Journal articles: 'Windkessel model'

1

Burkhoff, D., J. Alexander, and J. Schipke. "Assessment of Windkessel as a model of aortic input impedance." American Journal of Physiology-Heart and Circulatory Physiology 255, no. 4 (October 1, 1988): H742—H753. http://dx.doi.org/10.1152/ajpheart.1988.255.4.h742.

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To facilitate the analysis of aortic-ventricular coupling, simplified models of aortic input properties have been developed, such as the three-element Windkessel. Even though the impedance spectrum of the Windkessel reproduces the gross features of the real aortic input impedance, it fails to reproduce many of its details. In the present study we assessed the physiological significance of the differences between real and Windkessel impedance. We measured aortic input impedance spectra from five anesthetized open-chest dogs under a wide range of conditions. For each experimentally determined spectrum we estimated the corresponding values of the best-fit Windkessel parameters. By computer simulation we imposed both the real and best-fit Windkessel impedances on a model left ventricle and assessed the differences in seven different coupling variables. The analysis indicated that the Windkessel model provides a reasonable representation of afterload for purposes of predicting stroke volume, stroke work, oxygen consumption, and systolic and diastolic aortic pressures. However, the Windkessel model significantly underestimates peak aortic flow, slightly underestimates mean arterial pressure, and, of course, does not provide realistic aortic pressure and flow waveforms.

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Stergiopulos, Nikos, Berend E. Westerhof, and Nico Westerhof. "Total arterial inertance as the fourth element of the windkessel model." American Journal of Physiology-Heart and Circulatory Physiology 276, no. 1 (January 1, 1999): H81—H88. http://dx.doi.org/10.1152/ajpheart.1999.276.1.h81.

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In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method ( P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different ( P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies ( P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.

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Wang, Jiun-Jr, Jacqueline A. Flewitt, Nigel G. Shrive, Kim H. Parker, and John V. Tyberg. "Systemic venous circulation. Waves propagating on a windkessel: relation of arterial and venous windkessels to systemic vascular resistance." American Journal of Physiology-Heart and Circulatory Physiology 290, no. 1 (January 2006): H154—H162. http://dx.doi.org/10.1152/ajpheart.00494.2005.

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Compared with arterial hemodynamics, there has been relatively little study of venous hemodynamics. We propose that the venous system behaves just like the arterial system: waves propagate on a time-varying reservoir, the windkessel, which functions as the reverse of the arterial windkessel. During later diastole, pressure increases exponentially to approach an asymptotic value as inflow continues in the absence of outflow. Our study in eight open-chest dogs showed that windkessel-related arterial resistance was ∼62% of total systemic vascular resistance, whereas windkessel-related venous resistance was only ∼7%. Total venous compliance was found to be 21 times larger than arterial compliance ( n = 3). Inferior vena caval compliance (0.32 ± 0.015 ml·mmHg−1·kg−1; mean ± SE) was ∼14 times the aortic compliance (0.023 ± 0.002 ml·mmHg−1·kg−1; n = 8). Despite greater venous compliance, the variation in venous windkessel volume (i.e., compliance × windkessel pulse pressure; 7.8 ± 1.1 ml) was only ∼32% of the variation in aortic windkessel volume (24.3 ± 2.9 ml) because of the larger arterial pressure variation. In addition, and contrary to previous understanding, waves generated by the right heart propagated upstream as far as the femoral vein, but excellent proportionality between the excess pressure and venous outflow suggests that no reflected waves returned to the right atrium. Thus the venous windkessel model not only successfully accounts for variations in the venous pressure and flow waveforms but also, in combination with the arterial windkessel, provides a coherent view of the systemic circulation.

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Sridharan, Sarup S., Lindsay M. Burrowes, J. Christopher Bouwmeester, Jiun-Jr Wang, Nigel G. Shrive, and John V. Tyberg. "Classical electrical and hydraulic Windkessel models validate physiological calculations of Windkessel (reservoir) pressure." Canadian Journal of Physiology and Pharmacology 90, no. 5 (May 2012): 579–85. http://dx.doi.org/10.1139/y2012-027.

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Our “reservoir–wave approach” to arterial hemodynamics holds that measured arterial pressure should be considered to be the sum of a volume-related pressure (i.e., reservoir pressure, Preservoir) and a wave-related pressure (Pexcess). Because some have questioned whether Preservoir (and, by extension, Pexcess) is a real component of measured physiological pressure, it was important to demonstrate that Preservoir is implicit in Westerhof’s classical electrical and hydraulic models of the 3-element Windkessel. To test the validity of our Preservoir determinations, we studied a freeware simulation of the electrical model and a benchtop recreation of the hydraulic model, respectively, measuring the voltage and the pressure distal to the proximal resistance. These measurements were then compared with Preservoir, as calculated from physiological data. Thus, the first objective of this study was to demonstrate that respective voltage and pressure changes could be measured that were similar to calculated physiological values of Preservoir. The second objective was to confirm previous predictions with respect to the specific effects of systematically altering proximal resistance, distal resistance, and capacitance. The results of this study validate Preservoir and, thus, the reservoir–wave approach.

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Chan, Gregory S. H., Philip N. Ainslie, Chris K. Willie, Chloe E. Taylor, Greg Atkinson, Helen Jones, Nigel H. Lovell, and Yu-Chieh Tzeng. "Contribution of arterial Windkessel in low-frequency cerebral hemodynamics during transient changes in blood pressure." Journal of Applied Physiology 110, no. 4 (April 2011): 917–25. http://dx.doi.org/10.1152/japplphysiol.01407.2010.

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The Windkessel properties of the vasculature are known to play a significant role in buffering arterial pulsations, but their potential importance in dampening low-frequency fluctuations in cerebral blood flow has not been clearly examined. In this study, we quantitatively assessed the contribution of arterial Windkessel (peripheral compliance and resistance) in the dynamic cerebral blood flow response to relatively large and acute changes in blood pressure. Middle cerebral artery flow velocity (MCAV; transcranial Doppler) and arterial blood pressure were recorded from 14 healthy subjects. Low-pass-filtered pressure-flow responses (<0.15 Hz) during transient hypertension (intravenous phenylephrine) and hypotension (intravenous sodium nitroprusside) were fitted to a two-element Windkessel model. The Windkessel model was found to provide a superior goodness of fit to the MCAV responses during both hypertension and hypotension ( R2 = 0.89 ± 0.03 and 0.85 ± 0.05, respectively), with a significant improvement in adjusted coefficients of determination ( P < 0.005) compared with the single-resistance model ( R2 = 0.62 ± 0.06 and 0.61 ± 0.08, respectively). No differences were found between the two interventions in the Windkessel capacitive and resistive gains, suggesting similar vascular properties during pressure rise and fall episodes. The results highlight that low-frequency cerebral hemodynamic responses to transient hypertension and hypotension may include a significant contribution from the mechanical properties of vasculature and, thus, cannot solely be attributed to the active control of vascular tone by cerebral autoregulation. The arterial Windkessel should be regarded as an important element of dynamic cerebral blood flow modulation during large and acute blood pressure perturbation.

