Effect of porous media of the stenosed artery wall to the coronary physiological diagnostic parameter: A computational fluid dynamic analysis

Numerical investigation of LDL nanoparticle collision in coronary artery grafts with porous wall and different implantation angles and two state of inlet velocity

This study aimed to reduce the risk of graft occlusion by evaluating the two-phase flow of blood and LDL nanoparticles in coronary artery grafts. The study considered blood as an incompressible Newtonian fluid, with the addition of LDL nanoparticles, and the artery wall as a porous medium. Two scenarios were compared, with constant inlet velocity (CIV) and other with pulsatile inlet velocity (PIV), with LDL nanoparticles experiencing drag, wall-induced lift, and induced Saffman lift forces, or drag force only. The study also evaluated the concentration polarization of LDLs (CP of LDLs) near the walls, by considering the artery wall with and without permeation. To model LDL nanoparticles, the study randomly injected 100, 500, and 1000 nanoparticles in three release states at each time step, using different geometries. Numerical simulations were performed using COMSOL software, and the results were presented as relative collision of nanoparticles to the walls in tables, diagrams, and shear stress contours. The study found that a graft implantation angle of 15° had the most desirable conditions compared to larger angles, in terms of nanoparticle collision with surfaces and occlusion. The nanoparticle release modes behaved similarly in terms of collision with the surfaces. A difference was observed between CIV and PIV. Saffman lift and wall-induced lift forces having no effect, possibly due to the assumption of a porous artery wall and perpendicular outlet flow. In case of permeable artery walls, relative collision of particles with the graft wall was larger, suggesting the effect of CP of LDLs.

Numerical simulation of hemodynamics in patient-specific pulmonary artery stenosis

BACKGROUND

The incidence rate of pulmonary artery stenosis is increasing year by year and its numerical simulation has become a key project of biomedical engineering.

OBJECTIVE

The purpose of this work is to study the changes of hemodynamic parameters in patient-specific pulmonary artery stenosis.

METHODS

A pulmonary artery stenosis model is established based on patient-specific computed tomography (CT) images. According to the actual anatomy of patient-specific pulmonary artery stenosis, the stenosis area is simulated using a porous medium to study its hemodynamic changes. The computational fluid dynamics (CFD) method is used to simulate the hemodynamic changes of pulmonary artery stenosis, and to explore the mechanical characteristics between blood flow and vessel wall.

RESULTS

The results suggest that the blood pressures of arterial branches increase and the pressure drop at both ends of the stenosis is higher. There is a high flow rate and wall shear stress at the stenosis.

CONCLUSION

This study shows that the hemodynamic model of pulmonary artery stenosis can be accurately reconstructed by achieving numerical simulation of the local stenosis through CT images, and this work has important implications for improving the confidence of clinical diagnosis and treatment of pulmonary artery diseases.

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Investigation of two-way fluid-structure interaction of blood flow in a patient-specific left coronary artery

BACKGROUND

The blood flow in the human artery has been a subject of sincere interest due to its prime importance linked with human health. The hemodynamic study has revealed an essential aspect of blood flow that eventually proved to be paramount to make a correct decision to treat patients suffering from cardiac disease.

OBJECTIVE

The current study aims to elucidate the two-way fluid-structure interaction (FSI) analysis of the blood flow and the effect of stenosis on hemodynamic parameters.

METHODS

A patient-specific 3D model of the left coronary artery was constructed based on computed tomography (CT) images. The blood is assumed to be incompressible, homogenous, and behaves as Non-Newtonian, while the artery is considered as a nonlinear elastic, anisotropic, and incompressible material. Pulsatile flow conditions were applied at the boundary. Two-way coupled FSI modeling approach was used between fluid and solid domain. The hemodynamic parameters such as the pressure, velocity streamline, and wall shear stress were analyzed in the fluid domain and the solid domain deformation.

RESULTS

The simulated results reveal that pressure drop exists in the vicinity of stenosis and a recirculation region after the stenosis. It was noted that stenosis leads to high wall stress. The results also demonstrate an overestimation of wall shear stress and velocity in the rigid wall CFD model compared to the FSI model.

Comparison Between 5- and 1-Year Outcomes Using Cutoff Values of Pressure Drop Coefficient and Fractional Flow Reserve for Diagnosing Coronary Artery Diseases

Background

The current pressure-based coronary diagnostic index, fractional flow reserve (FFR), has a limited efficacy in the presence of microvascular disease (MVD). To overcome the limitations of FFR, the objective is to assess the recently introduced pressure drop coefficient (CDP), a fundamental fluid dynamics-based combined pressure–flow index.

