Beat-to-beat noninvasive stroke volume from arterial pressure and Doppler ultrasound

The proper understanding of the cardiovascular mechanisms involved in complaints of short-lasting dizziness and the evaluation of unexplained recurrent syncope requires continuous monitoring of cardiac stroke volume (SV) in addition to blood pressure and heart rate. The primary aim of the present study was to evaluate a pulse wave analysis method that calculates beat-to-beat flow from non-invasive arterial pressure by simulating a non-linear, time-varying model of human aortic input impedance (Modelflow; MF), by comparing MF stroke volume (SV_MF) to Doppler ultrasound (US) flow velocity SV (SV_US). A second purpose was to compare the two methods under two different conditions: the supine and head-up tilt (30°) position. SV_US and SV_MF with non-invasive arterial pressure (Finapres) as input to the aortic model were measured beat-to-beat during spontaneous supine breathing and in the passive 30° head-up tilt (HUT30) position in six normotensive healthy humans [three females, mean age 24 (21–26) years]. There were variations in supine SV track between the two methods with zero difference and a SD of the beat-to-beat difference (MF–US) of 4.2%. HUT30 induced a systematic difference of 10.5% and an increase in SD to 6.9%, which was reproducible. Beat-to-beat changes in SV in the supine resting condition were equally well assessed by both methods. Systematic differences appear during HUT30 and show opposite signs. The difference between the two methods upon a change in body position may be attributed to limitations in each method.     

Quantification of aortic regurgitation by Doppler echocardiography: a new method evaluated in pigs

We have developed a method to quantify aortic regurgitant orifice and volume, based on measurements of the velocity of the regurgitant jet, aortic systolic flow, the systolic and diastolic arterial pressures, a Windkessel arterial model, and a parameter estimation technique. In six pigs we produced aortic regurgitant flows between 2·1 and 17·8 ml per beat, i.e. regurgitant fractions from 0·06 to 0·58. Pulmonary and aortic flows were measured with electromagnetic flow probes, aortic pressure was measured invasively, and the regurgitant jet velocity was obtained with continuous-wave Doppler. The parameter estimation procedure was based on the Kalman filter principle, resulting primarily in an estimate of the regurgitant orifice area. The area was multiplied by the velocity integral of the regurgitant jet to estimate regurgitant volume. A strong correlation was found between the regurgitant volumes obtained by parameter estimation and the electromagnetic flow measurement. These results from our study in pigs suggest that it may be possible to quantify regurgitant orifice and volume in patients completely noninvasively from Doppler and blood pressure measurements.     

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.     

Stroke volume decreases during mild dynamic and static exercise in supine humans

Aim: The contributions of cardiac output (CO) and total peripheral resistance to changes in arterial blood pressure are debated and differ between dynamic and static exercise. We studied the role stroke volume (SV) has in mild supine exercise. Methods: We investigated 10 healthy, supine volunteers by continuous measurement of heart rate (HR), mean arterial blood pressure, SV (ultrasound Doppler) and femoral beat volume (ultrasound Doppler) during both dynamic mild leg exercise and static forearm exercise. This made it possible to study CO, femoral flow (FF) and both total and femoral peripheral resistance beat‐by‐beat. Results: During a countdown period immediately prior to exercise, HR and mean arterial pressure increased, while SV decreased. During mild supine exercise, SV decreased by 5–8%, and most of this was explained by increased mean arterial pressure. Dynamic leg exercise doubled femoral beat volume, while static hand grip decreased femoral beat volume by 18%. FF is tightly regulated according to metabolic demand during both dynamic leg exercise and static forearm exercise. Conclusion: Our three major findings are, firstly, that SV decreases during both dynamic and static mild supine exercise due to an increase in mean arterial pressure. Secondly, femoral beat volume decreases during static hand grip, but FF is unchanged due to the increase in HR. Finally, anticipatory responses to exercise are apparent prior to both dynamic and static exercise. SV changes contribute to CO changes and should be included in studies of central haemodynamics during exercise.     

On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.     

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.     

Reproducibility of the alterations in circulation and cerebral oxygenation from supine rest to head-up tilt.

