Numerical and Asymptotic Solutions for Peristaltic Motion of Nonlinear Viscous Flows with Elastic Free Boundaries

A mathematical model for peristaltic motion of nonlinear viscous flows with elastic free boundaries is introduced. An iterative numerical method is used to solve the free boundary problem. Long wave asymptotic expansion is developed and the zeroth order approximation is used as the numerical initial condition. The existence and uniqueness of the solution for the free boundary equation derived from the long wave expansion are proved. Computations were conducted to study the long wave approximation, the numerical solutions for the exact equations, and the influences of the parameters on the solutions

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

Using optical coherence tomography and intravascular ultrasound imaging to quantify coronary plaque cap stress/strain and progression: A follow-up study using 3D thin-layer models

Accurate plaque cap thickness quantification and cap stress/strain calculations are of fundamental importance for vulnerable plaque research. To overcome uncertainties due to intravascular ultrasound (IVUS) resolution limitation, IVUS and optical coherence tomography (OCT) coronary plaque image data were combined together to obtain accurate and reliable cap thickness data, stress/strain calculations, and reliable plaque progression predictions. IVUS, OCT, and angiography baseline and follow-up data were collected from nine patients (mean age: 69; m: 5) at Cardiovascular Research Foundation with informed consent obtained. IVUS and OCT slices were coregistered and merged to form IVUS + OCT (IO) slices. A total of 114 matched slices (IVUS and OCT, baseline and follow-up) were obtained, and 3D thin-layer models were constructed to obtain stress and strain values. A generalized linear mixed model (GLMM) and least squares support vector machine (LSSVM) method were used to predict cap thickness change using nine morphological and mechanical risk factors. Prediction accuracies by all combinations (511) of those predictors with both IVUS and IO data were compared to identify optimal predictor(s) with their best accuracies. For the nine patients, the average of minimum cap thickness from IVUS was 0.17 mm, which was 26.08% lower than that from IO data (average = 0.23 mm). Patient variations of the individual errors ranged from ‒58.11 to 20.37%. For maximum cap stress between IO and IVUS, patient variations of the individual errors ranged from ‒30.40 to 46.17%. Patient variations of the individual errors of maximum cap strain values ranged from ‒19.90 to 17.65%. For the GLMM method, the optimal combination predictor using IO data had AUC (area under the ROC curve) = 0.926 and highest accuracy = 90.8%, vs. AUC = 0.783 and accuracy = 74.6% using IVUS data. For the LSSVM method, the best combination predictor using IO data had AUC = 0.838 and accuracy = 75.7%, vs. AUC = 0.780 and accuracy = 69.6% using IVUS data. This preliminary study demonstrated improved plaque cap progression prediction accuracy using accurate cap thickness data from IO slices and the differences in cap thickness, stress/strain values, and prediction results between IVUS and IO data. Large-scale studies are needed to verify our findings

Impact of flow rates in a cardiac cycle on correlations between advanced human carotid plaque progression and mechanical flow shear stress and plaque wall stress

<p>Abstract</p> <p>Background</p> <p>Mechanical stresses are known to play important roles in atherosclerotic plaque initiation, progression and rupture. It has been well-accepted that atherosclerosis initiation and early progression correlate negatively with flow wall shear stresses (FSS). However, mechanisms governing <it>advanced </it>plaque progression are not well understood.</p> <p>Method</p> <p>In vivo serial MRI data (patient follow-up) were acquired from 14 patients after informed consent. Each patient had 2-4 scans (scan interval: 18 months). Thirty-two scan pairs (baseline and follow-up scans) were formed with slices matched for model construction and analysis. Each scan pair had 4-10 matched slices which gave 400-1000 data points for analysis (100 points per slice on lumen). Point-wise plaque progression was defined as the wall thickness increase (WTI) at each data point. 3D computational models with fluid-structure interactions were constructed based on in vivo serial MRI data to extract flow shear stress and plaque wall stress (PWS) on all data points to quantify correlations between plaque progression and mechanical stresses (FSS and PWS). FSS and PWS data corresponding to both maximum and minimum flow rates in a cardiac cycle were used to investigate the impact of flow rates on those correlations.</p> <p>Results</p> <p>Using follow-up scans and maximum flow rates, 19 out of 32 scan pairs showed a significant <it>positive </it>correlation between WTI and FSS (positive/negative/no significance correlation ratio = 19/9/4), and 26 out of 32 scan pairs showed a significant <it>negative </it>correlation between WTI and PWS (correlation ratio = 2/26/4). Corresponding to minimum flow rates, the correlation ratio for WTI vs. FSS and WTI vs. PWS were (20/7/5) and (2/26/4), respectively. Using baseline scans, the correlation ratios for WTI vs. FSS were (10/12/10) and (9/13/10) for maximum and minimum flow rates, respectively. The correlation ratios for WTI vs. PWS were the same (18/5/9), corresponding to maximum and minimum flow rates.</p> <p>Conclusion</p> <p>Flow shear stress corresponding to the minimum flow rates in a cardiac cycle had slightly better correlation with WTI, compared to FSS corresponding to maximum flow rates. Choice of maximum or minimum flow rates had no impact on PWS correlations. Advanced plaque progression correlated positively with flow shear stress and negatively with plaque wall stress using follow-up scans. Correlation results using FSS at the baseline scan were inconclusive.</p

