
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39278964
72591
10.1038/s41598-024-72591-w
Article
Intracranial bypass for giant aneurysms treatment assessed by computational fluid dynamics (CFD) analysis
Wiśniewski Karol karol.lek@poczta.fm

123
Reorowicz Piotr 3
Tyfa Zbigniew 3
Price Benjamin 1
Jian Anne 1
Fahlström Andreas 14
Obidowski Damian damian.obidowski@p.lodz.pl

3
Jaskólski Dariusz J. 2
Jóźwik Krzysztof 3
Drummond Katharine 15
Wessels Lars 6
Vajkoczy Peter 6
Adamides Alexios A. 15
1 https://ror.org/005bvs909 grid.416153.4 0000 0004 0624 1200 Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050 Australia
2 https://ror.org/02t4ekc95 grid.8267.b 0000 0001 2165 3025 Department of Neurosurgery and Neurooncology, Medical University of Łódź, Kopcińskiego 22, 90-153 Lodz, Poland
3 https://ror.org/00s8fpf52 grid.412284.9 0000 0004 0620 0652 Institute of Turbomachinery, Lodz University of Technology, 219/223 Wolczanska Str, 90-924 Lodz, Poland
4 https://ror.org/048a87296 grid.8993.b 0000 0004 1936 9457 Department of Medical Sciences, Section of Neurosurgery, Uppsala University, 75185 Uppsala, Sweden
5 https://ror.org/01ej9dk98 grid.1008.9 0000 0001 2179 088X Department of Surgery, University of Melbourne, 300 Grattan St, Parkville, 3050 Australia
6 https://ror.org/001w7jn25 grid.6363.0 0000 0001 2218 4662 Department of Neurosurgery and Center for Stroke Research Berlin (CSB), Charité - Universitätsmedizin Berlin, Berlin, Germany
16 9 2024
16 9 2024
2024
14 2154818 4 2024
9 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Unruptured giant intracranial aneurysms (GIA) are those with diameters of 25 mm or greater. As aneurysm size is correlated with rupture risk, GIA natural history is poor. Parent artery occlusion or trapping plus bypass revascularization should be considered to encourage intra-aneurysmal thrombosis when other treatment options are contraindicated. The mechanistic background of these methods is poorly studied. Thus, we assessed the potential of computational fluid dynamics (CFD) and fluid–structure interaction (FSI) analyses for clinical use in the preoperative stage. A CFD investigation in three patient-specific flexible models of whole arterial brain circulation was performed. A C6 ICA segment GIA model was created based on CT angiography. Two models were then constructed that simulated a virtual bypass in combination with proximal GIA occlusion, but with differing middle cerebral artery (MCA) recipient vessels for the anastomosis. FSI and CFD investigations were performed in three models to assess changes in flow pattern and haemodynamic parameters alternations (wall shear stress (WSS), oscillatory shear index (OSI), maximal time averaged WSS (TAWSS), and pressure). General flow splitting across the entire domain was affected by virtual bypass procedures, and any deficiency was partially compensated by a specific configuration of the circle of Willis. Following the implementation of bypass procedures, a reduction in haemodynamic parameters was observed within the aneurysm in both cases under analysis. In the case of the temporal MCA branch bypass, the decreases in the studied parameters were slightly greater than in the frontal MCA branch bypass. The reduction in the magnitude of the chosen area-averaged parameters (averaged over the aneurysm wall surface) was as follows: WSS 35.7%, OSI 19.0%, TAWSS 94.7%, and pressure 24.2%. FSI CFD investigation based on patient-specific anatomy models with subsequent stimulation of virtual proximal aneurysm occlusion in conjunction with bypass showed that this method creates a pro-thrombotic favourable environment whilst reducing intra-aneurysmal pressure leading to shrinking. MCA branch recipient selection for optimum haemodynamic conditions should be evaluated individually in the preoperative stage.

Keywords

Computational fluid dynamics
Intracranial bypass
Giant aneurysms
Thrombosis
Cerebral blood flow hemodynamics
Subject terms

Cerebrovascular disorders
Neurovascular disorders
Biomedical engineering
Brain
http://dx.doi.org/10.13039/501100005632 Narodowe Centrum Badań i Rozwoju LIDER/12/0056/L-10/18/NCBR/2019 issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Aneurysm size is one of the most important risk factors for rupture risk1. Giant intracranial aneurysms (GIA), which constitute only 5% of all unruptured intracranial aneurysms2, are those with diameters 25 mm or greater and therefore carry a high risk of rupture1,3. The management of GIA continues to be debated, since the data concerning their treatment and long-term outcome is limited.

GIA of irregular shape or with perforator involvement may not be excluded from the circulation with endovascular techniques or surgical clipping. If so, bypass techniques leading to flow alteration may be the most appropriate treatment option. Bypass techniques may also be useful for temporary perfusion after a preoperative positive balloon occlusion test or when the parent artery or aneurysmal neck is injured during surgery4. The induced flow alteration is assumed to induce intra-aneurysmal thrombus formation to prevent further growth or rupture. Flow alteration is achieved via high-flow external carotid artery (ECA) to internal carotid artery (ICA) bypass with ICA proximal ligation or distal occlusion, or aneurysm trapping combined with high-flow bypass/revascularization of all distal ICA branches. The concept of bypass revascularization and flow reversal is presented in Fig. 1. This strategy carries a risk of regrowth and rupture as the mechanistic effects of flow reversal have not been studied. Trapping combined with bypass to maintain blood flow distal to the aneurysm is curative but may be difficult to implement, particularly if perforating arteries arising proximal to or directly from the aneurysm. In these cases, proximal or distal parent artery occlusion (PAO) with bypass provides an alternative solution5. Since those procedures reduce blood inflow to the aneurysm and create a haemodynamic environment conducive to thrombosis, there is a risk of perforator occlusion with uncertain outcome. Antiplatelet therapy should be applied in each case.Fig.1 (A). Bypass revascularization for giant intracranial aneurysm (GIA) with proximal parent artery occlusion (PAO). (B). Bypass revascularization for GIA with distal PAO. C. Bypass revascularization for GIA with trapping.

Aneurysm growth and rupture depend primarily on the balance between collagen synthesis and degradation in response to changing mechanical stimuli6. It is also accepted that haemodynamic forces plays a crucial role in these processes. As haemodynamic forces strongly depend on vascular geometry, image-based computational fluid dynamics (CFD) is capable of realistically representing this haemodynamic environment. In this study, we analyze haemodynamic changes after PAO with bypass revascularization in the treatment of unruptured GIA. We chose to model this technique as studies have shown superior results in comparison to distal PAO, with one study reporting a one-year aneurysm rupture risk after distal parent artery sacrifice of 15% compared to 0% for post-proximal PAO7.

We performed fluid–structure interaction (FSI) simulations that allowed visualization of intra-arterial blood flow within the model, taking into account the deformability of the vessels. We investigated haemodynamic changes in three models of the relevant part of the arterial system; before treatment (reference model with unruptured GIA in C6 ICA segment); after high-flow virtual bypass from the external carotid artery (ECA) to the frontal branch of the middle cerebral artery (MCA) with proximal PAO; and after virtual high-flow bypass from the ECA to the temporal branch of the MCA with proximal PAO. Despite enormous performance and settings optimization for the flow and structural aspects, and the interface connecting both modules, blood flow analysis in the entire relevant arterial system was performed as flow reversal techniques influence the whole system. This approach is unique and provides reliable information about the blood flow. We assessed FSI CFD analysis potential for clinical use in the preoperative stage, and shown the optimal recipient branch of the patient-specific bypass.

Numerical procedure methodology

In silico blood flow studies were performed in patient-specific models using patient-specific CT angiography and then with geometries modified after virtual surgery, creating bypasses with the selected intracranial arteries.

These analyses had to cover several steps. Description of the numerical methodology is provided in the following sections. For the sake of clarity, the main steps are divided into separate parts and only essential information regarding the geometric and numerical models is presented.

Modelling of the arterial lumen

Restricting the model morphology to a limited region is the standard for numerical simulation of aneurysms, whether cerebral or aortic. For the analysis of aortic aneurysms, most researchers assume that a geometric model starting at the aortic inlet just posterior to the valve or the coronary vessels and ending at a short segment beyond the femoral arteries is correct. These models usually include the arterial bifurcation from the arch of the aorta. We believe this approach is correct as the course of the aortic arch and the arterial branches have an important influence on the flow structure in the descending aortic segment and therefore on the abdominal aortic aneurysm (AAA)8,9. This is different from the analysis of the structure and the flow parameters in the intracranial aneurysms10. The geometric structure of the cerebral circulation is complex and tortuous. The carotid arteries originate from different parts of the aorta or brachiocephalic trunk and the vertebral arteries (VA) from the subclavian arteries. They then unite after various courses and lengths to form the cerebral arterial circle of Willis. Due to the pulsatile nature of the flow in the arterioles of the circle of Willis, there is an interference of pressure and flow waves, which makes it impossible to determine the correct boundary conditions in a single supply artery or arteriole of the cerebral circle without direct measurement of pressure and blood flow. For this reason, an individual and comprehensive mapping of the morphological characteristics of the corresponding part of the human cardiovascular system is essential.

As the models analysed in our study were of very high complexity (including aorta, visceral arteries, arteries of the lower and upper limbs as well as intracranial vasculature with all afferent arteries), it was not possible to generate such geometries based on a DICOM dataset for an individual patient. Mainly due to radiation overexposure, it is in fact not possible to study the whole human body with CT angiography. Therefore, the final model was composed of three different combined patient specific geometries including:aortic arch with all the major branches,

descending aorta (with the visceral arteries) up to the iliac arteries

cerebral vasculature with the distal fragments of the internal carotid artery and the vertebral arteries.

