Effect of age on the in vitro reflection coefficient of the aortoiliac bifurcation in humans

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

In silico hemodynamical simulations show additional benefits of artery wall softening induced by antihypertensive drugs

BACKGROUND AND OBJECTIVES

Age-related arterial stiffening increases peripheral resistance and decreases arterial distensibility, thus contributing to hypertension, an important risk factor of atherosclerosis. It causes abnormal blood flow, endothelial dysfunction, higher pulse wave velocity, and consequently elevated pressure wave amplitude.

METHODS

This paper presents the influence of these changes via multiscale 3D-0D transient computational fluid dynamics simulations of blood flow in five patient-specific geometries of human carotid bifurcation using archetypal flow waveforms for young and old subjects.

RESULTS

The proposed model shows a significant decrease in the time-averaged wall shear stress (TAWSS) for the old archetypal flow waveform. This is in good agreement with clinical data on a straight segment of common carotid arteries available for young and old subjects. Moreover, our study showed that the decrease of area-averaged TAWSS related to the old flow waveform is much more pronounced (2.5 ÷ 4.5 times higher) at risk areas (areas showing TAWSS below its threshold value of 0.48 Pa) than in straight segments commonly considered in clinical studies.

CONCLUSIONS

Since arterial stiffness can be lowered through long-term usage of any of the five basic groups of antihypertensives, possible benefits of such medical therapy could be not only lowering blood pressure and peripheral resistance but also in increasing the TAWSS and thus attenuating an important mechanism of the atherosclerotic process.

Effect of aortic bifurcation geometry on pressure and peak wall stress in abdominal aorta: Fluid-structure interaction study

BACKGROUND AND OBJECTIVE

Geometry of aorto-iliac bifurcation may affect pressure and wall stress in aorta and thus potentially serve as a predictor of abdominal aortic aneurysm (AAA), similarly to hypertension.

METHODS

Effect of aorto-iliac bifurcation geometry was investigated via parametric analysis based on two-way weakly coupled fluid-structure interaction simulations. The arterial wall was modelled as isotropic hyperelastic monolayer, and non-Newtonian behaviour was introduced for the fluid. Realistic boundary conditions of the pulsatile blood flow were used on the basis of experiments in literature and their time shift was tailored to the pulse wave velocity in the model to obtain physiological wave shapes. Eighteen idealized and one patient-specific geometries of human aortic tree with common iliac and renal arteries were considered with different angles between abdominal aorta (AA) and both iliac arteries and different area ratios (AR) of iliac and aortic luminal cross sections.

RESULTS

Peak wall stress (PWS) and systolic blood pressure (SBP) were insensitive to the aorto-iliac angles but sensitive to the AR: when AR decreased by 50%, the PWS and SBP increased by up to 18.4% and 18.8%, respectively.

CONCLUSIONS

Lower AR (as a result of the iliac stenosis or aging), rather than the aorto-iliac angles increases the BP in the AA and may be thus a risk factor for the AAA development.

The contribution of upper and lower body arterial vessels to the aortic root reflections: A one-dimensional computational study

BACKGROUND AND OBJECTIVES

Reflections measured at the aortic root are of physiological and clinical interest and thought to be composed of the superimposed reflections arriving from the upper and lower parts of the circulatory system. However, the specific contribution of each region to the overall reflection measurement has not been thoroughly examined. This study aims to elucidate the relative contribution of reflected waves arising from the upper and lower human body vasculature to those observed at the aortic root.

METHODS

We utilised a one-dimensional (1D) computational model of wave propagation to study reflections in an arterial model that included 37 largest arteries. A narrow Gaussian-shaped pulse was introduced to the arterial model from five distal locations: carotid, brachial, radial, renal, and anterior tibial. The propagation of each pulse towards the ascending aorta was computationally tracked. We calculated the reflected pressure and wave intensity at the ascending aorta in each case. The results are presented as a ratio of the initial pulse.

RESULTS

The findings of this study indicates that pressure pulses originated at the lower body can hardly be observed, while those originated from the upper body account for the largest portion of reflected waves seen at the ascending aorta.

CONCLUSIONS

Our study validates the findings of earlier studies, which demonstrated that human arterial bifurcations have a significantly lower reflection coefficient in the forward direction as compared to the backward direction. The results of this study underscore the need for further in-vivo investigations to provide a deeper understanding of the nature and characteristics of reflections observed in the ascending aorta, which can inform the development of effective strategies for the management of arterial diseases.

