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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 25 (1987), S. 269-276 
    ISSN: 1741-0444
    Keywords: Arterial compliance ; Baroreflex ; Mathematical model ; Negative-feedback control ; Open and closed loop ; Parameter estimation ; Peripheral resistance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract The purpose of this study was to characterise the dynamics of the short-term control of arterial pressure in the cat with the aid of a model consisting of a nonlinear negative-feedback control system. The arterial system was described by a three element windkessel model (peripheral resistance, R, aortic characteristic impedance, Rc, and total arterial compliance, C). The resistance regulation was represented by a second-order system with static gain GR, a damping factor σ and an undamped natural frequency ωn. The resistance gain, GR, and the windkessel parameters were obtained from measurements of aortic and venous pressures and cardiac output in two steady states. The parameters σ and ωn were estimated from mean pressure and mean flow during the transient from control to the new steady state. Pressure reductions averaged 10 per cent and resistance changes averaged 12 per cent. Average windkessel model parameters in the control condition were: C=(25·9±6·1) 10−6 g−1 cm4 s2, Rc=(2·51±0·53) 103 g cm−4 s−1, R=(40·9±9·8) 103 g cm−4 s−1. Average estimates of parameters of the resistance regulator were: GR=(4·14±2·38) 10−3 min ml−1, ωn = 1·0 ± 1·0 rad s−1, σ=0·41±0·19. A satisfactory fit was found between model predicted and measured pressure. The results suggest that the dynamic short-term control of pressure is underdamped and oscillatory. The amplitude of these oscillations is affected by arterial compliance, suggesting an interaction between the arterial system and short-term resistance regulation.
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  • 2
    ISSN: 1741-0444
    Keywords: Cardiac interference ; Digital filter ; Dolph-Chebyshev ; Dynamic lung compliance ; Lung volume ; Transpulmonary pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Description / Table of Contents: Sommaire La conformité dynamique des poumons est une mesure des propriétés élastiques de ceux-ci, dans la gamme de respiration normale, et, est interprétée comme étant la relation entre les changements de pression transpulmonaire et ceux correspondants du volume des poumons. Cette relation est établie comme une anse pression/volume, à partir de laquelle on calcule la conformité comme étant la ligne de descente joignant les extrémités de l'anse. A cause de l'interférence cardiaque qui se superpose aux signaux normaux de volume et de pression, les anses de conformité se trouvent souvent sérieusement déformées, ce qui rend difficile l'établissement des extrémités de l'anse. Par conséquent, il est nécessaire de traiter au préalable les données mesurées afin d'éliminer les pulsations cardiaques superposées. Au cours des recherches décrites dans cet essai, nous avons appliqué des techniques de filtrage digital afin de récupérer les anses de conformité résultant uniquement d'une origine respiratoire. La conception d'un filtre digital, basée sur une technique “d'affichage”, est à l'étude. La méthode est appliquée pour filtrer les données de volume des poumons et de pression pulmonaire, obtenues grâce à des expériences réalisées sur des chats et des nouveaux-nés. On démontre ainsi l'efficacité du filtrage digital à récupérer les anses de conformité qui sont contaminées par la présence de pulsations cardiaques.
    Abstract: Zusammenfassung Die dynamische Lungencompliance ist eine Messung der elastischen Eigenschaften der Lunge im normalen Atembereich und wird als die Beziehung zwischen den transpulmonarischen Druckveränderungen und den korrespondierenden Veränderungen im Lungenvolumen gemessen. Diese Beziehung wird als Druckvolumenschleife dargestellt, aus der die Compliance als Steigung der Linie, die die Endpunkte der Schleife zusammenfügt, kalkuliert wird. Aufgrund der herzbezüglichen Interferenzen, die den normalen Druck und Volumensignalen übergelagert sind, sind die Complianceschleifen oft ernsthaft enstellt, was es sehr schwierig macht, die Endpunkte in der Schleife zu erkennen. Aus diesem Grund ist es erforderlich, die gemessenen Daten so vorzufertigen, daß die übergelagerten Herztöne beseitigt werden. In den in diesem Papier beschriebenen Nachforschungen haben wir eine digitale Filtertechnik zur Wiedergewinnung der Complianceschleifen, die allein aus der Atmung stammen, angewandt. Es wird die Konstruktionsmethode eines auf der “windowing”-Technik basierenden Digitalfilters beschrieben. Die Methode wird zum Filtern von transpulmonaren Druck- und Lungenvolumendaten aus Experimenten mit Katzen und Neugeborenen verwendet.