The idealised arteries of the lower and upper limbs of the human body were also added to the model. A similar model preparation procedure was presented in11 with the difference that the delivery vessels and the cerebral vascular model were adopted from a patient diagnosed with GIA. Figure 2 shows the complete geometric model used in the study.Fig.2 Whole model of human arteries used in the study with magnified region of GIA.

All these parts of the circulatory system have different levels of complexity and different methods have been used for their reconstruction. Contour extraction from biomedical imaging data and a profile-lofting method in SolidWorks (Dassault Systèmes SE. Vélizy-Villacoublay, France) were used to obtain the geometries of the aortic arch with all major branches and the descending aorta to the iliac arteries. Using a technique known as profile lofting, idealised arteries of the lower and upper limbs were generated in SolidWorks along the predefined midline. A patient-specific model of the intracranial vasculature and all afferent arteries was created using image segmentation techniques, stereolithography (STL) file extraction and volumetric object transformation in ANSYS SpaceClaim (Ansys, Inc. Canonsburg (Pennsylvania), USA).

Modelling the bypass

Since the main objective of this research was to investigate flow haemodynamics after performing a virtual operation of an innovative bypass procedure, the authors modified the final geometry following recommendations of the neurosurgeon (KW, AA, PV). Modifications included insertion of an artificial bypass between the right ECA and the chosen M2 MCA branches, blocking the right ICA lumen to exclude the aneurysm from the circulation. The anatomical structure of the bypass mimicked a radial artery, with a lumen diameter of 3.0 mm and wall thickness of 0.37 mm. The pathway, curvature and general alignment of the bypass were inspected by the neurosurgeon and were modified as per suggestions. Two bypass configurations were prepared – in both cases the bypass arises from the same location at the right ECA artery, but terminates in either a frontal (bypass 1) or temporal (bypass 2) MCA branch as presented in Fig. 3.Fig.3 A volumetric model of the fluid domain of geometries with both bypass configurations comprising two different MCA branches for the distal bypass anastomosis. Bypass 1 to frontal MCA branch; Bypass 2 to temporal MCA branch.

Numerical simulation procedure

An advanced numerical model was used to analyse the effect of bypass insertion on GIA, taking into account:Pulsatile blood inflow and pressure,

Physiological vasomotion, i.e. elastic vessel walls deformed under pressure changes – Fluid Structure Interaction (FSI) methodology,

Non-Newtonian blood model,

Patient-specific model in region of aorta and cerebral circle.

FSI simulations are numerical analyses which mimic properties corresponding to a natural, physiological behaviour of the cardiovascular system12. Currently, the use of FSI to calculate patient-specific models of the arterial system is not common. Many papers considering aneurysms or stenotic arteries contain geometric simplifications13 or models that are limited to small sections of the arteries14–17. By utilizing a two-way coupling algorithm inside the numerical solver, force generated by the fluid results in a displacement of the model wall and vice versa – deformation of the wall affects the flow. In the context of blood flow simulation, this approach allows nature to be mimicked more faithfully than simulations assuming rigid walls. It allows the user to reproduce the vasomotion of the arteries, their pressure attenuation characteristics and their ability to maintain uninterrupted forward blood flow.

Due to the extremely high complexity of the FSI analyses, as well as their time-consuming nature, such simulations are limited usually only to a chosen fragment of the arterial system, such as the common carotid artery bifurcation14–17 or aortic arch18.

The main idea to simulate such a large part of the systemic circulation is based on two major advantages. The first is that most of the phenomena that occur in the afferent vessels (which influence flow in the efferent vessels) are present in the model during the computational phase. These phenomena include: mixing of flow jets at arterial junctions, specific flow separation at arterial bifurcations, development of specific flow distributions depending on vessel curvature, pressure drops along arteries of specific length, diameter and curvature, and generation of specific flow resistances resulting from vessel topology. The second reason is related to our FSI model. In order to obtain a correct blood flow throughout the whole organism, our simulation had to mimic a realistic behaviour of the circulatory system (physiological vasomotion). This implied that during systole the arterial walls had to expand. This led to an accumulation of energy in the walls and an increase in domain volume. Conversely, during diastole, the walls had to return to their original size, reducing domain volume and allowing continuous forward blood flow. It is worth noting that the largest changes in blood volume occur in the aortic regions, making it imperative to include this vessel in FSI simulations.

Compared to smaller models with user-specified boundary conditions near the area of interest, large model approach is less sensitive to patient-specific conditions. By setting boundary conditions only at the ostium of the aorta and at the ends of the arteries in our model, we reduce the need to determine and assume flow conditions in the individual arteries supplying blood to the cerebral arterial circle.

Performing reliable FSI simulations requires fulfilling numerous complex steps, including fluid and mechanical meshes generation, setting up mechanical properties of vessel walls, initial and boundary conditions that would result in physiological flow distribution, and general settings of simulations together with convergence criteria. A thorough description of each procedure is provided in11. It is also important to acknowledge that the implementation of FSI techniques markedly prolongs the duration of the calculations and requires a substantially greater computational resource than that which is typically required for CFD calculations in blood systems. For our case studies, one full FSI simulation required around 14 days to be calculated, whereas the corresponding CFD analysis with rigid-wall approach would take approximately one day to be finished.

Numerical mesh

The fluid domain volumetric mesh was generated in ANSYS Fluent (Ansys, Inc. Canonsburgu (Pennsylvania), USA). It consisted of a combination of polyhedral and prismatic elements embedded in an inflation layer in the vicinity of the wall. The inflation layer is essential to investigate the phenomena that occur close to the walls with sufficient accuracy. Typically, the more layers within the inflated layer, the better the near wall flow approximate. However, for FSI simulations, where the model can be deformed, expanded and contracted, having too many sublayers would lead to their incorrect deformation (negative volumes), which would cause the numerical solver to fail. Therefore, we limited their number to eight, which is a compromise between numerical data security and the possibility of mesh errors occurring. The final fluid mesh consisted of approximately 4.3 million elements and 10.7 million nodes.

The volumetric mesh of the arterial walls was generated in the ANSYS Transient Structural module (Ansys, Inc. Canonsburgu (Pensylwania), USA) using the linear order discretisation scheme. In order to reduce the computation time, we generated a mechanical mesh consisting of only a single layer of irregular tetrahedral SOLID285 elements (3D lower-order elements characterised by four nodes). The final mechanical mesh consisted of approximately 0.99 million elements and 0.28 million nodes.

Numerical simulations: solvers coupling settings

We analysed 20 complete cardiac cycles—each repetition had a period of 0.8 s and a time step of 0.016 s. Two-way coupling, i.e. mutual interaction between the mechanical wall and the fluid structure, was assumed for the FSI simulations performed in this research. Thus, the inner surface of the mechanical wall is also an outer surface of the fluid domain. This means that these facets act as an interface between the fluent and transient structural solvers. The force generated by the fluid flow is transferred to the inner part of the walls through an interface boundary condition (resulting in wall displacement) and vice versa.

We set the minimum number of iteration loops to five within the coupling module, where both fluid and mechanical solvers exchange information. The coupling calculation was treated as complete when either the residual value fell below 10−2 or when 20 iterations had occurred. For the Fluent solver, the convergence criteria were set as follows: maximum number of iterations—15; convergence criteria—10−3 (absolute) and 5∙10−2 (relative). For the Transient Structural solver we allowed 22 iterations, after which the time step was reduced until the correct solver stability was reached.

Numerical simulations: modelling of the walls

In the FSI model presented here, the task expected through the use of the structural solver was to determine the vessel deformation, which affects the behaviour of the fluid in the flow channels. The walls were modelled on the basis of the final geometry of the arterial lumina. The overall procedure for creating the walls entailed offsetting the surfaces of the volumetric object by a specific distance, which corresponded to the desired thickness at that particular arterial region. Given the variability in thickness observed among different arteries, the decision was taken to offset only the selected surfaces, thereby creating a gap between consecutive offsets. This approach enabled the generation of a smooth transition between regions of varying thickness. With regard to this research, the maximal thickness was equal to 1.5 mm for the ascending aorta, while the minimal thickness (for the distal parts of the intracranial arteries and aneurysms) was equal to 0.3–0.4 mm.

A neo-Hookean formula for a hyperelastic material, with an initial shear modulus of 0.2 MPa and an incompressibility parameter of 107 Pa−1 was defined in the mechanical solver. The Large Deformation Option was selected for the calculations. To prevent the emergence of instabilities, the outlet and inlet surfaces were fixed in three-dimensional space. The remaining wall regions were permitted to deform in response to external forces, but their movement was constrained by elastic support (a foundation stiffness coefficient, or FS, that simulated surrounding tissues) and external pressure on the model walls. In addition, the number of elastic supports was increased in the area of the indentation visible in the aneurysm, which was observed on imaging. This prevented this aneurysm wall from pushing out due to internal pressure and, at the same time, allowed for displacements similar to those observed in nearby arteries. The initial pressure was set to 0 Pa, and it was then increased linearly to 5 kPa over a period of 2.4 s, where it remained constant. The timestep for the mechanical solver was identical to that of the Fluent solver, set at 0.016 s.

