Discussion: "Comparison of Statistical Methods for Assessing Spatial Correlations Between Maps of Different Arterial Properties" (Rowland, E. M., Mohamied, Y., Chooi, K. Y., Bailey, E. L., and Weinberg, P. D., 2015, ASME J. Biomech. Eng., 137(10), p. 101003): An Alternative Approach Using Segmentation Based on Local Hemodynamics.

The biological response of living arteries to mechanical forces is an important component of the atherosclerotic process and is responsible, at least in part, for the well-recognized spatial variation in atherosusceptibility in man. Experiments to elucidate this response often generate maps of force and response variables over the arterial surface, from which the force-response relationship is sought. Rowland et al. discussed several statistical approaches to the spatial autocorrelation that confounds the analysis of such maps and applied them to maps of hemodynamic stress and vascular response obtained by averaging these variables in multiple animals. Here, we point out an alternative approach, in which discrete surface regions are defined by the hemodynamic stress levels they experience, and the stress and response in each animal are treated separately. This approach, applied properly, is insensitive to autocorrelation and less sensitive to the effect of confounding hemodynamic variables. The analysis suggests an inverse relation between permeability and shear that differs from that in Rowland et al. Possible sources of this difference are suggested.

Adaptive response of vascular endothelial cells to an acute increase in shear stress frequency.

Local shear stress sensed by arterial endothelial cells is occasionally altered by changes in global hemodynamic parameters, e.g., heart rate and blood flow rate, as a result of normal physiological events, such as exercise. In a recently study (41), we demonstrated that during the adaptive response to increased shear magnitude, porcine endothelial cells exhibited an unique phenotype featuring a transient increase in permeability and the upregulation of a set of anti-inflammatory and antioxidative genes. In the present study, we characterize the adaptive response of these cells to an increase in shear frequency, another important hemodynamic parameter with implications in atherogenesis. Endothelial cells were preconditioned by a basal-level sinusoidal shear stress of 15 ± 15 dyn/cm(2) at 1 Hz, and the frequency was then elevated to 2 Hz. Endothelial permeability increased slowly after the frequency step-up, but the increase was relatively small. Using microarrays, we identified 37 genes that are sensitive to the frequency step-up. The acute increase in shear frequency upregulates a set of cell-cycle regulation and angiogenesis-related genes. The overall adaptive response to the increased frequency is distinctly different from that to a magnitude step-up. However, consistent with the previous study, our data support the notion that endothelial function during an adaptive response is different than that of fully adapted endothelial cells. Our studies may also provide insights into the beneficial effects of exercise on vascular health: transient increases in frequency may facilitate endothelial repair, whereas similar increases in shear magnitude may keep excessive inflammation and oxidative stress at bay.

Adaptive response of vascular endothelial cells to an acute increase in shear stress magnitude.

The adaptation of vascular endothelial cells to shear stress alteration induced by global hemodynamic changes, such as those accompanying exercise or digestion, is an essential component of normal endothelial physiology in vivo. An understanding of the transient regulation of endothelial phenotype during adaptation to changes in mural shear will advance our understanding of endothelial biology and may yield new insights into the mechanism of atherogenesis. In this study, we characterized the adaptive response of arterial endothelial cells to an acute increase in shear stress magnitude in well-defined in vitro settings. Porcine endothelial cells were preconditioned by a basal level shear stress of 15 ± 15 dyn/cm(2) at 1 Hz for 24 h, after which an acute increase in shear stress to 30 ± 15 dyn/cm(2) was applied. Endothelial permeability nearly doubled after 40-min exposure to the elevated shear stress and then decreased gradually. Transcriptomics studies using microarray techniques identified 86 genes that were sensitive to the elevated shear. The acute increase in shear stress promoted the expression of a group of anti-inflammatory and antioxidative genes. The adaptive response of the global gene expression profile is triphasic, consisting of an induction period, an early adaptive response (ca. 45 min) and a late remodeling response. Our results suggest that endothelial cells exhibit a specific phenotype during the adaptive response to changes in shear stress; this phenotype is different than that of fully adapted endothelial cells.

