Computational analysis of coupled blood-wall arterial LDL transport

Comparative study of plaque surface temperature and blood heat transfer in a stenosed blood vessel with different symmetrical configurations

The presence of macrophage cells inside plaque can lead to a change in plaque temperature, which can be measured by using arterial wall thermographic techniques to predict the severity of stenosis in the vessel without complicated surgery. This study aims to analyze the effect of plaque symmetricity with a similar degree of stenosis (DOS) on plaque surface temperature and blood heat transfer in a straight vessel. This analysis aims towards predicting the severity of stenosis in a straight blood vessel through plaque temperature as an indicator. Two cases are being analyzed here; case 1 and case 2 refer to having similar vessel dimensions and an overall degree of stenosis (DOS) of 70%, with the exception of case 1 having a symmetrically developed plaque while case 2 refers to an asymmetrically developed plaque. Euler-Euler multiphase method with the application of the granular model is being applied in this study. At peak systole (0.2 s into the 10th cardiac cycle) in a cardiac cycle, the increase in plaque surface temperature at exit is higher in case of a symmetrically developed stenosis compared to an asymmetric one but the reverse situation happens during end systole (0.5 s into the 10th cardiac cycle). Although the population of macrophages in a plaque is a deciding factor of the thermal signature of a plaque, the symmetricity variation also needs to be taken into consideration while plaque progression is being diagnosed through thermographic technique.

Computational modeling of low-density lipoprotein accumulation at the carotid artery bifurcation after stenting

Restenosis typically occurs in regions of low and oscillating wall shear stress, which also favor the accumulation of atherogenic macromolecules such as low-density lipoprotein (LDL). This study aims to evaluate LDL transport and accumulation at the carotid artery bifurcation following carotid artery stenting (CAS) by means of computational simulation. The computational model consists of coupled blood flow and LDL transport, with the latter being modeled as a dilute substance dissolved in the blood and transported by the flow through a convection-diffusion transport equation. The endothelial layer was assumed to be permeable to LDL, and the hydraulic conductivity of LDL was shear-dependent. Anatomically realistic geometric models of the carotid bifurcation were built based on pre- and post-stent computed tomography (CT) scans. The influence of stent design was investigated by virtually deploying two different types of stents (open- and closed-cell stents) into the same carotid bifurcation model. Predicted LDL concentrations were compared between the post-stent carotid models and the relatively normal contralateral model reconstructed from patient-specific CT images. Our results show elevated LDL concentration in the distal section of the stent in all post-stent models, where LDL concentration is 20 times higher than that in the contralateral carotid. Compared with the open-cell stents, the closed-cell stents have larger areas exposed to high LDL concentration, suggesting an increased risk of stent restenosis. This computational approach is readily applicable to multiple patient studies and, once fully validated against follow-up data, it can help elucidate the role of stent strut design in the development of in-stent restenosis after CAS.

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Effect of transport parameters on atherosclerotic lesion growth: A parameter sensitivity analysis

BACKGROUND

Atherosclerosis is a degenerative disease of the arterial wall. It results in the formation of progressively growing plaque lesions that can harden and narrow their host arteries. Current computational models of the inflammatory process that govern atherosclerosis growth are reliant on a number of parameters that can freely vary and whose precise values are not well known.

METHODS

To identify the significance of variation in such parameters, a parametric sensitivity study had been conducted on the blood density, blood viscosity, plasma viscosity and bulk flow low density lipoprotein (LDL) concentration. Using computational modeling, the significance of variation in these parameters was assessed on the transport of LDL. The simulation was performed via the 2^k factorial experimental design, which was conducted to identify the significance of the select parameters on the intima LDL concentration and endothelial LDL coverage area.

RESULTS

Results identified the blood viscosity and bulk flow LDL concentration are the dominant parameters for the atherosclerotic lesion growth. The coverage of LDL on the arterial wall surface was strongly dependent on the blood viscosity. The significance of these findings was discussed.

CONCLUSION

This statistical study identifies two dominating blood factors, LDL concentration and blood viscosity, and how they influence atherosclerosis which will serves as a guideline for further investigation on the atherosclerosis topic.

