Instability in Computational Models of Vascular Smooth Muscle Cell Contraction.

PURPOSE: Through their contractile and synthetic capacity, vascular smooth muscle cells (VSMCs) can regulate the stiffness and resistance of the circulation. To model the contraction of blood vessels, an active stress component can be added to the (passive) Cauchy stress tensor. Different constitutive formulations have been proposed to describe this active stress component. Notably, however, measuring biomechanical behaviour of contracted blood vessels ex vivo presents several experimental challenges, which complicate the acquisition of comprehensive datasets to inform complex active stress models. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive datasets. METHODS: First, we prove analytically that a subset of constitutive active stress formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly for large contractile deformations. Second, using experimental literature data, we present two case studies where these formulations are used to capture the contractile response of VSMCs in the presence of (1) limited and (2) extensive contraction data. RESULTS: We show how limited contraction data complicates selecting an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours. CONCLUSION: Our data provide a useful reference for selecting an active stress model which balances the trade-off between accuracy and available biomechanical information. Whilst complex physiologically motivated models' superior accuracy is recommended whenever active biomechanics can be extensively characterised experimentally, a constant 2nd Piola-Kirchhoff active stress model balances well accuracy and applicability with sparse contractile data.

Developing technologies to assess vascular ageing: a roadmap from VascAgeNet.

Vascular ageing is the deterioration of arterial structure and function which occurs naturally with age, and which can be accelerated with disease. Measurements of vascular ageing are emerging as markers of cardiovascular risk, with potential applications in disease diagnosis and prognosis, and for guiding treatments. However, vascular ageing is not yet routinely assessed in clinical practice. A key step towards this is the development of technologies to assess vascular ageing. In this Roadmap, experts discuss several aspects of this process, including: measurement technologies; the development pipeline; clinical applications; and future research directions. The Roadmap summarises the state of the art, outlines the major challenges to overcome, and identifies potential future research directions to address these challenges.

Effect of rapid cooling, frozen storage, and thawing on the passive viscoelastic properties and structure of the rat aorta.

Biological tissues decay over time after harvesting, which alters their biomechanical properties. This poses logistical challenges for studies investigating passive arterial biomechanics as tissues need to be characterized shortly after excision. Freezing and cryopreservation methods can help alleviate the need for biomechanical testing of fresh tissue in human ex vivo studies. However, these methods tend to eliminate or reduce arterial cell functionality and affect passive biomechanics. Furthermore, their impact on dynamic arterial biomechanics remains unknown despite arterial viscoelastic properties being an integral component contributing to arterial stiffness under in vivo loading conditions. The present study aims to investigate the impact of rapid cooling and subsequent storage at -80 °C on the passive viscoelastic properties of arterial tissue and aid in ascertaining whether this is a suitable method to delay tissue analysis for studies investigating passive arterial biomechanics. Control and frozen abdominal rat aorta segments were quasi-statically and dynamically tested using a biaxial testing set-up. The results were modeled using a constituent-based quasi-linear viscoelastic modeling framework, yielding directional stiffness parameters, individual constituent biomechanical contributions, and a quantification of viscoelastic stiffening under dynamic pressurization conditions. Frozen samples displayed significantly decreased wall thickness, viscoelastic dissipation, viscoelastic stiffening, and significantly decreased circumferential deformation with changes in luminal pressure. Furthermore, frozen samples displayed significantly increased circumferential stiffness, pulse wave velocity, and collagen load bearing. Consequently, these changes should be considered when utilizing this tissue preservation method to delay biomechanical characterization of rat aortic tissue.

Significance of Dynamic Axial Stretching on Estimating Biomechanical Behavior and Properties of the Human Ascending Aorta.

