Journal of Biomechanics

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1 Journal of Biomechanics ] (]]]]) ]]] ]]] Contents lists available at SciVerse ScienceDirect Journal of Biomechanics journal homepage: Flow resistance analysis of extracranial-to-intracranial (EC IC) vein bypass Y. Zhang a, S.F. Sia a,b, M.K. Morgan a, Y. Qian a,n a Australian School of Advanced Medicine, Macquarie University, Sydney, Australia b Division of Neurosurgery, Faculty of Medicine, University of Malaya, Kuala Lumpur, Malaysia article info Article history: Accepted 21 February 2012 Keywords: Extracranial-to-intracranial (EC IC) bypass CFD Flow resistance Vein bypass abstract Although brain bypass surgery has often been selected to treat internal carotid arteries (ICA) which are restricted by aneurysm or artery stenosis, its effectiveness has not been quantitatively evaluated. The purpose of this study is to propose an innovative approach for the evaluation of brain extracranial-tointracranial (EC IC) vein bypass surgery, based on the analysis of flow resistance in vein bypasses and within their contralateral carotid arteries through the use of computational fluid dynamics (CFD). Seven patients who underwent vein bypass surgery were examined with the use of high-resolution; computed tomography angiogram (CTA). The reconstructed three-dimensional (3D) geometries were segmented to create CFD calculation domains. Colour Doppler ultrasound (CDU) was used to measure blood flow velocities at the common carotid arteries (CCA), in order to determine inflow conditions. Based on the pipe flow theory, pressure drop was expressed as A _m 2 þb _m where A and B represent flow resistance coefficients and _m represents blood mass flow rate. The CFD results revealed that for a healthy ICA, the average values of A and B were Pa/(ml/min) 2 and Pa/(ml/min), respectively. For the vein bypass, an average value of A was Pa/(ml/min) 2 and B Pa/(ml/min), which was approximately that of a healthy ICA. However, in the case of a bypass utilising a venous conduit possessing a large-sized valve or existing size alteration, the flow resistance in that bypass would be higher than those found in the healthy ICA. An imbalance of flow resistances may impose conditions that could predispose hemodynamic failure or distal aneurysm development. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Extracranial-to-intracranial (EC IC) vein bypass surgery is a surgical procedure to augment or re-establish the blood flow where flow is restricted by a pathological change in the internal carotid arteries (ICA). For high flow EC IC bypass, the venous conduit (harvested from the long saphenous vein) is interposed between the common carotid artery (CCA) and the intracranial ICA, the middle cerebral artery (MCA) or the posterior cerebral artery (PCA). EC IC bypass surgery has been available for treating selective intracranial vascular pathology for more than 40 years. Woringer et al. (1963) reported that the first high flow venous EC IC bypass surgery was conducted in the early 1960s. Since then, neuroradiologic studies have demonstrated the beneficial effects of bypass surgery on cerebral hemodynamics (Anderson et al., 1992). However, the evaluation of bypass surgery remains empirical (Sia et al., 2010) and the more common, but smaller volume EC IC bypass with a superficial temporal artery, has failed to improve n Corresponding author. Tel.: þ address: yi.qian@mq.edu.au (Y. Qian). clinical outcomes in a randomized trial (The EC IC Bypass Study Group, 1985). As a result, EC IC bypass surgery is not the first-line treatment of choice in any category of intracranial vascular disease (Thanvi and Robinson, 2007). In a recent meta-analysis from a subset of hemodynamic failure patients who underwent EC IC bypass surgery, 10% of patients sustained cerebral infarction despite optimum surgical intervention (Garrett et al., 2009). Eguchi (2002), having reported 70 EC IC bypass procedures in 61 patients performed over 25 years, indicated that failure during EC IC bypass surgery could best be avoided by untwisting the interposed venous conduit, maintaining careful blood pressure control following surgery and paying attention to maintaining euvolemia. Eguchi s results contributed to our hypothesis that a quantitative description of flow resistance would be helpful in the evaluation of bypass surgery. Our aim for this study is to understand the impact of EC IC bypass on cerebral hemodynamics. By using pipe flow theory (Brater and King, 1976) for laminar flow, pressure drops within a tube can be expressed as A _m 2 þb _m, where A and B are taken to represent flow resistance coefficients and _m to represent mass flow rate. It has already been demonstrated that blood flow obeys the pipe flow theory (Allan, 1976; Klanchar and Tarbell, 1989), and thus by calculation of both A and B the quantitative relation between flow rates and pressure drops can be obtained /$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi: /j.jbiomech

