Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation

Mounting evidence suggests that the pulsatile character of blood pressure and flow within large arteries plays a particularly important role as a mechano-biological stimulus for wall growth and remodeling. Nevertheless, understanding better the highly coupled interactions between evolving wall geometry, structure, and properties and the hemodynamics will require significantly more experimental data. Computational fluid–solid-growth models promise to aid in the design and interpretation of such experiments and to identify candidate mechanobiological mechanisms for the observed arterial adaptations. Motivated by recent aortic coarctation models in animals, we used a computational fluid–solid interaction model to study possible local and systemic effects on the hemodynamics within the thoracic aorta and coronary, carotid, and cerebral arteries due to a distal aortic coarctation and subsequent spatial variations in wall adaptation. In particular, we studied an initial stage of acute cardiac compensation (i.e., maintenance of cardiac output) followed by early arterial wall remodeling (i.e., spatially varying wall thickening and stiffening). Results suggested, for example, that while coarctation increased both the mean and pulse pressure in the proximal vessels, the locations nearest to the coarctation experienced the greatest changes in pulse pressure. In addition, after introducing a spatially varying wall adaptation, pressure, left ventricular work, and wave speed all increased. Finally, vessel wall strain similarly experienced spatial variations consistent with the degree of vascular wall adaptation.     

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.     

Bicuspid aortic valve aortopathies: An hemodynamics characterization in dilated aortas

Bicuspid aortic valve (BAV) aortopathy remains of difficult clinical management due to its heterogeneity and further assessment of related aortic hemodynamics is necessary. The aim of this study was to assess systolic hemodynamic indexes and wall stresses in patients with diverse BAV phenotypes and dilated ascending aortas. The aortic geometry was reconstructed from patient-specific images while the aortic valve was generated based on patient-specific measurements. Physiologic material properties and boundary conditions were applied and fully coupled fluid-structure interaction (FSI) analysis were conducted. Our dilated aortic models were characterized by the presence of abnormal hemodynamics with elevated degrees of flow skewness and eccentricity, regardless of BAV morphotype. Retrograde flow was also present. Both features, predicted by flow angle and flow reversal ratios, were consistently higher than those reported for non-dilated aortas. Right-handed helical flow was present, as well as elevated wall shear stress (WSS) on the outer ascending aortic wall. Our results suggest that the abnormal flow associated with BAV may play a role in aortic enlargement and progress it further on already dilated aortas.     

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.     

Comparative study of flow in right-sided and left-sided aortas: numerical simulations in patient-based models

A right-sided aorta is a rare malformation which may be associated with other various types of congenital heart disease. We utilised haemodynamic, echocardiographic measurements, computerised tomography and image reconstruction software packages that were integrated in a computational fluid dynamics model to determine blood flow patterns in patient-based aortas. In the left-sided aorta, a systolic clockwise rotational component was present, while helical flow was depicted in the aortic arch that was converted in the descending aorta as counter-rotating vortices with accompanying retrograde flow. The right-sided configuration has not altered the orientation of the three-dimensional vortex, but intensification of polymorphic flow patterns, alterations in wall shear stress distribution and development of a lateral pressure gradient at the area of an aneurysmal anomaly was observed. Moreover, increments of Reynolds, Womersley and Dean numbers were evident. These phenomena along with the formation of the aneurysm might influence cardiovascular risk in patients with right-sided aortas.     

Direct correlation between calcium content and blood pressure: a study of aortic coarctation in rats

The calcium content of aorta was measured by atomic absorption after coarctation in the rat. At 7 and 14 days, the calcium content was elevated on the proximal side of the coarctation, where pressure was increased significantly. On the distal, low pressure side of the aortic coarctation, calcium was reduced significantly. There is a direct correlation between the blood pressure and the content of calcium (r = 0.69, P less than 0.001). The width of the aortic media on the high pressure side was increased significantly at 7 and 14 days after coarctation, whereas no significant changes in width were present on the low pressure side of the constriction. We conclude that pressure regulates the aortic calcium content, likely acting through a local effect.     

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.     

Pulsatile flow visualization in the abdominal aorta under differing physiologic conditions: implications for increased susceptibility to atherosclerosis.