Contrary to most vessels, the ascending thoracic aorta (ATA) not only distends but also elongates in the axial direction. The purpose of this study is to investigate the biomechanical behavior of the ascending thoracic aorta (ATA) in response to dynamic axial stretching during the cardiac cycle. In addition, the implications of neglecting this dynamic axial stretching when estimating the constitutive model parameters of the ATA are investigated. The investigations were performed through in silico simulations by assuming a Gasser-Ogden-Holzapfel (GOH) constitutive model representative of ATA tissue material. The GOH model parameters were obtained from biaxial tests performed on four human ATA tissues in a previous study. Pressure-diameter curves were simulated as synthetic data to assess the effect of neglecting dynamic axial stretching on estimating constitutive model parameters. Our findings reveal a significant increase in axial stress (~ 16%) and stored strain energy (~ 18%) in the vessel when dynamic axial stretching is considered, as opposed to assuming a fixed axial stretch. All but one artery showed increased volume compliance while considering a dynamic axial stretching condition. Furthermore, we observe a notable difference in the estimated constitutive model parameters when dynamic axial stretching of the ATA is neglected, compared to the ground truth model parameters. These results underscore the critical importance of accounting for axial deformations when conducting in vivo biomechanical characterization of the ascending thoracic aorta.

Pharmacological modulation of vascular ageing: A review from VascAgeNet.

Vascular ageing, characterized by structural and functional changes in blood vessels of which arterial stiffness and endothelial dysfunction are key components, is associated with increased risk of cardiovascular and other age-related diseases. As the global population continues to age, understanding the underlying mechanisms and developing effective therapeutic interventions to mitigate vascular ageing becomes crucial for improving cardiovascular health outcomes. Therefore, this review provides an overview of the current knowledge on pharmacological modulation of vascular ageing, highlighting key strategies and promising therapeutic targets. Several molecular pathways have been identified as central players in vascular ageing, including oxidative stress and inflammation, the renin-angiotensin-aldosterone system, cellular senescence, macroautophagy, extracellular matrix remodelling, calcification, and gasotransmitter-related signalling. Pharmacological and dietary interventions targeting these pathways have shown potential in ameliorating age-related vascular changes. Nevertheless, the development and application of drugs targeting vascular ageing is complicated by various inherent challenges and limitations, such as certain preclinical methodological considerations, interactions with exercise training and sex/gender-related differences, which should be taken into account. Overall, pharmacological modulation of endothelial dysfunction and arterial stiffness as hallmarks of vascular ageing, holds great promise for improving cardiovascular health in the ageing population. Nonetheless, further research is needed to fully elucidate the underlying mechanisms and optimize the efficacy and safety of these interventions for clinical translation.

Aging and Vascular Disease: A Multidisciplinary Overview.

Vascular aging, i.e., the deterioration of the structure and function of the arteries over the life course, predicts cardiovascular events and mortality. Vascular degeneration can be recognized before becoming clinically symptomatic; therefore, its assessment allows the early identification of individuals at risk. This opens the possibility of minimizing disease progression. To review these issues, a search was completed using PubMed, MEDLINE, and Google Scholar from 2000 to date. As a network of clinicians and scientists involved in vascular medicine, we here describe the structural and functional age-dependent alterations of the arteries, the clinical tools for an early diagnosis of vascular aging, and the cellular and molecular events implicated. It emerges that more studies are necessary to identify the best strategy to quantify vascular aging, and to design proper physical activity programs, nutritional and pharmacological strategies, as well as social interventions to prevent, delay, and eventually revert the disease.

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries.

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

Time-course of the human thoracic aorta ageing process assessed using uniaxial mechanical testing and constitutive modelling.

Age-related remodelling of the arterial wall shifts the load bearing from the compliant elastin network to the stiffer collagen fibres. While this phenomenon has been widely investigated in animal models, human studies are lacking due to shortage of donors' arteries. This work aimed to characterise the effect of ageing on the mechanical properties of the human aortic wall in the circumferential direction. N = 127 thoracic aortic rings (age 18-81 years) were subjected to circumferential tensile testing. The tangential elastic modulus (Kθθθθ) was calculated at pressure-equivalent stresses ranging 60-100 mmHg. Further, the mechanical data were fitted using the Holzpafel-Gasser-Ogden hyperelastic strain energy function (HGO-SEF), modelling the superimposed response of an isotropic matrix (elastin) reinforced by collagen fibres. Kθθθθ increased with age across at all considered pressures (p < 0.001), although more strongly at higher pressures. Indeed, the slope of the linear Kθθθθ-pressure relationship increased by 300% from donors <30 to ≥70 years (4.72± 2.95 to 19.06± 6.82 kPa/mmHg, p < 0.001). The HGO-SEF elastin stiffness-like parameter dropped by 31% between 30 and 40 years (p < 0.05) with non-significant changes thereafter. Conversely, changes in HGO-SEF collagen parameters were observed later at age>60 years, with the exponential constant increasing by ∼20-50 times in the investigated age range (p < 0.001). The results provided evidence that the human thoracic aorta undergoes stiffening during its life-course. Constitutive modelling suggested that these changes in arterial mechanics are related to the different degeneration time-courses of elastin and collagen; likely due to considerable fragmentation of elastin first, with the load bearing shifting from the compliant elastin to the stiffer collagen fibres. This process leads to a gradual impairment of the aortic elastic function with age.

