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.     

Use of a simulation model for estimating cardiac output from aortic pressure curves

A method for calculating cardiac output from aortic pressure curves is presented. The method is based on a simulation model of the human cardiovascular system. The aortic compliance is calculated from the pulse transmission time in the aorta. The method has been tested against standard cardiac output measurements in 61 instances in 39 persons. 40 measurements have been performed at rest, while 21 have been performed during various changes in the cardiovascular state. The mean difference between the pulse method and the standard cardiac output determination was found to be 9% with a standard error of the difference of 7%. The correlation coefficient was r=0·96. The largest differences were found in patients suffering from atrial fibrillation, where changes in pressure in the aorta made compliance estimates based on pulse transmission time difficult. Using a servosystem, the model is capable of following changes in the cardiovascular state within a few beats. This method should therefore be useful for calculating cardiac output in the intensive-care situation.     

Viscoelasticity modulates resonance in the terminal aortic circulation.

We used an inertance-viscoelastic windkessel model (IVW) to interpret aortic impedance patterns as seen in the terminal aortic circulation of the dog, and to explain evident oscillatory phenomena in flow measurements. This IVW model consists of an inertance, L, connected in series with a viscoelastic windkessel (VW) where the peripheral resistance, Rp, is connected in parallel with a Voigt cell (a resistor, Rd, in series with a capacitor, C) to account for viscoelasticity. Pressure and flow measurements were taken from the terminal aorta, just downstream of the origin of renal arteries, in three anaesthetised open-chest dogs, under a variety of haemodynamic conditions induced by administering a vasoconstrictor agent (methoxamine) and a vasodilator (sodium nitroprusside). Mean pressure ranged from 40 to 140 mm Hg. The resistance Rp was calculated as the ratio of mean pressure to mean flow. Parameters L, C and Rd were estimated by fitting measured to model predicted flow waves. We found that prominent oscillations observed in flow waves, from midsystole to diastole, are related to resonance that occurs at a frequency, f(o), where reactance of inertance of blood motion matches the reactance of arterial compliance. Estimates of f(o) increased from 2.4 to 10 Hz with increasing pressure and showed a correlation with values of static elastic moduli plotted against mean pressure of dogs' peripheral arteries previously reported by others. Viscous losses, Rd, of arterial wall motion limited the amplitude of resonance peak. We conclude that viscoelasticity, rather than pure elasticity, is a key issue to interpret terminal aortic impedance as it relates to resonance.     

Observations on coronary collateral communications and the control of flow in the coronary circulation of the dog

1. Pressure was measured in the small arterial anastomosing branches of the coronary vascular network. The mean value was 30 mm Hg not significantly different from the mean value of 33 mm Hg for peripheral coronary pressure measured distal to a ligature on the anterior descending branch of the left coronary artery. Evidence was adduced to show that either the anterior descending or the circumflex artery had the capacity to maintain network pressure at levels adequate for tissue perfusion.2. The network has both capacity and compliance. Filling of the network compliance during systole probably accounts for the systolic phase of coronary flow. Flow through the microcirculation is probably entirely diastolic, the combined compliance of the aorta and large vessels together with the network provides the necessary reservoir, the potential energy indicated by diastolic pressure provides the perfusion pressure head.3. Resistance of vessels between the aorta and network cannula (pre-net) was approximately double that of the microcirculation (post-net). The smaller pre-network vessels are of the order 70 mum in diameter. Both pre- and post-network vessels are vaso-active and respond similarly to adrenaline and haemorrhage.     

