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.     

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.     

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).     

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.     

Assessment of distributed arterial network models

The aim of this study is to evaluate the relative importance of elastic non-linearities, viscoelasticity and resistance vessel modelling on arterial pressure and flow wave contours computed with distributed arterial network models. The computational results of a non-linear (time-domain) and a linear (frequency-domain) mode were compared using the same geometrical configuration and identical upstream and downstream boundary conditions and mechanical properties. Pressures were computed at the ascending aorta, brachial and femoral artery. In spite of the identical problem definition, computational differences were found in input impedance modulus (max. 15–20%), systolic pressure (max. 5%) and pulse pressure (max. 10%). For the brachial artery, the ratio of pulse pressure to aortic pulse pressure was practically identical for both models (3%), whereas for the femoral artery higher values are found for the linear model (+10%). The aortic/brachial pressure transfer function indicates that pressure harmonic amplification is somewhat higher in the linear model for frequencies lower than 6 Hz while the opposite is true for higher frequencies. These computational disparities were attributed to conceptual model differences, such as the treatment of geometric tapering, rather than to elastic or convective non-linearities. Compared to the effect of viscoelasticity, the discrepancy between the linear and non-linear model is of the same importance. At peripheral locations, the correct representation of terminal impedance outweights the computational differences between the linear and non-linear models.     

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part A: Identification of most influential model parameters

Previously, a pulse wave propagation model was developed that has potential in supporting decision-making in arteriovenous fistula (AVF) surgery for hemodialysis. To adapt the wave propagation model to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a sensitivity analysis the propagation of input uncertainties into output uncertainty can be studied which can give directions for input measurement improvement. In this study, a computational framework has been developed to perform such a sensitivity analysis with a variance-based method and Monte Carlo simulations. The framework was used to determine the influential parameters of our pulse wave propagation model applied to AVF surgery, with respect to parameter prioritization and parameter fixing. With this we were able to determine the model parameters that have the largest influence on the predicted mean brachial flow and systolic radial artery pressure after AVF surgery. Of all 73 parameters 51 could be fixed within their measurement uncertainty interval without significantly influencing the output, while 16 parameters importantly influence the output uncertainty. Measurement accuracy improvement should thus focus on these 16 influential parameters. The most rewarding are measurement improvements of the following parameters: the mean aortic flow, the aortic windkessel resistance, the parameters associated with the smallest arterial or venous diameters of the AVF in- and outflow tract and the radial artery windkessel compliance.     

Computer identification of models for the arterial tree input impedance: Comparison between two new simple models and first experimental results

Two new simple models for the arterial tree input impedance are presented. The first is a 4-element windkessel model, obtained by paralleling the characteristic resistance of the 3-element windkessel model (Westerhof, 1968) with an inductance. The second is a tube model with a complex load, which is characterised by four parameters also. The parameters of these models are estimated from aortic root pressure and flow, which are either simulated by a complex numerical model of the peripheral arterial tree or measured in dogs. The parameter estimation is carried out using an automatic procedure based on the Powell optimisation algorithm. The importance of the evaluation of the achievable accuracy in the estimation of parameters and its relationship to model identifiability is emphasised.     

Tuning Multidomain Hemodynamic Simulations to Match Physiological Measurements

In recent years, considerable progress has been made in creating more realistic models of the cardiovascular system, often based on patient-specific anatomic data, whereas comparatively little progress has been made on incorporating measured physiological data. We have developed a method to systematically adjust the parameters of three-element windkessel outlet boundary conditions of three-dimensional blood flow models such that desired features of pressure and flow waveforms are achieved. This tuning method was formulated as the solution of a nonlinear system of equations and employed a quasi-Newton method that was informed by a reduced-order model. The three-dimensional hemodynamic models were solved using a stabilized finite-element method incorporating deformable vessel walls. The tuning method was applied to an idealized common carotid artery, an idealized iliac arterial bifurcation, and a patient-specific abdominal aorta. The objectives for the abdominal aortic model were values of the maximum and minimum of the pressure waveform, an indicator of the pressure waveform’s shape, and the mean, amplitude, and diastolic mean of the flow waveform for an infrarenal measurement plane. The hemodynamic models were automatically generated and tuned by custom software with minimal user input. This approach enables efficient development of cardiovascular models for applications including detailed evaluation of cardiovascular mechanics, simulation-based design of medical devices, and patient-specific treatment planning.     