Numerical simulations: fluid domain definition

It was assumed that there was no heat exchange and that the fluid temperature remained constant, assuming that heat exchange predominantly occurs in capillaries rather than arteries. Furthermore, it was assumed that the density of blood could vary between 1053 and 1056 kg/m3. In the event that the fluid was deemed to be fully incompressible, the calculations could potentially fail as a result of solver instability.

In determining whether to employ the turbulence model in the simulations, several factors were taken into account. It is notable that calculations of Reynolds numbers based on arterial vessel diameters and averaged blood velocity values suggest that these may fall below the critical Reynolds number value for circular channels for the majority of the system under study. It is only in specific regions of the aorta that the value exceeds 3,000 during the time steps corresponding to the systolic peak. It should be noted, however, that the critical Reynolds number for turbulent flow is determined experimentally in rectilinear channels under steady-state flow conditions. In the arterial system, neither of these two conditions is met, so it can be assumed with a high degree of probability that even in long arteries, there will be a mixing of fluid layers in the channel during cardiac diastole. Consequently, the flow should not be considered to be purely laminar.

A turbulence model based on the two equations k-ω (Shear Stress Transport model) was selected due to its demonstrated efficacy in approximating laminar flow under low Reynolds numbers, as evidenced by publications19,20. Despite the increased computational time involved in determining the additional equations, it was deemed that assuming a turbulent model would more faithfully simulate the actual flow.

Non-Newtonian shear-thinning behaviour was incorporated into the blood rheological parameters. This implies that as the shear rate rises, the viscosity declines due to the deformation of blood cells. As the blood flow slows, the shear rates decrease and the cells form larger groups, increasing the viscosity.

A variety of mathematical models for blood rheology exist in the literature, as the behaviour of blood depends on a number of patient-specific factors, including sex, age and diet. For the purposes of this analysis, we have chosen to employ a modified power law, which is also used in other blood flow computational fluid dynamics (CFD) studies in various applications21–23. The equations for our blood model are provided below:1 η=0.55471Pa·sforγ˙≤0.001η=η0·γ˙n-1for0.001≤γ˙<327η=0.00345Pa·sforγ˙≥327

where: η0 = 0.035 kg∙m-1∙s-1.4; n = 0.6; while η = 0.00345 Pa·s is a reference viscosity of Newtonian blood.

At the inlet cross-section to the ascending aorta, a time-varying boundary condition was set by Prandtl profile distribution formula – see Eq. 2. Specific user-defined function (UDF) file was developed and imported into Ansys Fluent to correctly assign the time-dependent velocity function together with profile distribution constrains (oriented normally to the inlet surface). Figure 4 depicts the time-dependent function of the maximal velocity (Vmax) at the inlet cross section, limited to eight cardiac cycles for visualization purposes.2 Vp=Vmax·1-rRmax0.8

where: Vp is veolocity at inlet cross-section at location of r – radius, Vmax – maximum velocity and Rmax – maximum radius of the inlet cross-section.Fig.4 Blood mass flux function over time used to define inlet boundary condition.

In computational fluid dynamics (CFD) analyses of blood flow, pressure gradients between inlet and outlet cross-sections result in alterations to the flow direction. Flow resistances give rise to pressure drops. When pressure increases at an outlet cross-section, the volume of fluid reaching that area is reduced, while the volume of fluid passing through channels with lower resistances is increased. To control the distribution of flow across the entire systemic circuit, hybrid boundary conditions have been introduced at the outlet cross-section. At the end of each artery there was an additional porous cylinder with a length corresponding to the circumference of the respective vessel. The resistances in the porous cylinders were determined by the viscosity and inertia of the fluid according to the Ergun's equation (Eq. 3). A constant pressure of 6 kPa was set at the outlet surface as a boundary condition. The settings of resistance factors derived from viscosity and inertia for the different areas of the circulatory system were determined by tuning the numerical model and are detailed in11.3 ΔpL=U→150μDp2·(1-ε)2φ2ε3+U→21.75ρDp·1-εφε3

where Δp – pressure drop, L – porous body length, U→ – fluid velocity, μ – fluid dynamic viscosity, Dp – spherical diameter of particles ‘forming’ the porous body), ε – porosity of the body, φ – sphericity, ρ – fluid density.

Results

CFD investigations were performed on the reference case study CT angiography and two case studies after virtual surgical operation where the bypass was sutured to the chosen branch of the MCA and the ICA was ligated, thus preventing intensive blood supply to the GIA dome. Dozens of varied quantitative and qualitative data were gathered and the flow haemodynamics were assessed in pre- and post-operative geometries.

Firstly, the correctness of our numerical results for the reference geometry was verified. Data on the volume stroke that is distributed to the brain were compared with reports from the literature24–27 and presented in Table 1. For that purpose, an overall flow distribution across the entire body was assessed, with diastolic and systolic pressure at the walls and maximal deformations during the systolic peak.Table 1 Chosen haemodynamic parameters used during verification of the computational fluid dynamic analysis.

Blood distribution across the chosen regions of the systemic circuit [cm3]	
Total volume of delivered blood	Brain	Neck and face	Upper limbs	Abdominal viscera and lower limbs	
83.76	14.01

(16.7%)

	4.32

(5.2%)

	8.28

(9.9%)

	57.15

(68.2%)

	
Referencepercentage of the cardiac output	15–20% 24

ca 15%25–27

	ca 6%26	ca 12%26	ca 62%26	
Systolic/diastolic pressureat model walls	Systolic peak:	16.7 kPa (125 mmHg)	
Diastolic end:	11.5 kPa (86 mmHg)	
absolute values in cm3 are in bold.

After physiological correctness was validated, blood supply to specific regions of the numerical domain was analysed for the last full cardiac cycle. This determined if there is a significant blood volume delivery decrease for the right cerebral hemisphere ipsilateral to the bypass. Additionally, one could observe how the general flow splitting across the entire domain was affected by the virtual bypass procedure. This was achieved by calculating an integral of mass flow rate at each outlet cross section (or control surface) for the last cardiac cycle. Table 2 gathers data for control planes for the right side of the systemic circuit, Table 3 for the left side, and Table 4 presents data on the volume delivered through the descending aorta and bypass itself.Table 2 Blood volume delivered throughout the last cardiac cycle through the chosen outlet cross sections and control surfaces; right side of the circulatory system.

	Blood volume in a full cardiac cycle [cm3]	Relative difference	
	Artery	No bypass	Bypass 1	Bypass 2	Bypass 1	Bypass 2	
right side	ophthalmic	0.51	0.38	0.35	−24.8%	−30.5%	
posterior cerebral #1	0.78	0.60	0.55	−23.8%	−29.9%	
posterior cerebral #2	0.52	0.46	0.45	−11.2%	−13.9%	
superior cerebellar	0.31	0.30	0.30	−2.9%	−3.0%	
MCA branch #1	0.71	0.60	0.90	−15.6%	26.1%	
MCA branch #2	0.28	0.23	0.21	−17.6%	−23.9%	
MCA branch #3	0.33	0.27	0.25	−16.7%	−22.8%	
MCA branch #4	0.46	0.38	0.35	−18.4%	−25.2%	
MCA branch #5	0.46	0.38	0.35	−18.2%	−25.3%	
MCA branch #6	0.30	0.25	0.23	−17.7%	−24.4%	
MCA branch #7	0.65	0.77	0.5	18.7%	−23.2%	
Total sum	5.32	4.62	4.43	−13.1%	−16.6%	
right side	common carotid	6.76	5.38	5.08	−20.4%	−24.8%	
internal carotid	4.53	0.00	0.00	−100.0%	−100.0%	
external carotid	2.26	2.26	2.26	−0.1%	−0.2%	
middle cerebral	3.19	0.26	0.07	−91.9%	−97.9%	
posterior communicating	0.07	0.71	0.83	858.2%	1014.7%	
vertebral	0.16	0.19	0.19	17.7%	20.3%	
subclavian	4.20	4.05	4.04	−3.6%	−3.7%	
Total sum values are in bold.

Table 3 Blood volume delivered throughout the last cardiac cycle through the chosen outlet cross sections and control surfaces; left side of the systemic circuit.

	Blood volume in a full cardiac cycle [cm3]	Relative difference	
	Artery	No bypass	Bypass 1 (to frontal MCA branch)	Bypass 2 (to temporal MCA branch)	Bypass 1 (to frontal MCA branch)	Bypass 2 (to temporal MCA branch)	
left side	Anterior cerebral #1	0.92	0.91	0.91	 − 1.0%	 − 1.0%	
Anterior cerebral #2	1.07	1.06	1.06	 − 1.0%	 − 1.1%	
Ophthalmic	0.92	0.91	0.91	 − 1.1%	 − 1.2%	
Posterior cerebral #1	0.11	0.10	0.11	 − 6.4%	 − 2.2%	
Posterior cerebral #2	0.41	0.40	0.40	 − 1.5%	 − 2.2%	
Posterior cerebral #3	0.67	0.66	0.65	 − 1.6%	 − 2.3%	
Superior cerebellar #1	0.25	0.24	0.25	 − 2.9%	 − 2.2%	
Superior cerebellar #2	0.62	0.61	0.61	 − 1.3%	 − 1.8%	
Superior cerebellar #3	0.29	0.28	0.28	 − 2.9%	 − 2.5%	
MCA branch #1	0.90	0.89	0.89	 − 0.8%	 − 1.3%	
MCA branch #2	0.74	0.73	0.73	 − 0.5%	 − 1.2%	
MCA branch #3	0.60	0.60	0.59	 − 0.9%	 − 1.2%	
MCA branch #4	0.73	0.72	0.72	 − 0.8%	 − 1.3%	
MCA branch #5	0.47	0.46	0.46	 − 0.8%	 − 1.2%	
TOTAL SUM	8.69	8.59	8.57	 − 1.2%	 − 1.4%	
left side	Common carotid	8.18	8.28	8.30	1.3%	1.5%	
Internal carotid	6.13	6.24	6.26	1.8%	2.1%	
External carotid	2.06	2.04	2.04	 − 0.9%	 − 0.9%	
Middle cerebral	3.43	3.39	3.40	 − 1.3%	 − 0.7%	
Posterior communicating	0.18	0.01	0.03	 − 92.5%	 − 80.9%	
Vertebral	3.08	3.57	3.61	15.8%	17.4%	
Subclavian	4.08	4.05	4.05	 − 0.7%	 − 0.7%	
Total sum values are in bold.