    Notes: Abstract Dynamic lung compliance is a measure of the elastic properties of the lungs in the normal breathing range and is measured as the relationship between the transpulmonary pressure changes and the corresponding changes in lung volume. This relationship is given as a pressure-volume loop, from which the compliance is calculated as the slope of the line joining the end points of the loop. Owing to cardiac interference, which is superimposed on the normal pressure and volume signals, the compliance loops are often severely distorted, making it difficult to establish the end points in the loop. Therefore it is necessary to preprocess the measured data so that the superimposed cardiac pulsations are eliminated. In the investigations that are described in this paper, we have applied digital filtering techniques to recover compliance loops resulting solely from respiratory origin. The design method of a digital filter based on ‘windowing’ technique is discussed. The method is applied for filtering transpulmonary-pressure and lung-volume data obtained from experiments with cats and neonates. The effectiveness of digital filtering in recovering the compliance loops which are contaminated by the presence of cardiac pulsations is shown.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 18 (1980), S. 133-144 
    ISSN: 1741-0444
    Keywords: Ellipsoidal models ; Laplace's law ; Left ventricular wall force ; Myocardial wall stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract Myocardial wall force per area (=stress) is a major determinant of muscle function and oxygen consumption. It cannot be measured accurately but has to be derived from a mathematical model. Many models have been presented in the literature but a comparison between models has not been available. In this study angiographic data from the literature are used to calculate left ventricular wall force for normal and diseased hearts using a thin-walled spherical model, a thick-walled spherical model and six ellipsoidal models, and the results are compared. There appeared to be large differences between the stresses yielded by the models for the same cardiac geometry. The thick-walled sphere yields circumferential stresses that are approximately 25% lower than the stresses yielded by most of the ellipsoidal models. Of the ellipsoidal models the one suggested by Streeter el al. gives circumferential stresses that are 25% higher than those of the other ellipsoids. Similar differences are found for left ventricular wall stress in the longitudinal direction. However, all models correspond closely in the prediction of the deviation from normal stress in the various pathological states studied. Some of the models give information about the stress distribution over the thickness of the wall as well. We found substantial differences in this predicted stress distribution for models that employ similar assumptions. These differences plus the uncertainties with regard to the properties of the myocardial wall material, that change during the cardiac cycle, call for some scepticism concerning the calculated stress distribution over the wall. The ellipsoidal model suggested by Falsetti et al. is very simple and yields approximately the same mean wall stress values as the more complicated models that we studied. This model therefore appears to be the best choice.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 15 (1987), S. 427-441 
    ISSN: 1573-9686
    Keywords: Parameter estimation ; Model linearization ; Closed-loop gain ; Cardiac pacing ; Baroreflex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Open-loop gain of the short-term systemic pressure regulation was determined under closed-loop conditions in the closed chest anesthetized dog (n=5). For this purpose, cardiac output and mean systemic pressure were varied by ventricular pacing after the production of complete heart block. From the pressure-flow data resistance gain (the ratio of peripheral resistance change to pressure change in the steady state) was obtained by means of a simple model. The value of this gain was automatically estimated by fitting the pressure-flow relation described by the model to the experimental data. The model allows the pressure-flow relation to be straight or curved with or without a zero-flow pressure intercept. The best fit was obtained when the pressure-flow curve was convex to the pressure axis and had no intercept. When the model was linearized about the control values of pressure and flow (operating point), open-loop gain could be calculated from resistance gain. Its averaged value in the control condition, 1.63±0.45, is in agreement with values found by other investigators in open-loop conditions. During vasoconstriction open-loop gain, at the (new) operating point, increased to 2.51±0.51; during vasodilation it decreased to 1.17±0.27. Open-loop gain about an operating point thus can be determined in the intact animal from measurements of mean pressure and mean flow in the steady state.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 17 (1989), S. 309-311 
    ISSN: 1573-9686
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 3 (1975), S. 296-307 
    ISSN: 1573-9686
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The notions of effective length, effective reflection site, and resonance frequency of the arterial system stem from the start of the century. The effective length and effective reflection point describe a system analogous to the arterial tree by a uniform tube with one reflection point. The effective length and related effective reflection site may be obtained from the amplitudes of the various pressure harmonics measured at different locations along the aorta or from the input impedance as a function of frequency. We have studied the concept of effective length in hydraulic models of the systemic arterial tree. A uniform tube with both a frequency-independent load (resistive) and a frequency-dependent load was used. The effective length of a tube with a frequency-independent load is equal to the actual length. In the case of the frequency-dependent load (more resemblance with the arterial tree) the effective length depends on the applied method and is a function of frequency. Therefore, its application for quantitatively computing the stroke volume is doubtful.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 6 (1978), S. 16-32 
    ISSN: 1573-9686
