Correlations of coronary plaque wall thickness with wall pressure and wall pressure gradient: A representative case study

BACKGROUND: There are two major hemodynamic stresses imposed at the blood arterial wall interface by flowing blood: the wall shear stress (WSS) acting tangentially to the wall, and the wall pressure (WP) acting normally to the wall. The role of flow wall shear stress in atherosclerosis progression has been under intensive investigation, while the impact of blood pressure on plaque progression has been under-studied. METHOD: The correlations of wall thickness (WT) with wall pressure (WP, blood pressure on the lumen wall) and spatial wall pressure gradient (WPG) in a human atherosclerotic right coronary artery were studied. The pulsatile blood flow was simulated using a three dimensional mathematical model. The blood was treated as an incompressible viscous non-Newtonian fluid. The geometry of the artery was re-constructed using an in vivo intravascular ultrasound (IVUS) 44-slice dataset obtained from a patient with consent obtained. The WT, the WP and the WPG were averaged on each slice, respectively, and Pearson correlation analysis was performed on slice averaged base. Each slice was then divided into 8 segments and averaged vessel WT, WP and WPG were collected from all 352 segments for correlation analysis. Each slice was also divided into 2 segments (inner semi-wall of bend and outer semi-wall of bend) and the correlation analysis was performed on the 88 segments. RESULTS: Under mean pressure, the Pearson coefficient for correlation between WT and WP was r = − 0.52 (p < 0.0001) by 2-segment analysis and r = − 0.81 (p < 0.0001) by slice averaged analysis, respectively. The Pearson coefficient for correlation between WT and WPG was r = 0.30 (p = 0.004) by 2-segment analysis and r = 0.45 (p = 0.002) by slice averaged analysis, respectively. The r-values corresponding to systole and diastole pressure conditions were similar. CONCLUSIONS: Results from this representative case report indicated that plaque wall thickness correlated negatively with wall pressure (r = −0.81 by slice) and positively with wall pressure gradient (r = 0.45). The slice averaged WT has a strong linear relationship with the slice averaged WP. Large-scale patient studies are needed to further confirm our findings

Influence of model boundary conditions on blood flow patterns in a patient specific stenotic right coronary artery

BACKGROUND: In literature, the effect of the inflow boundary condition was investigated by examining the impact of the waveform and the shape of the spatial profile of the inlet velocity on the cardiac hemodynamics. However, not much work has been reported on comparing the effect of the different combinations of the inlet/outlet boundary conditions on the quantification of the pressure field and flow distribution patterns in stenotic right coronary arteries. METHOD: Non-Newtonian models were used to simulate blood flow in a patient-specific stenotic right coronary artery and investigate the influence of different boundary conditions on the phasic variation and the spatial distribution patterns of blood flow. The 3D geometry of a diseased artery segment was reconstructed from a series of IVUS slices. Five different combinations of the inlet and the outlet boundary conditions were tested and compared. RESULTS: The temporal distribution patterns and the magnitudes of the velocity, the wall shear stress (WSS), the pressure, the pressure drop (PD), and the spatial gradient of wall pressure (WPG) were different when boundary conditions were imposed using different pressure/velocity combinations at inlet/outlet. The maximum velocity magnitude in a cardiac cycle at the center of the inlet from models with imposed inlet pressure conditions was about 29% lower than that from models using fully developed inlet velocity data. Due to the fact that models with imposed pressure conditions led to blunt velocity profile, the maximum wall shear stress at inlet in a cardiac cycle from models with imposed inlet pressure conditions was about 29% higher than that from models with imposed inlet velocity boundary conditions. When the inlet boundary was imposed by a velocity waveform, the models with different outlet boundary conditions resulted in different temporal distribution patterns and magnitudes of the phasic variation of pressure. On the other hand, the type of different boundary conditions imposed at the inlet and the outlet did not have significant effect on the spatial distribution patterns of the PD, the WPG and the WSS on the lumen surface, regarding the locations of the maximum and the minimum of each quantity. CONCLUSIONS: The observations from this study indicated that the ways how pressure and velocity boundary conditions are imposed in computational models have considerable impact on flow velocity and shear stress predictions. Accuracy of in vivo measurements of blood pressure and velocity is of great importance for reliable model predictions

Intraplaque hemorrhage is associated with higher structural stresses in human atherosclerotic plaques: an in vivo MRI-based 3D fluid-structure interaction study.