Influence of central and peripheral changes on the hydraulic input impedance of the systemic arterial tree

The input impedance of the systemic arterial tree of the dog has been computed by Fourier analysis. It was shown that a distance between pressure and flow transducers of less than 2 cm results in appreciable errors which manifest themselves mainly in the phase of the input impedance. The input impedance for controls, occlusions at various locations in the aorta, and an increase and decrease of peripheral resistance were studied. For the same experiments, the total arterial compliance was calculated from the peripheral resistance of the diastolic aortic-pressure curve. The characterstic impedance of the ascending aorta was also estimated. The impedance in the control situation may be modelled by means of a 3-element Windkessel consisting of a peripheral resistance and (total) arterial compliance, together with a resistance equal to the characteristic impedance of the aorta. The occlusions of the aorta show that blockage at (and beyond) the trifurcation do not result in a detectable change in input impedance, except for a slight increase of the peripheral resistance. The more proximal an aortic occlusion, the more effect it has on the pattern of the input impedance. When the aorta is occluded at the diphragm, or higher, the single (uniform) tube appears to be a much better model than the Windkessel. Occlusion of one or both carotid arteries increases the mean pressure; consequently not only the peripheral resistance increases but also the total arterial compliance decreases. The Windkessel with increased peripheral resitance and decreased compliance is again a good model. After a sudden release of occlusion of the aorta, the arterial system has a low peripheral resistance and may also be modelled by the Windkessel.     

Isolated aorta setup for hemodynamic studies

A setup consisting of a high-performance hydraulic pump connected to the ascending part of an isolated aorta, including all major distal branches, each loaded with calibrated artificial resistors, was developed. The system was used to study total aortic compliance of the baboon as a function of mean aortic pressure (n=5). The aorta loaded with the resistors was mounted in a custom-designed sink table, such that it was submersed in physiological saline maintained at 37°C. Mean distending pressure in the entire aortic compliance from pressure and flow waves generated by the pump. Total aortic compliance as a function of mean pressure was fitted with a logarithmic function: Ln (Compliance)=A+B * P. The value of A(±SE) was: 1.565±0.319 and B: −0.020±0.003 (P<0.001). The results were compared with previously published results (also using the same three-element Windkessel fit) obtained in three of the same animalsin vivo. Thein vivo data were A: 1.095±0.235 and B: −0.019±0.003.In vitro data had a significantly higher value of A thanin vivo (P=0.017), implying a significantly higher aortic compliancein vitro thanin vivo. Occlusion of the proximal descending aorta was performed at a low distending pressure (55 mm Hg) to determine the proximal complicance. It was found (n=4) that 46±11% (SD) of the total arterial compliance is to be attributed to the ascending and proximal descending aorta. This work was supported in part by Grant RG 86/0066 from the scientific affairs division of Nato.     

The importance of slice location on the accuracy of aortic regurgitation measurements with magnetic resonance phase velocity mapping

Although several methods have been used clinically to evaluate the severity of aortic regurgitation, there is no purely quantitative approach for aortic regurgitant volume (ARV) measurements. Magnetic resonance phase velocity mapping can be used to quantify the ARV, with a single imaging slice in the ascending aorta, from through-slice velocity measurements. To investigate the accuracy of this technique,in vitro experiments were performed with a compliant model of the ascending aorta. Our goals were to study the effects of slice location on the reliability of the ARV measurements and to determine the location that provides the most accurate results. It was found that when the slice was placed between the aortic valve and the coronary ostia, the measurements were most accurate. Beyond the coronary ostia, aortic compliance and coronary flow negatively affected the accuracy of the measurements, introducing significant errors. This study shows that slice location is important in quantifying the ARV accurately. The higher accuracy achieved with the slice placed between the aortic valve and the coronary ostia suggests that this slice location should be considered and thoroughly examined as the preferred measurement site clinically.     

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.     

Implication of the systolic hump in systemic arterial pressure waves

The systolic hump in the aortic blood pressure wave is defined as the aorticresistance component proportional to the aortic blood flow superimposed on the windkessel component. An electrical analogue comprising a series resistance (aortic resistance) plus a resistance (peripheral resistance) and capacitance (aortic compliance) in parallel (i.e. windkessel component) is used for analysis. Curve fitting using the leastsquares method is performed on calculated and measured blood pressure waves from dogs under haemodynamical conditions induced by infusion of three drugs (noradrenaline, isoproterenol and acetylcholine). The curve fitting RMS (root mean square) errors are <3% for blood pressure waves and <30% for blood flow waves, with good agreement between measured and calculated blood flow waveforms. Infusion of noradrenaline and acetylcholine is found to induce a significant decrease and increase in the aortic resistance, respectively. Although only a small fraction of the blood pressure wave, the systolic hump has a marked effect on the systolic pressure waveform.     