A Mixture Theory Model for Blood Combined With Low-Density Lipoprotein Transport to Predict Early Atherosclerosis Regions in Idealized and Patient-Derived Abdominal Aorta

Genesis and onset of atherosclerosis are greatly influenced by hemodynamic forces. Two-phase transient computational fluid dynamic (CFD) simulations are performed using a mixture theory model for blood, and a transport equation for low-density lipoprotein (LDL), in idealized and patient-derived abdominal aorta to predict the sites at risk for atherosclerosis. Flow patterns at different time instants and relevant hemodynamic indicators-wall shear stress (WSS)-based (time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT)), and LDL concentration-are used concurrently to predict the susceptible sites of atherosclerosis. In the case of idealized geometry, flow recirculations are observed on the posterior wall opposite the superior mesenteric artery and below the renal bifurcations. Low TAWSS, high OSI, high RRT and high concentration of LDL are observed in these regions. This suggests that in idealized abdominal aorta, the posterior wall proximal to the renal artery junction is more prone to atherosclerosis. This matches qualitatively with the experimental and simulation data in the literature. In the case of patient-derived geometry, flow reversal, low TAWSS, high OSI and high RRT are observed infrarenal on the anterior wall. Further, high concentration of LDL is observed at the same location on the anterior wall suggesting anterior wall distal to the renal artery junction is more prone to atherosclerosis. These findings demonstrate the use of a novel method to predict the sites at risk for atherosclerosis in geometries where complexities like junctions and curvature play a major role.

Computer modeling of pulsatile blood flow in elastic artery using a software program for application in biomedical engineering

BACKGROUND AND OBJECTIVE

Atherosclerosis-a condition in which an artery is constricted-alters blood flow in the artery, that can exacerbate the condition. Focusing on previous studies, it can be seen that the k-ε model has been used in the simulation. Therefore, the reverse flow on the back of stenosis is not well represented. In this study, the simulated results are much closer to clinical results, relying on the use of physiological pulses, and considering elasticity of the vessel wall, and the applying k-ω model. It can therefore be claimed that a much more accurate prediction will be made regarding the formation, development and progression of the disease.

METHODS

Modeling biological systems usually contain many parameters, which cannot be calculated experimentally, or are too costly and time consuming. In addition, it is occasionally required to examine the influence of different physical variables, which, given the complexity of the governing equations, make analytical methods feasible (or very limited). The present study is an attempt to investigate the turbulent pulsatile blood flow in an elastic artery with single and double stenoses using a finite element software program, ADINA 8.8.

RESULTS

According to the results, the k - ω turbulence model predicted a larger reverse flow in the post-stenotic region and between the two stenoses in comparison with the k - ε model. In other words, the k - ω model results suggest that a larger region is prone to atherosclerosis. In addition, that the k - ε model predicted a greater maximum shear stress at the throat and a shorter reverse flow region (Mean WSS < 0) in both stenosis scenarios. In other words, relative to the k - ε model, the k - ω model underestimated the damage to the plaque and the risk of its rupture though it predicted new stenosis developing behind the previous one. It was observed that the presence of a double stenosis causes the upstream pressure to reach the critical value in less time. Velocity profiles revealed that in the stenosis throat, the maximum velocity exceeds the normal biological state, which may cause disorders in the blood circulation.

CONCLUSIONS

The artery wall displacement results are suggestive of the greater difference between the two turbulence models in the case with double stenosis compared with single stenosis. Moreover, the difference between the two turbulence models in double stenosis is minimized in both post-stenotic and pre-stenotic regions.

Effect of arterial curvature on hemodynamics and mass transport

BACKGROUND

Atherosclerotic lesions develop preferentially at certain sites in the human arterial system, such as the inner wall of curved segments and the outer wall of bifurcations. Local wall shear stress (WSS) and concentration of low density lipoprotein (LDL) have been identified as two important factors contributing to these lesions.

OBJECTIVE

To determine if a connection exists between arterial curvature and the formation of atherosclerosis.

METHODS

A set of 3-D vessel models with different bend angles was constructed. By comparing blood flow, WSS, and LDL aggregation, the influence of bend curvature on atherosclerotic lesions was assessed.

RESULTS

Upon increasing arterial bending, low WSS regions were formed at the outer wall of the junction between straight and curved segments, as well as the inner wall of curved segments. However, high LDL concentrations only appeared at the inner wall of the bend region. A connection between secondary flow and LDL concentration was observed; high LDL concentration regions had stronger secondary flow. Higher water infiltration velocity could enhance LDL aggregation, while blood non-Newtonian properties, by easing secondary flow, diminished its aggregation.

CONCLUSIONS

Under the same flow rate, a larger bend angle increased flow resistance, lowered WSS, and increased LDL surface concentrations, thus indicating an increased risk of atherosclerosis.

Cardiovascular disease models: A game changing paradigm in drug discovery and screening

Cardiovascular disease is the leading cause of death worldwide. Although investment in drug discovery and development has been sky-rocketing, the number of approved drugs has been declining. Cardiovascular toxicity due to therapeutic drug use claims the highest incidence and severity of adverse drug reactions in late-stage clinical development. Therefore, to address this issue, new, additional, replacement and combinatorial approaches are needed to fill the gap in effective drug discovery and screening. The motivation for developing accurate, predictive models is twofold: first, to study and discover new treatments for cardiac pathologies which are leading in worldwide morbidity and mortality rates; and second, to screen for adverse drug reactions on the heart, a primary risk in drug development. In addition to in vivo animal models, in vitro and in silico models have been recently proposed to mimic the physiological conditions of heart and vasculature. Here, we describe current in vitro, in vivo, and in silico platforms for modelling healthy and pathological cardiac tissues and their advantages and disadvantages for drug screening and discovery applications. We review the pathophysiology and the underlying pathways of different cardiac diseases, as well as the new tools being developed to facilitate their study. We finally suggest a roadmap for employing these non-animal platforms in assessing drug cardiotoxicity and safety.