Optimised design of an arterial network model reproduces characteristic central and peripheral hemodynamic waveform features in young adults

Abstract

The arterial network in healthy young adults is thought to be structured to optimize wave reflection in the arterial system, producing an ascending aortic pressure waveform with three key features: early systolic peak, negative systolic augmentation and diastolic hump. One‐dimensional computer models have provided significant insights into arterial haemodynamics, but no previous models of the young adult have exhibited these three features. Given that this issue was likely to be related to unrepresentative or non‐optimized impedance properties of the model arterial networks, we developed a new ‘YoungAdult’ model that incorporated the following features: (i) a new and more accurate empirical equation for approximating wave speeds, based on area and relative distance to elastic–muscular arterial transition points; (ii) optimally matched arterial junctions; and (iii) an improved arterial network geometry that eliminated ‘within‐segment’ taper (which causes wave reflection in conduit arteries) whilst establishing ‘impedance‐preserving’ taper. These properties of the model led to wave reflection occurring predominantly at distal vascular beds, rather than in conduit arteries. The model predicted all three typical characteristics of an ascending aortic pressure waveform observed in young adults. When compared with non‐invasively acquired pressure and velocity measurements (obtained via tonometry and Doppler ultrasound in seven young adults), the model was also shown to reproduce the typical waveform morphology observed in the radial, brachial, carotid, temporal, femoral and tibial arteries. The YoungAdult model provides support for the concept that the arterial tree impedance in healthy young adults is exquisitely optimized, and it provides an important baseline model for investigating cardiovascular changes in ageing and disease states.

Key points

The origin of wave reflection in the arterial system is controversial, but reflection properties are likely to give rise to characteristic haemodynamic features in healthy young adults, including an early systolic peak, negative systolic augmentation and diastolic hump in the ascending aortic pressure waveform, and triphasic velocity profiles in peripheral arteries. Although computational modelling provides insights into arterial haemodynamics, no previous models have predicted all these features.

An established arterial network model was optimized by incorporating the following features: (i) a more accurate representation of arterial wave speeds; (ii) precisely matched junctions; and (iii) impedance‐preserving tapering, thereby minimizing wave reflection in conduit arteries in the forward direction. Comparison with in vivo data (n = 7 subjects) indicated that the characteristic waveform features in young adults were predicted accurately.

Our findings strongly imply that a healthy young arterial system is structured to optimize wave reflection in the main conduit arteries and that reflection of forward waves occurs primarily in the vicinity of vascular beds.

Estimation of central pulse wave velocity from radial pulse wave analysis

BACKGROUND AND OBJECTIVE

Arterial stiffness, commonly assessed by carotid-femoral pulse wave velocity (cfPWV), is an independent biomarker for cardiovascular disease. The measurement of cfPWV, however, has been considered impractical for routine clinical application. Pulse wave analysis using a single pulse wave measurement in the radial artery is a convenient alternative. This study aims to identify pulse wave features for a more accurate estimation of cfPWV from a single radial pulse wave measurement.

METHODS

From a dataset of 140 subjects, cfPWV was measured and the radial pulse waveform was recorded for 30 s twice in succession. Features were extracted from the waveforms in the time and frequency domains, as well as by wave separation analysis. All-possible regressions with bootstrapping, McHenry's select algorithm, and support vector regression were applied to compute models for cfPWV estimation.

RESULTS

The correlation coefficients between the measured and estimated cfPWV were r = 0.81, r = 0.81, and r = 0.8 for all-possible regressions, McHenry's select algorithm, and support vector regression, respectively. The features selected by all-possible regressions are physiologically interpretable. In particular, the amplitude ratio of the diastolic peak to the notch of the radial pulse waveform (Rn,dr,P) is shown to be correlated with cfPWV. This correlation was further evaluated and found to be independent of wave reflections using a dataset (n = 3,325) of simulated pulse waves.

CONCLUSIONS

The proposed method may serve as a convenient surrogate for the measurement of cfPWV. Rn,dr,P is associated with aortic pulse wave velocity and this association may not be dependent on wave reflection.

Impact of tapering of arterial vessels on blood pressure, pulse wave velocity, and wave intensity analysis using one-dimensional computational model

The angle of arterial tapering increases with ageing, and the geometrical changes of the aorta may cause an increase in central arterial pressure and stiffness. The impact of tapering has been primarily studied using frequency-domain transmission line theories. In this work, we revisit the problem of tapering and investigate its effect on blood pressure and pulse wave velocity (PWV) using a time-domain analysis with a 1D computational model. First, tapering is modelled as a stepwise reduction in diameter and compared with results from a continuously tapered segment. Next, we studied wave reflections in a combination of stepwise diameter reduction of straight vessels and bifurcations, then repeated the experiments with decreasing the length to physiological values. As the model's segments became shorter in length, wave reflections and re-reflections resulted in waves overlapping in time. We extended our work by examining the effect of increasing the tapering angle on blood pressure and wave intensity in physiological models: a model of the thoracic aorta and a model of upper thoracic and descending aorta connected to the iliac bifurcation. Vessels tapering inherently changed the ratio between the inlet and outlet cross-sectional areas, increasing the vessel resistance and reducing the compliance compared with non-tapered vessels. These variables influence peak and pulse pressure. In addition, it is well established that pulse wave velocity increases in an ageing arterial tree. This work provides confirmation that tapering induces reflections and offers an additional explanation to the observation of increased peak pressure and decreased diastolic pressure distally in the arterial tree.

