Oxygen mass transfer calculations in large arteries

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.

Image-based insilico investigation of hemodynamics and biomechanics in healthy and diabetic human retinas

Retinal hemodynamics and biomechanics play a significant role in understanding the pathophysiology of several ocular diseases. However, these parameters are significantly affected due to changed blood vessel morphology ascribed to pathological conditions, particularly diabetes. In this study, an image-based computational fluid dynamics (CFD) model is applied to examine the effects of changed vascular morphology due to diabetes on blood flow velocity, vorticity, wall shear stress (WSS), and oxygen distribution and compare it with healthy. The 3D patient-specific vascular architecture of diabetic and healthy retina is extracted from Optical Coherence Tomography Angiography (OCTA) images and fundus to extract the capillary level information. Further, Fluid-structure interaction (FSI) simulations have been performed to compare the induced tissue stresses in diabetic and healthy conditions. Results illustrate that most arterioles possess higher velocity, vorticity, WSS, and lesser oxygen concentration than arteries for healthy and diabetic cases. However, an opposite trend is observed for venules and veins. Comparisons show that, on average, the blood flow velocity in the healthy case decreases by 42 % in arteries and 21 % in veins, respectively, compared to diabetic. In addition, the WSS and von Mises stress (VMS) in healthy case decrease by 49 % and 72 % in arteries and by 6 % and 28 % in veins, respectively, when compared with diabetic, making diabetic blood vessels more susceptible to wall rupture and tissue damage. The in-silico results may help predict the possible abnormalities region early, helping the ophthalmologists use these estimates as prognostic tools and tailor patient-specific treatment plans.

Analyzing the contribution of vasa vasorum in oxygenation of the aneurysmal wall: A computational study

The mechanisms of abdominal aortic aneurysm (AAA) formation and rupture are controversial in the literature. While the intraluminal thrombus (ILT) plays a crucial role in reducing oxygen flux to the tissue and therefore decreasing the aortic wall strength, other physiological parameters such as the vasa vasorum (VV) oxygen flow and its consumption contribute to altered oxygenation responses of the arterial tissue as well. The goal of this research is to analyse the importance of the aforementioned parameters on oxygen delivery to the aneurysmal wall in a patient-specific AAA. Numerical simulations of coupled blood flow and mass transport with varying levels of VV concentration and oxygen reaction rate coefficient are performed. The hypoperfusion of the adventitial VV and high oxygen consumption are observed to have critical effects on reducing aneurysmal tissue oxygen supply and can therefore exacerbate localized oxygen deprivation.

A numerical study of the hemodynamic behavior and gas transport in cardiovascular systems with severe cardiac or cardiopulmonary failure supported by venoarterial extracorporeal membrane oxygenation

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) has been extensively demonstrated as an effective means of bridge-to-destination in the treatment of patients with severe ventricular failure or cardiopulmonary failure. However, appropriate selection of candidates and management of patients during Extracorporeal membrane oxygenation (ECMO) support remain challenging in clinical practice, due partly to insufficient understanding of the complex influences of extracorporeal membrane oxygenation support on the native cardiovascular system. In addition, questions remain as to how central and peripheral venoarterial extracorporeal membrane oxygenation modalities differ with respect to their hemodynamic impact and effectiveness of compensatory oxygen supply to end-organs. In this work, we developed a computational model to quantitatively address the hemodynamic interaction between the extracorporeal membrane oxygenation and cardiovascular systems and associated gas transport. Model-based numerical simulations were performed for cardiovascular systems with severe cardiac or cardiopulmonary failure and supported by central or peripheral venoarterial extracorporeal membrane oxygenation. Obtained results revealed that: 1) central and peripheral venoarterial extracorporeal membrane oxygenation modalities had a comparable capacity for elevating arterial blood pressure and delivering oxygenated blood to important organs/tissues, but induced differential changes of blood flow waveforms in some arteries; 2) increasing the rotation speed of extracorporeal membrane oxygenation pump (ω) could effectively improve arterial blood oxygenation, with the efficiency being especially high when ω was low and cardiopulmonary failure was severe; 3) blood oxygen indices (i.e., oxygen saturation and partial pressure) monitored at the right radial artery could be taken as surrogates for diagnosing potential hypoxemia in other arteries irrespective of the modality of extracorporeal membrane oxygenation; and 4) Left ventricular (LV) overloading could occur when ω was high, but the threshold of ω for inducing clinically significant left ventricular overloading depended strongly on the residual cardiac function. In summary, the study demonstrated the differential hemodynamic influences while comparable oxygen delivery performance of the central and peripheral venoarterial extracorporeal membrane oxygenation modalities in the management of patients with severe cardiac or cardiopulmonary failure and elucidated how the status of arterial blood oxygenation and severity of left ventricular overloading change in response to variations in ω. These model-based findings may serve as theoretical references for guiding the application of venoarterial extracorporeal membrane oxygenation or interpreting in vivo measurements in clinical practice.

Influence of aortic aneurysm on the local distribution of NO and O2 using image-based computational fluid dynamics

There is a pressing need to establish novel biomarkers to predict the progression of thoracic aortic aneurysm (TAA) dilatation. Aside from hemodynamics, the roles of oxygen (O₂) and nitric oxide (NO) in TAA pathogenesis are potentially significant. As such, it is imperative to comprehend the relationship between aneurysm presence and species distribution in both the lumen and aortic wall. Given the limitations of existing imaging methods, we propose the use of patient-specific computational fluid dynamics (CFD) to explore this relationship. We have performed CFD simulations of O₂ and NO mass transfer in the lumen and aortic wall for two cases: a healthy control (HC) and a patient with TAA, both acquired using 4D-flow magnetic resonance imaging (MRI). The mass transfer of O₂ was based on active transport by hemoglobin, while the local variations of the wall shear stress (WSS) drove NO production. Comparing hemodynamic properties, the time-averaged WSS was considerably lower for TAA, while the oscillatory shear index and endothelial cell activation potential were notably elevated. O₂ and NO showed a non-uniform distribution within the lumen and an inverse correlation between the two species. We identified several locations of hypoxic regions for both cases due to lumen-side mass transfer limitations. In the wall, NO varied spatially, with a clear distinction between TAA and HC. In conclusion, the hemodynamics and mass transfer of NO in the aorta exhibit the potential to serve as a diagnostic biomarker for TAA. Furthermore, hypoxia may provide additional insights into the onset of other aortic pathologies.