Boundary layer considerations in a multi-layer model for LDL accumulation

Boundary layer effects for Low-Density Lipoprotein (LDL) concentration problems in a multi-layer artery model are analyzed in this work. Both a straight artery and aorta-iliac bifurcation are analyzed. Mass, momentum and species governing equations are based on the porous media theory and solved with the commercial finite-element based code COMSOL Multiphysics. For the straight artery, various inlet velocities, arterial sizes and intramural pressure values are investigated. Results are presented in terms of concentration profiles close to the lumen/endothelium interface and boundary layer thickness. It is shown that the boundary layer is affected by all of the three analyzed parameters. The results in this work will further clarify the concentration polarization effects imposed by the arterial wall.

Simulation of blood and oxygen distributions in a hepatic lobule with sinusoids obstructed by cancer cells

The liver is one of the common metastatic sites for many cancers. The obstruction of sinusoids by circulating tumor cells changes liver microenvironments and is thus considered a source of hepatic metastases. To date, few studies provide detailed information, either experimentally or theoretically, concerning the changes in blood and oxygen distributions induced by the obstruction of sinusoids. In this study, we utilized a 3D porous medium-vascular tree geometric structure to mimic the hepatic lobule and studied theoretical blood flow and oxygen transport in the lobule. The simulation was validated with data from the literature. Then, the distributions of blood and oxygen in the presence of the obstruction by cancer cells were simulated. The area and degree of the liver damage induced by the obstruction were analyzed by comparing the difference of liver microenvironments between physiological (non-blocked sinusoid) and pathological (fully or partially blocked sinusoid) conditions and the minimum cancer cell sizes causing liver damage for various obstruction positions were obtained. The work presented in this study can be used to predict the degree of liver damage induced by the local ischemia caused by the obstruction of sinusoids and to characterize the relationship between hepatic metastases and liver microenvironments.

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid-structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection-diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.

Low Density Lipoprotein and Non-Newtonian Oscillating Flow Biomechanical Parameters for Normal Human Aorta

Background

The temporal variation of the hemodynamic mechanical parameters during cardiac pulse wave is considered as an important atherogenic factor. Applying non-Newtonian blood molecular viscosity simulation is crucial for hemodynamic analysis. Understanding low density lipoprotein (LDL) distribution in relation to flow parameters will possibly spot the prone to atherosclerosis aorta regions.

Methods

The biomechanical parameters tested were averaged wall shear stress (AWSS), oscillatory shear index (OSI) and relative residence time (RRT) in relation to the LDL concentration. Four non-Newtonian molecular viscosity models and the Newtonian one were tested for the normal human aorta under oscillating flow. The analysis was performed via computational fluid dynamic.

Results

Tested viscosity blood flow models for the biomechanical parameters yield a consistent aorta pattern. High OSI and low AWSS develop at the concave aorta regions. This is most noticeable in downstream flow region of the left subclavian artery and at concave ascending aorta. Concave aorta regions exhibit high RRT and elevated LDL. For the concave aorta site, the peak LDL value is 35.0% higher than its entrance value. For the convex site, it is 18.0%. High LDL endothelium regions located at the aorta concave site are well predicted with high RRT.

Conclusions

We are in favor of using the non-Newtonian power law model for analysis. It satisfactorily approximates the molecular viscosity, WSS, OSI, RRT and LDL distribution. Concave regions are mostly prone to atherosclerosis. The flow biomechanical factor RRT is a relatively useful tool for identifying the localization of the atheromatic plaques of the normal human aorta.

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

Effect of Transmural Transport Properties on Atheroma Plaque Formation and Development

We propose a mathematical model of atheroma plaque initiation and early development in coronary arteries using anisotropic transmural diffusion properties. Our current approach is on the process on plaque initiation and intimal thickening rather than in severe plaque progression and rupture phenomena. The effect of transport properties, in particular the anisotropy of diffusion properties of the artery, on plaque formation and development is investigated using the proposed mathematical model. There is not a strong influence of the anisotropic transmural properties on LDL, SMCs and collagen distribution and concentrations along the artery. On the contrary, foam cells distribution strongly depends on the value of the radial diffusion coefficient of the substances [Formula: see text] and the ratio [Formula: see text]. Decreasing [Formula: see text] or diffusion coefficients ratio means a higher concentration of the foam cells close to the intima. Due to the fact that foam cells concentration is associated to the necrotic core formation, the final distribution of foam cells is critical to evolve into a vulnerable or fibrotic plaque.

