IVUS-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment

Image-based computational modeling has been introduced for vulnerable atherosclerotic plaques to identify critical mechanical conditions which may be used for better plaque assessment and rupture predictions. In vivo patient-specific coronary plaque models are lagging due to limitations on non-invasive image resolution, flow data, and vessel material properties. A framework is proposed to combine intravascular ultrasound (IVUS) imaging, biaxial mechanical testing and computational modeling with fluid-structure interactions and anisotropic material properties to acquire better and more complete plaque data and make more accurate plaque vulnerability assessment and predictions. Impact of pre-shrink-stretch process, vessel curvature and high blood pressure on stress, strain, flow velocity and flow maximum principal shear stress was investigated.     

Geometry-based pressure drop prediction in mildly diseased human coronary arteries

Pressure drop (△p) estimations in human coronary arteries have several important applications, including determination of appropriate boundary conditions for CFD and estimation of fractional flow reserve (FFR). In this study a △p prediction was made based on geometrical features derived from patient-specific imaging data.     

Collapse and viscoelasticity of diseased human arteries

A laboratory study of the hydrostatic collapse of diseased tibial arteries demonstrated hysteresis in the pressure-flow behaviour which resembled that seen in the stress-strain relations of the arterial tissue. The pressures at which the vessels collapsed were found to be considerably lower than expected on the basis of theoretical elastic models. Also, the pressures at which the vessels reopened were consistently lower than the pressures at which they collapsed. These findings were explained on the basis of viscoelasticity. The difference between collapse and opening pressure may provide insight into the mechanical properties of vessels, and a clue to errors in non-invasive measurements of blood pressure which depend upon collapse of arteries.     

Evolving biaxial mechanical properties of mouse carotid arteries in hypertension

Quantifying the time course of load-induced changes in arterial wall geometry, microstructure, and properties is fundamental to developing mathematical models of growth and remodeling. Arteries adapt to altered pressure and flow by modifying wall thickness, inner diameter, and axial length via marked cell and matrix turnover. To estimate particular biomaterial implications of such adaptations, we used a 4-fiber family constitutive relation to quantify passive biaxial mechanical behaviors of mouse carotid arteries 0 (control), 7-10, 10-14, or 35-56 days after an aortic arch banding surgery that increased pulse pressure and pulsatile flow in the right carotid artery. In vivo circumferential and axial stretches at mean arterial pressure were, for example, 11% and 26% lower, respectively, in hypertensive carotids 35-56 days after banding than in normotensive controls; this finding is consistent with observations that hypertension decreases distensibility. Interestingly, the strain energy W stored in the carotids at individual in vivo conditions was also less in hypertensive compared with normotensive carotids. For example, at 35-56 days after banding, W was 24%, 39%, and 47% of normal values at diastolic, mean, and systolic pressures, respectively. The energy stored during the cardiac cycle, W(sys)-W(dias), also tended to be less, but this reduction did not reach significance. When computed at normal in vivo values of biaxial stretch, however, W was well above normal for the hypertensive carotids. This net increase resulted from an overall increase in the collagen-related anisotropic contribution to W despite a decrease in the elastin-related isotropic contribution. The latter was consistent with observed decreases in the mass fraction of elastin.     

MRI-based quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries

Accurate assessment of wall shear stress (WSS) is vital for studies on the pathogenesis of atherosclerosis. WSS distributions can be obtained by computational fluid dynamics (CFD) using patient-specific geometries and flow measurements. If patient-specific flow measurements are unavailable, in- and outflow have to be estimated, for instance by using Murray’s Law. It is currently unknown to what extent this law holds for carotid bifurcations, especially in cases where stenoses are involved. We performed flow measurements in the carotid bifurcation using phase-contrast MRI in patients with varying degrees of stenosis. An empirical relation between outflow and degree of area stenosis was determined and the outflow measurements were compared to estimations based on Murray’s Law. Furthermore, the influence of outflow conditions on the WSS distribution was studied.For bifurcations with an area stenosis smaller than 65%, the outflow ratio of the internal carotid artery (ICA) to the common carotid artery (CCA) was 0.62±0.12 while the outflow ratio of the external carotid artery (ECA) was 0.35±0.13. If the area stenosis was larger than 65%, the flow to the ICA decreased linearly to zero at 100% area stenosis. The empirical relation fitted the flow data well (R²=0.69), whereas Murray’s Law overestimated the flow to the ICA substantially for larger stenosis, resulting in an overestimation of the WSS. If patient-specific flow measurements of the carotid bifurcation are unavailable, estimation of the outflow ratio by the presented empirical relation will result in a good approximation of calculated WSS using CFD.     

