Input Impedance at high and low frequencies reveals effects of pulse
wave propagation and reflection
C. M. Quick, David S. Berger, and A. Noordergraaf
Biomedical Engineering Society Annual Meeting, Seattle, WA, 2000
Input impedance (Zin) describes the load seen by the ventricle.
It depends on the length, radius, and stiffness of each vessel in the arterial
system. However, at low frequencies, the arterial system behaves like the
classical Windkessel model. Thus, at low frequencies, Zin
degenerates into the windkessel impedance, Zw, which is related to total
arterial compliance and peripheral resistance. At high frequencies, the arterial
system behaves like an infinitely long tube. Thus, at high frequencies,
Zin degenerates into characteristic impedance, Zo
, which is related to local aortic compliance and radius. These two limits,
where wavelength is very long, and reflection is very small, can be used
to understand the role of pulse wave propagation and reflection. Since
Zin=Zw when wavelength is infinite, the
theoretical pressure with pulse transit delay removed can be calculated from
flow·Zw. Applying this insight to measured Z
in indicates that a pulse transit delay has little effect on pulse
pressure (PP) and stroke work (SW). Since Zin
=Zo in the absence of reflection, the pressure with reflection
theoretically removed can be calculated from flow·Zo
. Applying this insight to measured Zin indicates that
reflection has little effect on PP or SW in normal blood pressure
conditions, but increases PP and SW in both reduced and elevated
pressures.