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Campbell, K. B., R. Burattini, D. L. Bell, R. D. Kirkpatrick, and G. G. Knowlen. "Time-domain formulation of asymmetric T-tube model of arterial system." American Journal of Physiology-Heart and Circulatory Physiology 258, no. 6 (June 1, 1990): H1761—H1774. http://dx.doi.org/10.1152/ajpheart.1990.258.6.h1761.

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An asymmetric T-tube model of the arterial system with complex terminal loads was formulated in the time domain. The model was formulated to allow it to be fitted to the aortic pressure waveform, the aortic flow waveform, or simultaneously to both the aortic and descending aortic flow waveforms. Pressure and flow measurements were taken in anesthetized open-chest dogs under basal, vasoconstricted, and vasodilated states. It was found that the T-tube model fitted the data well in all formulations and in all vasoactive states. However, all parameters were estimated accurately in all vasoactive states only with the formulation that fitted to both aortic and descending aortic flow simultaneously. The T-tube model was compared with the three-element windkessel model with regard to the respective models' ability to recreate specific aspects of the pressure waveform and with regard to the estimates of global arterial parameters. The T-tube model recremated those features of the pressure waveform, such as diastolic waves, that the windkessel model could not. Also, the T-tube model systematically estimated lower global arterial compliance and higher characteristic impedance than the windkessel. It was argued that the T-tube model accurately represented important wave transmission features of the arterial loading system. The model is recommended for use in characterizing the arterial load and for merging with representations of the left ventricle in studies of left ventricle-systemic arterial interaction.

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Mohiuddin, Mohammad W., Glen A. Laine, and Christopher M. Quick. "Increase in pulse wavelength causes the systemic arterial tree to degenerate into a classical windkessel." American Journal of Physiology-Heart and Circulatory Physiology 293, no. 2 (August 2007): H1164—H1171. http://dx.doi.org/10.1152/ajpheart.00133.2007.

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Two competing schools of thought ascribe vascular disease states such as isolated systolic hypertension to fundamentally different arterial system properties. The “windkessel school” describes the arterial system as a compliant chamber that distends and stores blood and relates pulse pressure to total peripheral resistance ( Rtot) and total arterial compliance ( Ctot). Inherent in this description is the assumption that arterial pulse wavelengths are infinite. The “transmission school,” assuming a finite pulse wavelength, describes the arterial system as a network of vessels that transmits pulses and relates pulse pressure to the magnitude, timing, and sites of pulse-wave reflection. We hypothesized that the systemic arterial system, described by the transmission school, degenerates into a windkessel when pulse wavelengths increase sufficiently. Parameters affecting pulse wavelength (i.e., heart rate, arterial compliances, and radii) were systematically altered in a realistic, large-scale, human arterial system model, and the resulting pressures were compared with those assuming a classical (2-element) windkessel with the same Rtot and Ctot. Increasing pulse wavelength as little as 50% (by changing heart rate −33.3%, compliances −55.5%, or radii +50%) caused the distributed arterial system model to degenerate into a classical windkessel ( r2 = 0.99). Model results were validated with analysis of representative human aortic pressure and flow waveforms. Because reported changes in arterial properties with age can markedly increase pulse wavelength, results suggest that isolated systolic hypertension is a manifestation of an arterial system that has degenerated into a windkessel, and thus arterial pressure is a function only of aortic flow, Rtot, and Ctot.

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Dutra, Maurício dos S., Walter C. de Lima, and Jorge M. Barreto. "Ventricular Ejection Simulation with Active Atrium using Windkessel Model." IFAC Proceedings Volumes 30, no. 2 (March 1997): 25–28. http://dx.doi.org/10.1016/s1474-6670(17)44536-8.

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9

Karamanoglu, M., D. E. Gallagher, A. P. Avolio, and M. F. O'Rourke. "Pressure wave propagation in a multibranched model of the human upper limb." American Journal of Physiology-Heart and Circulatory Physiology 269, no. 4 (October 1, 1995): H1363—H1369. http://dx.doi.org/10.1152/ajpheart.1995.269.4.h1363.

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The influence of the large arteries and the peripheral load on pressure wave propagation in the human upper limb was investigated in an anatomically realistic multibranched model based on linear transmission theory. To mimic vascular changes seen in life, the viscoelastic properties of large arteries and the peripheral load properties (represented as modified windkessels) were altered as follows: Young's modulus (from 10.9 x 10(6) to 15.3 x 10(6) dyn/cm2) and phase (from 0 to 15 degrees) of the complex elastance, windkessel time constant (from 0 to 0.6 s), and peripheral reflection coefficient (from 0 to 0.95). The relationship between the central aortic and peripheral radial pressure waveforms was analyzed in the time and the frequency domain. Results indicate that the large arterial properties have less influence (peak systolic pressure changed by 3% and peak of transfer function changed by 29%) than the properties of the peripheral load (systolic pressure changed by 14% and peak of transfer function changed by 74%) on the pressure wave propagation in the upper limb.

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10

Kong, Yazhuo, Ying Zheng, David Johnston, John Martindale, Myles Jones, Steve Billings, and John Mayhew. "A Model of the Dynamic Relationship between Blood Flow and Volume Changes during Brain Activation." Journal of Cerebral Blood Flow & Metabolism 24, no. 12 (December 2004): 1382–92. http://dx.doi.org/10.1097/01.wcb.0000141500.74439.53.

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The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level–dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBVαCBFΦ has been used extensively in the literature. Two similar models, the Balloon ( Buxton et al., 1998 ) and the Windkessel ( Mandeville et al., 1999 ), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

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Frasch, H. F., J. Y. Kresh, and A. Noordergraaf. "Two-port analysis of microcirculation: an extension of windkessel." American Journal of Physiology-Heart and Circulatory Physiology 270, no. 1 (January 1, 1996): H376—H385. http://dx.doi.org/10.1152/ajpheart.1996.270.1.h376.