2 2 Y. Zhang et al. / Journal of Biomechanics ] (]]]]) ]]] ]]] The measurement of flow resistance coefficients in intravascular continues to remain a challenging task. Colour Doppler ultrasound (CDU) may be utilised to measure the velocity and flow rates in the CCA, ICA, external carotid artery (ECA), and may be extended to the position of venous bypass. Considering the accuracy of measurement, however, operator-dependent probe handling and artery wall deformation due to probe placement may lead to uncertain results (William and Andrew, 1981; Morin et al., 1988; Zhang, 2006). Moreover, Kodoma et al. (1995) used phase contrast MRI to evaluate the EC IC bypass patency rate. Despite this useful technique, however, the patency rate itself is insufficient to describe flow regularity within a bypass. Though the invasive intra-aneurysm sac pressure measurements method has been used to assess the effectiveness of endovascular repair in the management of abdominal aorta aneurysm (Dias et al., 2004), it has not been applicable to aneurysms that occur intracranially. In addition to in-vivo measurements, computational fluid dynamic (CFD) is an alternative approach to the analysis of blood flow within aneurysms and carotid arteries (Qian et al., 2007). Previous publications have reported the use of CFD to evaluate blood mass flow patterns, pressure drop and wall shear stress (WSS) within aneurysms and the arteries of origin (Carallo et al., 2006). Advanced CFD methods such as direct numerical simulation, the lattice Boltzsmann method, and the smoothed particle hydrodynamics method were also used to analyse hemodynamic changes within aneurysms (Boyd and Buick, 2008; Lee, 2008; Chui and Henga, 2010). To date, few CFD publications have directly examined the relationship between flow resistance and the outcomes of EC IC high flow bypass surgeries. The objective of this study is to propose an innovative approach to evaluate the outcomes of EC IC bypass surgeries based on the pipe flow theory and to evaluate brain EC IC bypass surgery using CFD analysis on flow resistance in a vein bypass. In order to perform a meaningful CFD analysis, comparisons were then made with measurements taken from the patients contralateral carotid arteries as reference Pipe flow resistance The Darcy Weisbach equation (Brater and King, 1976), widely used for pipe flow calculation, is an equation that relates pressure drop due to friction along a given length of pipe, to the average velocity of the fluid flow. This equation can approximate blood flow in larger vessels under defined conditions (see below) (Bergel, 1961). If the flow is laminar, the pressure drop can be described as follows: Dp ¼ 1 2 l L ru 2 ð1þ D where Dp represents the pressure drop, u represents the blood velocity, l ¼ 64=Re ¼ 64m=ruD, m represents the viscosity of fluid, r represents the blood density, L represents the length of the tube and D represents the size of the tube. Eq. (1) can be re-written as: Dp ¼ 32m L u ð2þ D 2 If the tube has elbows and other bends, then the pressure drop for those specific elements need to be calculated using the following equation: Dp ¼ 1 2 xru2 where x is a constant for a specific shape of a bend. As with other fluids, in this study blood flow is assumed to be an incompressible. Pressure drop in the blood flow in an irregular conduit like a bypass or ICA can be expressed as: Dp ¼ A _m 2 þb _m where _m is the mass flow rate inside the tube, and A and B are coefficients that are only related to structural components. A and B have constant values for a specific artery. Thus, larger pressure drop will give higher values of A and B if the same volume of blood passes through different arteries. It should be pointed out that Eq. (4) is