Flow Dynamics in Brain Aneurysms: A Review of Computational and Experimental Studies

Abstract

A brain aneurysm is a structural deterioration of the arterial wall in the brain, resulting in the formation of a bulge in or ballooning of a blood vessel. Around 3–5% of the global population is affected by brain aneurysms, wherein only a small fraction results in rupture. Although an unruptured aneurysm is typically asymptomatic and not immediately life threatening, it poses a potential risk of rupture, which can lead to severe health complications or mortality. Therefore, it is crucial to detect and treat aneurysms during the unruptured phase. Moreover, a comprehensive understanding of the flow dynamics within the aneurysm and its parent artery is essential for accurate diagnosis and the prevention of aneurysm recurrence. While prior reviews have focused on computational fluid dynamics (CFD) studies on brain aneurysms, particularly patient-specific models from studies conducted over a decade ago, a more recent review is necessary. Additionally, reviewing various studies on the fluid dynamic behavior of treated aneurysms is crucial. Thus, the advancements in both experimental and computational studies on brain aneurysms must be explored to better understand their underlying fluid flow mechanisms and to develop robust treatment strategies. This review aims to summarize the different types of brain aneurysms, the screening and treatment processes, the key hemodynamic factors, and the fluid dynamic characteristics observed in aneurysms before and after treatment.

1. Introduction

Brain aneurysms, also known as cerebral aneurysms, are a cerebrovascular disease that forms a thin or weak spot in an artery in the brain, leading to bulging or ballooning of a blood vessel [1,2]. It happens due to disease, injury, or abnormality during birth [2]. Inflammation is the main reason behind brain aneurysms that alter the function of vascular smooth muscle cells (VSMCs), by causing endothelial injury. VSMC disfunction causes internal elastic lamina degradation, resulting in the disruption of collagen synthesis and extracellular matrix remodeling. These conditions enhance the activity of protein-breaking enzymes or proteases, accelerating the breakdown and weakening of the arterial wall, ultimately causing aneurysm formation, growth, and rupture [3].

Brain aneurysms typically occur in individuals aged between 35 and 60 [4]. Globally, approximately 5% of the adult population is affected by this cerebrovascular disease [5]. It was found by a clinical study that almost 50% of brain aneurysms are identified after they have ruptured [6]. In the US, around six million people have this condition. However, most brain aneurysms remain unruptured [4]. In general, most of these unruptured aneurysms tend to stabilize over time and do not lead to clinical consequences [7]. It was found that spontaneous thrombosis occurs in approximately 9–13% of cerebral aneurysms, wherein, for giant aneurysms, the likelihood of thrombosis increases with the aneurysm size, with reported rates ranging between 52 and 83%. Although partial healing or thrombus formation may occur in giant aneurysms, complete healing, as well as the disappearance of the aneurysm is rare [8]. While natural healing of an aneurysm can occur, unruptured aneurysms still pose a potential risk of rupture or blood leakage into the surrounding tissue, which can cause paralysis, permanent nerve damage, brain injury, and death [2,9]. Thus, treating an unruptured aneurysm in some cases is crucial to prevent future rupture. The treatment of unruptured aneurysms depends on the size and location of the lesion [5]. Moreover, treating an unruptured aneurysm is highly challenging due to the potential risk of rupture during surgery [10]. Various procedures have been utilized for aneurysm treatment, such as using flow diversion [11,12,13], bypass surgery [14,15], coil embolization [16,17], and surgical clipping [16,18]. These procedures involve a potential risk of morbidity [19]. For instance, surgical clipping of an unruptured aneurysm results in a mortality of 0.5–2.6% and a morbidity of 4.1–10.9% [20]. Poor outcomes are associated with the location of the aneurysm in the posterior circulation and the size of the aneurysm, particularly giant aneurysms [21]. A study performed by Nariai et al. that analyzed the outcomes of endovascular treatment of unruptured anterior communicating artery (AcomA) aneurysms found that the permanent morbidity rate was fairly minor (1%). However, the overall prevalence of procedure-related complications was ~19%, with thromboembolic complications, hemorrhagic complications, and intraprocedural aneurysm bleeding rates of 12.5%, 6.3%, and 3.1%, respectively. The study also found that an aneurysm size greater than 10 mm, a neck width greater than 4 mm, and the use of a stent, were each individually linked to stroke [22]. Irregularly shaped unruptured aneurysms may require earlier interventions, although their size did not reach the typical threshold for treatment [23]. Taken together, it is imperative to assess the risk of aneurysm rupture and the postoperative complications associated with surgery, which may result in permanent nerve damage or even mortality. Several factors must be considered when assessing the possible risk of aneurysm rupture or surgical complications, including the aneurysm’s size, shape, and location, the patient’s age and sex, as well as any underlying medical conditions (e.g., kidney disease) [24].

The flow dynamics in brain aneurysms before and after treatment, as well as the impact of hemodynamic properties on aneurysm growth and rupture, are topics that are already well-studied. Consequently, numerous reviews have already been performed on these topics. For instance, reviews have been conducted on various techniques and methods for assessing aneurysm growth and the risk of rupture, such as various imaging types, machine learning, deep learning, and computational approaches [25,26,27,28,29]. Other reviews highlight various treatment methods and their impact on hemodynamics, the healing of brain aneurysms, and the likelihood of retreatment [30,31,32,33,34]. Reviews on the role of hemodynamic properties on the aneurysm size, shape, growth, and rupture at different locations on the artery walls have also been conducted by different authors [35,36,37,38]. A review focusing on the computational fluid dynamics (CFD) of aneurysm growth and rupture, as well as the impact of hemodynamic factors on aneurysm growth and rupture, was conducted around a decade ago [28]. Additionally, no existing review has incorporated experimental outcomes on the fluid flow dynamics in aneurysms and their parent artery.

Significant advancements in this field since these reviews were conducted necessitate an updated review to reflect recent progress and developments in this area. This review summarizes the various types of aneurysms, hemodynamic factors, diagnostic processes, and fluid flow characteristics of brain aneurysms before and after treatment, using the available experimental and computational literature.

2. Types of Brain Aneurysms

Brain aneurysms are classified according to their relationship with nearby blood vessels within either the anterior or posterior circulation [39]. Additionally, other features, such as the etiology, size, shape, location, and branching, are vital for aneurysm classification [39]. The most common types of aneurysms are saccular and fusiform aneurysms [2,39]. Other types of aneurysms include mycotic, pseudo (dissecting), and blister aneurysms [40,41]. Figure 1 shows the different types of aneurysms, with the subsequent sections describing each type in detail.

2.1. Saccular Aneurysm (SA)

A saccular aneurysm (SA) is a berry or pouch-like pattern and develops as a thin-walled sac that protrudes from the arteries of the circle of Willis or its major branches [40,42]. It is a pathological dilation of intracranial arteries, due to a decreasing resistivity to withstand hemodynamic pressure and distension [43]. Approximately 90% of cerebral aneurysms are saccular, occurring in approximately 46–70% of the entire pediatric population [40,44]. While most SAs are stable, a few can rupture, because of changes in their structure, such as decellularization, matrix degeneration, or the formation of a disorganized blood clot [43]. Due to the aberrant blood flow associated with the pouch-like shape, cytotoxic and proinflammatory substances accumulate in the aneurysm wall, leading to decellularization and degeneration of the SA wall, which in turn promotes rupture [43]. SAs can be categorized based on their location, aneurysm size, and neck width, as shown in Figure 2.

2.2. Fusiform Aneurysm (FA)

A fusiform aneurysm (FA) is a severe form of artery widening, which can lead to serious complications, such rupture and thrombi formation [40,45]. Although rupture is uncommon, it can cause ischemia [40]. There are two main causes that may lead to this type of aneurysm: dissection and atherosclerosis. Other possible causes are the metabolic disorder of collagen and elastin, infections, neoplastic invasion of the arterial wall, and iatrogenesis [46]. Only 5% of aneurysms are of the fusiform type, and they typically occur in older patients [39,40]. A FA can be classified based on whether a side branch occurrence is absent (simple) or present (complex), with the complex type being less common compared to the simple type (Figure 2). The blood flow and vessel wall characteristics of these two types of FAs are different due to the presence or absence of branches, as well as the locations of the branches [39].