On the identification of hypoxic regions in subject-specific cerebral vasculature by combined CFD/MRI

A long-time exposure to lack of oxygen (hypoxia) in some regions of the cerebrovascular system is believed to be one of the causes of cerebral neurological diseases. In the present study, we show how a combination of magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) can provide a non-invasive alternative for studying blood flow and transport of oxygen within the cerebral vasculature. We perform computer simulations of oxygen mass transfer in the subject-specific geometry of the circle of Willis. The computational domain and boundary conditions are based on four-dimensional (4D)-flow MRI measurements. Two different oxygen mass transfer models are considered: passive (where oxygen is treated as a dilute chemical species in plasma) and active (where oxygen is bonded to haemoglobin) models. We show that neglecting haemoglobin transport results in a significant underestimation of the arterial wall mass transfer of oxygen. We identified the hypoxic regions along the arterial walls by introducing the critical thresholds that are obtained by comparison of the estimated range of Damköhler number (Da ⊂ 〈9; 57〉) with the local Sherwood number. Finally, we recommend additional validations of the combined MRI/CFD approach proposed here for larger groups of subject- or patient-specific brain vasculature systems.

Prediction of wall stress and oxygen flow in patient-specific abdominal aortic aneurysms: the role of intraluminal thrombus

In this study, the biomechanical role of intraluminal thrombus (ILT) in an abdominal aortic aneurysm (AAA) is investigated. The implications of ILT in AAA are controversial in literature. Previous studies have demonstrated that ILT provides a biomechanical advantage by decreasing wall stress, whereas other studies have associated ILT with inhibiting oxygen transport and inducing aortic wall weakening. Therefore, we sought to explore the connection between ILT, mechanical stresses, and oxygen flow in different geometries of patient-specific aneurysms with varying ILT morphologies. The objective is to investigate the extent to which ILT influences the prediction of aneurysmal wall stresses that are associated with rupture, as well as oxygen concentrations to measure tissue oxygen deprivation. Three patient-specific AAA geometries are considered, and two models, one with ILT and one without ILT, are created for each patient to assess the effect of ILT presence. A fluid-structure interaction approach is used to couple the blood flow, wall deformation, and oxygen mass transport. Results are presented for hemodynamics patterns, wall stress measures, and oxygen metrics within the arterial wall. While ILT is found to reduce wall stress, simulations confirm that ILT decreases oxygen transport within the tissue significantly, leading to wall hypoxia.

The Effects of Geometric Features of Intraluminal Thrombus on the Vessel Wall Oxygen Deprivation

The objective of this paper is to analyze the association of intraluminal thrombus (ILT) presence and morphology with oxygen transport in abdominal aortic aneurysms (AAA) and local hypoxia. The biomechanical role of the ILT layer in the evolution of the aneurysm is still not fully understood. ILT has been shown to create an inflammatory environment by reducing oxygen flux to the arterial wall and therefore decreasing its strength. It has been also hypothesized that the geometry of the ILT may further affect AAA rupture. However, no previous research has attempted to explore the effect of morphological features of ILT on oxygen distributions within the AAA, in a systematic manner. In this study, we perform a comprehensive analysis to investigate how physiologically meaningful variations in ILT geometric characteristics affect oxygen transport within an AAA. We simulate twenty-seven AAA models with variable ILT dimensions and investigate the extent to which ILT attenuates oxygen concentration in the arterial wall. Geometric variations studied include ILT thickness and ILT length, as well as the bulge diameter of the aneurysm which is related to ILT curvature. Computer simulations of coupled fluid flow-mass transport between arterial wall, ILT, and blood are solved and spatial variations of oxygen concentrations within the ILT and wall are obtained. The comparison of the results for all twenty-seven simulations supports the hypothesis that the presence of ILT in AAA correlates to significantly impaired oxygen transport to the aneurysmal wall. Mainly, we observed that ILT thickness and length are the parameters that influence decreased oxygen flow and concentration values the most, and thick thrombi exacerbate hypoxic conditions in the arterial wall, which may contribute to increased tissue degradation. Conversely, we observed that the arterial wall oxygen concentration is nearly independent of the AAA bulge diameter. This confirms that consideration of ILT size and anatomy is crucial in the analysis of AAA development.

Comparison of arteriovenous fistulas constructed with main or internal branch of the cephalic vein: a retrospective analysis of 32 cases

OBJECTIVE

To evaluate the effect on the maturation of arteriovenous fistulas (AVFs) when using the internal branch of the cephalic vein compared with the main branch of the cephalic vein.

METHODS

The study enrolled patients with end-stage renal disease and divided them into an internal branch group (AVF constructed using the internal branch of the cephalic vein) or a main branch group (AVF constructed using the main branch of the cephalic vein). The surgical outcomes including complications were observed in these patients after 12 weeks.

RESULTS

Thirty-two patients with end-stage renal disease were included in the study. There were 16 patients in each group. The demographic and clinical characteristics were not significantly different between the two groups. The diameter of the arteries and veins were not significantly different between the two groups before the operation. In the internal branch group, significantly more (n = 7) patients failed to mature or required surgical intervention compared with the main branch group (n = 1).

