Evaluation of the carotid artery stenosis based on minimization of mechanical energy loss of the blood flow

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1 Original Article Evaluation of the carotid artery stenosis based on minimization of mechanical energy loss of the blood flow Proc IMechE Part H: J Engineering in Medicine 2016, Vol. 230(11) Ó IMechE 2016 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / pih.sagepub.com Sheau Fung Sia 1, Xihai Zhao 2, Rui Li 2,YuZhang 3,4, Winston Chong 5,LeHe 2 andyuchen 2 Abstract Background: Internal carotid artery stenosis requires an accurate risk assessment for the prevention of stroke. Although the internal carotid artery area stenosis ratio at the common carotid artery bifurcation can be used as one of the diagnostic methods of internal carotid artery stenosis, the accuracy of results would still depend on the measurement techniques. The purpose of this study is to propose a novel method to estimate the effect of internal carotid artery stenosis on the blood flow based on the concept of minimization of energy loss. Methods: Eight internal carotid arteries from different medical centers were diagnosed as stenosed internal carotid arteries, as plaques were found at different locations on the vessel. A computational fluid dynamics solver was developed based on an open-source code (OpenFOAM) to test the flow ratio and energy loss of those stenosed internal carotid arteries. For comparison, a healthy internal carotid artery and an idealized internal carotid artery model have also been tested and compared with stenosed internal carotid artery in terms of flow ratio and energy loss. Results: We found that at a given common carotid artery bifurcation, there must be a certain flow distribution in the internal carotid artery and external carotid artery, for which the total energy loss at the bifurcation is at a minimum; for a given common carotid artery flow rate, an irregular shaped plaque at the bifurcation constantly resulted in a large value of minimization of energy loss. Thus, minimization of energy loss can be used as an indicator for the estimation of internal carotid artery stenosis. Keywords Internal carotid artery stenosis, internal carotid artery flow ratio, computational fluid dynamics, energy loss, minimization of energy loss Date received: 10 November 2015; accepted: 7 September 2016 Introduction Internal carotid artery (ICA) stenosis is usually caused by an atherosclerotic process and is one of the major causes of stroke and transient ischemic attack (TIA). An accurate risk assessment is developed to help patients receive timely treatment, especially for those who are asymptomatic. The North American Symptomatic Carotid Endarterectomy Trial (NASCET) is most commonly used in clinical trials. In the NASCET method, stenosis is measured as the ratio of the linear luminal diameter of the narrowest portion of the diseased artery to the healthy diameter of the distal carotid artery. 1 An alternative method is the European Carotid Surgery Trial (ECST), 2 which calculates the carotid bulb at the site of the maximal stenosis as the denominator in the previous ratio. However, it was found that for the same patient, NASCET and ECST may result in a controversial diagnosis. Apart from measurement inconsistencies, using a single reading of ICA stenosis ratio as a criterion 1 Division of Neurosurgery, Faculty of Medicine, University of Malaya, Kuala Lumpur, Malaysia 2 Center for Biomedical Imaging Research, Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China 3 Medical Center, Tsinghua University, Beijing, China 4 Australian School of Advanced Medicine (ASAM), Macquarie University, Sydney, NSW, Australia 5 Monash Medical Centre, Melbourne, VIC, Australia Corresponding author: Yu Zhang, Medical Center, Tsinghua University, Beijing , China. yuzhang2014@mail.tsinghua.edu.cn

