Experimental and numerical study on the hemodynamics of stenosed carotid bifurcation

Computational Assessment of Unsteady Flow Effects on Magnetic Nanoparticle Targeting Efficiency in a Magnetic Stented Carotid Bifurcation Artery

PURPOSE

Worldwide, cardiovascular disease is the leading cause of hospitalization and death. Recently, the use of magnetizable nanoparticles for medical drug delivery has received much attention for potential treatment of both cancer and cardiovascular disease. However, proper understanding of the interacting magnetic field forces and the hydrodynamics of blood flow is needed for effective implementation. This paper presents the computational results of simulated implant assisted medical drug targeting (IA-MDT) via induced magnetism intended for administering patient specific doses of therapeutic agents to specific sites in the cardiovascular system. The drug delivery scheme presented in this paper functions via placement of a faintly magnetizable stent at a diseased location in the carotid artery, followed by delivery of magnetically susceptible drug carriers guided by the local magnetic field. Using this method, the magnetic stent can apply high localized magnetic field gradients within the diseased artery, while only exposing the neighboring tissues, arteries, and organs to a modest magnetic field. The localized field gradients also produce the forces needed to attract and hold drug-containing magnetic nanoparticles at the implant site for delivering therapeutic agents to treat in-stent restenosis.

METHODS

The multi-physics computational model used in this work is from our previous work and has been slightly modified for the case scenario presented in this paper. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetic stented region using the magnetic properties of magnetite (Fe3O4) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. The electromagnetic coil produces a uniform magnetic field in the computational arterial flow model domain, while both the particles and the implanted stent are paramagnetic. A Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (Br = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10 nm-4 µm in diameter were evaluated. Two dimensionless numbers were evaluated in this work to characterize relative effects of Brownian motion (BM), magnetic force induced particle motion, and convective blood flow on particle motion.

RESULTS

The computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range of 0.7-4 µm, specifically in regions where flow separation and vortices are at a minimum. Similar to our previous work (which did not involve the use of a magnetic stent), it was also observed that the capture efficiency of particles decreases substantially with particle diameter, especially in the superparamagnetic regime. Contrary to our previous work, using a magnetic stent tripled the capture efficiency of superparamagnetic particles. The highest capture efficiency observed for superparamagnetic particles was 78% with an 8 T magnetic field strength and 65% with a 2 T magnetic field strength when analyzing 100 nm particles. For 10 nm particles and an 8 T magnetic field strength, the particle capture efficiency was 55% and for a 2 T magnetic field strength the particle capture efficiency was observed to be 43%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1 µm and above), and slower blood flow velocity improves the particle capture efficiency. The distribution of captured particles on the vessel wall along the axial and azimuthal directions is also discussed. Results for captured particles on the vessel wall along the axial flow direction showed that the particle density decreased along the axial direction, especially after the stented region. For the entrance section of the stented region, the captured particle density distribution along the axial direction is large, corresponding to the center-symmetrical distribution of the magnetic force in that section.

CONCLUSION

The simulation results presented in this work have shown to yield favorable capture efficiencies for micron range particles and superparamagnetic particles using magnetized implants such as the stent discussed in this work. The results presented in this work justify further investigation of MDT as a treatment technique for cardiovascular disease.

Computational Assessment of Magnetic Nanoparticle Targeting Efficiency in a Simplified Circle of Willis Arterial Model

This paper presents the methodology and computational results of simulated medical drug targeting (MDT) via induced magnetism intended for administering intravenous patient-specific doses of therapeutic agents in a Circle of Willis (CoW) model. The multi-physics computational model used in this work is from our previous works. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetized region using the magnetic properties of magnetite (Fe₃O₄) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. A Eulerian-Lagrangian technique is implemented to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (B_r = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10 nm to 4 µm in diameter were assessed. Two dimensionless numbers are also investigated a priori in this study to characterize relative effects of Brownian motion (BM), magnetic force-induced particle motion, and convective blood flow on particle motion. Similar to our previous works, the computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range, specifically in regions where flow separation and vortices are at a minimum. Additionally, it was observed that the capture efficiency of particles decreases substantially with smaller particle diameters, especially in the superparamagnetic regime. The highest capture efficiency observed for superparamagnetic particles was 99% with an 8T magnetic field strength and 95% with a 2T magnetic field strength when analyzing 100 nm particles. For 10 nm particles and an 8T magnetic field strength, the particle capture efficiency was 48%, and for a 2T magnetic field strength the particle capture efficiency was 33%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1 µm and above), and slower blood flow velocity increase the particle capture efficiency. The key finding in this work is that favorable capture efficiencies for superparamagnetic particles were observed in the CoW model for weak fields (B_r < 4T) which demonstrates MDT as a possible viable treatment candidate for cardiovascular disease.