Mass transport of low density lipoprotein in reconstructed hemodynamic environments of human carotid arteries: the role of volume and solute flux through the endothelium

The accumulation of low density lipoprotein (LDL) in the arterial intima is a critical step in the initiation and progression of atheromatous lesions. In this study we examine subject-specific LDL transport into the intima of carotid bifurcations in three human subjects using a three-pore model for LDL mass transfer. Subject-specific carotid artery computational models were derived using magnetic resonance imaging (MRI) to obtain the geometry and phase-contract MRI (PC-MRI) to acquire pulsatile inflow and outflow boundary conditions for each subject. The subjects were selected to represent a wide range of anatomical configurations and different stages of atherosclerotic development from mild to moderate intimal thickening. A fluid-solid interaction (FSI) model was implemented in the computational fluid dynamics (CFD) approach in order to consider the effects of a compliant vessel on wall shear stress (WSS). The WSS-dependent response of the endothelium to LDL mass transfer was modeled by multiple pathways to include the contributions of leaky junctions, normal junctions, and transcytosis to LDL solute and plasma volume flux from the lumen into the intima. Time averaged WSS (TAWSS) over the cardiac cycle was computed to represent the spatial WSS distribution, and wall thickness (WTH) was determined from black blood MRI (BBMRI) so as to visualize intimal thickening patterns in the bifurcations. The regions which are exposed to low TAWSS correspond to elevated WTH and higher mass and volume flux via the leaky junctions. In all subjects, the maximum LDL solute flux was observed to be immediately downstream of the stenosis, supporting observations that existing atherosclerotic lesions tend to progress in the downstream direction of the stenosis.

Modelling and simulation of low-density lipoprotein transport through multi-layered wall of an anatomically realistic carotid artery bifurcation

A high concentration of low-density lipoprotein (LDL) is recognized as one of the principal risk factors for development of atherosclerosis. This paper reports on modelling and simulations of the coupled mass (LDL concentration) and momentum transport through the arterial lumen and the multi-layered arterial wall of an anatomically realistic carotid bifurcation. The mathematical model includes equations for conservation of mass, momentum and concentration, which take into account a porous layer structure, the biological membranes and reactive source/sink terms in different layers of the arterial wall, as proposed in Yang & Vafai (2006). A four-layer wall model of an arterial wall with constant thickness is introduced and initially tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with previously published results demonstrated proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the arterial lumen and in the artery wall are obtained. Then, an anatomically realistic carotid artery bifurcation is studied. This is the main novelty of the presented research. We find a strong dependence between underlying blood flow pattern (and consequently the wall shear stress distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reactions within the multi-layered artery wall is crucial for accurate predictions of the LDL concentration in the media. It is shown that a four-layer wall model produced qualitatively good agreement with the experimental results of Meyer et al. (1996) in predicting levels of LDL within the media of a rabbit aorta under identical transmural pressure conditions. Finally, it is demonstrated that the adopted model represents a good initial platform for future numerical investigations of the initial stage of atherosclerosis for patient-specific geometries.

Kinetic modeling of low density lipoprotein oxidation in arterial wall and its application in atherosclerotic lesions prediction

Oxidation of low-density lipoprotein (LDL) is one of the major factors in atherogenic process. Trapped oxidized LDL (Ox-LDL) in the subendothelial matrix is taken up by macrophage and leads to foam cell generation creating the first step in atherosclerosis development. Many researchers have studied LDL oxidation using in vitro cell-induced LDL oxidation model. The present study provides a kinetic model for LDL oxidation in intima layer that can be used in modeling of atherosclerotic lesions development. This is accomplished by considering lipid peroxidation kinetic in LDL through a system of elementary reactions. In comparison, characteristics of our proposed kinetic model are consistent with the results of previous experimental models from other researches. Furthermore, our proposed LDL oxidation model is added to the mass transfer equation in order to predict the LDL concentration distribution in intima layer which is usually difficult to measure experimentally. According to the results, LDL oxidation kinetic constant is an important parameter that affects LDL concentration in intima layer so that existence of antioxidants that is responsible for the reduction of initiating rates and prevention of radical formations, have increased the concentration of LDL in intima by reducing the LDL oxidation rate.