Environment and vascular bed origin influence differences in endothelial transcriptional profiles of coronary and iliac arteries.

Atherosclerotic plaques tend to form in the major arteries at certain predictable locations. As these arteries vary in atherosusceptibility, interarterial differences in endothelial cell biology are of considerable interest. To explore the origin of differences observed between typical atheroprone and atheroresistant arteries, we used DNA microarrays to compare gene expression profiles of harvested porcine coronary (CECs) and iliac artery endothelial cells (IECs) grown in static culture out to passage 4. Fewer differences were observed between the transcriptional profiles of CECs and IECs in culture compared with in vivo, suggesting that most differences observed in vivo were due to distinct environmental cues in the two arteries. One-class significance of microarrays revealed that most in vivo interarterial differences disappeared in culture, as fold differences after passaging were not significant for 85% of genes identified as differentially expressed in vivo at 5% false discovery rate. However, the three homeobox genes, HOXA9, HOXA10, and HOXD3, remained underexpressed in coronary endothelium for all passages by at least nine-, eight-, and twofold, respectively. Continued differential expression, despite removal from the in vivo environment, suggests that primarily heritable or epigenetic mechanism(s) influences transcription of these three genes. Quantitative real-time polymerase chain reaction confirmed expression ratios for seven genes associated with atherogenesis and over- or underexpressed by threefold in CECs relative to IECs. The present study provides evidence that both local environment and vascular bed origin modulate gene expression in arterial endothelium. The transcriptional differences observed here may provide new insights into pathways responsible for coronary artery susceptibility.

Use of factor analysis to characterize arterial geometry and predict hemodynamic risk: application to the human carotid bifurcation.

The detailed geometry of atherosclerosis-prone vascular segments may influence their susceptibility by mediating local hemodynamics. An appreciation of the role of specific geometric variables is complicated by the considerable correlation among the many parameters that can be used to describe arterial shape and size. Factor analysis is a useful tool for identifying the essential features of such an inter-related data set, as well as for predicting hemodynamic risk in terms of these features and for interpreting the role of specific geometric variables. Here, factor analysis is applied to a set of 14 geometric variables obtained from magnetic resonance images of 50 human carotid bifurcations. Two factors alone were capable of predicting 12 hemodynamic metrics related to shear and near-wall residence time with adjusted squared Pearson's correlation coefficient as high as 0.54 and P-values less than 0.0001. One factor measures cross-sectional expansion at the bifurcation; the other measures the colinearity of the common and internal carotid artery axes at the bifurcation. The factors explain the apparent lack of an effect of branch angle on hemodynamic risk. The relative risk among the 50 bifurcations, based on time-average wall shear stress, could be predicted with a sensitivity and specificity as high as 0.84. The predictability of the hemodynamic metrics and relative risk is only modestly sensitive to assumptions about flow rates and flow partitions in the bifurcation.

The correspondence between coronary arterial wall strain and histology in a porcine model of atherosclerosis.

Atherosclerotic plaque rupture is the leading cause of mortality in cardiovascular disease. Intravascular ultrasound (IVUS) imaging is a powerful clinical technique that provides real-time cross-sectional images of the arterial wall and atherosclerotic plaques. However, it does not provide sufficient information about the histological composition of plaques to characterize their vulnerability. Arterial wall strain measurements may provide insights into plaque composition and vulnerability, complementing the information directly available in the IVUS echogram. We have developed a method to measure the transverse arterial wall strain tensor in response to luminal pressure change, by registering IVUS images acquired at different pressures. This method has been validated by using IVUS images with simulated motion and IVUS images of a vessel phantom. In this study, we further evaluate the method by assessing the correspondence of the calculated strain distribution and the histological composition of atherosclerotic coronary arteries from Sinclair miniature pigs following 12 months of a high fat diet. The images were acquired in situ using a clinical IVUS system and under computer-controlled pressurization. After image acquisition, the artery segments were fixed for histology to identify plaque components. The strain distributions were aligned with the corresponding histological sections. The stiffness of various components of the lesion, inferred from the wall strain distribution, was consistent with the tissue composition seen in the histological cross-sections. These findings suggest that strain measurements from IVUS are promising for assessing plaque vulnerability.