In vitro Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review

Cardiovascular diseases are one of the leading causes of death globally and the most common pathological process is atherosclerosis. Over the years, these cardiovascular complications have been extensively studied by applying in vivo, in vitro and numerical methods (in silico). In vivo studies represent more accurately the physiological conditions and provide the most realistic data. Nevertheless, these approaches are expensive, and it is complex to control several physiological variables. Hence, the continuous effort to find reliable alternative methods has been growing. In the last decades, numerical simulations have been widely used to assess the blood flow behavior in stenotic arteries and, consequently, providing insights into the cardiovascular disease condition, its progression and therapeutic optimization. However, it is necessary to ensure its accuracy and reliability by comparing the numerical simulations with clinical and experimental data. For this reason, with the progress of the in vitro flow measurement techniques and rapid prototyping, experimental investigation of hemodynamics has gained widespread attention. The present work reviews state-of-the-art in vitro macro-scale arterial stenotic biomodels for flow measurements, summarizing the different fabrication methods, blood analogues and highlighting advantages and limitations of the most used techniques.

Blood flow simulations in patient-specific geometries of the carotid artery: A systematic review

Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) are currently widely applied in the study of blood flow parameters and their alterations under pathological conditions, which are important indicators for diagnosis of atherosclerosis. In this manuscript, a systematic review of the published literature was conducted, according to the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses, on the simulation studies of blood flow in patient-specific geometries of the carotid artery bifurcation. Scopus, PubMed and ScienceDirect databases were used in the literature search, which was completed on the 3rd of August 2020. Forty-nine articles were included after the selection process and were organized in two distinct categories: the CFD studies (36/49 articles), which comprise only the fluid analysis and the FSI studies (13/49 articles), which includes both fluid and Fluid-Structure domain in the analysis. The data of the research works was structured in different categories (Geometry, Viscosity models, Type of Flow, Boundary Conditions, Flow Parameters, Type of Solver and Validation). The aim of this systematic review is to demonstrate the methodology in the modelling, simulation and analysis of carotid blood flow and also identify potential gaps and challenges in this research field.

A Systematic Review for the Design of In Vitro Flow Studies of the Carotid Artery Bifurcation

PURPOSE

In vitro blood flow studies in carotid artery bifurcation models may contribute to understanding the influence of hemodynamics on carotid artery disease. However, the design of in vitro blood flow studies involves many steps and selection of imaging techniques, model materials, model design, and flow visualization parameters. Therefore, an overview of the possibilities and guidance for the design process is beneficial for researchers with less experience in flow studies.

METHODS

A systematic search to in vitro flow studies in carotid artery bifurcation models aiming at quantification and detailed flow visualization of blood flow dynamics results in inclusion of 42 articles.

RESULTS

Four categories of imaging techniques are distinguished: MRI, optical particle image velocimetry (PIV), ultrasound and miscellaneous techniques. Parameters for flow visualization are categorized into velocity, flow, shear-related, turbulent/disordered flow and other parameters. Model materials and design characteristics vary between study type.

CONCLUSIONS

A simplified three-step design process is proposed for better fitting and adequate match with the pertinent research question at hand and as guidance for less experienced flow study researchers. The three consecutive selection steps are: flow parameters, image modality, and model materials and designs. Model materials depend on the chosen imaging technique, whereas choice of flow parameters is independent from imaging technique and is therefore only determined by the goal of the study.

A Methodology to Assess Subregional Geometric Complexity for Tetralogy of Fallot Patients

During surgical repair of tetralogy of fallot (TOF), pulmonary valve preservation (preservative repair) has demonstrated improved long-term outcomes compared to repairs that incise into the valve annulus (nonpreservative repair). Given the influence of geometry on hemodynamics, the success of preservative repair may be linked to the suitability of the preoperative patient geometry. However, the specific patient anatomies that may be predisposed to successful preservative repair are unknown due to significant interpatient variability in right ventricular outflow tract (RVOT) and pulmonary artery geometries, as well as the limitations in current methods of subregional geometric analysis. As a first step toward understanding the link between geometry and hemodynamics in TOF patients at a subregion level, we characterize the TOF geometry from the right ventricular infundibulum (INF) to the left and right pulmonary arteries. Our process consists of segmentation of magnetic resonance (MR) images and analysis of cross-sectional slices of the geometries along the centerlines. For the INF, main, left, and right pulmonary arteries individually, we quantify geometric parameters important in determining hemodynamic characteristics such as flow separation and recirculation, which can influence the degree of regurgitation. Specifically, we calculate the diameter along the subregion length, the average diameter, length, and tortuosity for each segment, as well as the bifurcation, left pulmonary artery (LPA) and right pulmonary artery (RPA) branch angles. This approach enables direct geometric comparisons within and among patients and allows for observation of the range in anatomic presentation. We have applied this approach to a dataset of 11 postoperative TOF patients, repaired with both preservative and nonpreservative surgical techniques.

