Wave propagation in a model of the arterial circulation

The propagation of the arterial pulse wave in the large systemic arteries has been calculated using a linearised method of characteristics analysis to follow the waves generated by the heart. The model includes anatomical and physiological data for the 55 largest arteries adjusted so that the bifurcating tree of arteries is well matched for forward travelling waves. The peripheral arteries in the model are terminated by resistance elements which are adjusted to produce a physiologically reasonable distribution of mean blood flow. In the model, the pressure and velocity wave generated by the contraction of the left ventricle propagates to the periphery where it is reflected. These reflected waves are re-reflected by each of the bifurcations that they encounter and a very complex pattern of waves is generated. The results of the calculations exhibit many of the features of the systemic arteries, including the increase of the pulse pressure with distance away from the heart as well as the initial decrease and then the large increase in the magnitude of back flow during late systole going from the ascending aorta to the abdominal aorta to the arteries of the leg. The model is then used to study the effects of the reflection or absorption of waves by the heart and the mechanisms leading to the incisura are investigated. Calculations are carried out with the total occlusion of different arterial segments in order to model experiments in which the effects of the occlusion of different arteries on pressure and flow in the ascending aorta were measured. Finally, the effects of changes in peripheral resistance on pressure and velocity waveforms are also studied. We conclude from these calculations that the complex pattern of wave propagation in the large arteries may be the most important determinant of arterial haemodynamics.     

A Bio-Inspired Approach for the Reduction of Left Ventricular Workload

Previous studies have demonstrated the existence of optimization criteria in the design and development of mammalians cardiovascular systems. Similarities in mammalian arterial wave reflection suggest there are certain design criteria for the optimization of arterial wave dynamics. Inspired by these natural optimization criteria, we investigated the feasibility of optimizing the aortic waves by modifying wave reflection sites. A hydraulic model that has physical and dynamical properties similar to a human aorta and left ventricle was used for a series of in-vitro experiments. The results indicate that placing an artificial reflection site (a ring) at a specific location along the aorta may create a constructive wave dynamic that could reduce LV pulsatile workload. This simple bio-inspired approach may have important implications for the future of treatment strategies for diseased aorta.     

Hedgehog signaling induces arterial endothelial cell formation by repressing venous cell fate

In vertebrate embryos, the dorsal aorta and the posterior cardinal vein form in the trunk to comprise the original circulatory loop. Previous studies implicate Hedgehog (Hh) signaling in the development of the dorsal aorta. However, the mechanism controlling specification of artery versus vein remains unclear. Here, we investigated the cell-autonomous mechanism of Hh signaling in angioblasts (endothelial progenitor cells) during arterial-venous specification utilizing zebrafish mutations in Smoothened (Smo), a G protein-coupled receptor essential for Hh signaling. smo mutants exhibit an absence of the dorsal aorta accompanied by a reciprocal expansion of the posterior cardinal vein. The increased number of venous cells is equivalent to the loss of arterial cells in embryos with loss of Smo function. Activation of Hh signaling expands the arterial cell population at the expense of venous cell fate. Time-lapse imaging reveals two sequential waves of migrating progenitor cells that contribute to the dorsal aorta and the posterior cardinal vein, respectively. Angioblasts deficient in Hh signaling fail to contribute to the arterial wave; instead, they all migrate medially as a single population to form the venous wave. Cell transplantation analyses demonstrate that Smo plays a cell-autonomous role in specifying angioblasts to become arterial cells, and Hh signaling-depleted angioblasts differentiate into venous cells instead. Collectively, these studies suggest that arterial endothelial cells are specified and formed via repressing venous cell fate at the lateral plate mesoderm by Hh signaling during vasculogenesis.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

A theoretical evaluation of cardiac output as a function of mean arterial pressure in the human cardiovascular system

