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Numerical simulation of fluid–structure interaction in bypassed DeBakey III aortic dissection a
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Aike Qiao , Wencong Yin & Bo Chu
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Center of Cardiovascular Medical Engineering, College of Life Science and Bioengineering, Beijing University of Technology, Beijing, P.R. China Published online: 17 Feb 2014.
To cite this article: Aike Qiao, Wencong Yin & Bo Chu (2014): Numerical simulation of fluid–structure interaction in bypassed DeBakey III aortic dissection, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2014.881806 To link to this article: http://dx.doi.org/10.1080/10255842.2014.881806
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Computer Methods in Biomechanics and Biomedical Engineering, 2014 http://dx.doi.org/10.1080/10255842.2014.881806
Numerical simulation of fluid – structure interaction in bypassed DeBakey III aortic dissection Aike Qiao*, Wencong Yin and Bo Chu Center of Cardiovascular Medical Engineering, College of Life Science and Bioengineering, Beijing University of Technology, Beijing, P.R. China
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(Received 1 November 2012; accepted 7 January 2014) It was found that bypass graft alone could achieve great effects in treating aortic dissection. In order to investigate the mechanical mechanism and the haemodynamic validity of the bypassing treatment for DeBakey III aortic dissection, patient-specific models of DeBakey III aortic dissection treated with different bypassing strategies were constructed. One of the bypassing strategies is bypassing between ascending aorta and abdominal aorta, and the other is bypassing between left subclavian artery and abdominal aorta. Numerical simulations under physiological flow conditions based on fluid– structure interaction were performed using finite element method. The results show that blood flow velocity, pressure and vessel wall displacement of false lumen are all reduced after bypassing. This phenomenon indicates that bypassing is an effective surgery for the treatment of DeBakey III aortic dissection. The effectiveness to cure through lumen is better when bypassing between left subclavian artery and abdominal aorta, while the effectiveness to cure blind lumen is better when bypassing between ascending aorta and abdominal aorta. Keywords: biomechanics; cardiovascular implants and devices; cardiovascular disease; computer aided surgical planning; haemodynamics
1. Introduction Aortic dissection is one of the usually occurred dangerous cardiovascular diseases with high mortality (Fuster and Halperin 1994; Johansson et al. 1995). According to the classification of DeBakey, the aortic dissection includes three types, i.e. DeBakey I, DeBakey II and DeBakey III, respectively (DeBakey et al. 1965; Beller et al. 2004). Different therapeutic treatments should be used to different types of aortic dissection. Surgery is an effective and successful approach beside the medical treatment. In 1979, Carpentier developed the thromboexclusion approach using bypass graft to treat DeBakey III aortic dissection (Carpentier et al. 1981). Some cardiovascular surgeons found that bypass graft alone can also achieve great effects in this surgery. Bypass graft is a surgical treatment of DeBakey III aortic dissection under certain conditions. Clinical practices have proved that it has good effects. However, the clinical cases treating DeBakey III aortic dissection with bypass graft are still very rare. The reason may be that the haemodynamic mechanism of bypass graft and many other issues still lacks a comprehensive understanding. Haemodynamic changes post-operation are closely related with the effect of bypass graft surgery, especially the changes of blood pressure and flow velocity in the dissecting region (Thubrikar et al. 1999; Gao and Matsuzawa 2006; Beller et al. 2008). Few literatures are actually related with the clinical surgery mechanisms, although there are many that focused on the topic of aortic dissection (Gasser and Holzapfel 2006;
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
Rajagopal et al. 2007; Zannoli et al. 2007; Laurant et al. 2013). The mechanism of the bypassing treatment of aortic dissection needs further studies. Two strategies of bypassing procedure were proposed in this study, i.e. bypassing between left subclavian artery and abdominal aorta, and bypassing between ascending aorta and abdominal aorta. The haemodynamics of DeBakey III aortic dissection and its bypassing treatment was studied based on numerical simulation of fluid – structure interaction (FSI) by using finite element method (FEM) in order to figure out the biomechanical mechanism and haemodynamic validity of this surgical therapy, and to provide valuable surgical planning guidance for clinical treatment.
2. Methods Patient-specific models of DeBakey III aortic dissection were reconstructed using commercial tool MIMICS (MATERIALISE EUROPE, Leuven, Belgium). MRI serial slices were integrated by medical image-processing techniques such as threshold segmentation and regiongrowing methods. Some segmentation approaches such as 3D region growing and 2D manual editing were applied to omit the unnecessary organs and obtain the model with only the aorta. Then, the model in STereo Lithography (STL) format was smoothed by optimising the surface triangular patches. The thickness of arterial wall cannot be recognised using MIMICS, while the vessel wall model is
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Figure 1. Models of aortic dissection: (a) vessel wall; (b) blood flow domain; (c) dissection wall. The distal exit of dissection is open (not shown) or closed/broken (b) for the trough lumen model and blind lumen model, respectively.
