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DE GRUYTER Current Directions in Biomedical Engineering 2022;8(1): 125-128 Janneck Stahl*, Anna Bernovskis, Daniel Behme, Sylvia Saalfeld, and Philipp Berg Impact of patient-specific inflow boundary conditions on intracranial aneurysm hemodynamics https://doi.org/10.1515/cdbme-2022-0032 the individual risk analysis, since direct blood flow measure- ment is not possible. This allows approximation of hemody- Abstract: For hemodynamic simulations of intracranial namic parameters that might correlate with potential rupture aneurysms boundary conditions (BC) are required. In most risk . For computer-aided simulations, it is necessary to cre- cases, these are not patient-specific and thus do not reflect the ate patient-specific models from medical image data. These real flow conditions in the patient. This study investigates the serve as a basis for the blood flow simulations within the ves- influence of patient-specific inflow BC on intra-aneurysmal sels. In addition, it is necessary to define several BC for the hemodynamics. The focus lies on gender and age variations of simulation. In contrast to the models, these BC are usually not the patients. To asses the impact, four different inflow curves patient-specific, since the values can often only be measured in representing the velocity profile of the inflow over one car- vivo with high effort and are thus not always available. There- diac cycle is modeled. These four inflow BC are varied in the fore, generalizations of the actual condition are made and mea- simulations of each aneurysm from selected subgroups. From surements or values from the literature are used. This leads to the results of the simulations, the hemodynamic parameters the fact that the calculated hemodynamic parameters deviate are determined for each inflow BC and the percent differences from the real values. Existing studies already show the influ- between inflow BC are determined. The results show that the ence of varying BC on blood flow and thus on rupture risk hemodynamic parameters are not robust to varying inflow BC. analysis [7, 10]. This study investigates the effect of inflow It can be seen that age has more influence on the hemody- BC on intra-aneurysmal hemodynamics. For this purpose, four namic parameters than gender. This study demonstrates the representative inflow curves are generated, which reflect the dependence of valid hemodynamic parameters on realistic in- patient-specific characteristics regarding age and gender, are flow BC. Thus, if available, patient-specific inflow curves are applied to eight patient-specific aneurysm models from a re- recommended. spective subgroup. Consequently, for each aneurysm four sim- Keywords: intracranial aneurysms, computational fluid dy- ulations are performed with the varying inflow BC, where one namics, hemodynamics, boundary conditions inflow BC corresponds to the patient’s age and gender and is thus considered as patient-specific. With the help of the sim- ulations, the hemodynamic parameters can be determined and 1 Introduction the influence of the characteristics age and gender can be in- vestigated. An intracranial aneurysm is a local, pathological vascular di- latation of the cerebral arteries. Due to the high prevalence of 3%  of intracranial aneurysms and the risk of rupture with a possible subarachnoid hemorrhage, it is of medical interest 2 Material and Methods to identify the individual rupture risks. Computer-aided sim- ulations of intra-aneurysmal blood flow are a useful tool for 2.1 Patient Selection For patient selection, subgroups were defined, which show dif- *Corresponding author: Janneck Stahl, Department of Fluid Dynamics and Technical Flows, Research Campus STIMULATE, ferences only in one specific characteristic. All eight cases are University of Magdeburg, Germany, e-mail: bifurcation aneurysms of the anterior communicating artery firstname.lastname@example.org (Acom) without multiple aneurysms. Table 1 shows the cate- Anna Bernovskis, Philipp Berg, Department of Fluid Dynamics gorization of the subgroups, whereby Case 1 (over 60 years), and Technical Flows, Research Campus STIMULATE, University Case 2 (between 40 and 60 years) and Case 3 (under 40 years) of Magdeburg, Germany Daniel Behme, Department of Neuroradiology, University Hospital divided the patients into age groups for which both genders of Magdeburg, Germany were selected. Sylvia Saalfeld, Department of Simulation and Graphics, Re- search Campus STIMULATE, University of Magdeburg, Germany Open Access. © 2022 The Author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 125 J. Stahl et al., Inflow BC for aneurysms Tab. 1: Selected cases and the patient-specific characteristics of sel walls are assumed to be rigid with no-slip conditions. The kg gender, age and rupture status. blood is considered as an incompressible (𝜌 = 1055 ), Newtonian (𝜂 = 4 mPa · s) fluid with laminar flow conditions. Case Gender age rupture status For all patient-specific models, two cardiac cycles are simu- 1.1a female 65 unruptured lated, whereas only the last is included in the calculation of 1.1b male 69 unruptured the hemodynamic parameters. 