Detectable Bias between Vascular Ultrasound Echo-Tracking Systems: Relevance Depends on Application.

The Esaote MyLab70 ultrasound system has been extensively used to evaluate arterial properties. Since it is reaching end-of-service-life, ongoing studies are forced to seek an alternative, with some opting for the Esaote MyLabOne. Biases might exist between the two systems, which, if uncorrected, could potentially lead to the misinterpretation of results. This study aims to evaluate a potential bias between the two devices. Moreover, by comparing two identical MyLabOne systems, this study also aims to investigate whether biases estimated between the MyLabOne and MyLab70 employed in this study could be generalized to any other pair of similar scanners. Using a phantom set-up, we performed n = 60 measurements to compare MyLab70 to MyLabOne and n = 40 measurements to compare the two MyLabOne systems. Comparisons were performed to measure diameter, wall thickness, and distension. Both comparisons led to significant biases for the diameter (relative bias: −0.27% and −0.30% for the inter- and intra-scanner model, respectively, p < 0.05) and wall thickness (relative bias: 0.38% and −1.23% for inter- and intra-scanner model, respectively p < 0.05), but not for distension (relative bias: 0.48% and −0.12% for inter- and intra-scanner model, respectively, p > 0.05). The biases estimated here cannot be generalized to any other pair of similar scanners. Therefore, longitudinal studies with large sample sizes switching between scanners should perform a preliminary comparison to evaluate potential biases between their devices. Furthermore, caution is warranted when using biases reported in similar comparative studies. Further work should evaluate the presence and relevance of similar biases in human data.

Noninvasive carotid pressure-diameter loops to identify viscoelastic properties in ageing, hypertension and type 2 diabetes.

OBJECTIVES: Arterial stiffness as pulse wave velocity (PWV) predicts cardiovascular events independently of blood pressure (BP). PWV does not distinguish between stiffness in systole and diastole. This cross-sectional study aimed to test the hypothesis that viscous and elastic carotid wall properties differ between systole and diastole, distinguishing effects of ageing, hypertension and T2 diabetes (T2DM). METHODS: We examined carotid visco-elasticity in 307 people (180 men), with hypertension alone (n = 69), combined hypertension/T2DM (H-T2DM, n = 99), normotensive (N-T2DM, n = 25) and healthy controls (n = 114). Diameter (D)/pressure (P) waveforms were measured at right /left common carotid arteries, respectively. Local carotid PWV and distensibility in systole and diastole were evaluated by the D2P-loop method, and wall viscosity from hysteresis, the area (HA) within the P--D loop, as a dynamic measure of systolic loading and diastolic unloading. RESULTS: Controls' hysteresis fell quadratically with age (R2 = 0.23, P < 0.001). Yet mean HA in hypertensive patients (0.95, 95% CI 0.65-1.23) was six-fold higher than in age-matched controls (0.14, -0.20 to 0.49, P < 0.001) with a 2.5× difference between diastolic (dDs) to systolic (sDs) distensibility (P < 0.05) in hypertensive patients. HA was higher in hypertensive patients and H-T2DMs (0.80, 0.58-1.04) than N-T2DMs (0.20, -0.17 to 0.54, P < 0.05), but similar between controls and N-T2DMs. BP-adjusted carotid diameters in all T2DM were significantly greater compared with controls and hypertensive patients. CONCLUSION: Higher BP increased wall viscosity, hysteresis and relative difference between systolic and diastolic distensibility across groups. Carotid diameters were increased in all T2DMs, more in H-T2DM, probably altering BP-flow dynamics in T2DM.

Transfer-function-free technique for the noninvasive determination of the human arterial pressure waveform.