Study of correlation between wall shear stress and elasticity in atherosclerotic carotid arteries

OBJECTIVE

This paper presents the use of the texture matching method to measure the rabbit carotid artery elasticity value of the experimental group and control group respectively. It compares the experimental rabbits, when they are prompted by pathological histology to be at the period of carotid atherosclerosis fatty streaks and fiber plaques, with the control group.

METHODS

We have used ultrasound linear array probe for scanning the rabbit carotid arteries. This allows us to obtain the wall shear stress (WSS) and the elasticity values in the atherosclerotic arteries. Using statistical analysis, we are able to clarify whether the texture matching method can diagnose atherosclerosis at the early stage. We also analyze the rabbit carotid artery elasticity and WSS values to make sure whether there is a correlation between both. Combining the texture matching method with the WSS quantitative analysis in the future can enable better prediction of the occurrence and development of atherosclerosis by using noninvasive medical imaging techniques.

RESULTS

This study has confirmed that from the 2nd to the 10th week, with the development of atherosclerosis, the arterial WSS reduction has a negative correlation with the increasing of artery wall elasticity, which means that as the arterial WSS decreases the arterial wall becomes less elastic. Correlating shear stress with atherosclerosis can clarify that WSS can be used as one of the effective parameters of early diagnosis of atherosclerosis.

CONCLUSION

In summary, we have found that the elasticity value can reflect the degree of atherosclerosis more objectively. Therefore, by using noninvasive imaging, the quantitative analysis of shear stress and combined with texture matching method can assist in the early diagnosis of atherosclerosis.

Large eddy simulations for blood dynamics in realistic stenotic carotids

In this paper, we consider large eddy simulations (LES) for human stenotic carotids in presence of atheromasic plaque, a pathological condition where transitional effects to turbulence may occur, with relevant clinical implications such as plaque rupture. We provide a reference numerical solution obtained at high resolution without any subgrid scale model, to be used to assess the accuracy of LES simulations. In the context we are considering, ie, hemodynamics, we cannot refer to a statistically homogeneous, isotropic, and stationary turbulent regime; hence, the classical Kolmogorov theory cannot be used. For this reason, a mesh size and a time step are deemed fine enough if they allow to capture all the features of the velocity field in the shear layers developed after the bifurcation. To assess these requirements, we consider a simplified model of the evolution of a 2D shear layer, a relevant process in the formation of transitional effects in our case. Then, we compare the results of LES σ model (both static and dynamic) and mixed LES models (where also a similarity contribution is considered). In particular, we consider a realistic scenario of a human carotid, and we use the reference solution as gold standard. The results highlight the accuracy of the LES σ models, especially for the static model.

Large eddy simulations of blood dynamics in abdominal aortic aneurysms

We study the effects of transition to turbulence in abdominal aortic aneurysms (AAA). The presence of transitional effects in such districts is related to the heart pulsatility and the sudden change of diameter of the vessels, and has been recorded by means of clinical measures as well as of computational studies. Here we propose, for the first time, the use of a large eddy simulation (LES) model to accurately describe transition to turbulence in realistic scenarios of AAA obtained from radiological images. To this aim, we post-process the obtained numerical solutions to assess significant quantities, such as the ensemble-averaged velocity and wall shear stress, the standard deviation of the fluctuating velocity field, and vortical structures educed via the so-called Q-criterion. The results demonstrate the suitability of the considered LES model and show the presence of significant transitional effects around the impingement region during the mid-deceleration phase.