Mean systemic filling pressure as a characteristic pressure for venous return

Guyton's theory on venous return, implying a linear relationship between blood flow and central venous pressure, was tested in an intact circulation after thoracotomy and airtight chest closure. In eleven Yorkshire pigs (approx. 10 kg) we measured flow in the pulmonary artery and aorta and pressure in the central veins and aorta during pentobarbital anesthesia and mechanical ventilation. To change central venous pressure different lung volumes were randomly applied at intervals of 5 min in a series of inspiratory hold procedures of 7.2 s. During these short periods hemodynamic steady state circumstances were met without involvement of cardiovascular control mechanisms.We confirmed the linear relationship between venous return and central venous pressure and derived mean systemic filling pressure from the regression equation. Mean systemic filling pressure was on average 10.5±2.3 (SD) mm Hg.The time dependent changes during the inspiratory hold procedure showed that the increase in central venous pressure was the primarily dependent variable, followed by a decrease in venous return and right ventricular output. After a delay of 2–4 heart beats also a decrease in left ventricular output and aortic pressure occurred. Subsequently, the lower venous return during inspiratory hold was mainly sustained by the lower aortic pressure, but nevertheless fulfilled the linear relationship mentioned above.For analysis of flow and pressure changes in the systemic circulation during changes of central venous pressure a tube of constant flow resistance was used as a conceptual model. Consequently, the point where mean systemic filling pressure exists during normal flow conditions was predicted at a characteristic location in the peripheral venous system. Downstream from this point blood pressure will rise and vessel capacity will be filled up during increases in central emptying vessel capacity partially.     

A novel miniature ventricular assist device for hemodynamic support

The HemoDynamics Systems enabler is a new cardiac assist pump that can expel blood from the left ventricle and provide pulsatile flow in the aorta. We evaluated the efficacy of the 18 Fr enabler. The enabler was inserted from the left ventricular apex into the ascending aorta in eight sheep. Heart failure (mild, moderate, and severe) was induced by microsphere injection into the coronary arteries to reduce cardiac output by 10-30%, 31-50%, and more than 50% from baseline, respectively. The enabler was activated, and its flow was increased to approximately 2.0 L/min. Hemodynamic variables were recorded before and after activation. In moderate heart failure, cardiac output and mean aortic pressure increased from 2.3 +/- 0.6 L/min and 59 +/- 12 mm Hg before assist to 2.8 +/- 0.6 L/min and 70 +/- 8 mm Hg at 30 minutes after activation, respectively (p < 0.01). Left atrial pressure decreased from 17 +/- 3 to 13 +/- 4 mm Hg (p < 0.05). Similar findings were observed in mild and severe heart failure. Despite its small diameter, the enabler significantly improved the hemodynamics of failing hearts and may potentially serve as a means of peripheral left ventricular support. Further study is warranted.     

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.     

Identification of the three-element windkessel model incorporating a pressure-dependent compliance

A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steadystate periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.     

Coarctation of the aorta—a theoretical and experimental analysis of the effects of a centrally located arterial stenosis

Aortic coarctation is a local constriction of the aorta that may severely affect haemodynamics. It is therefore important to quantify these effects. Using Bernoulli's equation and the momentum theorem, the pressure drop is described including the pressure recovery distal to the coarctation and the effects of collateral flow; both laminar and turbulent. Assuming the coarctation and collaterals to be stiff, a quadratic relationship between flow and pressure drop is expected for flow through the coarctation and for turbulent collateral flow. For laminar collateral flow, a linear relationship is expected. The coarctation flow was studied in a model consisting of a rigid tube with local constriction, connected to a flooded-level tank, containing a 36 per cent by weight solution of sucrose, with a viscosity equivalent to that of blood at body temperature. The pressure drop across the constriction showed a quadratic relationship to flow in agreement with theoretical expectations. Pressure recovery in this model was very slight (0–4 mm Hg). Nine patients with aortic coarctation were catheterised. Cardiac output and pressure drop across the coarctation were measured at rest and during supine cycle exercise at two different workloads. The relationship between mean pressure drop and cardiac output tended to be either ‘parabolic’ or, in some cases, approximately linear, suggesting that the flow situation in aortic coarctation can be quantified by expressions that either linearly or quadratically relate pressure and flow.     