CONCLUSION

For veins of the same diameter, these findings suggest that constructing AVFs using the main branch of the cephalic vein instead of the internal branch was more suitable for patients with end-stage renal disease requiring haemodialysis.

Coupled Hemodynamics and Oxygen Diffusion in Abdominal Aortic Aneurysm: A Computational Sensitivity Study

PURPOSE

Abdominal Aortic Aneurysms (AAA) have extreme medical prevalence as an asymptomatic cause of death in developed countries. The probability of AAA rupture is promoted by the localized oxygen loss in the AAA wall which occurs in part because many AAAs contain a layer called intraluminal thrombus (ILT). Considering this strong clinical association, the purpose of this study is to investigate the key features that constitute to the oxygen diffusion, and therefore hypoxia in AAA.

METHODS

A three-dimensional model of AAA containing ILT is created and numerical simulations are performed to simulate blood flow and oxygen distribution within the AAA. The model accounts for blood flow in the lumen and oxygen transport in the lumen, ILT, and arterial wall. The sub-model of the ILT is fully coupled with the wall sub-model as well as with the subdomain of the blood flow. The sensitivity of the oxygen flow with respect to the parameters of the problem is also analyzed.

RESULTS

Model simulations are used to investigate the relation between AAA physical properties, hemodynamics, and oxygen concentration in different geometries of AAA. The results demonstrate that the diameter of the AAA bulge has little effect on the oxygen flow, but that the thickness of the ILT layer has a profound effect. Moreover, a significant sensitivity to the oxygen supply from vasa vasorum and its notable impact on oxygen transport within AAA are observed. The variability of the arterial wall oxygen concentration to the oxygen reaction rate remains however very low.

CONCLUSION

The presence of an ILT significantly impairs oxygen transport from the lumen to the wall. This study confirms that consideration of ILT size and anatomy may be important in considering the severity of a AAA, however, other parameters can also affect thrombus-mediated oxygen delivery within the aneurysmal wall.

Oxygen transport in a permeable model of abdominal aortic aneurysm

This paper reports on modelling and simulation of the coupled mass and momentum transport through the arterial lumen and the porous arterial wall of an abdominal aortic aneurysm (AAA). The effect of porous structure and intramural flow, which is usually neglected, is essential to quantify the oxygen concentration in the aneurysmal wall and will be addressed in this work via a novel coupled fluid-porous structure-mass transport model for AAA. The computational solver provides a prediction of the filtration velocity and oxygen concentration in the artery and further simulations are used to investigate the relation between the wall oxygen concentration and permeability. The results demonstrate the essential coupling between blood and filtration flow and specifically how their interactions affect oxygen transport.

The role of oxygen transport in atherosclerosis and vascular disease

Atherosclerosis and vascular disease of larger arteries are often associated with hypoxia within the layers of the vascular wall. In this review, we begin with a brief overview of the molecular changes in vascular cells associated with hypoxia and then emphasize the transport mechanisms that bring oxygen to cells within the vascular wall. We focus on fluid mechanical factors that control oxygen transport from lumenal blood flow to the intima and inner media layers of the artery, and solid mechanical factors that influence oxygen transport to the adventitia and outer media via the wall's microvascular system-the vasa vasorum (VV). Many cardiovascular risk factors are associated with VV compression that reduces VV perfusion and oxygenation. Dysfunctional VV neovascularization in response to hypoxia contributes to plaque inflammation and growth. Disturbed blood flow in vascular bifurcations and curvatures leads to reduced oxygen transport from blood to the inner layers of the wall and contributes to the development of atherosclerotic plaques in these regions. Recent studies have shown that hypoxia-inducible factor-1α (HIF-1α), a critical transcription factor associated with hypoxia, is also activated in disturbed flow by a mechanism that is independent of hypoxia. A final section of the review emphasizes hypoxia in vascular stenting that is used to enlarge vessels occluded by plaques. Stenting can compress the VV leading to hypoxia and associated intimal hyperplasia. To enhance oxygen transport during stenting, new stent designs with helical centrelines have been developed to increase blood phase oxygen transport rates and reduce intimal hyperplasia. Further study of the mechanisms controlling hypoxia in the artery wall may contribute to the development of therapeutic strategies for vascular diseases.

COMPUTATIONAL STUDY OF THE INFLUENCE OF BIFURCATION ANGLE ON HAEMODYNAMICS AND OXYGEN TRANSPORT IN THE CAROTID BIFURCATION

In this study, blood flow associated with oxygen transport in the human carotid bifurcation was investigated numerically to assess the effects of bifurcation geometry on distribution and magnitude of the wall shear stress (WSS) and Sherwood number (Sh: dimensionless oxygen wall flux) at the favourable site of atherosclerotic lesion. Three-dimensional average models of the rigid-walled carotid bifurcation were constructed to perform simulations of steady blood flow under the wall boundary condition of a constant oxygen tension. The results demonstrated that changes in the bifurcation angle significantly altered the distribution of both the WSS and the Sh, even though the pattern of the axial flow was not very sensitive to the change in bifurcation angle. Flow with large inertia bifurcated at the flow divider and created a flow recirculation zone with low WSS and Sh on the outer wall of the internal carotid artery (ICA) sinus, where atherosclerotic lesions tend to develop. A wider bifurcation angle made the area of low Sh in the ICA sinus smaller, but the level of Sh along the outer wall of the ICA sinus extremely low. Another finding was that low Sh was associated with high WSS at the region distal to the ICA sinus. The Sh distribution did not readjust as fast as the WSS in this region, as reflected by the different rates of recovery of the WSS and Sh, thus uncoupling the transport process of oxygen transport from WSS.