Differences in aortic arch geometry, hemodynamics, and plaque patterns between C57BL/6 and 129/SvEv mice.

Atherosclerotic plaques are distributed differently in the aortic arches of C57BL/6 (B6) and 129/SvEv (129) apolipoprotein E (apoE)-deficient mice. It is now recognized that hemodynamic wall shear stress (WSS) plays an important role in the localization of atherosclerotic development. Since the blood flow field in the vessel is modulated by the vascular geometry, we quantitatively examined the difference in the aortic arch geometry and hemodynamic WSS between the two corresponding wild-type mouse strains. The three-dimensional (3D) geometry of 14 murine aortic arches, seven from each strain, was characterized using casts and stereo microscopic imaging. Based on the geometry of each cast, an average 3D geometry of the aortic arch for each mouse strain was obtained, and computational fluid dynamic calculations were performed in the two average aortic arches. Many geometric features, including aortic arch shape, vessel diameter, and branch locations, were significantly different at p<0.05 between the two mouse strains. Lower shear stress was found at the inner curvature of the aortic arch in the 129 strain, corresponding to greater involvement in the corresponding apoE-deficient mice relative to the B6 strain. These results support the notion that heritable features of arterial geometry can contribute to individual differences in local susceptibility to arterial disease.

Measurement of the transverse strain tensor in the coronary arterial wall from clinical intravascular ultrasound images.

Atherosclerotic plaque rupture is the major cause of acute coronary syndromes. Currently, there is no reliable diagnostic tool to predict plaque rupture. Knowledge of plaque mechanical properties based on local artery wall strain measurements would be useful for characterizing its composition and predicting its vulnerability. Due to cardiac motion, strain estimation in clinical intravascular ultrasound (IVUS) images is extremely challenging. A method is presented to estimate cross-sectional coronary artery wall strain in response to cardiac pulsatile pressure using clinically acquired IVUS images, which are acquired in continuous pullback mode. First, cardiac phase information is retrieved retrospectively from an IVUS image sequence using an image-based gating method, and image sub-sequences at systole and diastole are extracted. Then, images at branch sites are used as landmarks to align the two image sub-sequences. Finally, the paired images at each site are registered to measure the 2D strain tensor of the coronary artery cross-section. This method has been successfully applied to IVUS images of a left anterior descending (LAD) coronary artery acquired clinically during a standard procedure. Such complete strain information should be useful for identifying vulnerable plaque.

Effect of hypercholesterolemia on transendothelial EBD-albumin permeability and lipid accumulation in porcine iliac arteries.

Hypercholesterolemia is associated with increased cardiovascular mortality and is known to promote the advancement of atherosclerotic lesions in experimental animal models. Juvenile swine were fed a normal or high-cholesterol diet, and the transendothelial macromolecular permeability of the external iliac arteries of these animals was assessed by measuring the uptake rate of circulating Evans blue dye (EBD). The extent and patterns of lipid-containing lesions were also determined using en face staining with Oil Red O (ORO). Sites of ORO staining often excluded EBD, possibly via the fragmentation of the internal elastic lamina, to which EBD binds. By spatially averaging the EBD uptake in arterial segments relatively free of ORO-positive lesions, it was found that endothelial permeability to albumin was greater in hypercholesterolemic pigs than in those on a normal diet (p=0.056).

Relationship between the dynamic geometry and wall thickness of a human coronary artery.

