Cardiac timing modulates the contribution of compliance to effective arterial elastance.

Effective arterial elastance (Ea) is a lumped descriptor of arterial load. The contributions of arterial characteristics to Ea, and their interactions with cardiac timing parameters, have not been fully elaborated. Previous studies have shown that Ea can be approximated by equations of the form Ea ≈ R/T + k/C, where R is either total or peripheral resistance, T is cardiac cycle time, and C is arterial compliance, but reported values for the coefficient k vary substantially, and some analyses suggest that compliance contributes little to Ea. Here, an analytical approximation is derived from Sunagawa's Windkessel expression for Ea by replacing the exponential term with a truncated Taylor expansion. The resulting approximation predicts that k is not constant but varies with cardiac timing, such that k ≈ 0.5 (td/T)2, where td is diastolic time. Approximation accuracy was assessed across 693 combinations of resistance, compliance, and heart rate and in a virtual population of 4374 adults derived from a published one-dimensional vascular model. The linear approximation for Ea closely tracked the Windkessel expression across the full parameter space (R2 > 0.9999, mean absolute percentage error 0.51%). In the virtual population, the approximation showed good agreement with the E surrogate PES/SV (end-systolic pressure/stroke volume), surpassing previous approximations. These findings show that the contribution of compliance to Ea is modulated by cardiac timing and provide a mechanistic explanation for previously reported values of k.