A correlation function of cardiac output and mean arterial pressure is presented for the human cardiovasular system. The function is developed using an energy transfer balance for a unit volume of blood which flows in the vascular system between the aorta and the vena cava. The energy transfer balance equates the energy utilized in the vascular system to the algebraic sum of the pulse energy, the kinetic energy and the potential energy in the vascular system. Each of these energies is defined in terms of the physiology of the cardiovascular system. Pulse energy is defined in terms of the work done by the heart on the aorta. Kinetic energy is defined in terms of the cardiac output and the potential energy is defined in terms of the diastolic pressure in the aorta. The utilization energy is equivalent to the energy transfer in the work done by the blood on the viscoelastic blood vessels, and to the frictional energy loss due to drag on the blood mass as it flows through the vascular system.The correlation function of cardiac output with mean arterial pressure demonstrates that the cardiac output is a double-valued function of the mean arterial pressure. The function also varies with the ratio of the fourth power of the Shear Modulus of the blood vessels to the third power of Young's Modulus. The function shows that mean arterial pressure minimizes for a cardiac output of approximately 51 per min when one holds the ratio of the elastic moduli constant. Further discussion indicates how clinicians can use the function, developed in this research, to interpret the experimental data obtained from cardiac output studies.     

Wave intensity in the ascending aorta: effects of arterial occlusion

We examine the effects of arterial occlusion on the pressure, velocity and the reflected waves in the ascending aorta using wave intensity analysis. In 11 anaesthetised, open-chested dogs, snares were used to produce total arterial occlusion at 4 sites: the upper descending aorta at the level of the aortic valve (thoracic); the lower thoracic aorta at the level of the diaphragm (diaphragm); the abdominal aorta between the renal arteries (abdominal) and the left iliac artery, 2 cm downstream from the aorta iliac bifurcation (iliac). Pressure and flow in the ascending aorta were measured, and data were collected before and during the occlusion. During thoracic and diaphragm occlusions a significant increase in mean aortic pressure (46% and 23%) and in wave speed (25% and 10%) was observed, while mean flow rate decreased significantly (23% and 17%). Also, the reflected compression wave arrived significantly earlier (45% and 15%) and its peak intensity was significantly greater (257% and 125%), all compared with control. Aortic occlusion distal to the renal arteries, however, caused an indiscernible change in the pressure and velocity waveforms, and in the intensities and timing of the waves in the forward and backward directions. The measured pressure and velocity waveforms are the result of the interaction between the heart and the arterial system. The separated pressure, velocity and wave intensity are required to provide information about arterial hemodynamic such as the timing and magnitude of the forward and backward waves. The net wave intensity is simpler to calculate but provides information only about the predominant direction of the waves and can be misleading when forward and backward waves of comparable magnitudes are present simultaneously.     

In-vitro investigation of a potential wave pumping effect in human aorta

An impedance pump – also known as Liebau pump – is a simple valveless pump that operates based on the principles of wave propagation and reflection. It has been shown in embryonic zebrafish that a similar mechanism is responsible for the pumping action in the embryonic heart during the early stages before valve formation. Recent studies suggest that the cardiovascular system is designed to take advantage of wave propagation and reflection phenomena in the arterial network. In this study we report the results of an in-vitro study that examines the hypothesis that the adult human aorta acts as a passive pump based on Liebau effect. A hydraulic model with different compliant models of an artificial aorta was used for a series of in-vitro experiments. Our result indicates that wave propagation and reflection can result in a pumping mechanism in a compliant aorta.     

Evaluation of blood flow velocity waveform in common carotid artery using multi-branched arterial segment model of human arteries

Arteriosclerosis is considered to be a major cause of cardiovascular diseases, which account for approximately 30% of the causes of death in the world. We have recently demonstrated a strong correlation between arteriosclerosis (arterial elasticity) and two characteristics: maximum systolic velocity (S1) and systolic second peak velocity (S2) of the common carotid artery flow velocity waveform (CCFVW). The CCFVW can be measured by using a small portable measuring device. However, there is currently no theoretical evidence supporting the causes of the relation between CCFVW and arterial elasticity, or the origin of the CCFVW characteristics. In this study, the arterial blood flow was simulated using a one-dimensional systemic arterial segments model of human artery in order to conduct a qualitative evaluation of the relationship between arterial elasticity and the characteristics of CCFVW. The simulation was carried out based on the discretized segments with the physical properties of a viscoelastic tube (the cross-sectional area at the proximal and terminal ends, the length, and the compliance per unit area of the tube (C_S)). The findings obtained through this study revealed that the simulated CCFVW had shape similar characteristics to that of the measured CCFVW. Moreover, when the compliance C_S of the model was decreased, the first peak of the simulated-CCFVW decreased and the second peak increased. Further, by separating the anterograde pulse wave and the reflected pulse wave, which form the CCFVW, we found that the decrease in the first peak of the simulated CCFVW was due to the arrival of a reflected pulse wave from the head after the common carotid artery toward the arrival of a anterograde pulse wave ejected directly from the heart and that the increase in the second peak resulted from the arrival of the peak of the reflected pulse wave from the thoracic aorta. These results establish that the CCFVW characteristics contribute to the assessment of arterial elasticity.     

