Numerical simulation of steady flow fields in a model of abdominal aorta with its peripheral branches

In the present study, a numerical calculation procedure based on a finite volume method was developed to simulate steady flow fields in a model of abdominal aorta with its peripheral branches. The study focused on the steady baseline flow fields and the wall shear stress (WSS) distribution as well as the localization of the reversed flow regions and results were compared to those obtained by other investigators. In the case of resting conditions, the existence of a region of reversed flow of about one to two diameters in size and next to the renal arteries and along the posterior wall as observed by other researchers was confirmed. However, under the exercise conditions this region could be wiped out. The flow reversal along the lateral walls proximal to the bifurcation persisted in both rest and exercise conditions. The WSS distribution and the wall shear stress gradient distribution were obtained. The lowest WSS occurred near the ostia of the renal arteries and the lateral walls of the iliac arteries. And the highest is always at the turn to the branch. The results were generally consistent with those obtained experimentally and numerically by other investigators. It was also shown that the steady flow might be used to depict the averaged behavior of pulsatile flow. The present computer code provides a platform for the future more realistic simulations.     

Mesoscopic simulations of systolic flow in the human abdominal aorta

The complex nature of blood flow in the human arterial system is still gaining more attention, as it has become clear that cardiovascular diseases localize in regions of complex geometry and complex flow fields. In this article, we demonstrate that the lattice Boltzmann method can serve as a mesoscopic computational hemodynamic solver. We argue that it may have benefits over the traditional Navier-Stokes techniques. The accuracy of the method is tested by studying time-dependent systolic flow in a 3D straight rigid tube at typical hemodynamic Reynolds and Womersley numbers as an unsteady flow benchmark. Simulation results of steady and unsteady flow in a model of the human aortic bifurcation reconstructed from magnetic resonance angiography, are presented as a typical hemodynamic application.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

The relationship between wall shear stress distributions and intimal thickening in the human abdominal aorta

Purpose

The goal of this work was to determine wall shear stress (WSS) patterns in the human abdominal aorta and to compare these patterns to measurements of intimal thickness (IT) from autopsy samples.

Methods

The WSS was experimentally measured using the laser photochromic dye tracer technique in an anatomically faithful in vitro model based on CT scans of the abdominal aorta in a healthy 35-year-old subject. IT was quantified as a function of circumferential and axial position using light microscopy in ten human autopsy specimens.

Results

The histomorphometric analysis suggests that IT increases with age and that the distribution of intimal thickening changes with age. The lowest WSS in the flow model was found on the posterior wall inferior to the inferior mesenteric artery, and coincided with the region of most prominent IT in the autopsy samples. Local geometrical features in the flow model, such as the expansion at the inferior mesenteric artery (common in younger individuals), strongly influenced WSS patterns. The WSS was found to correlate negatively with IT (r² = 0.3099; P = 0.0047).

Conclusion

Low WSS in the abdominal aorta is co-localized with IT and may be related to atherogenesis. Also, rates of IT in the abdominal aorta are possibly influenced by age-related geometrical changes.

     

Pulsatile flow past aortic valve bioprostheses in a model human aorta

Pulsatile flow development past tissue valve prostheses in a model human aorta has been studied using qualitative flow visualization and quantitative laser-Doppler techniques. Experiments were conducted both in steady and physiological pulsatile flow situations and the measurements included the pressure drop across the valve, the instantaneous flow rate as well as the velocity profiles and turbulent stresses downstream to the valves. Our study shows that the velocity profiles with pericardial valves are closer to those measured past natural aortic valves. The porcine valves with a smaller valve opening area produce a narrower and stronger jet downstream from the valve with relatively larger turbulent axial stresses in the boundary of the jet. Our study suggests that the pericardial valves with turbulent stresses comparable to those of caged ball and tilting disc valves are preferable from a hemodynamic point of view.     

HOXA4 protein levels and localization in the aorta and in human abdominal aortic aneurysms

This report presents evidence for the specificities of select commercially available HOXA4 antibodies in regards to concerns about the specificity of the HOXA4 antibody used by Lillvis et al. (Regional expression of HOXA4 along the aorta and its potential role in human abdominal aortic aneurysms. BMC Physiol 2011, 11:9). Using an antibody characterized extensively by us, Lillvis et al. report detecting HOXA4 at a size of 33 kDa despite our previous reports that HOXA4 is detected at ~37-39 kDa and that the ~30-33 kDa band is non-specific. Using small interfering RNA targeting HOXA4, forced expression of full-length HOXA4 and HOXA4-positive and -negative ovarian cancer cell lines, we confirm our previous findings that the ~30-33 kDa band is non-specific and that HOXA4 is detected at ~37-39 kDa. Moreover, we demonstrate that HOXA4 small interfering RNA reduces the ~37-39 kDa HOXA4 band, but not the ~30-33 kDa non-specific band, in a human acute monocytic leukemia cell line used by Lillvis et al. Western blot analysis performed with two additional commercially available HOXA4 antibodies also detected HOXA4 at ~37-39 kDa. Lastly, immunofluorescent staining of a HOXA4-negative ovarian cancer cell line with the antibody used by Lillvis et al. yields strong perinuclear staining, similar to that observed by Lillvis et al., which cannot be attributed to HOXA4. Our results highlight and briefly discuss the importance of careful antibody validation and selection for use in various applications.     

