Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions

Dynamic cerebral autoregulation is governed by two time constants: Arterial transit time and feedback time constant

Dynamic cerebral autoregulation (dCA) is the mechanism that describes how the brain maintains cerebral blood flow approximately constant in response to short-term changes in arterial blood pressure. This is known to be impaired in many different pathological conditions, including ischaemic and haemorrhagic stroke, dementia and traumatic brain injury. Many different approaches have thus been used both to analyse and to quantify this mechanism in a range of healthy and diseased subjects, including data-driven models (in both the time and the frequency domain) and biophysical models. However, despite the substantial body of work on both biophysical models and data-driven models of dCA, there remains little work that links the two together. One of the reasons for this is proposed to be the discrepancies between the time constants that govern dCA in models and in experimental data. In this study, the processes that govern dCA are examined and it is proposed that the application of biophysical models remains limited due to a lack of understanding about the physical processes that are being modelled, partly due to the specific model formulation that has been most widely used (the equivalent electrical circuit). Based on the analysis presented here, it is proposed that the two most important time constants are arterial transit time and feedback time constant. It is therefore time to revisit equivalent electrical circuit models of dCA and to develop a more physiologically realistic alternative, one that can more easily be related to experimental data. KEY POINTS: Dynamic cerebral autoregulation is governed by two time constants. The first time constant is the arterial transit time, rather than the traditional 'RC' time constant widely used in previous models. This arterial transit time is approximately 1 s in the brain. The second time constant is the feedback time constant, which is less accurately known, although it is somewhat larger than the arterial transit time. The equivalent electrical circuit model of dynamic cerebral autoregulation should be replaced with a more physiologically representative model.

Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

The influence of aortic stiffness on carotid stiffness: computational simulations using a human aorta carotid model

Increased aortic and carotid stiffness are independent predictors of adverse cardiovascular events. Arterial stiffness is not uniform across the arterial tree and its accurate assessment is challenging. The complex interactions and influence of aortic stiffness on carotid stiffness have not been investigated. The aim of this study was to evaluate the effect of aortic stiffness on carotid stiffness under physiological pressure conditions. A realistic patient-specific geometry was used based on magnetic resonance images obtained from the OsiriX library. The luminal aortic-carotid model was reconstructed from magnetic resonance images using 3D Slicer. A series of aortic stiffness simulations were performed at different regional aortic areas (levels). By applying variable Young's modulus to the aortic wall under two pulse pressure conditions, one could examine the deformation, compliance and von Mises stress between the aorta and carotid arteries. An increase of Young's modulus in an aortic area resulted in a notable difference in the mechanical properties of the aortic tree. Regional deformation, compliance and von Mises stress changes across the aorta and carotid arteries were noted with an increase of the aortic Young's modulus. Our results indicate that increased carotid stiffness may be associated with increased aortic stiffness. Large-scale clinical validation is warranted to examine the influence of aortic stiffness on carotid stiffness.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

MATLAB-Based Algorithm and Software for Analysis of Wavy Collagen Fibers

Knowledge of soft tissue fiber structure is necessary for accurate characterization and modeling of their mechanical response. Fiber configuration and structure informs both our understanding of healthy tissue physiology and of pathological processes resulting from diseased states. This study develops an automatic algorithm to simultaneously estimate fiber global orientation, abundance, and waviness in an investigated image. To our best knowledge, this is the first validated algorithm which can reliably separate fiber waviness from its global orientation for considerably wavy fibers. This is much needed feature for biological tissue characterization. The algorithm is based on incremental movement of local regions of interest (ROI) and analyzes two-dimensional images. Pixels belonging to the fiber are identified in the ROI, and ROI movement is determined according to local orientation of fiber within the ROI. The algorithm is validated with artificial images and ten images of porcine trachea containing wavy fibers. In each image, 80-120 fibers were tracked manually to serve as verification. The coefficient of determination R2 between curve lengths and histograms documenting the fiber waviness and global orientation were used as metrics for analysis. Verification-confirmed results were independent of image rotation and degree of fiber waviness, with curve length accuracy demonstrated to be below 1% of fiber curved length. Validation-confirmed median and interquartile range of R2, respectively, were 0.90 and 0.05 for curved length, 0.92 and 0.07 for waviness, and 0.96 and 0.04 for global orientation histograms. Software constructed from the proposed algorithm was able to track one fiber in about 1.1 s using a typical office computer. The proposed algorithm can reliably and accurately estimate fiber waviness, curve length, and global orientation simultaneously, moving beyond the limitations of prior methods.

Active and passive mechanical characterization of a human descending thoracic aorta with Klippel-Trenaunay syndrome

A human aorta from a female donor affected by Klippel-Trenaunay syndrome was retrieved during a surgery for organ donation for transplant. The aorta was preserved in refrigerated Belzer UW organ preservation solution and tested within a few hours for mechanical characterization with and without vascular smooth muscle activation. KCl and Noradrenaline were used as vasoactive agents in bubbled Krebs-Henseleit buffer solution at 37 °C. A quasi-static and a dynamic mechanical characterization of the full wall and the three individual layers were carried out for strips taken in longitudinal and circumferential directions. The full wall in the descending portion of the aorta underwent mechanical tests with and without smooth muscle activation. Results were compared to data obtained from healthy aortas and show a reduced stiffness of the full wall in circumferential direction. Also, a significant reduction of the response to vasoactive agents in circumferential direction was observed, while the longitudinal response was similar to healthy cases.