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

IVUS-based Fluid-structure Interaction Models for Novel Plaque Vulnerability Indices: A Study in Patients with Coronary Artery Disease

AbstractIt is believed that mechanical stresses play an important role in atherosclerotic plaque rupture process and may be used for better plaque vulnerability assessment and rupture risk predictions. IVUS data were acquired from 14 patients (11M, 3F, Mean age: 59,) for constructing 3D computational models combining fluid-structure interaction (FSI), cyclic bending due to cardiac contraction and patient-specific pressure loading to quantify mechanical conditions in the human coronary. The computational models were solved by a finite element package ADINA to obtain plaque wall stress (PWS), strain (PWSn) and flow shear stress (FSS) and investigate correlation between the mechanical conditions and morphological characteristics. For all 617 IVUS slices yielded from the 14 patients, plaque morphological features lipid percentage and min cap thickness were calculated for each slice, and three types of plaque morphology related indices: lipid index, cap index and morphological index (MPVI) were introduced as quantitative measures of plaque vulnerability. PWS, PWSn and FSS values at critical sites were denoted as critical plaque wall stress (CPWS), critical plaque wall strain (CPWSn) and critical flow shear stress (CFSS) for each slice, and a stress index was proposed based on the value of the CPWS. The conventional Pearson's correlation is used to analyze the correlation between each of the mechanical conditions and each plaque morphological feature indices. Our results suggest there is significant correlation between the CPWS and min cap thickness, cap index with the correlation coefficient r=-0.6570, r=0.8016 respectively, while the correlation between CPWS and lipid percentage and the lipid index are weaker (r=0.2209, r=0.2304) even though they are significantly correlated. The correlation results between CPWS and morphological index (r=0.7725, p-value<0.0001) showed there is a strong positive relationship between the mechanical stress and morphological features. For all 617 slices, the stress index has a 66.77% agreement with morphological index. More patient follow-up data and large-scale studies are needed to continue our investigations

Predicting coronary stenosis progression using plaque fatigue from IVUS-based thin-slice models: A machine learning random forest approach

Introduction: Coronary stenosis due to atherosclerosis restricts blood flow. Stenosis progression would lead to increased clinical risk such as heart attack. Although many risk factors were found to contribute to atherosclerosis progression, factors associated with fatigue is underemphasized. Our goal is to investigate the relationship between fatigue and stenosis progression based on in vivo intravascular ultrasound (IVUS) images and finite element models. Methods: Baseline and follow-up in vivo IVUS and angiography data were acquired from seven patients using Institutional Review Board approved protocols with informed consent obtained. Three hundred and five paired slices at baseline and follow-up were matched and used for plaque modeling and analysis. IVUS-based thin-slice models were constructed to obtain the coronary biomechanics and stress/strain amplitudes (stress/strain variations in one cardiac cycle) were used as the measurement of fatigue. The change of lumen area (DLA) from baseline to follow-up were calculated to measure stenosis progression. Nineteen morphological and biomechanical factors were extracted from 305 slices at baseline. Correlation analyses of these factors with DLA were performed. Random forest (RF) method was used to fit morphological and biomechanical factors at baseline to predict stenosis progression during follow-up. Results: Significant correlations were found between stenosis progression and maximum stress amplitude, average stress amplitude and average strain amplitude (p < 0.05). After factors selection implemented by random forest (RF) method, eight morphological and biomechanical factors were selected for classification prediction of stenosis progression. Using eight factors including fatigue, the overall classification accuracy, sensitivity and specificity of stenosis progression prediction with RF method were 83.61%, 86.25% and 80.69%, respectively. Conclusion: Fatigue correlated positively with stenosis progression. Factors associated with fatigue could contribute to better prediction for atherosclerosis progression