7.4 Input impedance
Figure 72: The input impedance of a young healthy subject (Adapted from O'Rourke 1992).
The input impedance \( Z_{in} \) is defined in a very similar manner as the characteristic impedance, namely as the ratio of the pulsatile components of pressure and flow: $$ \begin{equation} Z_{in}(\omega) = \frac{P(\omega)}{Q(\omega)} \tag{7.109} \end{equation} $$ where uppercase denotes the Fourier-component of the corresponding lowercase primary variable for a given angular frequency \( \omega \). However, the input impedance is not restricted to unidirectional waves, i.e., reflected wave components are included. Thus, \( Z_{in} \) is a global quantity that characterize the properties distal (downstream) to the measuring point. The cumulative effect of all distal contributions is incorporated in the input impedance. In the aorta \( Z_{in} \) represents the afterload on the heart.
In Figure 72 the input impedance of a young healthy subject is depicted. For high frequencies the phase angles are close to zero, as high frequency components are more damped and reflections tend to cancel out. The negative phase angle for the low-frequency components correspond to that flow components lead pressure, i.e., the aorta first sees flow and the pressure.