necessary in FSI simulations. Thus, the surface model in STL format was exported to GeoMagic Studio (GeoMagic, Inc., Research Triangle Park, NC, USA) to generate the inner surface of vessel wall after checking and repairing the defects of triangular patches. Then, the thickness of arterial wall was built by offsetting the inner vessel wall 2 £ 1023 m outwards according to the statistical value of human aortic wall (Figure 1(a)). The models in STL format should be transformed to NURBS format in order to be exported to ANSYS Workbench (ANSYS, Inc., Canonsburg, PA, USA) to perform finite element analysis. The 3D patient-specific geometric models of DeBakey III aortic dissection are shown in Figure 1. Models with blind false lumen and through false lumen were established separately. The model with blind false lumen was constructed artificially by cutting the false lumen for the sake of comparison between different models (Figure 1(b)). The dissection wall was extracted separately which is of thickness (Figure1(c)). Two kinds of bypass graft strategy were applied to these dissection models, including the graft bypassing between ascending aorta and abdominal aorta, and the graft bypassing between left subclavian artery and abdominal aorta. The bypass graft was designed by using computer-aided design tools. The vessel wall model, the blood flow domain, the bypass graft and the dissection wall model were assembled together via Boolean operation to form the whole FSI model. The four models of bypassed aortic dissection with different grafting procedures are shown in Figure 2. The aortic dissection models with the through and blind false lumens were also reserved to perform numerical simulation for comparison with the bypassed models. Thus, totally there are six models for the simulation. Blood and vessel wall of the geometric models before and after bypassing were meshed, respectively and then the finite element models were obtained. Before this work,
Figure 2. Models of blood flow domain after bypassing. (a) Through lumen model bypassing between ascending aorta and abdominal aorta; (b) through lumen model bypassing between left subclavian artery and abdominal aorta; (c) blind lumen model bypassing between ascending aorta and abdominal aorta; (d) blind lumen model bypassing between left subclavian artery and abdominal aorta.
numerous simulations were performed to verify the mesh independence. Different meshes were also tested, and the minimum meshes were selected for the numerical simulation to save the computation consumption. The blood flow domain was meshed first using hexahedron element. Gradually, finer meshes were used near the vessel walls to obtain accurate result in the boundary layer. Computational fluid dynamics (CFD) simulations of blood flow were tested several times with different mesh sizes so as to decide the feasible meshes. Then, the vessel walls were meshed using tetrahedral element as the request of mesh quality for solid domain is relatively loose. The mesh size should be small enough to ensure the iteration convergence of physical variables (such as velocity and force) in the blood – wall interface. The material properties were defined and the boundary conditions were imposed. The blood was assumed to be
Figure 3. Longitudinal velocity at the inlet of ascending aorta in a cardiac cycle.
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Computer Methods in Biomechanics and Biomedical Engineering
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Figure 4. Velocity vectors contour of blood flow at a time of 0.04 s. (a) Through lumen model; (b) blind lumen model. In each figure, left: before bypassing; middle: bypassing between ascending aorta and abdominal aorta; right: bypassing between left subclavian artery and abdominal aorta.
homogeneous, adiabatic, isotropic, incompressible and unsteady continuous Newtonian fluid, and the material of vessel wall was assumed to be linear elastic. The viscosity and the density of blood are 3.5 £ 1023 Pa s and 1.05 £ 103 kg/m3, respectively. The maximum Reynolds number is 1295 based on the entrance diameter of 38 £ 1023 m and the peek velocity of 1.136 m/s. Under such low Re numbers, the flow keeps laminar in the configurations (Liu et al. 2009; Liu 2010; Liu et al. 2011; Vincent et al. 2011). The density, Young’s modulus and Poisson’s ratio of wall are 2.0 £ 103 kg/m3, 1.08 £ 108 Pa and 0.45, respectively (He and Li 2008). The period of the cardiac cycle was assumed to be 0.8 s. The following are the boundary conditions: (1) Figure 3 shows the longitudinal velocity at the entrance of ascending aorta in a cardiac cycle; (2) velocities on all walls were zero according to no-slip flow condition and (3) at the outlet section of abdominal aorta, a constant reference pressure was given as zero (Sui et al. 2009). FSI simulations were performed under physiological flow conditions using the CFD module of the commercial FEM package ANSYS 12.1 which is capable of computing the transient blood flow through the aortic dissection. The time step of iteration is 0.01 s. In order to improve the precision of the calculation, three periods of simulation were performed. Rajagopal et al. proposed that the intimal tear of aortic dissection occurs due to aortic normal and shear stresses; the development is a consequence of elevated mean and maximum aortic pressures, and the anisotropy of the layered composite aortic wall; while the propagation of the dissection flap is due to cyclic loading (the severity of which is dictated by the amplitude of the pressure waveform, and the number of cycles of exposure) of the anisotropic layered aorta (Rajagopal et al. 2007). Rajagopal et al. also
suggested that aortic imaging may be used as a screening test for aortic dissection. In patients deemed to be at high risk by imaging criteria, there may be a role for prophylactic medical or interventional/surgical therapy (Rajagopal et al. 2007). Rudenick et al. thought that dilatation of aortic dissection is triggered by haemodynamic parameters (pressures/wall shear stresses (WSS)) and geometry of false and true lumen, information not captured by channel diameter alone (Rudenick et al. 2013). Rudenick et al. suggested that false lumen haemodynamics heavily depends on cumulative tear size, and thus, it is an important parameter to take into account when clinically assessing chronic aortic dissections (Rudenick et al. 2013). Cheng et al. suggested that aortic morphology and primary entry tear size and position exert significant effects on flow and other haemodynamic parameters in the aortic dissection (Cheng et al. 2013). Here, we selected three typical factors of solid mechanics and haemodynamics, i.e. the pressure, blood flow velocity (which can indirectly denote the WSS) and the displacement of dissection wall (which can be evaluated by aortic imaging), as the criteria for performance that differentiates various surgical planning options and configurations (Qiao et al. 2007). 3. Results The spatial and temporal distribution of haemodynamic parameters of DeBakey III aortic dissection before and after bypassing, such as blood flow velocity, mass flow rate, pressure and vessel wall displacement, was obtained. Haemodynamic changes before and after bypassing were compared, and the effects when applying different types of graft to bypasss aortic dissection with different types of false lumen were also analysed and compared. In addition, the results of FSI simulation and non-FSI
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Figure 5.
Mean velocity in the false lumen of the through lumen model (a) and the blind lumen model (b) before and after bypassing.