OBJECTIVE: It is widely recognized that hemodynamic and wall mechanical forces are involved in the initiation and development of atherosclerosis. In the coronary vasculature, these forces are likely mediated by arterial dynamics and geometry. This research examines the hypothesis that coronary artery motion and geometry affect the local predisposition to disease, presumably through their influence on the stresses at and in the artery wall. METHODS AND RESULTS: The dynamics of a human right coronary artery and the variation of wall thickness along its length were characterized from biplane cineangiograms and intravascular ultrasound records, respectively. The dynamic geometry parameters were distance along the vessel, cyclic displacement, axial strain, curvature, and torsion. Multiple regression analyses using principal components show that (1) no single dynamic geometry parameter has a dominant influence on wall thickness, (2) linear combinations of such parameters predict wall thickness measures with high confidence (P<0.001; R2 between 0.17 and 0.44), and (3) both the time-average values of curvature and torsion and their excursion during the cardiac cycle are positively correlated with maximum wall thickness and cross-sectional asymmetry. CONCLUSIONS: The relationships seen here support the hypothesis that dynamic geometry plays a role in the localization of early coronary artery thickening.

Influence of curvature dynamics on pulsatile coronary artery flow in a realistic bifurcation model.

The coronary arteries undergo large dynamic variations during each cardiac cycle due to their position on the beating heart. The local artery curvature varies significantly. In this study the influence of dynamic curvature on coronary artery hemodynamics is analyzed numerically. A realistic model of the bifurcation of the left anterior descending coronary artery and its first diagonal branch is curved by attaching it to the surface of a sphere with time-varying radius based on experimental dynamic curvature data. The description of the blood flow uses the time-dependent, three-dimensional, incompressible Navier-Stokes equations for Newtonian fluids, where the influence of the time-dependent flow domain is taken into account employing the Arbitrary Lagrangian-Eulerian technique. The inlet velocity profiles used in the computer simulation are physiologically realistic. The results show that the skewing of the axial velocity profiles near the branching site is mainly determined by the vessel branch; the bifurcating flow generally dominates the effect of curvature. The influence of curvature increases downstream of the branch. During systole, when curvature is greatest and high curvature variations appear, their effect on the flow patterns and the wall shear stress is dominated by the flow wave. Due to the smaller curvature changes during diastole, only minor effects of curvature variation on the high and relatively constant diastolic flow occur. The results demonstrate the importance of including physiologically realistic flow in the correct phase relationship with vessel motion when simulating coronary artery hemodynamics.

Comparison of coronary artery dynamics pre- and post-stenting.

Stents have dramatically improved the treatment of coronary artery disease. Since the implantation of stents changes the geometry and dynamics of the coronary artery, it is reasonable to hypothesize that some of these changes may have an important effect on the development of atherosclerosis by modulating the mechanical environment. In this paper, we presented a method to compare the geometric dynamics of the coronary artery before and after stenting using biplane angiography. Two cases are reviewed and a number of parameters are proposed to describe the longitudinal change of the vessel before and after stenting. This analysis technique has the potential to identify some aspects of stent design and procedure that might improve the success rate with this therapeutic approach.

Variability of 3D arterial geometry and dynamics, and its pathologic implications.

Geometric parameters and features vary within the vasculature. Furthermore, at any given anatomic site, there are substantial variations in geometry among individuals. These variations can contribute to a corresponding variability in the hemodynamic environment and, to the extent that hemodynamics affects the atherosclerotic process, the progress of vascular disease. Measurements of the geometry and wall morphometry of post-mortem human coronary arteries demonstrate a relationship between these variables that supports the notion that geometric variations can contribute to a corresponding variability in the local rate of progression of arterial disease. The dynamic geometry of the coronary arteries also varies from site to site and among individuals, and this variability too may play a role in the epidemiology of coronary artery disease.

Microscope-based near-infrared stereo-imaging system for quantifying the motion of the murine epicardial coronary arteries in vivo.

Atherosclerosis is a leading cause of mortality in industrialized countries. In addition to "traditional" systemic risk factors for atherosclerosis, the geometry and motion of coronary arteries may contribute to individual susceptibility to the development and progression of disease in these vessels. To be able to test this, we have developed a high-speed (∼40 frames per second) microscope-based stereo-imaging system to quantify the motion of epicardial coronary arteries of mice. Using near-infrared nontargeted quantum dots as an imaging contrast agent, we synchronously acquired paired images of a surgically exposed murine heart, from which the three-dimensional geometry of the coronary arteries was reconstructed. The reconstructed geometry was tracked frame by frame through the cardiac cycle to quantify the in vivo motion of the vessel, from which displacements, curvature, and torsion parameters were derived. Illustrative results for a C57BL/6J mouse are presented.