2.3. Mycotic Aneurysm (MA)

A mycotic or infected aneurysm (MA) involves the dilation of the artery wall caused by an infection, typically due to bacterial pathogens [47]. It usually develops due to a preexisting infection in the artery wall, rather than direct trauma [47]. MAs are rare, accounting for almost 0.6% of aneurysms in western countries [48]. However, they have a higher risk of rupture compared to uninfected aneurysms, which leads to high morbidity and mortality [48,49]. The treatments for MAs remain unclear because of the non-specific nature of the clinical presentations and the lack of clear diagnostic criteria [49].

2.4. Pseudo Aneurysm (PA)

A pseudo aneurysm (PA), also known as a dissecting aneurysm, is a rare, but well-known, condition that can occur at any arterial site, where the blood vessel expands, particularly at the outer wall, due to arterial puncture [50]. This causes localized turbulent blood flow, leading to the formation of a hematoma with a neck, which does not close naturally after reaching a specific size [50]. It usually occurs due to trauma, mycotic infection, the tearing of blood vessels, and congenital collagen deficiency [51]. This type of aneurysm has a higher risk of rupture, due to the inadequate support of the artery wall and, therefore, requires immediate treatment [52].

2.5. Blister Aneurysm (BA)

A blister aneurysm (BA) is a small dome-shaped bulge in the parent vessel, whose wall is fragile, consisting of a thin layer of adventitia and a poorly defined broad-based neck [53]. It usually forms on the internal carotid artery. The treatment of BAs through surgery is typically difficult, with a risk of a rupture of up to 50% [54]. The flow diversion technique to treat BAs has garnered attention due to its high success rate in treating the target affected wall, without manipulating the fragile fibrous wall [54].

Figure 2. Classification of brain aneurysms. The information is taken from the following references [39,40,53,55].

Figure 2. Classification of brain aneurysms. The information is taken from the following references [39,40,53,55].

3. Diagnostic Methods for Brain Aneurysms

Brain aneurysms can be treated in many ways, but the first step is to identify the brain aneurysms and their condition (whether unruptured or ruptured). The diagnostic methods and steps are detailed below.

3.1. Screening of Brain Aneurysms

Various screening processes are used to detect brain aneurysms depending on the patient’s condition, as well as the state and severity of the aneurysm. Such methods include a computed tomography (CT) scan, computed tomographic angiography (CTA), magnetic resonance imaging (MRI), magnetic resonance angiography (MRA), transcranial doppler ultrasonography (TCD), digital subtraction angiography (DSA), and a spinal tap [2,56,57,58]. Each of these methods is described in detail below, with Table 1 summarizing the roles, advantages, disadvantages, and limitations of each process:

• A CT scan is a specialized X-ray that provides a rapid diagnosis of aneurysm rupture by producing 2-D images [59]. It helps identify any bleeding around the brain, as well as the location of brain aneurysms [2,59]. While CT scans are rapid and painless, they do not always identify brain hemorrhage, nor do they provide information about the size and pattern of the brain aneurysm [59];
• CTA is a more advanced screening process, which combines the regular CT scan with the injection of a contrast dye into the vein or artery. As the dye travels through the vein, an image is captured by the CT scan to observe the blood flow in the region, providing a valuable insight into brain hemorrhage and aneurysm rupture [2,60];
• MRI is another fast and non-invasive screening process to identify brain aneurysms [2]. The image quality and visualization of an aneurysm wall depends on the magnetic field strength. For instance, 3T MRI (3 Tesla MRI) provides a 57% lower image resolution and a 15% thicker appearance of the aneurysm wall compared to 7T MRI. High spatial resolution MRI images can identify various biological processes occurring in the aneurysm wall and can help develop post-processing protocols [61];
• MRA is also an advanced, non-invasive screening process, which does not involve radiation exposure [62]. In addition to the detection of aneurysms, it can also provide information about the size, shape, and hemodynamic flow characteristics of aneurysms [62]. Some MRA processes require the injection of a contrast dye; however, this dye is lower in quantity and less toxic compared to the CTA contrast dye [2,63];
• DSA is a gold standard digital angiography technique for detecting aneurysms as small as 0.5 mm [64] and is more effective at identifying false positive aneurysms compared to other non-invasive techniques [65]. However, it is an invasive procedure requiring sedation and may cause neurological complications [66];
• TCD is a non-invasive, inexpensive screening process that is used to detect vasospasms (VSPs) associated with aneurysm rupture or subarachnoid hemorrhage. The detection of VSPs is an indication of severe aneurysm rupture or bleeding between the brain and its covering. It can also help monitor hemodynamic changes in the intracerebral vasculature due to an aneurysm rupture [67];
• A spinal tap or lumbar puncture is an invasive method used to detect ruptured aneurysms, which may not be detected by a CT scan [68]. If a subarachnoid hemorrhage occurs, red blood cells will be present in the cerebrospinal fluid (CSF). Performing a spinal tap to test the CSF allows for the identification of such a subarachnoid hemorrhage associated with aneurysm rupture [68,69].

Table 1. Summary of roles, advantages, disadvantages, and limitations of various screening processes.

Screening Method	What It Identifies	Advantages	Disadvantages and Limitations
CT scan	Location of aneurysm [59] Blood leakage [2]	Highly accurate in terms of detection [59] Non-invasive process [59] Low risk during diagnosis [2] Fast and painless test [2]	Cannot distinguish aneurysm size and shape [2,59] Relatively high radiation dose compared to MRI [70]
MRI	Location of aneurysm [59] Blood leakage [2]	Better image quality than other imaging techniques [71] Non-invasive process [59] Low risk during diagnosis [2,72] Fast and painless test [2] Shorter assessment time than a CT scan [71] Multiplanar imaging is possible [72]	Actual scanning process is more complicated and time consuming than a CT scan [70] Cannot distinguish aneurysm size and shape [2,59] Not suitable for patients with claustrophobia [72]
CTA	Location of aneurysm [59] Size, shape, and orientation of aneurysm [2,59]	High quality imaging [59] Relatively non-invasive [73] High accuracy in measuring aneurysm size and shape [60] Reduced duration of contrast enhancement [63] Reduced toxicity and cost of contrast [63] Able to detect multiple aneurysms [62]	High level of radiation [56] Requires contrast injection [56] Low detection sensitivity for aneurysms smaller than 3 mm (~30%) [74,75]
MRA	Location of aneurysm [62] Size, shape, and orientation of aneurysm [2,62] Hemodynamic flow characteristics of aneurysm [62]	Preferred diagnostic method for asymptomatic patients [62] Non-invasive [73] No radiation exposure [59] Requires lower amount of contrast dye than CTA [2,63] Contrast dye is less toxic compared to CTA [2,63] Able to detect multiple aneurysms [62] High detection sensitivity for aneurysms smaller than 3 mm with 3T MRA (~85–93%) [62]	Poor detection sensitivity (~30%) for small aneurysms, similar to CTA [75] Poor resolution compared to CTA [73] Not suitable for clinically ill patients [62]
TCD	Detects severe aneurysms and subarachnoid hemorrhage [67] Monitors hemodynamic changes in the intracerebral vasculature due to aneurysm rupture [67]	Non-invasive method [67] Inexpensive screening process [67] Can be repeated when necessary [76] High sensitivity in regard to detection on the middle cerebral artery (MCA) [77]	High dependency on experts [76] Provides information on global flow velocity [76] Low sensitivity in regard to detection on the anterior and posterior cerebral artery [77]
DSA	Detects aneurysms [68] Detects the size, shape, and orientation of the aneurysm Flow dynamics [62,64]	Considered a gold standard [68] Can detect very small aneurysms (~0.5 mm) [64] High sensitivity and resolution [73] Highly effective in detecting false unruptured aneurysms with a size below 4 mm [65] Less expensive than other conventional angiography techniques [78]	Invasive process [65] Relatively high risk of neurological complications [66] Requires a high amount of injected contrast dye and a longer examination duration for obtaining multiple rotational and oblique views [62] Potential minor complications in regard to hematoma and fistula formation at the puncture site [62]
Spinal tap or LP	Identifies ruptured aneurysms [68]	Detects aneurysms that are not identified by a CT scan [68] Low severity of potential complications [79]	Invasive process [68] Accuracy of finding aneurysms is debatable [80]

Table 1. Summary of roles, advantages, disadvantages, and limitations of various screening processes.