1.2a female 68 ruptured 1.2b male 68 ruptured 2a female 51 ruptured 2.4 Analysis 2b male 50 ruptured 3a female 35 ruptured 3b male 36 ruptured Based on the time-dependent simulations, different hemody- namic parameters are calculated using the 3D post-processing software EnSight 10.2.8 (ANSYS Inc.; Canonsburg; PA; 2.2 Inflow Curve Generation USA): – Time-averaged Wall Shear Stress (AWSS) describes the For the creation of the four different inflow curves, two rep- tangential shear stress along the luminal vessel wall aver- resentative curves from Xu et al.  were taken which are aged over one cardiac cycle. assigned to the male gender. The curves originate from differ- – Oscillatory Shear Index (OSI) is a metric to describe ent age structures, so that they can be assigned to youngMale the change in magnitude and direction of wall shear stress (under 60 years) and oldMale (over 60 years). With the help throughout one cardiac cycle. of existing studies, gender differences representing variations – Inflow Concentration Index (ICI) representing the in- in systolic and diastolic peaks are extracted . The avail- flow concentration into the aneurysm related to the parent able curves are modified to youngFemale (under 60 years) and vessel. oldFemale (over 60 years) using Matlab (MATLAB Version R2018a; The Mathworks Inc.; Massachusetts; USA) (see Fig- ure 1). 3 Results In this study hemodynamic parameter deviations are compared qualitatively as well as quantitatively. Considering the exem- plary qualitative AWSS representations for Case 3b (see Fig- ure 2), the AWSS appears very similar for all inflow curves. Slight differences can be seen in the inflow curves of the older patients which show a larger area of high AWSS compared to the inflow curves of the young patients (see arrows in Figure Fig. 1: Inflow curves over one cardiac cycle for the male (a) and 2). A difference of the AWSS between the inflow curves for female gender (b). the genders of one age group is not clearly recognizable. In order to quantitatively assess the parameter variations, the relative deviation between the suited curve, which matches the patient based on their specific characteristics, and the un- 2.3 Hemodynamic Simulation suited curve, having the highest parameter deviation from the suited curve, is determined for each case. This demonstrates For the time-dependent blood flow simulations a finite- which inflow variation has the highest influence on the respec- volume-based computational fluid dynamics (CFD) approach tive parameter. using Star CCM+ 2020.1 (Siemens Product Lifecycle Man- Table 2 shows these relative deviations for the AWSS. For agement Software Inc.; Plato; TX; USA) is applied. For the the younger patients, the highest deviations occur when us- spatial discretization polyhedral and prism cells with a base ing the inflow curves of the older patients. For example, in size of 0.15 mm are used for the generation of the volume Case 3a, the patient-specific curve is the youngFemale inflow meshes. Three prism layers with a growth rate of 1.3 are ap- curve. If this case is simulated with all four inflow curves, the plied to account for the occurring velocity gradients. For the result shows that the inflow curve oldMale differs most con- inlet BC the inflow curves depicted in Figure 1 are used. At siderably from the patient-specific curve. The same relations the outlets constant pressure 𝑝 = 0 is applied and the ves- 126 J. Stahl et al., Inflow BC for aneurysms Tab. 3: Relative deviation of ICI when comparing patient-specific suited curve to unsuited curve. The case with the largest deviation is printed in bold. Case suited curve unsuited curve rel. deviation 1.1a oldFemale youngFemale 46.11 % 1.1b oldMale oldFemale -3.23 % 1.2a oldFemale youngMale 55.24 % 1.2b oldMale youngMale 27.57 % 2a youngFemale oldFemale -14.03 % 2b youngMale oldFemale -18.01 % 3a youngFemale oldFemale -13.52 % 3b youngMale oldFemale -31.47 % Tab. 4: Relative deviation of OSI when comparing patient-specific suited curve to unsuited curve. The case with the largest deviation is printed in bold. Fig. 2: Representation of the AWSS from Case 3b for the four dif- ferent inflow curves (a-d). The areas showing differences between Case suited curve unsuited curve rel. deviation the age groups are marked with arrows. 