Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during angioplasty

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied numerically by solving the convection-diffusion equations. Two geometries replicating stenosis before and after percutaneous transluminal coronary angioplasty (PTCA) are used for the analysis. The results are compared to evaluate the effect of the degree of stenosis on oxygen transport. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. The results show that the PO2 in the medial region of the arterial wall is approximately 10mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation, there is a small rise followed by a sharp fall in the oxygen flux. The drop in the oxygen flux to the wall at the point of flow reattachment for pre-PTCA stenosis is four times that for post-PTCA stenosis. The minimum PO2 in the avascular wall, PO2,min, at this location decreases to approximately 6.0 and 4.2mmHg for post- and pre-PTCA stenosis, respectively. The drop in PO2,w and PO2,min at the point of flow reattachment for pre-PTCA is approximately 2 times that for post-PTCA stenosis. Thus, the present study quantifies the oxygen transport to the arterial wall before and after cardiovascular intervention.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

Nitric Oxide Transport in Normal Human Thoracic Aorta: Effects of Hemodynamics and Nitric Oxide Scavengers

Despite the crucial role of nitric oxide (NO) in the homeostasis of the vasculature, little quantitative information exists concerning NO transport and distribution in medium and large-sized arteries where atherosclerosis and aneurysm occur and hemodynamics is complex. We hypothesized that local hemodynamics in arteries may govern NO transport and affect the distribution of NO in the arteries, hence playing an important role in the localization of vascular diseases. To substantiate this hypothesis, we presented a lumen/wall model of the human aorta based on its MRI images to simulate the production, transport and consumption of NO in the arterial lumen and within the aortic wall. The results demonstrated that the distribution of NO in the aorta was quite uneven with remarkably reduced NO bioavailability in regions of disturbed flow, and local hemodynamics could affect NO distribution mainly via flow dependent NO production rate of endothelium. In addition, erythrocytes in the blood could moderately modulate NO concentration in the aorta, especially at the endothelial surface. However, the reaction of NO within the wall could only slightly affect NO concentration on the luminal surface, but strongly reduce NO concentration within the aortic wall. A strong positive correlation was revealed between wall shear stress and NO concentration, which was affected by local hemodynamics and NO reaction rate. In conclusion, the distribution of NO in the aorta may be determined by local hemodynamics and modulated differently by NO scavengers in the lumen and within the wall.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

Fluid–structure interaction analysis of turbulent pulsatile flow within a layered aortic wall as related to aortic dissection

Turbulent pulsatile flow and wall mechanics were studied numerically in an axisymmetric three-layered wall model of a descending aorta. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this investigation. We calculated Von Mises wall stress, streamlines and fluid pressure contours. The findings of this study show that peak wall stress and maximum shear stress are highest in the media layer. The difference in the elastic properties of contiguous layers of the wall of the aorta probably determines the occurrence of dissection in the media layer. Moreover, the presence of aortic intramural hematoma is found to have a significant effect on the peak wall stress acting on the inner layer.     

The effects of erythrocythemia on blood viscosity,maximal systemic oxygen transport capacity and maximal rates of oxygen consumption in an amphibian

Graded erythrocythemia was induced by isovolemic loading of packed red blood cells in the toad, Bufo marinus. Blood viscosity, hematocrit, hemoglobin concentration, maximal aortic blood flow rate and maximal rates of oxygen consumption were determined after each load. Blood viscosity was related to hematocrit in the expected exponential manner; ln eta = 0.43 + 0.035 Hct. Maximal blood flow rates in the dorsal aorta were inversely proportional to blood viscosity and fit predictions of the Poiseuille-Hagen flow formula. The effect of increased blood viscosity was to reduce aortic pulse volume, but not maximal heart rate. Maximal systemic oxygen transport capacity (aortic blood flow rate X hemoglobin concentration X O2 binding capacity of hemoglobin) was linearly correlated with the maximal rate of oxygen consumption. These date indicate that optimal hematocrit theory is applicable for maximal blood flow rates in vivo, and that systemic oxygen transport is the primary limitation to aerial VO2 max in amphibians.     