Relationship between hemodynamics and atherosclerosis in aortic arches of apolipoprotein E-null mice on 129S6/SvEvTac and C57BL/6J genetic backgrounds.

OBJECTIVE: We investigated the relationships between hemodynamics and differential plaque development at the aortic arch of apolipoprotein E (apoE)-null mice on 129S6/SvEvTac (129) and C57BL/6J (B6) genetic backgrounds. METHODS: Mean flow velocities at the ascending and descending aorta (mVAA and mVDA) were measured by Doppler ultrasound in wild type and apoE-null male mice at 3 and 9 months of age. Following dissection of the aortic arches, anatomical parameters and plaque areas were evaluated. RESULTS: Arch plaques were five times bigger in 129-apoE than in B6-apoE mice at 3 months, and twice as large at 9 months. The geometric differences, namely larger vessel diameter in the B6 strain and broader inner curvature of the aortic arch in the 129 strain, were exaggerated in 9-month-old apoE-null mice. Cardiac output and heart rate under anesthesia were significantly higher in the B6 strain than in the 129 strain. The values of mVAA were similar in the two strains, while mVDA was lower in the 129 strain. However, there was a 129-apoE-specific reduction of flow velocities with age, and both mVAA and mVDA were significantly lower in 129-apoE than in B6-apoE mice at 9 months. The mean relative wall shear stress (rWSS) over the aortic arch in 129-apoE and B6-apoE mice were not different, but animals with lower mean rWSS had larger arch plaques within each strain. CONCLUSIONS: The plaque formation in the arch of apoE-null mice is accompanied by strain-dependent changes in both arch geometry and hemodynamics. While arch plaque sizes negatively correlate with mean rWSS, additional factors are necessary to account for the strain differences in arch plaque development.

Measurement of the 3D arterial wall strain tensor using intravascular B-mode ultrasound images: a feasibility study.

Intravascular ultrasound (IVUS) elastography is a promising tool for studying atherosclerotic plaque composition and assessing plaque vulnerability. Current IVUS elastography techniques can measure the 1D or 2D strain of the vessel wall using various motion tracking algorithms. Since biological soft tissue tends to deform non-uniformly in 3D, measurement of the complete 3D strain tensor is desirable for more rigorous analysis of arterial wall mechanics. In this paper, we extend our previously developed method of 2D arterial wall strain measurement based on non-rigid image registration into 3D strain measurement. The new technique registers two image volumes acquired from the same vessel segment under different levels of luminal pressure and longitudinal stress. The 3D displacement field obtained from the image registration is used to calculate the local 3D strain tensor. From the 3D strain tensor, radial, circumferential and longitudinal strain distributions can be obtained and displayed. This strain tensor measurement method is validated and evaluated using IVUS images of healthy porcine carotid arteries subjected to a luminal pressure increase and longitudinal stretch. The ability of the algorithm to overcome systematic noise was tested, as well as the consistency of the results under different longitudinal frame resolutions.

Flow interactions with cells and tissues: cardiovascular flows and fluid-structure interactions. Sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28-30, 2008, Pasadena, California.

Interactions between flow and biological cells and tissues are intrinsic to the circulatory, respiratory, digestive and genitourinary systems. In the circulatory system, an understanding of the complex interaction between the arterial wall (a living multi-component organ with anisotropic, nonlinear material properties) and blood (a shear-thinning fluid with 45% by volume consisting of red blood cells, platelets, and white blood cells) is vital to our understanding of the physiology of the human circulation and the etiology and development of arterial diseases, and to the design and development of prosthetic implants and tissue-engineered substitutes. Similarly, an understanding of the complex dynamics of flow past native human heart valves and the effect of that flow on the valvular tissue is necessary to elucidate the etiology of valvular diseases and in the design and development of valve replacements. In this paper we address the influence of biomechanical factors on the arterial circulation. The first part presents our current understanding of the impact of blood flow on the arterial wall at the cellular level and the relationship between flow-induced stresses and the etiology of atherosclerosis. The second part describes recent advances in the application of fluid-structure interaction analysis to arterial flows and the dynamics of heart valves.