Cytomegalovirus Seropositivity Is Associated with Increased Arterial Stiffness in Patients with Chronic Kidney Disease

Background

Patients with chronic kidney disease have an increased cardiovascular risk that is not fully explained by traditional risk factors but appears to be related to increased arterial stiffness. Cytomegalovirus (CMV) infection is associated with increased cardiovascular risk although the mechanisms for this are unknown. We examined whether CMV seropositivity was associated with increased arterial stiffness in patients with chronic kidney disease.

Methodology and Principal Findings

In 215 non-diabetic patients with chronic kidney disease, CMV seropositivity was determined using an anti-CMV IgG ELISA. Pulse wave velocity was measured and aortic distensibility assessed in the ascending, proximal descending and distal descending thoracic aorta. Patients seropositive for CMV had a higher pulse wave velocity and lower aortic distensibility at all 3 levels. These differences (except for ascending aortic distensibility) persisted in a subcohort matched for age, gender and renal function, and when the whole cohort was divided into quartiles of age. In multivariable analyses, CMV seropositivity was an independent determinant of pulse wave velocity and proximal and distal descending aortic distensibility.

Conclusions

In patients with chronic kidney disease, CMV seropositivity is associated with increased arterial stiffness and decreased distensibility of the proximal descending and distal aorta. These findings suggest that further research is required to examine CMV as a possible cause of arterial disease and increased cardiovascular risk in patients with CKD and may be relevant more widely for CMV seropositive patients with normal renal function.     

Disease patterns at arterial branches and their relation to flow

The distribution of lesions around arterial branch points is complex and changes with age. Four distinct patterns - here termed the arrowhead pattern, the lateral pattern, the upstream streak and the volcano - have been reported around the origins of intercostal arteries in the human aorta at different ages. The first two patterns also occur in young and old rabbits, the third in minipigs, and the fourth in apolipoprotein E/LDL receptor knockout mice. It is unclear how all four patterns can depend solely on flow; a particular problem is that the prevalence of lipid deposition remains highly nonuniform for several branch diameters upstream of the ostium. Variations in the prevalence of fatty streaks may originate near the branch and then spread by the migration of activated endothelial cells towards the heart. The pattern of raised lesions may reflect a different aetiology.     

Invited review: aging and the cardiovascular system.

Aging is associated with complex and diversified changes of cardiovascular structure and function. The heart becomes slightly hypertrophic and hyporesponsive to sympathetic (but not parasympathetic) stimuli, so that the exercise-induced increases in heart rate and myocardial contractility are blunted in older hearts. The aorta and major elastic arteries become elongated and stiffer, with increased pulse wave velocity, evidence of endothelial dysfunction, and biochemical patterns resembling early atherosclerosis. The arterial baroreflex is sizably altered in aging, but different components are differentially affected: there is a definite impairment of arterial baroreceptor control of the heart but much better preserved baroreceptor control of peripheral vascular resistance. Alterations at the afferent, central neural, efferent, and effector organ portions of the reflex arch have been claimed to account for age-related baroreflex changes, but no conclusive evidence is available on this mechanistic aspect. Reflexes arising from cardiopulmonary vagal afferents are also blunted in aged individuals. The cardiovascular and reflex changes brought about by aging may have significant implications for circulatory homeostasis in health and disease.     

On the propagation of a wave front in viscoelastic arteries

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.     

Linked mechanical and biological aspects of remodeling in mouse pulmonary arteries with hypoxia-induced hypertension

