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Schematic representation of a Kelvin model. SEC: series elastic component. PEC: parallel elastic component. CE: contractile element.
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Vascular wall viscoelasticity can be evaluated using a first-order lumped model. This model consists of a spring with elastic constant E and a dashpot with viscous constant η. More importantly, this viscoelastic model can be fitted in-vivo measuring arterial pressure and diameter. The aim of this work is to analyze the influence of heart rate over...
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Context 1
... objective of the present work is to analyze the dependence of the mechanic parameters of the arterial wall with heart rate using a first order simple model with elastic and viscous moduli. Figure 1 shows the complete model of the arterial wall [4]. The PEC corresponds to the elastic component composed by elastin and collagen fibres. ...
Context 2
... CE is conditioned to smooth muscle activity, in series with the SEC. In this way, we define two branches: the passive branch (corresponding to the left branch in figure 1) and the active branch (corresponding to the right branch in figure 1). For the present work, this model is reduced into a Voigt model of two elements, whose constitutive equation is the following: ...
Context 3
... CE is conditioned to smooth muscle activity, in series with the SEC. In this way, we define two branches: the passive branch (corresponding to the left branch in figure 1) and the active branch (corresponding to the right branch in figure 1). For the present work, this model is reduced into a Voigt model of two elements, whose constitutive equation is the following: ...
Context 4
... suggests an increase of flow, which would increase the shear stress on the endothelial layer causing the phenomena described as vascular wall relaxation mediated by endothelium [8]. Starting with the model presented in figure 1, opposed to changes in heart rate that would lead to flow changes, the CE- SEC branch (active branch) would be modulating the viscous modulus η through the contractile element CE, but without altering the SEC component, while maintaining the total elastic modulus of the wall constant. However, during smooth muscle activation with phenylephrine, the SEC would be modulating the viscoelasticity of the whole set. ...
Similar publications
Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has bee...
Citations
... Many other regulation mechanisms linked to viscosity, damping properties, and strain-dependent activation of smooth muscle tone are being investigated [19,99,100]. Such dynamic behaviors can be studied at local as well as systemic levels [101,102]. ...
Hemodynamic monitoring technologies are evolving continuously—a large number of bedside monitoring options are becoming available in the clinic. Methods such as echocardiography, electrical bioimpedance, and calibrated/uncalibrated analysis of pulse contours are becoming increasingly common. This is leading to a decline in the use of highly invasive monitoring and allowing for safer, more accurate, and continuous measurements. The new devices mainly aim to monitor the well-known hemodynamic variables (e.g., novel pulse contour, bioreactance methods are aimed at measuring widely-used variables such as blood pressure, cardiac output). Even though hemodynamic monitoring is now safer and more accurate, a number of issues remain due to the limited amount of information available for diagnosis and treatment. Extensive work is being carried out in order to allow for more hemodynamic parameters to be measured in the clinic. In this review, we identify and discuss the main sensing strategies aimed at obtaining a more complete picture of the hemodynamic status of a patient, namely: (i) measurement of the circulatory system response to a defined stimulus; (ii) measurement of the microcirculation; (iii) technologies for assessing dynamic vascular mechanisms; and (iv) machine learning methods. By analyzing these four main research strategies, we aim to convey the key aspects, challenges, and clinical value of measuring novel hemodynamic parameters in critical care.
... Artery Wall Viscosity, Heart Rate Reduction, Aging AWV. 15,[17][18][19][20] In a thermodynamic point of view, AWV is responsible for the dissipation as heat of a part of the mechanical energy stored within the arterial wall during each cardiac cycle. Thus, the hysteresis loop resulting from the shift between the loading and unloading phases of the pressure-lumen cross-sectional area curves (P-LCSA) corresponds to the dissipated energy (W V ), whereas the area under the loading curve reflects the elastic energy stored (W E ). 21,22 Consequently, AWV can be expressed as the absolute value of the loop area or as a ratio (W V /W E ), considering thus one of its major determinants. ...
... The study was registered at ClinicalTrials.gov Identifier: 2015/077/HP and EudraCT Number: 2015-002060- 17. The data that support the findings of this study are available from the corresponding author upon reasonable request. ...
... 24,53 In fact, η is not equivalent to W V , which corresponds to the dissipated energy related to both intrinsic viscosity and arterial working conditions and can be approximated by the product of η, HR, and distension. 17,38 Thus, the decrease in η observed when HR increases is concordant with our result showing an increase in W V when HR decreases. [17][18][19][20]53 Furthermore, we performed a planned exploratory analysis to evaluate the impact of aging on the adaptation of AWV to HR reduction. ...