Table 4 Blood volume delivered throughout the last cardiac cycle through the chosen control surfaces.

	Blood volume in a full cardiac cycle [cm3]	Relative difference	
Artery	No bypass	Bypass 1	Bypass 2	Bypass 1	Bypass 2	
Basilar	2.39	2.92	2.96	22.4%	24.0%	
Descending aorta	57.15	55.93	56.06	 − 2.1%	 − 1.9%	
Bypass	–	3.13	2.85	–	–	

As can be seen from Table 2, each post-operative geometry resulted in a significant relative decrease in the blood volume delivered to the right cerebral hemisphere. After summation of the volume delivered through each outlet cross section, these relative differences were equal to 13.1% for Bypass 1 and 16.6% for Bypass 2. Such high values of differences indicate that surgical bypassing might lead to a drastic reduction of the blood supply to the brain which could result in ischemic events. However, when one compared direct volumetric data, it turned out that the reduction of the inflow to the right hemisphere was not so high – approximately 0.7 and 0.9 cm3 for Bypass 1 (to frontal MCA branch) and Bypass 2 (to temporal MCA branch), respectively. Focusing on a purely local analysis, it can be noted which branch the bypass was stitched due to the increase in blood volume delivered through the given artery. For Bypass 1 there was an increase in volume delivered to branch #7 (frontal MCA branch) equal to 18.7%, while for Bypass 2 there was an increase of 26.1% at branch #1 (temporal MCA branch). Both bypassing configurations resulted in a drastic reduction of blood supply to the right globe (due to occlusions of the internal carotid artery as an afferent vessel) by 0.15 cm3. Our virtual operation analysis suggested that Bypass 1 is a more suitable configuration since there was a lesser impact on flow distribution. However, this difference can be treated as marginal since it was equal to 0.03 cm3.

By occluding the right ICA (no volume delivered through this vessel) and directing the blood to the bypass, the general resistance of the arterial system was changed. This is noted when comparing blood supply through the other control surfaces at the right side of systemic circuit presented in Table 2. For instance, there was 20.4 and 24.8% reductions of blood volume flowing through the right common carotid artery (CCA), for Bypass 1 and Bypass 2 respectively. Even in the subclavian artery the flow was reduced by 3.6% in both case studies. A slight increase in the blood volume delivered through the right VA resulted, suggesting the possibility of a flow compensation phenomenon presence in our simulations.

As stated before, creating a bypass between the ECA and MCA branches leads to changes in the resistance which, consequently, could affect flow splitting, not only in the region efferent to the bypass, but also in the entire fluid domain. To verify this hypothesis, blood volume delivered to the left upper side of the circulatory system was compared to the abdominal regions (Table 3, 4).

As presented in Table 3, for both bypass configurations, a slight decrease in blood supply occurred in the left cerebral hemisphere (1.2% and 1.4% for Bypass 1 and Bypass 2, respectively). Such low relative differences and even smaller absolute volumetric differences (0.1 cm3 per full cardiac cycle) suggest that blood supply to the healthy, unchanged side of the brain was nearly unaffected. However, when one focused on the flow through the left VA, a significant increase could be observed. Similarly, for the right VA, this could be related to flow compensation – any deficiency of blood supply was partially compensated by the specific configuration of the circle of Willis. To clarify this, blood volume delivered through the basilar artery (BA) is presented – see Table 4.

It can be noted that for both bypass configurations blood volume delivered through the BA increased by 23% which constitutes an approximate volume of 0.5 cm3. This clearly shows that even without setting additional controlling mechanisms, there is detectable flow compensation during the pre-processing stage. Blood volume delivered to the abdominal region of the systemic circulation and to the lower limbs was reduced in both bypass configurations by about 2%, which was equal to approximately 1.0 cm3. In the bypass, the distal connection to two different MCA branches (with resulting varied geometries) affected the flow resistance, which lead to differences in the blood supply (3.13 cm3 for Bypass 1 and 2.85 cm3 for Bypass 2). Similar analysis of to the maximal blood velocity during the systole peak can be found in the Appendix, as well as information on the maximal velocities at each investigated outlet cross section and control surface located in the entire circulatory system. Since these results are within the physiological range presented in literature, it can be concluded that our advanced simulations reliably approximated physiological blood flow behaviour.

To confirm that the aneurysm walls are subjected to lower tangent and normal stresses after virtual surgical bypass, the following parameters were analysed: area-averaged and maximal wall shear stress (WSS), area-averaged and maximal time-averaged WSS (TAWSS, calculated for the whole last cardiac cycle), area-averaged spatial gradient of WSS (WSSG), as well as minimal, area-averaged and maximal pressure. Furthermore, to determine whether post-operative geometries produce and environment suitable for thrombosis, the authors investigated dynamic viscosity as well. All abovementioned parameters were measured during the systolic peak of the last cardiac cycle (timestamp: 15.52 s) and at the late diastole of the last cardiac cycle (timestamp: 16.00 s) (Table 5).Table 5 Values of the analysed haemodynamic parameters in the giant aneurysm.

Parameter	Giant aneurysm parameter	Relative difference	
No bypass	Bypass 1	Bypass 2	Bypass 1	Bypass 2	
Systole peak (t = 15.52 s)	Max. WSS [Pa]	82.21	57.39	52.84	 − 30.2%	 − 35.7%	
Area-averaged WSS [Pa]	3.63	0.19	0.21	 − 94.8%	 − 94.2%	
Area-averaged WSSG [Pa/m]	11249	197	307	 − 98.3%	 − 97.3%	
Max. pressure [Pa]	15645	12299	11683	 − 21.4%	 − 25.3%	
Min. pressure [Pa]	14998	12010	11400	 − 19.9%	 − 24.0%	
Area-averaged pressure [Pa]	15395	12293	11673	 − 20.1%	 − 24.2%	
Late diastole (t = 16.00 s)	Max. WSS [Pa]	54.97	38.31	28.75	 − 30.3%	 − 47.7%	
Area-averaged WSS [Pa]	1.60	0.09	0.08	 − 94.4%	 − 95%	
Area-averaged WSSG [Pa/m]	3213	106	119	-96.7%	-96.3%	
Max. pressure [Pa]	11,100	9772	9490	 − 12.0%	 − 14.5%	
Min. pressure [Pa]	10,842	9590	9370	 − 11.5%	 − 13.6%	
Area-averaged pressure [Pa]	11,009	9771	9488	 − 11.2%	 − 13.8%	
WSS wall shear stress, WSSG spatial gradient of WSS.

Based on the results presented in Table 5, both bypass configurations induced a large reduction of all shear- and pressure-related parameters, not only during late diastole but also during the systolic peak. Since the changes in flow haemodynamics and systemic circulation response are greatest during the systolic peak, it was decided to focus on a thorough description of the results for this timestamp (t = 15.52 s).

Regarding tangent stress (WSS), the maximal value of this parameter dropped from 82 Pa for the reference case study to 57 Pa for Bypass 1 and 53 Pa for Bypass 2, with corresponding relative differences equal to 30.2 and 35.7%. Considering these significant variations, it can be concluded that bypass procedures affected the shear stress magnitude positively – generally, excessive values deteriorate the endothelium of the tunica interna which can weaken the vessel wall. However, it must be noted that maximal WSS is not a reliable bioindicator, since it indicates the greatest value calculated for the given control surface. Thus, there is a high chance that only a very small zone has such a high value, while all other regions could be characterized by lower values. Therefore, in our opinion, area-averaged WSS is a more reliable bioindicator. In both bypass configurations, a drastic reduction of this parameter was obtained (from 3.6 Pa for the reference to 0.2 Pa for Bypass 1 and Bypass 2), which constitutes a 95% decrease. Hence, occlusion of the main afferent artery of the giant aneurysm has a tremendous impact on the magnitude of WSS at the walls. A reduction of WSSG was also noted (11,250 Pa/m for the reference case to 197 and 307 Pa/m for Bypass 1 and Bypass 2, respectively). WSSG determines spatial changes in WSS magnitude, and thus may indicate regions prone to formation of atheromatous plaque or aneurysm growth28,29. Since we obtained a large reduction of WSSG in both bypass geometries, it can be concluded that bypass positively affects haemodynamics in the aneurysm. A qualitative comparison of shear-related parameters is presented in Fig. 5–6 and Supplementary video 1–3. For each geometry type it was decided to depict the aneurysm in a bottom view (upper projection) and an anterior view (lower projection).Fig.5 WSS distribution at the giant aneurysm walls in bottom (Bo) and anterior (An) projections; the last simulated cardiac cycle.

Fig.6 WSSG distribution at the giant aneurysm walls in bottom (Bo) and anterior (An) projections; the last simulated cardiac cycle.

