Effects of carotid hypotension on aortic hemodynamics in the unanesthetized dog.

The effects of occlusion of the brachiocephalic artery on aortic hemodynamics were assessed in 12 chronically instrumented dogs in the unanesthetized state. Continuous measurements of ascending aorta pressure and flow were made. In the steady state following occlusion, heart rate increased by 36% and mean arterial pressure by 45%, while cardiac output was unchanged from preocclusion levels. Hydraulic power delivery to the systemic circulation by the left ventricle was increased during occlusion, while the fraction of total power associated with pulsations decreased. Values of peripheral resistance and ascending aorta input impedance were both increased during occlusion. Graded occlusions of the brachiocephalic artery produced graded, monotonic increases in the entire aortic impedance spectrum between 2 and 20 Hz with more sensitive responses occurring with the smaller, submaximal responses. Considered with results of previous studies, these results suggest that activation of smooth muscle in large conduit arteries is also associated with the pressor response which accompanies carotid hypotension and that such activation has a hemodynamically significant effect.     

Estimation of arterial compliance in aortic regurgitation: three methods evaluated in pigs

Three methods for measuring arterial compliance when aortic regurgitation is present are examined. The first two methods are based on a Windkessel model composed of two elements, compliance C and resistance R. Arterial compliance was estimated from diastolic pressure waveforms and diastolic regurgitant flow for one method, and from systolic aortic pressure waveforms and systolic flow for the other method. The third method was based on a three-element Windkessel model, composed of characteristic resistance r, compliance C and resistance R. In this method arterial compliance was calculated by adjusting the model to the modulus and phase of the first harmonic term of the aortic input impedance. The three methods were compared and validated in six anaesthetised pigs over a broad range of aortic pressures. The three methods were found to give quantitatively similar estimates of arterial compliance at mean aortic pressures above 60 mm Hg. Below 60 mm Hg, estimates of arterial compliance varied widely, probably because of poor validity of the Windkessel models in the low pressure range.     

Role of total arterial compliance and peripheral resistance in the determination of systolic and diastolic aortic pressure.

The goal of the study was to define the major arterial parameters that determine aortic systolic (Ps) and diastolic (Pd) pressure in the dog. Measured aortic flows were used as input to the two-element windkessel model of the arterial system, with peripheral resistance calculated as mean pressure over mean flow and total arterial compliance calculated from the decay time in diastole. The windkessel model yielded an aortic pressure wave from which we obtained the predicted systolic (Ps, wk) and diastolic (Pd, wk) pressure. These predicted pressures were compared with the measured systolic and diastolic pressures. The measurements and calculations were carried out in 7 dogs in control conditions, during aortic occlusion at four locations (the trifurcation, between trifurcation and diaphragm, the diaphragm and the proximal descending thoracic aorta) and during occlusion of both carotid arteries. Under all conditions studied the predicted systolic and diastolic pressure matched the experimental ones very well: Ps, wk = (1.000 +/- 0.0055) Ps with r = 0.958 and Pd, wk = (1.024 +/- 0.0035) Pd with r = 0.995. Linear regression for pulse pressure gave PPwk = (0.99 +/- 0.016) PP (r = 0.911). We found the accuracy of prediction equally good under control conditions and in presence of aortic or carotid artery occlusions. Multiple regression between pulse pressure and arterial resistance and total arterial compliance yielded a poor regression constant (r2 = 0.19) suggesting that the two arterial parameters alone cannot explain pulse pressure and that flow is an important determinant as well. We conclude that, for a given ejection pattern (aortic flow), two arterial parameters, total arterial resistance and total arterial compliance are sufficient to accurately describe systolic and diastolic aortic pressure.     

Computing total arterial compliance of the arterial system from its input impedance

The total arterial compliance of the arterial system was computed from its input impedance by expressing the impedance in terms of its frequency-response vector diagram (f.r.v.) The f.r.v. plot of a 3-element windkessel subjected to random pacing follows, theoretically, a circular path. Since the windkessel model serves as a good approximation for the arterial system, we have used the simple properties of its f.r.v. plot to obtain the compliance, which is otherwise normally determined from the peripheral resistance and the time constant of the diastolic pressure decay. The arterial compliance can also be determined from the impulse response function of the arterial system. Data obtained from dog experiments during no intervention, aortic occlusion and during occlusion of both carotid arteries have been analysed.     

