Oxygen Mass Transport in a Compliant Carotid Bifurcation Model

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.

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.

Biomechanical Aspects of Closing Approaches in Postcarotid Endarterectomy

The carotid bifurcation tends to develop atherosclerotic stenoses which might interfere with cerebral blood supply. In cases of arterial blockage, the common clinical solution is to remove the plaque via carotid endarterectomy (CEA) surgery. Artery closure after surgery using primary closures along the cutting edge might lead to artery narrowing and restrict blood flow. An alternative approach is patch angioplasty which takes longer time and leads to more during-surgery complications. The present study uses numerical methods with fluid-structure interaction (FSI) to explore and compare the two solutions in terms of hemodynamics and stress and strain fields developed in the artery wall.

Segment-specific associations between local haemodynamic and imaging markers of early atherosclerosis at the carotid artery: an in vivo human study

Low and oscillatory wall shear stress (WSS) has long been hypothesized as a risk factor for atherosclerosis; however, evidence has been inferred primarily from model and post-mortem studies, or clinical studies of patients with already-developed plaques. This study aimed to identify associations between local haemodynamic and imaging markers of early atherosclerosis. Comprehensive magnetic resonance imaging allowed quantification of contrast enhancement (CE) (a marker of endothelial dysfunction) and vessel wall thickness at two distinct segments: the internal carotid artery bulb and the common carotid artery (CCA). Strict criteria were applied to a large dataset to exclude inward remodelling, resulting in 41 cases for which personalized computational fluid dynamic simulations were performed. After controlling for cardiovascular risk factors, bulb wall thickening was found to be weakly, but not significantly, associated with oscillatory WSS. CE at the bulb was significantly associated with low WSS (p < 0.001) and low flow helicity (p < 0.05). No significant associations were found for the CCA segment. Local haemodynamics at the bulb were significantly correlated with blood flow rates and heart rates, but not carotid bifurcation geometry (flare and curvature). Therefore low, but not oscillatory, WSS is an early independent marker of atherosclerotic changes preceding intimal thickening at the carotid bulb.

Hemodynamics and Oxygen Transport through Pararenal Aortic Aneurysm Treated with Multilayer Stent: A Numerical Study

BACKGROUND

As opposed to an endoluminal stent graft, a multilayer stent (MS) consists of a porous mesh, which allows for the possibility of treating pararenal aortic aneurysms (PRAAs) that involve a significant branch vessel. However, the choice of the density of the MS plays a vital role in isolating the aneurysm and allowing unobstructed blood flow in the branch vessel.

METHOD

In the present study, we examined 3 cases (without a stent and with single-layer and double-layer stents) via numerical simulations to explore the feasibility of the MSs used in the treatment of such aneurysms and estimate whether there is a more appropriate or optimal stent density.

RESULTS

With stent intervention, the velocity of blood flow in the sac decreased, but the pressure on the surface of the aneurysm did not decrease although it became more uniform. In addition, the "region of double low" (with low wall shear stress and a low Sherwood number) enlarged after stent implantation. Even with the double-layer stent, however, the flux of the branch vessel was still above normal, and we could predict that the optimal stent porosity was approximately 49.9%.

CONCLUSIONS

Unlike in previous studies, an MS could not be feasibly applied to high-risk PRAAs. However, an MS can induce sac thrombosis in the later stages while maintaining visceral vessel patency, and our results suggest that the optimal stent may be a 4-layer stent.

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 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.

Simulation of contrast agent transport in arteries with multilayer arterial wall: impact of arterial transmural transport on the bolus delay and dispersion

One assumption of DSC-MRI is that the injected contrast agent is kept totally intravascular and the arterial wall is impermeable to contrast agent. The assumption is unreal for such small contrast agent as Gd-DTPA can leak into the arterial wall. To investigate whether the unreal assumption is valid for the estimation of the delay and dispersion of the contrast agent bolus, we simulated flow and Gd-DTPA transport in a model with multilayer arterial wall and analyzed the bolus delay and dispersion qualified by mean vascular transit time (MVTT) and the variance of the vascular transport function. Factors that may affect Gd-DTPA transport hence the delay and dispersion were further investigated, such as integrity of endothelium and disturbed flow. The results revealed that arterial transmural transport would slightly affect MVTT and moderately increase the variance. In addition, although the integrity of endothelium can significantly affect the accumulation of contrast agent in the arterial wall, it had small effects on the bolus delay and dispersion. However, the disturbed flow would significantly increase both MVTT and the variance. In conclusion, arterial transmural transport may have a small effect on the bolus delay and dispersion when compared to the flow pattern in the artery.

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.

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.

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 the stress phase angle on the strain energy density of the endothelial plasma membrane

Endothelial cells are simultaneously exposed to the mechanical forces of fluid wall shear stress (WSS) imposed by blood flow and solid circumferential stress (CS) induced by the blood vessel's elastic response to the pressure pulse. Experiments have demonstrated that these combined forces induce unique endothelial biomolecular responses that are not characteristic of either driving force alone and that the temporal phase angle between WSS and CS, referred to as the stress phase angle, modulates endothelial responses. In this article, we provide the first theoretical model to examine the combined forces of WSS and CS on a model of the endothelial cell plasma membrane. We focus on the strain energy density of the membrane that modulates the opening of ion channels that can mediate signal transduction. The model shows a significant influence of the stress phase angle on the strain energy density at the upstream and downstream ends of the cell where mechanotransduction is most likely to occur.