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simulation based on idealised model and rigid vessel wall were compared. 3.1
Velocity and mass flow rate
Velocity vectors of blood flow at a typical time of 0.04 s during the acceleration segment of systolic phase are shown in Figure 4. Figure 5 shows the mean velocity in the through and blind false lumen before and after bypassing. Table 1 shows the maximum value of mean velocity in the false lumen during a cardiac cycle. The mean velocity of blood flow in the false lumen after bypassing is generally less than that before bypassing. The greater the velocity, the more obvious is the reduction. The change is not obvious when the velocity is low, but it does not affect the decreasing trend. Velocity decreases more significantly in the model with a blind lumen bypassed between the ascending aorta and the abdominal aorta. The mass flow ratios of the bypass graft are 18.7% and 8.4% for the through lumen model, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. The mass flow ratios of the bypass graft are 52.8% and 51.3% for the blind lumen model, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. 3.2 Pressure Figure 6 shows the distribution of blood pressure at a typical time of 0.04 s. Figure 7 shows the mean pressure of inner vessel wall of through and blind lumen before and after bypassing. The pressure of results is a relative value Table 1.
compared with the reference pressure at the outlet section of abdominal aorta. Table 2 shows the maximum value of mean pressure on vessel wall in a cardiac cycle. The mean blood pressure on vessel wall after bypassing is generally less than that before bypassing. The peak values of inlet pressure decrease, 1.09 £ 103 Pa and 6.84 £ 102 Pa, for the through lumen models, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. The peak values of inlet pressure decrease, 3.13 £ 103 Pa and 2.47 £ 103 Pa, for the blind lumen models, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. 3.3 Displacement Figure 8 shows the distribution of vessel wall displacement at a typical time of 0.08 s denoting the peek velocity of a cardiac cycle. Figure 9 shows the mean displacement of vessel wall of through and blind lumen models before and after bypassing. Table 3 shows the maximum value of mean displacement of wall in a cardiac cycle. The mean displacement of vessel wall is generally reduced after bypassing. Displacement decreases more significantly in the model with a through lumen bypassed between the left subclavian artery and the abdominal aorta. 3.4 Comparison of FSI and non-FSI It can be seen from Table 4 that the simulation results of FSI and non-FSI attribute largely the same trend. The effect of bypass graft is closely related to the
Maximum value of mean velocity in the false lumen in a cardiac cycle.
Model Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
Velocity (m/s) 2.35 1.50 1.60 0.242 0.119 0.154
Decreasing amplitude (%) 36.2 31.9 50.8 36.4
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Figure 6. Distribution of blood pressure at a time of 0.04 s. (a) Through lumen; (b) blind lumen. In each figure, left: before bypassing; middle: bypassing between ascending aorta and abdominal aorta; right: bypassing between left subclavian artery and abdominal aorta.
haemodynamic changes of aortic dissection after bypassing; especially the changes of blood pressure and blood flow velocity in the dissection played a very important role. The results show that blood flow velocity and pressure, and vessel wall displacement of false lumen are all reduced after bypassing, and the effects are more obvious when applying bypass graft between left subclavian artery and abdominal aorta to aortic dissection with through lumen, and applying bypass graft between ascending aorta and abdominal aorta to aortic dissection with blind lumen. Bypass graft can split blood stream of the aorta, and effectively ease the impulsion and stress of blood flow on the pathological dissection.
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Discussion
Bypass graft, as an alternative approach of treating aortic dissection, has many advantages compared with general thoracic aortic replacement, such as smaller trauma, simpler operation, shorter operation time and less surgical risk. It is also the treatment needed to be adopted inevitably for some patients under critical condition and unable to withstand major surgery. The simulation results
Figure 7.
of the present study demonstrate that bypass grafting can effectively divert blood flow from the aortic dissection. The pressure and velocity in the false lumen, the mass flow rate in the dissected aorta and the inlet pressure near the ascending aorta are greatly reduced after bypass grafting. These changes can lessen the blood pressure of the upper limbs and reduce the impact and stress of aortic dissection. It can be deduced that bypass grafting is beneficial to not only reduce and prevent the expansion and rupture of aortic dissection, but also promote the closure of the dissection layer and improve blood perfusion of the lower limbs. This treatment is an effective procedure to cure DeBakey III aortic dissection. Recently, hybrid surgery related with bypass graft has gained popularity for the treatment of aortic dissection. Botta found that retrograde coil embolisation of the left subclavian artery, as alternative to open subclavian ligature, is a safe and effective method of rapid false lumen sealing in patients requiring coverage of the left subclavian artery and carotid– subclavian bypass, even in the setting of acute aortic syndromes (Botta et al. 2009). Abdulamit et al. proposed a novel approach with an aortic debranching from the ascending aorta in order to reduce
Mean pressure of inner vessel wall of through lumen (a) and blind lumen (b) before and after bypassing.