Impact of disturbed flow and arterial stiffening on mechanotransduction in endothelial cells

Disturbed flow promotes progression of atherosclerosis at particular regions of arteries where the recent studies show the arterial wall becomes stiffer. Objective of this study is to show how mechanotransduction in subcellular organelles of endothelial cells (ECs) will alter with changes in blood flow profiles applied on ECs surface and mechanical properties of arterial wall where ECs are attached to. We will examine the exposure of ECs to atherogenic flow profiles (disturbed flow) and non-atherogenic flow profiles (purely forward flow), while stiffness and viscoelasticity of arterial wall will change. A multicomponent model of endothelial cell monolayer was applied to quantify the response of subcellular organelles to the changes in their microenvironment. Our results show that arterial stiffening alters mechanotransduction in intra/inter-cellular organelles of ECs by slight increase in the transmitted stresses, particularly over central stress fibers (SFs). We also observed that degradation of glycocalyx and exposure to non-atherogenic flow profiles result in significantly higher stresses in subcellular organelles, while degradation of glycocalyx and exposure to atherogenic flow profiles result in dramatically lower stresses in the organelles. Moreover, we show that increasing the arterial wall viscoelasticity leads to slight increase in the stresses transmitted to subcellular organelles. FAs are particularly influenced with the changes in the arterial wall properties and viscoelasticity. Our study suggests that changes in viscoelasticity of arterial wall and degradation state of glycocalyx have to be considered along with arterial stiffening in designing more efficient treatment strategies for atherosclerosis. Our study provides insight into significant role of mechanotransduction in the localization of atherosclerosis by quantifying the role of ECs mechanosensors and suggests that mechanotransduction may play a key role in design of more efficient and precision therapeutics to slow down or block the progression of atherosclerosis.

Signatures of obstructions and expansions in the arterial frequency response

BACKGROUND AND OBJECTIVE

The blood pressure and flow waveforms carry valuable information about the condition of the cardiovascular system and a patient's health. Waveform analysis in health and pathological conditions can be performed in the time or frequency domains; the information to be emphasised defines the use of either domain. However, physicians are more familiar with the time domain, and the changes in the waveforms due to cardiovascular diseases and ageing are better characterised in such domain. On the other hand, the analysis of the vascular and geometrical variables determining the signatures in the frequency response of local vascular anomalies, such as aneurysms and stenoses, has not been thoroughly explored. This paper aims to characterise the signatures of obstructions (stenoses) and expansions (aneurysms) in the frequency response of tapered arteries.

METHODS

The first step in our methodology was to incorporate the viscous response of the arterial wall into a one-dimensional elastic formulation that solves the governing equations in the frequency domain. As a second step, we imposed a volumetric flow excitation in arteries simulating the aorta with increasing geometry complexity: from straight to tapered arteries with local expansions or obstructions; and we assessed the frequency response.

RESULTS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that are distinguishable from a health condition. The signatures of obstruction and expansions differ; the obstructions increase the magnitude of fundamental frequency and work as a close boundary condition. On the other hand, the expansions diminish the fundamental frequency and work as an open boundary condition. Furthermore, such signatures correlate to the distance between the artery's inlet and the anomaly's starting point and have the potential to pinpoint abnormalities non-invasively.

CONCLUSIONS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that have the potential to detect and follow up on the development of vascular abnormalities. For the latter purpose, constant monitoring may be required; despite this not being a common clinical practice, the new wearable technology offers the possibility of continuous monitoring of biophysical markers such as the pressure waveform.

Evaluation of Arterial Stiffness in Depression Patients

Background

It has been known that there is a significant correlation between depression and cardiovascular diseases. However, the reasons behind this correlation that could affect mortality and morbidity were not fully identified. The present study aimed to analyze arterial stiffness diagnosed with ultrasonography, which could be associated with cardiovascular disease risks in depression patients, and to compare the findings with those of healthy controls.

Methods

The study was conducted with 35 depression patients and 35 healthy individuals. Routine complete blood and biochemistry tests were requested for all patients, and their weight and height, waist circumference, and diastolic and systolic arterial blood pressure were measured. Femoral and carotid artery intima-media thickness and other arterial stiffness parameters were determined with Doppler ultrasonography.

Results

It was determined that the systolic pressure (P = .028) was higher in the patient group (P = .028). Also, the carotid elastic modulus (P = .048) was significantly higher in the patient group. A negative and significant correlation was determined between femoral compliance and chlorpromazine equivalent dose (P = .021, r = -0.389).

Conclusion

It was determined that the systolic blood pressure and carotid elastic modulus arterial stiffness parameters were significantly higher in depression patients. Measurable arterial stiffness parameters should be investigated in depression patients as cardiovascular risk markers. Furthermore, the determination of the effects of psychotropic drugs employed in arterial stiffness treatment could play an important role in the determination of cardiovascular disease risk in these patients.

Viscoelasticity of human descending thoracic aorta in a mock circulatory loop

Healthy human descending thoracic aortas, obtained during organ donation for transplant and research, were tested in a mock circulatory loop to measure the mechanical response to physiological pulsatile pressure and flow. The viscoelastic properties of the aortic segments were investigated at three different pulse rates. The same aortic segments were also subjected to quasi-static pressure tests in order to identify the aortic dynamic stiffness ratio, which is defined as the ratio between the stiffness in case of pulsatile pressure and the stiffness measured for static pressurization, both at the same value of pressure. The loss factor was also identified. The shape of the deformed aorta under static and dynamic pressure was measured by image processing to verify the compatibility of the end supports with the natural deformation of the aorta in the human body. In addition, layer-specific experiments on 10 human descending thoracic aortas allowed to precisely identify the mass density of the aortic tissue, which is an important parameter in cardiovascular dynamic models.