Vascular Aging and Arterial Stiffness

Cardiovascular diseases (CVD) account annually for almost one third of all deaths worldwide. Among the CVD, systemic arterial hypertension (SAH) is related to more than half of those outcomes. Type 2 diabetes mellitus is an independent risk factor for SAH because it causes functional and structural damage to the arterial wall, leading to stiffness. Several studies have related oxidative stress, production of free radicals, and neuroendocrine and genetic changes to the physiopathogenesis of vascular aging. Indirect ways to analyze that aging process have been widely studied, pulse wave velocity (PWV) being considered gold standard to assess arterial stiffness, because there is large epidemiological evidence of its predictive value for cardiovascular events, and it requires little technical knowledge to be performed. A pulse wave is generated during each cardiac contraction and travels along the arterial bed until finding peripheral resistance or any bifurcation point, determining the appearance of a reflected wave. In young individuals, arteries tend to be more elastic, therefore, the reflected wave occurs later in the cardiac cycle, reaching the heart during diastole. In older individuals, however, the reflected wave occurs earlier, reaching the heart during systole. Because PWV is an important biomarker of vascular damage, highly valuable in determining the patient’s global cardiovascular risk, we chose to review the articles on vascular aging in the context of cardiovascular risk factors and the tools available to the early identification of that damage.

Computational assessment of hemodynamics-based diagnostic tools using a database of virtual subjects: Application to three case studies

Many physiological indexes and algorithms based on pulse wave analysis have been suggested in order to better assess cardiovascular function. Because these tools are often computed from in-vivo hemodynamic measurements, their validation is time-consuming, challenging, and biased by measurement errors.

Recently, a new methodology has been suggested to assess theoretically these computed tools: a database of virtual subjects generated using numerical 1D-0D modeling of arterial hemodynamics. The generated set of simulations encloses a wide selection of healthy cases that could be encountered in a clinical study.

We applied this new methodology to three different case studies that demonstrate the potential of our new tool, and illustrated each of them with a clinically relevant example: (i) we assessed the accuracy of indexes estimating pulse wave velocity; (ii) we validated and refined an algorithm that computes central blood pressure; and (iii) we investigated theoretical mechanisms behind the augmentation index.

Our database of virtual subjects is a new tool to assist the clinician: it provides insight into the physical mechanisms underlying the correlations observed in clinical practice.

Associations Between Cardio–Ankle Vascular Index and Aortic Structure and Sclerosis Using Multidetector Computed Tomography

Aortic pulse wave velocity (PWV) has been accepted as the gold standard for arterial stiffness measurement. However, PWV depends on blood pressure (BP). To eliminate the BP dependency of PWV, the cardio–ankle vascular index (CAVI) was developed. This study aimed to define the relationship between CAVI and aortic atherosclerosis or structure on multidetector computed tomography (MDCT). Patients with (n = 49) or without (n = 49) coronary artery disease were studied. The lumen and vessel diameters and wall thickness were calculated from the cross-sectional area at the pulmonary bifurcation level by 64-slice MDCT. The CAVI was measured within 3 days before MDCT. Multivariate analysis showed that the vessel diameter of the ascending and descending aorta on MDCT depends on age, body surface area, and diastolic BP. The CAVI significantly correlated with the vessel diameter ( r = .453) and wall thickness ( r = .387) of the thoracic descending aorta ( P < .001, respectively). The CAVI was an independent predictor of the descending aortic wall thickness on multiple stepwise regression analysis. These data suggest that CAVI, a simple index, is useful for evaluating thoracic aortic atherosclerosis.

Hemodynamics

A review is presented of the physical principles governing the distribution of blood flow and blood pressure in the vascular system. The main factors involved are the pulsatile driving pressure generated by the heart, the flow characteristics of blood, and the geometric structure and mechanical properties of the vessels. The relationship between driving pressure and flow in a given vessel can be understood by considering the viscous and inertial forces acting on the blood. Depending on the vessel diameter and other physical parameters, a wide variety of flow phenomena can occur. In large arteries, the propagation of the pressure pulse depends on the elastic properties of the artery walls. In the microcirculation, the fact that blood is a suspension of cells strongly influences its flow properties and leads to a nonuniform distribution of hematocrit among microvessels. The forces acting on vessel walls include shear stress resulting from blood flow and circumferential stress resulting from blood pressure. Biological responses to these forces are important in the control of blood flow and the structural remodeling of vessels, and also play a role in major disease processes including hypertension and atherosclerosis. Consideration of hemodynamics is essential for a comprehensive understanding of the functioning of the circulatory system.

