Two-layer model of coronary artery vasoactivity

Myocardial infarction impaired wall mechanics and hemodynamics in peripheral arteries

Myocardial infarction (MI) impaired both cardiac functions and peripheral arteries. The changes in normal and shear stresses in the peripheral artery wall are of importance for understanding the progression of MI-induced heart failure (HF). The aim of the study is to investigate the corresponding changes of normal and shear stresses. The coronary artery ligation was used to induce the MI in Wistar rats. The analysis of wall mechanics and hemodynamics was performed based on in vivo and in vitro measurements. Myocardial infarction increased wall stiffness in elastic carotid and muscular femoral arteries significantly albeit different changes occurred between the two vessels from 3 to 6 weeks postoperatively. Moreover, the hemodynamic analysis showed the gradually deteriorated wall shear stress, oscillatory shear index and relative residence time in the two arteries. This study probably shed light on understanding the interaction between abnormal systemic circulation and peripheral mechanics and hemodynamics during the development of MI-induced HF.

A comparison of passive and active wall mechanics between elastic and muscular arteries of juvenile and adult rats

The elastic abdominal aorta and muscular femoral artery are susceptible to aneurysm and atherosclerosis, respectively. The vessel wall mechanics should be an important element for the difference. The objective of the study is to demonstrate a comparison of vessel wall mechanics between elastic and muscular arteries of juvenile and adult rats to show the changes of mechanical properties relevant to aging. The passive and active mechanical tests, theoretical analysis, and histological evaluation were carried out to investigate mechanical properties of vessel walls in the abdominal aorta and carotid and femoral arteries of young and adult rats. There are stiffening femoral artery, unchanged carotid artery, and distensible abdominal aorta in adult rats as compared with the young. The opening angle has values of 54 ± 13°, 82 ± 13°, and 94 ± 13° in the abdominal aorta and carotid and femoral arteries of adult rats, respectively, as well as 80 ± 22°, 93 ± 19°, and 100 ± 23° in the young. The findings are explained by the significantly reduced width of collagen fibers in the abdominal aorta, relatively unchanged width in the carotid artery, and significantly increased width in the femoral artery of adult rats as compared with the young. In conjunction with available literatures, we concluded that inconsistency for nonlinear age-related changes of artery wall mechanics occurs between arteries of different types, which may be a risk factor for the occurrence of abdominal aorta aneurysm and femoral artery atherosclerosis.

Layer-Specific Residual Deformations and Their Variation Along the Human Aorta

This study described the regional distribution of layer-specific residual deformations in fifteen human aortas collected during autopsy. Circumferentially and axially cut strips of standardized dimensions from the anterior quadrant of nine consecutive aortic levels were photographed to obtain the zero-stress state for the intact wall. The strips were then dissected into layers that were also photographed to obtain their zero-stress state. Changes in layer-specific opening angle, residual stretches, and thickness at each aortic level and direction were determined via image analysis. The circumferential and axial opening angles of the intima were ∼240 deg and ∼30 deg, respectively, throughout the aorta; those of the adventitia were ∼150 deg and -20 deg to 70 deg. The opening angles of the intact wall and media were similar in either direction. The circumferential residual stretches of the intima and the axial residual stretches of the media showed high values in the aortic arch, decreasing in the descending thoracic aorta and increasing toward the iliac artery bifurcation, while the axial residual stretches of the adventitia increased distally. The remaining residual stretches did not vary significantly with aortic level, suggesting an intimal role in determining circumferential, as well as medial and adventitial roles in determining axial residual stretches. We conclude that the tensile residual stretches released in the intima and media upon separation, and the compressive residual stretches released in the adventitia may moderate the inverse transmural stress gradients under physiologic loads, resulting from the >180 deg circumferential opening angle of the intact wall.

Anisotropic residual stresses in arteries

The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7, 787-799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35, 530-545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries-intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12, 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13, 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.