Toward improved accuracy in shear wave elastography of arteries through controlling the arterial response to ultrasound perturbation in-silico and in phantoms

Dispersion-based inversion has been proposed as a viable direction for materials characterization of arteries, allowing clinicians to better study cardiovascular conditions using shear wave elastography. However, these methods rely ona prioriknowledge of the vibrational modes dominating the propagating waves induced by acoustic radiation force excitation: differences between anticipated and real modal content are known to yield errors in the inversion. We seek to improve the accuracy of this process by modeling the artery as a fluid-immersed cylindrical waveguide and building an analytical framework to prescribe radiation force excitations that will selectively excite certain waveguide modes using ultrasound acoustic radiation force. We show that all even-numbered waveguide modes can be eliminated from the arterial response to perturbation, and confirm the efficacy of this approach within silicotests that show that odd modes are preferentially excited. Finally, by analyzing data from phantom tests, we find a set of ultrasound focal parameters that demonstrate the viability of inducing the desired odd-mode response in experiments.

Sensitivity analysis and uncertainty quantification of 1-D models of pulmonary hemodynamics in mice under control and hypertensive conditions

Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub-types that are all linked to high mortality rates. In this study, we use a one-dimensional (1-D) fluid dynamics model driven by in vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions with in vivo MPA pressure measurements from a control and a hypertensive mouse and analyze results in three networks of increasing complexity, extracted from micro-computed tomography (micro-CT) images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that MPA pressure predictions are most sensitive to distal vascular resistance and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations.

Viscoelastic characterization of human descending thoracic aortas under cyclic load

Experiments were carried out on 15 human descending thoracic aortas from heart-beating healthy donors who donated organs for transplant. The aortas were kept refrigerated in organ preservation solution and tested were completed within 48 hours from explant. Donors' age was comprised between 25 and 70 years, with an average of 51.7 ± 12.8 years. Quasi-static and dynamic uniaxial tensile test were carried out in thermally controlled physiological saline solution in order to characterize the viscoelastic behavior. Strips were tested under harmonic deformation of different frequency, between 1 and 11 Hz, at three initial pre-stretches. Cyclic deformations of two different amplitudes were used: a physiological one and a small one, the latter one for comparison purposes to understand the accuracy limits of viscoelastic models. Aortic strips in circumferential and longitudinal directions were cut from each aorta. Some strips were dissected to separate the three layers: intima, media and adventitia. They were tested individually in order to obtain layer-specific data. However, strips of the intact wall were also tested. Therefore, 8 strips per donors were tested. Viscoelastic parameters are accurately evaluated from the hysteresis loops. Results show that small-amplitude cyclic strain over-estimate the storage modulus and under-estimate the loss-factor. Therefore, cyclic deformation of physiological amplitude is necessary to obtain correct viscoelastic data of aortic tissue. The value of the applied pre-stretch is significant on the dynamic stiffness ratio (storage modulus divided by the corresponding quasi-static stiffness), while it is less significant for the loss factor. The median of the dynamic stiffness ratios, in physiological conditions, varies between 1.14 and 1.33 for the different layers and the intact wall; the corresponding median of the loss factors varies between 0.050 and 0.066. The lowest dynamic stiffness ratios and loss factors were obtained from donors of the youngest age group. STATEMENT OF SIGNIFICANCE: There is an increasing interest in replacing traditional Dacron grafts used to repair thoracic aortas after acute dissection and aneurysm, with grafts in innovative biomaterials that mimic the mechanical properties and the dynamic behavior of the aorta. The human aorta is a complex laminated structure with hyperelastic and viscoelastic material properties and residual stresses. This study aims to characterize the nonlinear viscoelastic properties of ex-vivo human descending thoracic aortas by measuring hysteresis loops of physiological amplitude under harmonic strain. Results show the necessity to characterize the viscoelastic material properties of the aorta under physiological conditions, as well as the necessity to introduce improved models that take better into account the influence of the initial pre-stretch and amplitude of the cyclic load.

Fractional-order model representations of apparent vascular compliance as an alternative in the analysis of arterial stiffness: anin-silicostudy

Objective. Recent studies have demonstrated the advantages of fractional-order calculus tools for probing the viscoelastic properties of collagenous tissue, characterizing the arterial blood flow and red cell membrane mechanics, and modeling the aortic valve cusp. In this article, we present novel lumped-parameter equivalent circuit models for apparent arterial compliance using a fractional-order capacitor (FOC). FOCs, which generalize capacitors and resistors, display a fractional-order behavior that can capture both elastic and viscous properties through a power-law formulation.Approach. The proposed framework describes the dynamic relationship between the blood-pressure input and the blood volume, using linear fractional-order differential equations.Main results. The results show that the proposed models present a reasonable fit with thein-silicodata of more than 4000 subjects. Additionally, strong correlations have been identified between the fractional-order parameter estimates and the central hemodynamic determinants as well as the pulse-wave velocity indexes.Significance. Therefore, the fractional-order-based paradigm for arterial compliance shows notable potential as an alternative tool in the analysis of arterial stiffness.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Characterization of the dynamic viscoelastic response of the ascending aorta imposed via pulsatile flow