The infrarenal abdominal aorta is a common site for clinically significant atherosclerosis. As has been shown in other susceptible locations, vessel geometry, flow division rates, and pulsatility may result in hemodynamic conditions which influence the preferential localization of disease in the abdominal aorta segment. Pulsatile flow visualization was performed in a glass model of the aorta constructed from measurements of angiograms and cadaver aortas. Flow rates and pulsatile waveforms were varied to reflect typical physiological conditions. Under normal resting conditions, the flow patterns in the infrarenal aorta were more complex than those in the suprarenal location. Time varying vortex patterns appeared at the level of the renal arteries and propagated through the infrarenal aorta into the common iliac arteries. A region of oscillating velocity direction extended from the renal arteries to the aortic bifurcation along the posterior wall. Dye became trapped along the posterior wall, requiring several cardiac cycles for clearance. In contrast, there was rapid clearance of the dye in the anterior aorta. Under postprandial conditions, the flow patterns in the aorta were basically unchanged. Simulated exercise conditions created laminar hemodynamic features very different from the resting conditions, including a decrease in dye residence time. This study reveals significant time-dependent variations in the hemodynamics of the abdominal aorta under differing physiologic conditions. Hemodynamic factors such as low wall shear stress, oscillating shear direction, and high particle residence time may be related to the clinically seen preferential plaque localization in the infrarenal aorta.     

In vitro hemodynamic investigation of the embryonic aortic arch at late gestation

This study focuses on the dynamic flow through the fetal aortic arch driven by the concurrent action of right and left ventricles. We created a parametric pulsatile computational fluid dynamics (CFD) model of the fetal aortic junction with physiologic vessel geometries. To gain a better biophysical understanding, an in vitro experimental fetal flow loop for flow visualization was constructed for identical CFD conditions. CFD and in vitro experimental results were comparable. Swirling flow during the acceleration phase of the cardiac cycle and unidirectional flow following mid-deceleration phase were observed in pulmonary arteries (PA), head-neck vessels, and descending aorta. Right-to-left (oxygenated) blood flowed through the ductus arteriosus (DA) posterior relative to the antegrade left ventricular outflow tract (LVOT) stream and resembled jet flow. LVOT and right ventricular outflow tract flow mixing had not completed until approximately 3.5 descending aorta diameters downstream of the DA insertion into the aortic arch. Normal arch model flow patterns were then compared to flow patterns of four common congenital heart malformations that include aortic arch anomalies. Weak oscillatory reversing flow through the DA junction was observed only for the Tetralogy of Fallot configuration. PA and hypoplastic left heart syndrome configurations demonstrated complex, abnormal flow patterns in the PAs and head-neck vessels. Aortic coarctation resulted in large-scale recirculating flow in the aortic arch proximal to the DA. Intravascular flow patterns spatially correlated with abnormal vascular structures consistent with the paradigm that abnormal intravascular flow patterns associated with congenital heart disease influence vascular growth and function.     

Morphometry and strain distribution of the C57BL/6 mouse aorta

The goal of the present study was to obtain a systematic set of data along the length of the mouse aorta to study variations of morphometry (diameter, wall thickness, and curvature), strain, and stress of the mouse aorta. Five mice were imaged with a 13-MHz ultrasound probe to determine the in vivo diameter along the aorta. A cast was made of these aortas to validate the ultrasonic diameter measurements. The root mean squared and systematic errors for these measurements were 12.6% and 6.4% of the mean ultrasound diameter, respectively. The longitudinal variations of geometry, stress, and strain from the aortic valve to the common iliac bifurcation were documented. Our results show that the residual circumferential strain leads to a uniformity of transmural strain of the aorta in the loaded state along the entire length of the aorta. Furthermore, we validated the incompressibility condition along the length of the aorta. These data of normal mice will serve as a reference state for the study of disease in future knockout models.     

The effects of tapering and artery wall stiffness on treatments for Coarctation of the Aorta

Coarctation of the Aorta is a congenital narrowing of the aorta. Two commonly used treatments are resection and end-to-end anastomosis, and stent placements. We simulate blood flow through one-dimensional models of aortas. Different artery stiffnesses, due to treatments, are included in our model, and used to compare blood flow properties in the treated aortas. We expand our previously published model to include the natural tapering of aortas. We look at change in aorta wall radius, blood pressure and blood flow velocity, and find that, of the two treatments, the resection and end-to-end anastomosis treatment more closely matches healthy aortas.     

