Eur J Cardiothorac Surg 2008;33:164-167. doi:10.1016/j.ejcts.2007.11.021
Copyright © 2008, European Association for Cardio-thoracic Surgery. Published by Elsevier. All rights reserved.
Three-dimensional numerical simulation of blood flow in the aortic arch during cardiopulmonary bypass
Yoshiyuki Tokudaa,*,
Min-Ho Songa,
Yuichi Uedab,
Akihiko Usuib,
Toshiaki Akitab,
Shigeru Yoneyamac,
Shigeru Maruyamad
a Department of Cardiovascular Surgery, Gifu Prefectural Tajimi Hospital, 5-161 Maehata, Tajimi, Gifu 507-8522, Japan
b Department of Cardiothoracic Surgery, Nagoya University Graduate School of Medicine, 65 Tsurumai, Showa-ku, Nagoya, Aichi 466-8550, Japan
c Maxnet Co. Ltd., 5-52-15 Nakano, Nakano-ku, Tokyo 165-0001, Japan
d Numcraft Inc., 76-1735 Horiuchi, Hyama, Miura, Kanagawa 240-0112, Japan
Received 31 March 2007;
received in revised form 13 August 2007;
accepted 26 November 2007.
* Corresponding author. Tel.: +81 572 22 5311; fax: +81 572 25 1246. (Email: tokuda{at}mxb.mesh.ne.jp).
 |
Abstract
|
|---|
Objective: To better understand the mechanism of stroke during cardiopulmonary bypass, it is necessary to obtain information on the location of turbulence, wall pressure, and flow distribution within the aortic arch. Methods: Blood flow was numerically simulated using the finite element method in the following representative case: a curved arterial cannula was inserted into the anterior wall of the distal ascending aorta 2 cm below the orifice of brachiocephalic artery. Perfusion was performed, with a bypass flow index of 2.5 l min–1
m–2. Computational grids, consisting of 1,493,297 tetrahedral elements, were generated. Results: The highest wall pressure (3104.8 Pa) was observed at the superior-posterior wall of the aorta below the orifice of the brachiocephalic artery where jet flow impingement occurred. The maximum wall shear stress was 25.1 Pa. High velocity vortex started below the orifice of the brachiocephalic artery. The turbulent flows continued along the posterior wall and then mainly flowed off into the left subclavian artery. Therefore, in the present case, an embolic event in the territory of the left subclavian artery could occur if a plaque was present at the superior-posterior wall of the aorta below the orifice of the brachiocephalic artery. The flow rates in each of the branches were 132, 613, 175, and 821 ml/min for the right subclavian, right common carotid, left common carotid, and left subclavian artery, respectively. Conclusion: This study confirmed that blood flow during cardiopulmonary bypass can be simulated and visualized. Computational fluid dynamics could be applied in the future to assess an individual's risk of stroke. Further multiple representative cases need to be simulated.
Key Words: Cardiopulmonary bypass • Computer simulation
|
1. Introduction
|
|---|
Despite continuing improvements in the cardiopulmonary bypass (CPB) techniques used during cardiac surgery, stroke remains a devastating complication. It is strongly associated with significant morbidity and mortality. An increasing amount of evidence points to cerebral embolization during CPB as the principal etiologic factor of such neurological complications, although hypoperfusion may play a role [1]. Reducing the occurrence of stroke should be a major goal in the fields of cardiac surgery. To better understand the mechanism underlying stroke during CPB, detailed information is needed about turbulence and flow distribution in the aortic arch during cardiopulmonary bypass. Basic information such as the velocities of the flow or the wall pressure and the shear stress during CPB also needs to be investigated. The flow velocity during CPB has been studied using Doppler ultrasound, in order to prevent strokes [2,3]. However, it is very difficult to measure the wall pressure and the shear stress during an operation.
The recent development of computational fluid dynamics (CFD) technology now allows complex numerical simulation of the cardiovascular system. A few computational studies have been made of steady and unsteady blood flow in the human aortic arch [4,5]. In those studies that have been undertaken, CFD analyses have been used to evaluate specific parameters, such as the velocity distribution of blood flow in the aorta, wall pressure, and wall shear stress on the aortic wall, which are very difficult to measure in vivo.
Using CFD technology, we performed a three-dimensional (3D) numerical simulation of blood flow from an arterial cannula during cardiopulmonary bypass within a model of the human aortic arch.
|
2. Methods
|
|---|
2.1 Geometric modeling
To provide a representative case, the following model was chosen. It was assumed that a 22 Fr curved aortic cannula would be inserted via the anterior wall of the distal ascending aorta, 2 cm below the orifice of brachiocephalic artery. The tip of the cannula was angled slightly cephalad. This was done by moving the cannula 30° counter-clockwise away from the long axis of the aorta. The cannula was then fixed perpendicular to the aortic wall where it was inserted.