Supravalvular aortic stenosis (SVAS) is associated with decreased elastin and altered arterial mechanics. Mice with a single deletion in the elastin gene (ELN(+/-)) are models for SVAS. Previous studies have shown that elastin haploinsufficiency in these mice causes hypertension, decreased arterial compliance, and changes in arterial wall structure. Despite these differences, ELN(+/-) mice have a normal life span, suggesting that the arteries remodel and adapt to the decreased amount of elastin. To test this hypothesis, we performed in vitro mechanical tests on abdominal aorta, ascending aorta, and left common carotid artery from ELN(+/-) and wild-type (C57BL/6J) mice. We compared the circumferential and longitudinal stress-stretch relationships and residual strains. The circumferential stress-stretch relationship is similar between genotypes and changes <3% with longitudinal stretch at lengths within 10% of the in vivo value. At mean arterial pressure, the circumferential stress in the ascending aorta is higher in ELN(+/-) than in wild type. Although arterial pressures are higher, the increased number of elastic lamellae in ELN(+/-) arteries results in similar tension/lamellae compared with wild type. The longitudinal stress-stretch relationship is similar between genotypes for most arteries. Compared with wild type, the in vivo longitudinal stretch is lower in ELN(+/-) abdominal and carotid arteries and the circumferential residual strain is higher in ELN(+/-) ascending aorta. The increased circumferential residual strain brings the transmural strain distribution in ELN(+/-) ascending aorta close to wild-type values. The mechanical behavior of ELN(+/-) arteries is likely due to the reduced elastin content combined with adaptive remodeling during vascular development.     

Prediction of fibre architecture and adaptation in diseased carotid bifurcations

Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.     

Pulmonary arterial distension does not cause pulmonary vasoconstriction

Distension of the main pulmonary artery or its major branches with an intraluminal balloon has been reported to cause pulmonary vasoconstriction by an unknown mechanism. This study was an attempt to confirm the pressor response and explore its cause. Several balloon distension methods were tried and discarded because they caused unintentional obstruction. Ultimately, I inflated a balloon placed retrogradely and confined to the left main pulmonary artery of six anesthetized open-chest dogs after ligating left lobar arterial branches. Blood flow and systemic gas composition were controlled by interposing an external pump oxygenator between the left ventricle and aorta. Pressures in the aorta, main pulmonary artery, and left atrium were recorded. Alveolar hypoxia was used as an independent test of pulmonary vasoreactivity. Although hypoxic pressor responses occurred, challenges with arterial distension did not change lung perfusion pressure. Silicone rubber casts were made of the arteries of six dogs used in pilot experiments. These revealed the limited lengths in which distenders can be placed without unintentional encroachment on flow. I could not support the conclusion that arterial distension causes vasoconstriction and am suspicious that the perfusion pressure increases reported by others may have been caused by undetected obstruction of a major arterial branch.     

Scanning electron microscopic study of the effects of pressure on the luminal surface of the rabbit aorta.

The effects of pressure on the luminal surface of the rabbit aorta were investigated using the scanning electron microscope. The method followed was perfusion under hydrostatic pressure of a section of thoracic aorta, in vitro. The characteristic ridged pattern seen in sections fixed at zero hydrostatic pressure was to a large extent eliminated when fixation occurred at pressures equivalent to those experienced by the aorta at systole or diastole. This study suggests that the spiral ridged pattern is dependent upon the fixation pressure and may not be present in a normally functioning artery. Any attempts to characterize or interpret the appearance of the luminal arterial wall must take into account the effects of pressure.     

Role of tapering in aortic wave reflection: hydraulic and mathematical model study

Pressure and flow have been measured simultaneously at six locations along the aorta of an anatomically correct 1:1 scale hydraulic elastic tube model of the arterial tree. Our results suggest a discrete reflection point at the level of the renal arteries based on (i) the quarter-wavelength formula and (ii) the comparison of foot-to-foot (c(ff)) and apparent phase velocity (c(app)). However, separation of the pressure wave into an incident and reflected wave at all six locations indicates continuous reflection: a reflected wave is generated at each location as the forward wave passes by. We did a further analysis using a mathematical transmission line model with a simple tapering geometry (length 50 cm, 31 and 11 mm proximal and distal diameter, respectively) for a low (0.32 ml/mmHg), normal (1.6 ml mmHg) and high (8 ml/mmHg) value of total arterial compliance. Using the quarter-wavelength formula, a discrete reflection point is found at x = 33 cm, the level of the renal arteries, independent of the value of total compliance. However, local analysis comparing c(ff) and c(app) does not reveal a marked reflection site, and the analysis of incident and reflected waves merely suggests a continuous reflection. We therefore conclude that the measured in vivo aortic wave reflection indices are the result of at least two interacting phenomena: a continuous wave reflection due to tapering, and local reflections arising from branches at the level of the diaphragm. The continuous reflection is hidden in the input impedance pattern. Using the quarter-wavelength formula or the classical wave separation theory, it appears as a reflection coming from a single discrete site, confusingly also located at the level of the diaphragm. Therefore, the quarter-wavelength formula and the linear wave separation theory should be used with caution to identify wave reflection zones in the presence of tapering, i.e., in most mammalian arteries.     