A database of virtual healthy subjects to assess the accuracy of foot-to-foot pulse wave velocities for estimation of aortic stiffness

While central (carotid-femoral) foot-to-foot pulse wave velocity (PWV) is considered to be the gold standard for the estimation of aortic arterial stiffness, peripheral foot-to-foot PWV (brachial-ankle, femoral-ankle, and carotid-radial) are being studied as substitutes of this central measurement. We present a novel methodology to assess theoretically these computed indexes and the hemodynamics mechanisms relating them. We created a database of 3,325 virtual healthy adult subjects using a validated one-dimensional model of the arterial hemodynamics, with cardiac and arterial parameters varied within physiological healthy ranges. For each virtual subject, foot-to-foot PWV was computed from numerical pressure waveforms at the same locations where clinical measurements are commonly taken. Our numerical results confirm clinical observations: 1) carotid-femoral PWV is a good indicator of aortic stiffness and correlates well with aortic PWV; 2) brachial-ankle PWV overestimates aortic PWV and is related to the stiffness and geometry of both elastic and muscular arteries; and 3) muscular PWV (carotid-radial, femoral-ankle) does not capture the stiffening of the aorta and should therefore not be used as a surrogate for aortic stiffness. In addition, our analysis highlights that the foot-to-foot PWV algorithm is sensitive to the presence of reflected waves in late diastole, which introduce errors in the PWV estimates. In this study, we have created a database of virtual healthy subjects, which can be used to assess theoretically the efficiency of physiological indexes based on pulse wave analysis.

The control of blood pressure might be important in delaying progression of arterial aging in patients with type 2 diabetes mellitus

Objective

Arterial stiffness, as assessed by the brachial-ankle pulse wave velocity (baPWV), is associated with arterial aging and has been consistently linked to cardiovascular disease. The factors involved in reducing the progression of arterial stiffness in patients with type 2 diabetes mellitus (DM) have not yet been fully established.

Methods

Of 478 patients who underwent two baPWV measurements (at baseline and 1 year later) at the Department of Internal Medicine, St Vincent’s Hospital, from November 2009 to June 2011, 341 subjects were enrolled in this study (male to female ratio =150:191; mean age, 62.1±7.7 years). The 341 subjects were over the age of 50 with type 2 DM, were diagnosed without peripheral artery disease, and 170 if the subjects (50%) had hypertension.

Results

baPWV at baseline increased in a linear manner along with age (β=22.8, t=10.855; P<0.0001, R²=0.258). After 1 year follow-up, the change in baPWV (ΔbaPWV) was variable (median 32.7 cm/s [approximate range, −557 to ∼745]). In multiple linear regression, the change in systolic blood pressure (β=7.142, 95% confidence interval =4.557–9.727; P<0.0001, R²=0.305) was associated with ΔbaPWV during follow-up. The change in glycated hemoglobin (HbA_1c) and a glycemic control of keeping HbA_1c levels below 7.0% were not associated with ΔbaPWV.

Conclusion

We found that the variation of blood pressure was associated with the progression of vascular aging of the large- to middle-sized arteries in patients with type 2 DM. Therefore, control of blood pressure might be important in reducing arterial aging or PWV in patients with type 2 DM.

Validation of the pulse decomposition analysis algorithm using central arterial blood pressure

BACKGROUND

There is a significant need for continuous noninvasive blood pressure (cNIBP) monitoring, especially for anesthetized surgery and ICU recovery. cNIBP systems could lower costs and expand the use of continuous blood pressure monitoring, lowering risk and improving outcomes.The test system examined here is the CareTaker® and a pulse contour analysis algorithm, Pulse Decomposition Analysis (PDA). PDA's premise is that the peripheral arterial pressure pulse is a superposition of five individual component pressure pulses that are due to the left ventricular ejection and reflections and re-reflections from only two reflection sites within the central arteries.The hypothesis examined here is that the model's principal parameters P2P1 and T13 can be correlated with, respectively, systolic and pulse pressures.

METHODS

Central arterial blood pressures of patients (38 m/25 f, mean age: 62.7 y, SD: 11.5 y, mean height: 172.3 cm, SD: 9.7 cm, mean weight: 86.8 kg, SD: 20.1 kg) undergoing cardiac catheterization were monitored using central line catheters while the PDA parameters were extracted from the arterial pulse signal obtained non-invasively using CareTaker system.

RESULTS

Qualitative validation of the model was achieved with the direct observation of the five component pressure pulses in the central arteries using central line catheters. Statistically significant correlations between P2P1 and systole and T13 and pulse pressure were established (systole: R square: 0.92 (p < 0.0001), diastole: R square: 0.78 (p < 0.0001). Bland-Altman comparisons between blood pressures obtained through the conversion of PDA parameters to blood pressures of non-invasively obtained pulse signatures with catheter-obtained blood pressures fell within the trend guidelines of the Association for the Advancement of Medical Instrumentation SP-10 standard (standard deviation: 8 mmHg(systole: 5.87 mmHg, diastole: 5.69 mmHg)).

CONCLUSIONS

The results indicate that arterial blood pressure can be accurately measured and tracked noninvasively and continuously using the CareTaker system and the PDA algorithm. The results further support the physical model that all of the features of the pressure pulse envelope, whether in the central arteries or in the arterial periphery, can be explained by the interaction of the left ventricular ejection pressure pulse with two centrally located reflection sites.

