The arterial Windkessel

Westerhof, Nico; Lankhaar, Jan-Willem; Westerhof, Berend E.

doi:10.1007/s11517-008-0359-2

Cited by 911 publications

(731 citation statements)

References 70 publications

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“…The 3-element Windkessel adds aortic characteristic impedance to Frank Windkessel. 32,33 In principle at any location in the arterial system, the pressure-flow relation can be mimicked with a Windkessel. Strong and proximal reflections, aortic coarctation, low PWV with (short wavelength) as in young subjects, make the Windkessel less accurate.…”

Section: Reservoir-wave Conceptmentioning

confidence: 99%

“…Strong and proximal reflections, aortic coarctation, low PWV with (short wavelength) as in young subjects, make the Windkessel less accurate. 33,34 The RWC assumes that diastole (diastasis) is wave-free and that, therefore, the arterial system can be described by a reservoir (storage volume) and peripheral resistance (Frank Windkessel). This model explains the diastolic pressure decay in diastole.…”

Section: Reservoir-wave Conceptmentioning

confidence: 99%

“…This model explains the diastolic pressure decay in diastole. In systole, however, as Frank Windkessel does not describe pressure well, 16,32,33,35 an excess pressure, P exc (t)=Z c Q m (t) was introduced, 16,36 which is the difference between measured pressure and pressure predicted by Frank Windkessel. The basis of the RWC is described as follows: it is assumed that measured aortic pressure is the instantaneous sum of a constant (P inf , pressure reached after long asystole), a Windkessel or reservoir pressure (P res ), and a wave-related pressure (excess pressure, P exc ).…”

Section: Reservoir-wave Conceptmentioning

confidence: 99%

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Wave Separation, Wave Intensity, the Reservoir-Wave Concept, and the Instantaneous Wave-Free Ratio

2015

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Abstract-Wave separation analysis and wave intensity analysis (WIA) use (aortic) pressure and flow to separate them in their forward and backward (reflected) waves. While wave separation analysis uses measured pressure and flow, WIA uses their derivatives. Because differentiation emphasizes rapid changes, WIA suppresses slow (diastolic) fluctuations of the waves and renders diastole a seemingly wave-free period. However, integration of the WIA-obtained forward and backward waves is equal to the wave separation analysis-obtained waves. Both the methods thus give similar results including backward waves spanning systole and diastole. Nevertheless, this seemingly wave-free period in diastole formed the basis of both the reservoir-wave concept and the Instantaneous wave-Free Ratio of (iFR) pressure and flow. The reservoir-wave concept introduces a reservoir pressure, P res , (Frank Windkessel) as a wave-less phenomenon. Because this Windkessel model falls short in systole an excess pressure, P exc , is introduced, which is assumed to have wave properties. The reservoir-wave concept, however, is internally inconsistent. The presumed wave-less P res equals twice the backward pressure wave and travels, arriving later in the distal aorta. Hence, in contrast, P exc is minimally affected by wave reflections. Taken together, P res seems to behave as a wave, rather than P exc . The iFR is also not without flaws, as easily demonstrated when applied to the aorta. The ratio of diastolic aortic pressure and flow implies division by zero giving nonsensical results. In conclusion, presumptions based on WIA have led to misconceptions that violate physical principles, and reservoir-wave concept and iFR should be abandoned. (Hypertension. 2015;66:93-98.

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Section: Reservoir-wave Conceptmentioning

confidence: 99%

Section: Reservoir-wave Conceptmentioning

confidence: 99%

Section: Reservoir-wave Conceptmentioning

confidence: 99%

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Wave Separation, Wave Intensity, the Reservoir-Wave Concept, and the Instantaneous Wave-Free Ratio

2015

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“…Global arterial properties can be estimated by coupling the timevarying elastance heart model to a lumped parameter windkessel model representing the whole arterial tree (Segers et al, 2000(Segers et al, , 2002Stergiopulos et al, 1999;Westerhof et al, 2009). For an overall validation for the model, we coupled the heart model to a four-element windkessel model so as to compare the arterial model parameters of total systemic resistance, total compliance and aortic characteristic impedance to values reported by Segers et al (2005).…”

Section: Lumped Parameter Windkessel Modelmentioning

confidence: 99%

A 1D model of the arterial circulation in mice

Aslanidou

Trachet

Reymond

et al. 2016

ALTEX

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SummaryAt a time of growing concern over the ethics of animal experimentation, mouse models are still an indispensable source of insight into the cardiovascular system and its most frequent pathologies. Nevertheless, reference data on the murine cardiovascular anatomy and physiology are lacking. In this work, we developed and validated an in silico, one dimensional model of the murine systemic arterial tree consisting of 85 arterial segments. Detailed aortic dimensions were obtained in vivo from contrast-enhanced micro-computed tomography in 3 male, C57BL/6J anesthetized mice and 3 male ApoE -/-mice, all 12-weeks old. Physiological input data were gathered from a wide range of literature data. The integrated form of the Navier-Stokes equations was solved numerically to yield pressures and flows throughout the arterial network. The resulting model predictions have been validated against invasive pressure waveforms and noninvasive velocity and diameter waveforms that were measured in vivo on an independent set of 47 mice. In conclusion, we present a validated one-dimensional model of the anesthetized murine cardiovascular system that can serve as a versatile tool in the field of preclinical cardiovascular research.

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“…The Windkessel model by Westerhof and Noordergraaf is a classical demonstration of this approach [23]. The development of this model is well described in this issue by Nico Westerhof and co-authors [24]. In the time domain, the Windkessel model is characterized in terms of its constitutive differential equations, but it is easily translated into the frequency domain by applying the impedance analogs for such networks comprised of resistance, compliance and inertance.…”

mentioning

confidence: 99%