Computer simulation of three-dimensional plaque formation and progression in the carotid artery

Atherosclerosis is becoming the number one cause of death worldwide. In this study, three-dimensional computer model of plaque formation and development for human carotid artery is developed. The three-dimensional blood flow is described by the Navier-Stokes equation, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The low-density lipoproteins transports in lumen of the vessel and through the vessel tissue are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. Fluid-structure interaction is used to estimate effective wall stress analysis. Plaque growth functions for volume progression are correlated with shear stress and effective wall stress distribution. We choose two specific patients from MRI study with significant plaque progression. Plaque volume progression using three time points for baseline, 3- and 12-month follow up is fitted. Our results for plaque localization correspond to low shear stress zone and we fitted parameters from our model using nonlinear least-square method. Determination of plaque location and composition, and computer simulation of progression in time for a specific patient shows a potential benefit for the prediction of disease progression. The proof of validity of three-dimensional computer modeling in the evaluation of atherosclerotic plaque burden may shift the clinical information of MRI from morphological assessment toward a functional tool. Understanding and prediction of the evolution of atherosclerotic plaques either into vulnerable or stable plaques are major tasks for the medical community.

In silico vascular modeling for personalized nanoparticle delivery

AIMS

To predict the deposition of nanoparticles in a patient-specific arterial tree as a function of the vascular architecture, flow conditions, receptor surface density and nanoparticle properties.

MATERIALS & METHODS

The patient-specific vascular geometry is reconstructed from computed tomography angiography images. The isogeometric analysis framework integrated with a special boundary condition for the firm wall adhesion of nanoparticles is implemented. A parallel plate flow chamber system is used to validate the computational model in vitro.

RESULTS

Particle adhesion is dramatically affected by changes in patient-specific attributes, such as branching angle and receptor density. The adhesion pattern correlates well with the spatial and temporal distribution of the wall shear rates. For the case considered, the larger (2.0 µm) particles adhere two-times more in the lower branches of the arterial tree, whereas the smaller (0.5 µm) particles deposit more in the upper branches.

CONCLUSION

Our computational framework in conjunction with patient-specific attributes can be used to rationally select nanoparticle properties to personalize, and thus optimize, therapeutic interventions.

Effect of branchings on blood flow in the system of human coronary arteries

In this work, we investigate the behavior of the pulsatile blood flow in the system of human coronary arteries. Blood is modeled as an incompressible non-Newtonian fluid. The transient phenomena of blood flow through the coronary system are simulated by solving the three dimensional unsteady state Navier-Stokes equations and continuity equation. Distributions of velocity, pressure and wall shear stresses are determined in the system under pulsatile conditions on the boundaries. Effect of branching vessel on the flow problem is investigated. The numerical results show that blood pressure in the system with branching vessels of coronary arteries is lower than the one in the system with no branch. The magnitude of wall shear stresses rises at the bifurcation.

The Tolerance of the Maxilla to Blunt Impact

This study reports the results of 38 infraorbital maxilla impacts performed on male cadavers. Impacts were performed using an unpadded, cylindrical impactor (3.2 kg) at velocities between 1 and 5 m/s. The peak force and acoustic emission data were used to develop a statistical relationship of fracture risk as a function of impact force. Acoustic emission sensors were used to provide a noncensored measure of the maxilla tolerance and were essential due to the increase in impactor force after fracture onset. Parametric and nonparametric techniques were used to estimate the risk of fracture tolerance. The nonparametric technique produced an estimated 50% risk of fracture between 970 and 1223 N. The results obtained from the parametric and nonparametric techniques were in good agreement. Peak force values achieved in this study were similar to those of previous work and were unaffected by impactor velocity. The results of this study suggest that an impact to the infraorbital maxilla is a load-limited event due to compromise of structural integrity.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

3,3′-Dioctadecylindocarbocyanine-low-density lipoprotein uptake and flow patterns in the rabbit aorta–iliac bifurcation under three perfusion flow conditions

The aim of this study was to elucidate which of the following two factors plays a more important role in the localization of atherogenesis: the barrier function of the arterial endothelium modulated by wall shear stress or flow-dependent low-density lipoprotein (LDL) concentration at the blood/wall interface. To determine this, the rabbit aorto-iliac bifurcation was perfused with 3,3′-dioctadecylindocarbocyanine (DiI)-LDL solution under three different flow conditions: (i) forward flow (perfused in the in vivo flow direction); (ii) backward flow (perfused in a reversed flow direction); and (iii) static group (no flow). The results showed that there was a peak in the curve of DiI-LDL uptake distribution along the lateral wall of the bifurcation for all three groups, which was located in the branching areas where the endothelial cells were round and polygonal with no preferred orientation. Nevertheless, the peak of the forward flow group was much sharper than those of the other two groups. The overall DiI-LDL uptake was the highest for the static group. The present experimental study supports the concept that both the barrier function of the endothelium modulated by wall shear stress and the mass transport phenomenon of LDL concentration polarization are involved in the infiltration/accumulation of atherogenic lipids within the arterial wall. Nevertheless, the latter might play a larger role in the localization of atherogenesis.