Cardio-ankle vascular index (CAVI) correlates with aortic stiffness in the thoracic aorta using ECG-gated multi-detector row computed tomography

BACKGROUND

The cardio-ankle vascular index (CAVI) is an arterial stiffness index based on the stiffness parameter β, which is essentially independent of blood pressure. The objective of this study was to determine whether CAVI correlates with the regional stiffness parameter β and pulse wave velocity (PWV) in the thoracic aorta calculated from ECG-gated multi-detector row computed tomography (MDCT).

METHODS AND RESULTS

Forty-nine patients who underwent coronary MDCT for suspicious coronary artery disease were recruited. The largest and smallest vessel luminal cross-sectional areas of the thoracic aorta were measured from MDCT images to calculate PWV and stiffness parameter β of the ascending and descending aorta. CAVI was also measured by VaSera VS-1000. In univariate analysis, CAVI significantly correlated with regional stiffness parameter β and PWV, which was influenced by the inevitable part of the aging process in the ascending (r = 0.485, P < 0.001; r = 0.483, P < 0.001) and descending aortas (r = 0.304, P = 0.034; r = 0.327, P = 0.022), respectively. The regional stiffness parameter β did not correlate with systolic blood pressure (SBP), although the PWV correlated with SBP. In multivariate analysis, CAVI independently correlated with the stiffness parameter β, but not with the PWV.

CONCLUSION

These data suggest that CAVI, which correlated with stiffness parameter β in the thoracic aorta, has a potential role in evaluating integrated arterial stiffness including that of the central aorta.

MR pulse wave velocity increases with age faster in the thoracic aorta than in the abdominal aorta

PURPOSE

To assess the difference between thoracic and abdominal aortic pulse wave velocity (PWV) in apparently healthy subjects including young adults to elderly subjects.

MATERIALS AND METHODS

We performed PWV and distensibility measurements and analysis of thoracic and abdominal aortic segments in 96 apparently normal subjects aged 20-80 years with magnetic resonance (MR). Both unadjusted correlation and General Linear Model (GLM) analysis of log-transformed PWV (thoracic and abdominal aorta) and distensibility (four aortic cross-sections) were performed.

RESULTS

Both thoracic and abdominal PWV values and distensibility values increased with age. In unadjusted analyses the correlation between the ln(thoracic PWV) and age (r = 0.71; P < 0.001) was stronger than between ln(abdominal PWV) and age (r = 0.50; P < 0.001). In GLM analysis, the only determinant of thoracic and abdominal PWV was age (F = 42.5 and F = 14.8, respectively; both P < 0.001). Similarly, correlation between ln(distensibility) and age was strong (r = -0.79, r = -0.67, r = -0.71, and r = -0.65 for ascending, descending, diaphragmatic, and low abdominal aorta, respectively; all P < 0.001). In GLM analysis, age was the major determinant for distensibility of the ascending aorta (F = 81.7; P < 0.001), descending aorta (F = 42.2; P < 0.001), diaphragmatic aorta (F = 39.2; P < 0.001), and low abdominal aorta (F = 32.8; P < 0.001).

CONCLUSION

The thoracic aorta is less stiff than the abdominal aorta in young and middle-aged subjects, and stiffens more rapidly with age than the abdominal aorta, resulting in a stiffer thoracic than abdominal aorta at older age.

Are geometrical and structural variations along the length of the aorta governed by a principle of "optimal mechanical operation"?

It is well-documented that the geometrical dimensions, the longitudinal stretch ratio in situ, certain structural mechanical descriptors such as compliance and pressure-diameter moduli, as well as the mass fractions of structural constituents, vary along the length of the descending aorta. The origins of and possible interrelations among these observed variations remain open questions. The central premise of this study is that having considered the variation of the deformed inner diameter, axial stretch ratio, and area compliance along the aorta to be governed by the systemic requirements for flow distribution and reduction of cardiac preload, the zero-stress state geometry and mass fractions of the basic structural constituents of aortic tissue meet a principle of optimal mechanical operation. The principle manifests as a uniform distribution of the circumferential stress in the aortic wall that ensures effective bearing of the physiological load and a favorable mechanical environment for mechanosensitive vascular smooth muscle cells. A mathematical model is proposed and inverse boundary value problems are solved for the equations that follow from finite elasticity, structure-based constitutive modeling within constrained mixture theory, and stress-induced control of aortic homeostasis, mediated by the synthetic activity of vascular smooth muscle cells. Published experimental data are used to illustrate the predictive power of the proposed model. The results obtained are in agreement with published experimental data and support the proposed principle of optimal mechanical operation for the descending aorta.