6 Table 2.
A. Qiao et al. Maximum value of mean pressure on vessel wall in a cardiac cycle.
Model
Pressure (Pa)
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Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
the morbidity of aortic dissection (Abdulamit et al. 2012). Khoynezhad et al., Civilini et al. and Kim et al. reported, respectively, that axillofemoral bypass can be successful in relief of malperfusion to the affected limb in cases with anatomic obstruction (Khoynezhad et al. 2011; Civilini et al. 2012; Kim et al. 2013). Kuo et al. also concluded that managing patients with coexisting visceral and extremity malperfusion may be accomplished with axillofemoral bypass exclusively, which can relieve ischaemia of upstream abdominal organs and downstream lower extremities effectively and durably (Kuo et al. 2013). Ignat’ev reported a case of a patient with DeBakey type III B chronic aortic dissection treated with two-staged surgical procedures. Two months follow-up showed that the false lumen along the descending thoracic aorta is thrombosed. The finding of this case illustrated that the carotid– subclavian bypass is functioning (Ignat’ev et al. 2012). Other procedures related with bypass grafting treatment of aortic dissection are still emerging. The
4.59 £ 103 3.90 £ 103 3.97 £ 103 7.37 £ 103 4.87 £ 103 5.02 £ 103
Decreasing amplitude 6.83 £ 102 6.14 £ 102 2.50 £ 103 2.34 £ 103
potential biomechanics mechanism will be revealed with more numerical studies and clinical trials. A further understanding of the relevant fluid and solid mechanics may yield not only a better appreciation of its pathogenesis but also the development of improved diagnostic and therapeutic strategies (Rajagopal et al. 2007). Instead of WSS, the velocity in the false lumen was selected as a criterion which can indirectly represent WSS in the present study. The pressure and displacement are also illustrated in this study to evaluate the difference between different bypassing approaches. Aortic imaging, which can show the geometry and displacement of aortic dissection, may be used as a criterion of screening test for aortic dissection (Rajagopal et al. 2007). In addition to these employed factors, such as blood flow velocity, pressure and displacement of the vessel wall, attention should be paid to the influences of other parameters, such as the changes of pressure gradient, WSS, and flow distribution ratio before and after bypass, on the treatment
Figure 8. Distribution of vessel wall displacement at a time of 0.08 s. (a) Through lumen before bypass; (b) through lumen after bypassing between ascending aorta and abdominal aorta; (c) through lumen after bypassing between left subclavian artery and abdominal aorta; (d) blind lumen before bypassing; (e) blind lumen after bypassing between ascending aorta and abdominal aorta; (f) blind lumen after bypassing between left subclavian artery and abdominal aorta.
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Figure 9. Table 3.
Mean displacement of vessel wall of through lumen model (a) and blind lumen model (b) before and after bypassing. Maximum value of mean displacement of wall in a cardiac cycle.
Model
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Displacement (m)
Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
Decreasing amplitude (%)
23
2.75 £ 10 1.98 £ 1023 1.27 £ 1023 3.67 £ 1023 2.56 £ 1023 1.99 £ 1023
28.0 53.8 30.2 45.8
Bypassing between ascending aorta and abdominal aorta Through lumen Mean velocity 36.9% 27.7% Maximum velocity 36.2% 21.3% Mean pressure 3.60 £ 102 Pa 1.55 £ 102 Pa Blind lumen Mean velocity 36.9% 11.8% Maximum velocity 50.8% 21.1% Mean pressure 4.69 £ 102 Pa 5.38 £ 103 Pa Bypassing between left subclavian artery and abdominal aorta Through lumen Mean velocity 24.2% 9.90% Maximum velocity 31.9% 9.67% Mean pressure 1.33 £ 102 Pa 1.52 £ 102 Pa Blind lumen Mean velocity 25.7% 27.3% Maximum velocity 36.4% 30.6% Mean pressure 2.41 £ 102 Pa 7.83 £ 102 Pa
coronary perfusion and aortic valve dynamics (Kouchoukos et al. 1995). The clinical outcome of the proposed strategy needs more observation. Some limitations were presented in this study. For example, the geometry model was not as realistic as the patient-specific model. The arterial wall is not linear elastic and is also not isotropic, and the pressure boundary condition is not physiological. With the development of medical imaging and image-processing technology, the model will be more accurate, while the model construction time will be further reduced in the future study. Also, the models of transition flow state or turbulence flow state, and the vessel wall material of hyper-elasticity or viscoelasticity will be considered, which will make the results closer to reality. Producing physical models of blood vessels with rapid prototyping technology and performing experiments in vitro should be further studied. The influences of other haemodynamic parameters on the treatment and the effects of other bypass graft procedures need to be further investigated.
of aortic dissection. With regard to the WSS and pulsatile flow in the bypass graft, more clinical observation and haemodynamics studies are needed to reveal the potential influence of graft patency. Theoretically, the coronary artery and the aortic valve are not influenced by the bypass graft because there is no injury of bypassing anastomosis to the coronary artery and the aortic valve. Actually, there may be haemorrhage due to suturing techniques inducing the interference with
5. Conclusions According to the FSI simulation based on 3D patientspecific models, bypassing is an effective surgery for the treatment of DeBakey III aortic dissection. Considering the haemodynamic parameters, such as blood flow velocity, mass flow rate, pressure and vessel wall displacement, it can be indicated that bypass grafting can effectively divert blood flow from the aortic dissection. The effectiveness to
Table 4. Comparison of FSI and non-FSI simulation results. Decreasing amplitude FSI
Non-FSI
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cure through lumen is better when bypassing between left subclavian artery and abdominal aorta, while the effectiveness to cure blind lumen is better when bypassing between ascending aorta and abdominal aorta. These results might be of some theoretical significance for clinicians when they choose bypass graft procedures before the treatment of DeBakey III aortic dissection. An improved understanding of the mechanics of the disease process, aided by the development of predictive mathematical models, imaging technology, along with numerical simulation-based surgical planning, has the potential to improve treatment approaches and outcomes.
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Funding This work was supported by National Natural Science Foundation of China [grant number 10772010], [grant number 81171107]; Higher School Specialized Research Fund for the Doctoral Program Funding Issue [grant number 20111103110012]; and Natural Science Foundation of Beijing [grant number KZ201210005006].
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Numerical simulation of fluid–structure interaction in bypassed DeBakey III aortic dissection a
a
Aike Qiao , Wencong Yin & Bo Chu
a
a
Center of Cardiovascular Medical Engineering, College of Life Science and Bioengineering, Beijing University of Technology, Beijing, P.R. China Published online: 17 Feb 2014.