The arterial Windkessel

Frank’s Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload. J.-W. Lankhaar is supported by a grant from the Netherlands Heart Foundation, the Hague, the Netherlands (NHS2003B274).     

天麻素对动脉血管顺应性以及血流动力学的影响

本文旨在研究天麻素对动脉血管顺应性和血流动力学等的作用。采用改良风箱模型来计算动脉管的顺应性和血管中血流惯性。在静脉注射天麻素前后，分别记录和计算出狗的血压，心输出量，外周阻力，血流惯性以及中央和外周动脉血管的顺应性。结果表明天麻素具有降低血压和外周务管阻力，增加动脉血管中血流惯性，以及中央和外周动脉血管的顺应性等作用。因此，天麻素是一种有效的能够改善由血管顺应性下降所致的高血压－老年性高血压的中     

硝普钠对动物血管力学参数的影响

有研究表明硝普钠具有增加动脉顺应性的趋势和降低外周阻力的作用,但是硝普钠对血管中血流惯性的影响却不统一。本文以Coldwyn等建立的动脉系改良风箱力学模型为主要研究方法对动物动脉血管顺应性(包括中央和外周顺应性),血流惯性和外周阻力等进行了研究,并建立了动脉系总阻抗的公式。然后评价硝普钠对总阻抗的影响以及总阻抗做为一种血管力学参数的灵敏性。实验结果表明:硝普钠具有统计学意义地增加外周血管的顺应性(P<0.05);有增加中央动脉顺应性和血流惯性的趋性;并能降低外周阻力和动脉系总阻抗(P<0.05)。结果还表明动脉系总阻抗是一种灵敏度高的血管力学参数。因此,硝普钠能影响血管参数,对外周血管顺应性和血管总阻抗的作用尤其明显。     

Analytical relationship between arterial input impedance and the three-element Windkessel series resistance

The recently proposed energy-balance method for estimating the series resistance of the three-element Windkessel model is reformulated in the frequency domain. New mathematical expressions are analytically derived, involving Fourier harmonics of pulsatile arterial pressure and flow. It is shown that the series resistance of the arterial three-element Windkessel model can be expressed as a weighted sum of the arterial input impedance moduli.     

True Arterial System Compliance Estimated From Apparent Arterial Compliance

A new method has been developed to estimate total arterial compliance from measured input pressure and flow. In contrast to other methods, this method does not rely on fitting the elements of a lumped model to measured data. Instead, it relies on measured input impedance and peripheral resistance to calculate the relationship of arterial blood volume to input pressure. Generally, this transfer function is a complex function of frequency and is called the apparent arterial compliance. At very low frequencies, the confounding effect of pulse wave reflection disappears, and apparent compliance becomes total arterial compliance. This study reveals that frequency components of pressure and flow below heart rate are generally necessary to obtain a valid estimate of compliance. Thus, the ubiquitous practice of estimating total arterial compliance from a single cardiac cycle is suspect under most circumstances, since a single cardiac cycle does not contain these frequencies. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 8719Rr     

Impedance matching between ventricle and load

Impedance matching in the cardiovascular system is discussed in light of two models of ventricle and load: [1] a Thevenin equivalent consisting of a hydromotive pressure source and an internal, source resistance and compliance in parallel; and [2] a time-varying compliance filled from a constant pressure source and ejecting into a load of three components, a central resistor, a compliance, and a peripheral resistance. According to the Thevenin analog, the energy source and the load are matched when the load resistance is T/t times the internal source resistance (T is total cycle length, t is systolic time interval). Both from this model and from the variable compliance model it appears that optimum matching between source and load depends on the compliance of the Windkessel, as low compliance shifts the matching load resistance to a low value. Animal experiments (isolated cat hearts) indicated that both left and right ventricles at normal loads work close to their maxima of output hydraulic power, and according to experiments in the right ventricle, maximum power output is related to load resistance and compliance as predicted by the above models. From an experimentally determined relationship among instantaneous ventricular pressure and volume (right ventricle of isolated cat hearts), an optimum load impedance was calculated on the basis of the assumption that the ratio between stroke work and static, potential energy developed in the ventricular cavity is maximum. The optimum load impedance found by this procedure closely resembles the normal input impedance of the cat lung vessel bed.     