2 1052 Proc IMechE Part H: J Engineering in Medicine 230(11) for medical diagnosis is certainly unsatisfactory. The results from a study by Grogen showed that there are some cases where the NASCET may have exceeded the dangerous level of 64%, but the ICA flow ratio at the common carotid artery (CCA) bifurcation still remained at a safe value of 75%. Therefore, only a single reading for stenosis may mislead the estimation of the overall effect of ICA stenosis. 3 Besides direct measurement, computational fluid dynamics (CFD) is an alternative approach to analyze blood flow in the carotid arteries and provide detailed results, such as velocities, flow rates, and other thermodynamic parameters. Many studies were performed to investigate flow rate, static pressure, and wall shear stress (WSS) in human carotid arteries using CFD. 4 6 In general, accurate CFD calculation requires a realistic geometry as well as the inflow and outflow boundary conditions. 7,8 Three-dimensional (3D) patient-specific geometry of a carotid artery can be reconstructed from either computed tomography angiography (CTA) images or magnetic resonance angiography (MRA) imaging. 9 While the inflow condition of a carotid artery can be measured using color Doppler ultrasound (CDU), accurate measurements of outflow conditions in the ICA and external carotid artery (ECA) are not readily available. This is because the ECA and ICA taper and become smaller in diameter as they course toward the base of the skull. Due to this, both the CDU and MRA are limited in assessing these vessels intracranially. 9 To address the issue of outflow distribution, Murray 10 proposed that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power, based on the condition that the total energy required to drive blood flow should be minimal at a bifurcation. Murray s law has been widely used for setting up outlet flow rate at bifurcations; however, it was reported that Murray s law overestimates the flow ratio at the ICA branch for a larger stenosis. 3 Zhang et al. 11 reported that Murray s law is only suitable for blood vessels with uniform diameter; for an artery with stenosis, only the principle of minimization of energy loss (MEL) controls the blood flow distribution. This finding also implied that MEL could be a better indicator for the estimation of the stenosis effect on the blood flow, as it fully takes into account the 3D flow information. The objectives of this work were to further validate the occurrence of MEL through rigorous mathematical derivations and to discuss the methods of using MEL to estimate the ICA stenosis. Method MEL principle The relationship between blood flow rate and flow resistance in arteries has been studied over several decades. 12 It was found that the branch with a lesser flow resistance will have a greater blood flow. Furthermore, flow resistance is recognized as the main reason behind the mechanical energy loss of blood flow. As a result, for a specific flow system, mechanical energy loss will be minimized if blood is allowed to freely leave the system through the path that offers the least resistance; this is the principle of MEL. This principle has been tested and validated in several studies involving cardiovascular systems of different animals, including humans. 13 Mathematical derivation of MEL The energy loss (E loss ) is described as follows E loss = E in E out = Q ICA 3DP ICA + Q ECA 3DP ECA ð1þ where E, DP, and Q represent the mechanical energy, total pressure drop, and volume flow rate, respectively. Based on the pipe flow theory, the pressure drop in a given tube is expressed as DP = AQ 2 + BQ ð2þ where A is the inertial flow resistance coefficient, which represents the effect of elbow and other sudden changes in the tube configuration, and B is the viscous flow resistance coefficient, which is determined by the length and diameter of the tube. Based on our previous work 14 regarding ICA, the absolute value of B (3.105 Pa/(mL/min)) is approximately 250 times greater than that of A ( Pa/(mL/min) 2 ). Therefore, at a natural ICA flow rate (standard ml/min), 15 equation (2) can be simplified as a linear equation, in which the overall linear flow resistance coefficient is represented by a as follows Dp ICA = A ICA Q 2 ICA + B ICA Q ICA a ICA Q ICA Dp ECA = A ECA Q 2 ECA + B ECA Q ECA a ECA Q ECA ð3þ Combining equation (3) with equation (2), the energy loss can be expressed as EL loss = a ICA Q ICA 2 + a ECA (Q total Q ICA ) 2 =(a ICA + a ECA )Q 2 ICA 2a ECA Q total Q ICA 2 + a ECA Q total ð4þ The derivative of E loss with respect to the ICA flow ratio is de loss dq ICA =2(a ICA + a ECA )Q ICA 2a ECA Q total ð5þ If equation (5) equals to 0, E loss will have the minimum value and the comparable ICA flow ratio becomes Q ICA Q total = a ECA a ICA + a ECA ð6þ The method we proposed here (equation (6)) takes flow resistance in both the ICA and ECA into account.

