Wave-travel in a Non-uniform Transmission Line, in Relation to Pulses in Arteries

Pulse flow of liquid in flexible tube

The simulation of liquid flow in significantly deformed elastic material is one of the more challenging tasks. Tube wall motion prediction implemented directly into CFD software can noticeably reduce the computational and time demands of such problems. The FSI simulation of a liquid-flowed flexible plastic tube was analyzed on the FEA and CFD solvers coupling basis. The flexible tube is the basic symmetric test body that could be appropriately tested on the experimental stand. A comparison of experimental data and FSI problem using commercial code and one-dimensional tube models was made by evaluating the tube wall deformation magnitudes at defined flow ratios. The type of tube material, which can be understood as a nonlinear from the stress and deformation point of view, was considered. The paper shows several possibilities of tube modeling using the main constitutive relations of linear and nonlinear mechanics. The hyperelastic material models such as neo-Hookean and Mooney-Rivlin were tested. The results represent differences in impacts on the tube liquid flow and differences in the magnitudes of the wall tube deformations. Based on these findings it should be possible to simulate the problems of liquid flow in more complicated shape flow zones, such as arteries affected by various defects, in our future research.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

Alterations in Carotid Parameters in ApoE-/- Mice Treated with a High-Fat Diet: A Micro-ultrasound Analysis

Information on the common carotid artery and cerebral microcirculation can be obtained by micro-ultrasound (µUS). The aim of the study described here was to investigate high-fat diet-induced alterations in vascular parameters in ApoE-/- mice. Twenty-two ApoE-/- male mice were examined by µUS and divided into the standard diet (ApoE-/-_SD) and high-fat diet (ApoE-/-_HF) groups. The µUS examination was repeated after 4 mo (T₁). Carotid stiffness, reflection magnitude and reflection index were measured; the amplitudes of the first (W₁) and second (W₂) local maxima, the local minimum (W_b) and the reflection index (RI_WIA = W_b/W₁) were assessed with wave intensity analysis. At T₁, ApoE-/-_HF mice had increased carotid stiffness (1.48 [0.36] vs. 1.88 [0.51]) and reflection magnitude (0.89 [0.07] vs. 0.94 [0.07]) values. Longitudinal comparisons highlighted increases in carotid stiffness for ApoE-/-_HF mice (from 1.37 [0.25] to 1.88 [0.51] m/s) but not for ApoE-/-_SD mice (from 1.40 [0.62] to 1.48 [0.36] m/s). ApoE-/-_HF mice exhibited carotid artery stiffening and increased wave reflections.

A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree

For the purpose of optimization of the whole arterial tree, a fast method for solving of one-dimensional model of blood flow is required. A semi-analytic transmission line method for solving a linearized one-dimensional model of blood flow in an arterial tree with viscoelastic walls is proposed. The transmission line method that solves the linearized model in the frequency domain and the method of characteristics that solves either linearized or non-linear one-dimensional models in the time domain are compared regarding accuracy and computational time. For this purpose, the benchmark problem of a 37-artery network with available experimental data is used. In the case of the linearized model, the results from the transmission line method and the method of characteristics are practically the same. The difference between the transmission line method solution of the linearized model and the method of characteristics solution of the non-linear model is much smaller than the error of either method of characteristics or transmission line method numerical solutions with respect to the experimental data. For typical applications, the transmission line method is at least two orders of magnitude faster than the method of characteristics.

Arterial Stiffening in Perspective: Advances in Physical and Physiological Science Over Centuries

Arterial stiffening is not a new issue in medicine or research but was the prime concern of Richard Bright in the early 19th century and of the prominent London physicians and pathologists who tried to unscramble the relationship between kidney, heart, and cerebrovascular disease and hardness of the pulse in the late 19th century. It was of major concern to medical educators including Osler and Mackenzie who were still active in practice 100 years ago. It is all too easy (when dependent on the Internet) to consider arterial stiffness to be a new issue. The terms arterial stiffness, aortic stiffness, or wave reflection do not appear as categories for articles such as this in respectable journals, nor in categories for meetings of specialized physicians. Yet as described in this article, the subject was of interest to clinicians, to investigators such as Harvey in the 17th century, and to physicists who developed laws and principles of elasticity from the study of biological materials including ligaments and arteries. This paper provides a perspective on arterial stiffness from the time of William Harvey and Isaac Newton to the present, with a glance into the future.