For cycle-averaged shear-related data, time-averaged WSS (TAWSS) and oscillatory shear index (OSI) were also investigated. The latter parameter gives insight into direction changes of shear forces throughout the cardiac cycle – the higher the value, the more frequent the direction changes. It has been suggested that high local OSI and low WSS regions are prone to plaque aggregation and blood stagnation30–32. Table 6 shows quantitative data of the aforementioned parameters, while Fig. 7 depicts a qualitative comparison of OSI distributed in the aneurysm wall, for bottom and anterior projections.Table 6 Numerical data of TAWSS and OSI parameters.

Parameter	Giant aneurysm region	Relative difference	
No bypass	Bypass 1	Bypass 2	Bypass 1	Bypass 2	
TAWSS	area-averaged	2.66	0.13	0.14	 − 95.1%	 − 94.7%	
maximal	90.2	54.01	47.11	 − 40.1%	 − 47.8%	
OSI	area-averaged	0.216	0.177	0.175	 − 18.1%	 − 19.0%	
TAWSS time-averaged WSS, OSI oscillatory shear index.

Fig.7 OSI distribution at giant aneurysm walls; bottom (Bo) and anterior (An) projection.

The area-averaged TAWSS was reduced (2.66 Pa for the reference to 0.13 Pa for Bypass 1 and to 0.14 Pa for Bypass 2). Additionally, a decrease in OSI was non-negligible (0.216 for the reference to 0.178 for both bypass configurations). The relative differences of TAWSS and OSI suggest that the latter parameter was less affected (approximately 18.5%) than the former (44%). Nonetheless, all investigated case studies of the bypass indicate that the post-bypass GIA region is an excellent environment for blood stagnation and blood clotting due to elevated OSI and low WSS.

Concerning normal stresses acting on the aneurysm wall, that is. pressure, a significant reduction was observed in both post-bypass studies. Area-averaged pressure during the systolic peak was 15.4 kPa for the reference, while for Bypass 1 it dropped to 12.3 kPa and for Bypass 2 to 11.7 kPa. Since almost the entirety of the aneurysm wall was subjected to more or less uniform pressure distribution, maximal values were relatively similar to area-averaged values (Fig. 8). The case studies indicate that the configuration of Bypass 2 is more suitable for a surgical procedure since the pressure was reduced to a larger extent than for Bypass 1, by approximately 600 Pa. Therefore, the aneurysm wall is subjected to a lower stress in this configuration which, in turn, reduces the risk of aneurysm rupture. A similar correlation was noted for the already described tangent stresses – the maximal WSS was lowered by 4.5 Pa for Bypass 2 compared to Bypass 1. The values for the area-averaged WSS were similar.Fig.8 Pressure distribution at the giant aneurysm walls; bottom (Bo) and anterior (An) projections; the last simulated cardiac cycle.

Similar observations and conclusions could be drawn from the analysis performed at late systole. Firstly, there was a significant reduction of shear- and pressure-related parameters for both surgical configurations. Moreover, Bypass 2 exhibits the potential for creating a more protective environment against aneurysm rupture (lower tangent and normal stresses acting on the aneurysm wall). In both bypass models, pressure changes inside the aneurysm were accompanied by aneurysmal volume decrease in comparison to the reference model. The lower the pressure, the lower the aneurysm volume. Thus, the virtual bypass leads to a decrease in pressure at the aneurysm wall, followed by a reduction in aneurysm volume (Fig. 9 and Supplementary video 4–6).Fig.9 Pressure and accompanying volume changes inside the aneurysm, before and after the bypass with parent artery occlusion during the cardiac cycle.

The authors performed an additional analysis in which the right ICA was clipped, but no bypass connection created. This would determine whether the circle of Willis connections and possible flow compensation would be sufficient to maintain a blood supply to the right hemisphere (without the need for a surgical bypass). A similar analysis was performed on the stresses (pressure and shear stress) acting on the aneurysm wall. The results of this investigation are summarized in Table 7.Table 7 A comparison of the numerical data for the additional case study: the right ICA clipped and no bypass inserted.

Parameter	Region	No bypass	Bypass 1	Bypass 2	No bypass, ICA clipped	Bypass 1	Bypass 2	No bypass, ICA clipped	
Blood volume [cm3]	Right lobe	5.32	4.62	4.43	2.15	 − 13.1%	 − 16.6%	 − 59.6%	
Left lobe	8.69	8.59	8.57	8.76	 − 1.2%	 − 1.4%	0.8%	
Basilar artery	2.39	2.92	2.96	3.37	22.4%	24.0%	41.2%	
Area-averaged WSS at systole peak [Pa] (aneurysm walls)	3.63	0.19	0.21	0.20	 − 94.8%	 − 94.2%	 − 94.5%	
Area-averaged pressure at systole peak [Pa] (aneurysm walls)	15,395	12,293	11,673	8191	 − 20.1%	 − 24.2%	 − 46.8%	
Area-averaged TAWSS at aneurysm walls [Pa]	2.66	0.13	0.14	0.15	 − 95.1%	 − 94.7%	 − 94.2%	
Area-averaged OSI at aneurysm walls [-]	0.216	0.177	0.175	0.168	 − 18.1%	 − 19.0%	 − 22.3%	
Area-averaged WSS at systole peak [Pa] (right PComA)	1.81	14.77	18.65	45.14	716%	930%	2394%	
Maximum WSS at systole peak [Pa] (right PComA)	11.67	116.88	155.99	418.74	902%	1237%	3488%	

When the right ICA was clipped and no bypass connection created, the blood supply to the right hemisphere was significantly reduced by almost 60%. Thus, bypass was essential for this patient to maintain blood supply to the brain. Compared to the bypass case studies, the difference in blood supply was four-fold. Thus, despite flow compensation, the right hemisphere was insufficiently supplied. Flow compensation could be observed when analyzing the volume of blood passing through the BA, where there was a twofold increase when compared to the bypass studies. Although a greater volume of blood was delivered to the right hemisphere through the BA, this volume was still insufficient to maintain a proper blood supply.

Focusing on area-averaged and maximum WSS exerted on the walls of the right posterior communicating artery (PComA), a large, non-physiological increase was observed (Supplementary video 7). In this case study (ICA clipped, no bypass), the area-averaged WSS increased from 1.81 to 45.14 Pa, whereas maximum WSS increased from 11.67 to 418.74 Pa. This large increase in non-physiological WSS might contribute to degradation of the PComA endothelium, leading to faster mechanical fatigue of the wall tissues and potentially aneurysm formation. With regard to parameters related to shear stress at the aneurysm wall, that is area-averaged WSS, TAWSS, and OSI, very little difference was observed (between the bypass studies and that with the clipped ICA without bypass). However, when analyzing the pressure, a significant reduction is found (Supplementary video 8). In the reference case study, the pressure was approximately 15.4 kPa, whereas in the ICA clipped, no bypass study it dropped to approximately 8.2 kPa, a 47% reduction. In both bypass configurations, the pressure was higher by approximately 3.5–4.1 kPa when compared to the new geometry. Thus, when the ICA was clipped but no bypass was created, the aneurysm walls were subjected to the lowest normal stresses, indicating that this would be the optimal approach to reduce aneurysm rupture. However, due to the insufficient blood supply to the right hemisphere, this configuration would not to be suitable for this patient and a bypass is mandatory.

Discussion

Our main finding is that after bypass with PAO, the pressure inside the aneurysm decreases, as does the aneurysmal volume and associated mass effect. Our results provide the mechanistic background to those in the literature33.

Unruptured GIA account for about 5% of all unruptured intracranial aneurysms, thus understanding of their treatment and follow-up is limited. It is known that aneurysm size is a risk for rupture, and thus, the morbidity and mortality of GIA are high34. As the natural history of GIA is unfavourable, we performed CFD analysis in a whole brain arterial circulation model to calculate blood flow distribution in both hemispheres, assess the risk of rupture, and calculate changes after bypass/cerebral revascularization and proximal PAO. We focused on an ICA GIA model and constructed three CFD models to assess the haemodynamics before and after bypass surgery; the first with a GIA in the C6 ICA segment, and two after virtual bypass operation with PAO: bypass/revascularization to either the M2 frontal branch or the M2 temporal branch.

The bypass procedure with PAO significantly decreased blood flow in the hemisphere on the bypass side but also lead to changes in flow resistance. This affected flow in other arteries, as was observed in both VA, in which flow was increased. Each blood flow impairment was counterbalanced by the anatomy of the circle of Willis, so that each decrease in blood flow was compensated by an increase in flow in the other arteries. In both bypass models, the blood flow in the BA increased by 23%, which is in concordance with physiological cerebral blood flow (CBF). Thus, CBF remains constant (50 ml/100 g brain per 1 min). In further CFD investigation, we calculated WSS, TAWSS, OSI, and pressure within the aneurysm.