To cite this article: Aike Qiao, Wencong Yin & Bo Chu (2014): Numerical simulation of fluid–structure interaction in bypassed DeBakey III aortic dissection, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2014.881806 To link to this article: http://dx.doi.org/10.1080/10255842.2014.881806
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Computer Methods in Biomechanics and Biomedical Engineering, 2014 http://dx.doi.org/10.1080/10255842.2014.881806
Numerical simulation of fluid – structure interaction in bypassed DeBakey III aortic dissection Aike Qiao*, Wencong Yin and Bo Chu Center of Cardiovascular Medical Engineering, College of Life Science and Bioengineering, Beijing University of Technology, Beijing, P.R. China
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(Received 1 November 2012; accepted 7 January 2014) It was found that bypass graft alone could achieve great effects in treating aortic dissection. In order to investigate the mechanical mechanism and the haemodynamic validity of the bypassing treatment for DeBakey III aortic dissection, patient-specific models of DeBakey III aortic dissection treated with different bypassing strategies were constructed. One of the bypassing strategies is bypassing between ascending aorta and abdominal aorta, and the other is bypassing between left subclavian artery and abdominal aorta. Numerical simulations under physiological flow conditions based on fluid– structure interaction were performed using finite element method. The results show that blood flow velocity, pressure and vessel wall displacement of false lumen are all reduced after bypassing. This phenomenon indicates that bypassing is an effective surgery for the treatment of DeBakey III aortic dissection. The effectiveness to cure through lumen is better when bypassing between left subclavian artery and abdominal aorta, while the effectiveness to cure blind lumen is better when bypassing between ascending aorta and abdominal aorta. Keywords: biomechanics; cardiovascular implants and devices; cardiovascular disease; computer aided surgical planning; haemodynamics
1. Introduction Aortic dissection is one of the usually occurred dangerous cardiovascular diseases with high mortality (Fuster and Halperin 1994; Johansson et al. 1995). According to the classification of DeBakey, the aortic dissection includes three types, i.e. DeBakey I, DeBakey II and DeBakey III, respectively (DeBakey et al. 1965; Beller et al. 2004). Different therapeutic treatments should be used to different types of aortic dissection. Surgery is an effective and successful approach beside the medical treatment. In 1979, Carpentier developed the thromboexclusion approach using bypass graft to treat DeBakey III aortic dissection (Carpentier et al. 1981). Some cardiovascular surgeons found that bypass graft alone can also achieve great effects in this surgery. Bypass graft is a surgical treatment of DeBakey III aortic dissection under certain conditions. Clinical practices have proved that it has good effects. However, the clinical cases treating DeBakey III aortic dissection with bypass graft are still very rare. The reason may be that the haemodynamic mechanism of bypass graft and many other issues still lacks a comprehensive understanding. Haemodynamic changes post-operation are closely related with the effect of bypass graft surgery, especially the changes of blood pressure and flow velocity in the dissecting region (Thubrikar et al. 1999; Gao and Matsuzawa 2006; Beller et al. 2008). Few literatures are actually related with the clinical surgery mechanisms, although there are many that focused on the topic of aortic dissection (Gasser and Holzapfel 2006;
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
Rajagopal et al. 2007; Zannoli et al. 2007; Laurant et al. 2013). The mechanism of the bypassing treatment of aortic dissection needs further studies. Two strategies of bypassing procedure were proposed in this study, i.e. bypassing between left subclavian artery and abdominal aorta, and bypassing between ascending aorta and abdominal aorta. The haemodynamics of DeBakey III aortic dissection and its bypassing treatment was studied based on numerical simulation of fluid – structure interaction (FSI) by using finite element method (FEM) in order to figure out the biomechanical mechanism and haemodynamic validity of this surgical therapy, and to provide valuable surgical planning guidance for clinical treatment.
2. Methods Patient-specific models of DeBakey III aortic dissection were reconstructed using commercial tool MIMICS (MATERIALISE EUROPE, Leuven, Belgium). MRI serial slices were integrated by medical image-processing techniques such as threshold segmentation and regiongrowing methods. Some segmentation approaches such as 3D region growing and 2D manual editing were applied to omit the unnecessary organs and obtain the model with only the aorta. Then, the model in STereo Lithography (STL) format was smoothed by optimising the surface triangular patches. The thickness of arterial wall cannot be recognised using MIMICS, while the vessel wall model is
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Figure 1. Models of aortic dissection: (a) vessel wall; (b) blood flow domain; (c) dissection wall. The distal exit of dissection is open (not shown) or closed/broken (b) for the trough lumen model and blind lumen model, respectively.
necessary in FSI simulations. Thus, the surface model in STL format was exported to GeoMagic Studio (GeoMagic, Inc., Research Triangle Park, NC, USA) to generate the inner surface of vessel wall after checking and repairing the defects of triangular patches. Then, the thickness of arterial wall was built by offsetting the inner vessel wall 2 £ 1023 m outwards according to the statistical value of human aortic wall (Figure 1(a)). The models in STL format should be transformed to NURBS format in order to be exported to ANSYS Workbench (ANSYS, Inc., Canonsburg, PA, USA) to perform finite element analysis. The 3D patient-specific geometric models of DeBakey III aortic dissection are shown in Figure 1. Models with blind false lumen and through false lumen were established separately. The model with blind false lumen was constructed artificially by cutting the false lumen for the sake of comparison between different models (Figure 1(b)). The dissection wall was extracted separately which is of thickness (Figure1(c)). Two kinds of bypass graft strategy were applied to these dissection models, including the graft bypassing between ascending aorta and abdominal aorta, and the graft bypassing between left subclavian artery and abdominal aorta. The bypass graft was designed by using computer-aided design tools. The vessel wall model, the blood flow domain, the bypass graft and the dissection wall model were assembled together via Boolean operation to form the whole FSI model. The four models of bypassed aortic dissection with different grafting procedures are shown in Figure 2. The aortic dissection models with the through and blind false lumens were also reserved to perform numerical simulation for comparison with the bypassed models. Thus, totally there are six models for the simulation. Blood and vessel wall of the geometric models before and after bypassing were meshed, respectively and then the finite element models were obtained. Before this work,
Figure 2. Models of blood flow domain after bypassing. (a) Through lumen model bypassing between ascending aorta and abdominal aorta; (b) through lumen model bypassing between left subclavian artery and abdominal aorta; (c) blind lumen model bypassing between ascending aorta and abdominal aorta; (d) blind lumen model bypassing between left subclavian artery and abdominal aorta.