A review of selected pumping systems in nature and engineering--potential biomimetic concepts for improving displacement pumps and pulsation damping

The active transport of fluids by pumps plays an essential role in engineering and biology. Due to increasing energy costs and environmental issues, topics like noise reduction, increase of efficiency and enhanced robustness are of high importance in the development of pumps in engineering. The study compares pumps in biology and engineering and assesses biomimetic potentials for improving man-made pumping systems. To this aim, examples of common challenges, applications and current biomimetic research for state-of-the art pumps are presented. The biomimetic research is helped by the similar configuration of many positive displacement pumping systems in biology and engineering. In contrast, the configuration and underlying pumping principles for fluid dynamic pumps (FDPs) differ to a greater extent in biology and engineering. However, progress has been made for positive displacement as well as for FDPs by developing biomimetic devices with artificial muscles and cilia that improve energetic efficiency and fail-safe operation or reduce noise. The circulatory system of vertebrates holds a high biomimetic potential for the damping of pressure pulsations, a common challenge in engineering. Damping of blood pressure pulsation results from a nonlinear viscoelastic behavior of the artery walls which represent a complex composite material. The transfer of the underlying functional principle could lead to an improvement of existing technical solutions and be used to develop novel biomimetic damping solutions. To enhance efficiency or thrust of man-made fluid transportation systems, research on jet propulsion in biology has shown that a pulsed jet can be tuned to either maximize thrust or efficiency. The underlying principle has already been transferred into biomimetic applications in open channel water systems. Overall there is a high potential to learn from nature in order to improve pumping systems for challenges like the reduction of pressure pulsations, increase of jet propulsion efficiency or the reduction of wear.

Estimated in vivo postnatal surface growth patterns of the ovine main pulmonary artery and ascending aorta

Delineating the normal postnatal development of the pulmonary artery (PA) and ascending aorta (AA) can inform our understanding of congenital abnormalities, as well as pulmonary and systolic hypertension. We thus conducted the following study to delineate the PA and AA postnatal growth deformation characteristics in an ovine model. MR images were obtained from endoluminal surfaces of 11 animals whose ages ranged from 1.5 months/15.3 kg mass (very young) to 12 months/56.6 kg mass (adult). A bicubic Hermite finite element surface representation was developed for the each artery from each animal. Under the assumption that the relative locations of surface points were retained during growth, the individual animal surface fits were subsequently used to develop a method to estimate the time-evolving local effective surface growth (relative to the youngest measured animal) in the end-diastolic state. Results indicated that the spatial and temporal surface growth deformation patterns of both arteries, especially in the circumferential direction, were heterogeneous, leading to an increase in taper and increase in cross-sectional ellipticity of the PA. The longitudinal PA growth stretch of a large segment on the posterior wall reached 2.57 ± 0.078 (mean ± SD) at the adult stage. In contrast, the longitudinal growth of the AA was smaller and more uniform (1.80 ± 0.047). Interestingly, a region of the medial wall of both arteries where both arteries are in contact showed smaller circumferential growth stretches-specifically 1.12 ± 0.012 in the PA and 1.43 ± 0.071 in the AA at the adult stage. Overall, our results indicated that contact between the PA and AA resulted in increasing spatial heterogeneity in postnatal growth, with the PA demonstrating the greatest changes. Parametric studies using simplified geometric models of curved arteries during growth suggest that heterogeneous effective surface growth deformations must occur to account for the changes in measured arterial shapes during the postnatal growth period. This result suggests that these first results are a reasonable first-approximation to the actual effective growth patterns. Moreover, this study clearly underscores how functional growth of the PA and AA during postnatal maturation involves complex, local adaptations in tissue formation. Moreover, the present results will help to lay the basis for functional replacement by defining critical geometric metrics.

