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Stergiopulos_4_Element_Windkessel

Lumped parameter peripheral circulation model from Stergiopulos et al. (1999) Am J Physiol 276: H81-H88.

Model number: 0219

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Description

The model simulates a peripheral circulation using lumped 
parameters for arterial resistance, inertance, and compliance, 
and peripheral arterial network resistance. The single-
beat human aortic flow function in Figure 4A, Type C of 
Stergiopulos et al. (1999) was scanned and reproduced 
digitally. One-hundred copies were concatenated into an 
single data file used as the driving flow in the model. 
Constants used to fit the aortic pressure waveform in Figure
 4B, Type C were used to parameterize the model. The model 
produces an aortic pressure waveform fit comparable to 
Stergiopulos et al. (1999) Figure 4D, Type C. 

PARAMETERS:

 CODEWORD|SYMBOL|    NAME    |      UNITS       |          DESCRIPTION             
-----------------------------------------------------------------------------------

 C        C      Compliance   ml/mmHg            Total arterial compliance 
 L               Inertance    mmHg*sec^2/ml      Arterial inertance
 Pout     P      Pressure     mmHg               Downstream blood pressure
 Rc       R      Resistance   mmHg*sec/ml        Characteristic resistance
 Rp       R      Resistance   mmHg*sec/ml        Peripheral resistance
-----------------------------------------------------------------------------------


VARIABLES:

 CODEWORD|SYMBOL|    NAME    |      UNITS       |          DESCRIPTION             
-----------------------------------------------------------------------------------

 Fin      F      Flow         ml/sec             Aortic flow signal (Fig. 4A, Type C
                                                    in Stergiopulos et al. 1999)
 Pdata    P      Pressure     mmHg               Recorded aortic pressure (Fig. 4B,
                                                    Type C in Stergiopulos et al. 1999)
 FRc      F      Flow         ml/sec             Flow through characteristic resistor
 FL       F      Flow         ml/sec             Flow through inductor
 FC       F      Flow         ml/sec             Radial flow in periphery
 FRp      F      Flow         ml/sec             Forward flow in periphery
 Pao      P      Pressure     mmHg               Aortic pressure
 Pp       P      Pressure     mmHg               Peripheral (arterial) pressure
 Vp       V      Volume       ml                 Peripheral blood volume
-----------------------------------------------------------------------------------

 EXAMPLE PARAMETER SET:
 t.min = 0
 t.max = 25
 t.delta = 0.01
 Rc = 0.045
 C = 2.53
 L = 0.0054
 Rp = 0.64924
 tau = 30
 Pout = 0
 FL__init = 0
 Vp__init = 300
 Fin = Flow
 Pdata = Pressure
 solver.ode_which = CVode


Equations

The equations for this model may be viewed by running the JSIm model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

Download File

References

Stergiopulos N, Westerhof BE, Westerhof N. Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276: H81-H88, 1999.

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Key Terms

stergiopulos, 4, element, windkessel, lumped parameters, peripheral, circulation, Publication, Data, PMID9887020

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Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

Model development and archiving support at physiome.org provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.