Screening Method	What It Identifies	Advantages	Disadvantages and Limitations
CT scan	Location of aneurysm [59] Blood leakage [2]	Highly accurate in terms of detection [59] Non-invasive process [59] Low risk during diagnosis [2] Fast and painless test [2]	Cannot distinguish aneurysm size and shape [2,59] Relatively high radiation dose compared to MRI [70]
MRI	Location of aneurysm [59] Blood leakage [2]	Better image quality than other imaging techniques [71] Non-invasive process [59] Low risk during diagnosis [2,72] Fast and painless test [2] Shorter assessment time than a CT scan [71] Multiplanar imaging is possible [72]	Actual scanning process is more complicated and time consuming than a CT scan [70] Cannot distinguish aneurysm size and shape [2,59] Not suitable for patients with claustrophobia [72]
CTA	Location of aneurysm [59] Size, shape, and orientation of aneurysm [2,59]	High quality imaging [59] Relatively non-invasive [73] High accuracy in measuring aneurysm size and shape [60] Reduced duration of contrast enhancement [63] Reduced toxicity and cost of contrast [63] Able to detect multiple aneurysms [62]	High level of radiation [56] Requires contrast injection [56] Low detection sensitivity for aneurysms smaller than 3 mm (~30%) [74,75]
MRA	Location of aneurysm [62] Size, shape, and orientation of aneurysm [2,62] Hemodynamic flow characteristics of aneurysm [62]	Preferred diagnostic method for asymptomatic patients [62] Non-invasive [73] No radiation exposure [59] Requires lower amount of contrast dye than CTA [2,63] Contrast dye is less toxic compared to CTA [2,63] Able to detect multiple aneurysms [62] High detection sensitivity for aneurysms smaller than 3 mm with 3T MRA (~85–93%) [62]	Poor detection sensitivity (~30%) for small aneurysms, similar to CTA [75] Poor resolution compared to CTA [73] Not suitable for clinically ill patients [62]
TCD	Detects severe aneurysms and subarachnoid hemorrhage [67] Monitors hemodynamic changes in the intracerebral vasculature due to aneurysm rupture [67]	Non-invasive method [67] Inexpensive screening process [67] Can be repeated when necessary [76] High sensitivity in regard to detection on the middle cerebral artery (MCA) [77]	High dependency on experts [76] Provides information on global flow velocity [76] Low sensitivity in regard to detection on the anterior and posterior cerebral artery [77]
DSA	Detects aneurysms [68] Detects the size, shape, and orientation of the aneurysm Flow dynamics [62,64]	Considered a gold standard [68] Can detect very small aneurysms (~0.5 mm) [64] High sensitivity and resolution [73] Highly effective in detecting false unruptured aneurysms with a size below 4 mm [65] Less expensive than other conventional angiography techniques [78]	Invasive process [65] Relatively high risk of neurological complications [66] Requires a high amount of injected contrast dye and a longer examination duration for obtaining multiple rotational and oblique views [62] Potential minor complications in regard to hematoma and fistula formation at the puncture site [62]
Spinal tap or LP	Identifies ruptured aneurysms [68]	Detects aneurysms that are not identified by a CT scan [68] Low severity of potential complications [79]	Invasive process [68] Accuracy of finding aneurysms is debatable [80]

3.2. Treatment Methods

The factors that determine the appropriate method for the treatment of aneurysms and to prevent their rupture include the shape, size, and location of the aneurysm. Each technique includes further refinements aimed at improving treatment outcomes and reducing the need for retreatment. These treatment methods are briefly summarized as follows.

3.2.1. Surgical Techniques

Direct surgery for the treatment of an intracranial aneurysm (IA) was first established in the 1930s, when Sir Norman Dott successfully treated a ruptured aneurysm by opening up the brain or cranial cavity to access the aneurysm and reinforcing it using a muscle graft taken from the patient’s thigh [81]. Other surgical treatments were developed over the following decades. For example, aneurysm clipping, first applied by Walter Dandy in 1937 [81], involves the process of opening the skull, locating the aneurysm, and then ligating the aneurysm neck using single or multiple clips to prevent blood flow into the aneurysm. The success of the clipping process is dependent on effectively exposing the skull in order to visualize the aneurysm neck clearly [82]. Additionally, understanding the anatomy is crucial for selecting the optimal surgical approach, which could potentially impact the intraoperative exposure of the aneurysm and nearby blood vessels and post-surgical outcomes [83]. For instance, microsurgical clipping is the preferred method to treat aneurysms in the middle cerebral artery (MCA), due to ease of surgical access, and studies have shown promising outcomes for both ruptured and unruptured aneurysms [84,85]. This method is also preferrable for treating aneurysms with complex shapes, wherein endovascular techniques are not effective [86]. For instance, microsurgical repair is a viable option for treating vertebrobasilar dissecting (VBD) aneurysms, and the success rate is generally satisfactory, reaching 95% [87]. Sriamornrattanakul et al. [88] reviewed recent studies on the anterior temporal approach for clipping supraclinoid internal carotid artery (ICA) aneurysms with posterior projection to achieve better visualization of the aneurysm neck and related branches. They found that this new approach is safe and effectively clips the aneurysm, with a high success rate. The same technique used in clipping upper basilar artery aneurysms also showed promising success rates [89]. Other surgical clipping approaches have been employed depending on the type, size, shape, and location of the aneurysms. These approaches include the transorbital approach for MCA and ICA aneurysms [90,91]; the entire orifice blocking-assisted microsurgical approach for intracranial giant wide-neck paraclinoid aneurysms [92]; the keyhole approach for ICA aneurysms [93]; one-stage multiple craniotomies (OSMCs) for multiple cerebral aneurysms [94]; cotton-assisted clipping for very small intracranial aneurysms (IAs) [95]; and the mass reduction clipping technique for giant complex MCA aneurysms [96]. Although these studies have produced promising results, further research is required to evaluate the long-term durability of these treatments to reduce the need for repeated surgery and assess the potential for aneurysm growth.

3.2.2. Embolization Technique

The embolization technique, also known as the simple coil embolization process, is a minimally invasive procedure, whereby a platinum coil is inserted through a microcatheter to fill the aneurysm [97]. This promotes blood clotting, effectively sealing the aneurysm from active blood circulation to prevent rupture [82,97]. It is safer and significantly more effective than surgical clipping, with complication rates almost half that of surgical clipping [97,98]. Common complications associated with coil embolization are thromboembolic events, aneurysmal perforation by the microcatheter or coil, parent artery obstruction, coil misposition and migration, and coil blocking [97,99]. Modifications to this simple embolization process aim to alleviate these complications and address the challenges associated with treating aneurysms of different sizes and shapes, for example, the double catheter technique, balloon-assisted coiling, stent-assisted coiling, and utilizing an intermediate catheter [82]. Each of these modifications is described in detail as follows:

• The double catheter technique, suitable for treating wide-neck aneurysms, is a much easier process compared to stent- and ballon-assisted coiling. In regard to this procedure, two microcatheters of different shapes are inserted into different portions of the aneurysm to obtain a stable frame. This technique can also be used for aneurysms with a daughter sac, branch-incorporated aneurysms, and elongated aneurysms, wherein the coil insertion process for each condition is different [100]. Although the double catheter technique has a high recurrence rate, this technique is much safer and easier for the treatment of recurrent aneurysms compared to using a flow-diverting stent. Due to the irregular shape of the recanalized cavity inside preexisting coils, it is challenging to form a stable frame at the initial stage of coiling. Thus, it is recommended to use the double catheter technique, wherein a small-diameter coil, based on the maximum length of the recanalized aneurysm, is selected for the first coil, and the diameter of the second coil is kept nearly the same as the first coil. This approach helps create a safe and stable frame within the recanalized cavity [101];
• The balloon-assisted coiling process is also used for complex wide-necked aneurysms, where a balloon is inflated across the aneurysm neck to create enough space for the coil to be inserted [102,103]. The balloon is removed upon insertion of the coil into the aneurysm. Both single-lumen and double-lumen balloons may be deployed, with the double-lumen balloon enabling the option of placing a stent, along with a coil, into the aneurysm. Both the single- and double-lumen balloon procedures have similar rates of potential complications, with most studies reporting low mortality and morbidity risks, except for the study by Sluzewski et al. (14.1%) [104,105,106,107]. However, in general, this process carries a higher risk of ischemic and hemorrhagic complications compared to stent-assisted coiling for the acute management of ruptured aneurysms [108];
• Stent-assisted coiling is suitable for wider neck, fusiform, and dissecting aneurysms, as well as aneurysms with irregular or complex geometry. The stent is placed at the neck, which allows the coil to be fully inserted into the aneurysm without protruding into the main blood vessel. Additionally, the stent diverts blood flow towards the aneurysm and facilitates intra-aneurysm stasis and thrombosis [109]. Stent overlapping (multiple stents are placed in a way that results in their ends overlapping each other) can also be applied to prevent coil protrusion, stent malposition, and in-stent blood clotting [110]. Studies have shown that stent-assisted coiling exhibits higher occlusion rates compared to simple coiling without a stent [111] and is much safer and effective, particularly for unruptured aneurysms. While complications are more likely when used to treat ruptured aneurysms [112], stent-assisted coiling is still favorable compared to simple or microsurgical clipping [113];
• The placement of an intermediate catheter in the blood vessel for coil embolization is a recent advancement in aneurysm treatment. This catheter is designed to provide a buttress at tortuous blood vessels by combining a flexible distal tip with a supportive proximal shaft to aid in the insertion of the coil into the aneurysm, thereby improving maneuverability and stability. This enhanced design improved occlusion rates, as well as the coil packing density inside the aneurysm [114]. This modification is particularly suitable for unruptured aneurysms; for ruptured aneurysms, there are possible risks of intraprocedural rupture (IPR) during coil embolization [114,115].

