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.     

Computational fluid dynamics analysis of surgical adjustment of left ventricular assist device implantation to minimise stroke risk

Background. Currently, mechanical support is the most promising alternative to cardiac transplantation. Ventricular assist devices (VADs) were originally used to provide mechanical circulatory support in patients awaiting planned heart transplantation (‘bridge-to-transplantation’ therapy). The success of short-term bridge devices led to clinical trials evaluating the clinical suitability of long-term support (‘destination’ therapy) with left ventricular assist devices (LVADs). The first larger scale, randomised trial that tested long-term support with an LVAD reported a 44% reduction in the risk of stroke or death in patients with an LVAD. In spite of the success of LVADs as bridge-to-transplantation and long-term support, patients managed by these devices are still at risk of several adverse events. The most devastating complication is caused by embolisation of thrombi formed within the LVAD or inside the heart into the brain. Prevention of thrombi formation is attempted through anticoagulation management and by improving LVADs design; however, there is still significant occurrence of thromboembolic events in patients. Investigators have reported that the incidence of thromboembolic cerebral events ranges from 14% to 47% over a period of 6–12 months.

Methods and approach. An alternative method to reduce the incidence of cerebral embolisation is proposed by the co-authors, and the hypothesis is that it is possible to minimise the number of thrombi flowing into the carotid and vertebral arteries by an optimal placement of the LVAD outflow conduit, with or without the addition of aortic bypass connecting the ascending aorta and the innominate artery (IA), or left carotid artery. This paper presents the computational fluid dynamics (CFD) analysis of the aortic arch haemodynamics using a representative geometry of the human aortic arch with or without an alternative aortic bypass. In order to study the trajectory of the thrombi within the aortic arch bed, the CFD code, Fluent 6.3, is utilised to resolve the flow field and to solve the Lagrangian particle tracking of thrombi released randomly at the inlet of the LVAD cannula.

Results. Results are presented for simulations of thrombi in the range of 2–5 mm. The percentage of individual diameter as well as aggregate diameter thrombi flowing to the carotid and vertebral arteries as a function of LVAD conduit placement and aortic bypass implantation is reported. The influence of the LVAD conduit implantation and bypass reveals a nearly 50% variation in predicted cerebral embolism rates.

Conclusions. The adjustment of the location of the anastomosis of the LVAD outflow cannula as well as its angle of incidence plays a significant role in the level of thromboembolisms. By proper adjustment in this CFD study of a synthetic model of an aortic arch bed, we found that nearly a 50% reduction in cerebral embolism could be achieved for a configuration consisting of a shallow angle of implantation over a baseline normal incidence of the LVAD cannula. Within the limitations of our model, we have established that the LVAD implantation geometry is an important factor and should be taken into consideration when implanting an LVAD. It is possible that other parameters such as distance of the LVAD outflow cannula to the root of the IA could affect the thrombi embolisation probabilities. However, the results of this study suggest that the risk of stroke may be significantly reduced by as much as 50% by tailoring the VAD implantation by a simple surgical manoeuvre. The results of this line of research may ultimately lead to techniques that can be used to estimate the optimal LVAD configuration in a patient-specific manner by pre-operative imaging.     

The distal aorta in the Marfan syndrome

Prolonged survival of patients with Marfan syndrome after aortic root replacement has led to an increased number of patients with aortic complications beyond the root. Elective replacement of the aortic root removes the most important predilection site for aneurysms, but the distal aorta remains at risk. Predictors for aortic growth and adverse events in the distal aorta include aortic diameter, aortic distensiblity, previous aortic root replacement, hypertension and aortic regurgitation. After aortic dissection, the initial false lumen diameter is an independent predictor for late aneurysm formation. Although there are a few reports of short-term success after endovascular stent grafting of the descending thoracic aorta, stent grafting in patients with Marfan syndrome is not recommended unless intervention is clearly indicated and the risk of conventional open surgical repair is deemed prohibitive. Optimal long-term outcome demands lifelong radiographic follow-up and medical treatment with β-blocker therapy. After aortic dissection rigorous antihypertensive medication is of utmost importance. Losartan, an angiotensin II type I receptor antagonist, might offer the first potential for primary prevention of clinical manifestations in Marfan syndrome, but the results of clinical trials have to be awaited. (Neth Heart J 2008;16:382-6.)     

Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier-Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.     

Modeling the relationship between LVAD support time and gene expression changes in the human heart by penalized partial least squares

MOTIVATION: Heart failure affects more than 20 million people in the world. Heart transplantation is the most effective therapy, but the number of eligible patients far outweighs the number of available donor hearts. The left mechanical ventricular assist device (LVAD) has been developed as a successful substitution therapy that aids the failing ventricle while a patient is waiting for the donor heart. We obtained genomics data from paired human heart samples harvested at the time of LVAD implant and explant. The heart failure patients in our study were supported by the LVAD for various periods of time. The goal of this study is to model the relationship between the time of LVAD support and gene expression changes. RESULTS: To serve the purpose, we propose a novel penalized partial least squares (PPLS) method to build a regression model. Compared with partial least squares and Breiman's random forest method, PPLS gives the best prediction results for the LVAD data.     

Aortic velocity contours at abdominal branches in anesthetized dogs

Pulsed Doppler velocimetry was used to record a grid of velocity waveforms 0.5 cm downstream of the cephalic mesenteric and left renal branches of the aorta in anesthetized dogs. Aortic velocity contours at different phases of the pulse cycle were developed from the grid of waveforms. Transient flow recirculation occurred in the post-systolic phase of the pulse cycle at the aortic wall opposite the branch artery. There was no recirculation at the systolic peak but there was asymmetry of the velocity profile. In contrast, in the in vivo post-stenotic velocity field recirculation persists throughout most of the cycle. These results compare well with similar results from pulsatile model studies. Spectral width of the Doppler signal was not increased in any of the velocity waveforms immediately downstream of the branches, this suggests that flow is relatively undisturbed in these locations.     

Intraventricular flow patterns and stasis in the LVAD-assisted heart

Left ventricular assist device (LVAD) support disrupts the natural blood flow path through the heart, introducing flow patterns associated with thrombosis, especially in the presence of medical devices. The aim of this study was to quantitatively evaluate the flow patterns in the left ventricle (LV) of the LVAD-assisted heart, with a focus on alterations in vortex development and stasis. Particle image velocimetry of a LVAD-supported LV model was performed in a mock circulatory loop. In the Pre-LVAD flow condition, a vortex ring initiating from the LV base migrated toward the apex during diastole and remained in the LV by the end of ejection. During LVAD support, vortex formation was relatively unchanged although vortex circulation and kinetic energy increased with LVAD speed, particularly in systole. However, as pulsatility decreased and aortic valve opening ceased, a region of fluid stasis formed near the left ventricular outflow tract. These findings suggest that LVAD support does not substantially alter vortex dynamics unless cardiac function is minimal. The altered blood flow introduced by the LVAD results in stasis adjacent to the LV outflow tract, which increases the risk of thrombus formation in the heart.     

Effects of aortic irregularities on blood flow

Anatomic aortic anomalies are seen in many medical conditions and are known to cause disturbances in blood flow. Turner syndrome (TS) is a genetic disorder occurring only in females where cardiovascular anomalies, particularly of the aorta, are frequently encountered. In this study, numerical simulations are applied to investigate the flow characteristics in four TS patient- related aortic arches (a normal geometry, dilatation, coarctation and elongation of the transverse aorta). The Quemada viscosity model was applied to account for the non-Newtonian behavior of blood. The blood is treated as a mixture consisting of water and red blood cells (RBC) where the RBCs are modeled as a convected scalar. The results show clear geometry effects where the flow structures and RBC distribution are significantly different between the aortas. Transitional flow is observed as a jet is formed due to a constriction in the descending aorta for the coarctation case. RBC dilution is found to vary between the aortas, influencing the WSS. Moreover, the local variations in RBC volume fraction may induce large viscosity variations, stressing the importance of accounting for the non-Newtonian effects.     