Endocardial Tip Cells in the Human Embryo – Facts and Hypotheses

Experimental studies regarding coronary embryogenesis suggest that the endocardium is a source of endothelial cells for the myocardial networks. As this was not previously documented in human embryos, we aimed to study whether or not endothelial tip cells could be correlated with endocardial-dependent mechanisms of sprouting angiogenesis. Six human embryos (43–56 days) were obtained and processed in accordance with ethical regulations; immunohistochemistry was performed for CD105 (endoglin), CD31, CD34, α-smooth muscle actin, desmin and vimentin antibodies. Primitive main vessels were found deriving from both the sinus venosus and aorta, and were sought to be the primordia of the venous and arterial ends of cardiac microcirculation. Subepicardial vessels were found branching into the outer ventricular myocardium, with a pattern of recruiting α-SMA+/desmin+ vascular smooth muscle cells and pericytes. Endothelial sprouts were guided by CD31+/CD34+/CD105+/vimentin+ endothelial tip cells. Within the inner myocardium, we found endothelial networks rooted from endocardium, guided by filopodia-projecting CD31+/CD34+/CD105+/ vimentin+ endocardial tip cells. The myocardial microcirculatory bed in the atria was mostly originated from endocardium, as well. Nevertheless, endocardial tip cells were also found in cardiac cushions, but they were not related to cushion endothelial networks. A general anatomical pattern of cardiac microvascular embryogenesis was thus hypothesized; the arterial and venous ends being linked, respectively, to the aorta and sinus venosus. Further elongation of the vessels may be related to the epicardium and subepicardial stroma and the intramyocardial network, depending on either endothelial and endocardial filopodia-guided tip cells in ventricles, or mostly on endocardium, in atria.     

Descending aorta subject-specific one-dimensional model validated against in vivo data

The aorta plays a major role in the cardiovascular system and its function and structure are primarily affected by aging, eating habits, life style and other cardiovascular risk factors, inducing increased stiffness which is associated with cardiovascular and cerebral morbi-mortality. Our objective was to develop and validate a robust subject-specific one-dimensional wave propagation numerical model of the descending aorta. This model with a cross-sectional area, velocity and pressure formulation is built using geometric and hemodynamic data measured on a specific person and is validated against in vivo data acquired on the same subject at three distinct anatomical locations along the thoracic aorta. We studied seven healthy volunteers, who underwent carotid applanation tonometry and aortic cardiovascular magnetic resonance (CMR). Responses of our model in terms of changes in central pressure waveform with arterial alterations were consistent with previously described physiological knowledge. Quantitative validation averaged over the three descending aortic locations and the seven subjects provided low rms errors (given in percentage of the maximal clinical value) between simulated and CMR data, i.e. area: 10±6%, velocity: 11±3%, flow rate: 9±3%. Finally, we also found low rms (5±2%) when comparing simulated pressure in the proximal aortic location against tonometric carotid pressure curves. In conclusion, this simple model performs similar to more complex models of the entire systemic arterial tree at a fraction of the cost, and could be of major usefulness in the non-invasive and local estimation of proximal biomechanical and hemodynamic indices.     

Arterial hypertension and neurofibromatosis: renal artery stenosis and coarctation of abdominal aorta.

A 10-year-old girl had arterial hypertension, generalized neurofibromatosis, coarctation of the abdominal aorta and multiple stenoses at the origin of each renal artery. After resection of the stenotic areas and reimplantation of the renal arteries in the aorta, her arterial pressure decreased substantially. However, hypertension recurred and radiologic follow-up 4 1/2 years later showed distinct progression of the coarctation and renewed stenosis of all renal arteries at their origin. The stenotic areas showed eccentric intimal proliferation, frequently bulging into the lumen, with small nodular aggregates of smooth muscle cells and proliferation of fibrous tissue containing spindle-shaped nuclei in a palisading pattern. Hypertension associated with neurofibromatotic vascular disease has been described in 47 other patients in the literature. These patients have been young (mean age, 14 years) and predominantly male. In contrast to fibromuscular dysplasia, in which 95% of all stenoses are found in the distal two thirds of the renal arteries, in vascular neurofibromatosis more than 50% of the stenoses are found at the origin.