To generate the geometric information needed for the present study, a series of helical contrast scans (1 mm/slice) were acquired of normally shaped aorta, in vivo, from a single healthy 54-year-old male patient. This was done using an Aquilion 16 multi detector computed tomography (CT) system (Toshiba Medical Systems Inc., Tochigi, Japan). The patient displayed no anatomical abnormality of the aorta. The patient's body surface area was 1.64 m2. The patient provided informed, written consent allowing the information obtained by the CT scan to be used.
By using the Amira advanced 3D visualization and volume modeling software (Mercury Computer Systems, Inc., Chelmsford, MA, USA), the centerline data of the aorta and its branches was determined from the CT scans using the successive region growing method [6]. The cross sections were superimposed perpendicular to the centerline data. Based on the centerline and diameter information, by using a sweeping technique, the solid geometry of the aorta and its branches were generated in form of the nonuniform rational B-spline (NURBS) curves [7,8].
The geometry of the arterial cannula was also modeled, based on a drawing of the structure of a 22 Fr curved tip arterial cannula (DLP Model 88122, Medtronic Inc., Minneapolis, MN, USA). The geometries of the aortic arch and the cannula were then combined using Boolean operations.
The shape of the sinus of Valsalva was not reconstructed because, most of the time during CPB the proximal ascending aorta is cross-clamped. It is impossible to obtain a CT scan image of a cross-clamped aorta. Therefore, rather than attempting to reconstruct the geometry of a clamped aorta, the study assumed the proximal aorta to be a hemisphere at the same level as the right pulmonary artery. This assumption was used to minimize the effect of the shape of the aorta behind the cannula orifice from which the jet issued.
Finally, based on the reconstructed geometry described above, computational grids with tetrahedral cells (called elements in finite element method) were generated using the advancing front method for the purposes of CFD analysis [9]. The reconstructed grids consisted of 265,856 nodes and 1,493,297 tetrahedral elements (Fig. 1
).
View larger version (102K):
[in this window]
[in a new window]
|
Fig. 1. Computational grids. Based on the CT scan data computational grids consisting of 1,493,297 tetrahedral elements were generated.
|
|
2.2 Governing equations and boundary conditions
Shear rates in large arteries are typically large enough to assume that the blood involved behaves as a Newtonian fluid [10]. Thus, blood flow in the thoracic aorta and its large branches is governed by the Navier–Stokes equations. For the purposes of this study, therefore, the blood was assumed to be an incompressible, homogeneous and Newtonian fluid, with a constant viscosity of 0.0035 Pa. The density of blood was taken to be 1050 kg m–3
[4,5,10]. The vessel walls were considered to be rigid, and a no-slip condition was applied at the walls. At the ends of the branches and the distal end of the aorta, natural outflow boundary conditions were applied. In a CFD analysis for an incompressible fluid, because the density is taken constant, the calculated pressures are relative to the pressure boundary conditions, rather than absolute. Thus the wall pressure (the pressure perpendicular to the wall) is expressed by the relative pressure value. In the present model, the pressures at the ends of the vessels were assumed to be the base reference pressure.
Within the reconstructed model, a cardiopulmonary bypass flow of 4.1 l/min was simulated. This was equivalent to a CPB flow index of 2.5 l min–1
m–2 in this case. The Navier–Stokes equations that govern fluid motion were solved by the finite element method using Acusolve CFD solver (ACUSIM Software, Inc., Mountain View, CA, USA) [4,5,10]. Amira was used again for the 3D visualization of the results. The wall shear rate was determined by the velocity parallel to the wall within the grid adjacent to the wall, since a no-slip condition was applied to the wall. Wall shear stress was then determined from the product of the viscosity of the fluid and the wall shear rate [11]. The average distance from the wall to the adjacent grid was 0.68 mm.
|
3. Results
|
|---|
The wall pressure, which is the force applied perpendicular to the wall surface, was highest at the superior-posterior wall of the aortic arch at the point where the jet flow from the cannula impinged on the wall. The maximum wall pressure was 3104.8 Pa. The wall pressure was higher at the walls distal to the orifices of cervical branches of the aortic arch (Fig. 2
). The wall shear stress (which is the force applied parallel to the wall as a result of flow viscosity) was 25.1 Pa at its maximum (Fig. 3
). The maximum velocity of flow (3.77 m/s) occurred just past the tip of the arterial cannula. The streamline is shown in Fig. 4
. High velocity vortex was observed below the orifice of the brachiocephalic artery; this was caused by the jet flow impingement. The turbulent flow then continued along the aortic wall, with some flowing into the left subclavian artery. No high velocity flow was observed to head into the left carotid artery. A low velocity vortex flow (which whirled around) was observed throughout the aortic arch. The flow rates in each of the branches were 132, 613, 175, and 821 ml/min for the right subclavian, right common carotid, left common carotid, and left subclavian artery, respectively.