Adventitial Vasa Vasorum Arteriosclerosis in Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is a common disease among elderly individuals. However, the precise pathophysiology of AAA remains unknown. In AAA, an intraluminal thrombus prevents luminal perfusion of oxygen, allowing only the adventitial vaso vasorum (VV) to deliver oxygen and nutrients to the aortic wall. In this study, we examined changes in the adventitial VV wall in AAA to clarify the histopathological mechanisms underlying AAA. We found marked intimal hyperplasia of the adventitial VV in the AAA sac; further, immunohistological studies revealed proliferation of smooth muscle cells, which caused luminal stenosis of the VV. We also found decreased HemeB signals in the aortic wall of the sac as compared with those in the aortic wall of the neck region in AAA. The stenosis of adventitial VV in the AAA sac and the malperfusion of the aortic wall observed in the present study are new aspects of AAA pathology that are expected to enhance our understanding of this disease.     

Coupled oxygen transport analysis in the avascular wall of a post-angioplasty coronary artery stenosis

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied by numerically solving the convection-diffusion equations. Geometry, replicating residual stenosis after percutaneous transluminal coronary angioplasty (PTCA), is used for the analysis. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. Mean blood flow rate in the lumen is varied from basal to hyperemic conditions. The results show that the P(O2) in the medial region of the arterial wall is approximately 10 mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation there is a small rise and a sharp fall in the oxygen flux. The minimum P(O2) in the avascular wall, P(O2, min ), at the point of flow reattachment reduces to approximately 6 mmHg for a 300 micron wall thickness. For a thinner wall of 200 micron, the P(O2, min ) at the location of flow reattachment increases to 6 times that of a 300 micron wall. The P(O2, min ) in the wall decreases by 60% when volumetric oxygen consumption is increased by 30% for the same avascular wall thickness.     

A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta

The pulmonary artery (PA) wall, which has much higher hydraulic conductivity and albumin void space and approximately one-sixth the normal transmural pressure of systemic arteries (e.g, aorta, carotid arteries), is rarely atherosclerotic, except under pulmonary hypertension. This study constructs a detailed, two-dimensional, wall-structure-based filtration and macromolecular transport model for the PA to investigate differences in prelesion transport processes between the disease-susceptible aorta and the relatively resistant PA. The PA and aorta models are similar in wall structure, but very different in parameter values, many of which have been measured (and therefore modified) since the original aorta model of Huang et al. (23). Both PA and aortic model simulations fit experimental data on transwall LDL concentration profiles and on the growth of isolated endothelial (horseradish peroxidase) tracer spots with circulation time very well. They reveal that lipid entering the aorta attains a much higher intima than media concentration but distributes better between these regions in the PA than aorta and that tracer in both regions contributes to observed tracer spots. Solutions show why both the overall transmural water flow and spot growth rates are similar in these vessels despite very different material transport parameters. Since early lipid accumulation occurs in the subendothelial intima and since (matrix binding) reaction kinetics depend on reactant concentrations, the lower intima lipid concentrations in the PA vs. aorta likely lead to slower accumulation of bound lipid in the PA. These findings may be relevant to understanding the different atherosusceptibilities of these vessels.     

Computational analysis of blood flow in an integrated model of the left ventricle and the aorta

To study the effects of intraventricular flow dynamics on the aortic flow, we created an integrated model of the left ventricle and aorta and conducted a computer simulation of diastolic and systolic blood flow within this model. The results demonstrated that the velocity profile at the aortic annulus changed dynamically, and was influenced by the intraventricular flow dynamics. The profile was almost flat in early systole but became nonuniform as systole progressed, and was skewed toward the posterior side in midsystole and toward the anterior side in later systole. At a distance from the aortic annulus, a different velocity profile was induced by the twisting and torsion of the aorta. In the ascending aorta, the fastest flow was initially located in the posteromedial sector, and it moved to the posterior section along the circumference as systole progressed. The nonuniformity of the aortic inflow gave rise to a complex wall shear stress (WSS) distribution in the aorta. A comparison of the WSS distribution obtained in this integrated analysis with that obtained in flow calculations using an isolated aorta model with Poiseuille and flat inlet conditions showed that intraventricular flow affected the WSS distribution in the ascending aorta. These results address the importance of an integrated analysis of flow in the left ventricle and aorta.     