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.     

Rapid novel aortic arch replacement for thoracic aortic aneurysm using three continuous sutures and a felt cylindrical collar

This report describes the novel parachute technique of open distal anastomosis at the aortic arch replacement. Two Teflon felt cylindrical collars were initially placed on the anastomotic site of the descending aorta. All four to five outer loops of the stitches used in the parachute technique were tracked by the gathering suture. The anastomotic sutures and three gathering sutures were finally pulled simultaneously. The prosthetic graft and the aortic stump with Teflon felt were safely and completely anastomosed. Surgical or hospital death and serious complications were not found. The mean anastomotic duration (circulatory arrest duration) in 16 patients was 23 minutes. Our novel technique using a Teflon felt cylindrical collar and modified continuous suturing was not only safe but also reduced the duration of anastomosis and minimized blood loss. This technique is simple and can be applied to aortic valve replacement.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.     

Laminar and turbulent flow in the mammalian aorta: Reynolds number

Laminar to turbulent flow transition in the mammalian aorta is generally characterized by Reynolds number. When dimensional analysis is applied to obtain the Reynolds number in allometric form, it is found that this number is not invariant of body weight but is approximately proportional to body length dimensions. This implies that flow in the aorta of large mammals is turbulent and laminar in smaller mammals during most of ventricular ejection. Since Reynolds number is defined for steady flow through rigid tubes, it may not reflect the actual fluid behavior of pulsatile flow in compliant vessels such as the aorta. In addition, turbulence is frequency dependent. The larger compliance of the aorta and the slower heart rate in larger mammals and the shorter entrance length and higher heart rate in smaller mammals lead to equal prevalence of turbulence. The consequence is that the aortic flow waveforms remain similar in all mammals.     

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.     

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.     

Effects of diabetes on glucose oxidation in rat aorta after hypophysectomy and adrenalectomy

The influence of diabetes, hypophysectomy and adrenalectomy on glucose oxidation in rat aorta was studied. Diabetes was induced in normal, adrenalectomized and hypophysectomized-cortisone substituted rats by streptozotocin (65 mg/kg body weight). The oxidation of glucose to CO2 was determined during incubation of rat aorta in vitro for 2-3 hours. The aortic glucose oxidation was reduced after hypophysectomy but was unaffected by adrenalectomy. After streptozotocin treatment the rise in blood glucose concentration was similar in normal, adrenalectomized and hypophysectomized-cortisone substituted rats. In shamoperated diabetic rats the aortic glucose oxidation was reduced after a diabetes duration of 4 days. In adrenalectomized diabetic rats the aortic glucose oxidation was not significantly affected after 4 days but was reduced after a diabetes duration of 14 days. When adrenalectomized diabetic rats were treated with hydrocortisone the aortic glucose oxidation was reduced after diabetes for 4 days. After incubation of normal rat aorta in vitro for 6 hours with cortisol (1 microgram/ml) in the incubation medium a decrease in the aortic glucose oxidation was found. Incubation of aorta with only growth hormone had no effect. These results suggest that cortisol is of importance for the lowered glucose oxidation in diabetic rat aorta.     

Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study

The main purpose of the study was to verify if helical flow, widely observed in several vessels, might be a signature of the blood dynamics of vein graft anastomosis. We investigated the existence of a relationship between helical flow structures and vascular wall indexes of atherogenesis in aortocoronary bypass models with different geometric features. In particular, we checked for the existence of a relationship between the degree of helical motion and the magnitude of oscillating shear stress in conventional hand-sewn proximal anastomosis. The study is based on the numerical evaluation of four bypass geometries that are attached to a simplified computer representation of the ascending aorta with different angulations relative to aortic outflow. The finite volume technique was used to simulate realistic graft fluid dynamics, including aortic compliance and proper aortic and graft flow rates. A quantitative method was applied to evaluate the level of helicity in the flow field associated with the four bypass models under investigation. A linear inverse relationship (R = -0.97) was found between the oscillating shear index and the helical flow index for the models under investigation. The results obtained support the hypothesis that an arrangement of the flow field in helical patterns may elicit damping in wall shear stress temporal gradients at the proximal graft. Accordingly, helical flow might play a significant role in preventing plaque deposition or in tuning the mechanotransduction pathways of cells. Therefore, results confirm that helical flow constitutes an important flow signature in vessels, and its strength as a fluid dynamic index (for instance in combination with magnetic resonance imaging flow visualization techniques) for risk stratification, in the activation of both mechanical and biological pathways leading to fibrointimal hyperplasia.     