Influence of Vessel Distension and Myogenic Tone on Pulmonary Arterial Input Impedance. A Study using a Computer Model of Rabbit Lung

A computer model of the pulmonary arterial (PA) bed of rabbit lungs was designed in order to test experimental observations of changes in PA input impedance and pulsatile hydraulic power (cap.) during increased PA pressure. The computer model was based on a simple 3-component analog representation of single vessels (i.e. resistance, inertance and compliance). 16 generations of arterial vessels, from PA to 60 μm diameter, were combined to calculate PA input impedance. Input impedance was found to mimic closely that observed experimentally. Both venous pressure elevation and arteriolar constriction was found to reduce input impedance and Wp. By combining arteriolar constriction with increased myogenic tone of the larger arteries, Wp was found to show a minimum level at a certain PA pressure, dependent on the degree of arterial stiffening. Wp was found to follow changes in arterial volume and resistance during simulated vasoconstriction. Wp dissipation in arterial vessels was calculated to approx. 50% of total input Wp at physiological pressure conditions, and could be reduced by one half after PA pressure increase from 20 to 50 cm H₂O, despite a concurrent halving of arterial compliance. Arterial vessels smaller than 200 pm diameter were found to have negligible direct influence on PA input impedance.     

A physical model of the human systemic arterial tree

A physical model of the human arterial tree has been developed to be used in a computer controlled mock circulatory system (MCS). Its aim is to represent systemic arterial tree properties and extend the capacity of the MCS to intraortic balloon pump (IABP) testing. The main problem was to model the aorta simply and to accurately reproduce aortic impedance and related flow and pressure waveforms at different sections. The model is composed of eight segments; lumped parameter models are used for its peripheral loads. After the numerical simulation, the physical model was reproduced as a silicon rubber tapered tube. This rubber was chosen for its stability over time and the acceptable behaviour of its Young's modulus (Ey = 22.23 gf x mm(-2)) with different loads and in comparison with data from the literature (Ey approximately 20.4 gf x mm(-2)). The properties of each segment of the aorta were defined in terms of compliance, resistance and inertance as a function of length, radius and thickness. The variable thickness was obtained using positive and negative molds. Total static compliance of the aorta model is about 1.125 x 10(-3) g(-1) x cm4 x sec2 (1.5 cm3 x mmHg(-1)). Measurements were performed both on numerical and physical models (in open and closed loop configuration). Data reported show pressure and flow waveforms along with input impedance modulus and phase. The results are in good agreement with data from the literature.     

Local and regional wave speed in the aorta: effects of arterial occlusion

Arterial wave speed is widely used to determine arterial distensibility and has been utilised as a surrogate marker for vascular disease. A comparison between the results of the traditional foot-to-foot method for measuring wave speed to those of the pressure-velocity loop (PU-loop) method is one of the primary objectives of this paper. We also investigate the regional wave speed along the aorta, and the effect of arterial occlusion on the PU-loop measured in the ascending aorta. In 11 anaesthetised dogs, a total occlusion lasting 3 min was produced at four sites: upper thoracic, diaphragm, abdominal and left iliac artery. Pressure and flow in the ascending aorta and pressure proximal to the occlusion site were measured, and data were collected before, during the occlusion and after the occlusion had been removed. In control conditions, the wave speeds determined by the PU-loop in the aortic root were systematically lower than those measured by the foot-to-foot method. During thoracic and diaphragm occlusions, mean aortic pressure and wave speed increased significantly but returned to control values after each occlusion had been removed. The PU-loop is an objective and easy to use method for determining wave speed and can be advantageous for use in short arterial segments when local measurements of pressure and velocity are available.     