Variation of Axial Residual Strains Along the Course and Circumference of Human Aorta Considering Age and Gender

Our understanding of aortic biomechanics is customarily limited by lack of information on the axial residual stretches of the vessel in both humans and experimental animals that would facilitate the identification of its actual zero-stress state. The aim of this study was thus to acquire hitherto unreported quantitative knowledge of axial opening angle and residual stretches in different segments and quadrants of the human aorta according to age and gender. Twenty-three aortas were harvested during autopsy from the aortic root to the iliac bifurcation and were divided into ≥12 segments and 4 quadrants. Morphometric measurements were taken in the excised/curled configuration of rectangular strips considered to be under zero-stress using image-analysis software to study the axial/circumferential variation of axial opening angle, internal/external residual stretch, and thickness of the aortic wall. The measured data demonstrated: (1) an axial opening angle peak at the arch branches, decreasing toward the ascending and to a near-constant value in the descending thoracic aorta, and increasing in the abdominal aorta; (2) the variation of residual stretches resembled that of opening angle, but axial differences in external residual stretch were more prominent; (3) wall thickness showed a progressive diminution along the vessel; (4) the highest opening angle/residual stretches were found in the inner quadrant and the lowest in the outer quadrant; (5) the anterior was the thinnest quadrant throughout the aorta; (6) age caused thickening but greatly reduced axial opening angle/residual stretches, without differences between males and females.

Acute Tachycardia Increases Aortic Distensibility, but Reduces Total Arterial Compliance Up to a Moderate Heart Rate

Background: The differential effects of rapid cardiac pacing on small and large vessels have not been well-established. The objective of this study was to investigate the effect of pacing-induced acute tachycardia on hemodynamics and arterial stiffness.

Methods: The pressure and flow waves in ascending aorta and femoral artery of six domestic swine were recorded simultaneously at baseline and heart rates (HR) of 135 and 155 beats per minutes (bpm) and analyzed by the models of Windkessel and Womersley types. Accordingly, the flow waves were simultaneously measured at carotid and femoral arteries to quantify aortic pulse wave velocity (PWV). The arterial distensibility was identified in small branches of coronary, carotid and femoral arteries with diameters of 300–600 μm by ex vivo experiments.

Results: The rapid pacing in HR up to 135 bpm reduced the total arterial compliance, stroke volume, systemic pulse pressure, and central systolic pressure by 36 ± 17, 38 ± 26, 29 ± 16, and 23 ± 12%, respectively, despite no statistical difference of mean aortic pressure, cardiac output, peripheral resistance, and vascular flow patterns. The pacing also resulted in a decrease of distensibility of small muscular arteries, but an increase of aortic distensibility. Pacing from 135 to 155 bpm had negligible effects on systemic and local hemodynamics and arterial stiffness.

Conclusions: There is an acute mismatch in the response of aorta and small arteries to pacing from basal HR to 135 bpm, which may have important pathological implications under chronic tachycardia conditions.

The Structure-function remodeling in rabbit hearts of myocardial infarction

Animal models are of importance to investigate basic mechanisms for ischemic heart failure (HF). The objective of the study was to create a rabbit model through multiple coronary artery ligations to investigate the postoperative structure‐function remodeling of the left ventricle (LV) and coronary arterial trees. Here, we hypothesize that the interplay of the degenerated coronary vasculature and increased ventricle wall stress relevant to cardiac fibrosis in vicinity of myocardial infarction (MI) precipitates the incidence and progression of ischemic HF. Echocardiographic measurements showed an approximately monotonic drop of fractional shortening and ejection fraction from 40% and 73% down to 28% and 58% as well as persistent enlargement of LV cavity and slight mitral regurgitation at postoperative 12 weeks. Micro‐CT and histological measurements showed that coronary vascular rarefaction and cardiac fibrosis relevant to inflammation occurred concurrently in vicinity of MI at postoperative 12 weeks albeit there was compensatory vascular growth at postoperative 6 weeks. These findings validate the proposed rabbit model and prove the hypothesis. The post‐MI rabbit model can serve as a reference to test various drugs for treatment of ischemic HF.