Wall shear stress on LDL accumulation in human RCAs

The blood flow and transportation of molecules in the cardiovascular system plays crucial role in the genesis and progression of atherosclerosis. Atherosclerosis shows predilection in regions of the arterial tree with hemodynamic particularities, as local disturbances of wall shear stress in space, and locally high concentrations of lipoprotein. A semi-permeable nature of the arterial wall computational model is incorporated with hydraulic conductivity and permeability treated as wall shear stress dependent. Six image-based human diseased right coronary arteries (RCA) are used to elucidate the low-density lipoprotein (LDL) transport. The 3D reconstruction technique is a combination of angiography and IVUS. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall. The coupling of fluid dynamics and solute dynamics at the endothelium is achieved by the Kedem-Katchalsky equation (water infiltration). The luminal surface LDL concentration at the arterial wall is flow-dependent with local variations due to geometric features. The relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. There is medium correlation (Pearson) between low WSS and high LDL. The degree of elevation in luminal surface LDL concentration is mostly affected by the water infiltration velocity at the vessel wall. Under constant water infiltration the shear dependent endothelial permeability effects, in comparison to those using constant value, are marginal. Area-averaged normalized LDL concentration over the RCAs, using constant water infiltration and endothelial permeability is 3.6% higher than that at the entrance. Area-averaged normalized LDL concentration over the RCAs, using shear dependent water infiltration and endothelial permeability is 9.6%. Perspective computational fluid dynamics users, incorporating mass transfer (LDL) within the blood flow, are forced to treat the problem using shear dependent endothelial values.

Factors that affect mass transport from drug eluting stents into the artery wall

Coronary artery disease can be treated by implanting a stent into the blocked region of an artery, thus enabling blood perfusion to distal vessels. Minimally invasive procedures of this nature often result in damage to the arterial tissue culminating in the re-blocking of the vessel. In an effort to alleviate this phenomenon, known as restenosis, drug eluting stents were developed. They are similar in composition to a bare metal stent but encompass a coating with therapeutic agents designed to reduce the overly aggressive healing response that contributes to restenosis. There are many variables that can influence the effectiveness of these therapeutic drugs being transported from the stent coating to and within the artery wall, many of which have been analysed and documented by researchers. However, the physical deformation of the artery substructure due to stent expansion, and its influence on a drugs ability to diffuse evenly within the artery wall have been lacking in published work to date. The paper highlights previous approaches adopted by researchers and proposes the addition of porous artery wall deformation to increase model accuracy.

Influence of oscillating flow on LDL transport and wall shear stress in the normal aortic arch

Lipid accumulation in the aortic wall is an important factor in the development of atherosclerosis. The Low Density Lipoprotein (LDL) at the surface of the endothelium in relation to Wall Shear Stress (WSS) in the normal human aortic arch under unsteady, normal flow and mass conditions was computationally analysed. Concave sides of the aortic arch exhibit, relatively to the convex ones, elevated LDL levels at the surface of the endothelium for all time steps. At the peak systolic velocity, the LDL level reaches a value 23.0% higher than that at entrance in the ascending-descending aorta region. The corresponding LDL levels at the surface of the endothelium for the near minimum entrance velocity instant reaches 26.0%. During the cardiac cycle, the highest area averaged normalized LDL taken up as compared to the lowest one is 0.69%. WSS plays an important role in the lipid accumulation. Low WSS regions are exposed to high LDL levels at the surface of the endothelium. Regions of elevated LDL levels do not necessarily co-locate to the sites of lowest WSS. The near wall paths of the velocities might be the most important factor for the elevated LDL levels at the surface of the endothelium.

The effect of a spatially heterogeneous transmural water flux on concentration polarization of low density lipoprotein in arteries

Uptake of low density lipoprotein (LDL) by the arterial wall is likely to play a key role in atherogenesis. A particular process that may cause vascular scale heterogeneity in the rate of transendothelial LDL transport is the formation of a flow-dependent LDL concentration polarization layer on the luminal surface of the arterial endothelium. In this study, the effect of a spatially heterogeneous transmural water flux (that traverses the endothelium only via interendothelial cell clefts) on such concentration polarization is investigated numerically. Unlike in previous investigations, realistic intercellular cleft dimensions are used here and several values of LDL diffusivity are considered. Particular attention is paid to the spatially averaged LDL concentration adjacent to different regions of the endothelial surface, as such measures may be relevant to the rate of transendothelial LDL transport. It is demonstrated in principle that a heterogeneous transmural water flux can act to enhance such measures, and cause them to develop a shear dependence (in addition to that caused by vascular scale flow features, affecting the overall degree of LDL concentration polarization). However, it is shown that this enhancement and additional shear dependence are likely to be negligible for a physiologically realistic transmural flux velocity of 0.0439 mum s(-1) and an LDL diffusivity (in blood plasma) of 28.67 mum(2) s(-1). Hence, the results imply that vascular scale studies of LDL concentration polarization are justified in ignoring the effect of a spatially heterogeneous transmural water flux.