This study characterizes the material properties of a viscoelastic, ex vivo porcine ascending aorta under dynamic-loading conditions via pulsatile flow. The deformation of the opaque vessel wall and the pulsatile flow field inside the vessel were recorded using ultrasound imaging. The internal pressure was extracted from the pulsatile flow results and, when coupled with the vessel-wall expansion, was used to calculate the instantaneous elastic modulus from a novel, time-resolved two-dimensional (i.e. axial and circumferential) stress model. The circumferential instantaneous elasticity obtained from the two-dimensional stress model was found to match the uniaxial tensile test for strains below 50%. The agreement in elasticity between the two stress states reveals that the two-dimensional stress model accurately resolves the circumferential stress of the viscoelastic aorta at physiological strains (8%-30%). At higher strains, results from pulsatile flow generated a more compliant response than the uniaxial measurements. Viscoelastic properties (storage modulus and loss factor) were also calculated using the two-dimensional stress model and compared to those obtained from uniaxial tests. While instantaneous elasticity matched between the cylindrical and uniaxial loading, the viscoelastic behaviour significantly diverged between stress states. The storage modulus obtained from the pulsatile flow data was dependent on mean Reynolds number, while the uniaxial storage modulus results exhibited a strong inverse dependency on the frequency. The loss factor for the pulsatile flow data increased alongside the frequency, while the uniaxial data indicated a constant loss factor over the entire frequency range. The results of the current study show that the two-dimensional stress model can accurately extract the material properties of the ex vivo porcine aorta.

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Stress distribution analysis in healthy and stenosed carotid artery models reconstructed from in vivo ultrasonography

Purpose

This study investigated the accuracy of models reconstructed from ultrasound image processing by comparing the radial displacement waveforms of a subject-specific artery model and evaluated stress changes in the proximal shoulder, throat, and distal shoulder of the plaques depending on the degree of carotid artery stenosis.

Methods

Three groups of subjects (healthy and with less than 50% or more carotid stenosis) were evaluated with ultrasonography. Two-dimensional transverse imaging of the common carotid artery was performed to reconstruct the geometry. A longitudinal view of the same region was recorded to extract the Kelvin viscoelastic model parameters. The pulse pressure waveform and the effective pressure of perivascular tissue were loaded onto the internal and external walls of the model. Effective, circumferential, and principal stresses applied to the plaque throat, proximal shoulder, and distal shoulder in the transverse planes were extracted.

Results

The radial displacement waveforms of the model were closely correlated with those of image processing in all three groups. The mean of the effective, circumferential, and principal stresses of the healthy arteries were 15.01±4.93, 12.97±5.07, and 12.39±2.86 kPa, respectively. As stenosis increased from mild to significant, the mean values of the effective, circumferential, and first principal stresses increased significantly (97%, 74%, and 103% at the plaque throat, respectively) (P<0.05). The minimum effective stress was at the lipid pool. The effective stress in calcified areas was higher than in other parts of the artery wall.

Conclusion

This model can discriminate differences in stresses applied to mildly and severely stenotic plaques.

Mechanical Assessment and Hyperelastic Modeling of Polyurethanes for the Early Stages of Vascular Graft Design

The material design of vascular grafts is required for their application in the health sector. The use of polyurethanes (PUs) in vascular grafts intended for application in the body appears to be adequate due to the fact that native tissues have similar properties as PUs. However, the influence of chemical structure on the biomechanics of PUs remains poorly described. The use of constitutive models, together with numerical studies, is a powerful tool for evaluating the mechanical behavior of materials under specific physiological conditions. Therefore, the aim of this study was to assess the mechanical properties of different PU mixtures formed by polycaprolactone diol, polyethylene glycol, and pentaerythritol using uniaxial tensile, strain sweep, and multistep creep-recovery tests. Evaluations of the properties were also recorded after samples had been soaked in phosphate-buffer saline (PBS) to simulate physiological conditions. A hyperelastic model based on the Mooney–Rivlin strain density function was employed to model the performance of PUs under physiological pressure and geometry conditions. The results show that the inclusion of polyethylene glycol enhanced viscous flow, while polycaprolactone diol increased the elastic behavior. Furthermore, tensile tests revealed that hydration had an important effect on the softening phenomenon. Additionally, after the hydration of PUs, the ultimate strength was similar to those reported for other vascular conduits. Lastly, hyperelastic models revealed that the compliance of the PUs showed a cyclic behavior within the tested time and pressure conditions and is affected by the material composition. However, the compliance was not affected by the geometry of the materials. These tests demonstrate that the materials whose compositions are 5–90–5 and 46.3–46.3–7.5 could be employed in the designs of vascular grafts for medical applications since they present the largest value of compliance, ultimate strength, and elongation at break in the range of reported blood vessels, thus indicating their suitability. Moreover, the polyurethanes were revealed to undergo softening after hydration, which could reduce the risk of vascular trauma.