Some Physical Properties of the Pulmonary Arterial Bed Deduced from Pulsatile Arterial Flow and Pressure

This study aimed to quantify changes of vascular compliance and resistance of the proximal and the peripheral pulmonary arterial vessels when vascular smooth muscle was stimulated. These above vascular characteristics were derived from registrations of pulsatile pressure and flow in the pulmonary artery (PA). An in situ cat lung preparation was used, with the right heart by-passed by a pulsatile blood pump. Vascular input impedance was derived from PA pulsatile pressure and flow recordings, and impedance characteristics were used for calculation of the variables of a simple lumped analog representation of the arterial bed. PA smooth muscle was stimulated by infusions of collagen suspension, by general hypoxia and by nor-adrenaline injections. Collagen caused 40% reduction of vascular compliance (C), no changes in proximal arterial resistance (Rl) and 18076 increase in peripheral vascular resistance (R2). Hypoxia caused 5096 reduced C, 20% increased R1 and 70% increased R2. Noradrenaline caused 20:6 reduced C and 30 % increased R1 and R2. These results, together with results derived from simulation of the observed impedance changes in a computer model of the lung arterial bed, indicated that collagen infusion elicited contraction of small and medium-sized arteries, with increased arterial volume as result of increased distending pressure. Hypoxia and noradrenaline, seemed both to cause contraction of the total arterial bed. This effect being most pronounced during hypoxia.     

Systolic Hypertension Mechanisms: Effect of Global and Local Proximal Aorta Stiffening on Pulse Pressure

Decrease in arterial compliance leads to an increased pulse pressure, as explained by the Windkessel effect. Pressure waveform is the sum of a forward running and a backward running or reflected pressure wave. When the arterial system stiffens, as a result of aging or disease, both the forward and reflected waves are altered and contribute to a greater or lesser degree to the increase in aortic pulse pressure. Two mechanisms have been proposed in the literature to explain systolic hypertension upon arterial stiffening. The most popular one is based on the augmentation and earlier arrival of reflected waves. The second mechanism is based on the augmentation of the forward wave, as a result of an increase of the characteristic impedance of the proximal aorta. The aim of this study is to analyze the two aforementioned mechanisms using a 1-D model of the entire systemic arterial tree. A validated 1-D model of the systemic circulation, representative of a young healthy adult was used to simulate arterial pressure and flow under control conditions and in presence of arterial stiffening. To help elucidate the differences in the two mechanisms contributing to systolic hypertension, the arterial tree was stiffened either locally with compliance being reduced only in the region of the aortic arch, or globally, with a uniform decrease in compliance in all arterial segments. The pulse pressure increased by 58% when proximal aorta was stiffened and the compliance decreased by 43%. Same pulse pressure increase was achieved when compliance of the globally stiffened arterial tree decreased by 47%. In presence of local stiffening in the aortic arch, characteristic impedance increased to 0.10 mmHg s/mL vs. 0.034 mmHg s/mL in control and this led to a substantial increase (91%) in the amplitude of the forward wave, which attained 42 mmHg vs. 22 mmHg in control. Under global stiffening, the pulse pressure of the forward wave increased by 41% and the amplitude of the reflected wave by 83%. Reflected waves arrived earlier in systole, enhancing their contribution to systolic pressure. The effects of local vs. global loss of compliance of the arterial tree have been studied with the use of a 1-D model. Local stiffening in the proximal aorta increases systolic pressure mainly through the augmentation of the forward pressure wave, whereas global stiffening augments systolic pressure principally though the increase in wave reflections. The relative contribution of the two mechanisms depends on the topology of arterial stiffening and geometrical alterations taking place in aging or in disease.     

Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method

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.     