Manipulation of arterial stiffness, wave reflections, and retrograde shear rate in the femoral artery using lower limb external compression

Exposure of the arterial wall to retrograde shear acutely leads to endothelial dysfunction and chronically contributes to a proatherogenic vascular phenotype. Arterial stiffness and increased pressure from wave reflections are known arbiters of blood flow in the systemic circulation and each related to atherosclerosis. Using distal external compression of the calf to increase upstream retrograde shear in the superficial femoral artery (SFA), we examined the hypothesis that changes in retrograde shear are correlated with changes in SFA stiffness and pressure from wave reflections. For this purpose, a pneumatic cuff was applied to the calf and inflated to 0, 35, and 70 mmHg (5 min compression, randomized order, separated by 5 min) in 16 healthy young men (23 ± 1 years of age). Doppler ultrasound and wave intensity analysis was used to measure SFA retrograde shear rate, reflected pressure wave intensity (negative area [NA]), elastic modulus (Ep), and a single-point pulse wave velocity (PWV) during acute cuff inflation. Cuff inflation resulted in stepwise increases in retrograde shear rate (P < 0.05 for main effect). There were also significant cuff pressure-dependent increases in NA, Ep, and PWV across conditions (P < 0.05 for main effects). Change in NA, but not Ep or PWV, was associated with change in retrograde shear rate across conditions (P < 0.05). In conclusion, external compression of the calf increases retrograde shear, arterial stiffness, and pressure from wave reflection in the upstream SFA in a dose-dependent manner. Wave reflection intensity, but not arterial stiffness, is correlated with changes in peripheral retrograde shear with this hemodynamic manipulation.

The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study

OBJECTIVES

Arterial wave reflection has traditionally been quantified from pressure and flow measurements using wave separation and wave intensity (WI) analysis. In the recently proposed reservoir-wave paradigm, these analyses are performed after dividing pressure into 'reservoir' and 'excess' components, yielding a modified wave intensity (WI(RW)). This new approach has led to controversial conclusions about the nature and significance of arterial wave reflection. Our aim was to assess whether WI or WI(RW) more accurately represent wave phenomena.

METHODS

We studied two computer models (a simple network and a full model of the systemic arterial tree) in which all systolic forward waves and reflection properties were known a priori. Results of these models were compared with haemodynamic measurements in the ascending aorta of five adult sheep at baseline and after incremental arterial constriction.

RESULTS

The key findings of model studies were that the reservoir-wave approach markedly underestimated or eliminated reflected compression waves, overestimated or artefactually introduced forward and backward expansion waves, and displayed nonphysical interactions between distal reflection sites and early systolic waves. These errors arose because, contrary to a key assumption of the reservoir-wave approach, reservoir pressure was not spatially uniform during systole. In-vivo results were qualitatively similar to model results, with baseline WI and WI(RW) suggesting that the arterial network was dominated by positive and negative wave reflection, respectively, while under all conditions, reflected WI(RW) compression waves were substantially smaller than corresponding WI waves.

CONCLUSION

We conclude that the reservoir-wave paradigm introduces error into arterial wave analyses.

Wave propagation and reflection in the canine aorta: analysis using a reservoir-wave approach

BACKGROUND

Our objective was to demonstrate wave propagation and reflection in the canine aorta. Recently we proposed that aortic pressure is the instantaneous sum of wave-related or "excess" pressure and reservoir or windkessel pressure. Accordingly, in this research we calculated reservoir pressure and subtracted it from measured pressure to identify the change in pressure due to forward- or backward-travelling waves.

METHODS

In 8 anesthetized dogs, excess pressures were calculated from pressure and flow measurements at 4 locations along the aorta; wave intensity analysis was employed to identify wavefronts and the type of waves.

RESULTS

We found that forward compression and decompression waves generated by the left ventricle are reflected, first, from a negative or "open-end" reflection site near the renal arteries (32.0 ± 0.8 cm [SEM] from the aortic root) and, second, from a positive site in the femoral arteries (65.3 ± 2.8 cm or 54.9 ± 2.1 cm, based on 2 alternative extrapolation techniques).

CONCLUSIONS

Aortic wave propagation and reflection can be demonstrated clearly and directly by wave intensity analysis after volume-related changes-changes in reservoir or windkessel pressure-in aortic pressure are accounted for.

Wave intensity amplification and attenuation in non-linear flow: implications for the calculation of local reflection coefficients

Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (R(PI)) or areas (R(CI)) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (R(DeltaP)). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of R(PI) and R(CI). To test this proposition, R(PI), R(CI) and R(DeltaP) were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (DeltaP(+)), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as DeltaP(+)-->0), R(DeltaP) is equivalent to the square-root of R(PI) and R(CI) (denoted by R(PI)(p) and R(CI)(p)). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in R(PI) and R(CI), and also R(PI)(p) and R(CI)(p), with greater errors associated with larger reflections. Conversely, R(Delta)(P) is unaffected by the degree of non-linearity and is thus more accurate than R(PI) and R(CI).