View larger version (76K):
[in this window]
[in a new window]
|
Fig. 2. The wall pressure distribution on the aortic wall during cardiopulmonary bypass. The wall pressure is the force applied perpendicular to the wall. The highest wall pressure was observed at the superior-posterior wall of the aorta where the jet flow impingement occurred. The highest wall pressure was 3104.8 Pa.
|
|
View larger version (72K):
[in this window]
[in a new window]
|
Fig. 3. The shear stress on the aortic wall during cardiopulmonary bypass (posterior view). The shear stress is the force applied parallel to the wall caused by flow viscosity. The maximum wall shear stress was 25.1 Pa.
|
|
View larger version (61K):
[in this window]
[in a new window]
|
Fig. 4. Streamlines of the turbulence flow within the aortic arch. The streamline of turbulence was visualized using color velocity mapping. The high velocity vortex flow eventually headed into the left subclavian artery.
|
|
|
4. Discussion
|
|---|
This study confirmed that blood flow during cardiopulmonary bypass can be simulated and visualized using the CFD techniques that are currently available. The CFD simulation of the blood flow within the native aorta in patients with a left ventricular assist device has been reported previously, using a simplified geometry of the aorta [12]. In that model, the aorta was assumed to be a curved tube without branches. Because the geometrical information is the most important factor in CFD analysis, in the present study we generated the computational grid from the thin slice contrast CT scans (1 mm/slice). The utilization of magnetic resonance imaging (MRI) has also been reported as an alternative approach to obtain precise geometrical information [13]. The flow velocity during scanning can be also measured if MRI is used.
In the present case, in light of the streamline and the location at which a high velocity vortex occurred, an embolic event in the territory of the left subclavian artery could occur if a mobile plaque was present at the superior-posterior wall of the aortic arch just below the orifice of the brachiocephalic artery. However, stroke would be unlikely to occur in the territory of the bilateral carotid arteries, because the high velocity vortex mainly flowed off into the left subclavian artery. It has been reported that the perioperative strokes caused by CPB occur predominantly on the left side and the posterior side [1]. These findings were consistent with the present simulation, indicating that thromboembolism may occur mainly in the left subclavian artery, which can subsequently cause stroke in the territory of the left vertebral artery.
Wall pressure was also visualized in this study, along with wall shear stress. To date, the influence of these parameters on embolism during CPB has not been clear. The highest wall pressure (expressed as a value relative to the basal pressure) was 3104.8 Pa. Thus if the base reference pressure (i.e. the mean blood pressure measured at the brachial artery) was assumed to be 70 mmHg, the absolute value of the highest wall pressure was expected to be 93.3 mmHg.
Although the wall shear stress (defined as the force parallel to the wall caused by flow viscosity) is known to be a very important factor in the development of atherosclerosis, the magnitude of the force itself is usually very small and normal shear stress on the aortic wall is usually below 15 Pa [11]. The highest shear stress in the present case was found to be higher than 15 Pa, but the magnitude was still similarly small, even under a high velocity flow.
Flow distribution in the present case was essentially sufficient for each branch, although the left subclavian artery may have received more flow than required, as a result of the high velocity flow which entered the branch, as described above.
Because the CFD analysis of the complex geometry of the aorta required multiple complex processes, we have only been able to perform the simulation using one representative case to date. Creating an appropriate geometric model and computational grids suitable for CFD analysis was an especially cumbersome and very time-consuming process as these processes have not yet been automated.
The technique shows promise and, once the processes are automated in the future, it may be possible to simulate every patient's vascular geometry before an operation in order to predict blood flow patterns and assess the risks associated with different cannulation methods. It is possible that this could reduce the risk of stroke significantly. A similar approach has been tried in other fields of surgery [14].
4.1 Technical limitations
The most important technical concern in the present case was the boundary condition of the terminus of the vessels. The pressures at the end of the vessels were assumed to be the same and constant, providing a reference pressure. In blood flow simulations, this is one of the most commonly used outflow boundary conditions [15]. The flow flowed off as free-flow at the end of the branches and, because the effect of the resistance of the downstream vascular beds is not taken into account, the flow split was dictated solely by the resistance to flow in the branches within the model.
Ideally, when simulating blood flow in large arteries, outlet boundary conditions should represent all downstream vasculature, including smaller arteries, arterioles, capillaries, venules, and veins returning blood to the heart. However, because the vascular bed from the major arteries to the capillaries can include tens of millions of blood vessels, the vast extent and complexity of blood circulation precludes a three-dimensional representation of the entire circuit. An alternative approach is to utilize (1) three-dimensional models for the major arteries, where high-fidelity information is needed, and (2) one-dimensional models to represent the remainder of the system [15]. This kind of approach is new, and has been reported only very recently. The methodology it uses to represent the peripheral vascular network is not well established [15]. Although the use of more realistic models of the outflow boundary condition of blood vessels would have been optimal, we applied a more commonly used simple outflow boundary condition for this initial study.