3.2.3. Flow Diversion Technique

Flow diversion is a technique wherein blood flow is redirected away from the aneurysm with the aid of a stent. The stent facilitates blood occlusion by stagnating the blood flow within the aneurysm. Consequently, an endothelium can form across the neck, leading to the reconstruction of the parent vessel and the healing of the aneurysm [116]. Five different types of flow diversion stents are widely used: (a) a pipeline embolization device (PED), (b) a silk flow diverter (SFD), (c) a flow redirection endoluminal device (FRED), (d) a p64 flow modulation device (pFMD), and (e) a surpass flow diverter (SUFD) [117]. The PED exhibited better outcomes with less complications compared to coil embolization for large unruptured intracranial saccular aneurysms [118]. Although this method is widely used, some complications were observed, associated with the alteration of the mechanical properties and flow reduction effects [119]. Therefore, the optimization of flow diversion stent parameters is essential to enhance the efficacy of flow diversion and reduce such complications. A study reported a high success rate (96.3%) with a low incidence of complications (3.7%) for a stent with an average diameter of 4.3 mm and a length of 21.6 mm. This study utilized three different types of stents: PEDs, SFDs, and FREDs [120].

3.2.4. Other Techniques

Other methods have been utilized for aneurysm treatment that have shown various success rates and morbidity, such as salvation techniques, intrasaccular flow disruption, the use of liquid embolic agents, target therapy, Woven EndoBridge (WEB) therapy, shape memory polymer foam (SMPF) treatment, and foreign body granuloma (FBG) therapy [82,121,122]. However, these treatment methods are less commonly used for aneurysm treatment in real life.

4. Hemodynamic Properties and Their Impact

Hemodynamic properties are primarily responsible for the initiation, growth, and rupture of aneurysms. Different hemodynamic properties, such as wall shear stress (WSS), normal stress (NS), tangential stress (TS), the oscillatory shear index (OSI), and the oscillatory velocity index (OVI), help regulate blood flow through the vessel [36,123]. However, these hemodynamic or biomechanical properties are not only factors in aneurysm initiation and growth, but their interaction with biological properties is also important [124]. Blood is supplied to the brain through internal carotid arteries (ICAs) and basilar arteries (BAs), wherein these arteries are connected to each other by the circle of Willis (CoW). The CoW is a ring-like structure that acts as a backup system to circulate blood in the brain when any artery becomes blocked or absent. Any abnormalities in the circle of Willis may alter the hemodynamic properties and lead to the formation and potential rupture of an aneurysm [125]. Shine et al. [126] found in their computational study that the wall weakening of the CoW and its adjoining arteries alters the core velocity of the blood flow, WSS, and von Mises stress (VMS), which in turn increases the risk of aneurysm initiation and rupture, particularly in the anterior communicating artery (ACoA) and the posterior communicating artery (PCoA). Mohan et al. [127] identified that alterations in the arterial wall due to inflammation associated with external factors (smoke, arterial hypertension, etc.) lead to aneurysm initiation and growth. Since the physical state of the artery wall changes the hemodynamic properties, a detailed understanding of these properties is necessary. The sections below provide a summary of the most critical and common parameters that represent the hemodynamic properties.

4.1. Wall Shear Stress (WSS)

Wall shear stress (WSS) is one of the most impactful hemodynamic parameters responsible for brain aneurysms, defined as the dynamic force along the blood vessel surface, induced by the movement of viscous fluid through the vessel [3,36]. A time-averaged WSS can be estimated using Equation (1), where WSS_i is the instantaneous wall shear stress vector and T is the duration of a cardiac cycle [36].

$$WSS={\displaystyle \frac{1}{T}}{\int }_0^T\left|WS{S}_i\right| dt$$

(1)

Both high and low WSS have adverse effects on aneurysm wall enhancement, depending on the aneurysm size [128]. In small aneurysms, the region of high WSS accelerates artery wall enhancement (AWE) due to inflammation. This inflammation occurs because high WSS causes the overproduction of nitric oxide, a decrease in arterial tone, and apoptosis of smooth muscle cells in vessel walls. Similarly, the region of low WSS in larger aneurysms also has adverse effects on AWE, due to an inflammatory response in the endothelium. Thus, both low and high WSS may lead to unruptured intracranial aneurysm (IA) initiation and growth [128]. Aneurysms with low WSS have a higher chance of rupturing compared to those with high WSS. This is because low WSS around the aneurysm area stimulates the proliferation of endothelial cells, and it also initiates programmable cell death by activating apoptotic pathways. The death of endothelial cells activates proinflammatory and procoagulant mediators, leading to the increased production of vasoconstrictive substances, while simultaneously reducing the production of vasodilators and antioxidative agents. Together, these changes weaken the vessel wall structure. Consequently, the weakened vessel wall is unable to tolerate the physiological hemodynamic stresses, leading to aneurysm formation and eventual rupture. In contrast, high WSS caused by the elevated blood flow, particularly in the bifurcation region, leads to endothelial dysfunction and damage over time [129]. Tang et al. [128] and Meng et al. [130] reported that both low and high WSS facilitate the growth and rupture of aneurysms, while Gao et al. [131] found that a larger aneurysm area with lower WSS promotes the risk of rupture. This adverse effect of WSS is primarily influenced by the aneurysm’s geometry and the blood flow dynamics within the aneurysm and its parent artery. In addition to the magnitude of the WSS (low or high), the WSS pattern also has significant effects on aneurysm rupture. For instance, higher and more heterogenous WSS, typically observed in aneurysms located in the bifurcation regions of the basilar, anterior, and posterior communicating artery, promotes bleb (blister-like protrusion) formation. During bleb formation, high intramural stresses develop at the bleb neck, ultimately causing aneurysm rupture. In contrast, lower and more homogenous WSS in sidewall aneurysms of the MCA and ICA facilitates wall thickening and may result in the rupture of aneurysms that are relatively larger in size without forming bleb [132].

4.2. Normal and Tensile (Circumferential) Stresses

Within a blood vessel, normal stresses act orthogonally in regard to a vessel wall (e.g., due to hydrostatic pressure), while circumferential stress is a force in the circumferential direction, acting against the blood vessel wall [36]. Both stresses cause the deformation of the aneurysm wall, as well as speed up the development of saccular aneurysms [133,134]. For instance, a traumatic brain injury (TBI) exerts a sudden load on the vessel wall, which causes mechanical failure or deformation, due to the stresses developing within the wall. A prior study found that TBI increases the deformation of the cerebral aneurysm wall by 0.072 mm [133]. The blood flow through the vessel also has an impact on the aneurysm wall. Jiang et al. [135] found that during peak systole, an increase in the blood hematocrit (HCT) level leads to elevated pressure on the aneurysm wall. This elevated pressure enhances the normal and tensile stress, causing wall deformation and potentially leading to rupture. Singh et al. [134] found that an increase in the aneurysm diameter and a decrease in the wall thickness also induce substantial strains on the aneurysm wall, which, in turn, can lead to rupture. Taken together, these studies demonstrate the importance of identifying the circumferential and normal stresses at play and how they affect brain aneurysms.