Ageing of the conduit arteries

Conduit arteries become stiffer with age due to alterations in their morphology and the composition of the their major structural proteins, elastin and collagen. The elastic lamellae undergo fragmentation and thinning, leading to ectasia and a gradual transfer of mechanical load to collagen, which is 100-1000 times stiffer than elastin. Possible causes of this fragmentation are mechanical (fatigue failure) or enzymatic (driven by matrix metallo proteinases (MMP) activity), both of which may have genetic or environmental origins (fetal programming). Furthermore, the remaining elastin itself becomes stiffer, owing to calcification and the formation of cross-links due to advanced glycation end-products (AGEs), a process that affects collagen even more strongly. These changes are accelerated in the presence of disease such as hypertension, diabetes and uraemia and may be exacerbated locally by atherosclerosis. Raised MMP activity, calcification and impaired endothelial function are also associated with a high level of plasma homocysteine, which itself increases with age. Impaired endothelial function leads to increased resting vascular smooth muscle tone and further increases in vascular stiffness and mean and/or pulse pressure. The effect of increased stiffness, whatever its underlying causes, is to reduce the reservoir/buffering function of the conduit arteries near the heart and to increase pulse wave velocity, both of which increase systolic and pulse pressure. These determine the peak load on the heart and the vascular system as a whole, the breakdown of which, like that of any machine, depends more on the maximum loads they must bear than on their average. Reversing or stabilising the increased arterial stiffness associated with age and disease by targeting any or all of its causes provides a number of promising new approaches to the treatment of systolic hypertension and its sequelae, the main causes of mortality and morbidity in the developed world.

Aortic reflection coefficients and their association with global indexes of wave reflection in healthy controls and patients with Marfan's syndrome

Early return of reflected pressure waves increases the load on central arteries and may increase the risk of aortic rupture in patients with Marfan's syndrome (MFS). To assess whether wave reflection is elevated in MFS, we used ultrasound and MRI to measure central pressure and flow waveforms in 26 patients (13-54 yr of age) and 26 age- and gender-matched controls. Aortic systolic and diastolic cross-sectional areas were measured at the ascending and descending aorta (AA and DA), diaphragm (DIA), and lower abdominal aorta (AB). From these measurements, local characteristic impedance (Z(0-xx)) and local reflection coefficients (Gamma(xx-yy)) were calculated. Calculated global wave reflection indexes were the augmentation index (AIx) and the ratio of backward to forward pressure wave (P(b)/P(f)). The aorta was wider in MFS patients at AA (P < 0.01) and DA (P < 0.01). Aortic pulse wave velocity was 42 cm/s higher in MFS patients (P < 0.05). Z(0-xx) was not different between groups, except at DA, where it was lower in MFS patients. In controls, Gamma(AA-DA) was 0.31 +/- 0.08, Gamma(DA-DIA) was 0.00 +/- 0.11, and Gamma(DIA-AB) was 0.31 +/- 0.16. Mean values of Gamma(xx-yy) were not different between MFS patients and controls. In controls, aging diminished Gamma(AA-DA) but increased Gamma(DIA-AB). Clear age-related patterns were absent in MFS patients. AIx or P(b)/P(f) was not higher in MFS patients than in controls. There were indications for enhanced wave reflection in young MFS patients. Our data demonstrated that the major determinants of AIx were pulse wave velocity and the effective length of the arterial system and, to a lesser degree, HR and P(b)/P(f).

Validation of a device to measure arterial pulse wave velocity by a photoplethysmographic method

We aimed to validate a new method for measuring arterial pulsewave transit time and pulsewave velocity (a measure of arterial elasticity), based on the principle of photoplethysmography (PPG), and to compare transcutaneous values with those obtained by intra-arterial measurements. Three validation experiments are described. (a) PPG pulse wave delay times (defined as the time interval between the ECG R wave and the foot of the arterial pulse wave measured at the wrist or ankle) were compared to values obtained simultaneously from an established methodology (Doppler ultrasound). (b) Aortic pulsewave delay times in 17 subjects obtained non-invasively by the PPG method were compared with those obtained from the intra-arterial pressure wave. (c) Repeatability measurements of PWV on the same subjects were carried out over two timescales (minutes and hours) in the arm, the leg and the trunk. The Doppler and PPG delay times correlated well, as did intra-arterial and transcutaneous values. Repeatability at short timescales was good (coefficients of variation (CV) < 6% for all measurement sites) and, at the longer timescale, was satisfactory (CVs in the aorta, the arm and leg were 6.3, 13.1 and 16.0, respectively). The PWV values agreed well with others in the literature. We conclude that the PPG technique provides a complement to existing methods for the non-invasive measurement of arterial compliance. Its simplicity and ease of use make it suitable for large-scale epidemiological studies.

