Simulations are performed with the Ben-Tal (2006) model, using prescribed HR functions. Positive Δ represents RSA, negative Δ represents inverse RSA, constant heart rate is marked by a cross at Δ= 0. E/E0 curves are plotted as a function of Δ (E is calculated by eqn (5), E0 is the value of E at Δ= 0), constraining the partial pressure of O2 along each curve. Data points are obtained from the simulation, and the continuous lines are least-squares quadratic fits. Data points represented by circles (fitted with a continuous line) were taken with T= 10 s, VT= 1.0 l, constraining the averaged arterial partial pressure of O2 to 105.7143 mmHg and normalizing E by 13.2576 Hz. Squares with a dashed line were taken with T= 5 s, VT= 0.5 l, constraining the averaged arterial partial pressure of O2 to 105.8179 mmHg and normalizing E by 4.974 Hz. Diamonds with dashed–dotted line were taken with T= 2.5 s, VT= 0.25 l, constraining the averaged arterial partial pressure of O2 to 105.1352 mmHg and normalizing E by 1.069 Hz.