Arterial windkessel parameter estimation: A new time-domain method

We developed and validated a new, more accurate, and easily applied method for calculating the parameters of the three-element Windkessel to quantitate arterial properties and to investigate ventriculoarterial coupling. This method is based on integrating the governing differential equation of the three-element Windkessel and solving for arterial compliance. It accounts for the interaction between characteristic impedance and compliance, an important phenomenon that has been ignored by previously implemented methods. The new integral method was compared with four previously published methods as well as a new independent linear least-squares analysis, using ascending aortic micromanometric and volumetric flow measurements from eight dogs. The parameters calculated by the new integral method were found to be significantly different from those obtained by the previous methods but did not differ significantly from maximum likelihood estimators obtained by a linear leastsquares approach. To assess the accuracy of parameter estimation, pressure and flow waveforms were reconstructed in the time domain by numerically solving the governing differential equation of the three-element Windkessel model. Standard deviations of reconstructed waveforms from the experimental ensemble-averaged waveforms, which solely reflect the relative accuracy of the Windkessel parameters given by the various methods, were calculated. The new integral method invariably yielded the smallest error. These results demonstrate the improved accuracy of our new integral method in estimating arterial parameters of the three-element Windkessel.     

Use of a model for simulating individual aortic dynamics in man

A simulation model is suggested for the analysis of aortic dynamics in man. The aortic model consists of six segments and is part of a larger model of the closed-loop human circulation. The model is simulated on a special-purpose analogue computer. Three parameters are employed to characterise the arterial system; peripheral resistance, aortic compliance and peripheral damping. Using a method for adapting the model to the individual patient, measurements of aortic pressure, cardiac output and pulse transmission time from 29 patients were used to test the validity of this approach. The model is able to simulate the pressure course along the aorta satisfactorily. The compliance calculated from the transmission properties of the aorta was compared with the complicance calculated from the stroke volume and pressure pulse. An adequate correlation (r=0.98) was found between these two independent methods. The mean compliance of the total aorta was 0.6 ml/mm Hg at a mean pressure of 104 mm Hg. The compliance showed large individual variations and decreasing values with increasing age of the patient. It is concluded that the model enables simulation of the individual aorta.     

Evaluation of the theory of cardiac-output computation from transthoracic impedance plethysmogram

To analyse the limit of the stimation of stroke volume by thoracic impedance plethysmography (SV_z), we considered an elastic tube forced with a trapezoidal flow input as a model of the aorta, and, based on Kubicek's equation, the volume input (SV_a) was related to its impedance change via the model system parameters such as elasticity, fiuid inertia, peripheral resistance, total impedance across the tube and the rise and fall time of the input. SV_z is equal to SV_a only when the inflow is a square wave. The ratio SV_z/SV_a decreases with increasing input rise time, while it increases with increasing fall time, if the maximum flow rate and ejection time of the inflow are held constant. SV_z hardly changes in association with changes in elasticity, fluid inertia, peripheral resistance or total impedance. A part of the results, the relationship between SV_z, transthoracic total impedance and aortic flow waveform, was also demonstrated in dogs.     

Quantitative evaluation of the systemic arterial bed by parameter estimation of a simple model

The parameters of a simple model (r-L-C-R) of the systemic circulation are estimated from aortic root pressure and flow, which are either simulated by a complex model of the systemic circulation or measured in dogs. This model contains one additional parameter (inductance L) as compared with the r-C-R model proposed by Westerhof; it allows for a better representation of the input impedance of the complex model and of the systemic circulation in dog, resulting in meaningful values for the parameters r, C, R. Because there is a good relation between C and the sum of the compliances of the complex model, and because C varies in the direction of the expected changes in compliance following angiotensin and sodium nitroprusside administration in dogs, C appears to be a valid estimate of the total systemic arterial compliance. The good relation between r and the characteristic impedance in the complex model or in the upper thoracic aorta of the dog indicates that r is a good measure of the characteristic impedance. The r-L-C-R model therefore appears to provide a better characterisation of the left ventricular afterload than the r-C-R model. The identification of this r-L-C-R model also permits a more convenient quantification of the afterload than the classical computation of input impedance.