Background
Changes in arterial wall viscosity, which dissipates the energy stored within the arterial wall, may contribute to the beneficial effect of heart rate (HR) reduction on arterial stiffness and cardiovascular coupling. However, it has never been assessed in humans and could be altered by aging. We evaluated the effect of a selective HR‐lowering agent on carotid arterial wall viscosity and the impact of aging on this effect.
Methods and Results
This randomized, placebo‐controlled, double‐blind, crossover study performed in 19 healthy volunteers evaluated the effects of ivabradine (5 mg BID, 1‐week) on carotid arterial wall viscosity, mechanics, hemodynamics, and cardiovascular coupling. Arterial wall viscosity was evaluated by the area of the hysteresis loop of the pressure‐lumen cross‐sectional area relationship, representing the energy dissipated (W V ), and by the relative viscosity (W V /W E ), with W E representing the elastic energy stored.
HR reduction by ivabradine increased W V and W E whereas W V /W E remained stable. In middle‐aged subjects (n=11), baseline arterial stiffness and cardiovascular coupling were less favorable, and W E was similar but W V and therefore W V /W E were lower than in youth (n=8). HR reduction increased W V /W E in middle‐aged but not in young subjects, owing to a larger increase in W V than W E . These results were supported by the age‐related linear increase in W V /W E after HR reduction ( P =0.009), explained by a linear increase in W V .
Conclusion
HR reduction increases arterial wall energy dissipation proportionally to the increase in W E , suggesting an adaptive process to bradycardia. This mechanism is altered during aging resulting in a larger than expected energy dissipation, the impact of which should be assessed.
Registration
URL: https://www.clinicaltrials.gov ; Unique identifier: 2015/077/HP. URL: https://www . eudract.ema.europa.eu; Unique identifier: 2015‐002060‐17.
... By definition, viscous material behav- iour is frequency-dependent, as evidenced by the units of viscosity (N⋅s⋅m -2 ), involving time [9]. In vitro and in vivo studies in arteries of canines [86,92], rats [18,93], sheep [94], as well as humans [95,96] have all shown a frequency dependency of arterial wall viscosity. This indicates that changes in heart rate would lead to changes in µ. ...
... However, its influence on arterial stiffness would be negligible if E dyn is unchanged and the viscous modulus is relatively much smaller than E dyn (<10%) [86]. Furthermore, most of these studies have shown that the viscous modulus remains rela- tively constant [94] or increases only slightly [86] with in- creasing frequency, with in vivo viscosity being three-fold lower than in vitro in rats [18], but with no significant in vivo-in vitro difference in humans [95]. ...
Vascular assessment is becoming increasingly important in the diagnosis of cardiovascular diseases. In particular, clinical assessment of arterial stiffness, as measured by pulse wave velocity (PWV), is gaining increased interest due to the recognition of PWV as an influential factor on the prognosis of hypertension as well as being an independent predictor of cardiovascular and all-cause mortality. Whilst age and blood pressure are established as the two major determinants of PWV, the influence of heart rate on PWV measurements remains controversial with conflicting results being observed in both acute and epidemiological studies. In a majority of studies investigating the acute effects of heart rate on PWV, results were confounded by concomitant changes in blood pressure. Observations from epidemiological studies have also failed to converge, with approximately just half of such studies reporting a significant blood-pressure-independent association between heart rate and PWV. Further to the lack of consensus on the effects of heart rate on PWV, the possible mechanisms contributing to observed PWV changes with heart rate have yet to be fully elucidated, although many investigators have attributed heart-rate related changes in arterial stiffness to the viscoelasticity of the arterial wall. With elevated heart rate being an independent prognostic factor of cardiovascular disease and its association with hypertension, the interaction between heart rate and PWV continues to be relevant in assessing cardiovascular risk.
... Several models exist that suggest different forms of interpretation based on mathematical models of the elastic behavior of the arterial wall, the majority of these models are based on the viscoelasticity theory. Some of the models that have been proposed to solve the strainstress relation of the arterial wall are: elastic parameters only (Rand, 1968) and viscoelasticity (Armentano et al., 1995;Salvucci, 2007). Furthermore, a typical arterial wall consists of three layers: an innermost layer, "the intima", mainly composed of endothelial cells, a middle layer, "the media", composed of elongated smooth cells, elastin and collagen, and an outer layer "the adventitia", comprising a varied number of elastic sheets, bundles of collagen fibrils, and a network of elastic fibrils (Valdez-Jasso, 2009). ...
