# The Arterial Windkessel

• Nicolaas Westerhof
• Nikolaos Stergiopulos
• Mark I. M. Noble
Chapter

## Abstarct

Figure 24.1 shows the three-element Windkessel as model for the load on the heart. This (hydraulic) model) as load of the real heart results in ventricular and aortic pressure and aortic flow that are similar to those measured in vivo Three Windkessel models are given in Fig. 24.2. Otto Frank, 1899, popularized the original two-­element Windkessel. He reasoned that the decay of diastolic pressure in the ­ascending aorta, when flow is zero, can be described by an exponential curve. The time constant, τ, i.e., the time for pressure to decrease to 37% of the starting pressure, is given by the product of peripheral resistance, R p , and the total arterial compliance, C, τ = R p C. The larger the resistance the slower the blood, stored in the compliant conduit vessels, leaves the system and the longer the time constant will be. Also, the larger the compliance the more blood is stored, and the longer the time constant will be. Frank’s objective was to derive Cardiac Output from aortic pressure. By measuring the pulse wave velocity over the aorta (carotid to femoral) together with, averaged, cross-sectional area, and using the Newton-Young equation () area compliance, C A , can de estimated. When aortic length is also known volume compliance, C, is derived. Using τ and C, the peripheral resistance can be calculated from R p = τ/C. From mean pressure and resistance, using Ohm’s law, mean flow is then found. The assumption that all compliance is located in the aorta, thus neglecting the compliance of the smaller conduit vessels, introduces a small error. After pulsatile flows could be ­measured, and arterial input impedance could be determined (), the shortcomings of the two-element Windkessel became clear.

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## Authors and Affiliations

• Nicolaas Westerhof
• 1
• Nikolaos Stergiopulos
• 2
• Mark I. M. Noble
• 3
1. 1.Departments of Physiology and Pulmonology ICaR-VUVU University Medical CenterAmsterdamthe Netherlands
2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologySwiss Federal Institute of TechnologyLausanneSwitzerland
3. 3.Cardiovascular MedicineAberdeen UniversityAberdeenScotland