Endothelial gene expression in regions of defined shear exposure in the porcine iliac arteries.

The effect of hemodynamic shear stress on endothelial gene expression was investigated in the porcine iliac arteries. A novel statistical approach was applied to computational fluid dynamics simulations of the iliac artery flow field to identify three anatomical regions likely to experience high, medium, and low levels of time average shear stress magnitude. Subsequently, endothelial cell mRNA was collected from these regions in the iliac arteries of six swine and analyzed by DNA microarray. Gene set enrichment analysis demonstrated a strong tendency for genes upregulated or downregulated in one of the extreme shear environments (low or high, relative to medium) to be regulated in the same direction in the other extreme shear environment. This tendency was confirmed for specific genes by real-time quantitative PCR. Specifically, beta-catenin, c-jun, VCAM-1, and MCP-1 were all upregulated in low and high shear stress regions relative to the medium shear stress region. eNOS expression was not significantly different in any of the regions. These results are consistent with the notion that endothelial cells chronically exposed to abnormally low or high shear levels in vivo exhibit similar genetic responses. Alternative explanations of this outcome are proposed, and its implications for the role of shear stress in atherogenesis are examined.

Integrative biomechanics: a paradigm for clinical applications of fundamental mechanics.

Integrative biomechanics uses biomechanics knowledge and methods at multiple scales and among biological entities to address fundamental and clinical problems at the tissue and organ level. Owing to the large ranges of scale involved, integrative biomechanics is intrinsically multidisciplinary, extending from molecular biophysics to contemporary engineering descriptions of kinematics and bulk constitutive properties. Much of this integration is accomplished through multiscale models of the interactions of interest. Applications can range from the development of new biological knowledge to the creation of new technologies for clinical application. In this white paper, the historical background of, and the rationale behind, integrative biomechanics are reviewed, followed by a sampling of clinical advances that were developed using the integrative approach. Refinements of many of these advances are still needed, and unsolved problems remain, in genomic applications, developing improved interventional procedures and protocols, and personalized medicine. Challenges to achieve these goals include the need for better models and the acquisition and organization of the data needed to parameterize, validate and apply them. These challenges will be overcome, because the advances in characterizing disease risk, personalization of care, and therapeutics that will follow, demand that we continue to move forward in this exciting field.

Cataloguing the geometry of the human coronary arteries: a potential tool for predicting risk of coronary artery disease.

BACKGROUND: The non-uniform distribution of atherosclerosis in the human vasculature suggests that local fluid dynamics or wall mechanics may be involved in atherogenesis. Thus certain aspects of vascular geometry, which mediates both fluid dynamics and wall mechanics, might be risk factors for coronary atherosclerosis. Cataloguing the geometry of normal human coronary arteries and its variability is a first step toward identifying specific geometric features that increase vascular susceptibility to the disease. METHODS: Images of angiographically normal coronary arteries, including 32 left anterior descending (LAD) and 35 right coronary arteries (RCA), were acquired by clinical biplane cineangiography from 52 patients. The vessel axes in end diastole were reconstructed and geometric parameters that included measures of curvature, torsion and tortuosity were quantified for the proximal, middle and distal segments of the arteries. RESULTS: Statistical analysis shows that (1) in the LAD, curvature, torsion and tortuosity are generally highest in the distal portion, (2) in the RCA, these parameters are smallest in the middle segment, (3) the LAD exhibits significant higher torsion than the RCA (P < 0.005), and (4) >80% of the variability of coronary arterial geometry can be expressed in terms of two factors, one dominated by the curvature measures and tortuosity, and the other emphasizing the torsion parameters. CONCLUSIONS: This study has comprehensively documented the normal arterial geometry of the LAD and RCA in end diastole. This information may be used to guide the identification of geometric features that might be atherogenic risk factors.