Patient-specific three-dimensional simulation of LDL accumulation in a human left coronary artery in its healthy and atherosclerotic states

We calculate low-density lipoprotein (LDL) transport from blood into arterial walls in a three-dimensional, patient-specific model of a human left coronary artery. The in vivo anatomy data are obtained from computed tomography images of a patient with coronary artery disease. Models of the artery anatomy in its healthy and diseased states are derived after segmentation of the vessel lumen, with and without the detected plaque, respectively. Spatial shear stress distribution at the endothelium is determined through the reconstruction of the arterial blood flow field using computational fluid dynamics. The arterial endothelium is represented by a shear stress-dependent, three-pore model, taking into account blood plasma and LDL passage through normal junctions, leaky junctions, and the vesicular pathway. Intraluminal pressures of 70 and 120 mmHg are employed as the normal and hypertensive operating pressures, respectively. By applying our model to both the healthy and diseased states, we show that the location of the plaque in the diseased state corresponds to one of the two sites with predicted high-LDL concentration in the healthy state. We further show that, in the diseased state, the site with high-LDL concentration has shifted distal to the plaque, which is in agreement with the clinical observation that plaques generally grow in the downstream direction. We also demonstrate that hypertension leads to increased number of regions with high-LDL concentration, elucidating one of the ways in which hypertension may promote atherosclerosis.

Numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model.

Blood flow and macromolecular transport in complex blood vessels

Numerical simulations of pulsatile flows and macromolecular (such as LDL) transport in complex blood vessels, including the cerebral artery, are carried out using the FLUENT software. The hemodynamic factors such as axial velocity, secondary flow as well as LDL concentration distribution in the complex vessel are obtained. It is found that in the case of pulsatile flow, the LDL concentration is higher in the central region of the flow than on the wall. Under the precondition of impermeability, the numerical results indicate that the blood flow is quite complicated in complex blood vessel. The complex flow can reduce the LDL concentration on the vessel wall, which is helpful to prevent the concentration polarization.

Computational Modeling of LDL and Albumin Transport in an In Vivo CT Image-Based Human Right Coronary Artery

Low wall shear stress (WSS) is implicated in endothelial dysfunction and atherogenesis. The accumulation of macromolecules is also considered as an important factor contributing to the development of atherosclerosis. In the present study, a fluid-wall single-layered model incorporated with shear-dependent transport parameters was used to investigate albumin and low-density lipoprotein (LDL) transport in an in vivo computed tomographic image-based human right coronary artery (RCA). In the fluid-wall model, the bulk blood flow was modeled by the Navier–Stokes equations, Darcy’s law was employed to model the transmural flow in the arterial wall, mass balance of albumin and LDL was governed by the convection-diffusion mechanism with an additional reaction term in the wall, and the Kedem–Katchalsky equations were applied at the endothelium as the interface condition between the lumen and wall. Shear-dependent models for hydraulic conductivity and albumin permeability were derived from experimental data in literature to investigate the influence of WSS on macromolecular accumulation in the arterial wall. A previously developed so-called lumen-free time-averaged scheme was used to approximate macromolecular transport under pulsatile flow conditions. LDL and albumin accumulations in the subendothelial layer were found to be colocalized with low WSS. Two distinct mechanisms responsible for the localized accumulation were identified: one was insufficient efflux from the subendothelial layer to outer wall layers caused by a weaker transmural flow; the other was excessive influx to the subendothelial layer from the lumen caused by a higher permeability of the endothelium. The comparison between steady flow and pulsatile flow results showed that the dynamic behavior of the pulsatile flow could induce a wider and more diffuse macromolecular accumulation pattern through the nonlinear shear-dependent transport properties. Therefore, it is vital to consider blood pulsatility when modeling the shear-dependent macromolecular transport in large arteries. In the present study, LDL and albumin accumulations were observed in the low WSS regions of a human RCA using a fluid-wall mass transport model. It was also found that steady flow simulation could overestimate the magnitude and underestimate the area of accumulations. The association between low WSS and accumulation of macromolecules leading to atherosclerosis may be mediated through effects on transport properties and mass transport and is also influenced by flow pulsatility.

Low-Density Lipoprotein concentration in the normal Left Coronary Artery tree

Background

The blood flow and transportation of molecules in the cardiovascular system plays a crucial role in the genesis and progression of atherosclerosis. This computational study elucidates the Low Density Lipoprotein (LDL) site concentration in the entire normal human 3D tree of the LCA.

Methods

A 3D geometry model of the normal human LCA tree is constructed. Angiographic data used for geometry construction correspond to end-diastole. The resulted model includes the LMCA, LAD, LCxA and their main branches. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall.