The estimation of central aortic blood pressure is a cardinal measurement, carrying effective physiological, and prognostic data beyond routine peripheral blood pressure. Transfer function-based devices effectively estimate aortic systolic and diastolic blood pressure from peripheral pressure waveforms, but the reconstructed pressure waveform seems to preserve features of the peripheral waveform. We sought to develop a new method for converting the local diameter distension waveform into a pressure waveform, through an exponential function whose parameters depend on the local wave speed. The proposed method was then tested at the common carotid artery. Diameter and blood velocity waveforms were acquired via ultrasound at the right common carotid artery while simultaneously recording pressure at the left common carotid artery via tonometer in 203 people (122 men, 50 ± 18 years). The wave speed was noninvasively estimated via the lnDU-loop method and then used to define the exponential function to convert the diameter into pressure. Noninvasive systolic and mean pressures estimated by the new technique were 3.8 ± 21.8 (p = 0.015) and 2.3 ± 9.6 mmHg (p = 0.011) higher than those obtained using tonometery. However, differences were much reduced and not significant in people >35 years (0.6 ± 18.7 and 0.8 ± 8.3 mmHg, respectively). This proof of concept study demonstrated that local wave speed, estimated from noninvasive local measurement of diameter and flow velocity, can be used to determine an exponential function that describes the relationship between local pressure and diameter. This pressure-diameter function can then be used for the noninvasive estimation of local arterial pressure.

Five years of cardio-ankle vascular index (CAVI) and CAVI0: how close are we to a pressure-independent index of arterial stiffness?

Pulse wave velocity, a common metric of arterial stiffness, is an established predictor for cardiovascular events and mortality. However, its intrinsic pressure-dependency complicates the discrimination of acute and chronic impacts of increased blood pressure on arterial stiffness. Cardio-ankle vascular index (CAVI) represented a significant step towards the development of a pressure-independent arterial stiffness metric. However, some potential limitations of CAVI might render this arterial stiffness metric less pressure-independent than originally thought. For this reason, we later introduced CAVI0. Nevertheless, advantages of one approach over the other are left debated. This review aims to shed light on the pressure (in)dependency of both CAVI and CAVI0. By critically reviewing results from studies reporting both CAVI and CAVI0 and using simple analytical methods, we show that CAVI0 may enhance the pressure-independent assessment of arterial stiffness, especially in the presence of large inter-individual differences in blood pressure.

From Uniaxial Testing of Isolated Layers to a Tri-Layered Arterial Wall: A Novel Constitutive Modelling Framework.

Mechanical testing and constitutive modelling of isolated arterial layers yields insight into the individual layers' mechanical properties, but per se fails to recapitulate the in vivo loading state, neglecting layer-specific residual stresses. The aim of this study was to develop a testing/modelling framework that integrates layer-specific uniaxial testing data into a three-layered model of the arterial wall, thereby enabling study of layer-specific mechanics under realistic (patho)physiological conditions. Circumferentially and axially oriented strips of pig thoracic aortas (n = 10) were tested uniaxially. Individual arterial layers were then isolated from the wall, tested, and their mechanical behaviour modelled using a hyperelastic strain energy function. Subsequently, the three layers were computationally assembled into a single flat-walled sample, deformed into a cylindrical vessel, and subjected to physiological tension-inflation. At the in vivo axial stretch of 1.10 ± 0.03, average circumferential wall stress was 75 ± 9 kPa at 100 mmHg, which almost doubled to 138 ± 15 kPa at 160 mmHg. A ~ 200% stiffening of the adventitia over the 60 mmHg pressure increase shifted layer-specific load-bearing from the media (65 ± 10% → 61 ± 14%) to the adventitia (28 ± 9% → 32 ± 14%). Our approach provides valuable insight into the (patho)physiological mechanical roles of individual arterial layers at different loading states, and can be implemented conveniently using simple, inexpensive and widely available uniaxial testing equipment.

Towards the non-invasive determination of arterial wall distensible properties: New approach using old formulae.