Fluid-Structure Interaction Analysis of Pulsatile Flow within a Layered and Stenotic Aorta

In this paper, the hemodynamic characteristics of blood flow and stress distribution in a layered and stenotic aorta are investigated. By introducing symmetrical and unsymmetrical stenosis, the influence of stenosis morphology and stenotic ratio on the coupled dynamic responses of aorta is clarified. In the analysis, the in-vivo pulsatile waveforms and fully fluid–structure interaction (FSI) between the layered elastic aorta and the blood are considered. The results show that the fluid domain is abnormal in the stenotic aorta, and the whirlpool forms at the obstructed and downstream unobstructed regions. The maximum wall shear stresses appear at the throat of the stenosis. Downstream region appears low and oscillated shear stresses. In addition, along with the increase of the stenotic ratio, the amplitude of the maximum shear stress will be intensively increased and localized, and the sensitivity is also increased. In the aorta with unsymmetrical stenosis, the Von Mises stresses reach the peak value at the side with the surface protuberance, but they are reduced at the side with no protuberance. The sign variation of the layer interface shear stresses near the throat indicates the variation of the shear direction which increases the opportunity of shear damage at the transition plane. Moreover, the shear stress levels at the fluid-solid and intima-media interfaces are higher than that at the media-adventitia interface. The unsymmetrical stenosis causes higher stresses at the side with the surface protuberance than symmetrical one, but lower at the side with no protuberance. These results provide an insight in the influence of the stenosis, as well as its morphology, on the pathogenesis and pathological evolution of some diseases, such as arteriosclerosis and aortic dissection.     

Respective impacts of aortic stenosis and systemic hypertension on left ventricular hypertrophy

It has been reported that 30-40% of patients with aortic stenosis are hypertensive. In such patients, the left ventricle faces a double (i.e. valvular and vascular) pressure overload, which results in subsequent wall volume hypertrophy. From a clinical standpoint, it is difficult to separate the respective contributions of aortic stenosis and systemic hypertension to left ventricular burden and patient's symptoms and thus to predict whether valve replacement would be beneficial. The objective of this theoretical study was therefore to investigate the relative effects of valvular and vascular afterloads on left ventricular hypertrophy. We used a ventricular-valvular-vascular mathematical model in combination with the Arts' model describing the myofiber stress. Left ventricular wall volume was computed for different aortic blood pressure levels and different degrees of aortic stenosis severity. Our simulations show that the presence of concomitant systemic hypertension has a major influence on the development of left ventricular hypertrophy in patients with aortic stenosis. These results also suggest that mild-to-moderate aortic stenosis has a minor impact on left ventricular wall volume when compared with hypertension. On the other hand, when aortic stenosis is severe, wall volume increases exponentially with increasing aortic stenosis severity and the impact of aortic stenosis on left ventricular hypertrophy becomes highly significant.     

Velocity distribution along an elastic model of human arterial tree

An experimental investigation of an elastic model of the human arterial tree, has been performed for physiological type flow by pulsed Doppler ultrasonic velocimetry. The arterial tree model, fabricated in clear polyurethane, includes the aortic arch, with a Starr-Edwards ball valve mounted in the root of the aorta, the descending aorta and the iliac bifurcation. Our study showed that the velocity profile, a few centimeters beyond the valve, is skewed, with higher velocities towards the top and the inner wall (anatomically the posterior and left lateral wall). An inward shift of the maximum velocity and reverse flow are denoted along the inner wall of the aortic arch. The velocity profiles in the descending aorta are blunted. Downstream from the vertex of the iliac bifurcation, there is vorticity creation, but the branching effect is quickly damped by the pulsatility of the flow and the elasticity of the wall.     