A tangential force exerted onto the vessel wall by the blood flow, WSS, is suspected to play a role in aneurysm initiation, growth, and rupture. Intuitively, a high WSS can cause endothelial injury, with subsequent vessel wall remodeling and degeneration. In our analysis, we observed a decrease in WSS in both bypass models. The maximal value of WSS diminished by around 30 Pa in comparison with the control model and the corresponding relative differences were equal to a 30.2 and 35.7% reduction. The literature on WSS is ambiguous6, as it may depend on a model mesh density. Therefore, particularly in the region of the aneurysm neck, it should be interpreted in combination with other haemodynamic parameters and not alone. Moreover, maximal WSS may not be a reliable parameter as it only demonstrates the value in a given vertex of the mesh, whilst in other zones it may be lower. Thus, area-averaged WSS is likely to be a more appropriate haemodynamic marker. In our results, in both virtual bypass procedures, the area-averaged gradient of WSS (WSSG) was decreased up to 98% (from ~ 11,250 Pa/m to 197 and 307 Pa/m for Bypass 1 and Bypass 2). This indicates that haemodynamic parameters after bypass in both models change in favour of lower flow within the GIA, causing localized stagnation of blood. As noted in the literature, high WSSG promotes atheroma formation and aneurysm initiation and growth28,29. Thus, the opposite effect observed after bypass creates a haemodynamic environment favouring aneurysm repair.

As mentioned above, WSS cannot be considered alone without TAWSS, OSI and pressure. Only altogether, are these parameters reliable haemodynamic markers in GIA. OSI describes the amplitude of WSS changes and describes the tangential oscillation of force throughout the cardiac cycle. Thus, WSS influences the OSI value and high OSI reflects intense oscillation35 and gives information about disturbance of the flow field in the vessel wall36. The combination of the low WSS and high OSI reflects the residence time of blood near the vessel wall37, and indicates regions predisposed to plaque formation and blood stagnation29–31.

We also focused on TAWSS and noted a 95% decrease in the bypass models. However, the TAWSS vector is dependent on disturbed flow conditions, and may not be well-defined in terms of direction in complex transitional flows. Therefore, again, it should not be interpreted alone. As previously reported, regions of low TAWSS and high OSI can be considered independent haemodynamic risk factors as predictors for intraoperative aneurysm rupture38. Low TAWSS and high OSI have also been shown to be associated with aneurysmal thrombus formation39. These parameters point to regions with endothelial cell activation potential that correlate with areas of aneurysmal thrombus formation40.

We also analysed the pressure on the aneurysm wall. There was a reduction in the area-averaged pressure by approximately 80% in both the bypass models in comparison with the control model. The pressure directly correlated with the aneurysm volume; the lower the pressure, the lower the aneurysm volume, during both systolic and diastolic peaks (Fig. 9). Hence, with time, the bypass changes the haemodynamics in a way which leads to the aneurysm shrinking. This is supported by the clinical observations published by Maldaner et al.41 Additionally, from a haemodynamic perspective, the MCA branch to which the bypass is anastomosed is important. Our analysis showed that Bypass 2 (anastomosis to an M2 temporal branch of the MCA) offered a greater pressure reduction and therefore should be the first choice. In the Bypass 2 study, there were better haemodynamic conditions for spontaneous aneurysm repair, with a better environment for thrombus formation and aneurysm shrinkage.

Hence, we propose an additional tool that may be used in the preoperative planning stage of GIA treatment. It may be particularly valuable for complex large aneurysms, including those with fusiform/dissecting morphology, intra-aneurysmal calcifications or thrombosis, perforating arteries arising from the aneurysm, and in GIA that had been previously treated endovascularly42. The FSI stimulation models take into consideration all brain arteries to describe haemodynamic conditions in a way that is close to physiological states and allows calculation of WSS, OSI, TAWSS, and pressure, much more accurately than small models limited to only the aneurysm. This approach is particularly important in bypass revascularization and flow reversal, as we can calculate and observe in advance the blood flow changes in the whole brain. Importantly, each model is personalized, as it is patient specific being created based on individual CT angiography. Thus, in a complex aneurysm, when the parent artery should be sacrificed, with bypass revascularization, to achieve aneurysm occlusion and reduce the rupture and mortality risk, CFD analysis provides crucial information on two aspects necessary for successful treatment: the location of the bypass, and the handling of the aneurysm and parent artery. This may improve the treatment outcome.

The limitation of our study is that we performed only three patient-specific CFD investigations for one patient. To validate our results, there should be an analysis of a larger cohort. A broad range of CFD investigations could also serve as an additional statistical database. However, conducting such well-defined numerical simulations constitutes a very large and time-consuming workload. It consists of model generation and processing; generation of high-quality mesh which meets all the quality criteria (such as positive mesh independence test); simulation processing and calculation (calculation of each transient numerical simulation in this research took about two weeks), post-processing, preparation of clear illustrations, export of the most relevant haemodynamic parameters in numerical form and their manipulation to present them in table form. An additional obstacle is limited data storage—results of such simulations (with high-quality meshes) require a significant computer memory; numerical simulations performed for only four similar geometries could result in over 1.0 TB of data to be stored.

Conclusions

Our CFD investigations deliver patient-specific information about the haemodynamics of the brain blood flow, thus giving the mechanistic background and explanation for clinically observed results. Partial occlusion after revascularization will lead to flow reversal and sluggish blood flow in the aneurysmal sac. These changes in the flow dynamics will induce aneurysmal thrombosis and remodeling over time. This slow occlusion permits collateralization of perforators arising from the aneurysm while leading to occlusion of the aneurysm with volume reduction. All of these measures improve the natural history of complex GIA.

Supplementary Information

Supplementary Video 1.

Supplementary Video 2.

Supplementary Video 3.

Supplementary Video 4.

Supplementary Video 5.

Supplementary Video 6.

Supplementary Video 7.

Supplementary Video 8.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72591-w.

Acknowledgements

Karol Wiśniewski gratefully acknowledges financial support provided by the Polish National Agency for Academic Exchange (the Bekker Programme).

Author contributions

KW: Conceptualization, Investigation, Resources, Writing – original draft preparation; PR: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing – original draft preparation, Funding acquisition; ZT: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing – original draft preparation, Writing – review and editing; BP: Conceptualization, Writing – review and editing; AJ: Conceptualization, Writing – review and editing; AF: Conceptualization, Writing – review and editing; DO: Conceptualization, Methodology, Validation, Writing – original draft preparation, Writing – review and editing; DJ: Resources, Writing – original draft preparation; KJ: Resources, Writing – original draft preparation, Supervision, Funding acquisition. KD: Conceptualization, Writing – original draft preparation, LW: Conceptualization, Writing – review and editing; PV: Conceptualization, Writing – original draft preparation, AA: Conceptualization, Resources, Writing – original draft preparation;

Funding

This research was funded by National Centre for Research and Development grant number LIDER/12/0056/L-10/18/NCBR/2019. The sponsor had no role in the design or conduct of this research.

Data availability

Due to the use of potentially sensitive patient medical data in the studies presented here, the datasets used and analysed during the current study are available from the correspondent author upon reasonable request.

Competing interests

The authors declare that the article content was composed in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Ethics approval