Cardiovascular stability, as affected by several diseases, may be assessed by head-up tilt testing. Follow-up studies are essential in both evaluating interventions and assessing progression. However, data on the reproducibility of the changes in circulatory status and cerebral oxygenation provoked by head-up tilt testing are fundamental to follow-up studies. The aim of this study was, therefore, to assess the reproducibility of the alterations in stroke volume (SV), mean arterial pressure (MAP), as well as oxygenated ([O2Hb]) and deoxygenated haemoglobin ([HHb]) concentration in cerebral tissue from supine rest (SUP) to head-up tilt (HUT). SV was calculated by Modelflow, a pulse contour method, from the finger arterial pressure wave measured by Portapres, the portable version of Finapres. [O2Hb] and [HHb] were measured using near-infrared spectroscopy (NIRS). Ten healthy individuals visited the laboratory on two different days. On both days, they underwent 10 min SUP followed by 10 min 70 degrees HUT twice. SV decreased, which was (in part) compensated for by an increased heart rate, while MAP increased slightly during HUT compared with SUP. Although [HHb] increased during HUT, no presyncope symptoms were experienced. The circulatory variables (SV, HR and MAP) as well as [HHb] showed an acceptably small systematic and random error as well as reproducibility error compared with the observed difference between HUT and SUP and were similar between and within visits. Therefore, it is concluded that MAP measured by Portapres and SV calculated by Modelflow as well as HHb measured by NIRS seem to be reproducible and may therefore be used in follow-up studies.     

Effects of ageing on cardiac performance and coronary flow in spontaneously hypertensive and normotensive rats

The aim of the present study was to assess the influence of ageing on cardiac function and coronary flow in Wistar Kyoto normotensive rats (WKY, 16 and 78 weeks of age) and spontaneously hypertensive rats (SHR) of the same age. Cardiac function was determined on isolated hearts by means of an antegrade heart perfusion technique. Left atrial pressure and peak aortic pressure could be altered independently of each other. Recordings of cardiac output and coronary flow were then obtained at both normotensive and hypertensive levels of peak aortic pressures. Peak stroke volume (SV) was reduced with age in both WKY and SHR. Peak SV determined at normotensive pressure loads became diminished with age in WKY, while it at hypertensive pressure loads showed a small decline with age, since peak SV was low as early as 16 weeks of age. The age-dependent fall in cardiac performance was greater in SHR than in WKY, due to the enhanced peak SV in 16-week-old SHR at hypertensive pressure loads. Peak SV was markedly decreased at normotensive pressure levels in both 16- and 78-week-old SHR v. age-matched WKY. Coronary flow per unit tissue declined with age both in WKY and SHR. Coronary flow was also lower in SHR compared to age-matched WKY. With ageing this elevated performance was reduced down to the same level as in 78-week-old WKY. The age-related coronary flow reduction and the consistently reduced flow in SHR indicate a structural narrowing of the coronary vascular bed, particularly in SHR.     

Finite element analysis of blood flow and heat transfer in an image-based human finger

The human finger is said to be the extension of the brain and can convey the information on mechanical, thermal, and tissue damaging. The quantitative prediction of blood flow rate and heat generation are of great importance for diagnosing blood circulation illness and for the noninvasive measurement of blood glucose. In this study, we developed a coupled thermofluid model to simulate blood flow in large vessels and living tissue. The finite element (FE) model to analyze the blood perfusion and heat transport in the human finger was developed based on the transport theory in porous media. With regard to the blood flow in the large arteries and veins, the systemic blood circulation in the upper limb was modeled based on the one-dimensional flow in an elastic tube. The blood pressure and velocity in each vessel were first computed and the corresponding values for the large vessels in the finger were subsequently transferred to the FE model as the boundary conditions. The realistic geometric model for the human finger was constructed based on the MRI image data. After computing the capillary pressure and blood velocity in the tissue, the temperatures in the large vessels and the tissue of the finger were computed simultaneously by numerically solving the energy equation in porous media. The computed blood flow in tissues is in agreement with the anatomical structure and the measurement. It is believed that this analysis model will have extensive applications in the prediction of peripheral blood flow, temperature variation, and mass transport.     

Effect of local cold provocation on systolic blood pressure and skin blood flow in the finger.