Differential passive and active biaxial mechanical behaviors of muscular and elastic arteries: basilar versus common carotid

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is, therefore, a pressing need to understand better the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. We used a validated four-fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries and we developed a new relation to model their active biaxial responses. These data and constitutive relations allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 (10(-10)M, 10(-9)M, 10(-8)M, and 10(-7)M) and predicts levels of smooth muscle cell activation associated with basal tone under specific in vitro testing conditions. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.     

Branching characteristics of human coronary arteries

Branching angles and branch diameters were measured in a total of 850 arterial junctions in the coronary networks of two human hearts. Comparison is made with similar data obtained previously from the coronary networks of rats, and with what is considered to be optimum on theoretical grounds. It is concluded that the branching characteristics of the human coronary arteries are closer to the theoretical optimum than those of the coronary networks of rats. While the human data exhibit some departure from optimality and a good amount of scatter, these are well within levels observed elsewhere in the cardiovascular systems of man and animals, and considerably better than those found in the coronary networks of rats. The departure from optimality, in terms of physiological cost to the system, is within 5% for most data points.     

Constitutive modeling of porcine coronary arteries using designed experiments

The development of new coronary artery constitutive models is of critical importance in the design and analysis of coronary replacement grafts. In this study, a two-parameter logarithmic complementary energy function, with normalized measured force and internal pressure as the independent variables and strains as the dependent variables, was developed for healthy porcine coronary arteries. Data was collected according to an experimental design with measured force ranging from 9.8 to 201 mN and internal pressure ranging from 0.1 to 16.1 kPa (1 to 121 mmHg). Comparisons of the estimated constitutive parameters showed statistically significant differences between the left anterior descending [LAD] and right coronary artery [RCA], but no differences between the LAD and left circumflex [LCX] or between the LCX and RCA. Point-by-point strain comparisons confirm the findings of the model parameter study and isolate the difference to the axial strain response. Average axial strains for the LAD, LCX, and RCA are 0.026 +/- 0.009, 0.015 +/- 0.005, and 0.011 +/- 0.009, respectively, at all physiologic loads, suggesting that the axial strains in the LAD are significantly higher than in the other regions.     

Constitutive modeling of mouse carotid arteries using experimentally measured microstructural parameters

Changes in the local mechanical environment and tissue mechanical properties affect the biological activity of cells and play a key role in a variety of diseases, such as cancer, arthritis, nephropathy, and cardiovascular disease. Constitutive relations have long been used to predict the local mechanical environment within biological tissues and to investigate the relationship between biological responses and mechanical stimuli. Recent constitutive relations for soft tissues consider both material and structural properties by incorporating parameters that describe microstructural organization, such as fiber distributions, fiber angles, fiber crimping, and constituent volume fractions. The recently developed technique of imaging the microstructure of a single artery as it undergoes multiple deformations provides quantitative structural data that can reduce the number of estimated parameters by using parameters that are truly experimentally intractable. Here, we employed nonlinear multiphoton microscopy to quantify collagen fiber organization in mouse carotid arteries and incorporated measured fiber distribution data into structurally motivated constitutive relations. Microscopy results demonstrate that collagen fibers deform in an affine manner over physiologically relevant deformations. The incorporation of measured fiber angle distributions into constitutive relations improves the model's predictive accuracy and does not significantly reduce the goodness of fit. The use of measured structural parameters rather than estimated structural parameters promises to improve the predictive capabilities of the local mechanical environment, and to extend the utility of intravital imaging methods for estimating the mechanical behavior of tissues using in situ structural information.     

On parameter estimation for biaxial mechanical behavior of arteries

This article considers the parameter estimation of multi-fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors. First, the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model. Then, the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data balancing between variance and bias errors.     

Anomalous course and branches of human coronary arteries

132 hearts obtained from cadavers were dissected in order to study anomalies in the course and branches of human coronary arteries. Only in 1 heart was a deviation of the circumflex branch of the left coronary artery taking a course inferior to the coronary sulcus observed. The right coronary artery travelled the entire length of the coronary sulcus on the back of the heart and gave both a posterior ventricular and a collateral branch. Circumflex branches of the right and left coronary arteries did not anastomose.     

