The influence of a nonlinear resistance element upon in vitro aortic pressure tracings and aortic valve motions

In vitro testing of biological heart valves requires pressure and flow waveforms closely simulating natural conditions, which are mainly influenced by the characteristics of the vascular system. Simulation of the arterial function in artificial circulations was mostly performed by the useful Windkessel model but sometimes failed by generating inadequate systolic pressures. The integration of a novel nonlinear resistance element may improve the Windkessel function. Native porcine aortic valves were studied in a mock circulation with a novel nonlinear resistance element combined with the Windkessel compared with an aperture plate resistance. Pressure and flow measurements were performed at varying heart rates and stroke volumes and analyzed in the time and frequency domain. Aortic valve motions were evaluated using high speed video recording. With the classical afterload configuration including an aperture plate resistance, the pressure tracings showed a nonphysiologic decrease of pressure during systole after early peak pressure. By integration of the novel nonlinear resistance, peak systolic pressure occured later, peak pressure was higher, and the pressure waveform was more physiologically shaped. Leaflet motions of the aortic valves were less oscillatory and compared well with in vivo characteristics. In conclusion, a novel nonlinear resistance element in a mock circulation has the potential to provide more physiologic aortic pressure waveforms as influencing aortic valve dynamics and thus may be a helpful tool for investigation of biological heart valves.     

Subject-specific estimation of central aortic blood pressure via system identification: preliminary in-human experimental study

This paper demonstrates preliminary in-human validity of a novel subject-specific approach to estimation of central aortic blood pressure (CABP) from peripheral circulatory waveforms. In this “Individualized Transfer Function” (ITF) approach, CABP is estimated in two steps. First, the circulatory dynamics of the cardiovascular system are determined via model-based system identification, in which an arterial tree model is characterized based on the circulatory waveform signals measured at the body’s extremity locations. Second, CABP waveform is estimated by de-convolving peripheral circulatory waveforms from the arterial tree model. The validity of the ITF approach was demonstrated using experimental data collected from 13 cardiac surgery patients. Compared with the invasive peripheral blood pressure (BP) measurements, the ITF approach yielded significant reduction in errors associated with the estimation of CABP, including 1.9–2.6 mmHg (34–42 %) reduction in BP waveform errors (p < 0.05) as well as 5.8–9.1 mmHg (67–76 %) and 6.0–9.7 mmHg (78–85 %) reductions in systolic and pulse pressure (SP and PP) errors (p < 0.05). It also showed modest but significant improvement over the generalized transfer function approach, including 0.1 mmHg (2.6 %) reduction in BP waveform errors as well as 0.7 (20 %) and 5.0 mmHg (75 %) reductions in SP and PP errors (p < 0.05).     

Wave intensity analysis and the development of the reservoir–wave approach

The parameters of wave intensity analysis are calculated from incremental changes in pressure and velocity. While it is clear that forward- and backward-traveling waves induce incremental changes in pressure, not all incremental changes in pressure are due to waves; changes in pressure may also be due to changes in the volume of a compliant structure. When the left ventricular ejects blood rapidly into the aorta, aortic pressure increases, in part, because of the increase in aortic volume: aortic inflow is momentarily greater than aortic outflow. Therefore, to properly quantify the effects of forward or backward waves on arterial pressure and velocity (flow), the component of the incremental change in arterial pressure that is due only to this increase in arterial volume—and not, fundamentally, due to waves—first must be excluded. This component is the pressure generated by the filling and emptying of the reservoir, Otto Frank’s Windkessel.     

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).     

Harvey Cushing and the regulation of blood pressure in giraffe, rat and man: introducing 'Cushing's mechanism'

The fundamental mechanism that underlies essential hypertension is a high total peripheral resistance. We review here possible origins of high total peripheral resistance in physiologically hypertensive giraffes, spontaneously hypertensive rats and humans with essential hypertension. We propose that a common link could be reduced brainstem perfusion, as first suggested by Cushing in 1901. Any tendency towards reduction of cerebral blood flow to the cardiovascular control centres in rest and sleep will be prevented by activation of a response arising in the brainstem. The response will proportionately increase systemic blood pressure and return cerebral blood flow to a new homeostatic level. New evidence we review here supports this idea and leads us to suggest that central regulation of blood pressure has two components: the classic Cushing's response, which is a terminal event, and a Cushing's mechanism, which is a physiological mechanism for long-term control of mean arterial pressure. In giraffes, Cushing's mechanism is activated by increasing neck length during growth and subsequent gravitational hypotension that stimulates a rise in basal arterial blood pressure. In man and rats, the mechanism is activated by narrowing of the arteries supplying the brainstem. If we are correct, future successful treatment of essential hypertension in man will include methods of reducing cerebral arterial resistance.     