Methods

We hypothesize that CDP will result in improved clinical outcomes in comparison to FFR. To test the hypothesis, chi-square test was performed to compare the percent major adverse cardiac events (%MACE) at 5 years between (a) FFR < 0.75 and CDP > 27.9 and (b) FFR < 0.80 and CDP > 25.4 groups using a prospective cohort study. Furthermore, Kaplan–Meier survival curves were compared between the FFR and CDP groups. The results were considered statistically significant for p < 0.05. The outcomes of the CDP arm were presumptive as clinical decision was solely based on the FFR.

Results

For the complete patient group, the %MACE in the CDP > 27.9 group (10 out of 35, 29%) was lower in comparison to the FFR < 0.75 group (11 out of 20, 55%), and the difference was near significant (p = 0.05). The survival analysis showed a significantly higher survival rate (p = 0.01) in the CDP > 27.9 group (n = 35) when compared to the FFR < 0.75 group (n = 20). The results remained similar for the FFR = 0.80 cutoff. The comparison of the 5-year MACE outcomes with the 1-year outcomes for the complete patient group showed similar trends, with a higher statistical significance for a longer follow-up period of 5 years.

Conclusion

Based on the MACE and survival analysis outcomes, CDP could possibly be an alternate diagnostic index for decision-making in the cardiac catheterization laboratory.

Clinical Trial Registration

www.ClinicalTrials.gov, identifier NCT01719016.

Numerical analysis of stenoses severity and aortic wall mechanics in patients with supravalvular aortic stenosis

Supravalvular aortic stenosis (SVAS) is an aortic malformation characterized by a narrowing of the ascending aorta, resulting in abnormal hemodynamics and pressure drop across the stenosed region. It has been observed that the pressure drops measured from Doppler ultrasound exams often tend to be higher than those obtained from invasive cardiac catheterization. These misleadingly elevated pressure measurements may drive the decision to refer patients for surgical treatment prematurely. Considering this strong clinical association, the purpose of this work is to develop a computational modeling approach using a two-way coupled fluid-structure interaction methodology to determine an accurate prediction of trans-stenotic pressure drop and to further highlight the discrepancy between the SVAS assessment methods. Blood is modeled using Navier-Stokes equations while the aortic wall is simulated by a composite poroelastic structure to represent the three main layers of the arterial wall. The relationship between aortic wall elasticity and the blood flow conditions is examined in varying levels of stenosis, ranging from mild to severe degrees of vessel diameter narrowing. A substantial overestimation of the traditional Doppler pressure drop measurement is observed, especially for severe stenosis levels. The simulation results indicate that elasticity of the aortic wall has a relatively little effect on trans-stenotic pressure drop for the range of mild to moderate SVAS cases, but predicted to have a profound effect for severe SVAS cases. Moreover, significant sensitivity to the pressure drop across the SVAS region from stenosis severity is observed.

Mathematical model of atherosclerotic aneurysm

Atherosclerosis is a major cause of abdominal aortic aneurysm (AAA) and up to 80% of AAA patients have atherosclerosis. Therefore it is critical to understand the relationship and interactions between atherosclerosis and AAA to treat atherosclerotic aneurysm patients more effectively. In this paper, we develop a mathematical model to mimic the progression of atherosclerotic aneurysms by including both the multi-layer structured arterial wall and the pathophysiology of atherosclerotic aneurysms. The model is given by a system of partial differential equations with free boundaries. Our results reveal a 2D biomarker, the cholesterol ratio and DDR1 level, assessing the risk of atherosclerotic aneurysms. The efficacy of different treatment plans is also explored via our model and suggests that the dosage of anti-cholesterol drugs is significant to slow down the progression of atherosclerotic aneurysms while the additional anti-DDR1 injection can further reduce the risk.

