Multi-branched model of the human arterial system

A model of the human arterial system was constructed based on the anatomical branching structure of the arterial tree. Arteries were divided into segments represented by uniform thin-walled elastic tubes with realistic arterial dimensions and wall properties. The configuration contains 128 segments accounting for all the central vessels and major peripheral arteries supplying the extremities including vessels of the order of 2·0 mm diameter. Vascular impedance and pressure and flow waveforms were determined at various locations in the system and good agreement was found with experimental measurements. Use of the model is illustrated in investigating wave propagation in the arterial system and in simulation of arterial dynamics in such pathological conditions as arteriosclerosis and presence of a stenosis in the femoral artery.     

Effects of oscillation on the arteries measured by arterial impedance during left ventricular assistance

Oscillating blood flow has effects on the arteries similar to the effects of pulsatile blood flow at lower frequencies. Alternating-current theory is useful to study the pulse in the circulatory system. Arterial impedance is a good index to estimate the frequency characteristics of the artery. In this study, total vascular resistance and arterial impedance were studied in animal experiments during left ventricular assistance. A centrifugal pump was used for comparison with a VFP (vibrating-flow pump). Left ventricular assistance was performed in animal experiments using goats. Total vascular resistance and arterial impedance were studied to estimate the frequency characteristics of the artery. Total vascular resistance during steady flow assistance decreased compared with that during nonassistance. Arterial walls were extended by the blood flow assistance at steady flow. The resistance during oscillating blood flow was different at each driving frequency, showing the frequency dependency, or pulse effect, of the arterial system under nonsteady flow. Arterial impedance was also studied during oscillating blood flow and showed a slight increase at a driving frequency of 25 or 30 Hz. These fluctuations in impedance are influenced by the reflection of the pulse. Arterial impedance should be taken into consideration when analyzing pulsatile blood flow because the pulse reflection may have some effects on the arterial wall. Some variation of blood pressure and blood flow might be necessary for stable support with artificial circulatory assistance.     

Theoretical model for assessing haemodynamics in arterial networks which include bypass grafts

The paper presents a theoretical model which can be used to simulate a vascular network which includes loops and bypass grafts, a feature not possible with previous models. Using the linearised Navier-Stokes equations, the linearised equation of a uniform thick-walled viscoelastic tube, and the equation of continuity, the model is applied to a vascular network which includes a bypass graft. This method represents each segment of an artery or graft by a four-terminal-network whose A, B, C, D parameters are functions of the frequency and physical characteristics of the segment. The model predicts the flow and pressure waveforms at any point in the human arterial network very accurately when compared with data obtained from normal patients, patients with arterial stenoses and for hypertensive patients. The model also gives results which are in close agreement with hydraulic experimental data for the input impedance of systems with bypass loops.     

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.     

Analysis of pig’s coronary arterial blood flow with detailed anatomical data

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: oneasymmetric model satisfies all anatomical data (including the meanconnectivity matrix) and the other, asymmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.     

Right ventricular-pulmonary arterial interactions

The application of pulsatile models to hemodynamic data has made possible a more complete understanding of the relationship of pulmonary pressure and flow. To review the genesis of these concepts, the unique characteristics of the pulmonary artery and right ventricle are outlined as a basis for understanding why differences in their pulsatile properties from the systemic circuit must exist. The pulmonary impedance spectrum is introduced and the concept of optimal right ventricular-pulmonary artery coupling is explored based on a review of extensive experimental data. Finally, available studies of normal pulmonary impedance in man and abnormal impedance in human disease states are reviewed, with emphasis on disturbances in optimal ventricular-vascular coupling. The important implications of these concepts for understanding and treatment of cardiovascular disease are developed.     

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.     