Long-term pressure monitoring with arterial applanation tonometry: a non-invasive alternative during clinical intervention?

Arterial tonometry is a non-invasive technique for continuous registration of arterial pressure waveforms. This study aims to assess tonometric blood pressure recording (TBP) as an alternative for invasive long-term bedside monitoring. A prospective study was set up where patients undergoing neurosurgical intervention were subjected to both invasive (IBP) and non-invasive (TBP) blood pressure monitoring during the entire procedure. A single-element tonometric pressure transducer was used to better investigate different inherent error sources of TBP measurement. A total of 5.7 hours of combined IBP and TBP were recorded from three patients. Although TBP performed fairly well as an alternative for IBP in steady state scenarios and some short-term variations, it could not detect relevant long-term pressure variations at all times. These findings are discussed in comparison to existing work. Physiological alterations at the site of TBP measurement are highlighted as a potentially important source of artifacts. It is concluded that at this point arterial tonometry remains not enough understood for long-term use during a delicate operative procedure. Physiological changes at the TBP measurement site deserve further investigation before tonometry technology is to be considered as an non-invasive alternative for long-term clinical monitoring.     

Mechanical principles. Arterial stiffness and wave reflection.

Arterial (and predominantly aortic) stiffening with age is now acknowledged as the cause of isolated systolic hypertension, and the predominant cause of cardiac failure in the elderly. Aortic stiffening is gauged clinically from increase in brachial pulse pressure, but this underestimates change with age, since aortic pulse pressure increases far more than brachial (on account of substantial amplification of the peripheral arterial pressure pulse in young adults). Aortic stiffness can be measured as pulse wave velocity, but this too underestimates ill effects on the heart and central vessels, since the direct effect is amplified by early return of wave reflection. Ill effects of arterial stiffening can best be assessed through analysis of pressure wave contour from the carotid or radial site. Exploitation of relatively constant brachial transfer function enables the central aortic pressure wave to be synthesised from the radial pulse. This new clinical approach links traditional sphygmography (originally introduced in France) with conventional cuff sphygmomanometry, and is being evaluated in clinical and epidemiological studies.     

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.     

Intravenous angiotensin II does not affect dynamic baroreflex characteristics of the neural or peripheral arc

Although the elevation of angiotensin II (Ang II) associated with cardiovascular diseases has been considered to suppress the arterial baroreflex function, how Ang II affects dynamic arterial pressure (AP) regulation remains unknown. The aim of the present study was to elucidate the acute effects of Ang II on dynamic AP regulation by the arterial baroreflex. In seven anesthetized Japanese white rabbits, we randomly perturbed intra-carotid sinus pressure (CSP) according to a binary white noise sequence while recording renal sympathetic nerve activity (RSNA) and AP. We estimated the neural arc transfer function from CSP to RSNA and the peripheral arc transfer function from RSNA to AP before and after 30-min intravenous administration of Ang II (100 ng/kg/min). Ang II increased mean AP from 75.7 +/- 3.1 to 95.5 +/- 5.1 mmHg (p < 0.01), while it did not affect mean RSNA (from 5.9 +/- 1.3 to 5.7 +/- 1.2 a.u.). The neural arc transfer functions did not differ before or after Ang II administration (dynamic gain: -0.94 +/- 0.04 vs. -0.94 +/- 0.13, corner frequency: 0.06 +/- 0.01 vs.0.06 +/- 0.01 Hz, pure delay: 0.16 +/- 0.01 vs. 0.17 +/- 0.02 s). The peripheral arc transfer function did not differ before or after Ang II administration (dynamic gain: 1.18 +/- 0.05 vs. 1.06 +/- 0.11, natural frequency: 0.07 +/- 0.01 vs. 0.08 +/- 0.01 Hz, damping ratio: 1.19 +/- 0.06 vs. 1.24 +/- 0.19, pure delay: 0.83 +/- 0.06 vs. 0.78 +/- 0.05 s). Intravenous Ang II hardly affects the dynamic characteristics of neural and peripheral arc around the physiological operating pressure.     