Comparison of different methods for the determination of the true wave propagation coefficient, in rubber tubes and the canine thoracic aorta

The results from studies of wave propagation in large arteries carried out over the last 25 years have shown that there is a good agreement among values of the imaginary part of the complex propagation coefficient, as expressed by pressure or flow-rate wave propagation velocity. However, there is considerable disparity among estimations of the degree of wave attenuation, the real part of the propagation coefficient. In order to determine whether this disparity is due to differences inherent in the various methods used to measure true wave propagation coefficients or whether it is caused by differences in experimental conditions, we have compared three techniques for determining true pulse wave propagation coefficients the three-point method, the occlusion method and a recently described iterative procedure. In addition, the results were compared to apparent propagation coefficients calculated without accounting for reflections. Measurements were carried out using each method in turn on a rubber tube of known transmission characteristics in which the magnitude of reflections was small. The iterative procedure and the three-point method were also compared under conditions of strong reflection. In the tube, the values of propagation velocity and attenuation coefficient determined by each method were similar. Although some discrepancies were noted, they did not amount to a systematic trend. The iterative procedure and the occlusion method were also used to analyse measurements on the thoracic aorta of three anaesthetized greyhounds. In the animal experiments, in spite of increased scatter, partly due to the variation between dogs, the two methods for determining true pulse-wave propagation yielded similar results. Since the differences between our estimates of propagation coefficients obtained by the methods tested are small with respect to those found when comparing the results from several reports in the literature, we conclude that any discrepancies between studies cannot be due to problems associated with the methods themselves but must have been caused by variations in experimental conditions or by other unknown artefacts.

Arterial wall remodelling and stiffness in hypertension: heterogeneous aspects

1. Hypertension is associated with hypertrophy and decreased operating distensibility of the large artery wall. Because similar pathological and functional changes are observed with ageing, hypertension is often looked upon as an accelerated form of aging. 2. Considering the decrease in arterial distensibility observed with both ageing and hypertension, whether the change is due to age, an increase in distending pressure or to hypertension-induced changes in large artery structural properties may be much debated. 3. The purpose of the present review is to study the effects of aging and hypertension on structural (lumen diameter and arterial wall thickness) and functional (distensibility) properties of large central and medium-sized arteries in humans. 4. From clinical studies in subjects with hypertension with or without advanced renal disease, it is suggested that age- and hypertension-induced structural arterial changes are quite heterogeneous, depending on the topography of the vessel and on the severity of the underlying disease.

Impedance matching at arterial bifurcations

Reflections of pulse waves will occur in arterial bifurcations unless the impedance is matched continuously through changing geometric and elastic properties. A theoretical model is presented which minimizes pulse wave reflection through bifurcations. The model accounts for the observed linear changes in area within the bifurcation, generalizes the theory to asymmetrical bifurcations, characterizes changes in elastic properties from parent to daughter arteries, and assesses the effect of branch angle on the mechanical properties of daughter vessels. In contradistinction to previous models, reflections cannot be minimized without changes in elastic properties through bifurcations. The theoretical model predicts that in bifurcations with area ratios (beta) less than 1.0 Young's moduli of daughter vessels may be less than that in the parent vessel if the Womersley parameter alpha in the parent vessel is less than 5. Larger area ratios in bifurcations are accompanied by greater increases in Young's moduli of branches. For an idealized symmetric aortic bifurcation (alpha = 10) with branching angles theta = 30 degrees (opening angle 60 degrees) Young's modulus of common iliac arteries relative to that of the distal abdominal aorta has an increase of 1.05, 1.68 and 2.25 for area ratio of 0.8, 1.0 and 1.15, respectively. These predictions are consistent with the observed increases in Young's moduli of peripheral vessels.(ABSTRACT TRUNCATED AT 250 WORDS)

Increased systolic pressure in chronic uremia. Role of arterial wave reflections

To assess the role of arterial wave reflections in the mechanism of systolic hypertension and altered pulsatile arterial dynamics in patients with end-stage renal disease (ESRD), 79 ESRD patients were compared with 73 age-matched control subjects with normal renal function and similar mean blood pressure. Wave reflections were investigated from the carotid pulse contour recorded by applanation tonometry using a Millar micromanometer-tipped probe. Wave reflections were quantified as the ratio (augmentation index, %) of the height of the late systolic peak to the total height of carotid pulse wave. Travel time of the reflected wave was timed from the foot of the pressure wave to the foot of the late systolic peak. Systolic and pulse pressure were increased in ESRD patients (p less than 0.001) and was not attributable to differences in left ventricular ejection pattern. The augmentation index was increased in ESRD patients (23.2 +/- 15.0 versus 9.8 +/- 15.6%; p less than 0.001) in association with a shorter travel time of reflected wave (109 +/- 24 versus 131 +/- 30 msec; p less than 0.001). Multiple regression analysis showed two principal factors associated (p less than 0.001) with the increase in augmentation index and shortened travel time of reflected wave: increased aortic pulse wave velocity and smaller stature with shorter body height in ESRD patients. The study points to the role of arterial wave reflections in the mechanisms producing alterations in pulsatile arterial dynamics in ESRD and is the first, through the mechanisms of early wave reflections, to show in humans that the increase in systolic and pulse pressures is associated with lesser body size.