Ultrasound Deep Learning for Wall Segmentation and Near-Wall Blood Flow Measurement

Studies of medical flow imaging have technical limitations for accurate analysis of blood flow dynamics and vessel wall interaction at arteries. We propose a new deep learning-based boundary detection and compensation (DL-BDC) technique in ultrasound (US) imaging. It can segment vessel boundaries by harnessing the convolutional neural network and wall motion compensation in the analysis of near-wall flow dynamics. The network enables training from real and synthetic US images together. The performance of the technique is validated through synthetic US images and tissue-mimicking phantom experiments. The neural network performs well with high Dice coefficients of over 0.94 and 0.9 for lumens and walls, outperforming previous segmentation techniques. Then, the performance of the wall motion compensation is examined for compliant phantoms. When DL-BDC is applied to flow influenced by wall motion, root-mean-square errors are less than 0.07%. The technique is utilized to analyze flow dynamics and wall interaction with varying elastic moduli of the phantoms. The results show that the flow dynamics and wall shear stress values are consistent with the expected values of the compliant phantoms, and their wall motion behavior is observed with pulse wave propagation. This strategy makes US imaging capable of simultaneous measurement of blood flow and vessel dynamics in human arteries for their accurate interaction analysis. DL-BDC can segment vessel walls fast, accurately, and robustly. It enables to measure the near-wall flow precisely by determining the vessel boundary dynamics. This approach can be beneficial in flow dynamics and wall interaction analyses in various biomedical applications.

A COUPLED EXPERIMENTAL AND NUMERICAL APPROACH TO CHARACTERIZE THE ANISOTROPIC MECHANICAL BEHAVIOR OF AORTIC TISSUES

Nowadays, the investigation of aortic wall biomechanics is a fundamental tool in clinical research and vascular prosthesis design. This study aims at analyzing the biomechanical behavior of aortic tissues using a coupled experimental and computational approach. Considering the typical fiber-reinforced configuration of aortic tissues, uni-axial tensile tests along six different loading directions were performed on specimens from pig aorta. Starting from the obtained experimental data, a suitable constitutive framework was defined and a methodology for the identification of the constitutive parameters was developed using the inverse analysis of mechanical tests. Transversal stretch versus loading stretch and nominal stress versus loading stretch curves were evaluated, showing the anisotropic and nonlinear mechanical behavior determined by tissue conformation with fibers distributed along preferential directions. In detail, experimental data showed different mechanical responses between longitudinal and circumferential directions, with a greater tissue stiffness along the longitudinal one. The reliability of the developed constitutive framework was evaluated by the comparison between experimental data and model results. The mentioned analysis can be considered as a useful tool for the development of reliable computational models, which allow a better understanding of the pathophysiology of cardiovascular diseases and can be applied for a proper planning of surgical procedures.

Ultrasound assessment of tensile stress in carotid arteries of healthy human subjects with varying age

Background

Arterial remodeling is thought to reflect the adaptation of the vessel wall to mechanical and hemodynamic stimuli and contributes to the progression of cardiovascular and cerebrovascular diseases. Tensile stress (TS) is one of the mechanical properties of the artery wall. The purpose of this study was to investigate the tensile stress change (TS) of carotid artery with varying viscoelasticity in healthy subjects within two groups of different ages.

Methods

Forty-five subjects were recruited and randomly assigned into the group at the age above 50 years and below 50 years. The carotid arteries were examined by ultrasonography, using the techniques of shear wave elastography (SWE), shear wave dispersion (SWD) and radiofrequency (RF) -based ultrasound. The following values, including elastic modulus (SWER) and viscous index (SWDR), as well as the peak and mean TS of the left and right carotid arteries (L-PTS, R-PTS, L-MTS and R-MTS) were measured. The correlations between SWER, SWDR and tensile stress were evaluated.

Results

The SWE_R and SWD_R of carotid arteries are lower in the subjects ≥50 years old than the subjects younger than 50 years (SWE_R, 10.29 ± 9.57 kPa VS 17.24 ± 14.07 kPa; SWD_R, 11.99 ± 3.51 (m/s)/kHz VS 13.97 ± 3.71 (m/s)/kHz, P < 0.05). The R-PTS was lower in the group with younger age (P < 0.05). Pearson correlation analysis showed that SWE_R of carotid artery was positively correlated with the parameters of tensile stress, R-PTS, R-MTS, L-PTS and L-MTS(r = 0.218, r = 0.359, r = 0.209 and r = 0.369, respectively, P < 0.05). However, SWD_R of carotid arteries was not significantly associated with TS.

Conclusion

Ultrasonic shear wave imaging could be used to quantitatively assess carotid viscoelasticity. The carotid TS was related to its elasticity while little related to its viscosity, suggesting that mechanical properties of the arterial wall might be better revealed.

Trial registration

Date of our trial registration: 2018-06-11. Registered with the official website of China Clinical Trial Registration Center (ChiCTR1800016590)

On the accuracy of displacement-based wave intensity analysis: Effect of vessel wall viscoelasticity and nonlinearity

Recent studies showed that wave intensity analysis (WIA) provides clinically valuable information about local and global cardiovascular function. Wave intensity (WI) is computed as the product of the pressure change and the velocity change during short time intervals. The major limitation of WIA in clinical practice is the need for invasive pressure measurement. Since vessel wall displacement can be measured non-invasively, the usage of WI will be expanded if the vessel wall dilation is used instead of pressure in derivation of WI waveform. Our goal in this study is to investigate the agreement between wall displacement-based WI and the pressure-based WI for different vessel wall models including linear elastic, nonlinear and viscoelastic cases. The arbitrary Eulerian Lagrangian finite element method is employed to solve the coupled fluid-structure interaction (FSI). Our computational models also include two types of vascular disease-related cases with geometrical irregularities, aneurysm and stenosis. Our results show that for vessels with linear elastic wall, the displacement-based WI is almost identical to the pressure-based WI. The existence of vessel irregularities does not impact the accuracy of displacement-based WI. However, in a viscoelastic wall where there is a phase difference between pressure and vessel wall dilation, displacement-based WI deviated from pressure-based WI. The error associated with this phase difference increased nonlinearly with increasing viscosity. This results in a maximum error of 6.8% and 7.13% for a regular viscoelastic vessel wall and an irregular viscoelastic vessel wall, respectively. A separate analysis has also been performed on the agreement of backward and forward running waves extracted from a decomposition of the displacement-based and pressure-based WI. Our findings suggest that displacement-based WI is a reliable method of WIA for large central arteries that do not show viscoelastic behaviors. This can be clinically significant since the required information can be measured non-invasively.