Forward electrical transmission line model of the human arterial system

A forward mathematical model of the human arterial system, based on an electrical transmission line analogy, has been developed, using a new method for the calculation of peripheral impedance. Simulations of the human arterial system under normal and stenotic arterial conditions were compared with other published simulations, as well as measured clinical data and known clinical quantitative and qualitative characteristics: the harmonic arterial input impedance spectrum demonstrated a mean error of 0.07–0.1 mmHg.s.cm⁻¹, compared with equivalent simulation and physiological data, respectively; qualitative and quantitative variation of blood pressure and flow waveforms along the arterial tree followed clinical trends; arterial pulse wave velocities compared favourably with physiological data close to the aortic root (−50–20 cm s⁻¹ difference), but there were larger differences in the periphery (149–1192 cm s⁻¹ difference); qualitative as well as quantitative variation of blood flow waveforms with progressive stenotic arterial disease, as measured by the pulsatility index, demonstrated an error between 2 and 16% in comparison with mean clinical data for critical stenosis. Under the given test conditions, the forward model was found closely to represent clinically observed haemodynamic characteristics of the human arterial system.     

Incorporating Autoregulatory Mechanisms of the Cardiovascular System in Three-Dimensional Finite Element Models of Arterial Blood Flow

The cardiovascular system is a closed-loop system in which billions of vessels interact with each other, and it enables the control of the systemic arterial pressure and varying organ flow through autoregulatory mechanisms. In this study, we describe the development of mathematical models of autoregulatory mechanisms for systemic arterial pressure and coronary flow and discuss the connection of these models to a hybrid numerical/analytic closed-loop model of the cardiovascular system. The closed-loop model consists of two lumped parameter heart models representing the left and right sides of the heart, a three-dimensional finite element model of the aorta with coronary arteries, three-element Windkessel models and lumped parameter coronary vascular models that represent the systemic circulation, and a three-element Windkessel model to approximate the pulmonary circulation. Using the connection between the systemic arterial pressure and coronary flow regulation systems, and the hybrid closed-loop model, we studied how the heart, coronary vascular beds, and arterial system respond to physiologic changes during light exercise and showed that these models can realistically simulate temporal behaviors of the heart, coronary vascular beds, and arterial system during exercise of healthy subjects. These models can be used to study temporal changes occurring in the heart, coronary vascular beds, and arterial system during cardiovascular intervention or changes in physiological states.     

Pressure and volume measurements from the eye for detecting possible arterial obstruction

Detection and evaluation of functionally significant carotid occlusive disease are effectively achieved by noninvasive pressure and/or volume measurements from the eye. Ocular arterial blood pressure is measured by applying either direct compression or suction to evaluate intraocular pressure to the point of arterial collapse. Carotid blood flow is evaluated as it affects ocular volume waveforms, which result from the difference between pulsatile arterial flow and relatively constant venous flow. The relationship between noninvasive measurements from the eyes and carotid blood flow can be predicted using simple models of the cervical-cerebral circulatory system. Proper models verify clinically observed correlations between pressure and volume measurements from the eye and the underlying carotid occlusive disease. Electrical analog circuits provide a method for varying model parameters to simulate abnormalities, producing waveforms with good similarity to waveforms recorded from patients with known vascular or ophthalmic pathology. Further model refinements can be contributed by interested investigators. By using the improved models the strengths and weaknesses of current tests and techniques can then be better defined. Techniques that have been widely used for screening and evaluating potential stroke patients can thereby be modified to give improved functional analysis of these patients.     

Fast Estimation of Arterial Vascular Parameters for Transient and Steady Beats with Application to Hemodynamic State under Variant Gravitational Conditions

Numerous parameter estimation techniques exist for characterizing the arterial system using electrical circuit analogs. These techniques are often limited by requiring steady-state beat conditions and can be computationally expensive. Therefore, a new method was developed to estimate arterial parameters during steady and transient beat conditions. A four-element electrical analog circuit was used to model the arterial system. The input impedance equations for this model were derived and reduced to their real and imaginary components. Next, the physiological input impedance was calculated by computing fast Fourier transforms of physiological aortic pressure (AoP) and aortic flow. The approach was to reduce the error between the calculated model impedance and the physiological arterial impedance using a Jacobian matrix technique which iteratively adjusted arterial parameter values. This technique also included algorithms for estimating physiological arterial parameters for nonsteady physiological AoP beats. The method was insensitive to initial parameter estimates and to small errors in the physiological impedance coefficients. When the estimation technique was applied to in vivo data containing steady and transient beats it reliably estimated Windkessel arterial parameters under a wide range of physiological conditions. Further, this method appears to be more computationally efficient compared to time-domain approaches. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8710+e, 0230Qy     

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).     

Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries

Coronary flow is different from the flow in other parts of the arterial system because it is influenced by the contraction and relaxation of the heart. To model coronary flow realistically, the compressive force of the heart acting on the coronary vessels needs to be included. In this study, we developed a method that predicts coronary flow and pressure of three-dimensional epicardial coronary arteries by considering models of the heart and arterial system and the interactions between the two models. For each coronary outlet, a lumped parameter coronary vascular bed model was assigned to represent the impedance of the downstream coronary vascular networks absent in the computational domain. The intramyocardial pressure was represented with either the left or right ventricular pressure depending on the location of the coronary arteries. The left and right ventricular pressure were solved from the lumped parameter heart models coupled to a closed loop system comprising a three-dimensional model of the aorta, three-element Windkessel models of the rest of the systemic circulation and the pulmonary circulation, and lumped parameter models for the left and right sides of the heart. The computed coronary flow and pressure and the aortic flow and pressure waveforms were realistic as compared to literature data.     

Measurement of arterial pressure-dimension relationships in conscious animals

Currently, considerable clinical interest exists in the vasoactivity of large coronary arteries due to the prevalence of coronary vasospasm in mediating angina pectoris and even myocardial infarction. Although arterial elastic properties have been studied extensively in acute, anesthetized animal experiments and in vitro preparations, few data are available on these properties in conscious, chronically instrumented animals, where the complicating influences of anesthesia, recent surgery, and acute manipulation of the vessel are minimized. To study vascular smooth muscle in the conscious animal we modified the transit-time dimension measurement technique by designing smaller, higher frequency (7 MHz) transducers, and introducing electronic refinements to accurately measure smaller dimensions (2 mm minimum). We applied this technique to the left circumflex coronary (LCC) artery, along with arterial pressure measurements from either chronically implantable strain-gauge manometers, or microtip catheter manometers, to study dynamic compliance and vascular control mechanisms of these arteries for periods of months in conscious, chronically instrumented animals. Infusion of an α-adrenergic vasoconstrictor, methoxamine (50 μg/kg/min), caused sustained reduction in LCC diameter (9%±2%) at a time when mean arterial pressure rose by 65%±5% and heart rate and mean coronary blood flow (electromagnetic flow probe) were returned to control levels. Methoxamine induced a marked leftward shift in the pressure-diameter and stress-radius relationships, reducing vascular caliber for any given stress and pressure level. Moreover, smooth-muscle activation raised the effective incremental modulus (E_inc) of the coronary arterial wall when compared at similar radii, but it reduced E_inc when compared at similar stress or pressure levels. Thus, for any given arterial pressure level the E_inc of the LCC artery wall can be reduced considerably by the enhanced smooth-muscle activation elicited by methoxamine. Nitroglycerin (25 μg/kg) induced an initial decrease in LCC diameter as pressure fell and LCC blood flow rose. However, dimensions then increased, reaching a maximum 5 minutes later, when LCC blood flow was reduced, and heart rate and left ventricular dP/dt were at control levels. The calcium-channel antagonist, nifedipine, caused similar early changes, with the increase in LCC caliber persisting for 46±5 minutes while LCC blood flow returned to control in 15±3 minutes. Thus the long-lasting effects on large coronary arteries induced by nitroglycerin and calcium channel blockers are particularly important therapeutically, compared to the less persistent effects upon the coronary resistance vessels. The results of these experiments demonstrate (1) that the direct and continuous measurement of arterial diameter provides a sensitive and illuminating technique for the study of vascular smooth muscle activity, and (2), that although the technique is potentially applicable to acute animal studies, its real utility lies in the area of chronically instrumented animals where the many complicating influences of acute experimental preparations are eliminated or minimized.     