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.     

Estimation of turbulent shear stresses in pulsatile flow immediately downstream of two artificial aortic valves in vitro

Measuring turbulent shear stresses is of major importance in artificial heart valve evaluation. Bi- and unidirectional fluid velocity measurements enable calculation of Reynolds shear stress ( ) and Reynolds normal stress ( ). τ is important due to the relation to hemolysis and thrombus formation, but σ is the only obtainable parameter in vivo. Therefore, determination of a correlation factor between τ and σ is pertinent.

In a pulsatile flow model, laser Doppler (LDA) and hot-film (HFA) anemometry were used for simultaneous bi- and unidirectional fluid velocity measurements downstream of a Hall Kaster and a Hancock Porcine aortic valve. Velocities were registered in two flow field locations and at four cardiac outputs. The velocity signals were subjected to analog signal processing prior to digital turbulence analysis, as a basis for calculation of τ and σ.

A correlation factor of 0.5 with a correlation coefficient of 0.97 was found between the maximum Reynolds shear stress and Reynolds normal stress, implying . In vitro estimation of turbulent shear stresses downstream of artificial aortic valves, based on the axial velocity component alone, seems possible.     

Haemodynamics and stresses in abdominal aortic aneurysms: A fluid-structure interaction study into the effect of proximal neck and iliac bifurcation angle

Our knowledge of how geometry influences abdominal aortic aneurysm (AAA) biomechanics is still developing. Both iliac bifurcation angle and proximal neck angle could impact the haemodynamics and stresses within AAA. Recent comparisons of the morphology of ruptured and intact AAA show that cases with large iliac bifurcation angles are less likely to rupture than those with smaller angles. We aimed to perform fluid-structure interaction (FSI) simulations on a range of idealised AAA geometries to conclusively determine the influence of proximal neck and iliac bifurcation angle on AAA wall stress and haemodynamics.Peak wall shear stress (WSS) and time-averaged WSS (TAWSS) in the AAA sac region only increased when the proximal neck angle exceeded 30°. Both peak WSS (p < 0.0001) and peak von Mises wall stress (p = 0.027) increased with iliac bifurcation angle, whereas endothelial cell activation potential (ECAP) decreased with iliac bifurcation angle (p < 0.001) and increased with increasing neck angle.These observations may be important as AAAs have been shown to expand, develop thrombus and rupture in areas of low WSS. Here we show that AAAs with larger iliac bifurcation angles have higher WSS, potentially reducing the likelihood of rupture. Furthermore, ECAP was lower in AAA geometries with larger iliac bifurcation angles, implying less likelihood of thrombus development and wall degeneration. Therefore our findings could help explain the clinical observation of lower rupture rates associated with AAAs with large iliac bifurcation angles.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

Estimation of turbulent shear stresses in pulsatile flow immediately downstream of two artificial aortic valves in vitro

Measuring turbulent shear stresses is of major importance in artificial heart valve evaluation. Bi- and unidirectional fluid velocity measurements enable calculation of Reynolds shear stress ( ) and Reynolds normal stress ( ). τ is important due to the relation to hemolysis and thrombus formation, but σ is the only obtainable parameter in vivo. Therefore, determination of a correlation factor between τ and σ is pertinent.In a pulsatile flow model, laser Doppler (LDA) and hot-film (HFA) anemometry were used for simultaneous bi- and unidirectional fluid velocity measurements downstream of a Hall Kaster and a Hancock Porcine aortic valve. Velocities were registered in two flow field locations and at four cardiac outputs. The velocity signals were subjected to analog signal processing prior to digital turbulence analysis, as a basis for calculation of τ and σ.A correlation factor of 0.5 with a correlation coefficient of 0.97 was found between the maximum Reynolds shear stress and Reynolds normal stress, implying . In vitro estimation of turbulent shear stresses downstream of artificial aortic valves, based on the axial velocity component alone, seems possible.     

Relation between diameter and flow in major branches of the arch of the aorta.

In the analysis of arterial branching the classical "cube law' has provided a working model for the relation between the diameter of a blood vessel and the flow which the vessel carries on a long-term basis. The law has shown good agreement with biological data, but questions remain regarding its applicability to all levels of the arterial tree. The present study tests the hypothesis that the cube law may not be valid in the first few generations of the arterial tree, where vessel capacitance and gross anatomy may play important roles. Biological data have shown some support for this hypothesis in the past but the heterogeneity characteristic of past data has not allowed a conclusive test so far. We present new data which have been obtained from the same location on the arterial tree and in sufficient number to make this test possible for the first time. Also, while past tests have been based primarily on correlation of the measured data with an assumed power law, we show here that this can be misleading. The present data allow a simpler test which does not involve correlation and which leads to more direct conclusions. For the vessels surveyed, the results show unequivocally that the relation between diameter and flow is governed by a 'square law' rather than the classical cube law. Coupled with past findings this suggests that the square law may apply at the first few levels of the arterial tree, while the cube law continues from there to perhaps the precapillary levels.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.