The left atrial appendage (LAA), originating from the left atrium during fetal development, is described as a long, tubular, hooked structure with variations in size, shape, and volume [1]. The morphology of the LAA is highly diverse from patient to patient and is typically divided into four distinct types based on the structure it evokes: “Chicken wing” is the most frequent morphology (48%), followed by “Cactus” (30%), “Windsock” (19%), and “Cauliflower” (3%) [2]. Nevertheless, the classification is frequently open to misinterpretation and is reliant on the imaging plane. The volume size of LAA also varies significantly with the morphology [3]. Due to the LAA’s characteristics mentioned above, its effect on left atrial (LA) flow is difficult to evaluate.

Literature reveals that LAA is the most prevalent region for thrombus formation, increasing the risk of stroke in patients with atrial fibrillation (AF) [4,5,6]. AF is an electrophysiological pathology with irregular atrial beats, affecting between 1% and 2% of the general population, approximately 8% of people over 80 years old [7,8]. It has been identified as the principal cause of thromboembolic events, such as stroke and vascular dementia [9]. Consequently, there is an urgent need for more effective strategies for identifying and preventing thromboembolic events in AF patients [10]. AF can result in electrical, structural, and contractile remodeling [11,12,13]. Atrial expansion, LA dysfunction, and inadequate atrial contraction result in thrombus development, especially in the LAA [11,12,13]. Furthermore, blood stagnation frequently occurs in the LAA since the blood flow velocity drops dramatically [1,6,13]. Consequently, LAA has received interest as a therapeutic target for preventing thrombosis, particularly in AF patients.

Several therapies are currently available to prevent thrombus formation: (i) oral anticoagulation (i.e., warfarin and direct oral anticoagulants) [14,15,16]; (ii) LAA surgical exclusion [17]; and (iii) LAA percutaneous occlusion [18,19]. However, all of these options have drawbacks that restrict their practice and effectiveness, such as the possibility of hemorrhagic consequences in the case of anticoagulation therapy [14,15,16] and the risks associated with invasive and transcatheter procedures (for example, vascular injury, air-embolic events, and peri-device leaks) [17] for surgical and percutaneous treatments, respectively [18,19]. Although numerous treatments have been proven to reduce the risk of thrombotic events, research has shown a significant residual risk [1,13,20,21]. Due to the diverse morphological factors, such as shape, size, and LAA volume, the reported approaches may fail. In addition, researchers have recognized hemodynamic parameters such as velocity, vorticity, and shear stress as thrombosis predictors [22,23].

Blood flow within the left atrium has currently been evaluated using several methodologies. Transesophageal echocardiography (TEE) can measure the speed at which the LAA empties. However, in clinical practice, TEE cannot accurately measure other hemodynamic parameters, especially in the thrombus regions, since it can either incorrectly label muscles as thrombi or misidentify thrombi hidden in one of the lobes [24,25]. Consequently, an improved strategy must be developed. In clinical research, 4D magnetic resonance imaging (MRI) is a cutting-edge technology that provides more information about 3D blood flow during the cardiac cycle. However, resolution limitations make it difficult to obtain blood flow parameters precisely. In addition, scan times are relatively long [26,27].

It is essential for diagnosis, treatment planning, and risk assessment to comprehend the hemodynamics of the left atrial appendage. Obtaining a CT scan and conducting a CFD simulation of the left atrial appendage is necessary to shed light on the methodology and considerations required for an accurate and meaningful analysis. The patient is placed on the examination table and positioned within the CT scanner. Multiple perspectives of the heart and left atrial appendage are captured. The resulting image data is saved for future examination. The CT images acquired are transferred to a computer and processed by specialized software. LA and LAA contours have been defined and segmented to produce a three-dimensional model of the structure. This model is the basis for subsequent CFD simulations. Mesh generation is the process of discretizing a 3D model into a computational mesh. In this phase, the model is subdivided into smaller elements that depict the geometry of the left atrial appendage and its surrounding structures. The resolution of the geometry is crucial for accurate CFD simulations. The CFD simulation’s conditions are specified. This includes identifying fluid properties such as viscosity and density, as well as the system’s initial and boundary conditions, such as inlet and outlet velocities, pressures, and flow characteristics. After defining the boundary conditions and generating the geometry, specialized software performs the CFD simulation. Mathematical equations are solved numerically, allowing for the prediction of flow behavior. After the CFD simulation has been completed, the results are analyzed and interpreted. Figure 1 presents a scheme of the process.