Cellular determinants of low-shear blood viscosity

Low-shear viscometry is one of the methods commonly used to estimate the degree of red blood cell (RBC) aggregation in various bloods and RBC suspensions. However, it has been previously shown that alterations in RBC morphology and mechanical behavior can affect the low-shear apparent viscosity of RBC suspensions; RBC aggregation is also sensitive to these cellular factors. This study used heat treatment (48°C, 5 min), glutaraldehyde (0.005–0.02%) and hydrogen peroxide (1 mM) to modify cell geometry and deformability. Red blood cell aggregation was assessed via a Myrenne Aggregometer (“M” and “Ml” indexes), RBC suspension viscosity was measured using a Contraves LS-30 viscometer, and RBC shape response to fluid shear stresses (i.e., deformability) was determined by ektacytometry (LORCA system). Our results indicate that low-shear apparent viscosity and related indexes may not always reflect changes of RBC aggregation if cellular properties are altered: for situations where RBC aggregation has been only moderately affected, cellular mechanical factors may be the major determinant of low-shear viscosity. These findings thus imply that in situations which may be associated alterations of RBC geometry and/or deformability, low-shear viscometry should not be the sole measurement technique used to assess RBC aggregation.     

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Local hemodynamic analysis after coronary stent implantation based on Euler-Lagrange method

Coronary stents are deployed to treat the coronary artery disease (CAD) by reopening stenotic regions in arteries to restore blood flow, but the risk of the in-stent restenosis (ISR) is high after stent implantation. One of the reasons is that stent implantation induces changes in local hemodynamic environment, so it is of vital importance to study the blood flow in stented arteries. Based on regarding the red blood cell (RBC) as a rigid solid particle and regarding the blood (including RBCs and plasma) as particle suspensions, a non-Newtonian particle suspensions model is proposed to simulate the realistic blood flow in this work. It considers the blood’s flow pattern and non-Newtonian characteristic, the blood cell-cell interactions, and the additional effects owing to the bi-concave shape and rotation of the RBC. Then, it is compared with other four common hemodynamic models (Newtonian single-phase flow model, Newtonian Eulerian two-phase flow model, non-Newtonian single-phase flow model, non-Newtonian Eulerian two-phase flow model), and the comparison results indicate that the models with the non-Newtonian characteristic are more suitable to describe the realistic blood flow. Afterwards, based on the non-Newtonian particle suspensions model, the local hemodynamic environment in stented arteries is investigated. The result shows that the stent strut protrusion into the flow stream would be likely to produce the flow stagnation zone. And the stent implantation can make the pressure gradient distribution uneven. Besides, the wall shear stress (WSS) of the region adjacent to every stent strut is lower than 0.5 Pa, and along the flow direction, the low-WSS zone near the strut behind is larger than that near the front strut. What’s more, in the regions near the struts in the proximal of the stent, the RBC particle stagnation zone is easy to be formed, and the erosion and deposition of RBCs are prone to occur. These hemodynamic analyses illustrate that the risk of ISR is high in the regions adjacent to the struts in the proximal and the distal ends of the stent when compared with struts in other positions of the stent. So the research can provide a suggestion on the stent design, which indicates that the strut structure in these positions of a stent should be optimized further.

     

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.     

Axial nonuniformity of geometric and mechanical properties of mouse aorta is increased during postnatal growth

The hemodynamic conditions of aorta are relatively uniform prenatally and become more heterogeneous postnatally. Our objective was to quantify the heterogeneity of geometry and mechanical properties during growth and development. To accomplish this objective, we obtained a systematic set of data on the geometry and mechanical properties along the length of mouse aorta during postnatal development. C57BL/6 mice of ages 1-33 days were studied. The ascending aorta was cannulated in situ and preconditioned with several cyclic changes in pressure. We investigated the axial variations of geometry (diameter and length) and mechanical properties (stress-stain relation, elastic modulus and compliance) of the mouse aorta from the aortic valve to the common iliac. Our results show that the arterial blood pressure of mice increased from approximately 30 to 80 mmHg during the first 2 wk of life. The stretch ratio, diameter, wall (intima-media) thickness, and total lumen volume of mouse aorta increased with age. The aorta was transformed from a cylindrical tube at birth to a tapered structure during growth. Furthermore, we found the mechanical properties were fairly uniform along the length of the aorta at birth and become more nonuniform with age. We conclude that the rapid change of blood pressure and blood flow after birth alter the geometric and mechanical properties differentially along the length of the aorta. Hence, the axial nonuniformity of the aorta increases as the organ becomes more specialized during growth and development.     