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We examined the suitability of the three-element windkessel as a reduced model of pulsatile pressure-flow relations at arteriolar and venular ends of a microcirculatory bed. Frequency domain (two-port) analysis of a distributed model of an idealized (single input, single output) microvascular network in skeletal muscle, consisting of 391 discrete vessel segments from a 20-microns-diameter arteriole to a 28-microns-diameter venule, demonstrated that the three-element windkessel is a good representation of arterial input impedance when pressure pulsations are absent at the venous end. The same model with different parameter values accounts well for venous pressure-flow relations if no pulsations occur at the arterial end. We showed that a five-element model (2 compliances, 3 resistors) provided a superior representation of pulsatile pressure-flow relations at both arterial and venous ends. Relating parameter values to known properties of the network revealed the physiological significance of the five elements. This model may prove a useful component in circulatory models incorporating both arteries and veins. While parameter values obtained herein were strictly valid for the particular microvascular network described, guidelines are provided based on physiological properties so that values may be estimated for different microvascular beds.

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Aboelkassem, Yasser, and Zdravko Virag. "A hybrid Windkessel-Womersley model for blood flow in arteries." Journal of Theoretical Biology 462 (February 2019): 499–513. http://dx.doi.org/10.1016/j.jtbi.2018.12.005.

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Kozarski, M., G. Ferrari, F. Clemente, K. Górczyńska, C. De Lazzari, M. Darowski, R. Mimmo, G. Tosti, and M. Guaragno. "A Hybrid Mock Circulatory System: Development and Testing of an Electro-hydraulic Impedance Simulator." International Journal of Artificial Organs 26, no. 1 (January 2003): 53–63. http://dx.doi.org/10.1177/039139880302600109.

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Mock circulatory systems are used to test mechanical assist devices and for training and research purposes; when compared to numerical models, however, they are not flexible enough and rather expensive. The concept of merging numerical and physical models, resulting in a hybrid one, is applied here to represent the input impedance of the systemic arterial tree, by a conventional windkessel model built out of an electro-hydraulic (E-H) impedance simulator added to a hydraulic section. This model is inserted into an open loop circuit, completed by another hybrid model representing the ventricular function. The E-H impedance simulator is essentially an electrically controlled flow source (a gear pump). Referring to the windkessel model, it is used to simulate the peripheral resistance and the hydraulic compliance, creating the desired input impedance. The data reported describe the characterisation of the E-H impedance simulator and demonstrate its behaviour when it is connected to a hybrid ventricular model. Experiments were performed under different hemodynamic conditions, including the presence of a left ventricular assist device (LVAD).

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Fogliardi, R., M. Di Donfrancesco, and R. Burattini. "Comparison of linear and nonlinear formulations of the three-element windkessel model." American Journal of Physiology-Heart and Circulatory Physiology 271, no. 6 (December 1, 1996): H2661—H2668. http://dx.doi.org/10.1152/ajpheart.1996.271.6.h2661.

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The three-element windkessel model incorporating a constant compliance (model A) was compared with two nonlinear versions of the same model (models B1 and B2) incorporating a pressure-dependent compliance. The aim was to test whether nonlinear elasticity yielded better model behavior in describing ascending aortic pressure-flow relationships and interpreting the physical properties of the arterial system. Exponential and bell-shaped compliance vs. pressure curves were assumed in models B1 and B2, respectively. To test these models, we used measurements of ascending aortic pressure and flow from three dogs under a wide variety of hemodynamic states obtained by administering vasoactive drugs and by pacing the heart. These data involved pressure waves with and without an evident oscillation during diastole. Model parameters were estimated by fitting experimental and model-predicted ascending aortic pressures. Our results indicated that only models A and B1 were identifiable. Fits to ascending aortic pressure obtained from model B1 were significantly better than fits obtained from model A. However, 1) the accuracy of parameter estimates, as judged from parameter estimation error analysis, was better in model A than in model B1, 2) the estimates of characteristic parameters of the compliance vs. pressure relation in model B1 were inconsistent with expected physiological trends of this relation, and 3) model B1 did not improve the approximation of diastolic pressure in the presence of an evident oscillation. We conclude that, even in the presence of better data fit, the nonlinear three-element windkessel cannot be preferred over the traditional linear version of this model.

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Chahour, Keltoum, Rajae Aboulaich, Abderrahmane Habbal, Nejib Zemzemi, and Chérif Abdelkhirane. "Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions." Computational and Mathematical Methods in Medicine 2020 (February 21, 2020): 1–14. http://dx.doi.org/10.1155/2020/3942152.

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Fractional flow reserve (FFR) has proved its efficiency in improving patient diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and use a coupled multidomain method to implement Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the virtual FFR and conduct several numerical experiments. We compare FFR results from the Navier–Stokes model versus generalized flow model and for Windkessel versus traction-free outlet boundary conditions or mixed outlet boundary conditions. We also investigate some sources of uncertainty that the FFR index might encounter during the invasive procedure, in particular, the arbitrary position of the distal sensor. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between the Navier–Stokes model and the non-Newtonian flow model adopted in classifying coronary lesions. Furthermore, we highlight that the lack of standardization while making FFR measurement might be misleading regarding the significance of stenosis.

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Molino, Paola, Catherine Cerutti, Claude Julien, Guy Cuisinaud, Marie-Paule Gustin, and Christian Paultre. "Beat-to-beat estimation of windkessel model parameters in conscious rats." American Journal of Physiology-Heart and Circulatory Physiology 274, no. 1 (January 1, 1998): H171—H177. http://dx.doi.org/10.1152/ajpheart.1998.274.1.h171.

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A windkessel model was applied on a beat-to-beat basis to evaluate the arterial mechanical characteristics in seven conscious rats. Ascending aortic arterial pressure (AP) and blood flow were recorded during steady-state in basal conditions, during infusions of isoprenaline, sodium nitroprusside, and phenylephrine, and after intravenous atenolol injection. For each cardiac cycle the exponential decay time constant (τ) was estimated from the aortic AP curve, peripheral resistances ( R) were taken as the ratio of mean AP to cardiac output, and systemic arterial compliance ( C) was calculated as τ/ R. In all conditions, mean correlation coefficients of the exponential regression and ∼70% of values in each rat were >0.99, demonstrating the model validity. In all conditions τ and C exhibited a large spontaneous variability over time, and beat-to-beat correlations were high between τ and C (0.83 ± 0.03). C was increased by sodium nitroprusside, decreased by isoprenaline, but not significantly decreased by phenylephrine [5.1 ± 0.2, 3.2 ± 0.3, and 3.9 ± 0.2 μl/mmHg, respectively, vs. 4.2 ± 0.3 μl/mmHg (baseline)]. In conclusion, the windkessel model enables τ and C to be reliably estimated in conscious rats during spontaneous and drug-induced hemodynamic variations.