... where ε(t) corresponds to the total deformation caused in the membrane or in the artery wall depending on whether the elastic and viscosity terms of the silicone rubber and the membrane are considered or neglected in Eq. 2. To solve it, we consider the values of E e =10 Mdyn/cm2, η a =0.1seg-Mdyn/cm2, E e =1x106 N/m2, η a =100 seg-N/m 2 , and E equiv-sm =1x10 6 N/m 2 as reported previously (Salvucci et al., 2007;Shin-Etsu, 2012). Also, it is worth to mention that in a similar way to the models presented in Figs. 2 and 3, our model does not consider the width of the different layers present in the artery wall and the layers of the MEMS device, due to the fact that the elasticity and viscosity terms are considered constants along these layers. ...
MEMS technology is an option for the development of a pressure sensor which allows the monitoring of several bio-signals in humans. In this work, a comparison is made between the typical elasticity and viscosity presented in several arteries in the human body and those present in MEMS silicon microstructures based on membranes in proximity with an arterial wall. The main purpose is to identify which types of microstructures are mechanically compatible with human arteries. The ultimate goal is to integrate a blood pressure sensor which can be implanted in proximity with an artery. The expected benefits for this type of sensor are mainly the reduction in problems associated with the use of bulk devices through the day and during several days. Such a sensor could provide precise blood pressure readings in a continuous or periodic form, i.e. information that is especially important for some critical cases of hypertension patients. The modeling work involved in this paper, accounts for the analysis of micro displacements present in the membrane of a MEMs silicone microstructure placed directly on a human arterial wall, at different heart rates. The modeling includes the effects of elasticity and viscosity of the silicone structure on the pressure measurement. Additionally, the sensitivity of the membrane to detect slight variations in the blood pressure is presented.
... then the null hypothesis is not rejected and one can conclude that the mean is not different from the hypothesized value. Moreover, our results showed that the pulsatile rate has an insignificant effect on the values of the elastic modulus, as also seen by Salvucci et al. 19 A limitation of this study is the temporal resolution of the CT post-processing. The images used to determine the cross-sectional areas are reconstructed at each 5% of the ReR interval. ...
This study was performed to determine the feasibility of measuring the elastic properties of the arterial wall in vivo. To prove this concept, elastic parameters were calculated from an aortic model of elastic behavior similar to a human aorta using computed tomography angiography (CTA) images.
We first constructed an aortic model from polydimethylsiloxane (PDMS). This model was inserted into a pulsatile flow loop. The model was then placed inside a computed tomography scanner. To estimate the elasticity values, we measured the cross-sectional area and the pressure changes in the model during each phase of the simulated cardiac cycle. A discrete wavelet transform (DWT) algorithm was applied to the CTA data to calculate the geometric changes in the pulsatile model over a simulated cardiac cycle for various pulsatile rates and elasticity values of the PDMS material. The elastic modulus of the aortic model wall was derived from these geometric changes. The elastic moduli derived from the CTA data were compared with those obtained by testing strips of the same PDMS material in a tensile testing machine. Our two aortic models had elastic values at both extremes of those found in normal human aortas.
The results show a good comparison between the elastic values derived from the CTA data and those obtained in a tensile testing machine. In addition, the elasticity values were found to be independent of the pulsatile rate for mixing ratios of 6:1 and 9:1 (p = .12 and p = .22, respectively).
The elastic modulus of a pulsatile aortic model may be measured by electrocardiographically-gated multi-detector CTA protocol. This preliminary study suggests the possibility of determining non-invasively the elastic properties of a living, functioning aorta using CTA data.
... Underlying mechanisms for this association have been investigated in experimental conditions in paced human subjects [30,58] as well as in rat models [59,60] and where interventions were controlled for changes in arterial pressure [31] . The effect has been suggested to be due to the viscoelastic properties of the arterial wall [61,62] . ...
... In addition to the important role of vascular smooth muscle in the regulation of vascular tone affecting peripheral resistance, the contractile properties of the vascular smooth muscle cells have a measurable effect on mechanics of the arterial wall of large conduit arteries [62,73,74] with suggestions of regulation of energetics of viscous damping [75] . There is a large body of literature spanning some five decades on the biology of smooth muscle cell phenotypic modulation, where the cell exits in a number of phenotypic states which depend on specific adaptive functional demands [76] . ...