Influence of bifurcation angle in left coronary artery with stenosis: A CFD analysis

BACKGROUND: The left coronary artery commonly known as LCA gets divided into two branches, such as the left circumflex (LCX) and left anterior descending (LAD) at a particular angle. This angle is varies from person to person. The present computational study contributes remarkable expertise about the influence of this angle variation on the hemodynamic parameters in the presence of 80% area stenosis at the LAD branch. OBJECTIVE: This study aimed to compare the effect of the bifurcation angle on hemodynamic parameters in the left coronary artery with 80% stenosis. METHOD: Computational models of left coronary bifurcation angles of 30°, 60°, 90°, 120° were developed to understand the flow behavior of left coronary artery branches. The 80% area stenosis (AS) is considered at the LAD branch immediate to bifurcation. RESULTS: Measurements of pressure, velocity and wall shear stress were carried out corresponding to various bifurcation angles. It was found that the drop-in pressure increases as the angle increases from narrow to wider. A slight elevation in the velocity at the stenosis was observed. In addition, the obtained results further reveal a recirculation region immediately after the plaque, which leads to more deposition of plaque in the flow obstructed area. It is known that the shear stress at the arterial wall across the stenosis increases as the angle of bifurcation increases from narrow to wider. CONCLUSIONS: The bifurcation of the left coronary artery and size of the stenosis have a notable impact on the pressure and wall shear stress. These two factors should be given due consideration by cardiologists to assess the complexity of stenosis in the LCA branches.

Analysis of the formation mechanism and occurrence possibility of Post-Stenotic Dilatation of the aorta by CFD approach

BACKGROUND AND OBJECTIVE

Post-Stenotic Dilatation (PSD), the common complication of coarctation of the aorta (COA), is a progressive disease involving aortic aneurysm and even rupture. However, there has been no definitive method that could investigate the mechanism of PSD formation, progression and rupture. The purpose of the present work is to analyze the mechanism behind PSD formation and to further assess the risk of COA patients with different coarctation degrees deteriorating into PSD.

METHOD

Three-dimensional non-Newtonian (Carreau-Yasuda) hemodynamic simulations are performed throughout the cardiac cycle, and a novel parameter (λ_ci¯ intensity) is proposed to evaluate the intensity of vortices within the aorta. The PSD geometry is reconstructed from Computed Tomography scans. To analyze the formation mechanism and occurrence possibility of PSD, the computer technology is utilized to restore the expansive and/or narrow regions to obtain its previous state (COA) and control group (Normal), and to modify the minimum diameter to obtain the aortas with different coarctation degrees. The clinical cases of pre- and post-operation are further introduced to verify the analysis.

RESULTS

Compared with the Normal, the vortical structures with higher swirling strength are generated and accumulated at the downstream of the coarctation segment after COA occurrence, and partially disappear in the wake of PSD formation. The sequence of λ_ci¯ intensity is COA > PSD > Normal and pre-operation > post-operation. With increasing the degree of coarctation, the λ_ci¯ intensity is higher and the jet-flow becomes more drastic.

CONCLUSIONS

The formation of PSD is caused by the vortical structures with higher swirling strength accumulating at the downstream of the coarctation segment. An increase in coarctation degree elevates the risk of PSD occurrence and even aneurysmal dilatation.

Bifurcation analysis of a free boundary model of the atherosclerotic plaque formation associated with the cholesterol ratio

The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown to have a high correlation with the cardiovascular risk assessment. Is it possible to quantify the correlation mathematically? In this paper, we develop a bifurcation analysis for a mathematical model of the plaque formation with a free boundary in the early stage of atherosclerosis. This bifurcation analysis, to the ratio of LDL/HDL, is based on explicit formulations of radially symmetric steady-state solutions. By performing the perturbation analysis to these solutions, we establish the existence of bifurcation branches and derive a theoretical condition that a bifurcation occurs for different modes. We also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all theoretical results.

Numerical investigation of the blood flow through the middle cerebral artery

Introduction: The middle cerebral artery (MCA) is one of the three major paired arteries that supply the blood to the cerebrum. In the present study, the three-dimensional (3D) blood flow in the left MCA was numerically simulated by using the medical imaging. Methods: The arterial geometry was obtained by applying the CT angiography of the MCA of a 75-year-old man. The blood flow was assumed to be laminar and unsteady. Numerical simulations were done by commercial software package COMSOL Multiphysics 5.2. In this software, the Galerkin's finite element method was applied to solve the governing equations. Results: It was found that the results obtained for the Newtonian and non-Newtonian models of blood do not differ from each other significantly. Thus, the Newtonian model for blood flow in the MCA is acceptable. Also, the most susceptible region of the MCA for Atherosclerosis was detected. Conclusion: It can be concluded that the application of the Newtonian model for the blood flowing in the MCA is acceptable. Also, atherosclerosis has the potential to occur at the middle of a branch of the MCA which has the highest geometrical curvature.