Dynamic model of the short-term regulation of arterial pressure in the cat

The purpose of this study was to characterise the dynamics of the short-term control of arterial pressure in the cat with the aid of a model consisting of a nonlinear negative-feedback control system. The arterial system was described by a three element windkessel model (peripheral resistance, R, aortic characteristic impedance, R_c, and total arterial compliance, C). The resistance regulation was represented by a second-order system with static gain G_R, a damping factor σ and an undamped natural frequency ω_n. The resistance gain, G_R, and the windkessel parameters were obtained from measurements of aortic and venous pressures and cardiac output in two steady states. The parameters σ and ω_n were estimated from mean pressure and mean flow during the transient from control to the new steady state. Pressure reductions averaged 10 per cent and resistance changes averaged 12 per cent. Average windkessel model parameters in the control condition were: C=(25·9±6·1) 10⁻⁶ g⁻¹ cm⁴ s², R_c=(2·51±0·53) 10³ g cm⁻⁴ s⁻¹, R=(40·9±9·8) 10³ g cm⁻⁴ s⁻¹. Average estimates of parameters of the resistance regulator were: G_R=(4·14±2·38) 10⁻³ min ml⁻¹, ω_n = 1·0 ± 1·0 rad s⁻¹, σ=0·41±0·19. A satisfactory fit was found between model predicted and measured pressure. The results suggest that the dynamic short-term control of pressure is underdamped and oscillatory. The amplitude of these oscillations is affected by arterial compliance, suggesting an interaction between the arterial system and short-term resistance regulation.     

Central cardiovascular dynamics of ducks.

Blood pressures and flows have been recorded from the heart and arterial arches of ducks in order to present a complete picture of central hemodynamics in an avian species. An attempt has also been made to define the characteristics of the avian central circulation in terms of either "windkessel", or wave-transmission models. Mean arterial pressure (143 plus or minus 2.2 mmHg) and cardiac output (219 plus or minus 7ml/kg per min) were high compared with those of similarly sized mammals, although therewas no evidence of elevated pulmonary pressures, perhaps because of the unusual structure of the avian lung. Only 25% of the total systemic flow was distributed by the aorta, the remainder supplying the wing, flight muscles, and head via the brachiocephalic arteries. The contours of central pressure and flow waves ressembled those recorded inmammal except that significant circulation impedance modulus graphs indicated that resistance to pulsatile flow fell sharply to a minimum of 1/30th the DC value at 9-12 Hz. Flow led pressure at frequencies below 9-12Hz and pressure led flow at higherfrequencies. Impedance modulus in the pulmonary circulation fell to one-half the DC value and remained constant over a wide range of frequencies with pressure and flow being in a phase at all frequencies. Aortic pulse wave velocity varied with position inthe aorta as did the pressure pulse profile: these factors obviously limit the applicability of a windkessel model to the avian circulation.     

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.     

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.     

A transmission line model of the human foetal circulatory system

A transmission line model of the human foetal circulatory system is presented. The model has been developed in the frequency domain with the cardiac input modeled as a flow rather than as a pressure pulse and is structured upon electrical transmission line analogies. The model is formed by cascading solutions to the two-dimensional Navier-Stokes equations for both oscillatory and steady, laminar viscous fluid flow in isotropic visco-elastic tubes with thick walls, which are constrained by surrounding tissues. Simulations allow for representation of both forward and retrograde travelling flow and pressure waves in all of the main foetal arterial vessels. The solution is verified by a comparison of model generated Doppler indices in the thoracic aorta, abdominal aorta, iliac artery and both ends of the umbilical arteries with previously published indices obtained by clinical measurements in these arteries. For simulations of blood flow in a healthy foetus, the model generated Pulsatility and Resistance indices were on average within 8% of the corresponding clinical measurements. The model results also demonstrates that placental resistance must increase by a factor of three, corresponding to a 60% decrease in flow to the placenta, before umbilical arterial absent end diastolic flow is observed. Differences between indices obtained from simulations at opposite ends of the umbilical arteries increase with increasing placental resistance.     

Studies of cerebral circulation in series experiments by means of changes in the blood pressure gradient in vessels supplying the brain

Summary A method of graphic a recording of arterial blood pressure in the aorta and the circle of Willis in series experiments on dogs is described. Measurements were taken in the common carotid artery brought out into a skin flap, to which 3 cuffs were attached: medial, recording variations in the pulse, one placed caudad and one cephalad from the medial cuff, occluding corrspondingly the blood flow from the aorta and the circle of Willis. The blood pressure in the bead occluding collar corresponded to the blood pressure in the circle Willis, after disappearance of aorta during complete occlusion of the inflow of blood from the aorta. The cortic blood pressure was determined by the appearance of the first pulse beat in decrease of the pressure in “thoracic” cuff with preserved occlusion of the “head” portion of the common carotid artery. The changes of the gradient of the fall of blood pressure from aorta to the blood vessels of the circle of Willis served as an indication of changes of the lumen of blood vessels of the brain (Hurthle's principle). Presented by Active Member AMN SSSR N. A. Rozhansky     

Hybrid Cardiopulmonary Model for Analysis of Valsalva Maneuver with Radial Artery Pulse