Blood flow patterns and pressure loss in the ascending aorta: A comparative study on physiological and aneurysmal conditions

An aortic aneurysm is defined as a balloon-shaped bulging of all three histologic components of the aortic vessel walls (intima, media and adventitia). This dilation results from vessel weakening owing to remodeling, i.e. due to cystic degeneration of the Tunica media (Marfan), progression of atherosclerosis or presence of a bicuspid aortic valve. The growth rate of the aortic diameter varies from patient to patient and may progress until the aneurysm ultimately ruptures. The role of hemodynamics, i.e. blood flow patterns, and shear stresses that are supposed to intensify during aneurysm growth are not yet fully understood, but thought to play a key role in the enlargement process. The aim of this study is to characterize the aortic blood flow in a silicone model of a pathological aorta with ascending aneurysm, to analyze the differences in the blood flow pattern compared to a healthy aortic model, and to single out possible blood flow characteristics measurable using phase contrast magnetic resonance imaging (MRI) that could serve as indicators for aneurysm severity. MRI simulations were performed under physiological, pulsatile flow conditions using data obtained from optical three dimensional particle tracking measurements. In comparison to the healthy geometry, elevated turbulence intensity and pressure loss are measured in the diseased aorta, which we propose as a complimentary indicator for assessing the aneurysmal severity. Our results shed a light on the interplay between the blood flow dynamics and their contribution to the pathophysiology and possible role for future risk assessment of ascending aortic aneurysms.     

Non-Newtonian blood flow in human right coronary arteries: steady state simulations

This study looks at blood flow through four different right coronary arteries, which have been reconstructed from bi-plane angiograms. Five non-Newtonian blood models, as well as the usual Newtonian model of blood viscosity, are used to study the wall shear stress in each of these arteries at a particular point in the cardiac cycle. It was found that in the case of steady flow in a given artery, the pattern of wall shear stress is consistent across all models. The magnitude of wall shear stress, however, is influenced by the model used and correlates with graphs of shear stress versus strain for each model. For mid-range velocities of around 0.2 m s(-1) the models are virtually indistinguishable. Local and global non-Newtonian importance factors are introduced, in an attempt to quantify the types of flows where non-Newtonian behaviour is significant. It is concluded that, while the Newtonian model of blood viscosity is a good approximation in regions of mid-range to high shear, it is advisable to use the Generalised Power Law model (which tends to the Newtonian model in those shear ranges in any case) in order to achieve better approximation of wall shear stress at low shear.     

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase transient non-Newtonian three-dimensional (3-D) computational fluid dynamics (CFD) simulation has been performed for pulsatile hemodynamics in an idealized curved section of a human coronary artery. We present the first prediction, to the authors' knowledge, of particulate buildup on the inside curvature using the multiphase theory of dense suspension hemodynamics. In this study, the particulates are red blood cells (RBCs). The location of RBC buildup on the inside curvature correlates with lower wall shear stress (WSS) relative to the outside curvature. These predictions provide insight into how blood-borne particulates interact with artery walls and hence, have relevance for understanding atherogenesis since clinical observations show that atherosclerotic plaques generally form on the inside curvatures of arteries. The buildup of RBCs on the inside curvature is driven by the secondary flow and higher residence times. The higher viscosity in the central portion of the curved vessel tends to block their flow, causing them to migrate preferentially through the boundary layer. The reason for this is the nearly neutrally buoyant nature of the dense two-phase hemodynamic flow. The two-phase non-Newtonian viscosity model predicts greater shear thinning than the single-phase non-Newtonian model. Consequently, the secondary flow induced in the curvature is weaker. The waveforms for computed hemodynamic parameters, such as hematocrit, WSS, and viscosity, follow the prescribed inlet velocity waveforms. The lower oscillatory WSS produced on the inside curvature has implications for understanding thickening of the intimal layer.