Hemodynamic simulation study of a novel intra-aorta left ventricular assist device

The intra-aorta pump proposed here is a novel left ventricular assist device (LVAD). The mathematic model and the in vitro experiment demonstrate that the pump can satisfy the demand of human blood perfusion. However, the implantation of LVAD will change the fluid distribution or even generate a far-reaching influence on the aorta. At present, the characteristics of endaortic hemodynamics under the support of intra-aorta pump are still unclear. In this article, a computational fluid dynamics study based on a finite-element method was performed for the aorta under the support of intra-aorta pump. To explore the hemodynamic influence of intra-aorta pump on aorta, fully coupled fluid-solid interaction simulation was used in this study. From the flow profiles, we observed that the maximum disturbed flow and nonuniform flow existed within the aortic arch and the branches of the aortic arch. Flow waveforms at the inlets of aortas were derived from the lumped parameter model that we proposed in our previous study. The results demonstrated that the intra-aorta pump increased the blood flow in the aorta to normal physiologic conditions, but decreased the pulsatility of the flow and pressure. The pulsatility index changed from 2,540 to 1,370. The pressure gradient (PG) for heart failure conditions was 18.88 mm Hg/m vs. 25.51 mm Hg/m for normal physiologic conditions; for intra-aorta pump assist conditions, normal PG value could not be regained. Furthermore, our experimental results showed that the wall shear stress (WSS) of aorta under heart failure and normal physiologic conditions were 1.5 and 6.3 dynes/cm, respectively. The intra-aorta pump increased the WSS value from 1.5 to 4.1 dynes/cm.     

Continuous measurement of aortic radius changein vivo with an intra-aortic ultrasonic catheter

The radii of the inner and outer walls of the aorta and the intravascular blood pressure were recorded simultaneously in the descending thoracic aorta of intact, living dogs using 7·5 MHz ultrasound. Blood pressure and the A-mode signals containing wall echoes were also recorded on videotape which was later replayed for processing. Thein vivo data were compared with data obtained on the same vessels post mortem. The change in radius due to a pressure change from 80 to 125 mmHg was calculated from thein vivo andin vitro data. After normalising the radius changes with respect to the radius at 80 mm Hg, the ratio of thein vivo andin vitro values ranged from 0·66 to 1·36 with a mean of 0·94. The changes in radius were comparable with previously reported values obtained using various techniques.     

Finite element modeling of the thoracic aorta: including aortic root motion to evaluate the risk of aortic dissection

Objective: We propose that the aortic root motion plays an important role in aortic dissection.

Methods and results: A finite element model of the aortic root, arch and branches of the arch was built to assess the influence of aortic root displacement and pressure on the aortic wall stress. The largest stress increase due to aortic root displacement was found at approximately 2 cm above the top of the aortic valve. There, the longitudinal stress increased by 50% to 0.32 MPa when 8.9 mm axial displacement was applied in addition to 120 mmHg luminal pressure. A similar result was observed when the pressure load was increased to 180 mmHg without axial displacement.

Conclusions: Both aortic root displacement and hypertension significantly increase the longitudinal stress in the ascending aorta, which could play a decisive role in the development of various aortic pathologies, including aortic dissection.     