numerous simulations were performed to verify the mesh independence. Different meshes were also tested, and the minimum meshes were selected for the numerical simulation to save the computation consumption. The blood flow domain was meshed first using hexahedron element. Gradually, finer meshes were used near the vessel walls to obtain accurate result in the boundary layer. Computational fluid dynamics (CFD) simulations of blood flow were tested several times with different mesh sizes so as to decide the feasible meshes. Then, the vessel walls were meshed using tetrahedral element as the request of mesh quality for solid domain is relatively loose. The mesh size should be small enough to ensure the iteration convergence of physical variables (such as velocity and force) in the blood – wall interface. The material properties were defined and the boundary conditions were imposed. The blood was assumed to be
Figure 3. Longitudinal velocity at the inlet of ascending aorta in a cardiac cycle.
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Figure 4. Velocity vectors contour of blood flow at a time of 0.04 s. (a) Through lumen model; (b) blind lumen model. In each figure, left: before bypassing; middle: bypassing between ascending aorta and abdominal aorta; right: bypassing between left subclavian artery and abdominal aorta.
homogeneous, adiabatic, isotropic, incompressible and unsteady continuous Newtonian fluid, and the material of vessel wall was assumed to be linear elastic. The viscosity and the density of blood are 3.5 £ 1023 Pa s and 1.05 £ 103 kg/m3, respectively. The maximum Reynolds number is 1295 based on the entrance diameter of 38 £ 1023 m and the peek velocity of 1.136 m/s. Under such low Re numbers, the flow keeps laminar in the configurations (Liu et al. 2009; Liu 2010; Liu et al. 2011; Vincent et al. 2011). The density, Young’s modulus and Poisson’s ratio of wall are 2.0 £ 103 kg/m3, 1.08 £ 108 Pa and 0.45, respectively (He and Li 2008). The period of the cardiac cycle was assumed to be 0.8 s. The following are the boundary conditions: (1) Figure 3 shows the longitudinal velocity at the entrance of ascending aorta in a cardiac cycle; (2) velocities on all walls were zero according to no-slip flow condition and (3) at the outlet section of abdominal aorta, a constant reference pressure was given as zero (Sui et al. 2009). FSI simulations were performed under physiological flow conditions using the CFD module of the commercial FEM package ANSYS 12.1 which is capable of computing the transient blood flow through the aortic dissection. The time step of iteration is 0.01 s. In order to improve the precision of the calculation, three periods of simulation were performed. Rajagopal et al. proposed that the intimal tear of aortic dissection occurs due to aortic normal and shear stresses; the development is a consequence of elevated mean and maximum aortic pressures, and the anisotropy of the layered composite aortic wall; while the propagation of the dissection flap is due to cyclic loading (the severity of which is dictated by the amplitude of the pressure waveform, and the number of cycles of exposure) of the anisotropic layered aorta (Rajagopal et al. 2007). Rajagopal et al. also
suggested that aortic imaging may be used as a screening test for aortic dissection. In patients deemed to be at high risk by imaging criteria, there may be a role for prophylactic medical or interventional/surgical therapy (Rajagopal et al. 2007). Rudenick et al. thought that dilatation of aortic dissection is triggered by haemodynamic parameters (pressures/wall shear stresses (WSS)) and geometry of false and true lumen, information not captured by channel diameter alone (Rudenick et al. 2013). Rudenick et al. suggested that false lumen haemodynamics heavily depends on cumulative tear size, and thus, it is an important parameter to take into account when clinically assessing chronic aortic dissections (Rudenick et al. 2013). Cheng et al. suggested that aortic morphology and primary entry tear size and position exert significant effects on flow and other haemodynamic parameters in the aortic dissection (Cheng et al. 2013). Here, we selected three typical factors of solid mechanics and haemodynamics, i.e. the pressure, blood flow velocity (which can indirectly denote the WSS) and the displacement of dissection wall (which can be evaluated by aortic imaging), as the criteria for performance that differentiates various surgical planning options and configurations (Qiao et al. 2007). 3. Results The spatial and temporal distribution of haemodynamic parameters of DeBakey III aortic dissection before and after bypassing, such as blood flow velocity, mass flow rate, pressure and vessel wall displacement, was obtained. Haemodynamic changes before and after bypassing were compared, and the effects when applying different types of graft to bypasss aortic dissection with different types of false lumen were also analysed and compared. In addition, the results of FSI simulation and non-FSI
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Figure 5.
Mean velocity in the false lumen of the through lumen model (a) and the blind lumen model (b) before and after bypassing.
