An artificial arterial system for pumping hearts.

Westerhof, Nico; Elzinga, G.; Sipkema, Pieter

doi:10.1152/jappl.1971.31.5.776

Cited by 502 publications

(283 citation statements)

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“…The various distal organ beds were simulated by three-element Windkessels [24], i.e. by two resistances and a compliance, known to represent organ beds well.…”

Section: Distributed Modelmentioning

confidence: 99%

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Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation

Wijngaard

Siebes

Westerhof

2008

Med Biol Eng Comput

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Coarctation of the aorta may develop during fetal life and impair quality of life in the adult because upper body hypertension and aneurysm formation in the descending aorta may develop. We used our computational model of the young adult arterial circulation, incorporated aorta coarctation over a range from 0 to 80% and evaluated the effects in terms of forward pressure (P ? ) and backward pressure (P -). Predictions at several sites proximal and distal to the coarctation using an impedance-based waveform separation method (WSA) and the time-domain technique of wave intensity analysis (WIA) yielded comparable outcomes. A large reflected backward compression wave was seen proximal to the coarctation. Both techniques, WSA and WIA, gave the same results in terms of P ? and P -. A descending index (DI) was formulated as the difference between peak systolic pressure and valve closure pressure, divided by the pulse pressure. DI increased with stenosis severity for mild to moderate aortic coarctations that did not yet cause evident hypertension. This index may allow for early diagnosis by noninvasive estimation of coarctation severity.

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“…The various distal organ beds were simulated by three-element Windkessels [24], i.e. by two resistances and a compliance, known to represent organ beds well.…”

Section: Distributed Modelmentioning

confidence: 99%

“…The basic equations pertaining to frequency domain analysis approach are briefly outlines here. Details can be found elsewhere [11,24,25].…”

Section: Distributed Modelmentioning

confidence: 99%

Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation

Wijngaard

Siebes

Westerhof

2008

Med Biol Eng Comput

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“…The arterial system has been modeled in many ways: lumped models [18,73], tube models [8,41,80] and anatomically based distributed models [42,64,71]. In this paper we will discuss the lumped or Windkessel models.…”

Section: Introductionmentioning

confidence: 99%

The arterial Windkessel

Westerhof

Lankhaar

Westerhof³

2008

Med Biol Eng Comput

940

691

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Frank's Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload.

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“…3D [10,16,21,28,30,35] gives rise to a differential equation of the same form as equation (18), except the terms have a significantly different meaning. The equation for this circuit is: which also can be written in the form of equation (18):…”

Section: Mette S Olufsen and Ali Nadimmentioning

confidence: 99%

“…In this model, the additional resistor is thought to represent the characteristic impedance of the aorta and the large compliance vessels. The three-element windkessel model is widely used, and it produces realistic blood flow and pressure wave shapes as well as estimates experimental data [7,10,16,21,28,30,35]. Further expansions of the windkessel model into a four-element model have proven even better at getting good comparisons between measured blood flow and pressure.…”

mentioning

confidence: 99%

On deriving lumped models for blood flow and pressure in the systemic arteries

OLUFSEN¹,

NADIM²

2003

Computational Fluid and Solid Mechanics 2003

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Abstract. Windkessel and similar lumped models are often used to represent blood flow and pressure in systemic arteries. The windkessel model was originally developed by Stephen Hales (1733) and Otto Frank (1899) who used it to describe blood flow in the heart. In this paper we start with the onedimensional axisymmetric Navier-Stokes equations for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one, two, or more residues, we derive lumped models of successively higher order. We focus on zeroth, first and second order models and relate them to electrical circuit analogs, in which current is equivalent to flow and voltage to pressure. By incorporating effects of compliance through addition of capacitors, windkessel and related lumped models are obtained. Our results show that given the radius of a blood vessel, it is possible to determine the order of the model that would be appropriate for analyzing the flow and pressure in that vessel. For instance, in small rigid vessels (R < 0.2 cm) it is adequate to use Poiseuille's law to express the relation between flow and pressure, whereas for large vessels it might be necessary to incorporate spatial dependence by using a one-dimensional model accounting for axial variations.

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An artificial arterial system for pumping hearts.

Cited by 502 publications

References 0 publications

Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation

Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation

The arterial Windkessel

On deriving lumped models for blood flow and pressure in the systemic arteries

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