Defining Physiological Normoxia for Improved Translation of Cell Physiology to Animal Models and Humans

The extensive oxygen gradient between the air we breathe (Po₂ ~21 kPa) and its ultimate distribution within mitochondria (as low as ~0.5-1 kPa) is testament to the efforts expended in limiting its inherent toxicity. It has long been recognized that cell culture undertaken under room air conditions falls short of replicating this protection in vitro. Despite this, difficulty in accurately determining the appropriate O₂ levels in which to culture cells, coupled with a lack of the technology to replicate and maintain a physiological O₂ environment in vitro, has hindered addressing this issue thus far. In this review, we aim to address the current understanding of tissue Po₂ distribution in vivo and summarize the attempts made to replicate these conditions in vitro. The state-of-the-art techniques employed to accurately determine O₂ levels, as well as the issues associated with reproducing physiological O₂ levels in vitro, are also critically reviewed. We aim to provide the framework for researchers to undertake cell culture under O₂ levels relevant to specific tissues and organs. We envisage that this review will facilitate a paradigm shift, enabling translation of findings under physiological conditions in vitro to disease pathology and the design of novel therapeutics.

Finite element modeling of near-wall mass transport in cardiovascular flows

Many cardiovascular processes involve mass transport between blood and the vessel wall. Finite element methods are commonly used to numerically simulate these processes. Cardiovascular mass transport problems are typically characterized by high Péclet numbers, requiring fine near-wall mesh resolution as well as the use of stabilization techniques to avoid numerical instabilities. In this work, we develop a set of guidelines for solving high-Péclet-number near-wall mass transport problems using the finite element method. We use a steady, idealized test case to investigate the required mesh resolution and finite element basis order to accurately capture near-wall concentration boundary layers, as well as the performance of several commonly used stabilization techniques. Linear tetrahedral meshes were found to outperform quadratic tetrahedral meshes of equivalent degrees of freedom, and the commonly used discontinuity-capturing stabilization technique was found to be overly diffusive for these types of problems. Best practices derived from the idealized test case were then applied to a typical patient-specific vascular blood flow modeling application, where it was found that the commonly applied technique of avoiding numerical difficulties by artificially increasing mass diffusivity provides qualitatively similar but quantitatively erroneous results.

Low-density lipoprotein accumulation within the right coronary artery walls for physiological and hypertension conditions

We demonstrate how low-density lipoproteins (LDL) are transported and accumulated through walls of the coronary artery. The result of modeling is a map of the LDL concentration on the patient specific vessel. It identifies places at high risk for plague growth. Using the geometry of the same patient we compare the results of two-layer and four-layer models of LDL transport.

Three-dimensional flows in a hyperelastic vessel under external pressure

We study the collapsible behaviour of a vessel conveying viscous flows subject to external pressure, a scenario that could occur in many physiological applications. The vessel is modelled as a three-dimensional cylindrical tube of nonlinear hyperelastic material. To solve the fully coupled fluid-structure interaction, we have developed a novel approach based on the Arbitrary Lagrangian-Eulerian (ALE) method and the frontal solver. The method of rotating spines is used to enable an automatic mesh adaptation. The numerical code is verified extensively with published results and those obtained using the commercial packages in simpler cases, e.g. ANSYS for the structure with the prescribed flow, and FLUENT for the fluid flow with prescribed structure deformation. We examine three different hyperelastic material models for the tube for the first time in this context and show that at the small strain, all three material models give similar results. However, for the large strain, results differ depending on the material model used. We further study the behaviour of the tube under a mode-3 buckling and reveal its complex flow patterns under various external pressures. To understand these flow patterns, we show how energy dissipation is associated with the boundary layers created at the narrowest collapsed section of the tube, and how the transverse flow forms a virtual sink to feed a strong axial jet. We found that the energy dissipation associated with the recirculation does not coincide with the flow separation zone itself, but overlaps with the streamlines that divide the three recirculation zones. Finally, we examine the bifurcation diagrams for both mode-3 and mode-2 collapses and reveal that multiple solutions exist for a range of the Reynolds number. Our work is a step towards modelling more realistic physiological flows in collapsible arteries and veins.

Developing transmission line equations of oxygen transport for predicting oxygen distribution in the arterial system

The oxygen content in the arterial system plays a significant role in determining the physiological status of a human body. Understanding the oxygen concentration distribution in the arterial system is beneficial for the prevention and intervention of vascular disease. However, the oxygen concentration in the arteries could not be noninvasively monitored in clinical research. Although the oxygen concentration distribution in a vessel could be obtained from a three-dimensional (3D) numerical simulation of blood flow coupled with oxygen transport, a 3D numerical simulation of the systemic arterial tree is complicated and requires considerable computational resources and time. However, the lumped parameter model of oxygen transport derived from transmission line equations of oxygen transport requires fewer computational resources and less time to numerically predict the oxygen concentration distribution in the systemic arterial tree. In this study, transmission line equations of oxygen transport are developed according to the theory of oxygen transport in the vessel, and fluid transmission line equations are used as the theoretical reference for the development. The transmission line equations of oxygen transport could also be regarded as the theoretical basis for developing lumped parameter models of other substances in blood.