Demonstration of increased vascular cold reactivity in patients with Raynaud's syndrome is difficult. For medico-legal reasons, it is important to get objective measures of vasospasm in these patients. Evaluation of the degree of vasospasm also provides prognostic information which is useful for patient management. In this study, we compare two methods of arterial circulation measurement. The laser Doppler scanning is a new method, which uses the recently developed laser Doppler perfusion imaging (LDPI) instrument. The aim of the present study was to compare the effect on finger skin blood flow measured with LDPI with changes in finger systolic blood pressure during local cold provocation. The effect of such provocation, skin blood flow and systolic blood pressure, were studied in 15 healthy controls. Six patients with known traumatic vasospastic disease (TVD) were also tested with both methods. Finger skin blood flow was measured with LDPI on the distal phalanx of the index finger of the left hand, every minutes during 6 min of local heating at 40 degrees C followed by local cooling for 3 min at 15 degrees C and then for 3 min at 10 degrees C. Finger systolic blood pressure was measured with strain-gauge method before and after local cooling to 10 degrees C with a cuff perfused with water of desired temperature. The test was performed in the same finger within a week of the laser Doppler scanning. Local finger cooling to 15 degrees C and 10 degrees C caused a significant decrease in blood flow, most marked at 10 degrees C. There was, however, no correlation between the decrease in blood flow and blood pressure. In the TVD-patients decreases in skin blood flow were similar compared with the healthy controls. In contrast, the changes in systolic blood pressure, were outside normal range (systolic quotient <0.65) in five of the six patients (83%), and also in 11 of the 15 healthy controls (73%). In conclusion, there is no correlation between the decrease in finger skin blood flow and systolic blood pressure during local cold provocation. For diagnosis of traumatic vasospastic disease (TVD), local cold-induced changes in finger systolic blood pressure seems superior to changes in skin blood flow, but the ideal clinical method for demonstrating increased cold-induced vasospasm is, however, still lacking.     

Pressure-based simultaneous CFR and FFR measurements: understanding the physiology of a stenosed vessel

Arterial stenosis is known to be one of the most serious cardiovascular diseases. Angiographical estimation of arterial stenosis provides limited information on the severity of the occlusion and the flow of blood through it. Hemodynamical assessment of the flow and pressure behaviour, is known to be clinically important. Hemodynamically based parameters, such as pressure based myocardial fractional flow reserve (FFR) and the flow based coronary flow reserved (CFR) were introduced to provide a much better tool for treating arterial diseases.We have developed a new method for simultaneous measurement of pressure-derived CFR and FFR. The advantage of pressure derived hemodynamic parameters is very substantial, and its relatively straightforward application in clinical setting is solid. The method has been validated by means of a computational fluid dynamics (CFD) model of the arterial stenosis and in vitro bench studies.     

Vascular Unloading Method for Noninvasive Measurement of Instantaneous Arterial Pressure: Applicability in Psychophysiological Research

A new method proposed previously by us (1980) was described to evaluate its applicability in psychophysiological research. In this method, beat-to-beat systolic and diastolic pressure as well as the pressure waveform can be measured noninvasively in the human finger. By use of a hydraulicservosystem, the photoplethysmographically detected vascular volume changes associated with intraarterial pressure in the finger are compensated by an applied counterpressure (cuff pressure) to maintain a proper value corresponding to the unloaded vascular volume. At this state the controlled cuff pressure follows instantaneously the intraarterial pressure. Comparison data were obtained by direct measurement of blood pressure in the brachial artery in 3 normotensive and 3 hypertensive subjects. High correlations between the two measures were obtained in each subject under various conditions. By maintaining circulation in the finger, this method enables the noninvasive and continuous measurement of instantaneous arterial pressure for more than one hour without much discomfort. This indirect method should be useful in many areas of psychophysiological research.     

Determination of fractional flow reserve (FFR) based on scaling laws: a simulation study

Fractional flow reserve (FFR) provides an objective physiological evaluation of stenosis severity. A technique that can measure FFR using only angiographic images would be a valuable tool in the cardiac catheterization laboratory. To perform this, the diseased blood flow can be measured with a first pass distribution analysis and the theoretical normal blood flow can be estimated from the total coronary arterial volume based on scaling laws. A computer simulation of the coronary arterial network was used to gain a better understanding of how hemodynamic conditions and coronary artery disease can affect blood flow, arterial volume and FFR estimation. Changes in coronary arterial flow and volume due to coronary stenosis, aortic pressure and venous pressure were examined to evaluate the potential use of flow and volume for FFR determination. This study showed that FFR can be estimated using arterial volume and a scaling coefficient corrected for aortic pressure. However, variations in venous pressure were found to introduce some error in FFR estimation. A relative form of FFR was introduced and was found to cancel out the influence of pressure on coronary flow, arterial volume and FFR estimation. The use of coronary flow and arterial volume for FFR determination appears promising.     

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.     

左心循环系统的建模与仿真

将左心模型与四元件的动脉系统Windkessel模型耦合,构成左心-动脉系统交互的左心循环系统模型.模型包括左心房、左心室、二尖瓣、动脉辩和动脉系统,实现了对左心循环系统的血流动力学模拟.应用状态空间法和SIMULINK框图模型法两种技术和MATLAB工具,进行了数学建模和数值计算,具有模型直观、容易实现、方便调节参数等优点.应用这一仿真模型,可以对左心室容积、血压及主动脉血压和血流等进行动态模拟.仿真结果与生理实际情况相符.     