4.3. Oscillatory Shear Index (OSI)

The oscillatory shear index (OSI) is a non-dimensional parameter that characterizes oscillations during pulsatile flow. The OSI is calculated using Equation (2) [136] and ranges from 0 (steady flow) to 0.5 (intense oscillation) [36]. A higher OSI indicates a disturbed and non-uniform flow pattern (turbulent flow), which, along with irregular WSS, can damage the inner aneurysm wall and lead to aneurysm growth and rupture [137,138]. Although low WSS causes aneurysm rupture as discussed above, the presence of a low OSI alongside it can lead to reduced mechanical stress, thereby lowering the rupture risk [138]. In contrast, a low WSS combined with a high OSI usually indicate the location where an aneurysm is likely to rupture and suggest that the area is not exposed to the impact of direct blood flow [36]. The OSI intensity depends on the geometry of the aneurysm; a higher aspect ratio results in a higher OSI value, which leads to inflammation and remodeling of the aneurysm wall [137]. Note that although the OSI determines aneurysm growth and the risk of rupture, it does not differentiate between normal and hypertension conditions [137].

$$OSI={\displaystyle \frac{1}{2}}\left\{1-{\displaystyle \frac{\left|{\int }_0^{T}WS{S}_i dt\right|}{{\int }_0^T\left|WS{S}_i\right|dt}}\right\}$$

(2)

Here, the $WS{S}_i$ is the instantaneous wall shear stress, ${\int }_0^{T}WS{S}_i dt$ represents the sum of all the instantaneous wall shear stress vectors during a single cardiac cycle, and ${\int }_0^T\left|WS{S}_i\right|dt$ represents the sum of the magnitude of all the instantaneous wall shear stress vectors during a single cardiac cycle.

4.4. Aneurysm Formation Indicator (AFI)

The aneurysm formation indicator (AFI) is another hemodynamic index used to detect stagnation zones, by calculating the direction of the WSS vector blood flow in regard to the vessel wall [36]. Additionally, the AFI can measure fluctuations in the WSS vector at the location of the aneurysm formation [139]. Studies have shown that the AFI has a similar distribution pattern on the vascular wall as the OSI and minimal correlation with the area of intracranial aneurysm formation [140].

4.5. Oscillatory Velocity Index (OVI)

The oscillatory velocity index (OVI) quantifies the flow pattern, which is important for diagnosing aneurysm growth and the risk of rupture [141]. It is measured based on the local velocity magnitude and fluctuations in the flow patterns during a cardiac cycle [36]. A prior study reported that a high OVI is typically observed in ruptured aneurysms due to its complex and unstable flow patterns, along with the presence of multiple vortices at the rupture site [141,142,143].

4.6. Residence Time (RT)

The residence time (RT) is another important hydrodynamic parameter, defined as the average time that blood spends within the aneurysm. It plays a significant role in aneurysm rupture and the development of thrombi within the aneurysm [144]. The relative residence time (RRT) describes the blood flow distribution near the intra-aneurysmal vortex. It is used to estimate the RT of the blood cell flow circulation near the aneurysm wall [36]. An increased RT reflects impaired mass transfer between the blood flow and the vessel wall, which locally impacts the biological processes involving the artery wall [145]. However, the role of the RT in identifying aneurysm rupture and blood clotting (thrombus) is still unclear. For instance, Xu et al. [146] found that the relative RT (RRT) for ruptured and unruptured aneurysms is 0.34 ± 0.4 and 0.3 ± 0.26, respectively, indicating that the residence time for ruptured and unruptured aneurysms are not statistically different. Rayz et al. [145] found a correlation between the RT and WSS to predict the thrombus at the aneurysm site, wherein aneurysm wall regions with a high RT and a low WSS predict thrombus formation more effectively than either the RT or WSS alone. Hence, identifying strong correlations between the residence time and other hydrodynamic parameters may improve the predictive capabilities in regard to aneurysm rupture or thrombus formation.

Understanding the significance of hemodynamics through clinically relevant applications is important as it provides insights about the physical conditions of aneurysms and helps identify possible treatment strategies. For instance, microsurgical clipping is an effective method to identify rupture points. Li et al. [147] investigated the hemodynamics around a rupture point, wherein the rupture point was detected at the time of clipping, followed by hemodynamic analyses (e.g., WSS, OSI, etc.) of the rupture point and the entire aneurysm sac. It was found that the time-averaged WSS is significantly higher at the aneurysm sac compared to the rupture point, while the OSI is higher at the rupture point. Additionally, in about two-thirds of clinical cases, there was no blood flow impact observed at the aneurysm’s rupture point. Among the cases with daughter blebs, the rupture point was confirmed to be at the blebs in six cases. Liu et al. [148] investigated the risk factors related to intraoperative aneurysm rupture (IOR), by extracting both the morphological and hemodynamic features. They found that the average and maximum normalized WSS, as well as the aspect ratio, were lower for the IAs that ruptured during the pre-dissection stage compared to those that ruptured during the dissection stage. Suzuki et al. [149] conducted a CFD study based on the clinical outcomes of intraprocedural rupture (IPR) during coil embolization (CE) of an IA, examining the impact of hemodynamics on the rupture risk. They found that IPR occurred mostly in the ICA compared to the MCA and the anterior cerebral artery (ACA), and CFD analysis found that the rupture point coincided with a flow impingement zone, with maximum pressure. The time-averaged WSS in this location was also lower than the rest of the aneurysm dome. The unstable hemodynamics at this location were associated with a high risk of rupture. As such, to prevent rupture, a microcatheter was inserted into the inflow zone and directed towards the rupture point. Understanding patient-specific hemodynamic properties is also essential to ensure proper treatment, as the size, shape, and conditions of aneurysms vary from patient to patient. Davidson et al. [150] investigated the flow characteristics and hemodynamics of cerebral arteries before and after neurosurgical clipping. They selected two patient-specific cerebral artery geometries from an online dataset, one of which had an aneurysm located in the MCA bifurcation region. The CFD analysis showed that clipping altered the flow patterns and the WSS in the MCA, which confirmed the appropriateness of the treatment before proceeding. Taken together, these studies demonstrate the utility of clinical data to better understand the hemodynamics around an aneurysm, which could lead to the development of more effective diagnostic and treatment methods.

5. Fluid Flow Characteristics in the Aneurysm

Analyzing aneurysm fluid flow patterns before and after treatment helps assess the aneurysm’s condition and helps to guide the selection of the necessary precautions to reduce the risk of complications and death. Such fluid flow characteristics have been investigated using both experimental and computational approaches. However, computational approaches have been more prevalent compared to experimental approaches for the following reasons:

(1)

They can capture complex geometries with relative ease [28];

(2)

Such simulations can be used to investigate complex flow patterns and the corresponding hemodynamic properties [151];

(3)

They do not have the same limitations related to patient specific data as faced by experimental approaches [28,152];

(4)

Computational approaches allow for better control of the parameters and ease of executing multiple simulations [153,154];

(5)

They are more time and cost effective [153].

Computational studies on brain aneurysms are usually carried out in three different ways: (1) using computational fluid dynamics (CFD) models, (2) using fluid–structure interaction (FSI) models, and (3) using static structural analysis (SSA) models. Each model involves different aspects, based on the specific objectives of the study. In general, models that incorporate the vessel structure and properties (e.g., FSI and SSA), which includes the mechanical properties of the parent artery and aneurysm wall, are important because these properties influence aneurysm formation and rupture [155]. Excessive hemodynamic stress on the artery wall leads to the disruption of the internal elastic lamina, the loss of medial smooth muscle cells (SMCs), decreased SMC proliferation, and the loss of fibronectin, ultimately contributing to aneurysm initiation [19].

CFD models are used to simulate fluid domains only, wherein the vessel and aneurysm walls are assumed to be rigid. In contrast, FSI models account for flexible vessels and aneurysm walls, coupling them with the fluid domain [156]. This semi-realistic model enhances accuracy in regard to predicting fluid flow properties, by developing the interaction between the blood flow and the vessels’ structure [157]. Typically, the artery wall is modeled as either a linear or hyper-elastic model. While the linear elastic model is more stable and simpler compared to the hyper-elastic model, it does not accurately predict the nonlinear mechanical behavior of the parent artery [158]. In another study, Torii et al. found that the maximum displacement obtained from the hyper-elastic model was 36% smaller than that obtained from the linear elastic model [159]. Other hyper-elastic models used include the Mooney–Rivlin model, the Ogden model, the Yeoh model, the neo-Hookean model, the Exp–Ln model, and the Gent model [157,158,160]. A study found that the Exp–Ln model predicts the mechanical behavior of soft tissue more precisely than other hyper-elastic models [160]. SSA models primarily focus on the structural properties of blood vessels and aneurysm walls without accounting for fluid dynamic properties. Such models are less widely used compared to CFD and FSI models [156]. While computational approaches are more prevalent due to the reasons explained above, the use of experimental or clinical data are important for model validation. The following sections present a comprehensive review of various computational and experimental studies on the hemodynamics of aneurysms before and after treatment.