Passive and Active Triaxial Wall Mechanics in a Two-Layer Model of Porcine Coronary Artery

Triaxial active and passive mechanical properties of coronary arteries are needed for understanding arterial mechanics in health and disease. The aim of the study was to quantify both active and passive strain energy functions in circumferential, axial and radial directions based on the experimental measurement. Moreover, a two-layer computational model was used to determine the transmural distribution of stresses and strains across the vessel wall. The first Piola-Kirchhoff stresses in the three normal directions had the approximate relationship as:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,{T}_{\theta \theta }\cong 2{T}_{zz}\cong 5|{T}_{rr}|$$\end{document}Tθθ≅2Tzz≅5|Trr|. The two-layer model showed that circumferential Cauchy stresses increased significantly from the intima layer to the interface between media and adventitia layers (from ~80 to 160 kPa), dropped abruptly at the interface (from ~160 to <5 kPa), and increased slightly towards the outer boundary of the adventitia layer. In contrast, absolute values of radial Cauchy stress decreased continuously from the inner to outer boundaries of the vessel wall (from ~11 kPa to zero). Smooth muscle cell contraction significantly increased the ratio of radial to circumferential Cauchy stresses at the intima-media layer, which had the highest values at the intima layer.

Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

Microstructure-based biomechanics of coronary arteries in health and disease

Coronary atherosclerosis is the major cause of mortality and disability in developed nations. A deeper understanding of mechanical properties of coronary arteries and hence their mechanical response to stress is significant for clinical prevention and treatment. Microstructure-based models of blood vessels can provide predictions of arterial mechanical response at the macro- and micro-mechanical level for each constituent structure. Such models must be based on quantitative data of structural parameters (constituent content, orientation angle and dimension) and mechanical properties of individual adventitia and media layers of normal arteries as well as change of structural and mechanical properties of atherosclerotic arteries. The microstructural constitutive models of healthy coronary arteries consist of three major mechanical components: collagen, elastin, and smooth muscle cells, while the models of atherosclerotic arteries should account for additional constituents including intima, fibrous plaque, lipid, calcification, etc. This review surveys the literature on morphology, mechanical properties, and microstructural constitutive models of normal and atherosclerotic coronary arteries. It also provides an overview of current gaps in knowledge that must be filed in order to advance this important area of research for understanding initiation, progression and clinical treatment of vascular disease. Patient-specific structural models are highlighted to provide diagnosis, virtual planning of therapy and prognosis when realistic patient-specific geometries and material properties of diseased vessels can be acquired by advanced imaging techniques.

Remodeling of left circumflex coronary arterial tree in pacing-induced heart failure

Congestive heart failure (CHF) is a very serious heart disease that manifests an imbalance between left ventricle supply and demand. Although the mechanical demand of the failing heart has been well characterized, the systematic remodeling of the entire coronary arterial tree that constitutes the supply of the myocardium is lacking. We hypothesize that the well-known increase in ventricle wall stress during CHF causes coronary vascular rarefaction to increase the vascular flow resistance, which in turn compromises the perfusion of the heart. Morphometric (diameters, length, and numbers) data of the swine left circumflex (LCx) arterial tree were measured in both CHF (n = 6) and control (n = 6) groups, from which a computer reconstruction of the entire LCx tree was implemented down to the capillary level to enable a hemodynamic analysis of coronary circulation. The vascular flow resistance was increased by ∼75% due to a significant decrease of vessel numbers (∼45%) and diameters in the first capillary segments (∼10%) of the LCx arterial tree after 3-4 wk of pacing. The structural remodeling significantly changed the wall shear stress in vessel segments of the entire LCx arterial tree of CHF animals. This study enhances our knowledge of coronary arterial tree remodeling in heart failure, which provides a deeper understanding of the deterioration of supply-demand relation in left ventricle.