Systems engineering analysis of aortic root blood pressure

This paper describes the aortic blood pressure as a function of aortic blood flow and the parameters of the blood and circulatory system. The method of performance involves the analogue of a multi-branched electrical to hydraulic transmission line applying graphical convolution to the blood flow-transform impedance relationship resulting in a theoretical pressure curve for the infinite aorta. The difference between the single pressure pulse and the computed adjusted infinite aorta pressure curve is described as the reflected wave. This reflected wave is then shown to be of reasonable configuration in time and velocity. The blood pressure is thus finally described completely by the physical parameters of the blood and the circulatory system and the blood flow.     

Wall shear stress distribution in a model human aortic arch: assessment by an electrochemical technique

Wall shear stress (WSS) distribution in a human aortic arch model is studied using 130 cathode electrodes flush-mounted on the model walls. Flow visualizations are made in a transparent geometry model to identify the regions of fluid mechanical interests, e.g. regions of flow separation, eddy formation and flow stagnancy. The 130 electrodes are strategically positioned in the arch based on information obtained from the flow visualizations. The measured data indicate that the aortic arch may be categorized into eight regions: three along the inner wall of the arch (A,B,C); and five near the outer wall (D,E,F,G,H). (1) The regions of low WSS are distributed along the inner wall of the ascending aorta A; the inner wall of the descending aorta C; and the upstream inner wall of the innominate and the common carotid branchings F. (2) The high WSS regions are distributed along the outer wall of the arch E; and the inner wall in the arch opposite to the left subclavian branching B. (3) In certain regions, high and low WSS may be found next to each other (e.g. G and H) without a definable boundary in between; and (4) as the Reynolds number increases, the areas of low WSS decrease, while the high WSS areas increase with no obvious change in magnitude of the stress along the inner wall of the arch. At the branchings, the WSS distribution is not affected by the Reynolds number within the range of observations. The measured WSS distribution is compared with Rodkiewicz's map of early atherosclerotic lesions in the aortic arch of cholesterol fed rabbits.     

Theoretical analysis of magnetic field interactions with aortic blood flow

The flow of blood in the presence of a magnetic field gives rise to induced voltages in the major arteries of the central circulatory system. Under certain simplifying conditions, such as the assumption that the length of major arteries (e.g., the aorta) is infinite and that the vessel walls are not electrically conductive, the distribution of induced voltages and currents within these blood vessels can be calculated with reasonable precision. However, the propagation of magnetically induced voltages and currents from the aorta into neighboring tissue structures such as the sinuatrial node of the heart has not been previously determined by any experimental or theoretical technique. In the analysis presented in this paper, a solution of the complete Navier-Stokes equation was obtained by the finite element technique for blood flow through the ascending and descending aortic vessels in the presence of a uniform static magnetic field. Spatial distributions of the magnetically induced voltage and current were obtained for the aortic vessel and surrounding tissues under the assumption that the wall of the aorta is electrically conductive. Results are presented for the calculated values of magnetically induced voltages and current densities in the aorta and surrounding tissue structures, including the sinuatrial node, and for their field-strength dependence. In addition, an analysis is presented of magnetohydrodynamic interactions that lead to a small reduction of blood volume flow at high field levels above approximately 10 tesla (T). Quantitative results are presented on the offsetting effects of oppositely directed blood flows in the ascending and descending aortic segments, and a quantitative estimate is made of the effects of assuming an infinite vs. a finite length of the aortic vessel in calculating the magnetically induced voltage and current density distribution in tissue. © 1996 Wiley-Liss, Inc.