Roots and calibers of the human coronary arteries

The anatomical structure of the coronary-aortic junctions in humans is studied by using corrosion casts of the coronary network. A model is proposed for the specification of these junctions in terms of vessel diameters and branching angles, and the model is used to produce morphological data on these junctions which hitherto have not been available. This anatomical model correlates poorly with the accepted theoretical model of arterial bifurcations in the cardiovascular system. The results suggest that the structure of the coronary-aortic junctions is very different from the structure of typical arterial bifurcations and, by implication, that the flow conditions under which they function are very different. A good understanding of these junctions is important in coronary bypass surgery, where the coronary-aortic junctions are emulated by creating a new anastomosis for the graft at the base of the ascending aorta, and in coronary artery disease, where atherosclerotic lesions occur not far from the coronary-aortic junctions.     

Structural and functional characterization of human microsomal prostaglandin E synthase-1 by computational modeling and site-directed mutagenesis

Microsomal prostaglandin (PG) E synthase-1 (mPGES-1) has recently been recognized as a novel, promising drug target for inflammation-related diseases. Functional and pathological studies on this enzyme further stimulate to understand its structure and the structure-function relationships. Using an approach of the combined structure prediction, molecular docking, site-directed mutagenesis, and enzymatic activity assay, we have developed the first three-dimensional (3D) model of the substrate-binding domain (SBD) of mPGES-1 and its binding with substrates prostaglandin H2 (PGH2) and glutathione (GSH). In light of the 3D model, key amino acid residues have been identified for the substrate binding and the obtained experimental activity data have confirmed the computationally determined substrate-enzyme binding mode. Both the computational and experimental results show that Y130 plays a vital role in the binding with PGH2 and, probably, in the catalytic reaction process. R110 and T114 interact intensively with the carboxyl tail of PGH2, whereas Q36 and Q134 only enhance the PGH2-binding affinity. The modeled binding structure indicates that substrate PGH2 interacts with GSH through hydrogen binding between the peroxy group of PGH2 and the -SH group of GSH. The -SH group of GSH is expected to attack the peroxy group of PGH2, initializing the catalytic reaction transforming PGH2 to prostaglandin E2 (PGE2). The overall agreement between the calculated and experimental results demonstrates that the predicted 3D model could be valuable in future rational design of potent inhibitors of mPGES-1 as the next-generation inflammation-related therapeutic.     

Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling

At autopsy, 13 nonstenotic human left anterior descending coronary arteries [71.5 +/- 7.3 (mean +/- SD) yr old] were harvested, and related anamnesis was documented. Preconditioned prepared strips (n = 78) of segments from the midregion of the left anterior descending coronary artery from the individual layers in axial and circumferential directions were subjected to cyclic quasi-static uniaxial tension tests, and ultimate tensile stresses and stretches were documented. The ratio of outer diameter to total wall thickness was 0.189 +/- 0.014; ratios of adventitia, media, and intima thickness to total wall thickness were 0.4 +/- 0.03, 0.36 +/- 0.03, and 0.27 +/- 0.02, respectively; axial in situ stretch of 1.044 +/- 0.06 decreased with age. Stress-stretch responses for the individual tissues showed pronounced mechanical heterogeneity. The intima is the stiffest layer over the whole deformation domain, whereas the media in the longitudinal direction is the softest. All specimens exhibited small hysteresis and anisotropic and strong nonlinear behavior in both loading directions. The media and intima showed similar ultimate tensile stresses, which are on average three times smaller than ultimate tensile stresses in the adventitia (1,430 +/- 604 kPa circumferential and 1,300 +/- 692 kPa longitudinal). The ultimate tensile stretches are similar for all tissue layers. A recently proposed constitutive model was extended and used to represent the deformation behavior for each tissue type over the entire loading range. The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties. The intima showed significant thickness, load-bearing capacity, and mechanical strength compared with the media and adventitia.     

Targeted particle tracking in computational models of human carotid bifurcations

A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex flow patterns. The methods described may be combined and are generally applicable to CFD studies of fluid and gas flow and are, therefore, of relevance in hemodynamics, respiratory mechanics, and medical imaging science.     

The importance of blood rheology in patient-specific computational fluid dynamics simulation of stenotic carotid arteries

Biomechanics and Modeling in Mechanobiology - The initiation and progression of atherosclerosis, which is the main cause of cardiovascular diseases, correlate with local haemodynamic factors such...