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simulation based on idealised model and rigid vessel wall were compared. 3.1
Velocity and mass flow rate
Velocity vectors of blood flow at a typical time of 0.04 s during the acceleration segment of systolic phase are shown in Figure 4. Figure 5 shows the mean velocity in the through and blind false lumen before and after bypassing. Table 1 shows the maximum value of mean velocity in the false lumen during a cardiac cycle. The mean velocity of blood flow in the false lumen after bypassing is generally less than that before bypassing. The greater the velocity, the more obvious is the reduction. The change is not obvious when the velocity is low, but it does not affect the decreasing trend. Velocity decreases more significantly in the model with a blind lumen bypassed between the ascending aorta and the abdominal aorta. The mass flow ratios of the bypass graft are 18.7% and 8.4% for the through lumen model, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. The mass flow ratios of the bypass graft are 52.8% and 51.3% for the blind lumen model, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. 3.2 Pressure Figure 6 shows the distribution of blood pressure at a typical time of 0.04 s. Figure 7 shows the mean pressure of inner vessel wall of through and blind lumen before and after bypassing. The pressure of results is a relative value Table 1.
compared with the reference pressure at the outlet section of abdominal aorta. Table 2 shows the maximum value of mean pressure on vessel wall in a cardiac cycle. The mean blood pressure on vessel wall after bypassing is generally less than that before bypassing. The peak values of inlet pressure decrease, 1.09 £ 103 Pa and 6.84 £ 102 Pa, for the through lumen models, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. The peak values of inlet pressure decrease, 3.13 £ 103 Pa and 2.47 £ 103 Pa, for the blind lumen models, respectively, bypassing between ascending aorta and abdominal aorta and bypassing between left subclavian artery and abdominal aorta. 3.3 Displacement Figure 8 shows the distribution of vessel wall displacement at a typical time of 0.08 s denoting the peek velocity of a cardiac cycle. Figure 9 shows the mean displacement of vessel wall of through and blind lumen models before and after bypassing. Table 3 shows the maximum value of mean displacement of wall in a cardiac cycle. The mean displacement of vessel wall is generally reduced after bypassing. Displacement decreases more significantly in the model with a through lumen bypassed between the left subclavian artery and the abdominal aorta. 3.4 Comparison of FSI and non-FSI It can be seen from Table 4 that the simulation results of FSI and non-FSI attribute largely the same trend. The effect of bypass graft is closely related to the
Maximum value of mean velocity in the false lumen in a cardiac cycle.
Model Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
Velocity (m/s) 2.35 1.50 1.60 0.242 0.119 0.154
Decreasing amplitude (%) 36.2 31.9 50.8 36.4
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Figure 6. Distribution of blood pressure at a time of 0.04 s. (a) Through lumen; (b) blind lumen. In each figure, left: before bypassing; middle: bypassing between ascending aorta and abdominal aorta; right: bypassing between left subclavian artery and abdominal aorta.
haemodynamic changes of aortic dissection after bypassing; especially the changes of blood pressure and blood flow velocity in the dissection played a very important role. The results show that blood flow velocity and pressure, and vessel wall displacement of false lumen are all reduced after bypassing, and the effects are more obvious when applying bypass graft between left subclavian artery and abdominal aorta to aortic dissection with through lumen, and applying bypass graft between ascending aorta and abdominal aorta to aortic dissection with blind lumen. Bypass graft can split blood stream of the aorta, and effectively ease the impulsion and stress of blood flow on the pathological dissection.
4.
Discussion
Bypass graft, as an alternative approach of treating aortic dissection, has many advantages compared with general thoracic aortic replacement, such as smaller trauma, simpler operation, shorter operation time and less surgical risk. It is also the treatment needed to be adopted inevitably for some patients under critical condition and unable to withstand major surgery. The simulation results
Figure 7.
of the present study demonstrate that bypass grafting can effectively divert blood flow from the aortic dissection. The pressure and velocity in the false lumen, the mass flow rate in the dissected aorta and the inlet pressure near the ascending aorta are greatly reduced after bypass grafting. These changes can lessen the blood pressure of the upper limbs and reduce the impact and stress of aortic dissection. It can be deduced that bypass grafting is beneficial to not only reduce and prevent the expansion and rupture of aortic dissection, but also promote the closure of the dissection layer and improve blood perfusion of the lower limbs. This treatment is an effective procedure to cure DeBakey III aortic dissection. Recently, hybrid surgery related with bypass graft has gained popularity for the treatment of aortic dissection. Botta found that retrograde coil embolisation of the left subclavian artery, as alternative to open subclavian ligature, is a safe and effective method of rapid false lumen sealing in patients requiring coverage of the left subclavian artery and carotid– subclavian bypass, even in the setting of acute aortic syndromes (Botta et al. 2009). Abdulamit et al. proposed a novel approach with an aortic debranching from the ascending aorta in order to reduce
Mean pressure of inner vessel wall of through lumen (a) and blind lumen (b) before and after bypassing.
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A. Qiao et al. Maximum value of mean pressure on vessel wall in a cardiac cycle.