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The pumping ability of the left ventricle may be characterized by a graph relating mean left ventricular pressure with mean left ventricular output. This graph is obtained by making the heart eject against different arterial loads, and measuring the resulting left ventricular pressure and aortic flow. For isolated heart muscle an equivalent relationship can be found. The isolated muscle is made to contract in such a fashion that it seems part of the myocardium, i.e., force relaxation precedes lengthening, just as isometric relaxation of pressure precedes left ventricular filling. Mean force should now be related with mean velocity of shortening. This relationship is a straight line and its slope has the dimension of resistance. We cannot understand such a relationship in terms of resistance in a preparation that changes its characteristics with time during contraction. A attempt is made to elucidate this relationship. The contracting muscle is represented by a time varying compliance. Calculations show that this model exhibits an almost linear relationship between mean force and mean velocity of shortening just as the muscle does. The intercept with the mean force axis (mean isometric force, $$\bar F_{ISO} $$ ) is: $$\bar F_{ISO} $$ , where F a is preload, C max is compliance of the passive muscle, T is repetition period, and C (t) is the instantaneous muscle compliance. The intercept, with the mean velocity axis $$(\bar v_{max} )$$ is: $$\bar v_{max} $$ with C min the minimum value of compliance during the contraction. It is concluded that the straight line relationship found in an isolated heart muscle between mean force and mean velocity of shortening can be explained in terms of a time varying compliance.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 12 (1984), S. 151-162 
    ISSN: 1573-9686
    Keywords: Matching ; Cardiac pump function ; Power ; Apparent source resistance ; Peripheral resistance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We have studied the interrelation of left ventricle and arterial system in the anesthetized open-thorax cat. The ventricle was characterized by its pump function graph, relating mean ventricular pressure ( $$\bar P_{lv}$$ ) and mean aortic flow ( $$\bar F$$ ). The pump function graph was determined by means of an artificial periphery and on a beat-to-beat basis. The periphery was characterized by relating mean aortic pressure ( $$\bar P_{ao}$$ ) and mean flow. Mean aortic and mean left ventricular pressure could be related over a wide range of values by a proportionality factor $$\bar P_{ao} = a \cdot \bar P_{lv}$$ . In a series of five separate experiments a value of a=1.72±0.14 (mean±SD) was found. This simplified relation allows direct comparison of apparent source resistance (i.e., slope of pump function graph), (Rs), and peripheral resistance (Rp). It was also found experimentally that total external power ( $$\bar \dot w$$ ) could be calculated from mean aortic pressure and mean flow as well as from mean left ventricular pressure and mean flow (thus from the pump function graph) by $$\bar \dot w = c \cdot \bar P_{ao} \cdot \bar F = c \cdot a \cdot \bar P_{lv} \cdot \bar F$$ . The value of c=1.16±0.12 (mean±SD, n=4). Maximum external power was predicted for $$R_p /R_s = \bar P_{ao} /\bar P_{lv} = a$$ . In six different cats Rp/Rs ratio in the working point (i.e., mean left ventricular pressure and mean flow when the normal periphery loaded the heart) was found to be Rp/Rs=2.63±0.92. This value could not be shown to differ from that in the point where maximal external power was found, i.e., Rp/Rs=1.81±0.08 (n=6).
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 22 (1994), S. 392-397 
    ISSN: 1573-9686
    Keywords: Windkessel model ; Computer simulation ; Nonlinear arterial system ; Input impedance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We derived and tested a new, simple, and accurate method to estimate the compliance of the entire arterial tree and parts thereof. The method requires the measurements of pressure and flow and is based on fitting the pulse pressure (systolic minus diastolic pressure) predicted by the two-element windkessel model to the measured pulse pressure. We show that the two-element windkessel model accurately describes the modulus of the input impedance at low harmonics (0–4th) of the heart rate so that the gross features of the arterial pressure wave, including pulse pressure, are accounted for. The method was tested using a distributed nonlinear model of the human systemic arterial tree. Pressure and flow were calculated in the ascending aorta, thoracic aorta, common carotid, and iliac artery. In a linear version of the systemic model the estimated compliance was within 1% of the compliance at the first three locations. In the iliac artery an error of 7% was found. In a nonlinear version, we compared the estimates of compliance with the average compliance over the cardiac cycle and the compliance at the mean working pressure. At the first three locations we found the estimated and “actual” compliance to be within 12% of each other. In the iliac artery the error was larger. We also investigated an increase and decrease in heart rate, a decrease in wall elasticity and exercise conditions. In all cases the estimated total arterial compliance was within 10% of mean compliance. Thus, the errors result mainly from the nonlinearity of the arterial system. Segmental compliance can be obtained by subtraction of compliance determined at two locations.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 25 (1987), S. 277-283 
    ISSN: 1741-0444
    Keywords: Arterial compliance ; Baroreflex ; Frequency response ; Linearisation ; Mathematical model ; Negative-feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract The purpose of this study was to investigate the role of the interaction between peripheral resistance regulation and arterial compliance in the overall short-term regulation of mean arterial pressure. A nonlinear model previously proposed was linearised about control values of mean arterial pressure and cardiac output so that it could be reformulated in terms of transfer functions. The resulting pressure to pressure open-loop transfer function H(s) consists of a complex conjugate pair of poles (pertaining to the resistance regulating system) and a real pole (pertaining to the arterial system, 1/(R0 C), R0=control resistance). Such a structure suggests an interaction between the resistance regulation and the arterial compliance (C). Quantitative evaluation of this interaction was obtained by estimating the model parameters during partial vena cava occlusions in four cats. Using these parameters the time response of the open-loop control system to a pressure step was found to be underdamped and oscillatory in all four cats (damping factor ξ ranged from 0·20 to 0·66), the amplitude of oscillations depending on the value of ξ and on the relative amplitude of the arterial time constant (compliance and peripheral resistance) with respect to the time constant 1/(ξωn). Bode diagrams of H(jω) showed that the resonance peak due to the resistance regulating system may not be detectable, either because of the relatively high value of ξ or because it is masked by the pole of the arterial system.
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