Arterial function and wall mechanical properties are important determinants of hemodynamics in the circulation. However, their non-invasive determination is not widely available. Therefore, the aim of this work is to present a novel approach for the non-invasive determination of vessel's distensibility and elastic modulus. Simultaneous measurements of vessel's Diameter (D) and flow velocity (U) were recorded to determine local wave speed (nC) in flexible tubes and calf aortas non-invasively using the lnDU-loop method, which was used to calculate the Distensibility (nDs) and Elastic Modulus (nE), also non-invasively. To validate the new approach, the non-invasive results were compared to traditionally invasive measurements of Dynamic Distensibility (Dsd) and Tangential Elastic Modulus (Em). In flexible tubes, the average nDs was higher and nE was lower than Dsd and Em by 1.6% and 6.9%, respectively. In calf aortas, the results of nDs and nE agreed well with those of Dsd and Em, as demonstrated by Bland-Altman technique. The results of nDs and nE are comparable to those determined using traditional techniques. Our results suggest that nDs and nE could be measured in-vivo non-invasively, given the possibility of measuring D and U to obtain nC. Further studies are warranted to establish the clinical usefulness of the new approach.

Subject-Specific Pressure Normalization of Local Pulse Wave Velocity: Separating Intrinsic From Acute Load-Dependent Stiffening in Hypertensive Patients.

Pulse wave velocity (PWV) is a powerful predictor of cardiovascular events. However, its intrinsic blood pressure (BP)-dependency complicates distinguishing between acute and chronic effects of increased BP on arterial stiffness. Based on the assumption that arteries exhibit a nearly exponential pressure-area (P-A) relationship, this study proposes a method to assess intersubject differences in local PWV independently from BP. The method was then used to analyze differences in local carotid PWV (cPWV) between hypertensive and healthy normotensive people before and after BP-normalization. Pressure (P) and diameter (D) waveforms were simultaneously acquired via tonometer at the left and ultrasound scanning at right common carotid artery (CCA), respectively, in 22 patients with Grade 1 or 2 hypertension and 22 age- and sex-matched controls. cPWV was determined using the D 2 P-loop method. Then, the exponential modeling of the P-area (A = πD 2/4) relationships allowed defining a mathematical formulation to compute subject-specific changes in cPWV associated with BP changes, thus enabling the normalization of cPWV against intersubject differences in BP at the time of measurement. Carotid systolic BP (SBP) and diastolic BP (DBP) were, on average, 17.7 (p < 0.001) and 8.9 mmHg (p < 0.01) higher in hypertensives than controls, respectively. cPWV was 5.56 ± 0.86 m/s in controls and 6.24 ± 1.22 m/s in hypertensives. BP alone accounted for 68% of the cPWV difference between the two groups: 5.80 ± 0.84 vs. 6.03 ± 1.07 m/s after BP-normalization (p = 0.47). The mechanistic normalization of cPWV was in agreement with that estimated by analysis of covariance (ANCOVA). In conclusion, the proposed method, which could be easily implemented in the clinical setting, allows to assess the intersubject differences in PWV independently of BP. Our results suggested that mild hypertension in middle-aged subjects without target organ damage does not significantly alter the stiffness of the CCA wall independently of acute differences in BP. The results warrant further clinical investigations to establish the potential clinical utility of the method.

Review of the Techniques Used for Investigating the Role Elastin and Collagen Play in Arterial Wall Mechanics.

The arterial wall is characterised by a complex microstructure that impacts the mechanical properties of the vascular tissue. The main components consist of collagen and elastin fibres, proteoglycans, Vascular Smooth Muscle Cells (VSMCs) and ground matrix. While VSMCs play a key role in the active mechanical response of arteries, collagen and elastin determine the passive mechanics. Several experimental methods have been designed to investigate the role of these structural proteins in determining the passive mechanics of the arterial wall. Microscopy imaging of load-free or fixed samples provides useful information on the structure-function coupling of the vascular tissue, and mechanical testing provides information on the mechanical role of collagen and elastin networks. However, when these techniques are used separately, they fail to provide a full picture of the arterial micromechanics. More recently, advances in imaging techniques have allowed combining both methods, thus dynamically imaging the sample while loaded in a pseudo-physiological way, and overcoming the limitation of using either of the two methods separately. The present review aims at describing the techniques currently available to researchers for the investigation of the arterial wall micromechanics. This review also aims to elucidate the current understanding of arterial mechanics and identify some research gaps.