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Liu, Shing-Hong, Da-Chuan Cheng, and Jia-Jung Wang. "ESTIMATING THE MEAN BLOOD FLOW OF ARM BASED ON WINDKESSEL MODEL." Biomedical Engineering: Applications, Basis and Communications 23, no. 05 (October 2011): 349–56. http://dx.doi.org/10.4015/s101623721100275x.

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The blood flow is always used to evaluate the arterial obstruction or arteriosclerosis. The echo-method is the standard. In this study, we propose a new method for assessing the total mean blood flow of the arm using a known brachial arterial compliance and based on a two-element Windkessel (WK) model, in which the arterial hemodynamics consists of a peripheral arterial resistor and a peripheral arterial capacitor in parallel. The known compliance of the brachial artery belonging to a local and relative amount has been estimated from the pattern of the oscillometric waveform in our previous study. An estimating peripheral arterial compliance and resistance are got from the known compliance. The governing equation of the two-element WK model is then used to get the blood flow waveform. The accuracy of WK-based mean blood flow (FWK) is validated by comparing it with the mean blood flow (Fecho) estimated by an echo-based method in the brachial arteries of 32 subjects. The results showed that the values of FWKand Fechowere significantly correlated (r = 0.671). This suggests that a total mean blood flow can be evaluated by the known arterial compliances derived by regional or relative changed measurements.

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Tsanas, Athanasios, John Y. Goulermas, Vassiliki Vartela, Dimitrios Tsiapras, Georgios Theodorakis, Antony C. Fisher, and Petros Sfirakis. "The Windkessel model revisited: A qualitative analysis of the circulatory system." Medical Engineering & Physics 31, no. 5 (June 2009): 581–88. http://dx.doi.org/10.1016/j.medengphy.2008.11.010.

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Karamanoglu, M., and M. P. Feneley. "Derivation of the ascending aortic-carotid pressure transfer function with an arterial model." American Journal of Physiology-Heart and Circulatory Physiology 271, no. 6 (December 1, 1996): H2399—H2404. http://dx.doi.org/10.1152/ajpheart.1996.271.6.h2399.

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To devise a method of deriving the ascending aortic pressure waveform from the noninvasively determined carotid arterial waveform, ascending aortic and carotid arterial pressures were recorded in 13 patients aged 58.5 +/- 10.0 (SD) yr. A single viscoelastic tube terminated with a modified windkessel was used to model the carotid arterial system. For each patient the model parameters, characteristic impedance of the tube (Z0), reflection coefficient at the termination (gamma), and time constant of the windkessel (tau), were estimated by minimizing the root-mean-square error between the measured and predicted carotid waveforms, with the ascending aortic pressure waveform as input. The resulting arterial parameters were realistic: Z0 = 729.5 +/- 246.8 dyn.s.cm-3, gamma = 0.75 +/- 0.19, and tau = 0.16 +/- 0.17 s. A generalized model constructed with these mean parameters yielded a smaller error between predicted and measured carotid arterial pressures (3.4 +/- 1.3 mmHg) than between ascending aortic pressure and measured carotid arterial pressure (4.4 +/- 1.6 mmHg, P < 0.01) and also reproduced the carotid wave contour indexed by the ratio of late systolic to early systolic peak amplitude: predicted = 1.26 +/- 0.05 and measured = 1.24 +/- 0.16 vs. aortic = 1.55 +/- 0.19.

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Quick, Christopher M., David S. Berger, and Abraham Noordergraaf. "Apparent arterial compliance." American Journal of Physiology-Heart and Circulatory Physiology 274, no. 4 (April 1, 1998): H1393—H1403. http://dx.doi.org/10.1152/ajpheart.1998.274.4.h1393.

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Recently, there has been renewed interest in estimating total arterial compliance. Because it cannot be measured directly, a lumped model is usually applied to derive compliance from aortic pressure and flow. The archetypical model, the classical two-element windkessel, assumes 1) system linearity and 2) infinite pulse wave velocity. To generalize this model, investigators have added more elements and have incorporated nonlinearities. A different approach is taken here. It is assumed that the arterial system 1) is linear and 2) has finite pulse wave velocity. In doing so, the windkessel is generalized by describing compliance as a complex function of frequency that relates input pressure to volume stored. By applying transmission theory, this relationship is shown to be a function of heart rate, peripheral resistance, and pulse wave reflection. Because this pressure-volume relationship is generally not equal to total arterial compliance, it is termed “apparent compliance.” This new concept forms the natural counterpart to the established concept of apparent pulse wave velocity.

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Lankhaar, Jan-Willem, Nico Westerhof, Theo J. C. Faes, Koen M. J. Marques, J. Tim Marcus, Piet E. Postmus, and Anton Vonk-Noordegraaf. "Quantification of right ventricular afterload in patients with and without pulmonary hypertension." American Journal of Physiology-Heart and Circulatory Physiology 291, no. 4 (October 2006): H1731—H1737. http://dx.doi.org/10.1152/ajpheart.00336.2006.

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Right ventricular (RV) afterload is commonly defined as pulmonary vascular resistance, but this does not reflect the afterload to pulsatile flow. The purpose of this study was to quantify RV afterload more completely in patients with and without pulmonary hypertension (PH) using a three-element windkessel model. The model consists of peripheral resistance ( R), pulmonary arterial compliance ( C), and characteristic impedance ( Z). Using pulmonary artery pressure from right-heart catheterization and pulmonary artery flow from MRI velocity quantification, we estimated the windkessel parameters in patients with chronic thromboembolic PH (CTEPH; n = 10) and idiopathic pulmonary arterial hypertension (IPAH; n = 9). Patients suspected of PH but in whom PH was not found served as controls (NONPH; n = 10). R and Z were significantly lower and C significantly higher in the NONPH group than in both the CTEPH and IPAH groups ( P < 0.001). R and Z were significantly lower in the CTEPH group than in the IPAH group ( P < 0.05). The parameters R and C of all patients obeyed the relationship C = 0.75/ R ( R2 = 0.77), equivalent to a similar RC time in all patients. Mean pulmonary artery pressure P and C fitted well to C = 69.7/P (i.e., similar pressure dependence in all patients). Our results show that differences in RV afterload among groups with different forms of PH can be quantified with a windkessel model. Furthermore, the data suggest that the RC time and the elastic properties of the large pulmonary arteries remain unchanged in PH.

