Cardiac timing modulates the contribution of compliance to effective arterial elastance

Abstract Effective arterial elastance ( E a ) is a lumped descriptor of arterial load. The contributions of arterial characteristics to E a , and their interactions with cardiac timing parameters, have not been fully elaborated. Previous studies have shown that E a can be approximated by equations of the form E a ≈ 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 E a . Here, an analytical approximation is derived from Sunagawa's Windkessel expression for E a 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 ( t d / T ) 2 , where t d 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 E a closely tracked the Windkessel expression across the full parameter space ( R 2 > 0.9999, mean absolute percentage error 0.51%). In the virtual population, the approximation showed good agreement with the E surrogate P ES /SV (end‐systolic pressure/stroke volume), surpassing previous approximations. These findings show that the contribution of compliance to E a is modulated by cardiac timing and provide a mechanistic explanation for previously reported values of k .