5.1. Hemodynamics Around Aneurysms Before Treatment

5.1.1. Aneurysm Initiation and Growth

The blood flow through the artery and its impact on altering the hemodynamic properties significantly influence the formation, growth, and rupture of aneurysms. As discussed above, in addition to inflammation, the aneurysm size, shape, location, and hemodynamic properties are also important variables. Various computational studies have been performed to investigate the effects of these variables on aneurysm formation. Lauric et al. [161] developed a CFD model to investigate the curvature effect at the ICA siphon on aneurysm formation. They found that sharp bends or curvature in a blood vessel cause fluctuations and high levels of WSS and WSS gradients at the inner wall. These high stresses are followed by a region in which the blood flow slows down and even recirculates, contributing to the weakening of blood vessel walls and, ultimately, initiating aneurysm formation. Lampropoulos et al. [162] also used CFD for multiphase blood flow analysis and found that local curvature in blood vessels has a significant effect on aneurysm formation. An increase in blood vessel curvature causes high stress and flow stagnation in localized regions, enhancing the risk of aneurysm formation. Csippa et al. [163] observed from their CFD analysis that blood vessel topology may impact the development of a strong secondary flow pattern at the site of aneurysm initiation. This magnitude of high velocity close to the wall and a high flow angle are the main reasons for the high WSS and OSI at the wall, which contribute to aneurysm initiation. Gao et al. [164] found through their CFD simulations that the initiation of an anterior communicating artery aneurysm mostly occurs in the daughter vessel, which has a smaller diameter, as well as a smaller angular distance from the parent blood vessel. They also reported that aneurysm formation is a self-adaptive process of the blood vessel wall to alleviate the impact of hemodynamic factors at the site of aneurysm initiation. Yu et al. [165] performed an experimental study to investigate the effect of the flow structure on the vortex strength, impinging location, and WSS. Their results indicate that a high Reynolds number (Re = 270) and Womersley number (α = 5) contribute to the movement and prolonged presence of a vortex structure within the aneurysm, leading to higher incidences of flow impingement on the aneurysm wall. Furthermore, a low bottleneck factor (BF = ${\displaystyle \frac{Maximum aneurysm sac diameter}{Neck diamter}}=$1) allows more incoming blood flow to enter and circulate within the aneurysm sac. These factors, when taken together, facilitate aneurysm formation, growth, and rupture.

Experimental approaches to investigating the fluid flow characteristics in aneurysms before treatment are less prevalent. Chi et al. [166] experimentally investigated the effect of the aspect ratio (AR) of imaged-based aneurysms on wall deformation under various pulsatile flows, wherein wall deformation oscillations were detected using laser displacement sensors. They found that the wall deformation oscillations increase with an increasing pulsatile inflow frequency, which also causes the AR to increase. Additionally, the maximum wall deformation at the aneurysm dome decreases during the systolic phase. Souza et al. [167] used both particle-tracking velocimetry (PTV) and CFD to investigate the flow structure in aneurysms and found that recirculation, vorticity, and jet impingement and flow disturbances in localized regions occur due to an increase in the flow rate, providing insight into the state of aneurysms (e.g., initial state or fully grown aneurysm).

5.1.2. Aneurysm Rupture

Several studies have also been conducted both experimentally and computationally to identify possible factors for aneurysm rupture. For instance, Lai et al. [168] performed a study to identify the impact of the aspect ratio (aneurysm height: neck width) on blood flow dynamics, with experiments conducted to validate the CFD model. It was found that a blood stream jet entering the aneurysmal sac becomes high and narrower with an increase in the aspect ratio, potentially directly impinging on the weaker wall. Additionally, the distal portion of the neck exhibits variable shear stresses. The strong and narrow jet impingement, along with variable shear stress, enhances the chance of an aneurysm rupture. Shamloo et al. [169] developed a two-way FSI model to investigate the effect of aneurysm wall thickness on aneurysm rupture. They noticed that thicker walled aneurysms exhibit lower deformations and Von Mises stresses compared to aneurysms with thinner walls, hence lowering the risk of rupture. Philip et al. [170] found through their FSI model, that the shape of an aneurysm impacts the flow stability within the aneurysm. Pear- and beehive-shaped aneurysms exhibit high flow instability, while spherical-shaped aneurysms showed more stable flow; hence, the former two shapes have a higher risk of rupture. While aneurysm rupture depends primarily on the aneurysm’s size and shape, the flow structure also plays a critical role not just in its formation and growth, but also in regard to the likelihood of rupture. For instance, Huang et al. [171] developed a model to investigate the impact of flow fluctuations on aneurysm rupture. Generally, the fluid flow begins to fluctuate and becomes unstable immediately after peak systole, followed by a gradual decay, and, finally, returns to the laminar pulsatile phase during diastole. Thus, fluid flow instabilities start after the peak systole phase. This group found that pulsatile flow around the aneurysm neck enhances flow instability, which leads to rupture. Cebral et al. [172], based on their computational model, found that an abnormally high WSS causes aneurysm rupture at thinner and stiffer walls. Using another CFD model to investigate the effect of the flow conditions on wall remodeling and inflammation, they also found that a high WSS, high vorticity, high shear rate, and high viscous dissipation enhance inflammation, leading to aneurysm rupture [173]. Yu et al. [174] conducted an experimental study, wherein the inflow conditions in an aneurysm were investigated using particle image velocimetry (PIV). The study found that a high Reynolds number (Re = 150 and 250) and Womersley number (α = 5) enhance the vortex strength and generate secondary vortices. A high Re also alters the location of jet impingement. Taken together, these factors increase the risk of aneurysm rupture.

In addition,

Table 2. A compressive summary of most recent articles highlighting the flow conditions of brain or cerebral aneurysms.