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Kind, Taco, Theo J. C. Faes, Jan-Willem Lankhaar, Anton Vonk-Noordegraaf, and Michel Verhaegen. "Estimation of Three- and Four-Element Windkessel Parameters Using Subspace Model Identification." IEEE Transactions on Biomedical Engineering 57, no. 7 (July 2010): 1531–38. http://dx.doi.org/10.1109/tbme.2010.2041351.

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Huppert, Theodore J., Monica S. Allen, Solomon G. Diamond, and David A. Boas. "Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model." Human Brain Mapping 30, no. 5 (May 2009): 1548–67. http://dx.doi.org/10.1002/hbm.20628.

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Manning, Timothy S., Barbara E. Shykoff, and Joseph L. Izzo. "Validity and Reliability of Diastolic Pulse Contour Analysis (Windkessel Model) in Humans." Hypertension 39, no. 5 (May 2002): 963–68. http://dx.doi.org/10.1161/01.hyp.0000016920.96457.7c.

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Cappello, Angelo, Gianni Gnudi, and Claudio Lamberti. "Identification of the three-element windkessel model incorporating a pressure-dependent compliance." Annals of Biomedical Engineering 23, no. 2 (March 1995): 164–77. http://dx.doi.org/10.1007/bf02368323.

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Mandeville, Joseph B., John J. A. Marota, C. Ayata, Greg Zaharchuk, Michael A. Moskowitz, Bruce R. Rosen, and Robert M. Weisskoff. "Evidence of a Cerebrovascular Postarteriole Windkessel with Delayed Compliance." Journal of Cerebral Blood Flow & Metabolism 19, no. 6 (June 1999): 679–89. http://dx.doi.org/10.1097/00004647-199906000-00012.

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A pronounced temporal mismatch was observed between the responses of relative cerebral blood volume (rCBV) measured by magnetic resonance imaging and relative cerebral blood flow measured by laser—Doppler flowmetry in rat somatosensory cortex after electrical forepaw stimulation, The increase of relative cerebral blood flow after stimulus onset and decrease after stimulus cessation were accurately described with a single exponential time constant of 2.4 ± 0.8 seconds. In contrast, rCBV exhibited two distinct and nearly sequential processes after both onset and cessation of stimulation. A rapid change of rCBV (1.5 ± 0.8 seconds) occurring immediately after onset and cessation was not statistically different from the time constant for relative cerebral blood flow. However, a slow phase of increase (onset) and decrease (cessation) with an exponential time constant of 14 ± 13 seconds began approximately 8 seconds after the rapid phase of CBV change. A modified windkessel model was developed to describe the temporal evolution of rCBV as a rapid elastic response of capillaries and veins followed by slow venous relaxation of stress. Venous delayed compliance was suggested as the mechanism for the poststimulus undershoot in blood oxygen-sensitive magnetic resonance imaging signal that has been observed in this animal model and in human data.

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Wang, Jiun-Jr, Aoife B. O'Brien, Nigel G. Shrive, Kim H. Parker, and John V. Tyberg. "Time-domain representation of ventricular-arterial coupling as a windkessel and wave system." American Journal of Physiology-Heart and Circulatory Physiology 284, no. 4 (April 1, 2003): H1358—H1368. http://dx.doi.org/10.1152/ajpheart.00175.2002.

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The differences in shape between central aortic pressure (PAo) and flow waveforms have never been explained satisfactorily in that the assumed explanation (substantial reflected waves during diastole) remains controversial. As an alternative to the widely accepted frequency-domain model of arterial hemodynamics, we propose a functional, time-domain, arterial model that combines a blood conducting system and a reservoir (i.e., Frank's hydraulic integrator, the windkessel). In 15 anesthetized dogs, we measured PAo, flows, and dimensions and calculated windkessel pressure (PWk) and volume (VWk). We found that PWk is proportional to thoracic aortic volume and that the volume of the thoracic aorta comprises 45.1 ± 2.0% (mean ± SE) of the total VWk. When we subtracted PWk from PAo, we found that the difference (excess pressure) was proportional to aortic flow, thus resolving the differences between PAo and flow waveforms and implying that reflected waves were minimal. We suggest that PAo is the instantaneous summation of a time-varying reservoir pressure (i.e., PWk) and the effects of (primarily) forward-traveling waves in this animal model.

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Arai, Tatsuya, Kichang Lee, Robert P. Marini, and Richard J. Cohen. "Estimation of changes in instantaneous aortic blood flow by the analysis of arterial blood pressure." Journal of Applied Physiology 112, no. 11 (June 1, 2012): 1832–38. http://dx.doi.org/10.1152/japplphysiol.01565.2011.

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The purpose of this study was to introduce and validate a new algorithm to estimate instantaneous aortic blood flow (ABF) by mathematical analysis of arterial blood pressure (ABP) waveforms. The algorithm is based on an autoregressive with exogenous input (ARX) model. We applied this algorithm to diastolic ABP waveforms to estimate the autoregressive model coefficients by requiring the estimated diastolic flow to be zero. The algorithm incorporating the coefficients was then applied to the entire ABP signal to estimate ABF. The algorithm was applied to six Yorkshire swine data sets over a wide range of physiological conditions for validation. Quantitative measures of waveform shape (standard deviation, skewness, and kurtosis), as well as stroke volume and cardiac output from the estimated ABF, were computed. Values of these measures were compared with those obtained from ABF waveforms recorded using a Transonic aortic flow probe placed around the aortic root. The estimation errors were compared with those obtained using a windkessel model. The ARX model algorithm achieved significantly lower errors in the waveform measures, stroke volume, and cardiac output than those obtained using the windkessel model ( P < 0.05).

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Burattini, Roberto, and Paola Oriana Di Salvia. "Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models." Journal of Applied Physiology 103, no. 1 (July 2007): 66–79. http://dx.doi.org/10.1152/japplphysiol.00664.2006.

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Aortic impedance data of infants, children and adults (age range 0.8–54 yr), previously reported by others, were interpreted by means of three alternative four-element windkessel models: W4P, W4S, and IVW. The W4P and W4S are derived from the three-element windkessel (W3) by connecting an inertance ( L) in parallel or in series, respectively, with the aortic characteristic resistance ( Rc). In the IVW, L is connected in series with a viscoelastic windkessel (VW). The W4S and IVW (same input impedance) fit the data best. The W4S, however, suffers from the assumption that Rc is part of total peripheral resistance ( Rp). The IVW model offers a new paradigm for interpretation of resistive properties in terms of viscous ( Rd) properties of vessel wall motion, distinguished from Rp. Results indicated that rapid reduction of Rd/ Rp during early development is functional to modulation of decay time constant (τd) of pressure in diastole, such that normalization over heart period (τd/T) is independent of body size. Estimates of total arterial compliance ( C) vs. age were fitted by a bell-shaped curve with a maximum at 33 yr. With body weight (BW) factored out by normalization, the C/BW data scattered about a bell-shaped curve centered at 66 mmHg. Inertance was significantly higher in pediatric patients than in adults, in accordance with a lower cross-sectional area of the vasculature, commensurate to a lower aortic flow. Changes of arterial properties appear functional to control the ratio of pulsatile power to active power and keep arterial efficiency as high as 97% in infants and children.