A comprehensive model, which has the advantages of both lumped parameter and distributed parameter, has been developed with the objective of investigating the respiratory influences in radial artery pressure pulse as in photoplethysmography (PPG). It integrates lumped parameter cardiopulmonary (CP) model and transmission line arterial tree model from aorta to radial artery. The cardio-pulmonary interaction is realized by incorporating respiratory-induced variations in intrapleural pressure (Ppl) in circulatory system. The PPG signal of the model is considered as the radial artery pulse. To investigate the interaction Valsalva Maneuver (VM) condition has been simulated for different Ppl magnitude (10, 20, 30, and 40 mmHg) and for different time duration (5, 10, 15, and 20 s), and validated with PPG signal recorded in 10 normal subjects performing VM. The effects of test duration and VM pressure are studied in both the simulation and the experiments with specific focus on the maximal (%∆) changes in Heart Rate (HR), and Mean Arterial Pressure (MAP) during phases II and IV of VM. The correlation coefficients derived from model result have good agreement with experimental results. As radial artery pulse plays important role in both allopathy and alternate medicine systems, this model can serve to study its clinical importance in detecting cardiac and respiratory pathologies.     

主动脉转流对腹主动脉阻断所致血液动力学等改变的影响

目的:探讨不同流量主动脉转流对腹主动脉暂时性阻断时全身血液动力学等改变的影响。方法:实验建立在小猪腹腔动脉开口以上阻断腹主动脉1h和同时应用辅助主动脉转流的模型,监测血液动力学的变化,并观察组织学的改变。结果:阻断组发生了明显的血液动力学紊乱,尿量明显减少,代谢性酸中毒也极为明显,肝、肾和小肠组织及超微结构均发生了明显的病变。在主动脉转流组血液动力学的紊乱得到明显改善。结论:腹主动脉阻断1h将造成严重的全身血液动力学紊乱,当转流量达到原腹主动脉血流量的70%时主动脉转流能较好地防止这一损伤改变。     

牙髓牙本质复合体中VIP阳性神经纤维的研究

目的:研究血管活性肠肽(VIP)在牙髓牙本质复合体中的表达,探讨其功能。方法:收集人前磨牙,石蜡包埋切片,作免疫组织化学和图象定量分析。结果:VIP阳性神经纤维自根尖孔呈束状进入牙髓,至颈部扇形分开,在冠髓大量分支,部分围绕在血管周围,部分终止于牙髓基质,部分参与形成成牙本质细胞层下Raschkow神经丛,然后发出分支伸入成牙本质细胞层和前期牙本质,但不进入成熟牙本质。VIP阳性神经纤维在冠髓的积分光密度为12.74±1.807,体密度为0.0192±0.0127,线密度为0.0046±0.0029,在前期牙本质的积分光密度为13.07±1.927,线段长度为(19.60±8.597)mm。结论:VIP阳性神经纤维存在于人牙髓牙本质复合体,部分纤维围绕血管,部分纤维止于牙髓基质和前期牙本质,这种分布提示该纤维除与血管运动有关外,可能还与感觉有关,在痛觉传导、血管调节等方面发挥重要作用。     

Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions

A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from 10 ovine aortas and 10 human carotid arteries. Ex vivo measurements (from both locations) were made in 11 male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates, we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the artery type. Results showed that for the thoracic descending aorta (under both experimental conditions), the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure–area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure–area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties.     

实验性低血压大鼠动脉的生物力学特性

为了研究低血压状态下动脉重建后,动脉的生物力学特性的变化,在大鼠左肾动脉起点以下缩窄腹主动脉,建立实验性低血压大鼠模型,按不同的时相点,观察腹主动脉、股动脉和胫前动脉张开角的变化,并进行在体腹主动脉的压力－容积（P－V）关系实验。结果显示,低血压大鼠的动脉血压降低,导致动脉壁的非均匀性生长,表现为动脉零应力状态下张开角减小。低血压状态时,腹主动脉的C／E比值减小,顺应性增加。     

Mathematical modelling of non-invasive oscillometric finger mean blood pressure measurement by maximum oscillation criterion

A mathematical study is performed to assess how the arterial pressure-volume (P-V) relationship, blood pressure pulse amplitude and shape affect the results of non-invasive oscillometric finger mean blood pressure estimation by the maximum oscillation criterion (MOC). The exponential models for a relaxed finger artery and for a partly contracted artery are studied. A new modification of the error equation is suggested. This equation and the results of simulation demonstrate that the value of pressure estimated by the MOC does not exactly agree with the value of the true mean blood pressure (the latter being defined as pressure corresponding to maximum arterial compliance). The error depends on the arterial pressure pulse amplitude, as well as on the difference between the arterial pressure pulse shape index and the arterial P-V curve shape index. In the case of contracted finger arteries, the MOC can give an overestimation of up to 19 mmHg, the pressure pulse shape index being 0.21 and the pulse amplitude 60 mmHg. In the case of relaxed arteries, the error is less evident.