BACKGROUND: Studies using medical images have shown that intraplaque hemorrhage may accelerate plaque progression and may produce a stimulus for atherosclerosis development by increasing lipid core and plaque volume and creating new destabilizing factors. Image-based 3D computational models with fluid-structure interactions (FSI) will be used to perform plaque mechanical analysis and investigate possible associations between intraplaque hemorrhage and both plaque wall stress (PWS) and flow shear stress (FSS). METHODS: In vivo MRI data of carotid plaques from 5 patients with intraplaque hemorrhage confirmed by histology were acquired. 3D multi-component FSI models were constructed for each plaque to obtain mechanical stresses. Plaque Wall Stress (PWS) and Flow Shear Stress (FSS) were extracted from all nodal points on the lumen surface of each plaque for analysis. RESULTS: The mean PWS value from all hemorrhage nodes of the 5 plaques combined was higher than that from non-hemorrhage nodes (75.6 versus 68.1 kPa, P = 0.0003). The mean PWS values from hemorrhage nodes for each of the 5 plaques were all significantly higher (5 out of 5) than those from non-hemorrhage nodes (P < 0.05). The mean FSS value from all hemorrhage nodes of the 5 plaques combined was 30.4% higher than that from all non-hemorrhage nodes (15.0 versus 11.5 dyn/cm2, P = 0.0002). However, the mean flow shear stress values from individual cases showed mixed results: only one out of five plaques showed mean FSS value from hemorrhage nodes was higher than that from non-hemorrhage nodes; three out of five plaques showed that their mean FSS values from hemorrhage nodes were lower than those from non-hemorrhage nodes; and one plaque showed that the difference had no statistical significance. CONCLUSION: The results of this study suggested that intraplaque hemorrhage nodes were associated with higher plaque wall stresses. Compared to flow shear stress, plaque wall stress has a better correlation with plaque component feature (hemorrhage) linked to plaque progression and vulnerability. With further validation, plaque stress analysis may provide additional stress indicators for image-based vulnerability assessment.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Influence of non-Newtonian Properties of Blood on the Wall Shear Stress in Human Atherosclerotic Right Coronary Arteries

The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively

Computer Simulations of Atherosclerotic Plaque Growth in Coronary Arteries

A three dimensional mathematical model with a linear plaque growth function was developed to investigate the geometrical adaptation of atherosclerotic plaques in coronary arteries and study the influences of flow wall shear stress (WSS), blood viscosity and the inlet flow rate on the growth of atherosclerotic plaques using computational plaque growth simulations. The simulation results indicated that the plaque wall thickness at the neck of the stenosis increased at a decreasing rate in the atherosclerosis progression. The simulation results also showed a strong dependence of the plaque wall thickness increase on the blood viscosity and the inlet flow rate. The progression rate in a coronary artery was lower with a higher inlet velocity flow rate and higher with a smaller value of the blood viscosity

Morphological and stress vulnerability indices for human coronary plaques and their correlations with cap thickness and lipid percent: An IVUS-based fluid-structure interaction multi-patient study

Plaque vulnerability, defined as the likelihood that a plaque would rupture, is difficult to quantify due to lack of in vivo plaque rupture data. Morphological and stress-based plaque vulnerability indices were introduced as alternatives to obtain quantitative vulnerability assessment. Correlations between these indices and key plaque features were investigated. In vivo intravascular ultrasound (IVUS) data were acquired from 14 patients and IVUS-based 3D fluid-structure interaction (FSI) coronary plaque models with cyclic bending were constructed to obtain plaque wall stress/strain and flow shear stress for analysis. For the 617 slices from the 14 patients, lipid percentage, min cap thickness, critical plaque wall stress (CPWS), strain (CPWSn) and flow shear stress (CFSS) were recorded, and cap index, lipid index and morphological index were assigned to each slice using methods consistent with American Heart Association (AHA) plaque classification schemes. A stress index was introduced based on CPWS. Linear Mixed-Effects (LME) models were used to analyze the correlations between the mechanical and morphological indices and key morphological factors associated with plaque rupture. Our results indicated that for all 617 slices, CPWS correlated with min cap thickness, cap index, morphological index with r = -0.6414, 0.7852, and 0.7411 respectively (p<0.0001). The correlation between CPWS and lipid percentage, lipid index were weaker (r = 0.2445, r = 0.2338, p<0.0001). Stress index correlated with cap index, lipid index, morphological index positively with r = 0.8185, 0.3067, and 0.7715, respectively, all with p<0.0001. For all 617 slices, the stress index has 66.77% agreement with morphological index. Morphological and stress indices may serve as quantitative plaque vulnerability assessment supported by their strong correlations with morphological features associated with plaque rupture. Differences between the two indices may lead to better plaque assessment schemes when both indices were jointly used with further validations from clinical studies

Fluid-Structure Interaction Human Carotid Plaque Progression Simulation Using 3D Meshless Generalized Finite Difference Models Based on Patient-Tracking In Vivo MRI Data

