Three-element windkessel model with a connecting inductor in parallel (W4P), in series (W4S), and with a low-resistance Rc, in series with a viscoelastic windkessel (IVW).
W4P is an alternative four-element windkessel formulation, derived from the three-element windkessel by connecting an inductance L in parallel with a low-resistance term, Rc, which is given the meaning of aortic characteristic impedance. W4S is an alternative four-element windkessel formulation, derived from the three-element windkessel by connecting an inductance L in series with a low-resistance term, Rc, which is given the meaning of aortic characteristic impedance. IVW is an alternative four-element windkessel formulation, derived from the three-element windkessel by connecting an inductance L in series with a viscoelastic windkessel, where a Voigt cell (a resistance, Rd, in series with compliance, C) accounts for viscoelastic properties of vessel wall motion.
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.
We welcome comments and feedback for this model. Please use the button below to send comments:
- Burattini R, Di salvia PO: "Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models", J Appl Physiol 103:66-79, 2007
Please cite https://www.imagwiki.nibib.nih.gov/physiome 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.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.