外周血压和中心动脉压的差异性研究

目的中心动脉压比外周动脉压对心血管终点事件具有更好的预测价值,本研究的目的是分析高血压人群中心动脉压和肱动脉压的差异。方法研究对象为640名(46岁±8岁)无明显心血管病体检者,根据肱动脉压分为高血压组和非高血压组,计算两组人群的中心动脉压和肱动脉压的脉压比值,来描述两动脉压的差异,通过逐步多变量线性回归分析确定脉压比值的独立影响因子。结果年龄和高血压是脉压比值的独立影响因子。随着年龄的增加,脉压比值不断增大。与非高血压人群相比,高血压人群脉压比值显著增加(P0.05)。对研究人群按照肱动脉收缩压进行风险等级划分,不同风险等级之间中心动脉收缩压的分布存在大量的重叠。结论中心动脉压不能由肱动脉压完全代替,准确评估中心动脉压可能提高对心血管事件的识别,完善对高血压人群的健康管理。     

Aortic pressure wave reconstruction during exercise is improved by adaptive filtering: a pilot study

Reconstruction of central aortic pressure from a peripheral measurement by a generalized transfer function (genTF) works well at rest and mild exercise at lower heart rates, but becomes less accurate during heavy exercise. Particularly, systolic and pulse pressure estimations deteriorate, thereby underestimating central pressure. We tested individualization of the TF (indTF) by adapting its resonance frequency at the various levels of exercise. In seven males (age 44–57) with coronary artery disease, central and peripheral pressures were measured simultaneously. The optimal resonance frequency was predicted from regression formulas using variables derived from the individual’s peripheral pressure pulse, including a pulse contour estimation of cardiac output (pcCO). In addition, reconstructed pressures were calibrated to central mean and diastolic pressure at each exercise level. Using a genTF and without calibration, the error in estimated aortic pulse pressure was −7.5 ± 6.4 mmHg, which was reduced to 0.2 ± 5.7 mmHg with the indTFs using pcCO for prediction. Calibration resulted in less scatter at the cost of a small bias (2.7 mmHg). In exercise, the indTFs predict systolic and pulse pressure better than the genTF. This pilot study shows that it is possible to individualize the peripheral to aortic pressure transfer function, thereby improving accuracy in central blood pressure assessment during exercise.     

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.     

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.     

Respiratory effect on the pulse spectrum

During the last decade, progressive achievements in haemodynamics have shown that radial artery pulse pressure can be used to estimate the vascular properties of the internal organs. Clinical experiments have shown that slow and regular respiration has a large effect on the heart rate variability (HRV). This phenomenon is called respiratory sinus arrhythmia (RSA). It is known that respiration-related oscillations in venous return cause oscillations in stroke volume and blood pressure. It also can be inferred from cardiac output that systemic blood pressure has a similar respiration-related cycle. Moreover we found that the fluctuations of harmonics of arterial pulse are consistent with the fluctuation of HRV. This means that the whole cardiovascular system (CVS) makes rapid adaptation during respiration, and the harmonic proportions of arterial pulse were modified during different breath rates. This result shows that the regular respiration also has a large effect upon Windkessel properties of CVS.     

Respiratory effect on the pulse spectrum

During the last decade, progressive achievements in haemodynamics have shown that radial artery pulse pressure can be used to estimate the vascular properties of the internal organs. Clinical experiments have shown that slow and regular respiration has a large effect on the heart rate variability (HRV). This phenomenon is called respiratory sinus arrhythmia (RSA). It is known that respiration-related oscillations in venous return cause oscillations in stroke volume and blood pressure. It also can be inferred from cardiac output that systemic blood pressure has a similar respiration-related cycle. Moreover we found that the fluctuations of harmonics of arterial pulse are consistent with the fluctuation of HRV. This means that the whole cardiovascular system (CVS) makes rapid adaptation during respiration, and the harmonic proportions of arterial pulse were modified during different breath rates. This result shows that the regular respiration also has a large effect upon Windkessel properties of CVS.     