accurate only under the assumption that the vessels are rigid tubes. Bergel s work demonstrated that for an artery under approximately 100 mmhg, the elastic modulus of the carotid artery will be reach around 0.65 MPa (Bergel, 1961). Torii et al. (2006) found that for a similar blood pressure and arterial elastic module, the change in arterial radius was very small. Based on previous studies where average pressure within the CCA was around 90 mmhg, changes in arterial radius may not be significant. Thus, the vessels were assumed to have rigid walls in this study. Furthermore, as the purpose of this study is to compare the pressure difference between the bypass side and a healthy ICA (contralateral side), it would be reasonable to assume that the influence of vessel elasticity is cancelled. ð3þ ð4þ 2. Method 2.1. Patient information Seven patients (four females and three males) with ages ranging from 28 to 63, were examined by computerised tomography angiography (CTA) after undergoing EC IC vein bypass surgery. Demographic features of patient age, gender, and graft anastomosis are listed in Table 1. All proximal anastomosis were end-to-side to the CCA and all distal anastomosis were either end-to-end to the intracranial ICA or anastomosed end-to-side to the middle cerebral artery (MCA) (dependent upon intracranial vascular pathology and the requirement for surgical arterial trapping). In order for comparisons to be made with contralateral ICA, all bypass simulations were calculated from the CCA to the MCA. Three-dimensional (3D) geometries of the vein bypasses and their contralateral carotid arteries were reconstructed and segmented using a commercial software package MIMICS (Materialise Interactive Medical Image Control System) for the CFD calculation domain CFD modelling A segmented diseased ICA, bypass and contralateral ICA are shown in Fig. 1. The geometry was built based on contour interpolation to generate 2-D contours from grey scales of pixels, with 3-D geometry segmented by interpolation of those 2-D contours in the normal direction. This method prevents the intrusion of surface noise. Instead of using global smoothing, we used manual local smoothing to keep the 3-D geometry as realistic as possible. This method sets the average error at one-third of a pixel in size (Jamali et al., 2007). The grid independent tests were carried out in our previous study (Sia et al., 2010). More than three-hundred thousand (300,000) elements were used for the entire bypass calculation. Among of them over 100,000 elements were applied in prism boundary, which helped to calculate wall shear stress (WSS) within boundary layers that caused friction and led to pressure drop in the arteries. It should be noted that 100 mm of the artery section was extruded in the outer normal direction for all Table 1 Demographic features and position of distal graft anastomosis. Case Gender Age Distal graft anastomosis 1 F 28 CCA MCA 2 M 32 CCA ICA 3 M 62 CCA MCA 4 F 56 CCA ICA 5 M 35 CCA ICA 6 F 45 CCA MCA 7 F 63 CCA ICA Fig. 1. Segmented diseased ICA, bypass, and contralateral ICA.

3 Y. Zhang et al. / Journal of Biomechanics ] (]]]]) ]]] ]]] 3 boundaries. This allows the formation of a velocity profile at the inlet, and full recovery of the pressure wave at the outlet edge. The Navier Stokes equations for 3-D steady flow with rigid walls were solved using the CFX finite-volume-based CFD solver in the ANSYS 13.0 package. Blood was assumed to be a Newtonian fluid with density of 1050 kg/m 3 and dynamic viscosity of Pa s. The flow reached a steady state, and the flow pattern was assumed as laminar flow throughout the cardiac cycle. Following bypass surgery, CCA inflow average velocities measured by CDU were used as inflow conditions for CFD simulations. Distal graft anastomoses were connected either to the MCA or the intracranial ICA. Currently, CDU is unable to be used on intracranial vessels. The circle of Willis is the anastomotic ring linking the major intracranial vessels at the base of the brain. This consists of the internal carotid arteries among the posterior communicating artery and the anterior cerebral artery, the anterior cerebral arteries (from their origin to and including the interconnecting anterior communicating artery), and the terminal basilar artery (with its two posterior cerebral arteries connected to each of the posterior communicating