Stiffness of large arteries has been long recognized as a significant determinant of pulse pressure. However, it is only in recent decades, with the accumulation of longitudinal data from large and varied epidemiological studies of morbidity and mortality associated with cardiovascular disease, that it has emerged as an independent predictor of cardiovascular risk. This has generated substantial interest in investigations related to intrinsic causative and associated factors responsible for the alteration of mechanical properties of the arterial wall, with the aim to uncover specific pathways that could be interrogated to prevent or reverse arterial stiffening. Much has been written on the haemodynamic relevance of arterial stiffness in terms of the quantification of pulsatile relationships of blood pressure and flow in conduit arteries. Indeed, much of this early work regarded blood vessels as passive elastic conduits, with the endothelial layer considered as an inactive lining of the lumen and as an interface to flowing blood. However, recent advances in molecular biology and increased technological sophistication for the detection of low concentrations of biochemical compounds have elucidated the highly important regulatory role of the endothelial cell affecting vascular function. These techniques have enabled research into the interaction of the underlying passive mechanical properties of the arterial wall with the active cellular and molecular processes that regulate the local environment of the load-bearing components. This review addresses these emerging concepts.
... Results from more recent studies on the frequency dependency of arterial wall viscosity have not resulted in a convergence in findings. Although some investigators have found that wall viscosity decreases with HR with no change in arterial stiffness, 35 others have found that, at higher frequencies, in the range of HRs tested in this study (300 -450 oscillations per minute), the rat aorta wall may become more susceptible to stiffening, 36 especially at higher pressures. 33 Our finding that the effect of HR on PWV was more evident at higher MAP is consistent with the latter observation. ...
Arterial stiffness, as measured by aortic pulse wave velocity (PWV), is an independent marker of cardiovascular disease and events in both healthy and diseased populations. Although some cardiovascular risk factors, such as age and blood pressure, show a strong association with PWV, the association between heart rate (HR) and PWV is not firmly established. Furthermore, this association has not been investigated at different arterial blood pressures. To study effects of HR on aortic PWV at different mean arterial pressures (MAPs), adult (12 weeks; n=7), male, anesthetized Sprague-Dawley rats were randomly paced at HRs of between 300 and 450 bpm, at 50-bpm steps. At each pacing step, aortic PWV was measured across a physiological MAP range of 60 to 150 mmHg by infusing sodium nitroprusside and phenylephrine. When compared at the same MAP, increases in HR resulted in significant increases in PWV at all of the MAPs >80 mmHg (ANOVA, P<0.05), with the greatest significant change of 6.03±0.93% observed in the range 110 to 130 mmHg. The positive significant association between HR and PWV remained when PWV was adjusted for MAP (ANOVA, P<0.001). These results indicate that HR dependency of PWV is different at higher pressures than at lower pressures and that HR may be a confounding factor that should be taken into consideration when performing analysis based on PWV measurements.
... This allowed us to investigate the consequence of aortic wall stiffening and valve thickening on the energy stored in this elastic component, which would ultimately affect coronary perfusion. The roll of viscous terms become significant when the smooth muscle cells are activated [37, 38]. Since the microstructure of the vessel has not been the focus of this study and the smooth muscle cells have not been considered, the viscous effects could be neglected. ...
In some pathological conditions like aortic stiffening and calcific aortic stenosis (CAS), the microstructure of the aortic root and the aortic valve leaflets are altered in response to stress resulting in changes in tissue thickness, stiffness, or both. This aortic stiffening and CAS are thought to affect coronary blood flow. The goal of the present paper was to include the flow in the coronary ostia in the previous fluid structure interaction model we have developed and to analyze the effect of diseased tissues (aortic root stiffening and CAS) on coronary perfusion. Results revealed a significant impact on the coronary perfusion due to a moderate increase in the aortic wall stiffness and CAS (increase of the aortic valve leaflets thickness). A marked drop of coronary peak velocity occurred when the values of leaflet thickness and aortic wall stiffness were above a certain threshold, corresponding to a threefold of their normal value. Consequently, mild and prophylactic treatments such as smoking cessation, exercise, or diet, which have been proven to increase the aortic compliance, may significantly improve the coronary perfusion.
... In particular, the LF/HF ratio of SBP is almost 4 times higher than that of PTT. This may be due to the frequency dependency of artery properties that determine the relationship between PTT and BP [30][31][32]. Thus, it is postulated that in order to estimate SBP from PTT, different gains should be considered for the different frequency components. ...