The numerical study on the effects of cardiac function on the aortic oxygen distribution

Although venoarterial extracorporeal membrane oxygenation (VA-ECMO) was widely used in clinical practice, the effects of cardiac output on the aortic oxygen distribution were still unclear. Hence, the present study aims to evaluate the effect of cardiac function on the aortic oxygen distribution under VA-ECMO support. A novel model, combining computational fluid dynamics, multiphase fluid approach, and oxygen transport theory together, was established. According to the clinical practice, four cardiac output conditions, including 0, 1, 2, and 2.5 L/min, were designed. The results demonstrated that the proposed method could accurately calculate the distribution of oxygen in the aorta. Moreover, the aortic oxygen distribution was significantly regulated by the local blood flow pattern. The deoxygenated blood flow and oxygenated blood flow met at the aortic arch and formed the so-called oxygenshed phenomenon. Along with the cardiac output increase, the oxygenshed was moved from the proximal of the aortic arch to the descending aorta. Meanwhile, the oxygen contents in the brachiocephalic artery and left common carotid artery were reduced along with the increase of cardiac output. The study could provide much useful information on the oxygen distribution in the aorta to surgeons and operators of VA-ECMO. Graphical abstract The results showed the deoxygenated blood and oxygenated blood met at the aortic arch and formed the so-called "oxygenshed" phenomenon. This phenomenon is consistent with the phenomenon called "watershed".

The Effect of Arterial Curvature on Blood Flow in Arterio-Venous Fistulae: Realistic Geometries and Pulsatile Flow

Arterio-Venous Fistulae (AVF) are regarded as the "gold standard" method of vascular access for patients with End-Stage Renal Disease (ESRD) who require haemodialysis. However, up to 60% of AVF do not mature, and hence fail, as a result of Intimal Hyperplasia (IH). Unphysiological flow and oxygen transport patterns, associated with the unnatural and often complex geometries of AVF, are believed to be implicated in the development of IH. Previous studies have investigated the effect of arterial curvature on blood flow in AVF using idealized planar AVF configurations and non-pulsatile inflow conditions. The present study takes an important step forwards by extending this work to more realistic non-planar brachiocephalic AVF configurations with pulsatile inflow conditions. Results show that forming an AVF by connecting a vein onto the outer curvature of an arterial bend does not, necessarily, suppress unsteady flow in the artery. This finding is converse to results from a previous more idealized study. However, results also show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can suppress exposure to regions of low wall shear stress and hypoxia in the artery. This finding is in agreement with results from a previous more idealized study. Finally, results show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can significantly reduce exposure to high WSS in the vein. The results are important, as they demonstrate that in realistic scenarios arterial curvature can be leveraged to reduce exposure to excessively low/high levels of WSS and regions of hypoxia in AVF. This may in turn reduce rates of IH and hence AVF failure.

Low-density lipoprotein transport through an arterial wall under hypertension - A model with time and pressure dependent fraction of leaky junction consistent with experiments

The influence of hypertension on low-density lipoproteins intake into the arterial wall is an important factor for understanding mechanisms of atherosclerosis. It has been experimentally observed that the increased pressure leads to the higher level of the LDL inside the wall. In this paper we attempt to construct a model of the LDL transport which reproduces quantitatively experimental outcomes. We supplement the well-known four-layer arterial wall model to include two pressure induced effects: the compression of the intima tissue and the increase of the fraction of leaky junctions. We demonstrate that such model can reach the very good agreement with experimental data.

Relative Effects of Fluid Oscillations and Nutrient Transport in the In Vitro Growth of Valvular Tissues

Engineered valvular tissues are cultured dynamically, and involve specimen movement. We previously demonstrated that oscillatory shear stresses (OSS) under combined steady flow and specimen cyclic flexure (flex-flow) promote tissue formation. However, localized efficiency of specimen mass transport is also important in the context of cell viability within the growing tissues. Here, we investigated the delivery of two essential species for cell survival, glucose and oxygen, to 3-dimensional (3D) engineered valvular tissues. We applied a convective-diffusive model to characterize glucose and oxygen mass transport with and without valve-like specimen flexural movement. We found the mass transport effects for glucose and oxygen to be negligible for scaffold porosities typically present during in vitro experiments and non-essential unless the porosity was unusually low (<40%). For more typical scaffold porosities (75%) however, we found negligible variation in the specimen mass fraction of glucose and oxygen in both non-moving and moving constructs (p > 0.05). Based on this result, we conducted an experiment using bone marrow stem cell (BMSC)-seeded scaffolds under Pulsatile flow-alone states to permit OSS without any specimen movement. BMSC-seeded specimen collagen from the pulsatile flow and flex-flow environments were subsequently found to be comparable (p > 0.05) and exhibited some gene expression similarities. We conclude that a critical magnitude of fluid-induced, OSS created by either pulsatile flow or flex-flow conditions, particularly when the oscillations are physiologically-relevant, is the direct, principal stimulus that promotes engineered valvular tissues and its phenotype, whereas mass transport benefits derived from specimen movement are minimal.

The effect of in-plane arterial curvature on blood flow and oxygen transport in arterio-venous fistulae

Arterio-Venous Fistulae (AVF) are the preferred method of vascular access for patients with end stage renal disease who need hemodialysis. In this study, simulations of blood flow and oxygen transport were undertaken in various idealized AVF configurations. The objective of the study was to understand how arterial curvature affects blood flow and oxygen transport patterns within AVF, with a focus on how curvature alters metrics known to correlate with vascular pathology such as Intimal Hyperplasia (IH). If one subscribes to the hypothesis that unsteady flow causes IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto the outer-curvature of a curved artery. However, if one subscribes to the hypothesis that low wall shear stress and/or low lumen-to-wall oxygen flux (leading to wall hypoxia) cause IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto a straight artery, or the inner-curvature of a curved artery. We note that the recommendations are incompatible-highlighting the importance of ascertaining the exact mechanisms underlying development of IH in AVF. Nonetheless, the results clearly illustrate the important role played by arterial curvature in determining AVF hemodynamics, which to our knowledge has been overlooked in all previous studies.