Mechanics and Function of the Pulmonary Vasculature: Implications for Pulmonary Vascular Disease and Right Ventricular Function

The relationship between cardiac function and the afterload against which the heart muscle must work to circulate blood throughout the pulmonary circulation is defined by a complex interaction between many coupled system parameters. These parameters range broadly and incorporate system effects originating primarily from three distinct locations: input power from the heart, hydraulic impedance from the large conduit pulmonary arteries, and hydraulic resistance from the more distal microcirculation. These organ systems are not independent, but rather, form a coupled system in which a change to any individual parameter affects all other system parameters. The result is a highly nonlinear system which requires not only detailed study of each specific component and the effect of disease on their specific function, but also requires study of the interconnected relationship between the microcirculation, the conduit arteries, and the heart in response to age and disease. Here, we investigate systems-level changes associated with pulmonary hypertensive disease progression in an effort to better understand this coupled relationship.

Evaluation of digital blood pressure measured with the Omron F3 device as an index of brachial arterial pressure, under different thermal and hormonal conditions

BACKGROUND

Devices that record from the finger have potential practical advantages for home monitoring of blood pressure. However, digital arterial pressure may vary substantially from that in the brachial artery, due to the influence of peripheral wave reflection.

AIMS

(1) To compare digital arterial pressure, as measured with the Omron F3 device, with brachial arterial pressure and (2) to determine the effect on digital pressure of changing local vascular resistance.

METHOD

The subjects were normotensive young adult non-smokers (12 males, 14 females). Pressures were recorded simultaneously from arm (using an Omron HEM-705CP) and finger with subjects seated and both recording sites at the level of the xiphisternum. Measurements were made at ambient temperatures of 19 degrees C and 30 degrees C; at rest, during brief contralateral hand cooling and after hand rewarming.

RESULTS

In many cases, resting finger values differed substantially from arm values; sometimes by 20 mm Hg or more. The extent of individual variations was not correlated with gender or temperature. However, group pressure differences between the sites were greater in females at ovulation than at menstruation and greater at 30 degrees C than at 19 degrees C. For all groups, pressure differences between sites were attenuated during hand cooling and restored by rewarming.

CONCLUSIONS

Finger blood pressure, as measured with the Omron F3, misestimates brachial blood pressure in a high proportion of normal subjects. This error is increased under circumstances associated with cutaneous vasodilation. The Omron F3 does not appear to be suitable for unsupervised home monitoring of blood pressure.

Infinite number of solutions to the hemodynamic inverse problem

Investigators have had much success solving the "hemodynamic forward problem," i.e., predicting pressure and flow at the entrance of an arterial system given knowledge of specific arterial properties and arterial system topology. Recently, the focus has turned to solving the "hemodynamic inverse problem," i.e., inferring mechanical properties of an arterial system from measured input pressure and flow. Conventional methods to solve the inverse problem rely on fitting to data simple models with parameters that represent specific mechanical properties. Controversies have arisen, because different models ascribe pressure and flow to different properties. However, an inherent assumption common to all model-based methods is the existence of a unique set of mechanical properties that yield a particular pressure and flow. The present work illustrates that there are, in fact, an infinite number of solutions to the hemodynamic inverse problem. Thus a measured pressure-flow pair can result from an infinite number of different arterial systems. Except for a few critical properties, conventional approaches to solve the inverse problem for specific arterial properties are futile.

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.