An efficient full space-time discretization method for subject-specific hemodynamic simulations of cerebral arterial blood flow with distensible wall mechanics

A computationally inexpensive mathematical solution approach using orthogonal collocations for space discretization with temporal Fourier series is proposed to compute subject-specific blood flow in distensible vessels of large cerebral arterial networks. Several models of wall biomechanics were considered to assess their impact on hemodynamic predictions. Simulations were validated against in vivo blood flow measurements in six human subjects. The average root-mean-square relative differences were found to be less than 4.3% for all subjects with a linear elastic wall model. This discrepancy decreased further in a viscoelastic Kelvin-Voigt biomechanical wall. The results provide support for the use of collocation-Fourier series approach to predict clinically relevant blood flow distribution and collateral blood supply in large portions of the cerebral circulation at reasonable computational costs. It thus opens the possibility of performing computationally inexpensive subject-specific simulations that are robust and fast enough to predict clinical results in real time on the same day.

Quantitative Vascular Evaluation: From Laboratory Experiments to Point-of-Care Patient (Experimental Approach)

This paper illustrates the evolution of our knowledge of arterial mechanics from our initial research works up to the present time. Several techniques focusing on this topic in terms of our experience are dis-cussed. An interdisciplinary team composed by different institutions from Argentina, Uruguay, France and Spain was created to conduct research, to train human resources and to fulfill the inevitable social role of gaining access to technological inno-vation to improve public health.

Cardiovascular mechanics in the early stages of pulmonary hypertension: a computational study

We formulate and study a new mathematical model of pulmonary hypertension. Based on principles of fluid and elastic dynamics, we introduce a model that quantifies the stiffening of pulmonary vasculature (arteries and arterioles) to reproduce the hemodynamics of the pulmonary system, including physiologically consistent dependence between compliance and resistance. This pulmonary model is embedded in a closed-loop network of the major vessels in the body, approximated as one-dimensional elastic tubes, and zero-dimensional models for the heart and other organs. Increasingly severe pulmonary hypertension is modeled in the context of two extreme scenarios: (1) no cardiac compensation and (2) compensation to achieve constant cardiac output. Simulations from the computational model are used to estimate cardiac workload, as well as pressure and flow traces at several locations. We also quantify the sensitivity of several diagnostic indicators to the progression of pulmonary arterial stiffening. Simulation results indicate that pulmonary pulse pressure, pulmonary vascular compliance, pulmonary RC time, luminal distensibility of the pulmonary artery, and pulmonary vascular impedance are much better suited to detect the early stages of pulmonary hypertension than mean pulmonary arterial pressure and pulmonary vascular resistance, which are conventionally employed as diagnostic indicators for this disease.

Comparative in vivo analysis of the role of the adventitia and the endothelium on arterial mechanical function: relevance for aortic counterpulsation

PURPOSE

The comparative effect of the intimal and adventitial layers on arterial biomechanics control, in basal and altered conditions, remains to be elucidated. This study aimed (1) to characterize the arterial conduit (CF) and buffering (distensibility) function of the iliac arteries in in vivo animals, in which the intimal and adventitial layers were removed; (2) to determine the effects of intra-aortic ballon pumping (IABP) on simultaneously de-adventitialized (DA) and de-endothelialized (DE) iliac arteries before and after induced heart failure.

METHODS

Pressure and diameter signals were measured in the iliac arteries of sheep (n = 7) in which the adventitial and intima layer were removed. Intra-aortic balloon pump (IABP) assistance was used in a control state and after heart failure induction.

RESULTS

Both DE and DA determined significant changes in arterial diameter, distensibility and CF. Changes were higher after DA than after DE in terms of distensibility and CF (p<0.05). DA followed by DE (DA + DE) showed significant increases in arterial diameter and CF, accompanied by a decrease in distensibility (p<0.05) with respect to intact arteries. Heart failure induction caused significant hemodynamic changes without modifying the already impaired local biomechanical parameters. Nonsignificant improvements in the biomechanical parameters of DA + DE iliac arteries were observed during IABP before and after heart failure induction.

CONCLUSIONS

Biomechanical changes caused by DA of iliac arteries were more important than those observed after DE. The DA + DE arteries showed significant differences with respect to intact arteries and with DA or DE arteries. IABP-related effects on arterial mechanics were absent in DA + DE arteries.

Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator

Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals

This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a nonlinear Kelvin–Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin–Voigt model and the experimental measurements. We found that the viscoelastic relaxation time—defined by the ratio between the viscoelastic coefficient and the Young's modulus—is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high-frequency waves is clear especially at the peripheral sites.