Biaxial Contractile Mechanics of Common Carotid Arteries of Rabbit

Few multiaxial constitutive laws under the vasoactive condition have been proposed as compared with those under the passive condition. The biaxial isometric properties of vasoactive rabbit arteries were studied, although the constitutive law was not proposed. The purpose of the present study is also to describe the multiaxial active mechanical properties of arteries. A novel strain energy function for the active stress has been proposed. This function is simple and may describe the multiaxial characteristics of constricted vessels. Although this study used mean stress and mean stretch ratio to determine the mechanical properties of vessels, a triaxial constitutive law of constricted vessels may be developed. There remains the subject of residual strains under active condition. If this problem will be solved, the accurate stress analysis under vasoactive conditions is possible.

Perspective on CFD studies of coronary artery disease lesions and hemodynamics: a review

Coronary artery disease (CAD) is the most common cardiovascular disease. Early diagnosis of CAD's physiological significance is of utmost importance for guiding individualized risk-tailored treatment strategies. In this paper, we first review the state-of-the-art clinical diagnostic indices to quantify the severity of CAD and the associated invasive and noninvasive imaging technologies in order to quantify the anatomical parameters of diameter stenosis, area stenosis, and hemodynamic indices of coronary flow reserve and fractional flow reserve. With the development of computational technologies and CFD methods, tremendous progress has been made in applying image-based CFD simulation techniques to elucidate the effects of hemodynamics in vascular pathophysiology toward the initialization and progression of CAD. So then, we review the advancements of CFD technologies in patient-specific modeling, involving the development of geometry reconstruction, boundary conditions, and fluid-structure interaction. Next, we review the applications of CFD to stenotic sites, in order to compute their hemodynamic parameters and study the relationship between the hemodynamic conditions and the clinical indices, to thereby assess the amount of viable myocardium and candidacy for percutaneous coronary intervention. Finally, we review the strengths and limitations of current researches of applying CFD to CAD studies.

Biaxial deformation of collagen and elastin fibers in coronary adventitia

The microstructural deformation-mechanical loading relation of the blood vessel wall is essential for understanding the overall mechanical behavior of vascular tissue in health and disease. We employed simultaneous mechanical loading-imaging to quantify in situ deformation of individual collagen and elastin fibers on unstained fresh porcine coronary adventitia under a combination of vessel inflation and axial extension loading. Specifically, the specimens were imaged under biaxial loads to study microscopic deformation-loading behavior of fibers in conjunction with morphometric measurements at the zero-stress state. Collagen fibers largely orientate in the longitudinal direction, while elastin fibers have major orientation parallel to collagen, but with additional orientation angles in each sublayer of the adventitia. With an increase of biaxial load, collagen fibers were uniformly stretched to the loading direction, while elastin fibers gradually formed a network in sublayers, which strongly depended on the initial arrangement. The waviness of collagen decreased more rapidly at a circumferential stretch ratio of λθ = 1.0 than at λθ = 1.5, while most collagen became straightened at λθ = 1.8. These microscopic deformations imply that the longitudinally stiffer adventitia is a direct result of initial fiber alignment, and the overall mechanical behavior of the tissue is highly dependent on the corresponding microscopic deformation of fibers. The microstructural deformation-loading relation will serve as a foundation for micromechanical models of the vessel wall.

Microstructural constitutive model of active coronary media

Although vascular smooth muscle cells (VSMCs) are pivotal in physiology and pathology, there is a lack of detailed morphological data on these cells. The objective of this study was to determine dimensions (width and length) and orientation of swine coronary VSMCs and to develop a microstructural constitutive model of active media. The dimensions, spatial aspect ratio and orientation angle of VSMCs measured at zero-stress state were found to follow continuous normal (or bimodal normal) distributions. The VSMCs aligned off circumferential direction of blood vessels with symmetrical polar angles 18.7° ± 10.9°, and the local VSMC deformation was affine with tissue-level deformation. A microstructure-based active constitutive model was developed to predict the biaxial vasoactivity of coronary media, based on experimental measurements of geometrical and deformation features of VSMCs. The results revealed that the axial active response of blood vessels is associated with multi-axial contraction as well as oblique VSMC arrangement. The present morphological database is essential for developing accurate structural models and is seminal for understanding the biomechanics of muscular vessels.