3 Sia et al The mathematical expression quantitatively proves Kassab and Fung s 16 finding that the branch with lesser flow resistance must have greater blood flow; ICA flow rate is greater than ECA flow rate only when a ICA is smaller than a ECA. Clinical case for validation Patient A was a 70-year-old male patient from Monash Medical Centre. CTA showed a right-side high-grade ICA stenosis. The maximum stenosis was only 1.6 mm in diameter as compared to that of 5.0 mm in normal ICA. The stenosis ratio was approximately 90% (Figure 1(a)). The peak systolic velocity at ICA, after endovascular stent placement, reduced to 70 cm/s. We chose this patient for the validation of the occurrence of MEL. Patient B was a 74-year-old male from the University of Malaya Medical Centre. He had a background history of hypertension and hyperlipidemia; on medication, he was presented with sudden onset of dysarthria, difficulty in speech, and right-sided body weakness. He had no other history of stroke, TIAs, or amaurosis fugax. The CT brain scan revealed a left posterior parietal middle cerebral artery (MCA) territory ischemic infarct. Cardioechography showed a good ejection fraction of 74% with grade 1 diastolic dysfunction of the right ventricle and no source of embolus. Further comprehensive neurovascular examination and imaging of the carotid system revealed a severe tight stenosis with ulcerated soft plague at the origin of the left ICA. Carotid duplex ultrasonography showed left high-grade carotid artery stenosis with a peak systolic blood flow velocity of 375 cm/s, corresponding to around 90% stenosis. Carotid endarterectomy (CEA) was advised to remove the source of embolus and followed by lifelong antiplatelet therapy (Figure 1(b)). We chose this patient for the validation of the negative relation between stenosis and ICA flow. Figure 1. (a) Configuration of patient A and (b) configuration of patient B. CFD modeling The geometry of arteries was built from Digital Imaging and Communications in Medicine (DICOM) files, based on contour interpolation to generate twodimensional (2D) contours from gray scales of pixels. The 3D geometry is constructed by interpolation of those 2D contours in the normal direction. This method has been used previously to treat irregularly shaped flow regime in an industrial device. 17 The reading and segmentation of DICOM files were performed using the software packages ( cal.materialise.com/mimics, 3d-doctor/). The Navier Stokes equations for 3D steady flow with rigid walls were solved using a CFD solver with a high accurate mathematical scheme. 11 Blood was assumed to be a Newtonian fluid with a density of 1050 kg/m 3 and dynamic viscosity of Pa s. The flow reached a steady state, and the flow pattern was assumed to be laminar throughout the cardiac cycle. The mesh independence has been assessed that the simulation results will be stable as the grid number is beyond 300,000. In this work, we generated a tetrahedron/hexahedron combined mesh with maximum size smaller than 0.3 mm, resulting in a mesh number greater than 500,000 cells in total, across all the instances. At close-wall regions, the body-fitted prism layers were brought forth at the boundaries to improve the result of the relevant scales in fluid motion, and was set up as a convergency criteria of conservation equations. Different inflow rates at ICA were used as an inlet condition, while equation (6) offered the flow distribution at both outlets of ICA and ECA. Results Validation of MEL In patient A, a ECA was Pa/(mL/min), while a ICA was Pa/(mL/min), which indicates that the flow resistance in the ICA was significantly higher than that of ECA (Figure 2(a) and (b)). According to equation (6), MEL will occur when the ICA flow ratio is reduced to 18%. Figure 2(c) shows the comparison of E loss as calculated using equation (4) and summarized results from CFD simulations. It can be seen that the MEL occurred at the position where the ICA flow ratio was 18% as predicted, which was significantly smaller than that of normal people (65%). We also demonstrated that for different CCA flow rates ranging from 325 to 500 ml/min, MEL constantly occurs at the fixed ICA flow ratio of 18%. This comparison validated the accuracy of equation (6). For patient B, we used the same method to test the ICA flow ratio with MEL. It showed that when MEL occurs, the ICA flow ratio was less than 5%, which indicates a high grade of ICA stenosis. Figure 3 further shows the detailed flow and pressure distribution at this