Synergy between shear-induced migration and secondary flows on red blood cells transport in arteries: considerations on oxygen transport

Shear-induced migration of red blood cells (RBCs) is a well-known phenomenon characterizing blood flow in the small vessels (micrometre to millimetre size) of the cardiovascular system. In large vessels, like the abdominal aorta and the carotid artery (millimetre to centimetre size), the extent of this migration and its interaction with secondary flows has not been fully elucidated. RBC migration exerts its influence primarily on platelet concentration, oxygen transport and oxygen availability at the luminal surface, which could influence vessel wall disease processes in and adjacent to the intima. Phillips' shear-induced particle migration model, coupled to the Quemada viscosity model, was employed to simulate the macroscopic behaviour of RBCs in four patient-specific geometries: a normal abdominal aorta, an abdominal aortic aneurysm (AAA), a normal carotid bifurcation and a stenotic carotid bifurcation. Simulations show a migration of RBCs from the near-wall region with a lowering of wall haematocrit (volume fraction of RBCs) on the posterior side of the normal aorta and on the lateral-external side of the iliac arteries. A marked migration is observed on the outer wall of the carotid sinus, along the common carotid artery and in the carotid stenosis. No significant migration is observed in the AAA. The spatial and temporal patterns of wall haematocrit are correlated with the near-wall shear layer and with the secondary flows induced by the vessel curvature. In particular, secondary flows accentuate the initial lowering in RBC near-wall concentration by convecting RBCs from the inner curvature side to the outer curvature side. The results reinforce data in literature showing a decrease in oxygen partial pressure on the inner curvature wall of the carotid sinus induced by the presence of secondary flows. The lowering of wall haematocrit is postulated to induce a decrease in oxygen availability at the luminal surface through a diminished concentration of oxyhaemoglobin, hence contributing, with the reported lowered oxygen partial pressure, to local hypoxia.

A computational model of drug delivery through microcirculation to compare different tumor treatments

Starting from the fundamental laws of filtration and transport in biological tissues, we develop a computational model to capture the interplay between blood perfusion, fluid exchange with the interstitial volume, mass transport in the capillary bed, through the capillary walls and into the surrounding tissue. These phenomena are accounted at the microscale level, where capillaries and interstitial volume are viewed as two separate regions. The capillaries are described as a network of vessels carrying blood flow. We apply the model to study drug delivery to tumors. The model can be adapted to compare various treatment options. In particular, we consider delivery using drug bolus injection and nanoparticle injection into the blood stream. The computational approach is suitable for a systematic quantification of the treatment performance, enabling the analysis of interstitial drug concentration levels, metabolization rates and cell surviving fractions. Our study suggests that for the treatment based on bolus injection, the drug dose is not optimally delivered to the tumor interstitial volume. Using nanoparticles as intermediate drug carriers overrides the shortcomings of the previous delivery approach. This work shows that the proposed theoretical and computational framework represents a promising tool to compare the efficacy of different cancer treatments.

From Histology and Imaging Data to Models for In-Stent Restenosis

The implantation of stents has been used to treat coronary artery stenosis for several decades. Although stenting is successful in restoring the vessel lumen and is a minimally invasive approach, the long-term outcomes are often compromised by in-stent restenosis (ISR). Animal models have provided insights into the pathophysiology of ISR and are widely used to evaluate candidate drug inhibitors of ISR. Such biological models allow the response of the vessel to stent implantation to be studied without the variation of lesion characteristics encountered in patient studies.

This paper describes the development of complementary in silico models employed to improve the understanding of the biological response to stenting using a porcine model of restenosis. This includes experimental quantification using microCT imaging and histology and the use of this data to establish numerical models of restenosis. Comparison of in silico results with histology is used to examine the relationship between spatial localization of fluid and solid mechanics stimuli immediately post-stenting. Multi-scale simulation methods are employed to study the evolution of neointimal growth over time and the variation in the extent of neointimal hyperplasia within the stented region. Interpretation of model results through direct comparison with the biological response contributes to more detailed understanding of the pathophysiology of ISR, and suggests the focus for follow-up studies.

In conclusion we outline the challenges which remain to both complete our understanding of the mechanisms responsible for restenosis and translate these models to applications in stent design and treatment planning at both population-based and patient-specific levels.

Simulation of oxygen transfer in stented arteries and correlation with in-stent restenosis

Computational models are used to study the combined effect of biomechanical and biochemical factors on coronary in-stent restenosis, which is a postoperative remodeling and regrowth pathology of the stented arteries. More precisely, we address numerical simulations, on the basis of Navier-Stokes and mass transport equations, to study the role of perturbed wall shear stresses and reduced oxygen concentration in a geometrical model reconstructed from a real porcine artery treated with a stent. Joining in vivo and in silico tools of investigation has multiple benefits in this case. On one hand, the geometry of the arterial wall and of the stent closely correspond to a real implanted configuration. On the other hand, the inspection of histological tissue samples informs us on the location and intensity of in-stent restenosis. As a result, we are able to correlate geometrical factors, such as the axial variation of the artery diameter and its curvature; the numerical quantification of biochemical stimuli, such as wall shear stresses; and the availability of oxygen to the inner layers of the artery, with the appearance of in-stent restenosis. This study shows that the perturbation of the vessel curvature could induce hemodynamic conditions that stimulate undesired arterial remodeling.