Authors	What Has Been Investigated	Methodology	Key Findings
Azhaganmaadevi et al. [175]	The influence of patient-specific aneurysm wall thickness on rupture risk	FSI	The maximum wall shear stress, displacement, and average wall stress were higher for patient-specific wall thickness models compared to uniform wall thickness models
Fujimura et al. [176]	Hemodynamic factors related to aneurysm initiation based on angiographic images taken before and after aneurysm formation	CFD	Aneurysm initiation occurred in the area experiencing high tensile force and significant total pressure loss
Cherkaoui et al. [177]	Effect of the magnetic field on pulsatile blood flow and heat transfer in an artery with an aneurysm	Carreau–Yasuda rheological model Mesoscopic lattice Boltzmann method with BGK approximation (LBGK)	Heat transfer increased at the aneurysm inlet with an increase in the Hartmann number Magnetic field reduced the recirculation zone and increased the WSS
Moghadasi et al. [178]	Effect of hemodynamic properties and biomechanical response of extracranial carotid artery aneurysms Windkessel effect was considered for pressure profile simulation	FSI	Aneurysm carotid artery exhibited higher pressure, WSS, OSI, and relative residence time (RRT) compared to carotid artery without aneurysm Large deformation of carotid wall due to high von Mises stresses
Muhib et al. [137]	Effect of clinical conditions and geometry on aneurysms for patients with hypertension and atrial fibrillation	Two-way FSI	Larger aneurysms carried a higher risk of rupture due to a decrease in the WSS of 50% Maximum pressure in the aneurysm with larger aspect during systole was 33% lower than medium-sized aneurysm due to unusual geometry Wall deformation was significantly higher in larger aneurysm compared to medium- and small-sized aneurysms
Sharzehee et al. [179]	Buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow and their effects on rupture	FSI	Aneurysm arteries buckled at critical buckling pressure, leading to nonlinear deflection Buckling enhanced the WSS and lumen shear stress and enlarged the vortex flow, which increased the risk of aneurysm rupture
Shen et al. [180]	Effect of blood flow characteristics on ICA aneurysm rupture	CFD	Aneurysm growth was directly proportional to the orientation and location of the aneurysm Average WSS was around 50% higher on the outside of the aneurysm compared to inside
Singla et al. [123]	Effect of aneurysm size and wall thickness on blood flow behavior inside an aneurysm, as well as the rupture risk	CFD	For thicker walls, the pressure and WSS decreased with an increase in the aneurysm size For thinner walls, the flow velocity and WSS increased with an increase in the aneurysm size The rupture risk was high with an aneurysm size of 4 mm and a wall thickness of 0.075 mm (thin wall)
Fattahi et al. [181]	Effect of mean diameter of parent vessels on hemodynamic factors	CFD	A 40% increase in the mean diameter, from 3.18 to 4.48 mm, resulted in a decrease in the minimum WSS, OSI, and mean flow velocity by 71%, 43%, and 44%, respectively
Cho et al. [182]	Predicted rupture risk of an aneurysm by comparing clinical cases with FSI simulations	The thin-walled area (TWA) was modeled using CFD Strain in the TWA was modeled using FSI	The equivalent strain was higher for ruptured aneurysms compared to unruptured aneurysms Approximately 88% of unruptured and 63% of ruptured aneurysms matched the clinical outcomes
Oliveira et al. [183]	Analyzed the growth of unruptured lateral aneurysms over five years using CFD, based on two consecutive examinations	CFD	Aneurysm growth accelerated with an increase in the WSS and WSS spatial gradient Different biological pathways affected the hemodynamic factors, ultimately contributing to aneurysm growth. Thus, it was found that a low WSS and a high OSI are also associated with aneurysm growth
Zhu et al. [184]	The role of hemodynamic and morphological parameters in evaluating rupture risk	CFD	The following hemodynamic factors were higher in the ruptured aneurysms compared to unruptured aneurysms: size ratio (SR), AR, aneurysm vessel angle (θF), aneurysm inclination angle (θA), undulation index (UI), ellipticity index (EI), and non-sphericity index (NSI), OSI, ruptured resemblance score (RRC) The SR and OSI were critical factors for predicting ruptures The WSS could change before and after rupture
Rahma et al. [185]	Effect of hemodynamic parameters on anterior communicating artery aneurysm rupture	CFD	Flow recirculation occurred inside the bulge due to the presence of an aneurysm in the vessels, which resulted in the uneven distribution of the WSS The wall pressure and WSS reached the highest value in the flow–wall interaction zone
Závodszky et al. [186]	Effect of moving tiny particles through cerebral vessel sections with aneurysmal malformations	CFD	The particle trajectory within the flow formed a fractal structure Chaotic (irregular) blood flow within the vessel near the aneurysm played a critical role in its formation and growth
Lampropoulos et al. [23]	Hemodynamic characteristics of irregular-shaped IAs	CFD	Low WSS and viscous dissipation rate (VDR) observed in the dome area of the IA, which were associated with blood flow stagnation and disorganized streamlines Low shear stress and energy dissipation caused aneurysm progression and increased the rupture risk Structured recirculation flow reduced the localized stress concentration
Ashkezari et al. [187]	Hemodynamics in the aneurysm over time from the early stage of formation to the later stage involving significant enlargement	CFD	Aneurysm with fixed neck developed more stable flow inside it; less likely to rupture Aneurysm with growing neck caused an unstable flow inside it, increasing the risk of rupture
Usmani et al. [188]	How pulsatile blood flow affects the risk of rupture in regard to three different intracranial aneurysm geometries (three different angles of the dome relative to the plane of the parent vessel) Effect of dome orientation changes on hemodynamic loading	Both experimental (PIV) and computational (FSI)	Areas of WSS and wall pressure shifted spatially from the distal end at low inclination angles. At higher inclination angles, these stresses were distributed around the entire aneurysm wall Higher angle of inclination predicted a higher rupture risk
Li et al. [189]	Investigated the flow pattern of a patient-specific cerebral aneurysm using both computational and experimental approaches	Experimental approach (PIV) and medical imaging (PC-MRI) CFD	The flow pattern obtained from PIV and PC-MRI showed good agreement with the CFD simulations CFD predicted the highest velocity. The PIV measurement was lower than the CFD, but higher than PC-MRI The difference in velocity predictions between the CFD and PIV ranged from 22 to 28%, while the difference between CFD and PC-MRI ranged from 32 to 41%
Wu et al. [190]	Comparative evaluation of hemodynamics of patient-specific intracranial saccular aneurysm	PIV (both tomographic and stereoscopic) and in vivo MRI CFD	The 4D flow MRI exhibits 2–4 times lower peak WSS and 1.6–2 times lower mean WSS compared to Tomo-PIV, Stereo-PIV, and CFD The difference in WSS between the MRI-based approach and the PIV- and the CFD-based methods increased at higher WSS magnitudes
Tupin et al. [191]	Effect of wall compliance on intracranial aneurysm (IA) hemodynamic patterns and flow field variables	Experimental approach (PIV)	The compliant (flexible) model captured three distinct features compared to a rigid model (silicone): (1) greater trapped mass, (2) a larger stagnation zone with secondary vortices, and (3) a highly transient shear layer at the neck and increased near-wall velocity oscillations in the dome The WSS was also impacted by wall compliance (flexible model)
Ikeya et al. [192]	Effect of wall deformation on the WSS of elastic cerebral aneurysms	Experimental approach (PIV) Experiment with deformation referred to the wall deformation model and minimized deformation referred to the model with less deformation	Middle plane: maximum and average WSS were reduced by 20% during systole in the wall deformation model compared to the model with less deformation Perpendicular plane: average WSS was increased by 10% in the wall deformation model compared to the model with less deformation
Shen et al. [193]	Effect of aspect ratio (AR) on internal flow patterns and the hemodynamics of IAs	Experimental (PIV)	Primary, coherent, and shear-driven vortex flow occupied the aneurysm region The shear effect of the flow decreased with an increase in the aspect ratio, leading to slow flow in the aneurysm sac The WSS increased as the AR decreased Both transient and retrograde flow played significant roles in aneurysm rupture Transient flow affected the nutrients’ transport and exchange between the IA and parent artery
Yazdi et al. [194]	Effect of eCLIPs (a coil retention device) implanted bifurcation flow diverter on flow diversion from the aneurysm (the eCLIPs implanted bifurcation flow diverter is termed the eBFD)	Experimental (PIV)	The eBFD with a 35% metal density showed greater flow diversion compared to the PED (pipeline embolization device) with a 30% metal density The eBFD showed a similar flow reduction to the PED in the sidewall aneurysm The eBFD exhibited promising flow diversion for bifurcation treatment, thus avoid adjunctive coiling

provides a summary of the most recent articles (Year: 2020–2025) highlighting the impact of various factors associated with the alteration of the fluid flow behavior in brain aneurysms.

5.2. Hemodynamics Around Aneurysms After Treatment

Flow diagnostics using computational approaches after aneurysm treatment are crucial for evaluating the effectiveness of the devices used, the healing process, the flow conditions in the treated regions, and the possibility of recurrence [195,196]. For instance, Cebral et al. [197] performed a CFD analysis to investigate the hemodynamics of treated ruptured and unruptured giant aneurysms. They found that for a successfully treated aneurysm, the flow diversion device reduces the flow velocity and WSS in the aneurysm, which validates the flow diversion device in regard to its ability to effectively divert the flow from the aneurysm sac into the parent artery. In contrast, for post-treatment aneurysms, the use of flow diversion devices caused the development of high pressures in the aneurysm. Otani et al. [17] conducted a blood flow analysis of coil-embolized aneurysms using CFD approaches and found that the blood flow velocity decreases with an increase in the packing density, although the effect of coil configuration was insignificant. However, the strength of the local shear flow varies with the coil configuration. The total shear rate decreases with an increase in the packing density, which is an important factor for blood clot formation inside the aneurysm, for successful aneurysm occlusion. The effectiveness of coil embolization also varies based on the patient’s gender. Sheidani at al. [198] performed a CFD study to examine the impact of hemodynamics on the coil porosity in both male and female patients. They found that a decrease in coil porosity from 0.89 to 0.79 reduces the maximum OSI value by 75% in males and 45% in females. Zhang et al. [199] compared the efficacy of using large-sized coils with the conventional coil for embolization. The diameter of the large-sized coil is 1.4–1.8 times higher than the diameter of the conventional coil. Their results show that the large-sized coil achieved a similar initial occlusion rate, while significantly reducing the percent packing volume (PPV), the coil number, the length of the total coil compared to the conventional coil, and the recurrence rate. Jeong et al. [200] investigated the effect of the coil shape and orientation on hemodynamics and found that the orthogonal orientation of a vortex coil and the parallel orientation of a cage-shaped coil exhibited a higher inflow velocity, WSS at the dome, and vorticity, which, in turn, is unfavorable for thrombus formation. Moreover, a thicker coil also negatively affects the hemodynamics. However, blocking the distal mid-transverse plane of the aneurysm significantly reduces the blood flow inside the aneurysm, ultimately creating favorable conditions for thrombus formation. Thus, the effectiveness of various aneurysm treatment methods primarily depends on the size, shape, and orientation of implanted devices, along with patient-specific conditions.

In addition,

Table 3. Comprehensive summary of recent articles highlighting the hemodynamics and flow conditions of treated aneurysms.

