Two-Element Fractional-Order Windkessel Model to Assess the Arterial Input Impedance

2019 ◽  
Author(s):  
Mohamed A. Bahloul ◽  
Taous-Meriem Laleg Kirati
Keyword(s):  
Fractional Order ◽  
Input Impedance ◽  
Windkessel Model

A Hybrid Mock Circulatory System: Development and Testing of an Electro-hydraulic Impedance Simulator

2003 ◽  
Vol 26 (1) ◽  
pp. 53-63 ◽  
Author(s):  
M. Kozarski ◽  
G. Ferrari ◽  
F. Clemente ◽  
K. Górczyńska ◽  
C. De Lazzari ◽  
...  
Keyword(s):  
Input Impedance ◽  
Numerical Models ◽  
Peripheral Resistance ◽  
Left Ventricular ◽  
Physical Models ◽  
Gear Pump ◽  
Arterial Tree ◽  
Windkessel Model ◽  
Mock Circulatory System ◽  
Hydraulic Impedance

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).

Differential Effects of Isoflurane and Halothane on Aortic Input Impedance Quantified Using a Three-element Windkessel Model

1995 ◽  
Vol 83 (2) ◽  
pp. 361-373. ◽  
Author(s):  
Douglas A. Hettrick ◽  
Paul S. Pagel ◽  
David C. Warltier
Keyword(s):  
Blood Flow ◽  
Input Impedance ◽  
Wave Reflection ◽  
Conscious State ◽  
Left Ventricular ◽  
Arterial System ◽  
Windkessel Model ◽  
Frequency Dependent ◽  
Aortic Input Impedance ◽  
Arterial Wave Reflection

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.

scholarly journals Fractional-Order Models for the Input Impedance of the Respiratory System

10.5772/7472 ◽  
2009 ◽  
Author(s):  
Clara Ionescu ◽  
Robin De ◽  
Kristine Desager ◽  
Eric Derom
Keyword(s):  
Fractional Order ◽  
Respiratory System ◽  
Input Impedance

Conductance catheter-based assessment of arterial input impedance, arterial function, and ventricular-vascular interaction in mice

2005 ◽  
Vol 288 (3) ◽  
pp. H1157-H1164 ◽  
Author(s):  
Patrick Segers ◽  
Dimitrios Georgakopoulos ◽  
Marina Afanasyeva ◽  
Hunter C. Champion ◽  
Daniel P. Judge ◽  
...  
Keyword(s):  
Input Impedance ◽  
Augmentation Index ◽  
Characteristic Impedance ◽  
Systolic Pressure ◽  
Numerical Differentiation ◽  
Left Ventricular ◽  
Conductance Catheter ◽  
Windkessel Model ◽  
Arterial Elastance ◽  
Arterial Function

Global assessment of both cardiac and arterial function is important for a meaningful interpretation of pathophysiological changes in animal models of cardiovascular disease. We simultaneously acquired left ventricular (LV) and aortic pressure and LV volume (VLV) in 17 open-chest anesthetized mice (26.7 ± 3.2g) during steady-state (BL) and caval vein occlusion (VCO) using a 1.4-Fr dual-pressure conductance catheter and in a subgroup of eight animals during aortic occlusion (AOO). Aortic flow was obtained from numerical differentiation of VLV. AOO increased input impedance ( Zin) for the first two harmonics, increased characteristic impedance (0.025 ± 0.007 to 0.040 ± 0.011 mmHg·μl−1·s, P < 0.05), and shifted the minimum in Zin from the third to the sixth harmonic. For all conditions, the Zin could be well represented by a four-element windkessel model. The augmentation index increased from 116.7 ± 7.8% to 145.9 ± 19.5% ( P < 0.01) as well as estimated pulse-wave velocity (3.50 ± 0.94 to 5.95 ± 1.62 m/s, P < 0.05) and arterial elastance ( Ea, 4.46 ± 1.62 to 6.02 ± 1.43 mmHg/μl, P < 0.01). AOO altered the maximal slope ( Emax, 3.23 ± 1.02 to 5.53 ± 1.53 mmHg/μl, P < 0.05) and intercept (−19.9 ± 8.6 to 1.62 ± 13.51 μl, P < 0.01) of the end-systolic pressure-volume relation but not Ea/ Emax (1.44 ± 0.43 to 1.21 ± 0.37, not significant). We conclude that simultaneous acquisition of Zin and arterial function parameters in the mouse, based solely on conductance catheter measurements, is feasible. We obtained an anticipated response of Zin and arterial function parameters following VCO and AOO, demonstrating the sensitivity of the measuring technique to induced physiological alterations in murine hemodynamics.

Assessment of Windkessel as a model of aortic input impedance

1988 ◽  
Vol 255 (4) ◽  
pp. H742-H753 ◽  
Author(s):  
D. Burkhoff ◽  
J. Alexander ◽  
J. Schipke
Keyword(s):  
Input Impedance ◽  
Impedance Spectrum ◽  
Aortic Pressure ◽  
Stroke Work ◽  
Windkessel Model ◽  
The Real ◽  
Wide Range ◽  
Aortic Input Impedance ◽  
Coupling Variables ◽  
Best Fit

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.

Stroke volume effect of changing arterial input impedance over selected frequency ranges

1985 ◽  
Vol 248 (4) ◽  
pp. H477-H484 ◽  
Author(s):  
K. Sunagawa ◽  
W. L. Maughan ◽  
K. Sagawa
Keyword(s):  
Stroke Volume ◽  
High Frequency ◽  
Input Impedance ◽  
Characteristic Impedance ◽  
Low Frequency ◽  
Volume Effect ◽  
High Frequency Range ◽  
Frequency Range ◽  
Windkessel Model ◽  
End Diastolic Volume

We investigated the effect of changing arterial input impedance over three selected frequency ranges on stroke volume (SV) in nine isolated canine left ventricles. The input impedance was simulated with a three-element Windkessel model (i.e., resistance, characteristic impedance, and compliance) and was imposed on the ventricles with a servo-controlled loading system. Under a constant end-diastolic volume [33.1 +/- 1.5 (SE) ml], we changed the modulus of the afterloaded impedance over a low frequency range (below 0.13 Hz) by changing the resistance, over a transitional frequency range (in which the impedance modulus decreases from total resistance to characteristic impedance) by changing the compliance, and over a high frequency range (above 2.0 Hz) by changing the characteristic impedance. Each of the impedance components was changed from control to 50 and 200% of control. SV sensitively decreased from 16.1 +/- 0.7 to 7.4 +/- 0.5 ml in response to the increase in the low-frequency impedance modulus. SV was relatively insensitive, however, to the same percent increase in the impedance modulus over the transitional frequency range (from 11.2 +/- 0.6 to 12.3 +/- 0.7 ml) and over the high frequency range (from 11.9 +/- 0.6 to 11.6 +/- 0.7 ml). The average relative sensitivities of SV to the increase and decrease in impedance moduli in these frequency ranges were 1.2:0.12:0.04. We conclude that the modulus of impedance in the low frequency range is, by far, a more important determinant of SV than those in the transitional and high frequency ranges.

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