Identification algorithm for systemic arterial parameters with application to total artificial heart control

A new algorithm for estimating systemic arterial parameters from systolic pressure and flow measurements at the root of the aorta is developed and tested through a systems identification approach. The resulting procedure has direct application to a total artificial heart (TAH) control system currently under development. Identification models, representing the systemic arterial system, are developed from existing work in the area of cardiovascular modeling. The resistive and compliance components of these models are physically significant, representing overall hydraulic properties of the systemic arterial system. A unique method of parameterizing the identification models is designed which operates on the basis of aortic pressure and flow measurements taken exclusively during systole. The estimator is a modified recursive least squares algorithm which utilizes covariance modification to track time-varying parameters and a dead-zone to improve the robustness. Performance of the estimation algorithm was tested on data generated by a higher-order distributed model of the systemic arterial bed using normal canine parameters. Results from model-to-model experiments verify the consistency of the estimates and the ability of the estimator to converge quickly and track dynamically varying parameters.     

A simple method of obtaining quasi-continuous frequency spectra of the input impedance of arterial systems

Summary A simple method is described which permits a complete determination of the input impedance of the arterial system from a single flow and its accompanying pressure pulse. The method is based on the assumption that the pulse under consideration is a non-periodic function and not a periodic one. Thus, an approximation to the Fourier integral permits us to obtain a quasi-continuous frequency spectrum instead of the non-continuous spectrum provided by the usual Fourier analysis of natural pulses.     

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.     

Noninvasive measurement of arterial blood pressure and elastic properties using photoelectric plethysmography technique

The objective of this paper is to review our developed method for measuring noninvasively the arterial blood pressure as well as the mechanical properties of the vascular system in a thin portion of the biological segment such as human fingers or small animal extremities like rat tails and rabbit forelegs. This measurement is based on a principle called the 'volume-oscillometric method'. During the gradual change in cuff pressure, the amplitude of consecutive arterial volume pulsations associated with pulse pressure shows change characteristically due to the nonlinearity of arterial pressure-volume(P-V) relation. Arterial pressure can be accurately determined by detecting this characteristic change in the amplitude, while the arterial elastic properties such as P-V relationship and volume elastic modulus can be noninvasively obtained as a function of arterial transmural pressure, provided that the arterial volume changes are quantitatively determined during this pressure measurement. The validity and accuracy of this pressure and elasticity measurement with photoelectric plethysmography technique for detecting arterial volume changes are clearly demonstrated on the in vitro and in vivo experiments. Considering the simplicity and practicability of this measurement using the photoelectric plethysmography, we present a new portable instrument for the long-term ambulatory monitoring of indirect arterial pressure and a handy fully-automatic instrument for the noninvasive measurement of arterial elastic properties, and a few examples obtained by each instrument are also described.     

犬肺动脉高压模型连续热稀释法的应用

背景：以往小动物肺动脉高压模型有创测压方法一般根据生物信号采集系统的压力波形图引导,采用右心导管法进行压力测定;由于设备技术和动物体积的限制无法应用肺动脉导管测定心输出量及肺血管阻力。 目的：在脱氢野百合碱诱导建立犬肺动脉高压模型中利用Swan-Ganz七腔漂浮导管和Vigilance系统根据连续热稀释法测定心输出量、肺血管阻力,肺动脉压力,探讨连续心排量法在肺动脉高压动物模型中的应用价值。 方法：10只比格犬随机分成2组：实验组用脱氢野百合碱右心房注射的方法建立肺动脉高压的动物模型,对照组右心房注射二甲基酰胺做对照;在用药前,用药后8周使用漂浮导管和Vigilance系统分别测定两组犬右心房收缩压、右心室收缩压、肺动脉收缩压、平均肺动脉压力、肺毛细血管楔压及心输出量。 结果与结论：实验组用药后肺血管阻力显著上升(P=0.00),实验组用药后心输出量显著减少(P < 0.05)。使用连续热稀释法测定肺血管阻力和心输出量较传统的间断热稀释法更准确稳定。利用漂浮导管和Vigilance系统根据连续热稀释法原理在脱氢野百合碱诱导的犬肺动脉高压模型中进行肺血管阻力和心输出量测定,该方法具有准确稳定、可重复操作和对实验模型创伤小的优点。     

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).