Numerical investigation of mass transport through patient-specific deformed aortae

Blood flow in human arteries has been investigated using computational fluid dynamics tools. This paper considers flow modeling through three aorta models reconstructed from cross-sectional magnetic resonance scans of female patients. One has the normal control configuration, the second has elongation of the transverse aorta, and the third has tortuosity of the aorta with stenosis. The objective of this study is to determine the impact of aortic abnormal geometries on the wall shear stress (WSS), luminal surface low-density lipoproteins (LDLs) concentration, and oxygen flux along the arterial wall. The results show that the curvature of the aortic arch and the stenosis have significant effects on the blood flow, and in turn, the mass transport. The location of hypoxia areas can be predicted well by ignoring the effect of hemoglobin on the oxygen transport. However, this simplification indeed alters the absolute value of Sherwood number on the wall.

Computer simulation and experimental analysis of LDL transport in the arteries

Atherosclerosis develops from oxidized low-density lipoprotein molecules (LDL). When oxidized LDL evolves in plaque formations within an artery wall, a series of reactions occur to repair the damage to the artery wall caused by oxidized LDL. Macrophages accumulate inside arterial intima, they started to collect oxidized LDL and form foam cells. Smooth muscle cells accumulate in the atherosclerotic arterial intima, where they proliferate and secrete extracellular matrix to form a fibrous cap. In this study, experimental model of LDL transport on the isolated blood vessel from rabbit on high fat diet after 8 weeks is simulated numerically by using a specific model and histological data. The 3D blood flow is governed by the Navier-Stokes equations, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow by the convection-diffusion equation. LDL transport in lumen of the vessel is described by Kedem-Katchalsky equations. The inflammatory process is solved using three additional reaction-diffusion partial differential equations. Matching of histological rabbit data is performed using 3D histological image reconstruction and 3D deformation of elastic body. Computed concentrations of labeled LDL of 5.2 % and macrophages distribution of 4.2% inside the media are found to be in good agreement with experimental results. This simulation study provides a useful tool for understanding and prediction of LDL transport through the arterial wall and evolution of atherosclerotic plaques.

A mathematical model of evolving mechanical properties of intraluminal thrombus

Quantifying mechanical properties of blood clots is fundamental to understanding many aspects of cardiovascular disease and its treatment. Nevertheless, there has been little attention to quantifying the evolving composition, structure and properties when a clot transforms from an initial fibrin-based mesh to a predominantly collagenous mass. Although more data are needed to formulate a complete mathematical model of the evolution of clot properties, we propose a general constrained mixture model based on diverse data available from in vitro tests on fibrinogenesis, the stiffness of fibrin gels, and fibrinolysis as well as histological and mechanical data from clots retrieved from patients at surgery or autopsy. In particular, albeit resulting from complex kinetics involving many clotting factors, we show that the rapid (minutes) in vitro production of fibrin from fibrinogen can be modeled well by an Avrami-type relation and similarly that the fast (tens of minutes) in vitro degradation of fibrin in response to different concentrations of plasmin can be captured via a single "master function" parameterized by appropriate half-times that can be inferred from laboratory or clinical data. Accounting simultaneously for the production and removal of fibrin as well as chemo-mechano-stimulated production of fibrillar collagens yields predictions of changing mass fractions and bulk mechanical properties that correspond well to experimentally available data. Constrained mixture models thus hold considerable promise for modeling the biomechanics of clot evolution and can guide the design and interpretation of needed experiments and stress analyses.

Computational analysis of oxygen transport in the retinal arterial network

PURPOSE

The retina has a high oxygen consumption, making it particularly vulnerable to vascular insults, impairing oxygen and nutrient supply. The aim of this study was to develop a detailed computational model for quantitative analysis of blood flow and oxygen transport in physiologically realistic retinal arterial networks. Such a model will allow us to examine the effect of topological changes in retinal vasculature on hemodynamics and oxygen distribution in the retinal circulation.

MATERIALS AND METHODS

The Navier-Stokes equations for blood flow and the convection-diffusion equation for oxygen transfer were solved numerically to obtain detailed blood flow and oxygen distribution patterns in a retinal arterial tree. The geometrical outlines of the central retinal artery and its major branches were extracted from retinal images acquired from a healthy young adult by a Zeiss FF450+ fundus camera. The reconstructed subject-specific retinal arterial network geometry was combined with a structured tree model for the distal peripheral vessels. The non-Newtonian rheological properties of blood were incorporated by using an empirical viscosity model to account for the Fahraeus-Lindqvist effect.

RESULTS

The model predicted pressure drops in the range of 11-14.6 mmHg between the inlet and outlets of the reconstructed network and non-uniform oxygen tension, which varied with the vessel diameter and distance from the optic disc. The mean oxygen saturation in retinal arteries was 93.1% for vessels larger than 50 mum in diameter and 82.2% for smaller arterioles.

CONCLUSIONS

Our numerical results are in good agreement with in vivo measurements reported in the literature, demonstrating the potential of our model for prediction of oxygen distribution and intravascular oxygen tension profiles in the retinal arterial network. This paves the way for investigating the effects of parameter variation, simulating cases not available from experimental studies.

ATP transport in saccular cerebral aneurysms at arterial bends

ATP acts as an extracellular signaling molecule in purinergic signaling that regulates vascular tone. ATP binds purinergic P2 nucleotide receptors on endothelial cells. Understanding the mass transport of ATP to endothelial cells by blood flow is thus important to predict functional changes in aneurysmal walls. While some clinical observations indicate a difference of wall pathology between ruptured and unruptured aneurysms, no study has focused on the mass transport in aneurysms. We investigated the characteristics of ATP concentration at aneurysmal wall using a numerical model of ATP transport in aneurysms formed at arterial bends. The magnitude of ATP concentration at the aneurysmal wall was significantly smaller than that at the arterial wall. In particular, significantly low concentration was predicted at the proximal side of the aneurysmal sac. A strong correlation was revealed between the inflow flux at the aneurysmal neck and the resultant concentration at the aneurysmal wall.