1.1a oldFemale youngMale 73.09 % Tab. 2: Relative deviation of AWSS when comparing patient- 1.1b oldMale youngFemale -15.04 % specific suited curve to unsuited curve. The case with the largest 1.2a oldFemale youngFemale -22.76 % deviation is printed in bold. 1.2b oldMale youngFemale -12.86 % 2a youngFemale youngMale 21.76 % Case suited curve unsuited curve relative deviation 2b youngMale oldFemale -16.55 % 3a youngFemale oldMale 29.99 % 1.1a oldFemale youngMale -13.45 % 3b youngMale oldFemale -30.01 % 1.1b oldMale youngMale -10.43 % 1.2a oldFemale youngMale -10.40 % 1.2b oldMale youngMale -9.30 % 2a youngFemale oldMale 12.33 % 4 Discussion 2b youngMale oldMale 17.36 % 3a youngFemale oldMale 8.06 % The definition of appropriate BC for hemodynamic simula- 3b youngMale oldFemale 17.51 % tions is of particular importance. The study investigates the ef- fect of specific inflow conditions on hemodynamic parameters, can be observed for the older patients of Case 1.1 and 1.2. which are particularly relevant for risk analysis of intracranial For the impact of the inflow on the ICI, Table 3 indicates that aneurysms . The modeled four inflow curves reflect differ- for Case 2 and Case 3 in all four simulations, regardless of ences between age and gender groups. The results show that gender, the oldFemale inflow curve leads to the largest devi- each hemodynamic parameter changes during simulation with ations. For the older patients, an inflow curve of a younger a varying inflow curve. Consequently, they are not robust to the patient leads to the largest deviation in three scenarios. The varying inflow curves. These findings are in agreement with largest relative deviation is 55.24 % in Case 1.2a between the the study of Detmer et al. , where the effect of the inflow ICI values of the inflow curve oldFemale and youngMale. For BC of CFD simulations are investigated as well. Furthermore, the effect on OSI, it is visible in Table 4 that for Case 1.1 and the results also support the findings of Jansen et al. regarding for Case 1.2, the inflow curve of the other age group leads to the choice of patient-specific inlet BCs, as there are signifi- the highest difference regarding the OSI. This behavior can cant differences in hemodynamic parameters with generalized be seen for Case 2 and Case 3 with one exception as well. BCs . Despite the many studies regarding the rupture risks No pattern can be identified for the influence of gender in this of an aneurysm, there are no generalized defined thresholds table. For example, in Case 1.2, regardless of patient gender, for any of the hemodynamic parameters that can classify the the youngFemale inflow curve produces the largest deviation aneurysm as being at risk of rupture. However, there are ten- in average OSI. Case 1.1a shows the largest relative difference dencies, that a low WSS and a high OSI might promote rupture (73.09 %) in terms of OSI for the inflow curves oldFemale and . Nevertheless, there are studies, such as by Cerebral et al. youngMale. , which try to define such thresholds based on robust sta- tistical analyses. Exemplarily, in this study, an ICI value for 127 J. Stahl et al., Inflow BC for aneurysms pulsatile flow starting at a value of 1.012 is assigned to a rup- References tured aneurysm, and an unruptured aneurysm is assigned an average value of 0.66. With the available results, although no  Berg P, Beuing O. Multiple intracranial aneurysms: a direct change in inflow curves within a case results in an aneurysm hemodynamic comparison between ruptured and unrup- being assessed as at risk of rupture for one inflow curve and tured vessel malformations. Int J Comput Assist Radiol Surg. 2018;13(1):83-93. doi:10.1007/s11548-017-1643-0 not for another inflow curve. However, the difference between  Cebral JR, Mut F, Weir J, Putman CM. Association of the values of Cerebral et al. is 0.352. This magnitude of change hemodynamic characteristics and cerebral aneurysm is even exceeded in four cases, and the variation of the inflow rupture. AJNR Am J Neuroradiol. 