Model
Pressure (Pa)
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Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
the morbidity of aortic dissection (Abdulamit et al. 2012). Khoynezhad et al., Civilini et al. and Kim et al. reported, respectively, that axillofemoral bypass can be successful in relief of malperfusion to the affected limb in cases with anatomic obstruction (Khoynezhad et al. 2011; Civilini et al. 2012; Kim et al. 2013). Kuo et al. also concluded that managing patients with coexisting visceral and extremity malperfusion may be accomplished with axillofemoral bypass exclusively, which can relieve ischaemia of upstream abdominal organs and downstream lower extremities effectively and durably (Kuo et al. 2013). Ignat’ev reported a case of a patient with DeBakey type III B chronic aortic dissection treated with two-staged surgical procedures. Two months follow-up showed that the false lumen along the descending thoracic aorta is thrombosed. The finding of this case illustrated that the carotid– subclavian bypass is functioning (Ignat’ev et al. 2012). Other procedures related with bypass grafting treatment of aortic dissection are still emerging. The
4.59 £ 103 3.90 £ 103 3.97 £ 103 7.37 £ 103 4.87 £ 103 5.02 £ 103
Decreasing amplitude 6.83 £ 102 6.14 £ 102 2.50 £ 103 2.34 £ 103
potential biomechanics mechanism will be revealed with more numerical studies and clinical trials. A further understanding of the relevant fluid and solid mechanics may yield not only a better appreciation of its pathogenesis but also the development of improved diagnostic and therapeutic strategies (Rajagopal et al. 2007). Instead of WSS, the velocity in the false lumen was selected as a criterion which can indirectly represent WSS in the present study. The pressure and displacement are also illustrated in this study to evaluate the difference between different bypassing approaches. Aortic imaging, which can show the geometry and displacement of aortic dissection, may be used as a criterion of screening test for aortic dissection (Rajagopal et al. 2007). In addition to these employed factors, such as blood flow velocity, pressure and displacement of the vessel wall, attention should be paid to the influences of other parameters, such as the changes of pressure gradient, WSS, and flow distribution ratio before and after bypass, on the treatment
Figure 8. Distribution of vessel wall displacement at a time of 0.08 s. (a) Through lumen before bypass; (b) through lumen after bypassing between ascending aorta and abdominal aorta; (c) through lumen after bypassing between left subclavian artery and abdominal aorta; (d) blind lumen before bypassing; (e) blind lumen after bypassing between ascending aorta and abdominal aorta; (f) blind lumen after bypassing between left subclavian artery and abdominal aorta.
Computer Methods in Biomechanics and Biomedical Engineering
Figure 9. Table 3.
Mean displacement of vessel wall of through lumen model (a) and blind lumen model (b) before and after bypassing. Maximum value of mean displacement of wall in a cardiac cycle.
Model
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Displacement (m)
Through lumen before bypassing Through lumen bypassing between ascending aorta and abdominal aorta Through lumen bypassing between left subclavian artery and abdominal aorta Blind lumen before bypassing Blind lumen bypassing between ascending aorta and abdominal aorta Blind lumen bypassing between left subclavian artery and abdominal aorta
Decreasing amplitude (%)
23
2.75 £ 10 1.98 £ 1023 1.27 £ 1023 3.67 £ 1023 2.56 £ 1023 1.99 £ 1023
28.0 53.8 30.2 45.8
Bypassing between ascending aorta and abdominal aorta Through lumen Mean velocity 36.9% 27.7% Maximum velocity 36.2% 21.3% Mean pressure 3.60 £ 102 Pa 1.55 £ 102 Pa Blind lumen Mean velocity 36.9% 11.8% Maximum velocity 50.8% 21.1% Mean pressure 4.69 £ 102 Pa 5.38 £ 103 Pa Bypassing between left subclavian artery and abdominal aorta Through lumen Mean velocity 24.2% 9.90% Maximum velocity 31.9% 9.67% Mean pressure 1.33 £ 102 Pa 1.52 £ 102 Pa Blind lumen Mean velocity 25.7% 27.3% Maximum velocity 36.4% 30.6% Mean pressure 2.41 £ 102 Pa 7.83 £ 102 Pa
coronary perfusion and aortic valve dynamics (Kouchoukos et al. 1995). The clinical outcome of the proposed strategy needs more observation. Some limitations were presented in this study. For example, the geometry model was not as realistic as the patient-specific model. The arterial wall is not linear elastic and is also not isotropic, and the pressure boundary condition is not physiological. With the development of medical imaging and image-processing technology, the model will be more accurate, while the model construction time will be further reduced in the future study. Also, the models of transition flow state or turbulence flow state, and the vessel wall material of hyper-elasticity or viscoelasticity will be considered, which will make the results closer to reality. Producing physical models of blood vessels with rapid prototyping technology and performing experiments in vitro should be further studied. The influences of other haemodynamic parameters on the treatment and the effects of other bypass graft procedures need to be further investigated.
of aortic dissection. With regard to the WSS and pulsatile flow in the bypass graft, more clinical observation and haemodynamics studies are needed to reveal the potential influence of graft patency. Theoretically, the coronary artery and the aortic valve are not influenced by the bypass graft because there is no injury of bypassing anastomosis to the coronary artery and the aortic valve. Actually, there may be haemorrhage due to suturing techniques inducing the interference with
5. Conclusions According to the FSI simulation based on 3D patientspecific models, bypassing is an effective surgery for the treatment of DeBakey III aortic dissection. Considering the haemodynamic parameters, such as blood flow velocity, mass flow rate, pressure and vessel wall displacement, it can be indicated that bypass grafting can effectively divert blood flow from the aortic dissection. The effectiveness to
Table 4. Comparison of FSI and non-FSI simulation results. Decreasing amplitude FSI
Non-FSI
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cure through lumen is better when bypassing between left subclavian artery and abdominal aorta, while the effectiveness to cure blind lumen is better when bypassing between ascending aorta and abdominal aorta. These results might be of some theoretical significance for clinicians when they choose bypass graft procedures before the treatment of DeBakey III aortic dissection. An improved understanding of the mechanics of the disease process, aided by the development of predictive mathematical models, imaging technology, along with numerical simulation-based surgical planning, has the potential to improve treatment approaches and outcomes.
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Funding This work was supported by National Natural Science Foundation of China [grant number 10772010], [grant number 81171107]; Higher School Specialized Research Fund for the Doctoral Program Funding Issue [grant number 20111103110012]; and Natural Science Foundation of Beijing [grant number KZ201210005006].
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