The entrainment of low frequency breathing periodicity. It has been predicted by mathematical models of the respiratory control system that the delay between the lung and the respiratory controller may determine the cycle time found in periodic breathing. We examined cycle time of periodic breathing and circulation time in 11 patients known to have circulation delay due to heart failure. We did not find a significant relationship between the amount of periodic breathing and circulation delay, but found a very high correlation between circulation delay and the cycle time of periodic breathing (r2 = 0.825; p = 0.0001). 