THE MECHANICAL FACTORS INFLUENCING THE ASSESSMENT OF INTERMEDIATE STENOSIS SEVERITY EXPLAINED THROUGH FRACTIONAL FLOW RESERVE

Assessment of intermediate coronary lesions with diameter stenosis of 40% to 70% severity is being a challenge for cardiologist to identify potentially ischemic stenosis for revascularization and nonculprit stenosis which can be deferred from stenting. An invasive coronary angiography and intravascular ultrasound provide anatomic information of stenosis severity whereas an invasive fractional flow reserve index (FFR) provides the functional significance of the stenosis severity. The measurement of functional significance of stenosis severity minimizes the procedural complications such as coronary dissection, in stent restenosis etc. rather than anatomical significance measure. The FFR cutoff value of [Formula: see text]0.8 is used to distinguish ischemic and nonischemic stenosis. The FFR is clinically well validated even though it is influenced by the mechanical factors such as hyperemic flow and guide wire insertion. In recent times, noninvasive coronary computed tomography (CCTA) modality has become popular in the diagnosis of coronary artery disease. The CCTA permits the assessment of cross-sectional parameters such as minimum lumen area and lumen diameter, lesion length and plaque morphology. However, the CCTA provides limited information on the functional significance of stenotic lesions as compared to FFR. The purpose of this review is to discuss the mechanical factors influencing the invasive FFR while assessing the functional significance of intermediate stenosis severity. In addition, the hidden mechanical factors influencing the noninvasive CCTA assessment of stenosis severity will be discussed from the critical information obtained from FFR which could be beneficial for the clinician particularly in the assessment of intermediate stenosis severity.

The influence of artery wall curvature on the anatomical assessment of stenosis severity derived from fractional flow reserve: a computational fluid dynamics study

This study aims to investigate the influence of artery wall curvature on the anatomical assessment of stenosis severity and to identify a region of misinterpretation in the assessment of per cent area stenosis (AS) for functionally significant stenosis using fractional flow reserve (FFR) as standard. Five artery models of different per cent AS severity (70, 75, 80, 85 and 90%) were considered. For each per cent AS severity, the angle of curvature of the arterial wall varied from straight to an increasingly curved model (0°, 30°, 60°, 90° and 120°). Computational fluid dynamics was performed under transient physiologic hyperemic flow conditions to investigate the influence of artery wall curvature on the pressure drop and the FFR. The findings in this study may be useful in in vitro anatomical assessment of functionally significant stenosis. The FFR decreased with increasing stenosis severity for a given curvature of the artery wall. Moreover, a significant decrease in FFR was found between straight and curved models discussed for a given severity condition. These findings indicate that the curvature effect was included in the FFR assessment in contrast to minimum lumen area (MLA) or per cent AS assessment. The MLA or per cent AS assessment may lead to underestimation of stenosis severity. From this numerical study, an uncertainty region could be evaluated using the clinical FFR cutoff value of 0.8. This value was observed at 81.98 and 79.10% AS for arteries with curvature angles of 0° and 120° respectively. In conclusion, the curvature of the artery should not be neglected in in vitro anatomical assessment.

Numerical investigation of the effect of stenosis geometry on the coronary diagnostic parameters

The present study deals with the functional severity of a coronary artery stenosis assessed by the fractional flow reserve (FFR). The effects of different geometrical shapes of lesion on the diagnostic parameters are unknown. In this study, 3D computational simulation of blood flow in three different geometrical shapes of stenosis (triangular, elliptical, and trapezium) is considered in steady and transient conditions for 70% (moderate), 80% (intermediate), and 90% (severe) area stenosis (AS). For a given percentage AS, the variation of diagnostic parameters which are derived from pressure drop across the stenosis was found in three different geometrical shapes of stenosis and it was observed that FFR is higher in triangular shape and lower in trapezium shape. The pressure drop coefficient (CDP) was higher in trapezium shape and lower in triangular model whereas the LFC shows opposite trend. From the clinical perspective, the relationship between percentage AS and FFR is linear and inversely related in all the three models. A cut-off value of 0.75 for FFR was observed at 76.5% AS in trapezium model, 79.5% in elliptical model, and 82.7% AS for the triangular shaped model. The misinterpretation of the functional severity of the stenosis is in the region of 76.5%-82.7 % AS from different shapes of stenosis models.