Abnormal electrical impulses in the roots of the pulmonary vein primarily cause AF. These impulses induce an uneven and inefficient contraction of the LA. This atypical contraction pattern promotes thrombus development in the LAA and is five times more prevalent in people with AF than in healthy patients [46,54]. Although several clinical investigations have analyzed the correlation between LAA morphology and stroke risk in individuals with AF, the underlying mechanisms are still unclear. Current risk categorization approaches for patients are obtained from major clinical trials based on demographic and clinical characteristics such as age, sex, hypertension, and a history of thromboembolic disease [14]. Since they are all non-patient-specific, their predictive value for a particular patient could be enhanced by incorporating mechanical or local patient-specific indicators, such as cardiac morphology or blood flow.

Developments in medical imaging, including TEE, MRI, and 3D computed tomography (CT), have opened up the possibility of applying computational fluid dynamic (CFD) tools for the analysis of intracardiac flow. Early research on LA CFD was performed using complete left-heart simulations; hence, CFD analyses focusing on LAA are comparatively recent [55]. Few publications provide numerical analyses of flow patterns in the LA, with some including the LAA model.

According to the literature, the chicken wing morphology is the least critical when compared to the other geometries, which reveals a link between the LAA morphology and the risk of clot formation [33,35,36,46]. However, varied quantifications of the risks can be found in the literature depending on the population that was analyzed; thus, it is difficult to generalize the significance of this association [5,49]. Notably, the Cauliflower shape appears to be related to an increased risk of thrombus formation [4,35,36].

Several clinical investigations suggested that the risk of stroke could be reduced by utilizing hemodynamic data on the LA and mainly on the LAA [22,26,36,38,46,53,56]. Using a CFD approach, it is possible to access various biophysical indicators in a complex fluid dynamics system, such as velocity and pressure fields, cardiac blood flow rates, vorticity and turbulent kinetic energy, as well as specific metrics such as Wall Shear Stress (WSS), Time-Averaged Wall Shear Stress (TAWS), Oscillatory Shear Index (OSI), Residence Time (RT), and Endothelial Cell Activation Potential (ECAP) [3,33,34,35,36,39,40,42,43,44,45,47,50,53].

The evaluation of velocity and pressure fields revealed insightful information regarding regions of disturbed flow, recirculation, and stagnation, which are known to contribute to thrombotic events [57,58]. These results confirm previous research that linked abnormal blood flow patterns to an increased risk of thrombus formation. The estimation of cardiac blood flow rates enabled a comprehensive evaluation of blood volume passing through various vasculature regions. Both low and high abnormal flow rates have been linked to an increased risk of thrombosis. The computation of vorticity and turbulent kinetic energy distributions yielded important information regarding the presence and magnitude of turbulent flow patterns. Vorticity denotes the local rotation of blood flow, whereas turbulent kinetic energy denotes the presence of turbulent flow patterns [53]. There is evidence that turbulent flow promotes endothelial dysfunction and thrombus formation. Both variables can affect the likelihood of thrombus formation. CFD permits the computation of vorticity and turbulent kinetic energy distributions, which aids in the identification of thrombosis-prone regions. WSS emerged as an important indicator of thrombus formation among the specific metrics investigated [59]. High WSS values were associated with endothelial cell damage, whereas low WSS values were associated with stagnant blood flow. It quantifies the frictional force imparted by the blood against the vessel wall as it flows. Measuring WSS helps identify regions of blood vessels where thrombosis risk may be elevated. In addition, the TAWSS evaluation presented a more comprehensive understanding of the shear stress experienced by endothelial cells throughout a cardiac cycle [60]. It is the average WSS value over a complete cardiac cycle. TAWSS assists in the identification of regions of the vasculature in which sustained low or oscillatory shear stress may contribute to endothelial dysfunction and consequent thrombus formation. OSI analysis permitted quantification of the magnitude and directionality of shear stress changes throughout a cardiac cycle [60]. High OSI values are associated with an increased risk of endothelial dysfunction and thrombus formation in regions with disturbed blood flow and a change in flow directionality. Analysis of Residence Time (RT) revealed the average time blood particles spend in specific regions of the vasculature [61]. Extended residence time caused by flow recirculation or stagnation can contribute to the formation of a thrombus. The identification of regions with extended residence time facilitates the identification of regions with an increased risk of thrombotic events. ECAP is a metric used to estimate the risk of endothelial cell activation, which contributes to thrombus formation [62]. It evaluates the potential for endothelial cell activation by combining multiple hemodynamic parameters, including WSS, pressure, and strain. ECAP assists in identifying regions where endothelial dysfunction increases the risk of thrombosis. These statistical metrics provide valuable insights into the risk of thrombus formation.