Age-dependent changes in oxygen tension, radiation dose and sensitivity within normal and diseased coronary arteries-Part A: dose from radon and thoron

PURPOSE

There is mounting evidence that a significant fraction of radiation-induced mortality and years-life lost are non-cancerous in nature. This study quantifies the radon dose to the coronary artery walls, especially the intimal layer, vulnerable to the development of atherosclerosis, and associated cardiovascular disease (CVD). Two accompanying papers determine the oxygen levels (Part B) in coronary arteries and the oxygen effect for radon and other exposures (Part C).

MATERIALS AND METHODS

The alpha-radiation dose to coronary artery walls was calculated from the proportion of inhaled radon ((222)Rn), thoron ((220)Rn) and their short-lived progeny, which was not deposited in the lung and passed into blood. Age- and gender-dependent morphology and composition for the wall layers of coronary arteries were developed from published data for a normal population and also for individuals with cardiovascular disease. The alpha particle dose to the coronary artery walls was evaluated taking account the diffusion of radon from blood and the solubility of radon-gas in tissues.

RESULTS

Diseased arteries exhibited a moderate increase in the solubility of lipophylic radon (190%) in arteries with 88% luminal narrowing, as the high Rn solubility in fat was partially offset by the lower solubility in calcium deposits. The average worldwide dose rate to the diseased intimal layer from (222)Rn and its short-lived progeny was estimated to be as high as 68 muSv y(-1) per 40 Bq m(-3) in air, whereas the corresponding dose rate from (220)Rn per 0.3 Bq m(-3) in air was <or=0.1% in comparison. Gender had little influence on the dose.

CONCLUSION

The Rn dose to the coronary arteries is significant, but has a large uncertainty due to poor knowledge of Rn and its progeny concentrations in the body.

Age-dependent changes in oxygen tension, radiation dose and sensitivity within normal and diseased coronary arteries-Part B: modeling oxygen diffusion into vessel walls

PURPOSE

The aim is to assess the change with age and disease of the oxygen concentration within the coronary artery walls.

MATERIALS AND METHODS

In an accompanying paper, Part A, the age-dependent morphology and composition for the wall layers of normal and diseased coronary arteries were developed from published data. In this paper, Part B, the oxygen concentration in the coronary artery walls was evaluated taking account the diffusion of oxygen from blood and the solubility of oxygen in tissues. Part C evaluates the oxygen effect and its biological implications for different radiations.

RESULTS

Diseased arteries exhibited a relatively moderate increase in the solubility of oxygen (<or=59%) in arteries with 88% luminal narrowing, as the high solubility in fat was partially offset by the lower solubility in calcium deposits. The oxygen partial pressure across the arterial wall was modeled and the avascular regions of arteries with >or=38% stenosis had anoxic areas.

CONCLUSION

Based on simulation results from the one-dimensional diffusion model, extensive hypoxic areas were determined for atherosclerotic arteries in this analysis of oxygen levels in coronary arteries modelling for the first time the effects of age and disease and associated changes in oxygen solubility due to the presence of lipids and calcium.

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.

Oxygen mass transfer in a model three-dimensional artery

Arterial geometry is commonly non-planar and associated with swirling blood flow. In this study, we examine the effect of arterial three-dimensionality on the distribution of wall shear stress (WSS) and the mass transfer of oxygen from the blood to the vessel wall in a U-bend, by modelling the blood vessels as either cylindrical or helical conduits. The results show that under physiological flow conditions, three-dimensionality can reduce both the range and extent of low WSS regions and substantially increase oxygen flux through the walls. The Sherwood number and WSS distributions between the three-dimensional helical model and a human coronary artery show remarkable qualitative agreement, implying that coronary arteries may potentially be described with a relatively simple idealized three-dimensional model, characterized by a small number of well-defined geometric parameters. The flow pattern downstream of a planar bend results in separation of the Sh number and WSS effects, a finding that implies means of investigating them individually.

Effect of Blood Viscosity on Oxygen Transport in Residual Stenosed Artery Following Angioplasty

The effect of blood viscosity on oxygen transport in a stenosed coronary artery during the postangioplasty scenario is studied. In addition to incorporating varying blood viscosity using different hematocrit (Hct) concentrations, oxygen consumption by the avascular wall and its supply from vasa vasorum, nonlinear oxygen binding capacity of the hemoglobin, and basal to hyperemic flow rate changes are included in the calculation of oxygen transport in both the lumen and the avascular wall. The results of this study show that oxygen transport in the postangioplasty residual stenosed artery is affected by non-Newtonian shear-thinning property of the blood viscosity having variable Hct concentration. As Hct increases from 25% to 65%, the diminished recirculation zone for the increased Hct causes the commencement of pO2 decrease to shift radially outward by ∼20% from the center of the artery for the basal flow, but by ∼10% for the hyperemic flow at the end of the diverging section. Oxygen concentration increases from a minimum value at the core of the recirculation zone to over 90mmHg before the lumen-wall interface at the diverging section for the hyperemic flow, which is attributed to increased shear rate and thinner lumen boundary layer for the hyperemic flow, and below 90mmHg for the basal flow. As Hct increases from 25% to 65%, the average of pO2,min beyond the diverging section drops by ∼25% for the basal flow, whereas it increases by ∼15% for the hyperemic flow. Thus, current results with the moderate stenosed artery indicate that reducing Hct might be favorable in terms of increasing O2 flux and pO2,min, in the medial region of the wall for the basal flow, while higher Hct is advantageous for the hyperemic flow beyond the diverging section. The results of this study not only provide significant details of oxygen transport under varying pathophysiologic blood conditions such as unusually high blood viscosity and flow rate, but might also be extended to offer implications for drug therapy related to blood-thinning medication and for blood transfusion and hemorrhage.