Biaxial Properties of the Left and Right Pulmonary Arteries in a Monocrotaline Rat Animal Model of Pulmonary Arterial Hypertension

In a monocrotaline (MCT) induced-pulmonary arterial hypertension (PAH) rat animal model, the dynamic stress–strain relation was investigated in the circumferential and axial directions using a linear elastic response model within the quasi-linear viscoelasticity theory framework. Right and left pulmonary arterial segments (RPA and LPA) were mechanically tested in a tubular biaxial device at the early stage (1 week post-MCT treatment) and at the advanced stage of the disease (4 weeks post-MCT treatment). The vessels were tested circumferentially at the in vivo axial length with matching in vivo measured pressure ranges. Subsequently, the vessels were tested axially at the mean pulmonary arterial pressure by stretching them from in vivo plus 5% of their length. Parameter estimation showed that the LPA and RPA remodel at different rates: axially, both vessels decreased in Young's modulus at the early stage of the disease, and increased at the advanced disease stage. Circumferentially, the Young's modulus increased in advanced PAH, but it was only significant in the RPA. The damping properties also changed in PAH; in the LPA relaxation times decreased continuously as the disease progressed, while in the RPA they initially increased and then decreased. Our modeling efforts were corroborated by the restructuring organization of the fibers imaged under multiphoton microscopy, where the collagen fibers become strongly aligned to the 45 deg angle in the RPA from an uncrimped and randomly organized state. Additionally, collagen content increased almost 10% in the RPA from the placebo to advanced PAH.

Modeling the differentiation of A- and C-type baroreceptor firing patterns

The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion channel dynamics within the baroreceptor neurons. With this model, we were able to predict firing rates observed in previously published experiments in both A- and C-type neurons. These results were obtained by adjusting model parameters determining the maximal ion-channel conductances. The observed variation in the model parameters are hypothesized to correspond to physiological differences between A- and C-type neurons. In agreement with published experimental observations, our simulations suggest that a twofold lower potassium conductance in C-type neurons is responsible for the observed sustained basal firing, where as a tenfold higher mechanosensitive conductance is responsible for the greater firing rate observed in A-type neurons. A better understanding of the difference between the two neuron types can potentially be used to gain more insight about pathophysiology and treatment of diseases related to baroreflex function, e.g. in patients with autonomic failure, a syndrome that is difficult to diagnose in terms of its pathophysiology.

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Energy-based constitutive modelling of local material properties of canine aortas

This study aims at determining the in vitro anisotropic mechanical behaviour of canine aortic tissue. We specifically focused on spatial variations of these properties along the axis of the vessel. We performed uniaxial stretch tests on canine aortic samples in both circumferential and longitudinal directions, as well as histological examinations to derive the tissue's fibre orientations. We subsequently characterized a constitutive model that incorporates both phenomenological and structural elements to account for macroscopic and microstructural behaviour of the tissue. We showed the two fibre families were oriented at similar angles with respect to the aorta's axis. We also found significant changes in mechanical behaviour of the tissue as a function of axial position from proximal to distal direction: the fibres become more aligned with the aortic axis from 46° to 30°. Also, the linear shear modulus of media decreased as we moved distally along the aortic axis from 139 to 64 kPa. These changes derived from the parameters in the nonlinear constitutive model agreed well with the changes in tissue structure. In addition, we showed that isotropic contribution, carried by elastic lamellae, to the total stress induced in the tissue decreases at higher stretch ratios, whereas anisotropic stress, carried by collagen fibres, increases. The constitutive models can be readily used to design computational models of tissue deformation during physiological loading cycles. The findings of this study extend the understanding of local mechanical properties that could lead to region-specific diagnostics and treatment of arterial diseases.

A Coupled Lumped-Parameter and Distributed Network Model for Cerebral Pulse-Wave Hemodynamics

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

The simulation of magnetic resonance elastography through atherosclerosis

The clinical diagnosis of atherosclerosis via the measurement of stenosis size is widely acknowledged as an imperfect criterion. The vulnerability of an atherosclerotic plaque to rupture is associated with its mechanical properties. The potential to image these mechanical properties using magnetic resonance elastography (MRE) was investigated through synthetic datasets. An image of the steady state wave propagation, equivalent to the first harmonic, can be extracted directly from finite element analysis. Inversion of this displacement data yields a map of the shear modulus, known as an elastogram. The variation of plaque composition, stenosis size, Gaussian noise, filter thresholds and excitation frequency were explored. A decreasing mean shear modulus with an increasing lipid composition was identified through all stenosis sizes. However the inversion algorithm showed sensitivity to parameter variation leading to artefacts which disrupted both the elastograms and quantitative trends. As noise was increased up to a realistic level, the contrast was maintained between the fully fibrous and lipid plaques but lost between the interim compositions. Although incorporating a Butterworth filter improved the performance of the algorithm, restrictive filter thresholds resulted in a reduction of the sensitivity of the algorithm to composition and noise variation. Increasing the excitation frequency improved the techniques ability to image the magnitude of the shear modulus and identify a contrast between compositions. In conclusion, whilst the technique has the potential to image the shear modulus of atherosclerotic plaques, future research will require the integration of a heterogeneous inversion algorithm.

WAVE PROPAGATION IN A 1D FLUID DYNAMICS MODEL USING PRESSURE-AREA MEASUREMENTS FROM OVINE ARTERIES

This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.