Identification and physiological relevance of an exponentially tapered tube model of canine descending aortic circulation

The aim of this study was to evaluate the effect of incorporating aortic tapering in a tube model of descending aortic circulation. We described the descending aorta and its peripheral load by an exponentially tapered transmission tube terminating in a first-order, low-pass filter load. Under the assumption of adaptation between the transmission tube and the terminal load, the input impedance of this model was characterized by five free parameters, the characteristic impedance, Zce(0), at the tube entrance; the product, qde, between the tapering factor q and the tube length, de, the product ce(0)de, between the compliance, ce(0), at the tube entrance and the tube length; the time constant, tau ne, of the load and the peripheral resistance, Rp. We estimated these parameters making use of experimental pressure and flow measurements taken from the high descending aorta of three anaesthetized dogs. We contrasted the behaviour of this model with that of a competing model constituted by a uniform transmission tube also terminating in a first-order low-pass filter load. We compared the data fits and, with the aid of an extra measurement of pressure in the abdominal aorta, we tested the congruence between the estimates of the transmission tubes' parameters and the physical and geometrical properties of descending thoracic aorta. The tapered tube model showed a slightly better ability in fitting to experimental flow and reproducing input impedance data. However, the estimates of the transmission tube parameters failed to assess the physical properties of descending aorta. By contrast, the estimates of tube parameters provided by the uniform model allowed location of the junction between the tube and its terminal load in the abdominal aorta at level of major branches. These estimates were well correlated with the real system's properties. In conclusion, the complexity added to the uniform tube model by accounting for exponential aortic tapering gave rise only to a better curve fitting, but did not show any identifiable benefits regarding physiological interpretation of the physical properties of the descending aorta.

Impedance and wave reflection in arterial system: simulation with geometrically tapered T-tubes

The aortic input impedance is simulated by an asymmetric T-tube model loaded with complex loads. A geometric tapering is incorporated to represent the vasculature, assuming a triangular distribution of the wave transmission paths. Parametric analyses using physiological data demonstrate that the predicted impedance and reflection coefficient spectrum (RCS) closely mimic the experimental data. The simulation also reveals several significant features. As diameter tapering can minimise the presence and influence of wave reflections, the impedance modulus stays relatively constant with two distinct minima. The frequency of first minimum of impedance modulus is evidence of the tube elasticity and load compliance in the lower extremity, and the frequency of second minimum is evidence of those in the upper extremity. The high-frequency portion of the impedance modulus is affected by the tube elasticity, but not by the load compliance. The impedance spectrum at higher frequencies shows no notable fluctuations corresponding to a decrease in blood or wall viscosity. Furthermore, the low-frequency range in RCS is dominated by the longer lower body tube, and the high-frequency range by the shorter upper body tube. This geometrically tapered T-tube is considered a more natural model for the description of the systemic arterial system.

Exponentially tapered t-tube model of systemic arterial system in dogs

This study determines the role of an asymmetric T-tube model as a representation of arterial mechanical properties. The model consists of two non-uniform tubes connected in parallel. The non-uniform properties of each tube include geometric and elastic tapering and each tube terminates in a complex load. Pulsatile pressure and flow velocity of the ascending aorta were measured in 10 closed-chest, anaesthetized dogs. An exponentially tapered transmission line is used to describe the non-uniform properties of the vasculature. The phase constant is a function of position along the path length due to geometric and elastic tapers. This non-uniform T-tube model makes it possible to fit the measured pressure waveform in the ascending aorta. Model parameters could be estimated and used to interpret the physical properties of the arterial system. The mathematical and experimental model impedance spectra are similar. There is a close correspondence between the impedance parameters derived from the non-uniform T-tube model and values computed from measurements on dogs. The results suggest that inclusion of tube tapering improves the mathematical model so that it closely represents the experimentally derived arterial impedance in closed-chest dogs. We conclude that the non-uniform properties of wave-transmission paths may play an important role in governing the behaviour of an asymmetric T-tube for the description of the arterial system.