Feasibility study of a direct endo-aortic clamp balloon

We have developed a new end-aortic clamp balloon catheter intended to be inserted directly into, thereby occluding, the ascending aorta. We examined the performance of this catheter in a canine model. We evaluated the extent of migration tolerance of the catheter under cardiopulmonary bypass perfusion in 12 mongrel dogs, weighing 20 kg, under general anesthesia. After institution of cardiopulmonary bypass, this catheter was inserted into the ascending aorta, and the balloon was inflated to occlude the ascending aorta. After the canine heart was arrested following the administration of cardioplegic solution, balloon migration was examined over a period of 3 hours, with hourly increases in perfusion pressure from 50 mm Hg to 80 mm Hg and finally to 100 mm Hg. After the migration test, ascending aortic wall sections, where the balloon was inflated, were examined microscopically. At internal balloon pressure of 300 to 400 mm Hg, migration occurred at perfusion pressure of > or =90 to 100 mm Hg. No histological differences were observed with use of the balloon catheter, compared with an extra-aortic clamp forceps. Based on these results, this device is safe, feasible, and can adequately occlude the ascending aorta during cardiopulmonary bypass. We conclude that this device is effective in patients weighing 20 kg.     

Surgical repair of congenital supravalvular aortic stenosis in adult

Supravalvular aortic stenosis is a rare congenital cardiac anomaly occurring mainly as a part of Williams-Beuren syndrome. Aortic narrowing above the level of the aortic valve causes obstruction of the left ventricular outflow tract, and a pressure gradient between the left ventricle and the aorta causes left ventricle hypertrophy. We report here a case of a 22-year-old man who underwent extended patch aortoplasty because of supravalvular aortic stenosis accompanying Williams-Beuren syndrome. He was in New York Heart Association functional class III with localized hourglass type supravalvular aortic stenosis. Related to arterial hypertension he was in a cardiac decompensation. Mean pressure gradient was 73 mm Hg and maximum gradient 104 mm Hg. Electrocardiography indicated left ventricle hypertrophy, which was also seen in x-ray, as heart enlargement. We successfully treated this patient with extended patch aortoplasty and immediate postoperative echocardiography showed reduction of gradient. Good surgical outcome of congenital supravalvular aortic stenosis in adults can be achieved with this treatment. This technique provides symmetric reconstruction of the aorta with good postoperative results and no gradient across aortic valve and aortic valve insufficiency remains, providing excellent long-term relief of localized supravalvular gradients and preservation of aortic valve competence.     

Three decades of follow-up of aortic and pulmonary vascular lesions in the Williams-Beuren syndrome

The diagnostic criteria of the Williams-Beuren syndrome (WBS) were established almost 3 decades ago. Until now there has been little knowledge about the natural and post-surgical history of vascular lesions in this syndrome. In order to evaluate the long term follow-up of aortic and pulmonary vascular lesions, we have analysed the catheterization data, angiocardiograms, and Doppler-echo measurements in 59 patients who were seen at least twice in our institution between 1961 and 1993. Their follow-up periods ranged from 2.1 to 28.2 years. Of 45 patients with supravalvular aortic stenosis (SVAS) with a mean follow-up period of 12.9 years, it became evident that pressure gradients of less than 20 mm Hg in infancy generally remained unchanged during the first two decades of life. Pressure gradients exceeding 20 mm Hg increased from an average of 35.5 mm Hg to 52.7 mm Hg in 13 patients. Of these, 8 required surgical relief of the narrowing. In 7 patients aortic hypoplasia was documented. In 5 of them the caliber of the aorta showed a tendency towards normalisation within a period of 11.9 to 23.9 years. Of 6 individuals with aortic hypoplasia and surgical relief of SVAS, 4 patients developed restenosis at the distal end of the aortoplasty patch. In contrast, 9 patients with operated SVAS—but without aortic hypoplasia—remained free of restenosis over a period of 11 years (mean). Coarctation occurred in 4/59 patients; restenosis was seen in 2 after 5 and 16 years. Peripheral pulmonary stenosis was followed in 23 patients over 14.4 years (mean). During this period the systolic pressure gradients fell from 23 to 9.3 mm Hg (mean). In adolescence and adulthood the gradients were below 20 mm Hg in 22/23 individuals. In WBS there is a good long-term prognosis for SVAS if gradients during infancy are low. SVAS with gradients above 20 mm Hg tend to increase; 60% of them require surgical relief with good long-term results. But aortic hypoplasia impairs the prognosis of operated SVAS, because restenosis may occur. Peripheral pulmonary stenosis generally shows a good long-term prognosis. © 1994 Wiley-Liss, Inc.