Among the reported studies, one of the main discussed topics is the interaction between LAA hemodynamic parameters, morphological type, and further obtained results’ comparison with the data collected by Di Biase et al. [4]. It is important to highlight that blood flow is critical in determining the possibility of thrombosis formation, particularly under AF conditions [44]. The flow patterns in the LA have been numerically analyzed in CFD studies [3,34,37], with some explicitly focusing on the LAA stasis in AF situations [33,35,50]. Some LAA morphological descriptors, such as ostium characteristics and pulmonary configuration, influenced LAA blood flow patterns [42]. As a result, these investigations were able to provide further knowledge on the AF phenomena and calculate inaccessible blood stasis-related parameters, such as residence time, vorticity, and shear stress. High volume, low blood flow velocity, and two-lobe-appendage are more likely to have blood stasis [42]. Furthermore, the distal part of LAA is reported as the most common region for blood stasis because of the lowest velocity magnitude [44]. Slow flow in the LAA increases blood viscosity, altering secondary swirling flows and intensifying blood stasis [47]. Non-Newtonian effects of blood rheology, neglected in several previous CFD studies, aggravate blood stasis and increase the likelihood of LAA thrombosis, a recognized risk factor in ischemic stroke. Non-Newtonian effects can be subtle when examined using instantaneous metrics but are manifested in the blood residence time [48]. Patient-specific CFD analyses of LA hemodynamics suggest that the thixotropic, shear-thinning rheology of blood can significantly affect flow patterns inside the atrial appendage in a hematocrit-dependent manner [47,48].

CFD simulations have some issues in assessing and quantifying the stasis risk for a particular patient since blood flow washing the LAA is a complex, multi-factorial process. There are primarily two ways to simulate CFD: fixed-wall simulations [3,34,35,36] and moving-wall simulations [34,37]. The first one does not account for the movement of the atrial wall; therefore, it may not accurately represent the atrial flow in all circumstances, especially in sinus rhythm. The other is based on reproducing the patient-specific heart action using medical imaging data. Thus, with this last approach, CFD simulations can properly replicate the hemodynamic state of the patient’s atrium when medical imaging is performed. This presents a challenge for forecasting medium- and long-term stasis in patients with paroxysmal atrial fibrillation. The comparison of the outcomes of fixed-wall and moving-wall simulations has revealed that flow patterns and residence time are remarkably comparable in the case of a compromised function, particularly when both the reservoir and booster functions of the appendage are diminished [33,37]. By employing the rigid-wall concept, it becomes feasible to faithfully reproduce the important conditions corresponding to a specific atrial morphology, irrespective of the atrial function during the period of data acquisition. Consequently, this approach mitigates the potential for inaccurately prognosticating the long-term stability in paroxysmal atrial fibrillation (AF) patients, thereby addressing a significant apprehension associated with the moving-wall simulation method.

The presence of closure devices is also analyzed in the literature [3,41,43,51]. A comparison between the results indicated that LAA closure significantly impacted blood flow velocity and paths. LAA closure successfully reduced LA vortices in strength and duration, indicating that percutaneous LAA occlusion can effectively reduce flow patterns associated with thrombus formation.