Derivation of closed-form expression for the cerebral circulation models

Loops which occur due to anastomosing vascular networks, such as the circle of Willis, cannot be analyzed analytically using any of the published mathematical models. This paper presents the theoretical basis of a new model of the cerebral circulation loops which occur due to the circle of Willis. Equations of the model are presented and justified. The transmission line equations obtained from the linearized Navier-Stokes equations and the linearized dynamic deformation equations of the arterial wall are solved analytically to compute the hemodynamic parameters. A comparison of simulation result with experimental data shows that the agreement between experimental and theoretical results is satisfactory and more accurate than the numerical solution.

Regional wave travel and reflections along the human aorta: a study with six simultaneous micromanometric pressures

The human aorta and its terminal branches were investigated in normal subjects during elective cardiac catheterization to evaluate regional wave travel and arterial wave reflections. A specially designed catheter with six micromanometers equally spaced at 10 cm intervals was positioned with the tip sensor in the distal external iliac artery and the proximal sensor in the aortic arch. Simultaneous pressures were obtained and analyzed for foot-to-foot wave velocity, and Fourier analysis was used to derive apparent phase velocity. These quantities were assessed during control (n = 9), during Valsalva (n = 8) and Müller (n = 4) maneuvers, and during femoral artery occlusion by bilateral manual compression (n = 8). During control, regional cross-sectional areas, determined from aortography, and regional foot-to-foot pulse wave velocities were used to calculate the local reflection coefficient in the proximal descending aorta (gamma = 0.05), at the junction of the renal arteries (gamma = 0.43), and at the terminal aortic bifurcation (gamma = 0.13). To test the hypothesis that significant reflections originate in the aorta, at the level of the renal arteries, aortograms were used to design a latex tube model with geometric properties similar to the descending aorta. Velocities and reflection characteristics in the model and in vivo were compared. Inspection of thoracic aortic pressures under control conditions revealed a reflected wave originating from the region of the aorta at the level of the renal arterial branches while abdominal pressures exhibited reflection from a site peripheral to the terminal aortic bifurcation. In the low frequency range, apparent phase velocity was found to be higher proximal to the renal arteries as compared with at the distal sites. In addition, the minimum value occurred at a higher frequency in the lower thoracic aorta than at more distal sites. The effects of reflection on apparent wave velocity in the tube model were consistent with data obtained in vivo. The Valsalva maneuver diminished the reflection from the aortic region of the renal arteries, thus allowing the distal reflected wave to become more evident on the thoracic pressure waveforms. Bilateral femoral artery occlusion usually enhanced the distal reflection and the Müller maneuver usually resulted in small increases in reflections. In conclusion, the geometric and elastic nonuniformity of the aorta results in two major sites of arterial wave reflection that influence the aortic pressure waveforms in man.(ABSTRACT TRUNCATED AT 400 WORDS)

Physiological and pathophysiological implications of ventricular/vascular coupling

The purpose of this paper is to consider "ideal" ventricular/vascular coupling, and how this may be manifest in the time domain and in the frequency domain. The paper will also consider how such "ideal" coupling is achieved, and how it might be disturbed. The arterial system plays a crucial role in ventricular/vascular coupling since it separates the smallest vessels where flow is almost perfectly continuous from the ventricle, whose output is intermittent. Ventricular/vascular coupling can be assessed from measurements of pressure and flow in the ascending aorta (AA) (for left ventricle/systemic circulation), and in the main, pulmonary artery (MPA) (for right ventricle/pulmonary circulation). Ideal coupling is manifest as low pressure fluctuation in AA and MPA. Low pressure fluctuation results in pressure during systole being only slightly greater than pressure throughout the whole cardiac cycle, and pressure during diastole being only slightly less. This is desirable because pressure during systole determines ventricular output (when inotropic state and ventricular filling are constant), and ventricular metabolic requirement, while pressure during diastole in AA is a major determinant of coronary blood flow. In the frequency domain, "ideal" coupling is manifest as a correspondence between minimal values of impedance modulus in AA and MPA with maximal values of flow harmonics in AA and MPA, respectively. Factors responsible for "ideal" coupling have been identified as high distensibility of proximal arteries (with decreasing distensibility in peripheral arteries), wave reflection at arterial terminations, and a "match" between heart rate on the one hand and arterial length and wave velocity on the other. This favourable "match" results in the heart operating for both systemic and pulmonary circulations close to a node of pressure and antinode of flow; this match is improved under conditions which simulate flight and fight. While ventricular/vascular coupling appears to be close to ideal in most large mammals, it appears to be less than ideal in adult humans and some small mammals including guinea pigs, rats, and mice. The cause for mismatch in small mammals is unclear. In humans however, findings are attributable to progressive arterial degeneration which is known to commence in childhood and is apparent in the elderly as dilated tortuous arteries, high pulse pressure, and high likelihood of developing ventricular failure.