Results

High concentration of LDL values appears at bifurcation opposite to the flow dividers in the proximal regions of the Left Coronary Artery (LCA) tree, where atherosclerosis frequently occurs. The area-averaged normalized luminal surface LDL concentrations over the entire LCA tree are, 1.0348, 1.054 and 1.23, for the low, median and high water infiltration velocities, respectively. For the high, median and low molecular diffusivities, the peak values of the normalized LDL luminal surface concentration at the LMCA bifurcation reach 1.065, 1.080 and 1.205, respectively. LCA tree walls are exposed to a cholesterolemic environment although the applied mass and flow conditions refer to normal human geometry and normal mass-flow conditions.

Conclusion

The relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. Concave sides of the LCA tree exhibit higher concentration of LDL than the convex sides. Decreased molecular diffusivity increases the LDL concentration. Increased water infiltration velocity increases the LDL concentration. The regional area of high luminal surface concentration is increased with increasing water infiltration velocity. Regions of high LDL luminal surface concentration do not necessarily co-locate to the sites of lowest WSS. The degree of elevation in luminal surface LDL concentration is mostly affected from the water infiltration velocity at the vessel wall. The paths of the velocities in proximity to the endothelium might be the most important factor for the elevated LDL concentration.

Numerical analysis of the cooling effect of blood over inflamed atherosclerotic plaque

Atherosclerotic plaques with high likelihood of rupture often show local temperature increase with respect to the surrounding arterial wall temperature. In this work, atherosclerotic plaque temperature was numerically determined during the different levels of blood flow reduction produced by the introduction of catheters at the vessel lumen. The temperature was calculated by solving the energy equation and the Navier-Stokes equations in 2D idealized arterial models. Arterial wall temperature depends on three basic factors: metabolic activity of the inflammatory cells embedded in the plaque, heat convection due to luminal blood flow, and heat conduction through the arterial wall and plaque. The calculations performed serve to simulate transient blood flow reduction produced by the presence of thermography catheters used to measure arterial wall temperature. The calculations estimate the spatial and temporal alterations in the cooling effect of blood flow and plaque temperature during the measurement process. The mathematical model developed provides a tool for analyzing the contribution of factors known to affect heat transfer at the plaque surface. Blood flow reduction leads to a nonuniform temperature increase ranging from 0.1 to 0.25 degrees Celsius in the plaque/lumen interface of the arterial geometries considered in this study. The temperature variation as well as the Nusselt number calculated along the plaque surface strongly depended on the arterial geometry and distribution of inflammatory cells. The calculations indicate that the minimum required time to obtain a steady temperature profile after arterial occlusion is 6 s. It was seen that in arteries with geometries involving bends, the temperature profiles appear asymmetrical and lean toward the downstream edge of the plaque.

Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress

The work herein represents a novel approach for the modeling of low-density lipoprotein (LDL) transport from the artery lumen into the arterial wall, taking into account the effects of local wall shear stress (WSS) on the endothelial cell layer and its pathways of volume and solute flux. We have simulated LDL transport in an axisymmetric representation of a stenosed coronary artery, where the endothelium is represented by a three-pore model that takes into account the contributions of the vesicular pathway, normal junctions, and leaky junctions also employing the local WSS to yield the overall volume and solute flux. The fraction of leaky junctions is calculated as a function of the local WSS based on published experimental data and is used in conjunction with the pore theory to determine the transport properties of this pathway. We have found elevated levels of solute flux at low shear stress regions because of the presence of a larger number of leaky junctions compared with high shear stress regions. Accordingly, we were able to observe high LDL concentrations in the arterial wall in these low shear stress regions despite increased filtration velocity, indicating that the increase in filtration velocity is not sufficient for the convective removal of LDL.

Influence of Pulsatile Flow on LDL Transport in the Arterial Wall

The accumulation of low-density lipoprotein (LDL) is one of the important factors in atherogenesis. Two different time scales may influence LDL transport in vivo: (1) LDL transport is coupled to blood flow with a pulse cycle of around 1 s in humans; (2) LDL transport within the arterial wall is mediated by transmural flow in the order of 10(-8) m/s. Most existing models have assumed steady flow conditions and overlooked the interactions between physical phenomena with different time scales. The objective of this study was to investigate the influence of pulsatile flow on LDL transport and examine the validity of steady flow assumption. The effect of pulsatile flow on transmural transport was incorporated by using a lumen-free cyclic (LFC) and a lumen-free time-averaged (LFTA) procedures. It is found that the steady flow simulation predicted a focal distribution in the post-stenotic region, differing from the diffuse distribution pattern produced by the pulsatile flow simulation. The LFTA procedure, in which time-averaged shear-dependent transport properties calculated from instantaneous wall shear stress (WSS) were used, predicted a similar distribution pattern to the LFC simulations. We conclude that the steady flow assumption is inadequate and instantaneous hemodynamic conditions have important influence on LDL transmural transport in arterial geometries with disturbed and complicated flow patterns.

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.