Pharmacological models and approaches for pathophysiological conditions associated with hypoxia and oxidative stress

Hypoxia is the failure of oxygenation at the tissue level, where the reduced oxygen delivered is not enough to satisfy tissue demands. Metabolic depression is the physiological adaptation associated with reduced oxygen consumption, which evidently does not cause any harm to organs that are exposed to acute and short hypoxic insults. Oxidative stress (OS) refers to the imbalance between the generation of reactive oxygen species (ROS) and the ability of endogenous antioxidant systems to scavenge ROS, where ROS overwhelms the antioxidant capacity. Oxidative stress plays a crucial role in the pathogenesis of diseases related to hypoxia during intrauterine development and postnatal life. Thus, excessive ROS are implicated in the irreversible damage to cell membranes, DNA, and other cellular structures by oxidizing lipids, proteins, and nucleic acids. Here, we describe several pathophysiological conditions and in vivo and ex vivo models developed for the study of hypoxic and oxidative stress injury. We reviewed existing literature on the responses to hypoxia and oxidative stress of the cardiovascular, renal, reproductive, and central nervous systems, and discussed paradigms of chronic and intermittent hypobaric hypoxia. This systematic review is a critical analysis of the advantages in the application of some experimental strategies and their contributions leading to novel pharmacological therapies.

Biomechanical Changes After Thoracic Endovascular Aortic Repair in Type B Dissection

Thoracic endovascular aortic repair (TEVAR) has evolved into an established treatment option for type B aortic dissection (TBAD) since it was first introduced 2 decades ago. Morbidity and mortality have decreased due to the minimally invasive character of TEVAR, with adequate stabilization of the dissection, restoration of true lumen perfusion, and subsequent positive aortic remodeling. However, several studies have reported severe setbacks of this technique. Indeed, little is known about the biomechanical behavior of implanted thoracic stent-grafts and the impact on the vascular system. This study sought to systematically review the performance and behavior of implanted thoracic stent-grafts and related biomechanical aortic changes in TBAD patients in order to update current knowledge and future perspectives.

A viscoelastic fluid-structure interaction model for carotid arteries under pulsatile flow

In this study, a fluid-structure interaction model (FSI) incorporating viscoelastic wall behaviour is developed and applied to an idealized model of the carotid artery under pulsatile flow. The shear and bulk moduli of the arterial wall are described by Prony series, where the parameters can be derived from in vivo measurements. The aim is to develop a fully coupled FSI model that can be applied to realistic arterial geometries with normal or pathological viscoelastic wall behaviour. Comparisons between the numerical and analytical solutions for wall displacements demonstrate that the coupled model is capable of predicting the viscoelastic behaviour of carotid arteries. Comparisons are also made between the solid only and FSI viscoelastic models, and the results suggest that the difference in radial displacement between the two models is negligible.

Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations

Patient-specific one-dimensional (1D) blood flow modeling requires estimating model parameters from available clinical data, ideally acquired noninvasively. The larger the number of arterial segments in a distributed 1D model, the greater the number of input parameters that need to be estimated. We investigated the effect of a reduction in the number of arterial segments in a given distributed 1D model on the shape of the simulated pressure and flow waveforms. This is achieved by systematically lumping peripheral 1D model branches into windkessel models that preserve the net resistance and total compliance of the original model. We applied our methodology to a model of the 55 larger systemic arteries in the human and to an extended 67-artery model that contains the digital arteries that perfuse the fingers. Results show good agreement in the shape of the aortic and digital waveforms between the original 55-artery (67-artery) and reduced 21-artery (37-artery) models. Reducing the number of segments also enables us to investigate the effect of arterial network topology (and hence reflection sites) on the shape of waveforms. Results show that wave reflections in the thoracic aorta and renal arteries play an important role in shaping the aortic pressure and flow waves and in generating the second peak of the digital pressure and flow waves. Our novel methodology is important to simplify the computational domain while maintaining the precision of the numerical predictions and to assess the effect of wave reflections.

Rational macromodeling of 1D blood flow in the human cardiovascular system

In this paper, we present a novel rational macromodeling approach for the description of 1D blood flow in the human cardiovascular system, which is suitable for time-domain simulations. Using the analogy of the blood flow propagation problem with transmission lines and considering the hypothesis of linearized Navier-Stokes equations, a frequency-domain rational macromodel for each arterial segment has been built. The poles and the residues of each arterial segment macromodel have been calculated by means of the Vector Fitting technique. Finally, the rational macromodel of the whole cardiovascular system is obtained by properly combining the macromodels of the single arterial segments using an interconnect matrix. The rational form of the proposed cardiovascular model leads to a state-space or electrical circuit model suitable for time-domain analysis. The stability and passivity properties of the global cardiovascular model are discussed to guarantee stable time-domain simulations. The proposed macromodeling approach has been validated by pertinent numerical results. Copyright © 2015 John Wiley & Sons, Ltd.

Noninvasive Characterization of Vascular Tone by Model-Based System Identification in Healthy and Heart Failure Patients

Current markers for heart failure (HF) diagnosis and prognosis are mainly for the evaluation of cardiac functions. Since previous studies have reported that HF patients demonstrated abnormal vascular responses to external stimuli, it is speculated that vascular tone, a measure of activation level of vascular wall, may be able to reflect these abnormalities to assist HF detection. Nevertheless, vascular tone is difficult to be objectively quantified using existing tools. In this study, a vascular tone index was estimated from noninvasive blood pressure and pulse transit time measurements using system identification technique. This method was evaluated in 35 subjects (10 healthy, 13 with HF risk factors and 12 HF patients) in a regular maximal exercise test. It was found that the vascular tone index significantly increased by 24.4 ± 26.6% (p < 0.01) during maximal exercise in the healthy subjects. Moreover, the response was gradually attenuated in the risk-factor and HF groups (15.8 ± 36.5 and 0.9 ± 17.9%, respectively). The results reveal the association between the vascular tone response to maximal exercise and HF disease or risks. To conclude, the proposed method provides a quantitative characterization of vascular tone which may be a useful indicator of the pathological changes of the arteries or the heart.