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.     

Non-invasive monitoring of central blood pressure by electrical impedance tomography: first experimental evidence

There is a strong clinical demand for devices allowing continuous non-invasive monitoring of central blood pressure (BP). In the state of the art a new family of techniques providing BP surrogates based on the measurement of the so-called pulse wave velocity (PWV) has been proposed, eliminating the need for inflation cuffs. PWV is defined as the velocity at which pressure pulses propagate along the arterial wall. However, no technique to assess PWV within central arteries in a fully unsupervised manner has been proposed so far. In this pilot study, we provide first experimental evidence that electrical impedance tomography (EIT) is capable of measuring pressure pulses directly within the descending aorta. To obtain a wide range of BP values, we administrated noradrenalin and nitroglycerine to an anesthetized pig under mechanical ventilation. An arterial line was inserted into the ascending aorta for measuring reference BP. EIT images were generated from 32 impedance electrodes placed around the chest at the level of the axilla. Regions of Interest (ROI) such as the descending aorta and the lungs were automatically identified by a novel time-based processing algorithm as the respective EIT pixels representing these structures. The correct positions of these ROIs were confirmed by bolus injections of highly conductive concentrated saline into the right heart and into the ascending aorta. Aortic pulse transit time (PTT) values were determined as the delay between the opening of the aortic valve (obtained from arterial line) and the arrival of pressure pulses at the aortic ROI within the EIT plane. For 11 experimental conditions, with mean BP ranging from 73 to 141 mmHg, strongly significant correlation (r = −0.97, P < 0.00001) between central BP and aortic PTT was observed, suggesting that EIT-derived aortic PTT is a potential non-invasive surrogate of central BP.     

An MRI compatible loading device for the reconstruction of clinically relevant plantar pressure distributions and loading scenarios of the forefoot

The purpose of this study is to demonstrate a new MRI compatible loading device capable of reconstructing realistic loading scenarios of the human foot for research in the field of foot biomechanics. This device has two different configurations: one used to compress the forefoot and one to bend the metatarsophalangeal joints. Required plantar pressure distribution under the metatarsal heads can be achieved by modifying the distribution of the dorsally applied forces. To validate the device, subject-specific plantar pressures were measured and then reconstructed using the device. For quiet stance the peak pressure reconstruction error was 3% while for mid-stance phase of gait it was 8%. The device was also used to measure the passive bending stiffness of the metatarsophalangeal joints of one subject with low intra-subject variability. A series of preliminary MRI scans confirmed that the loading device can be used to produce static weight-bearing images of the foot (voxel size: 0.23 mm × 0.23 mm × 1.00 mm).The results indicate that the device presented here can accurately reconstruct subject specific plantar pressure distributions and measure the foot's metatarsophalangeal passive stiffness. Possible future applications include the validation of finite element models, the investigation of the relationship between plantar pressure and internal stresses/strains and the study of the foot's inter-segmental passive stiffness.     

Pulsatile pressure and flow in the mesenteric vascular bed of the cat

Summary The transmission of arterial pressure and flow pulse through the mesenteric vascular bed was studied in 18 experiments on cats. Pressures were measured in the superior mesenteric artery and in small mesenteric veins, red blood cell flow velocities in mesenteric microvessels smaller than 60 diameter. Venous pressures were found to show heart beat synchronous oscillatory components of 0.2–0.5mmHg amplitude. Venous pressure pulses were delayed in time in comparison to the arterial pressure pulses: mean transit times varied between 85 and 110 msec. Blood flow velocities in arterioles and venules were generally pulsatile, the amplitude of the arteriolar pulses averaging 52.5% of mean velocity, of the venular pulses 32.5%. The velocity pulses were found to be similar in shape as flow pulses in larger arteries. Infusion of vasoactive drugs showed transmission of arterial pulses to be inversely dependent upon vascular resistance. It is concluded that the concept of complete damping of the arterial pulse during the passage of blood through the intestinal vascular bed cannot be maintained. Two different mechanisms of pulse transmission are discussed: direct hydraulic transmission through the capillary network and transmission across the vascular wall from the arteriole to the venule.Supported by USPHS Grant HE-08977.