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One can derive flow (Q) from pressure (P) or pressure from flow if compliance (C), impedance (Z), and resistance (R) are known. Transformation of the
aortic flow signal into an aortic pressure signal using a two-element Windkessel model commonly used by minimally invasive monitoring techniques.
Compliance (C) is the arterial compliance, resistance (R) is outflow resistance, where inflow is modeled as current Q(t), generated by the current source
J(t), pressure is modeled by the pressure drop P(t) across the resistor R. The impedance Z of this model is the total impedance of the circuit and given by
equation 1, where, ω = 2πf is the angular frequency, f is the frequency (60/heart rate in this case), and j is the complex number operator. Z(jω) is
computed using the Fourier transform of both the flow Q(jω) and the pressure P(jω), as shown in equation 2. R is computed at the value of Z(jω) at the 0th
Source: Assessing the Circulation: Oximetry, Indicator Dilution, and Pulse Contour Analysis, Principles of Critical Care, 4e
harmonic (when f = 0, the model simplifies to a single element model consisting only of R) as shown in equation 3. The reactive component is computed
Hall
Schmidt
GA,compliance
Kress JP. Principles
Critical
Care, 4e;
2015 Available
at: http://mhmedical.com/
Accessed: May 14, 2017
from Z and RCitation:
as shown
in JB,
equation
4 and
computed of
from
the reactive
component
as shown
in equation 5.
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