# 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.

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## Model History

Get Model history in CVS.## 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.