Does vibration cause poststenotic dilatation in vivo and influence atherogenesis in cholesterol-fed rabbits?

Arterial post-stenotic dilatation (PSD) is a fusiform swelling immediately down-stream to a stenosis. It is characterized by the presence of turbulent blood flow and wall vibration which has been claimed by others to be causal by producing structural weakening. We tested the hypothesis that vibration causes PSD in vivo by attaching electromagnetic and pneumatic vibrators to the aortic wall in chronic rabbits. We also observed whether mechanical vibration of the aorta in vivo influenced the distribution of oil-red-O lesions during one percent dietary cholesterol feeding. Low mass vibration gauges were developed to measure the vibration. Electromechanical vibrators having a ceramic magnet slug within a coil supplied with 50 Hz were glued to the aorta of chronic rabbits and the vibration maintained for an average of 8 weeks. Despite greater amounts of energy imparted to the wall there was no dilatation or difference in oil-red-O staining from the controls. Five weeks vibration at 100 Hz and an amplitude equal to the normal diameter pulse also produced no dilatation. We conclude that vibration does not cause PSD in vivo and suggest that its cause is likely to involve the vascular muscle stimulated by the effect of turbulent flow on the endothelium.     

Fluid Dynamics of Coarctation of the Aorta and Effect of Bicuspid Aortic Valve

Up to 80% of patients with coarctation of the aorta (COA) have a bicuspid aortic valve (BAV). Patients with COA and BAV have elevated risks of aortic complications despite successful surgical repair. The development of such complications involves the interplay between the mechanical forces applied on the artery and the biological processes occurring at the cellular level. The focus of this study is on hemodynamic modifications induced in the aorta in the presence of a COA and a BAV. For this purpose, numerical investigations and magnetic resonance imaging measurements were conducted with different configurations: (1) normal: normal aorta and normal aortic valve; (2) isolated COA: aorta with COA (75% reduction by area) and normal aortic valve; (3) complex COA: aorta with the same severity of COA (75% reduction by area) and BAV. The results show that the coexistence of COA and BAV significantly alters blood flow in the aorta with a significant increase in the maximal velocity, secondary flow, pressure loss, time-averaged wall shear stress and oscillatory shear index downstream of the COA. These findings can contribute to a better understanding of why patients with complex COA have adverse outcome even following a successful surgery.     

Tissue reaction to three different types of tissue glues in an experimental aorta dissection model: a quantitative approach

Tissue glues are used during surgical treatment of acute aorta dissection although some glues release toxic products and thus alter the histological structure of the vessel wall. The aim of our study was to use a porcine experimental model of infrarenal aorta dissection to compare histological changes of the vessel wall 1, 6 and 12 months after application of BioGlue, Gelatin-resorcin-formaldehyde (GRF) glue and Tissucol. For quantification, stereological methods were used. All types of glue caused stenosis, GRF most and Tissucol least severely. With increasing postoperative survival time, stenosis was again reduced. Elastine length density decreased with increasing survival time in Control as well as in all Experimental groups. The immunohistochemical phenotype of vascular smooth muscle cells was similar in Tissucol and Control samples. In GRF samples, actin, desmin and vimentin expression changed most severely. Similarly, number and distribution of vasa vasorum in the aortic wall was altered most severely in GRF samples. They tended to return to normal with increasing postoperative survival time, but at a slow rate in the GRF samples. It can be concluded that GRF causes the most severe histopathological changes within the treated aorta, which could be a reason for late failures of dissection surgery. However, glue handling and adhesive properties have to be taken into account, too, when certain glue is chosen for surgical intervention. Increased inflammation and vascularisation might even stabilise the aortic wall. Long-term experimental studies would be helpful to assess healing processes after initial disorganisation of the aortic wall structure.     

