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# Circ.Windkessel3

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).

Model number: 0295

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## Description

```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.

```

## 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.

## References

```	- 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

```

None.

## Key Terms

aortic characteriastic resistance, viscoelastic windkessel, electrical analogue, pulsatile ascending aortic flow, systemic arterial compliance, connecting an inductance, multi-models

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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.