The other issue is that we considered the vessel walls as rigid, despite the fact that a normal aorta clearly expands during systole. This decision was made because models that simulate the movement of the boundary wall while it is being influenced by the flow are mathematically very complex, and it is difficult technically to solve the equations governing such complex models. The present case simulates non-pulsatile flow, and the issue of the deformity of the wall probably would not influence the validity of the study. For practical reasons, therefore, we did not consider the deformation of the vessels when developing the model. This is not unusual, as the majority of previously published blood flow simulation models also ignore the effects of deformation of the aorta [4,5].
In the present study we focused on establishing a simple three-dimensional computational simulation of blood flow during CPB, which involved precise geometry based on commonly used boundary conditions.
|
5. Conclusion
|
|---|
The present study showed that blood flow during CPB can be simulated using CFD techniques. It provides a good example of how computational fluid dynamics could be applied in the future to assess an individual's risk of stroke, as a result of CPB. Further multiple representative cases need to be simulated.
|
References
|
|---|
- Barbut D, Grassineau D, Lis E, Heier L, Hartman GS, Isom OW. Posterior distribution of infarcts in strokes related to cardiac operations. Ann Thorac Surg 1998;65(6):1656-1659.[Abstract/Free Full Text]
- Grooters RK, Ver Steeg DA, Stewart MJ, Thieman KC, Schneider RF. Echocardiographic comparison of the standard end-hole cannula, the soft-flow cannula, and the dispersion cannula during perfusion into the aortic arch. Ann Thorac Surg 2003;75(6):1919-1923.[Abstract/Free Full Text]
- Grossi EA, Kanchuger MS, Schwartz DS, McLoughlin DE, LeBoutillier M, Ribakove GH, Marschall KE, Galloway AC, Colvin SB. Effect of cannula length on aortic arch flow: protection of the atheromatous aortic arch. Ann Thorac Surg 1995;59(3):710-712.[Abstract/Free Full Text]
- Shahcheraghi N, Dwyer HA, Cheer AY, Barakat AI, Rutaganira T. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J Biomech Eng 2002;124(4):378-387.[CrossRef][Medline]
- Morris L, Delassus P, Callanan A, Walsh M, Wallis F, Grace P, McGloughlin T. 3-D numerical simulation of blood flow through models of the human aorta. J Biomech Eng 2005;127(5):767-775.[CrossRef][Medline]
- Hanaizumi H, Ohmori K. Development of a 3D skeletonizing algorithm and its application. Technical report of the institute of electronics. Information Commun Engineers (IEICE) 2002;101(581):89-94.
- Ward RC, Yambert MW, Toedte RJ, Munro NB, Easterly CE, Difilippo EP, Stallings DC. Creating a human phantom for the virtual human program. Stud Health Technol Inform 2000;70:368-374.[Medline]
- Anastasi G, Cutroneo G, Tomasello F, Lucerna S, Vitetta A, Bramanti P, Di Bella P, Parenti A, Porzionato A, Macchi V, De Caro R. In vivo basal ganglia volumetry through application of NURBS models to MR images. Neuroradiology 2006;48(5):338-345.[CrossRef][Medline]
- Ito Y, Nakahashi K. Surface triangulation for polygonal models based on CAD data. Int J Numer Methods Fluids 2002;39(1):75-96.[CrossRef]
- Fung YC. Biomechanics circulation. 2nd ed.. New York: Springer; 1997p. 108–200.
- Walsh M, McGloughlin T, Liepsch DW, O’Brien T, Morris L, Ansari AR. On using experimentally estimated wall shear stresses to validate numerically predicted results. Proc Inst Mech Eng 2003;217(2):77-90.[CrossRef]
- May-Newman K, Hillen B, Dembitsky W. Effect of left ventricular assist device outflow conduit anastomosis location on flow patterns in the native aorta. ASAIO J 2006;52(2):132-139.[CrossRef][Medline]
- Svensson J, Gårdhagen R, Heiberg E, Ebbers T, Loyd D, Länne T, Karlsson M. Feasibility of patient specific aortic blood flow CFD simulation. Med Image Comput Comput Assist Interv Int Conf Med Image Comput Comput Assist Interv 2006;9(1):257-263.[Medline]
- Castro MA, Putman CM, Cebral JR. Patient-specific computational modeling of cerebral aneurysms with multiple avenues of flow from 3D rotational angiography images. Acad Radiol 2006;13(7):811-821.[CrossRef][Medline]
- Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 2006;195:3776-3796.[CrossRef]
Top
Abstract
1. Introduction