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Kotani, Kiyoshi, Fumiaki Iida, Yutaro Ogawa, Kiyoshi Takamasu, and Yasuhiko Jimbo. "Evaluation of the Circulatory Dynamics by using the Windkessel Model in Different Body Positions." IEEJ Transactions on Electronics, Information and Systems 131, no. 1 (2011): 140–45. http://dx.doi.org/10.1541/ieejeiss.131.140.

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Pochet, Th, P. Gerard, J. M. Marnette, V. D'orio, R. Marcelle, M. Fatemi, A. Fossion, and J. Juchmes. "Identification of three-element windkessel model: Comparison of time and frequency domain techniques." Archives Internationales de Physiologie, de Biochimie et de Biophysique 100, no. 3 (January 1992): 295–301. http://dx.doi.org/10.3109/13813459208998118.

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Zheng, Ying, and John Mayhew. "A time-invariant visco-elastic windkessel model relating blood flow and blood volume." NeuroImage 47, no. 4 (October 2009): 1371–80. http://dx.doi.org/10.1016/j.neuroimage.2009.04.022.

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Jana, Biswabandhu, Kamal Oswal, Sankar Mitra, Goutam Saha, and Swapna Banerjee. "Windkessel Model-Based Cuffless Blood Pressure Estimation Using Continuous Wave Doppler Ultrasound System." IEEE Sensors Journal 20, no. 17 (September 1, 2020): 9989–99. http://dx.doi.org/10.1109/jsen.2020.2990648.

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Segers, Patrick, Serge Brimioulle, Nikos Stergiopulos, Nico Westerhof, Robert Naeije, Marco Maggiorini, and Pascal Verdonck. "Pulmonary arterial compliance in dogs and pigs: the three-element windkessel model revisited." American Journal of Physiology-Heart and Circulatory Physiology 277, no. 2 (August 1, 1999): H725—H731. http://dx.doi.org/10.1152/ajpheart.1999.277.2.h725.

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In six dogs and six weight-matched miniature pigs at baseline and after pulmonary embolization, pulmonary arterial compliance was determined using the pulse pressure method (CPPM), the three-element windkessel model (CWK-3), and the ratio of stroke volume to pulse pressure (SV/PP). CPPM was lower in pigs than in dogs at baseline (0.72 ± 0.23 vs. 1.14 ± 0.29 ml/mmHg, P < 0.05) and after embolism (0.37 ± 0.14 vs. 0.54 ± 0.16 ml/mmHg, P = 0.07) at matched flow, but not at matched flow and pressure. CPPM showed the expected inverse relation with pressure and a direct relation with flow. CWK-3 was closely correlated with CPPM, except for all dogs at baseline where CWK-3 was up to 100% higher than CPPM. Excluding these data, regression analysis yielded CWK-3 = −0.01 + 1.30 ⋅ CPPM( r 2 = 0.97). CWK-3 was found to be unreliable when input impedance first harmonic modulus was close to characteristic impedance, i.e., when reflections were small. SV/PP correlated well with CPPM (SV/PP = −0.10 + 1.76 ⋅ CPPM, r 2 = 0.89). We conclude that 1) CPPM is a consistent estimate of pulmonary arterial compliance in pigs and dogs, 2) CWK-3 and SV/PP overestimate compliance, and 3) CWK-3 is unreliable when wave reflections are small.

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Bahloul, Mohamed A., and Taous-Meriem Laleg-Kirati. "Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance." IEEE Open Journal of Engineering in Medicine and Biology 1 (2020): 123–32. http://dx.doi.org/10.1109/ojemb.2020.2988179.

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Kuchumov, Alex. "Biomechanical modelling of bile flow in the biliary system." MATEC Web of Conferences 145 (2018): 04004. http://dx.doi.org/10.1051/matecconf/201814504004.

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The biliary system consists of the biliary tree, gallbladder and major duodenal papilla. Soft tissues compliance plays important role in the bio-fluids transport. Particularly, bile flow disturbances due to bile duct wall motor function changes in the extra-hepatic ducts, from medicine point of view are called dyscinesia of biliary tract. Fluid motion in the elastic and compliant ducts can be described by different models (for example, Windkessel model, peristaltic fluid motion, FSI algorithm). Our approach is decomposition of the biliary system into three compartments (extra-hepatic biliary tree, gallbladder, major duodenal papilla). Bile flow in the extra-hepatic ducts is simulated using FSI algorithm. Bile flow in the gallbladder can be described as flow in the reservoir with compliant ducts using Windkessel model. Bile flow in the major duodenal papilla is considered as peristaltic fluid motion, because the wall contraction is really important factor of fluid motion in that segment. The coupling of these compartments is performed by boundary conditions. The biliary system geometry was obtained using MRI patient-specific data. It was confirmed that normal bile can be modeled as Newtonian fluid and lithogenic bile can be modeled as non-Newtonian fluid (Carreau fluid). Bile ducts were modeled as hyperelastic material.

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Hamalainen, J. J., and R. P. Hamalainen. "Energy cost minimization in left ventricular ejection: an optimal control model." Journal of Applied Physiology 61, no. 5 (November 1, 1986): 1972–79. http://dx.doi.org/10.1152/jappl.1986.61.5.1972.

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A new optimization model for explaining the observed left ventricular ejection patterns is presented. In the system model, arterial load is described by a modified windkessel load. The ejection pattern for a given cardiac output with fixed stroke volume and duration of ejection is predicted by minimizing a criterion that describes the total ventricular O2 consumption. The ejection patterns of the model closely resemble the observed ejection patterns. Also, the model predictions for changes in the values of the system parameters are qualitatively correct. The results strongly suggest that the control of ejection pattern satisfies the principle of energy cost minimization.

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Slife, D. M., R. D. Latham, P. Sipkema, and N. Westerhof. "Pulmonary arterial compliance at rest and exercise in normal humans." American Journal of Physiology-Heart and Circulatory Physiology 258, no. 6 (June 1, 1990): H1823—H1828. http://dx.doi.org/10.1152/ajpheart.1990.258.6.h1823.

