent ventricular rate during AF affects the coronary perfusion.
  Methods. AF is simulated at different ventricular rates (50, 70, 90, 110, 130
bpm) through a 0D-1D multiscale validated model, which combines the left
heart-arterial tree together with the coronary circulation. Artificially-built
RR stochastic extraction mimics the \emph{in vivo} beating features. All the
hemodynamic parameters computed are based on the left anterior descending (LAD)
artery and account for the waveform, amplitude and perfusion of the coronary
blood flow.
  Results. Alterations of the coronary hemodynamics are found to be associated
either to the heart rate increase, which strongly modifies waveform and
amplitude of the LAD flow rate, and to the beat-to-beat variability. The latter
is overall amplified in the coronary circulation as HR grows, even though the
input RR variability is kept constant at all HRs.
  Conclusions. Higher ventricular rate during AF exerts an overall coronary
blood flow impairment and imbalance of the myocardial oxygen supply-demand
ratio. The combined increase of heart rate and higher AF-induced hemodynamic
variability lead to a coronary perfusion impairment exceeding 90-110 bpm in AF.
Moreover, it is found that coronary perfusion pressure (CPP) is no longer a
good measure of the myocardial perfusion for HR higher than 90 bpm.