Sensitivity study on modelling a flow-diverting stent as a porous medium using computational fluid dynamics

The flow-diverting (FD) stent has become a commonly used endovascular device to treat cerebral aneurysms. This discourages blood from entering the aneurysm, thereby reducing the likelihood of aneurysm rupture. Using computational fluid dynamics (CFD) to simulate the aneurysmal haemodynamics after FD treatment could help clinicians predict the stent effectiveness prior to the real procedure in the patient. As an alternative to modelling the stent as a fine wire mesh, modelling the FD stent as a porous medium was established to save computational time, and has also been proved capable of predicting the same haemodynamics as obtained using the real FD stent geometry. The flow resistance effect of a porous-medium stent may differ with respect to its morphology or permeability; however, the flow resistance effect after adjusting these parameters had not been clarified. In this study, we analysed the haemodynamic changes caused by alterations of porous-medium thickness and permeability, thereby providing future porous-medium stent simulations with important information on the respective parametric sensitivities. We found significant sensitivity to permeability. Results were insensitive to thickness when permeability was adjusted beforehand to compensate. We also compared our results with observations from an in-vitro model, and found good agreement. This supports adoption of porous-medium models in future work.

STENOSIS EFFECTS ON THE FLUID MECHANICS OF THE COMMON CAROTID ARTERY BIFURCATION FOR UNSTEADY FLOWS

The time-varying blood flow in the common carotid artery (CCA) bifurcation is numerically studied on the basis of Navier-Stokes equations for four different cases, including cases with stenoses at different sites in the vicinity of the bifurcation. The cases studied were: (a) without stenoses, (b) with one stenosis upstream the bifurcation, (c) with two opposite stenoses upstream the bifurcation and (d) with an additional stenosis on the apex of the bifurcation. The mesh was generated via a geometry reconstruction and imported into a computational fluid dynamics (CFD) solver. The numerical results of the blood flow in the CCA bifurcation gave a detailed picture of the axial velocity and presented as velocity and vorticity magnitudes. More specifically, it was observed that the appearance of stenotic regions upstream the bifurcation affect both the velocity and vorticity characteristics, whereas a stenoses on the apex of the bifurcation seems to have a small effect on the vorticity characteristics downstream the flow.

A PARAMETRIC NUMERICAL INVESTIGATION OF LOCAL HAEMODYNAMICS IN THE END-TO-SIDE ANASTOMOSIS OF CERVICAL-TO-PETROUS BYPASS BASED ON REAL GEOMETRY OF INTERNAL CAROTID ARTERY

Bypass reconstructed from the cervical segment of internal carotid artery (ICA) to its petrous segment allows high-volume bypass flow without any risk of intracranial dissection. The purpose of this study was to investigate the geometric effect on the end-to-side anastomosis of cervical-to-petrous bypass, for its close relationship to local haemodynamic and the long-term performance of bypass. We focused on two controllable geometric parameters: diameter ratio (Φ) and angle (α) between the graft and host arteries. Different models covering a range of Φ (0.75, 1 and 1.25) and α (30°, 45°, 60° and 90°) were constructed based on real geometry of human ICA. Numerical simulations of blood flow were performed in physiological flow condition. The flow patterns, flow distributions, time-average wall shear stress (TAWSS) and oscillatory shear index (OSI) in different models were compared. Our results showed geometric factors have influence on both the local haemodynamic parameters and the flow velocity through downstream branches. Of models with different geometric parameters, the model with Φ ≥ 1 or α = 45° were the most optimized considering haemodynamic performance.

WALL SHEAR STRESSES IN A FLUID–STRUCTURE INTERACTION MODEL OF PULSE WAVE PROPAGATION

In our prior paper, a fluid–structure interaction model of pulse wave propagation, called the elastic tube model, has been developed. The focus of this paper is wall shear stress (WSS) in this model and the effects of different parameters, including rigid walls, wall thickness, and internal radius. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic isotropic, and incompressible. A fluid–structure interaction scheme is constructed using a finite element method. The results demonstrate the elastic tube plays an important role in WSS distributions of wave propagation. It is shown that there is a time delay between the WSS waveforms at different locations in the elastic tube model while the time delay cannot be observed clearly in the rigid tube model. Compared with the elastic tube model, the increase of the wall thickness makes disturbed WSS distributions, however WSS values are increased greatly due to the decrease of the internal radius. The results indicate that the effects of different parameters on WSS distributions are significant. The proposed model gives valid results.