Control of intraaortic balloon pumping: Theory and guidelines for clinical applications

The effectiveness of intraaortic balloon pumping was investigated by using a lumped parameter model of the cardiovascular/assist device system. The model consists of a time-varying elastance left ventricular simulation, a 2-element windkessel arterial simulation, and an RC venous return and pulmonary simulation. The four major hemodynamic variables, stroke volume (SV), aortic mean diastolic pressure (MDP), tension time index (TTI), and aortic end diastolic pressure (EDP), were divided into two categories related to system energy supply and demand: “external” and “internal” variables. The effects of balloon pumping on these variables can be described by closed-form equations that yield an optimal solution. The model prediction suggests that, in the ideal case, optimization of balloon pumping calls for instantaneous inflation of the balloon to maximum volume at end systole and instantaneous complete deflation at end diastole. For finite inflation/deflation rates, the optimal time for the start of inflation is end systole. Deflation timing, however, involves a tradeoff between maximizing the external variables and minimizing the internal variables. These predictions were tested using a nonlinear digital computer model. The results also suggest that when SV is not being monitored, optimal inflation timing can be controlled from the measurements of TTI or pulmonary venous pressure; optimal deflation timing can be controlled by a weighted combination of MDP and EDP.     

The central arterial pulses

Summary In order to examine the contours of central aortic and coronary flow pulses as well as those of pressure and flow pulses along the aorta, a hybrid model of the arterial system and the heart was designed. The digitally programmed model of the aortic system is an inhomogeneous transmission line with adjustable reflection factors at the end and at three intermediate locations. For the reflection factor at the entrance different values may be chosen for the ejection time and the diastole. The influence of a stenosis and of frequency-independent damping may be examined.The model of the ventricle is the analog solution of a system consisting of an internal isometric pressure source and an internal resistance and capacitance.The model of the coronary artery is the analog solution of a windkessel model of the system.The digital and analog models are interlocked by AD and DA converters. All programs can be executed in real time.The characteristic contour of the aortic flow is determined by the relation between the internal impedance of the ventricle and the magnitude of the characteristic impedance of the aorta. Furthermore, the influence of reflections within the arterial system is shown to be quite remarkable. Natural pressure pulses can be simulated by the model under normal and pathological conditions including aortic coarctation.The contour of the left coronary artery flow is determined on the one hand by the fraction of the ventricular pressure which acts as a counterpressure at the site of the peripheral resistance, and by the time constant of the coronary windkessel on the other hand.This work was supported by the Austrian research fund (Österreichischer Fonds zur Förderung der wissenschaftlichen Forschung).     

Asymmetric time-dependent model for the dynamic finger arterial pressure–volume relationship

The volumetric pulses in the finger PPG signal appear as an information source for several indirect measurement methods. In this study we modelled transformation of pressure pulses into volume pulses in a wide transmural pressure range. The noninvasive finger arterial pressure and photoplethysmographic (PPG) signals were simultaneously registered in 13 healthy subjects while the pressure in the PPG cuff ramped up and down. The nonlinearity of the pressure–volume (P–V) relationship was modelled by an asymmetric function, consisting of two arctangents, each for a different pressure region. The time dependency was described by the first order lag. The disturbing effect of slow creeps in the PPG signal was suppressed by an equal filtering of the measured and model-predicted signal. The differences between the two estimates of the subject’s P–V relationship for the increasing and decreasing cuff pressure were small thus showing the repeatability of this method, which can be used for the characterization of individual finger arterial behaviour as well as its changes.     

A comparative study of pulsatile arterial hemodynamics in rabbits and guinea pigs.

Pulsatile pressure and flow were measured in the ascending aorta and other arteries of 22 anesthetized rabbits and 16 anesthetized guinea pigs. Pressure/flow relationships were expressed as vascular impedance. Aortic flow waves were almost identical in the two species, but pressure waves were quite different. Reflected pressure waves returned earlier from the periphery in guinea pigs, augmenting pressure during late systole and resulting in relatively high external left ventricular work, an inappropriately larger difference between mean systolic and mean diastolic pressure and absence of any aortic diastolic pressure wave. Values of impedance modulus and phase were similar but differed in the frequency at which maxima and minima occurred. In both species, impedance curves were interpreted to indicate a functionally discrete reflecting site in the lower body whose position corresponded to the region of the aortic bifurcation. In addition, rabbits showed evidence of an upper body reflecting site approximately one-third as far distant from the heart. As in dogs, the arterial system in both species can be represented by an asymmetrical T-shaped model of realistic dimensions.