The study was approved by the local Bioethical Committee at the Medical University of Lodz, application number RNN/119/15/KE. All experiments were performed in accordance with relevant guidelines and regulations. The study was designed in accordance with the Good Clinical Practice (GCP) guidelines and was conducted according to the principles of the Declaration of Helsinki. Informed consent was obtained from the participant prior to inclusion.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Greving JP Wermer MJ Brown RD Jr Morita A Juvela S Yonekura M Development of the PHASES score for prediction of risk of rupture of intracranial aneurysms: A pooled analysis of six prospective cohort studies Lancet Neurol. 2014 13 59 66 10.1016/S1474-4422(13)70263-1 24290159
Greving, J. P. et al. Development of the PHASES score for prediction of risk of rupture of intracranial aneurysms: A pooled analysis of six prospective cohort studies. Lancet Neurol. 13, 59–66 (2014).24290159 10.1016/S1474-4422(13)70263-1
2. Wiebers DO Whisnant JP Huston J III Meissner I Brown RD Jr Piepgras DG Unruptured intracranial aneurysms: Natural history, clinical outcome, and risks of surgical and endovascular treatment Lancet 2003 362 103 110 10.1016/S0140-6736(03)13860-3 12867109
Wiebers, D. O. et al. Unruptured intracranial aneurysms: Natural history, clinical outcome, and risks of surgical and endovascular treatment. Lancet 362, 103–110 (2003).12867109 10.1016/S0140-6736(03)13860-3
3. Dengler J Giant intracranial aneurysm study group. giant intracranial aneurysms: Natural history and 1 year case fatality after endovascular or surgical treatment J. Neurosurg. 2019 134 1 49 57 10.3171/2019.8.JNS183078 31812141
Dengler, J. et al. Giant intracranial aneurysm study group. giant intracranial aneurysms: Natural history and 1 year case fatality after endovascular or surgical treatment. J. Neurosurg. 134(1), 49–57. 10.3171/2019.8.JNS183078 (2019) (PMID: 31812141).31812141 10.3171/2019.8.JNS183078
4. Hara T Arai S Goto Y Takizawa T Uchida T Bypass surgeries in the treatment of cerebral aneurysms Acta Neurochir Suppl. 2016 123 57 64 10.1007/978-3-319-29887-0_8 27637629
Hara, T., Arai, S., Goto, Y., Takizawa, T. & Uchida, T. Bypass surgeries in the treatment of cerebral aneurysms. Acta Neurochir Suppl. 123, 57–64. 10.1007/978-3-319-29887-0_8 (2016) (PMID: 27637629).27637629 10.1007/978-3-319-29887-0_8
5. Shi X Qian H Fang T Zhang Y Sun Y Liu F Management of complex intracranial aneurysms with bypass surgery: A technique application and experience in 93 patients Neurosurg. Rev. 2015 38 109 120 10.1007/s10143-014-0571-5 25154436
Shi, X. et al. Management of complex intracranial aneurysms with bypass surgery: A technique application and experience in 93 patients. Neurosurg. Rev. 38, 109–120 (2015).25154436 10.1007/s10143-014-0571-5
6. Sforza DM Putman CM Cebral JR Computational fluid dynamics in brain aneurysms Int. J. Numer. Method Biomed. Eng. 2012 10.1002/cnm.1481 25364852
Sforza, D. M., Putman, C. M. & Cebral, J. R. Computational fluid dynamics in brain aneurysms. Int. J. Numer. Method Biomed. Eng.10.1002/cnm.1481 (2012).25364852 10.1002/cnm.1481
7. Wessels L Hecht N Faust K Schneider U Czabanka M Vajkoczy P Complete or partial parent artery sacrifice: Effect of vessel-occlusion strategies on complete obliteration of complex aneurysms World Neurosurg. 2021 147 e282 e292 10.1016/j.wneu.2020.12.050 33340722
Wessels, L. et al. Complete or partial parent artery sacrifice: Effect of vessel-occlusion strategies on complete obliteration of complex aneurysms. World Neurosurg. 147, e282–e292. 10.1016/j.wneu.2020.12.050 (2021).33340722 10.1016/j.wneu.2020.12.050
8. Polanczyk A Piechota-Polanczyk A Huk I Neumayer C Balcer J Strzelecki M Computational fluid dynamic technique for assessment of how changing character of blood flow and different value of hct influence blood hemodynamic in dissected aorta Diagnostics 2021 11 10 1866 10.3390/diagnostics11101866 34679564
Polanczyk, A. et al. Computational fluid dynamic technique for assessment of how changing character of blood flow and different value of hct influence blood hemodynamic in dissected aorta. Diagnostics 11(10), 1866 (2021).34679564 10.3390/diagnostics11101866
9. Reorowicz P Tyfa Z Obidowski D Wiśniewski K Stefańczyk L Jóźwik K Levy ML Blood flow through the fusiform aneurysm treated with the flow diverter stent–numerical investigations Biocybern. Biomed. Eng. 2022 42 1 375 390 10.1016/j.bbe.2022.02.008
Reorowicz, P. et al. Blood flow through the fusiform aneurysm treated with the flow diverter stent–numerical investigations. Biocybern. Biomed. Eng. 42(1), 375–390 (2022).10.1016/j.bbe.2022.02.008
10. Liu Y Jiang G Wang F An X Quantitative assessment of changes in hemodynamics after obliteration of large intracranial carotid aneurysms using computational fluid dynamics Front. Neurol. 2021 12 632066 10.3389/fneur.2021.632066 33995243
Liu, Y., Jiang, G., Wang, F. & An, X. Quantitative assessment of changes in hemodynamics after obliteration of large intracranial carotid aneurysms using computational fluid dynamics. Front. Neurol. 12, 632066 (2021).33995243 10.3389/fneur.2021.632066
11. Wiśniewski K Tyfa Z Reorowicz P Brandel MG Adel T Obidowski D Jóźwik K Levy ML Numerical flow experiment for assessing predictors for cerebrovascular accidents in patients with PHACES syndrome Sci. Rep. 2024 14 1 5161 10.1038/s41598-024-55345-6 38431727
Wiśniewski, K. et al. Numerical flow experiment for assessing predictors for cerebrovascular accidents in patients with PHACES syndrome. Sci. Rep. 14(1), 5161 (2024).38431727 10.1038/s41598-024-55345-6
12. Jodko D Jeckowski M Tyfa Z Fluid structure interaction versus rigid-wall approach in the study of the symptomatic stenosed carotid artery: Importance of wall compliance and resilience of loose connective tissue Int. J. Numer. Methods Biomed. Eng. 2022 38 8 e3630 10.1002/cnm.3630
Jodko, D., Jeckowski, M. & Tyfa, Z. Fluid structure interaction versus rigid-wall approach in the study of the symptomatic stenosed carotid artery: Importance of wall compliance and resilience of loose connective tissue. Int. J. Numer. Methods Biomed. Eng. 38(8), e3630 (2022).10.1002/cnm.3630
13. Shahzad H Wang X Ghaffari A Iqbal K Hafeez MB Krawczuk M Wojnicz W Fluid structure interaction study of non-Newtonian Casson fluid in a bifurcated channel having stenosis with elastic walls Sci. Rep. 2022 12 1 1 13 10.1038/s41598-022-16213-3 34992227
Shahzad, H. et al. Fluid structure interaction study of non-Newtonian Casson fluid in a bifurcated channel having stenosis with elastic walls. Sci. Rep. 12(1), 1–13 (2022).34992227 10.1038/s41598-022-16213-3
14. Carvalho PC Bazani MA Numerical analysis of a brain artery in ANSYS J. Braz. Soc. Mech. Sci. Eng. 2022 44 11 1 14 10.1007/s40430-022-03787-2
Carvalho, P. C. & Bazani, M. A. Numerical analysis of a brain artery in ANSYS. J. Braz. Soc. Mech. Sci. Eng. 44(11), 1–14 (2022).10.1007/s40430-022-03787-2
15. Jahed M Ghalichi F Farhoudi M Fluid-structure interaction of patient-specific Circle of Willis with aneurysm: Investigation of hemodynamic parameters Bio-med. Mater. Eng. 2018 29 3 357 368 10.3233/BME-181732
Jahed, M., Ghalichi, F. & Farhoudi, M. Fluid-structure interaction of patient-specific Circle of Willis with aneurysm: Investigation of hemodynamic parameters. Bio-med. Mater. Eng. 29(3), 357–368 (2018).10.3233/BME-181732
16. Kumar N Pai R Abdul Khader SM Khan SH Kyriacou PA Influence of blood pressure and rheology on oscillatory shear index and wall shear stress in the carotid artery J. Braz. Soc. Mech. Sci. Eng. 2022 44 11 1 16 10.1007/s40430-022-03792-5
Kumar, N., Pai, R., Abdul Khader, S. M., Khan, S. H. & Kyriacou, P. A. Influence of blood pressure and rheology on oscillatory shear index and wall shear stress in the carotid artery. J. Braz. Soc. Mech. Sci. Eng. 44(11), 1–16 (2022).10.1007/s40430-022-03792-5
17. Muraoka S Takagi R Araki Y Uda K Sumitomo M Okamoto S Nishihori M Izumi T Nakamura M Saito R Blood flow stagnation after treatment of a giant internal carotid artery aneurysm: A computed fluid dynamics analysis Sci. Rep. 2022 12 1 7283 10.1038/s41598-022-11321-6 35508591
Muraoka, S. et al. Blood flow stagnation after treatment of a giant internal carotid artery aneurysm: A computed fluid dynamics analysis. Sci. Rep. 12(1), 7283 (2022).35508591 10.1038/s41598-022-11321-6
18 Zhu Y Mirsadraee S Rosendahl U Pepper J Xu XY Fluid-structure interaction simulations of repaired type A aortic dissection: A comprehensive comparison with rigid wall models Front. Phys. 2022 10.3389/fphys.2022.913457
Zhu, Y., Mirsadraee, S., Rosendahl, U., Pepper, J. & Xu, X. Y. Fluid-structure interaction simulations of repaired type A aortic dissection: A comprehensive comparison with rigid wall models. Front. Phys.10.3389/fphys.2022.913457 (2022).10.3389/fphys.2022.913457
19. V. Carvalho, N. Rodrigues, R. A. Lima and S. Teixeira, “Numerical simulation of blood pulsatile flow in stenotic coronary arteries: The effect of turbulence modeling and non-Newtonian assumptions,” 2020 24th International Conference on Circuits, Systems, Communications and Computers (CSCC), Chania, Greece, pp. 112–116, (2020)
20. R. Tabe, F. Ghalichi, S. Hossainpour and K. Ghasemzadeh, “Numerical simulation of transitional blood flow in large arteries,” 2011 18th Iranian Conference of Biomedical Engineering (ICBME), Tehran, Iran, pp. 68-71, (2011).