arteries that anastomose with the internal carotid artery). Because of this anastomosis, pressure gradients and the distribution of oxygen-rich arterial blood is equalized throughout the cerebrum (Cieslicki and Ciesla, 2005). Therefore, in the normal cerebral circulation, common pressure points could be assumed at corresponding outlet boundaries in the CFD simulation, hence minimising numerical error. The major focus of this study is thus to calculate the pressure gradient from the CCA to the circle of Willis. In the flow resistance assessment, different mass flow rates in the bypass and ICA were obtained by adjusting the CCA inlet mass flow rate. Based on the pressure drop regression curve at different mass flow rates, flow resistance coefficients (A and B) were determined. 3. Results 3.1. Pressure drop and mass flow rates after the vein bypass surgery Following bypass surgery, the pressure gradient was comparable and similar in both the bypass and contralateral ICA (Fig. 2a). With the exception of cases 6 and 7, the pressure gradients were below 3000 Pa (25 mmhg). The distribution of mass flow rates at both the bypass and ICA (Fig. 2) showed that the mass flow rates of both sides were statistically balanced after surgery Comparisons of flow resistance, before and after the vein bypass surgery CFD simulation of case 1 was used to compare flow resistance prior to and following bypass surgery. As shown in Fig. 3, prior to bypass surgery, the flow resistance in the diseased ICA [A¼ Pa/(ml/min) 2 and B¼6.153 Pa/(ml/min)] was found to be three times higher than that in the contralateral ICA [A¼0.027 Pa/(ml/min) 2 and B¼2.828 Pa/(ml/min)]. Following bypass surgery, the flow resistance in the bypass [A¼ Pa/ (ml/min) 2 and B¼2.874 Pa/(ml/min)] was closer to or lower than that of the contralateral ICA. Comparing pre- and post-surgery results showed improved flow resistance was achieved by replacing the diseased ICA with the vein bypass Flow resistances of bypasses and their contralateral ICA Comparisons of flow resistance in bypasses and their contralateral ICA were made after surgery. As shown in Fig. 4(a) and (b) cases 2, 3, 4 and 5 demonstrated similar flow resistances between the bypasses and their corresponding contralateral ICAs. For these cases, the presence of a bypass made a significant contribution to hemodynamic balance between the left and right CCA. However, in cases 6 and 7 (Fig. 4), the flow resistances in the bypasses were higher than those found in corresponding contralateral ICA. Table 2 shows the average size (D) for each graft used. In case 6, the bypass size was 2.65 mm, significantly smaller than an average bypass size (4.2 mm). As a result, the flow resistance within the bypass was increased. In case 7, the bypass size was 3.37 mm, similarly smaller than an average bypass size. Furthermore, as shown in Fig. 5, the narrowing of the interposition venous graft at the site of a large valve resulted in an increase of local flow resistance Modelling flow resistance in bypass and contralateral ICA In this study, the modelling of blood flow through the bypass is carried out for velocities between 0 and 150 ml/min. This was based upon the clinical demonstration of an average bypass flow rate of 109 ml/min (Eguchi, 2002). Pressure gradient simulation results between the proximal and distal bypass under various flow conditions, are shown in Fig. 6. The calculated average for the resistance value of A (the resistance coefficient) in the contralateral ICA was found to be Pa/(ml/min) 2 and B Fig. 2. (a) Pressure reduction at contralateral ICA vs. bypass. (b) Mass flow rate at contralateral ICA vs. bypass. Fig. 3. Flow resistances before and after a bypass surgery (case 1).

4 4 Y. Zhang et al. / Journal of Biomechanics ] (]]]]) ]]] ]]] Fig. 4. (a) and (b) Flow resistance: bypass vs. ICA for case 2, 3, 4 and 5. (c) Flow resistance: bypass vs. ICA for case 6 and 7. Table 2 Internal size (D) of each venous graft used. Case D (mm) Pa/(ml/min) with standard deviations (SD) less than 25% of the calculated pressure gradient. With the exclusion of cases 6 and 7, the average resistance (both A and B) in the bypass graft was found to be Pa/(ml/min) 2 and Pa/(ml/min) 2, respectively. These flow resistances following bypass surgery were similar to those in corresponding contralateral ICAs. In Fig. 5. CFD bypass model of case 7.