Authors	What Has Been Investigated	Methodology	Research Outcome
Yao et al. [201]	Improvement of hemodynamic efficiency after coil embolization in MCA aneurysm (original and scaled-down geometries)	CFD	The use of coiling effectively reduced the shear stress on the surface of the sac The change in pressure around the sac region due to the coil was not significant Coil embolization reduced the rupture risk, particularly in MCA aneurysms with a larger sac volume
Sadeh et al. [202]	Impact of endovascular coiling on blood hemodynamics and MCA aneurysm rupture	CFD	During peak systolic conditions, an increase in coil porosity reduced the pressure at the dome, increased the WSS at the aneurysm surface, and increased the blood velocity near the aneurysm wall The effect of coiling was limited at the aneurysm neck because of the variation in the WSS and the high OSI during the diastolic condition For a fully porous domain, both the maximum and minimum blood flow velocities were higher compared to the less porous coil during the systolic condition
Rostamian et al. [203]	Effect of coiling on aneurysm progress and risk of rupture	CFD	A decrease in coil porosity reduced the aneurysm WSS and limited the high OSI area on the aneurysm wall The blood interaction with the aneurysm wall decreased with a decrease in coil porosity
Yang et al. [204]	Effect of coil embolization on hemodynamic factors of the aneurysm	CFD	A decrease in coil porosity reduced the blood flow velocity inside the aneurysm The blood flow circulation was intense near the neck
Boniforti et al. [205]	Effect of flow diversion stents (FDSs) on hemodynamic factors	CFD	FDS placement reduced flow velocity and increased the RRT, facilitating thrombus formation and leading to aneurysm occlusion A FDS increased the OSI, endothelial cell activation potential (ECAP), and RRT, but decreased the time-averaged WSS (TAWSS), which positively impacted the aneurysmal flow pattern An increase in the porosity of the FDS caused a significant increase in the RRT, thus facilitating aneurysm occlusion
Kim et al. [206]	Effect of overlapping and compacting stents on hemodynamic factors Compared the enterprise and low-profile visualized intraluminal support (LVIS) stent with the pipeline flow diverter	CFD	The compacted stent provided better flow diversion than the uncompacted stent Two overlapped and uncompacted LVIS stents exhibited similar flow diversion effects as the single uncompacted pipeline Both a single LVIS stent and three overlapping enterprise stents provided similar flow diversion effects The LVIS stent with a single uncompacted stent provided similar flow diversion as two-overlapped uncompacted LVIS stents
Pei et al. [207]	Hemodynamic evaluation was performed on coil embolization and stent to reduce the rupture risk of ICA aneurysm	Both CFD and FSI	Coiling was effective for small aneurysms, while stenting was preferred for giant aneurysms, but only if the parent vessel was properly aligned and minimal blood flow entered the sac The rupture risk of giant aneurysms was reduced by deforming the parent vessel completely with the aid of a stent
Horn et al. [208]	Effect of shape memory polymer foam (SMPF) treatment technique on clot formation to prevent rupture risk	CFD	The aneurysm filled with SMPF had higher thrombus occlusion (at least 94%) compared to the coil embolization method The foam orientation and its pore size had little impact on blood clot formation inside the aneurysm sac, while coil embolization had a strong dependency on the packing density
Chen et al. [209]	Investigated the effect of the hemodynamics on the recurrence of the vertebral artery dissecting aneurysm (VADA) A ruptured VADA was first treated with LVIS stent-assisted coiling and, subsequently, a pipeline embolization device (PED) after recurrence	FEA (coiling and stent deployment) and CFD (hemodynamics)	The WSS was not sufficiently reduced to avoid recurrence after placement of LVIS stent-assisted coiling After placement of the PED, the sac shrunk and blood flow within it increased gradually, eventually stabilizing the aneurysm after 27 months
Davidson et al. [210]	Role of flow characteristics and hemodynamic variables on cerebral arteries before and after neurosurgical clipping treatment	CFD	Clipping treatment altered the velocity profile, secondary flow structure, and WSS in the MCA The model assisted in predicting the hemodynamics before treatment and, thus, reduced the potential for complications
Sanches et al. [211]	Effect of flow diversion stent (FDS) and regular stent (RS) on IAs	CFD	The use of a FDS resulted in a greater reduction in the WSS, inflow rate, intra-aneurysmal flow velocity, and turnover time compared to an RS, causing rapid thrombotic occlusion
Juan et al. [212]	Effect of blood inflow rate, wall compliance, and stent on hemodynamics factors of elastic aneurysm	Experimental	Low blood inflow rate had lower stability than high inflow rate into the aneurysm Wall compliance facilitated the blood flow in and out of the aneurysm, and adding a stent enhanced its efficacy by adding a flow diversion effect, thereby reducing the risk of rupture
Roloff et al. [213]	Effect of malposition of flow-diverting stent on hemodynamic factors of intracranial aneurysm	Experimental (PIV)	The successful placement of a flow diversion stent reduced the blood flow velocity by 63–89% The stent malposition increased the flow oscillation towards the lateral direction, leading to the reduction of blood clotting in the aneurysms
Chodzyǹski et al. [214]	Flow diversion stent performance in a cerebral aneurysm	Experimental (in vitro study)	Lower porosity (44%) flow diverter caused an effective reduction in the intra-aneurysmal flow, with a complex flow pattern The placement of the flow diverter influenced its performance, with a complex flow pattern Change in physical properties of the stent after placement had significant effect on its performance

provides a summary of the most recent articles (Year: 2020–2025) that highlight the hemodynamics of treated aneurysms.

The use of the computational process is still controversial, due to concerns regarding the validity of the governing models and the conflicting outcomes from several studies [28]. Thus, combining experimental approaches to complement and validate computational simulation predictions is a worthwhile endeavor to try to capture the relevant physiological characteristics accurately.

6. Conclusions

The identification and treatment of brain aneurysms are of great importance, regardless of their state (ruptured and unruptured). While unruptured aneurysms are not immediately life threatening, treatment is necessary because they carry the potential risk of rupture, due to the change in hemodynamic factors within the aneurysm and parent artery, leading to morbidity and mortality risks. This review highlights various types of brain aneurysms and their hemodynamic factors, the diagnostic methods used, and the fluid flow characteristics before and after treatment. Based on this review, the key observations are summarized as follows:

• While hemodynamic factors are crucial for aneurysm initiation, growth, and rupture, changes in the relevant biological properties accelerate the hemodynamic alterations both in the parent arteries and aneurysms. Additionally, the aneurysm’s geometry and location influence whether the hemodynamic factors become critical and whether they may lead to the rupture of the aneurysm. Thus, various screening and treatment processes are widely used to identify and treat both unruptured and ruptured aneurysms;
• An understanding of the fluid flow characteristics in the parent artery and adjacent aneurysms is important because this information helps to determine the state of the aneurysm in order to reduce the possible risk of complications and death. While computational methods are widely used compared to experimental approaches, because of their ease in capturing complex geometry, the ease of controlling the variables in hemodynamic investigations, the ability to execute multiple simulations across various parameters, and time efficiency, the accuracy of computational study is still questionable. Thus, validating computational simulations using experimental data is critical to help improve the model’s accuracy associated with its assumptions and governing equations;
• The majority of recent studies within the last 5 years (2020–2025) were computational simulations, with limited experimental studies, particularly using patient-specific models. This represents an important gap for future research, potentially contributing significantly to the advancement of knowledge in this field;
• Prior experimental and computational studies mostly focus on the aneurysm size, shape, and orientation, as well as the blood flow structure and stability in various arteries with aneurysms. These studies primarily highlight how hemodynamic changes due to changes in these properties ultimately lead to the formation, growth, and rupture of aneurysms. Further investigations are necessary to identify any correlation or interaction effects between these variables, which may change the interpretations of these findings;
• Preventing aneurysm recurrence after treatment is still challenging. The current research primarily focuses on hemodynamic changes before and after treatment, particularly on flow diversion and coil embolization techniques. Most of these studies rely on computational predictions, but the accuracy of the outcomes remains debated, due to the geometric complexity and model simplifications made for easier analysis, particularly in regard to stent or coil inclusions. Thus, combined experimental and computational approaches would provide a way for model validation to take place and enhance data reliability. Furthermore, extensive experimental investigations are necessary to evaluate the efficacy and reliability of embolization and flow diversion techniques in real-world conditions;
• It is crucial to explore new treatment techniques, instead of relying solely on coil embolization and flow diversion methods.