4 1054 Proc IMechE Part H: J Engineering in Medicine 230(11) Figure 2. (a) Pressure drop at ECA for patient A, (b) pressure drop at ICA for patient A and (c) EL curve with the increase in the ICA flow ratio for patient A. Figure 3. Streamline and pressure distribution of patient B: (a) streamline and (b) pressure. bifurcation. It is observed that even a small amount of blood flow (20 ml/min) in the ICA results in a large pressure drop of over 5 mmhg. The remarkable restriction of blood flow in the ICA also confirmed the high grade of stenosis. When stenosis occurs only in the ICA, the flow ratio with MEL is able to represent the grade of arterial stenosis. MEL application for the evaluation of the effect of atherosclerotic plaque on the blood flow Different types of stenosis. In clinical practices, stenosis can be found only in the ICA branch after the bifurcation, as depicted in patients A and B and Figure 4(a). However, in some other cases, irregularly shaped atherosclerotic plaque is observed on the proximal inner wall

5 Sia et al Center for Biomedical Imaging Research (CBIR) of Tsinghua University. All patients were diagnosed to have NASCET stenosis ranging from 50% to 75%. To have a thorough comparison, we included a seventh healthy ICA patient. We recorded demographics, clinical indications, and radiological and other related information. Furthermore, to highlight the effect of artery stenosis, an idealized healthy artery model was created and calculated. As shown in Figure 5, the diameters of CCA, ICA, and ECA are 8, 5.6, and 4.2 mm, respectively. The artery angles of the ICA and ECA are set up as 25 to the centerline of CCA. 18 Figure 4. Plaque position (marked by gray color). Flow distribution at MEL. The 3D stenosed arteries, flow distributions, and WSSs of seven patients and an additional idealized model are summarized in Table 1. It is observed that patients 1 5 have multi-edged irregular plaques. Patient 6 has a plaque with smooth outer surface. Under the normal average CCA inflow rate of 400 ml/min, 19 CFD simulations showed that patients 1 5 with MEL possess higher WSS and pressure drops as compared to other patients/model. Figure 5. Idealized model. of the bifurcation and thus covers both the CCA and ICA (Figure 4(b)). In this case, the risk of stroke is even higher as the plaque can break off due to the stress caused by unstable blood flow at the bifurcation, and the small portion of the embolic material that has broken off from the plaque will follow the blood stream and block the tiny arteries in the distal branches of the ICA. This represents an important risk factor for ischemic stroke. In this section, we will discuss the different ways of using MEL to estimate this type of stenosis/plaque. Clinical cases and idealized model. Six patients were selected and scanned with Philips MRI system at the Direct comparison of ICA flow ratio and MEL. Figure 6 depicts the direct comparison of the ICA flow ratio with MEL of the seven patients and idealized model. The ICA flow ratio of healthy ICA and idealized model cannot be easily differentiated from the diseased patients. This was due to the fact that as the irregularly shaped plaque covers both the CCA and ICA, it restricts blood flow through both the arteries. As a result, the increase or decrease in the ICA flow ratio is still a controversial issue. Figure 7 shows the direct comparison of MEL. The values of E loss in patients 1 5 were about 2.5 mw, almost two times higher than that of the normal ICA (1.2 mw). The highest MEL occurs in patient 5 (4.5 mw), in which a giant and irregular shaped plaque was noted at the bifurcation as shown in Table 1. In patient 6, the values of MEL, normal ICA, and idealized model were close to each other. The lowest MEL (0.8 mw) occurred in the idealized model, as idealized ICA and ECA are assumed to be straight tubes. The direct comparison of MEL can differentiate the diseased arteries from normal arteries (patient 6 is exceptional). The results confirmed that the irregularly shaped plaque causes higher energy loss than the normal ICA and idealized model, and thus, the absolute value of MEL at the average ICA flow rate can be used to estimate the resistive effect of the plaque on the blood flow for such types of artery stenosis. Discussion To prevent thromboembolic ischemic stroke, an accurate assessment of ICA stenosis is required for clinical diagnoses. Both ECST 20 and NASCET 21 proposed a formulation to calculate the stenosis ratio based on a

6 1056 Proc IMechE Part H: J Engineering in Medicine 230(11) Table 1. Patient Configuration Streamline WSS (Pa) Idealized WSS: wall shear stress. Figure 6. Direct comparisons of ICA flow ratio for different patients. single and local reading of medical images. However, those angiographic methods only take into account the narrowest segment of the ICA. In addition, measurements taken from different examiners and different centers may vary considerably. 22 Figure 7. Direct comparison of MEL for different patients. CFD is capable of simulating hemodynamic details of carotid arteries for varying degrees of stenosis. We proposed a new methodology based on MEL to estimate the ICA stenosis. Two patients with high ICA stenosis were tested. The ICA flow ratios with MEL were