The congenital bicuspid aortic valve can experience high-frequency unsteady shear stresses on its leaflet surface

The bicuspid aortic valve (BAV) is a common congenital malformation of the aortic valve (AV) affecting 1% to 2% of the population. The BAV is predisposed to early degenerative calcification of valve leaflets, and BAV patients constitute 50% of AV stenosis patients. Although evidence shows that genetic defects can play a role in calcification of the BAV leaflets, we hypothesize that drastic changes in the mechanical environment of the BAV elicit pathological responses from the valve and might be concurrently responsible for early calcification. An in vitro model of the BAV was constructed by surgically manipulating a native trileaflet porcine AV. The BAV valve model and a trileaflet AV (TAV) model were tested in an in vitro pulsatile flow loop mimicking physiological hemodynamics. Laser Doppler velocimetry was used to make measurements of fluid shear stresses on the leaflet of the valve models using previously established methodologies. Furthermore, particle image velocimetry was used to visualize the flow fields downstream of the valves and in the sinuses. In the BAV model, flow near the leaflets and fluid shear stresses on the leaflets were much more unsteady than for the TAV model, most likely due to the moderate stenosis in the BAV and the skewed forward flow jet that collided with the aorta wall. This additional unsteadiness occurred during mid- to late-systole and was composed of cycle-to-cycle magnitude variability as well as high-frequency fluctuations about the mean shear stress. It has been demonstrated that the BAV geometry can lead to unsteady shear stresses under physiological flow and pressure conditions. Such altered shear stresses could play a role in accelerated calcification in BAVs.     

Effect of intraluminal thrombus thickness and bulge diameter on the oxygen diffusion in abdominal aortic aneurysm.

The intraluminal thrombus (ILT) commonly found within abdominal aortic aneurysm (AAA) may serve as a barrier to oxygen diffusion from the lumen to the inner layers of the aortic wall. The purpose of this work was to address this hypothesis and to assess the effects of AAA bulge diameter (dAAA) and ILT thickness (delta) on the oxygen flow. A hypothetical, three-dimensional, axisymmetric model of AAA containing ILT was created for computational analysis. Commercial software was utilized to estimate the volume flow of O2 per cell, which resulted in zero oxygen tension at the AAA wall. Solutions were generated by holding one of the two parameters fixed while varying the other. The supply of O2 to the AAA wall increases slightly and linearly with dAAA for a fixed delta. This slight increase is due to the enlarged area through which diffusion of O2 may take place. The supply of O2 was found to decrease quickly with increasing delta for a fixed dAAA due to the increased resistance to O2 transport by the ILT layer. The presence of even a thin, 3 mm ILT layer causes a diminished O2 supply (less than 4 x 10(-10) mumol/min/cell). Normally functioning smooth muscle cells require a supply of 21 x 10(-10) mumol/min/cell. Thus, our analysis serves to support our hypothesis that the presence of ILT alters the normal pattern of O2 supply to the AAA wall. This may lead to hypoxic cell dysfunction in the AAA wall, which may further lead to wall weakening and increased potential for rupture.     

Experimental investigation of steady flow through a model of the human aortic arch

Steady flow through a model of the human aortic arch has been studied with hot-film anemometry. A three sensor hot-film velocity probe was inserted into an acrylic flow chamber fabricated from the in situ casting of a human aorta, and the axial, radial and tangential velocity profiles were determined for steady flows in the region of the aortic arch. These studies demonstrated the presence of a potential core throughout the arch region, with a concomitant boundary layer adjacent to the inner wall of curvature of the arch. Trapped secondary flows in this fluid layer along the inner wall were quantitatively determined. Our steady flow studies in the model human aortic arch suggests that a shear-dependent mass transfer mechanism may play a significant role in the development and propagation of atherosclerotic lesions in this segment of the human cardiovascular system.