2011;32(2):264-270. curves may cause a change in the ICI value of up to 1.18. Con- doi:10.3174/ajnr.A2274 sequently, a different threshold could result in the aneurysm  Cebral JR, Castro MA, Burgess JE, Pergolizzi RS, Sheridan being considered at risk of rupture with one inflow curve com- MJ, Putman CM. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific com- pared with another one. Thus, consideration of patient-specific putational hemodynamics models. AJNR Am J Neuroradiol. inflow curves is important for all hemodynamic parameters. 2005;26(10):2550-2559. Furthermore, patient-specific inflow curves also consider flow  Cebral JR, Mut F, Weir J, Putman C. Quantitative charac- data changes due to cardiovascular diseases . terization of the hemodynamic environment in ruptured Limitations: The presented approach has several limita- and unruptured brain aneurysms. AJNR Am J Neuroradiol. 2011;32(1):145-151. doi:10.3174/ajnr.A2419 tions. Although a considerable number of over 300 cases of  Detmer FJ, Mut F, Slawski M, Hirsch S, Bijlenga P, Cebral JR. aneurysms were evaluated, only eight cases could be identi- Incorporating variability of patient inflow conditions into sta- fied for the complex research question. The localization was tistical models for aneurysm rupture assessment. Acta Neu- limited to aneurysms at the Acom to avoid the influence of the rochir (Wien). 2020;162(3):553-566. doi:10.1007/s00701- localization and keeping the aneurysm site constant. Due to 020-04234-8 technical limitations and the lack of a direct in vivo blood flow  Durka MJ, Wong IH, Kallmes DF, et al. A data-driven ap- proach for addressing the lack of flow waveform data measurement, no ground truth exists. The inflow curves are in studies of cerebral arterial flow in older adults. Phys- thus not generated from patient measurements, but are taken iol Meas. 2018;39(1):015006. Published 2018 Feb 1. from the literature and subsequently modified. doi:10.1088/1361-6579/aa9f46  Jansen IG, Schneiders JJ, Potters WV, et al. Generalized versus patient-specific inflow boundary conditions in compu- tational fluid dynamics simulations of cerebral aneurysmal 5 Conclusion hemodynamics. AJNR Am J Neuroradiol. 2014;35(8):1543- 1548. doi:10.3174/ajnr.A3901  Lv N, Wang C, Karmonik C, et al. Morphological and The study addresses the influence of different inflow BC on Hemodynamic Discriminators for Rupture Status in hemodynamic parameters of eight aneurysm cases. While Posterior Communicating Artery Aneurysms. PLoS modeling the inflow curves with the patient-specific character- One. 2016;11(2):e0149906. Published 2016 Feb 24. istics, differences between gender and the age of the patients doi:10.1371/journal.pone.0149906 are visible among the different curves. The results of the  Vlak MH, Algra A, Brandenburg R, Rinkel GJ. Prevalence of simulations indicate that all considered hemodynamic param- unruptured intracranial aneurysms, with emphasis on sex, age, comorbidity, country, and time period: a systematic re- eters are not robust to varying inflow BC. The age difference view and meta-analysis. Lancet Neurol. 2011;10(7):626-636. leads to larger differences than the gender difference for all doi:10.1016/S1474-4422(11)70109-0 hemodynamic parameters. Thus, it is recommended to use  Xiang J, Siddiqui AH, Meng H. The effect of inlet wave- patient-specific inflow BC in computer-aided simulations of forms on computational hemodynamics of patient-specific intra-aneurysmal blood flow in research and clinical practice if intracranial aneurysms. J Biomech. 2014;47(16):3882-3890. doi:10.1016/j.jbiomech.2014.09.034 available, especially for the analysis of potential rupture risks.  Xu L, Liang F, Zhao B, Wan J, Liu H. Influence of aging- induced flow waveform variation on hemodynamics in Author Statement aneurysms present at the internal carotid artery: A computa- Research funding: This work is partly funded by the tional model-based study. Comput Biol Med. 2018;101:51-60. Federal Ministry of Education and Research within the doi:10.1016/j.compbiomed.2018.08.004 Forschungscampus STIMULATE (grant no. 13GW0473A) and  Hoi Y, Wasserman BA, Xie YJ, et al. Characterization of volu- metric flow rate waveforms at the carotid bifurcations of older the German Research Foundation (BE 6230/6-1, SA 3461/3- adults. Physiol Meas. 2010;31(3):291-302. doi:10.1088/0967- 1). The authors state no conflict of interest. 3334/31/3/002
Current Directions in Biomedical Engineering – de Gruyter
Published: Jul 1, 2022
Keywords: intracranial aneurysms; computational fluid dynamics; hemodynamics; boundary conditions
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