21 Tyfa Z Reorowicz P Obidowski D Jóźwik K Influence of fluid rheology on blood flow haemodynamics in patient-specific arterial networks of varied complexity–in-silico studies Acta Mech. Automatica 2024 10.2478/ama-2024-0002
Tyfa, Z., Reorowicz, P., Obidowski, D. & Jóźwik, K. Influence of fluid rheology on blood flow haemodynamics in patient-specific arterial networks of varied complexity–in-silico studies. Acta Mech. Automatica10.2478/ama-2024-0002 (2024).10.2478/ama-2024-0002
22 Jodko DM Obidowski DS Reorowicz P Jóźwik K A two-stage model of an arteriovenous fistula maturation process Acta Bioeng. Biomech. 2020 10.37190/ABB-01571-2020-02 32868947
Jodko, D. M., Obidowski, D. S., Reorowicz, P. & Jóźwik, K. A two-stage model of an arteriovenous fistula maturation process. Acta Bioeng. Biomech.10.37190/ABB-01571-2020-02 (2020).32868947 10.37190/ABB-01571-2020-02
23. Obidowski D Reorowicz P Witkowski D Sobczak K Jóźwik K Methods for determination of stagnation in pneumatic ventricular assist devices Artif. Organs. 2018 41 653 663 10.1177/0391398818790204
Obidowski, D., Reorowicz, P., Witkowski, D., Sobczak, K. & Jóźwik, K. Methods for determination of stagnation in pneumatic ventricular assist devices. Artif. Organs. 41, 653–663 (2018).10.1177/0391398818790204
24. Xing CY Tarumi T Liu J Zhang Y Turner M Riley J Tinajero CD Yuan LJ Zhang R Distribution of cardiac output to the brain across the adult lifespan J. Cereb. Blood Flow Metab. 2017 37 8 2848 2856 10.1177/0271678X16676826 27789785
Xing, C. Y. et al. Distribution of cardiac output to the brain across the adult lifespan. J. Cereb. Blood Flow Metab. 37(8), 2848–2856 (2017).27789785 10.1177/0271678X16676826
25. Willie CK Smith KJ Fuelling the exercising brain: A regulatory quagmire for lactate metabolism J. physiol. 2011 589 4 779 10.1113/jphysiol.2010.204776 21486846
Willie, C. K. & Smith, K. J. Fuelling the exercising brain: A regulatory quagmire for lactate metabolism. J. physiol. 589(4), 779 (2011).21486846 10.1113/jphysiol.2010.204776
26. Lantz BM Foerster JM Link DP Holcroft JW Regional distribution of cardiac output: normal values in man determined by video dilution technique Am. J. Roentgenol. 1981 137 5 903 907 10.2214/ajr.137.5.903 7027775
Lantz, B. M., Foerster, J. M., Link, D. P. & Holcroft, J. W. Regional distribution of cardiac output: normal values in man determined by video dilution technique. Am. J. Roentgenol. 137(5), 903–907 (1981).7027775 10.2214/ajr.137.5.903
27. Ovsenik A Podbregar M Fabjan A Cerebral blood flow impairment and cognitive decline in heart failure Brain Behav. 2021 11 6 e02176 10.1002/brb3.2176 33991075
Ovsenik, A., Podbregar, M. & Fabjan, A. Cerebral blood flow impairment and cognitive decline in heart failure. Brain Behav. 11(6), e02176 (2021).33991075 10.1002/brb3.2176
28. Holland, Watton, and Ventikos, “5.17 - Biological Fluid Mechanics: Integrative and Multiscale Computational Modeling,” in Comprehensive Biotechnology (Second Edition), Second Edi., Moo-Young, Ed. Academic Press, pp. 203–216 (2011)
29. Zuleger P Valavanis, and Kollias, “Combining magnetic resonance measurements with numerical simulations—Extracting blood flow physiology information relevant to the investigation of intracranial aneurysms in the circle of Willis” Int. J. Heat Fluid Flow 2010 31 6 1032 1039 10.1016/j.ijheatfluidflow.2010.07.003
Zuleger, P. Valavanis, and Kollias, “Combining magnetic resonance measurements with numerical simulations—Extracting blood flow physiology information relevant to the investigation of intracranial aneurysms in the circle of Willis”. Int. J. Heat Fluid Flow 31(6), 1032–1039 (2010).10.1016/j.ijheatfluidflow.2010.07.003
30. DiCarlo AL Holdsworth DW Poepping TL Study of the effect of stenosis severity and non-Newtonian viscosity on multidirectional wall shear stress and flow disturbances in the carotid artery using particle image velocimetry Med. Eng. Phys. 2019 65 8 23 10.1016/j.medengphy.2018.12.023 30745099
DiCarlo, A. L., Holdsworth, D. W. & Poepping, T. L. Study of the effect of stenosis severity and non-Newtonian viscosity on multidirectional wall shear stress and flow disturbances in the carotid artery using particle image velocimetry. Med. Eng. Phys. 65, 8–23 (2019).30745099 10.1016/j.medengphy.2018.12.023
31. Moradicheghamahi J Sadeghiseraji J Jahangiri M Numerical solution of the Pulsatile, non-Newtonian and turbulent blood flow in a patient specific elastic carotid artery Int. J. Mech. Sci. 2019 150 393 403 10.1016/j.ijmecsci.2018.10.046
Moradicheghamahi, J., Sadeghiseraji, J. & Jahangiri, M. Numerical solution of the Pulsatile, non-Newtonian and turbulent blood flow in a patient specific elastic carotid artery. Int. J. Mech. Sci. 150, 393–403 (2019).10.1016/j.ijmecsci.2018.10.046
32. Wisniewski T Tyfa, Reorowicz, and Bobeff, “porous media computational fluid dynamics and the role of the first coil in the embolization of ruptured intracranial aneurysms” J. Clin. Med. 2021 10 7 1348 10.3390/jcm10071348 33805169
Wisniewski, T. Tyfa, reorowicz, and bobeff, “porous media computational fluid dynamics and the role of the first coil in the embolization of ruptured intracranial aneurysms”. J. Clin. Med. 10(7), 1348 (2021).33805169 10.3390/jcm10071348
33 Maldaner N Giant intracranial aneurysms treated by surgical strategies other than direct clipping Acta Neurochir. (Wien). 2015 157 7 1117 1123 10.1007/s00701-015-2448-y 26002711
Maldaner, N. et al. Giant intracranial aneurysms treated by surgical strategies other than direct clipping. Acta Neurochir. (Wien). 157(7), 1117–1123. 10.1007/s00701-015-2448-y (2015).26002711 10.1007/s00701-015-2448-y
34 Dengler J Giant intracranial aneurysm study group giant intracranial aneurysms: Natural history and 1 year case fatality after endovascular or surgical treatment J. Neurosurg. 2019 134 1 49 57 10.3171/2019.8.JNS183078 31812141
Dengler, J. et al. Giant intracranial aneurysm study group giant intracranial aneurysms: Natural history and 1 year case fatality after endovascular or surgical treatment. J. Neurosurg. 134(1), 49–57. 10.3171/2019.8.JNS183078 (2019).31812141 10.3171/2019.8.JNS183078
35. Wang J Liu J Zhao C Yang X Li M Hemodynamics in ruptured intracranial aneurysms with known rupture points World Neurosurg. 2018 118 e721 e726 10.1016/j.wneu.2018.07.026 30010065
Wang, J., Liu, J., Zhao, C., Yang, X. & Li, M. Hemodynamics in ruptured intracranial aneurysms with known rupture points. World Neurosurg. 118, e721–e726 (2018).30010065 10.1016/j.wneu.2018.07.026
36. Xiang J Hemodynamic-morphologic discriminants for intracranial aneurysm rupture Stroke 2011 42 144 152 10.1161/STROKEAHA.110.592923 21106956
Xiang, J. et al. Hemodynamic-morphologic discriminants for intracranial aneurysm rupture. Stroke 42, 144–152 (2011).21106956 10.1161/STROKEAHA.110.592923
37. Himburg HA Friedman Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability Am J. Physiol. Circ. Physiol. 2004 286 5 H1916 H1922 10.1152/ajpheart.00897.2003
Himburg, H. A. et al. Friedman Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability Am. J. Physiol. Circ. Physiol. 286(5), H1916–H1922 (2004).10.1152/ajpheart.00897.2003
38. Liu Q Jiang P Wu J Gao B Wang S The morphological and hemodynamic characteristics of the intraoperative ruptured aneurysm Front. Neurosci. 2019 13 233 10.3389/fnins.2019.00233 30971874
Liu, Q., Jiang, P., Wu, J., Gao, B. & Wang, S. The morphological and hemodynamic characteristics of the intraoperative ruptured aneurysm. Front. Neurosci. 13, 233. 10.3389/fnins.2019.00233 (2019).30971874 10.3389/fnins.2019.00233
39. Kelsey LJ Powell JT Norman PE Miller K Doyle BJ A comparison of hemodynamic metrics and intraluminal thrombus burden in a common iliac artery aneurysm Int. J. Numer. Method Biomed. Eng. 2017 33 e2821 10.1002/cnm.2821
Kelsey, L. J., Powell, J. T., Norman, P. E., Miller, K. & Doyle, B. J. A comparison of hemodynamic metrics and intraluminal thrombus burden in a common iliac artery aneurysm. Int. J. Numer. Method Biomed. Eng. 33, e2821. 10.1002/cnm.2821 (2017).10.1002/cnm.2821
40. Ong C Xiong F Kabinejadian F Praveen Kumar G Cui F Chen G Hemodynamic analysis of a novel stent graft design with slit perforations in thoracic aortic aneurysm J. Biomech. 2019 85 210 217 10.1016/j.jbiomech.2019.01.019 30704763
Ong, C. et al. Hemodynamic analysis of a novel stent graft design with slit perforations in thoracic aortic aneurysm. J. Biomech. 85, 210–217. 10.1016/j.jbiomech.2019.01.019 (2019).30704763 10.1016/j.jbiomech.2019.01.019
41. Maldaner N Guhl S Mielke D Musahl C Schmidt NO Wostrack M Rüfenacht DA Vajkoczy P Dengler J Giant intracranial aneurysm study group changes in volume of giant intracranial aneurysms treated by surgical strategies other than direct clipping Acta Neurochir. (Wien). 2015 10.1007/s00701-015-2448-y 26395008
Maldaner, N. et al. Giant intracranial aneurysm study group changes in volume of giant intracranial aneurysms treated by surgical strategies other than direct clipping. Acta Neurochir. (Wien).10.1007/s00701-015-2448-y (2015).26395008 10.1007/s00701-015-2448-y
42. Esposito G Regli L Surgical decision-making for managing complex intracranial aneurysms Acta Neurochir. Suppl. 2014 119 3 11 10.1007/978-3-319-02411-0_1 24728625
Esposito, G. & Regli, L. Surgical decision-making for managing complex intracranial aneurysms. Acta Neurochir. Suppl. 119, 3–11 (2014).24728625 10.1007/978-3-319-02411-0_1
