Abstract
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
.