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We evaluated the feasibility of determining pulmonary arterial compliance (Cp) by a parameter estimation procedure based on the three-element windkessel model. Eight normal patients studied with multisensor micromanometry technology had simultaneous rest and exercise pulmonary artery pressures (PAP) and flows recorded. These were submitted to the model and independent methods to determine Cp, pulmonary characteristic impedance (Zc), and pulmonary vascular resistance (PVR). Significant changes in heart rate, PAP, and stroke volume (P less than 0.05) occurred with exercise. In comparing rest and exercise Zc and PVR values determined by the model and independent methods, and in comparing each method for these values, there was no significant difference. Model-derived and independently derived estimates of Cp were significantly different at rest (P less than 0.04) and exercise (P less than 0.001). There was no significant difference between rest and exercise values of Cp by either method. The model estimates of PVR at rest (64 +/- 11 dyn.s.cm-5) and exercise (41 +/- 7 dyn.s.cm-5) (P = 0.06) and the model Zc value at rest (22 +/- 3 dyn.s.cm5) were appropriate. The model Cp values at rest (0.22 +/- 0.05 ml.mmHg-1.kg-1) correlated with previously reported normalized values in other species. This study reports the successful use of a parameter estimation procedure based on the three-element windkessel model to describe pulmonary artery compliance in normal humans.

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Mohiuddin, Mohammad W., Ryan J. Rihani, Glen A. Laine, and Christopher M. Quick. "Increasing pulse wave velocity in a realistic cardiovascular model does not increase pulse pressure with age." American Journal of Physiology-Heart and Circulatory Physiology 303, no. 1 (July 1, 2012): H116—H125. http://dx.doi.org/10.1152/ajpheart.00801.2011.

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The mechanism of the well-documented increase in aortic pulse pressure (PP) with age is disputed. Investigators assuming a classical windkessel model believe that increases in PP arise from decreases in total arterial compliance ( Ctot) and increases in total peripheral resistance ( Rtot) with age. Investigators assuming a more sophisticated pulse transmission model believe PP rises because increases in pulse wave velocity ( cph) make the reflected pressure wave arrive earlier, augmenting systolic pressure. It has recently been shown, however, that increases in cph do not have a commensurate effect on the timing of the reflected wave. We therefore used a validated, large-scale, human arterial system model that includes realistic pulse wave transmission to determine whether increases in cph cause increased PP with age. First, we made the realistic arterial system model age dependent by altering cardiac output (CO), Rtot, Ctot, and cph to mimic the reported changes in these parameters from age 30 to 70. Then, cph was theoretically maintained constant, while Ctot, Rtot, and CO were altered. The predicted increase in PP with age was similar to the observed increase in PP. In a complementary approach, Ctot, Rtot, and CO were theoretically maintained constant, and cph was increased. The predicted increase in PP was negligible. We found that increases in cph have a limited effect on the timing of the reflected wave but cause the system to degenerate into a windkessel. Changes in PP can therefore be attributed to a decrease in Ctot.

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Barbe, Kurt, Wendy Van Moer, and Danny Schoors. "Analyzing the Windkessel Model as a Potential Candidate for Correcting Oscillometric Blood-Pressure Measurements." IEEE Transactions on Instrumentation and Measurement 61, no. 2 (February 2012): 411–18. http://dx.doi.org/10.1109/tim.2011.2161933.

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Kamoi, Shun, Dougie Squire, James Revie, Christopher Pretty, Paul Docherty, Yeong Shiong Chiew, Thomas Desaive, Geoffrey M. Shaw, and J. Geoffrey Chase. "Accuracy of Stroke Volume Estimation via Reservoir Pressure Concept and Three Element Windkessel Model." IFAC Proceedings Volumes 47, no. 3 (2014): 5647–52. http://dx.doi.org/10.3182/20140824-6-za-1003.01104.

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Absi, Rafik, Stéphane Marchandon, and Rachid Bennacer. "Thermal-electrical analogy and inertia for thermal performance of building envelops." MATEC Web of Conferences 330 (2020): 01037. http://dx.doi.org/10.1051/matecconf/202033001037.

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For transient thermal performance of building envelops adequate parameters are needed to capture the time lag and decrement factor. It is surprising that, in the formal electrical analogy, "inertia" is not represented by same components in fluid mechanics and heat transfer. In Windkessel model for fluid flow in elastic tubes, the fluid inertia is represented by an electrical inductance while in thermal-electric analogy, thermal inertia is given by a capacitance. Some authors argued that the terminology of ''thermal inertia'' is used incorrectly in the literature. The aim of our communication is to provide some clarification about this controversy. We will show that the thermal effusivity which is the geometric mean of thermal conductivity and volumetric heat capacity plays the role of a "thermal mass". The revisited notion of inertia in mechanics will allow to show the analogy between: mechanical inertia (mass), thermal effusivity and electrical inductance. The three parameters show a tendency to keep invariant a certain physical quantity: velocity, temperature and current intensity respectively. However, the analogy is not complete, the capacitance used in the heat transfer seems to be similar to the one used in the Windkessel model which accounts for tube compliance and therefore to a local storage.

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Marx, Laura, Matthias A. F. Gsell, Armin Rund, Federica Caforio, Anton J. Prassl, Gabor Toth-Gayor, Titus Kuehne, Christoph M. Augustin, and Gernot Plank. "Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2173 (May 25, 2020): 20190342. http://dx.doi.org/10.1098/rsta.2019.0342.

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Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global–local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

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44

Diourté, Badié, Jean-Philippe Siché, Vincent Comparat, Jean-Philippe Baguet, and Jean-Michel Mallion. "Study of arterial blood pressure by a Windkessel-type model: influence of arterial functional properties." Computer Methods and Programs in Biomedicine 60, no. 1 (July 1999): 11–22. http://dx.doi.org/10.1016/s0169-2607(99)00002-4.

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Gostuski, Vladimir, Ignacio Pastore, Gaspar Rodriguez Palacios, Gustavo Vaca Diez, H. Marcela Moscoso-Vasquez, and Marcelo Risk. "Time Domain Estimation of Arterial Parameters using the Windkessel Model and the Monte Carlo Method." Journal of Physics: Conference Series 705 (April 2016): 012028. http://dx.doi.org/10.1088/1742-6596/705/1/012028.