7 Sia et al significantly smaller than those of healthy ICA. Six patients with plaques in both the CCA and ICA were evaluated. In five of the patients, the MEL is found to be two times higher than that of the normal ICA and idealized model. Patient 6 also has a 50% 75% ICA stenosis with plaque, but the outer surface of the plaque is smoother than that of other patients. As a result, the MEL of patient 6 was a small value (1.3 mw). However, this only shows that the effect of the plaque on the blood flow was not significant; it does not mean that patient 6 is safe from plaque rupturing. Conclusion The occurrence of MEL at a bifurcation is confirmed by both mathematical derivation and CFD simulations using real patient images. For a given patient, the flow distributions (ratio) at the side branches are constant as MEL occurs at the bifurcation. As an alternative (or supplementary method), the ICA flow ratio under MEL and the value of MEL under average ICA flow rate are found to be evidently helpful to indicate the ICA stenosis. Acknowledgements The authors thank Dr Yi Qian (ASAM, Macquarie University) and Dr Chang-Joon Lee (ASAM, Macquarie University) for discussing the concept of mechanical energy loss. The authors also thank ASAM for the software support of the DICOM file process of patient A in this article. The authors also thank Dr Retnagowri Rajandram for article proofreading. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding This research was supported by the independent research fund of Tsinghua University (No ). References 1. Sackett DL. NASCET and ECST: identifying clinically relevant carotid disease. Stroke 1994; 25: Warlow CP. Symptomatic patients: the European Carotid Surgery Trial (ECST). J Mal Vascul 1993; 18: Groen HC, Simons L, Van den Bouwhuijsen QJA, et al. MRI-based quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries. J Biomech 2010; 43: Bark DL Jr and Ku DN. Wall shear over high degree stenoses pertinent to atherothrombosis. J Biomech 2010; 43: Doriot PA, Dorsaz PA, Dorsaz L, et al. In-vivo measurements of wall shear stress in human coronary arteries. Coronary Artery Dis 2000; 11: Lee SE, Lee SW, Fischer PF, et al. Direct numerical simulation of transitional flow in a stenosed carotid bifurcation. J Biomech 2008; 41: Izquierdo S and Fueyo N. Momentum transfer correction for macroscopic-gradient boundary conditions in lattice Boltzmann methods. J Comput Phys 2010; 229: Vignon-Clementel IE, Figueroa CA, Jansen KE, et al. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Method Appl M 2006; 195: Marshall I, Zhao SZ, Papathanasopoulou P, et al. MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models. J Biomech 2004; 37: Murray CD. The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 1926; 9: Zhang Y, Takao H, Murayama Y, et al. Propose a wall shear stress divergence to estimate the risks of intracranial aneurysm rupture. Sci World J 2013; 2013: Roth AC, Young DF and Cholvin NR. Effect of collateral and peripheral resistance on blood-flow through arterial stenoses. J Biomech 1976; 9: Thomas JB, Antiga L, Che SL, et al. Variation in the carotid bifurcation geometry of young versus older adults: implications for geometric risk of atherosclerosis. Stroke 2005; 36: Zhang Y, Sia SF, Morgan MK, et al. Flow resistance analysis of extracranial-to-intracranial (EC-IC) vein bypass. J Biomech 2012; 45: Ford MD, Alperin N, Lee SH, et al. Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries. Physiol Meas 2005; 26: Kassab GS and Fung YCB. The pattern of coronary arteriolar bifurcations and the uniform shear hypothesis. Ann Biomed Eng 1995; 23: Zhang Y, Deshpande R, Huang D, et al. Numerical analysis of blast furnace hearth inner profile by using CFD and heat transfer model for different time periods. Int J Heat Mass Tran 2008; 51: Zhang Y, Furusawa T, Sia SF, et al. Proposition of an outflow boundary approach for carotid artery stenosis CFD simulation. Comput Method Biomec 2013; 16: Berg M, Zhang Z, Ikonen A, et al. Multi-detector row CT angiography in the assessment of carotid artery disease in symptomatic patients: comparison with rotational angiography and digital subtraction angiography. Am J Neuroradiol 2005; 26: Slattery J. Endarterectomy for moderate symptomatic carotid stenosis: interim results from the MRC European Carotid Surgery Trial. Lancet 1996; 347: Taylor DW. Beneficial effect of carotid endarterectomy in symptomatic patients with high-grade carotid stenosis. New Engl J Med 1991; 325: Alexandrov V, Bladin CF, Maggisano R, et al. Measuring carotid stenosis: time for a reappraisal. Stroke 1993; 24:

8 1058 Proc IMechE Part H: J Engineering in Medicine 230(11) Appendix 1 Notation A, B inertial and viscous flow resistance coefficients DP ECA pressure drop at ECA DP ICA pressure drop at ICA E in energy at the inlet E loss energy loss energy at the outlet E out Q ECA Q ICA Q total a ECA a ICA blood flow rate at ECA blood flow rate at ICA blood flow rate at CCA (total blood flow rate) overall linear flow resistance coefficient at ECA overall linear flow resistance coefficient at ICA