5 Y. Zhang et al. / Journal of Biomechanics ] (]]]]) ]]] ]]] 5 This study proposes a new methodology that uses CFD calculation to measure the flow resistance coefficients (A and B) within the vein bypass and the contralateral ICA. Simulation results showed that for most cases, flow resistances within bypasses improved and exhibited values closer to those observed in contralateral ICAs. The simulation results indicated that the hemodynamic condition was improved after bypass treatment; it recovers flow and pressure balance between the left and right of the circle of Willis. The balance improvement may be available to evaluate the outcome of successful bypass surgeries. However, in the case of the vein bypasses exhibiting segmental narrowing or expanding (e.g., due to venous valves) flow resistance in that bypass increases. An imbalanced flow resistance between the left and right of the circle of Willis would result in asymmetrical blood flow rates, as well as asymmetrical shear stress magnitude and spatial distribution within the circle of Willis. This may predispose hemodynamic failure in the short-term or increase the risk of aneurysm development in the long-term (Alnaes et al., 2007). We suggested that further follow-up observations would be required, due to potential changes of vein bypass geometries over a period of time (Eguchi, 2002). 5. Conclusion Fig. 6. (a) Flow resistance in bypass and ICA. (b) Pressure gradient difference between bypass and ICA. contrast, the flow resistances, A and B, in both cases 6 and 7 were Pa/(ml/min) and Pa/(ml/min) 2, respectively. These values were considerably greater than those observed in their respective contralateral ICAs. The differences in pressure gradients between the bypass and contralateral ICA are shown in Fig. 6. In cases 1 5, the difference in pressure was measured to be less than 200 Pa (1.5 mmhg) at a blood flow rate of 109 ml/min. In cases 6 and 7, however, the simulation of flow rates within the bypass at a minimum of 40 ml/min resulted in a pressure difference between the bypass and contralateral ICA of 800 Pa (6 mmhg). Furthermore, the results indicated that if the flow in the bypass is simulated at 109 ml/min, the pressure difference between the bypass and contralateral ICA and would exceed 5,000 Pa (38 mmhg). This is a physiologically impossible condition. An imbalance between the flow resistances of each side would result in an imbalance in their pressure gradients, in turn influencing the flow equilibrium within the circle of Willis. In this series, saphenous vein grafts of length cm were chosen for all cases. Our results confirmed that with a graft length of cm, a balance in flow resistance between the bypass and the contralateral ICA could be achieved. We also observed from cases 6 and 7 that segmental narrowing (due to the valves in these cases) would influence flow resistance and result in an imbalanced flow between the bypass graft and the contralateral ICA. 4. Discussion The hemodynamic changes occuring after bypass surgery are poorly understood. Based on clinical data, most patients (490%) (Garrett et al., 2009) will recover without clinical evidence of hemodynamic insufficiency. However, blood flow rates in the bypass for some patients would be low, resulting in the occurrence of cerebral infarction. CFD technology can be used to predict flow resistance for both the vein bypass and the contralateral ICA. The results may be of use in predicting the outcome of bypass surgery for the interposition saphenous vein. In cases where the flow resistance within the bypass is similar to that within its contralaternal ICA, there is a tendency for the hemodynamic parameters of each side to balance. However, if the flow resistance within a bypass is significantly greater than the flow resistance found in the contralaternal ICA, the hemodynamic condition at the circle of Willis would become unbalanced. This flow resistance imbalance may result in further development of intracranial cerebrovascular disease. Conflict of interest statement None of the authors have any financial interests to disclose. Acknowledgement The author would like to thank members of Macquarie Medical Imaging, Macquarie University Hospital, for their kind support and contributions to these cases. References Allan, C.R., Effect of collateral and peripheral resistance on blood flow through arterial stenoses. Journal of Biomechanics 9, Alnaes, M.S., Isaksen, J., et al., Computation of hemodynamics in the circle of Willis. 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