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Hametner, B., S. Wassertheurer, J. Kropf, C. Mayer, B. Eber, and T. Weber. "4.2 WINDKESSEL-MODEL DERIVED RESERVOIR AND EXCESS PRESSURES PREDICT CARDIOVASCULAR EVENTS IN HIGH-RISK PATIENTS." Artery Research 6, no. 4 (2012): 147. http://dx.doi.org/10.1016/j.artres.2012.09.026.

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Hettrick, Douglas A., Paul S. Pagel, and David C. Warltier. "Differential Effects of Isoflurane and Halothane on Aortic Input Impedance Quantified Using a Three-element Windkessel Model." Anesthesiology 83, no. 2 (August 1, 1995): 361–73. http://dx.doi.org/10.1097/00000542-199508000-00017.

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Background Systemic vascular resistance (the ratio of mean aortic pressure [AP] and mean aortic blood flow [AQ]) does not completely describe left ventricular (LV) afterload because of the phasic nature of pressure and blood flow. Aortic input impedance (Zin) is an established experimental description of LV afterload that incorporates the frequency-dependent characteristics and viscoelastic properties of the arterial system. Zin is most often interpreted through an analytical model known as the three-element Windkessel. This investigation examined the effects of isoflurane, halothane, and sodium nitroprusside (SNP) on Zin. Changes in Zin were quantified using three variables derived from the Windkessel: characteristic aortic impedance (Zc), total arterial compliance (C), and total arterial resistance (R). Methods Sixteen experiments were conducted in eight dogs chronically instrumented for measurement of AP, LV pressure, maximum rate of change in left ventricular pressure, subendocardial segment length, and AQ. AP and AQ waveforms were recorded in the conscious state and after 30 min equilibration at 1.25, 1.5, and 1.75 minimum alveolar concentration (MAC) isoflurane and halothane. Zin spectra were obtained by power spectral analysis of AP and AQ waveforms and corrected for the phase responses of the transducers. Zc and R were calculated as the mean of Zin between 2 and 15 Hz and the difference between Zin at zero frequency and Zc, respectively. C was determined using the formula C = (Ad.MAP).[MAQ.(Pes-Ped)]-1, where Ad = diastolic AP area; MAP and MAQ = mean AP and mean AQ, respectively; and Pes and Ped = end-systolic and end-diastolic AP, respectively. Parameters describing the net site and magnitude of arterial wave reflection were also calculated from Zin. Eight additional dogs were studied in the conscious state before and after 15 min equilibration at three equihypotensive infusions of SNP. Results Isoflurane decreased R (3,205 +/- 315 during control to 2,340 +/- 2.19 dyn.s.cm-5 during 1.75 MAC) and increased C(0.55 +/- 0.02 during control to 0.73 +/- 0.06 ml.mmHg-1 during 1.75 MAC) in a dose-related manner. Isoflurane also increased Zc at the highest dose. Halothane increased C and Zc but did not change R. Equihypotensive doses of SNP decreased R and produced marked increases in C without changing Zc. No changes in the net site or the magnitude of arterial wave reflection were observed with isoflurane and halothane, in contrast to the findings with SNP. Conclusions The major difference between the effects of isoflurane and halothane on LV afterload derived from the Windkessel model of Zin was related to R, a property of arteriolar resistance vessels, and not to Zc or C, the mechanical characteristics of the aorta. No changes in arterial wave reflection patterns determined from Zin spectra occurred with isoflurane and halothane. These results indicate that isoflurane and halothane have no effect on frequency-dependent arterial properties.

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SHADWICK, R. E., and E. K. NILSSON. "The Importance of Vascular Elasticity in the Circulatory System of the Cephalopod Octopus Vulgaris." Journal of Experimental Biology 152, no. 1 (September 1, 1990): 471–84. http://dx.doi.org/10.1242/jeb.152.1.471.

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The passive mechanical properties of the dorsal aorta and the vena cava of Octopus vulgaris were investigated in vitro. Both vessels are highly distensible structures that exhibit non-linear elasticity, but have substantially different material properties. The volume compliance of each vessel is maximal within the resting physiological pressure range (2–3 kPa in the aorta and 0–0.5 kPa in the vena cava) but is five times greater in the vena cava than in the aorta. The aorta is mechanically suited to function as an elastic storage reservoir in the arterial circulation, while the vena cava is appropriately designed to be a low-pressure capacitance element. Pressure wave velocity in the aorta was calculated from the elastic modulus to be 1.8 ms−1 under resting conditions. Therefore, pressure changes will occur almost simultaneously throughout the arterial tree and pressure wave transmission properties can be described by a two-element Windkessel model. Predictions of vascular impedance amplitude made from this model are presented. The effectiveness of the aorta as an elastic reservoir appears to be severely reduced during exercise in Octopus. Because blood pressure increases while heart rate does not, the efficiency of the Windkessel will be diminished as the time constant of the system decreases and the pulsatile work of the heart subsequently increases. Note: Address for reprint requests.

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Kim, Joon Yeong, Sung Min Kang, and Sung Wook Choi. "Cardiovascular Hemodynamic States Supported by a Counter-pulsation Controlled Pulsatile Ventricular Assist Device During Arterial Fibrillation by Using Windkessel Model." Transactions of the Korean Society of Mechanical Engineers - B 42, no. 6 (June 30, 2018): 395–403. http://dx.doi.org/10.3795/ksme-b.2018.42.6.395.

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Liu, Z. R., F. Shen, and F. C. Yin. "Impedance of arterial system simulated by viscoelastic t tubes terminated in windkessels." American Journal of Physiology-Heart and Circulatory Physiology 256, no. 4 (April 1, 1989): H1087—H1099. http://dx.doi.org/10.1152/ajpheart.1989.256.4.h1087.

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An improved asymmetric t-tube model of the arterial system is proposed. The model consists of two viscoelastic tubes of differing lengths, each terminated in a modified windkessel with inductance as well as resistance and compliance. Equations for calculating the input impedance of this model are presented. Using typical data from the literature, the model predicts a more realistic impedance modulus and phase than previous models of the circulation. Parametric analysis shows that when peripheral compliances are altered, sharp peaks in the very low frequency portions of the impedance spectra are produced, whereas alterations of either the characteristic impedances or inductances of the terminations have little effect on input impedance. Alteration of the elasticity or relative lengths of the tubes results in shifts in the positions of the maxima and minima akin to those observed experimentally. Change in the viscosity of the walls or of the blood only affects the fluctuations of the impedance spectra without affecting the positions of the maxima and minima. Thus, with this still simple model, very realistic impedance spectra are obtainable. The model provides more insight than previously proposed models into the individual influence of various parameters of the proximal and peripheral vasculature on central hemodynamics.

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Journal articles on the topic 'Windkessel model'

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