Cardiovascular disease is the leading cause of death worldwide. Many victims of the disease died suddenly without prior symptoms. It is a great challenge for clinicians and researchers to develop screening techniques and assessment methodologies to identify those patients for early treatment and prevention of the fatal clinical event. Considerable effort has been devoted investigating mechanisms governing atherosclerotic plaque progression and rupture [Friedman, Bargeron, Deters, Hutchins and Mark (1987); Friedman and Giddens (2005); Giddens, Zarins, Glagov, S. (1993); Ku, Giddens, Zarins and Glagov (1985); Gibson et al. (1993); Liu and Tang (2010); Stone et al. (2003); Yang, Tang, Atluri et al. (2008,2010)]. Previously, we introduced a computational procedure based on three-dimensional meshless generalized finite difference (MGFD) method and serial magnetic resonance imaging (MRI) data to quantify patient-specific carotid atherosclerotic plaque growth functions and simulate plaque progression. Structure-only models were used in our previous report [Yang, Tang, Atluri et al. (2010)]. In this paper, a meshless modeling procedure for fluid-structure interaction (FSI) human carotid plaque progression simulation using 3D generalized finite difference (GFD) models was introduced based on multi-year patient-tracking in vivo magnetic resonance imaging (MRI) data. Multi-year patient-tracking data was obtained three times (T1, T2, and T3, at intervals of about 18 months) to obtain plaque progression data after informed consent. Blood flow was assumed to laminar, Newtonian, viscous and incompressible. Plaque material was assumed to be uniform, homogeneous, isotropic, linear, and nearly incompressible. Meshless GFD FSI models were constructed and validated by ADINA for the plaque at T1, T2 and T3 to obtain plaque wall (structure) stress and flow shear stress to determine plaque growth functions which were used in progression simulation. Four growth functions with various combinations of morphology, plaque wall stress (PWS) and flow shear stress (FSS) were quantified using least-squares approximation and T1 and T2 data to fit T3 plaque morphology

Green remanufacturer’s mixed collection channel strategy considering enterprise’s environmental responsibility and the fairness concern in reverse green supply chain

In reverse green supply chain, the mixed collection channel strategy of green remanufacturer is analyzed by building a dynamic game model in which we consider that the green remanufacturer undertakes the environmental responsibility and the green collector shows strong fairness concern for the profit. We analyze the impact of the environmental responsibility level of the green remanufacturer, the preference coefficient of the green remanufacturer, the fairness concern coefficient of the green collector, and the coefficient of cross collection price on optimal decision and profit of the green remanufacturer. The result shows that (1) the green remanufacturer can further improve the collection price, so that it makes many more customers participate in the collection activity; (2) the green remanufacturer pays more attention to fulfill the environmental responsibility, which will increase the intensity of collection of the waste green product, and improve the collection price, as the old green product’s remanufacturing cost is lower than the production cost of the new product, and it can improve the green remanufacturer’s profits; (3) the green remanufacturer’s profit in the mixed collection channel is higher than those in online or offline collection channels

Modeling Active Contraction and Relaxation of Left Ventricle Using Different Zero-load Diastole and Systole Geometries for Better Material Parameter Estimation and Stress/Strain Calculations

Modeling ventricle active contraction based on in vivo data is extremely challenging because of complex ventricle geometry, dynamic heart motion and active contraction where the reference geometry (zero-stress geometry) changes constantly. A new modeling approach using different diastole and systole zero-load geometries was introduced to handle the changing zero-load geometries for more accurate stress/strain calculations. Echo image data were acquired from 5 patients with infarction (Infarct Group) and 10 without (Non-Infarcted Group). Echo-based computational two-layer left ventricle models using one zero-load geometry (1G) and two zero-load geometries (2G) were constructed. Material parameter values in Mooney-Rivlin models were adjusted to match volume data. Effective Young’s moduli (YM) were calculated for easy comparison. For diastole phase, begin-filling (BF) mean YM value in the fiber direction (YMf) was 738%higher than its end-diastole (ED) value (645.39 kPa vs. 76.97 kPa, p=3.38E-06). For systole phase, end-systole (ES) YMf was 903% higher than its begin-ejection (BE) value (1025.10 kPa vs. 102.11 kPa, p=6.10E-05). Comparing systolic and diastolic material properties, ES YMf was 59% higher than its BF value (1025.10 kPa vs. 645.39 kPa. p=0.0002). BE mean stress value was 514% higher than its ED value (299.69 kPa vs. 48.81 kPa, p=3.39E-06), while BE mean strain value was 31.5% higher than its ED value (0.9417 vs. 0.7162, p=0.004). Similarly, ES mean stress value was 562% higher than its BF value (19.74 kPa vs. 2.98 kPa, p=6.22E-05), and ES mean strain value was 264% higher than its BF value (0.1985 vs. 0.0546, p=3.42E-06). 2G models improved over 1G model limitations and may provide better material parameter estimation and stress/strain calculations