Elastic properties of blood vessels determined by photoelectric plethysmography

The dynamic elastic properties and vascular reactions of human blood vessels in vivo are studied by means of the photoplethysmographic method. The measurement of the mechanical properties of the blood vessel walls is based on measurement of blood volume changes resulting from changes in external pressure. The blood volume changes are mon itored by measuring the opacity changes in vascular bed, in this case, the distal phalanx of the finger. The elastic properties thus measured reflect some average property of a whole vascular bed. The technique is simple, noninvasive, and does not cause any damage or discomfort to the subject.

In healthy young subjects, blood vessel elasticity was found to be constant in the range between the systolic and diastolic pressure. However the volume-pressure curves showed a hysteresis loop, i.e., the curves obtained during the increase of intravascular pressure differed from those obtained when pressure was decreased.

The elasticity of the vascular walls of patients suffering from peripheral vascular diseases was found to be significantly different; their volume- pressure curves were nonlinear and had a much wider hysteresis loop (indicating a lower critical opening pressure), and their vascular reactions to changes in pressure were different.

Possible uses of the method for diagnosing and evaluating arterio sclerotic and other vascular diseases and for studying vascular changes and reactions under conditions such as shock, heart failure, external abnormal pressures, and various drugs, are discussed.

Determination of arterial input impedance spectra from non-invasively recorded pulses

The frequency spectra of modulus and phase of the input impedance (Zin) of large human arteries (abdominal aorta, femoral and subclavian arteries) were computed from transcutaneously recorded, uncalibrated pressure and flow pulses picked up as sphygmograms and Doppler flow velocity pulses, respectively. Since these pulses cannot be calibrated, the modulus (Zin) of the input impedance is calculated in relative units; its spectrum, however, is not influenced by this fact. A modification of the computing procedure makes it possible to determine approximately quasi-continuous frequency spectra of Zin from natural pressure and flow pulses which may be regarded as periodic functions. This is the prerequisite for a detailed analysis of the wave transmission properties of the arterial bed which manifest themselves of the input impedance. For this purpose the peripheral reflection site was moved in a proximal direction by bilateral occlusion of limb arteries. This was done by inflating cuffs placed symmetrically on both sides around the upper or lower parts of the respective limbs. When the occluding cuffs were placed around both lower legs or both thighs, the shortening of the arterial wave transmission line resulted in a marked shift of the first maximum of Zin to higher frequencies in the spectrum of Zin of the abdominal aorta and femoral artery. Bilateral occlusion of the arteries of the forearms or upper arms, however, did not have any measurable influence on Zin of the subclavian artery. Theoretical considerations show that this difference in behaviour of the several parts of the arterial system may be attributed to the varying extent of their inhomogeneity.