Time–frequency (T–F) analysis is often used to study the non-stationary cardiovascular oscillations such as heart rate and blood pressure variabilities in dynamic situations. This study intends to use the T–F recursive autoregressive technique to investigate variability in pulse transit time (PTT), which is a cardiovascular parameter of emerging interest due to its potential to estimate blood pressure non-invasively, continuously and without a cuff. Recent studies suggest that PTT is not only related to systolic blood pressure (SBP) but also to heart rate. Therefore, in this study, variability of PTT is analyzed together with the variabilities of R–R interval (RRI) from electrocardiogram and beat-to-beat SBP on 9 normotensive subjects before and shortly after three successive bouts of treadmill exercise. The results showed that both low frequency (LF) and high frequency (HF) components were found in the spectra of RRI, SBP and PTT in the 5-min recordings collected before and after exercise. Compared to the baseline, a decrease in the power of the HF component of RRI followed by an increase in its LF component indicated firstly a vagal withdrawal and then sympathetic activity enhancement after successive bouts of exercise. On the other hand, although changes in the LF and HF components of PTT were more similar to those of SBP than of RRI, the LF/HF ratio of SBP was almost 4 times higher than that of PTT. Based on the results, it is therefore suggested that the relationship between SBP and PTT is frequency-dependent.
Les artères de conductance ont un comportement viscoélastique mais la composante visqueuse a été moins étudiée chez l’homme, que la composante élastique. Cette viscosité pariétale artérielle participe à la dissipation d’une partie de l’énergie élastique emmagasinée au cours du cycle cardiaque. Elle pourrait altérer l’efficience du couplage cardio-circulatoire au cours du vieillissement ou de l’HTA. A l’inverse, une baisse de cette composante pourrait être délétère en n’atténuant pas suffisamment l’énergie élastique transmise à la paroi artérielle et aux organes périphériques. Dans ce contexte, l’évaluation de ce paramètre chez l’homme en physiologie et au cours du vieillissement normal ou accéléré est nécessaire. De plus, l’identification des déterminants de la viscosité pariétale et la recherche de cibles pharmacologiques modifiant spécifiquement la viscosité semblent pertinentes. Ce travail a pour objectifs d’évaluer la viscosité pariétale au niveau des artères de conductance chez le sujet jeune mais également au cours du vieillissement et de l’HTA, de déterminer le rôle de l’endothélium et du tonus musculaire dans la régulation de la viscosité pariétale à l’état basal et stimulé et enfin d’évaluer l’effet de la réduction pharmacologique de la fréquence cardiaque (FC) sur la viscosité pariétale et l’impact du vieillissement sur cet effet. Nous avons évalué la viscosité pariétale par deux méthodes, l’une au niveau carotidien et l’autre au niveau radial à partir de techniques d’écho-tracking vasculaire haute résolution et de tonométrie ou de pléthysmographie. Ceci nous a permis d’obtenir des relations pression-diamètre ou pression-section permettant une évaluation thermodynamique du phénomène visqueux. Ainsi, nous avons montré que la viscosité pariétale artérielle est régulée, au niveau de l’artère radiale, par le monoxyde d’azote et les acides époxyeicosatriénoïques endothéliaux, chez le sujet sain comme chez le patient hypertendu. Ces facteurs semblent agir par des mécanismes tonus-dépendants et indépendants. Au cours de l’hypertension artérielle, on constate une augmentation de l’énergie dissipée parallèle à l’augmentation d’énergie emmagasinée dans la paroi résultant en une viscosité relative stable à l’état basal. Cependant, lors de l’augmentation du flux, ce mécanisme adaptatif est altéré, du fait de la dysfonction endothéliale au cours de l’hypertension, résultant en une augmentation de la viscosité absolue et relative. Au niveau carotidien, la réduction de la FC par l’ivabradine augmente la viscosité absolue parallèlement à l’augmentation de l’énergie élastique, aboutissant à une viscosité relative stable, chez le sujet sain ayant une FC supérieure à 70 bpm au repos. Dans cette population, les sujets d’âge moyen présentent des viscosités absolue et relative moindres que les sujets jeunes à l’état basal. Lors de la réduction pharmacologique de la FC, ils présentent également une augmentation majeure de la viscosité absolue et relative suggérant une altération de ce mécanisme adaptatif.