THE IMPACT OF THE NUMBER OF TEARS IN PATIENT-SPECIFIC STANFORD TYPE B AORTIC DISSECTING ANEURYSM: CFD SIMULATION

It is believed that the progression of Stanford type B aortic dissection is closely associated with vascular geometry and hemodynamic parameters. The hemodynamic differences owing to the presence of greater than two tears have not been explored. The focus of the present study is to investigate the impact of an additional re-entry tear on the flow, pressure and wall shear stress distribution in the dissected aorta. A 3D aorta model with one entry and one re-entry tear was generated from computed tomography (CT) angiographic images of a patient with Stanford Type B aortic dissection. To investigate the hemodynamic effect of more than two tear locations, an additional circular re-entry tear was added 24 mm above the original re-entry tear. Our simulation results showed that the presence of an additional re-entry tear provided an extra return path for blood back to the true lumen during systole, and an extra outflow path into the false lumen during diastole. The presence of this additional path led to a decrease in the false lumen pressure, particularly at the distal region. Meanwhile, the presence of this additional tear causes no significant difference on the time average wall shear stress (TAWSS) distribution except at regions adjacent to re-entry tear 2. Moderate and concentrated TAWSS was observed at the bottom region of this additional tear which may lead to further extension of the tear distally.

Mild anastomotic stenosis in patient-specific CABG model may enhance graft patency: a new hypothesis

It is well known that flow patterns at the anastomosis of coronary artery bypass graft (CABG) are complex and may affect the long-term patency. Various attempts at optimal designs of anastomosis have not improved long-term patency. Here, we hypothesize that mild anastomotic stenosis (area stenosis of about 40–60%) may be adaptive to enhance the hemodynamic conditions, which may contribute to slower progression of atherosclerosis. We further hypothesize that proximal/distal sites to the stenosis have converse changes that may be a risk factor for the diffuse expansion of atherosclerosis from the site of stenosis. Twelve (12) patient-specific models with various stenotic degrees were extracted from computed tomography images using a validated segmentation software package. A 3-D finite element model was used to compute flow patterns including wall shear stress (WSS) and its spatial and temporal gradients (WSS gradient, WSSG, and oscillatory shear index, OSI). The flow simulations showed that mild anastomotic stenosis significantly increased WSS (>15 dynes⋅cm⁻²) and decreased OSI (<0.02) to result in a more uniform distribution of hemodynamic parameters inside anastomosis albeit proximal/distal sites to the stenosis have a decrease of WSS (<4 dynes⋅cm⁻²). These findings have significant implications for graft adaptation and long-term patency.

HEMOLYSIS ANALYSIS OF AXIAL BLOOD PUMPS WITH VARIOUS STRUCTURE IMPELLERS

Low hemolysis is an important factor for axial blood pumps that has been used in patients with heart failure. The structure of impellers plays a key role in the hemolytic properties of axial blood pumps. Axial blood pumps with various structure impellers exhibit different hemolytic characteristic. In the present study, we aimed to investigate the type of impellers structures in axial blood pumps that contain the best low hemolytic properties. Also, it is expensive and time-consuming to validate the axial blood pump's hemolytic property by in vivo experiments. Therefore, in the present study, the numerical method was applied to analyze the hemolytic property in a blood pump. Specifically, the hemolysis of the pump was calculated by using a forward Euler approach based on the changes in shear stress and related exposure times along the particle trace lines. The different vane structures and rotational speed that affect hemolysis were analyzed and compared. The results showed that long–short alternant vanes exhibited the best hemolytic property which could be utilized in the optimization design of axial blood pumps.

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.

Hemodynamic Changes Caused by Flow Diverters in Rabbit Aneurysm Models: Comparison of Virtual and Realistic FD Deployments Based on Micro-CT Reconstruction

Adjusting hemodynamics via flow diverter (FD) implantation is emerging as a novel method of treating cerebral aneurysms. However, most previous FD-related hemodynamic studies were based on virtual FD deployment, which may produce different hemodynamic outcomes than realistic (in vivo) FD deployment. We compared hemodynamics between virtual FD and realistic FD deployments in rabbit aneurysm models using computational fluid dynamics (CFD) simulations. FDs were implanted for aneurysms in 14 rabbits. Vascular models based on rabbit-specific angiograms were reconstructed for CFD studies. Real FD configurations were reconstructed based on micro-CT scans after sacrifice, while virtual FD configurations were constructed with SolidWorks software. Hemodynamic parameters before and after FD deployment were analyzed. According to the metal coverage (MC) of implanted FDs calculated based on micro-CT reconstruction, 14 rabbits were divided into two groups (A, MC >35%; B, MC <35%). Normalized mean wall shear stress (WSS), relative residence time (RRT), inflow velocity, and inflow volume in Group A were significantly different (P<0.05) from virtual FD deployment, but pressure was not (P>0.05). The normalized mean WSS in Group A after realistic FD implantation was significantly lower than that of Group B. All parameters in Group B exhibited no significant difference between realistic and virtual FDs. This study confirmed MC-correlated differences in hemodynamic parameters between realistic and virtual FD deployment.