The genesis of the pulse contours of the distal leg arteries in man

In order to clarify the genesis of the human pressure and flow pulse contours of the distal leg arteries, in particular the posterior tibial artery, pulse recordings were performed with transcutaneous techniques under normal conditions and in the state of strong vasodilatation (reactive hyperaemia) in the distal parts of the lower legs. From the experimental results it is concluded that the contour of the incident pressure wave arriving in the leg arteries is very similar to the pressure pulse contour of the abdominal aorta, while the resulting contour in the leg arteries is determined by this incident wave and superimposed reflected waves. The latter arise from positive reflection in the periphery of the lower legs. The travel in retrograde direction, are reflected negatively in proximal regions, particularly in the abdominal aorta, and appear again, with opposite sign, in the leg arteries. In addition, retrograde waves reflected positively at the aortic valve and then traveling in antegrade direction also influence the pulse contours. By considering this wave travel, the genesis of the characteristic contours of the pressure and flow pulses of the lower leg arteries is explained in a satisfactory way. This is demonstrated by a simplified graphical pulse construction as well as by the calculation of pulse contours on the basis of a theoretical tube model of the arterial system with the aid of a digital computer. The results of these calculations are discussed with respect to the findings of previous investigators who used analog and digital models of the arterial system.

Input impedance of the systemic circulation

The hydraulic load presented to the left ventricle by the systemic circulation was characterized by expressing pressure-flow relationships in the ascending aorta as input impedance. This was determined by spectral or Fourier analysis of simultaneously recorded pressure and flow waves in 1 unanesthetized and 27 anesthetized dogs. Impedance modulus fell steeply from its value at zero frequency (the peripheral resistance) and its value was lowest (less than 1/20th of the peripheral resistance) over that band of frequencies (usually between 1.5 and 10 cycle/sec) which contained most of the energy of the left ventricular ejection (flow) wave. The patterns of modulus and phase of ascending aortic impedance were found to result from the presence of two functionally discrete reflecting sites in the systemic circulation, one in the upper part of the body and the other in the lower. The presence of these two sites appears to be an important factor in maintaining a low impedance modulus between 1.5 and 10 cycle/sec, and so in providing a favorable impedance to pulsatile flow from the heart. Both modulus and phase of impedance in the ascending aorta showed changes similar to those seen in other arteries when blood pressure was altered and when vasodilation occurred in the vascular bed.

Hydraulic power associated with pulmonary blood flow and its relation to heart rate

Pulmonary vascular input impedance and hydraulic power were measured at various heart rates in 29 anesthetized and 5 unanesthetized dogs. Hydraulic power at the pulmonary veno-atrial junction was measured in 5 dogs. The pulmonary vascular impedance spectrum in the unanesthetized dogs did not differ significantly from that in the anesthetized dogs. Average pulmonary arterial power in the anesthetized dogs was 157 milliwatts (mw), of which 108 mw was associated with mean pressure and flow, and 49 mw with the pulsations around these means. Seventy-eight per cent of this input power was dissipated in passage through the pulmonary bed. Kinetic energy accounted for 7% of the total input power.

Because of a steep fall in impedance between zero and 3 cycles/sec, and a rate-dependent change in the harmonic structure of flow pulsations, there was an inverse relationship between heart rate and the input power for a given mean flow, up to 180 beats/min. Pulmonary vascular dimensions and elasticity, which determine impedance, thus embody a mechanism whereby tachycardia can increase pulmonary blood flow by as much as 35% with an increase in pulmonary arterial input power of less than 5%, without the intervention of vasomotor activity.

Use of random excitation and spectral analysis in the study of frequency-dependent parameters of the cardiovascular system

If a randomly varying signal or noise is used as input, it is possible to study the input-output relations of a system, over a wide band of frequencies, by the use of power spectrum analysis. This technique has been applied to the cardiovascular system, by deliberately introducing irregularity in the pressure and flow pattern, by random electrical pacing of the heart. Examples are given of the determination, by spectral analysis in the range of 0.25 to 25 cycles/sec, of aortic and femoral arterial impedance in the dog, and also of the transmission ratio for pressure oscillations along the aorta. The results agreed satisfactorily with those obtained by the Fourier analysis of single pulses. When the time scale of the irregularities was made sufficiently great, it was possible to examine aortic impedance in the very low frequency range 0.00125 to 0.125 cycle/sec. In this range the operation of the baroreceptor reflexes became apparent.