Thrombus formation is mediated by the four-stages of the blood coagulation cascade, centred around the generation of the key enzyme thrombin (Figure 1B). In the initiation phase, injury to the endothelial lining exposes tissue factor (TF) and releases plasma von Willebrand Factor (vWf), forming trace amounts of thrombin from its precursor, prothrombin. The subsequent amplification and propagation phases lead to platelet activation near the injury, initiating large-scale thrombin generation which cleaves plasma fibrinogen to form insoluble fibrin monomers. In the ensuing stabilisation phase, polymerisation of fibrin monomers creates a crosslinked fibrin net that traps platelets and red blood cells (erythrocytes). This solidification of blood to a fibrin and erythrocyte-rich clot (rouleaux) finally generates a haemostatic plug over the area of endothelial injury to facilitate healing (10). AF alters this fine-tuned coagulation system and induces a pro-thrombotic state by the mechanisms outlined in Virchow’s triad (see details below), significantly increasing the risk of stroke (11).

The primary site of interest is the LA appendage (LAA), a muscular extension to the LA, in which over 91% of AF-related thrombi are formed (Figure 1C) (12–15). AF-related thrombi originating from the LAA are larger and have higher risk of mortality than other thromboembolic sources but can be prevented by oral anticoagulation (OAC) (2). The LAA has four clinically defined morphologies—chicken wing, windsock, cactus, and broccoli (Figure 1D)—each with thin trabeculated endothelial walls and varying risks of thrombogenesis associated with their size, shape and blood flow velocities (16–18). The LAA, especially the “broccoli” morphology, is most susceptible to pathological thrombus formation as it demonstrates all three aspects of Virchow’s triad.

Atrial fibrillation induces blood stasis by facilitating uncoordinated electrical activations which impair LA contractility and lead to reduced blood flow velocities, particularly in the LAA (19, 20). During AF episodes, increased blood residence times and peak flow velocities of <20 cm/s inside the LAA facilitate accumulation and interactions between procoagulant factors, platelets and erythrocytes in this region (Figure 1C) (21–24).

Hypercoagulability in AF patients is expressed by abnormal levels of vWf, thrombin-antithrombin complex (TAT), plasma fibrinogen and fibrin D-dimer, all of which are associated with increased propensity for thrombus formation in the LAA (11). Studies suggest the hypercoagulable state is induced by the onset of acute AF, with as little as 15 min of AF being sufficient to increase thrombin generation (25–27). Markers of endothelial dysfunction, such as inflammation and matrix remodelling, may be linked with this altered coagulability, but the precise mechanisms remain unclear (28).

Finally, endothelial dysfunction is caused by abnormalities in the endothelial lining which can trigger thrombus formation by release of thrombogenic proteins in the LAA (29). The reduced cardiac output due to the irregular contractility of the myocardium during AF is often compensated by LA volume dilation and stretching, resulting in the deposition of interstitial fibrosis, and are recognised predictors of all-cause mortality and ischemic stroke risk (30). Studies also suggest that fibrosis may promote the formation of miniature thrombi on the rough endocardial surface and create more arrhythmogenic substrate thereby perpetuating AF and its associated risk of stroke (31, 32).

For decades, 2D transoesophageal echocardiography (TEE) has been the gold standard modality for detecting the presence of LA thrombi and evaluating the appearance of spontaneous echo contrast (SEC), a predictor of flow stasis strongly correlated with LA thrombus formation, as shown in Figure 2 (34). SEC is generated by ultrasonic backscatter from erythrocytes aggregation, usually mediated by fibrinogen, and is present in ∼50% of AF patients and 90% of patients with thrombi. The severity of SEC is graded based on its visual appearance to assess the subsequent risk of LA thrombus with TEE having an excellent specificity of 100% and a sensitivity of 99% (35). However, the semi-invasive oesophageal intubation is time-consuming and contraindicated for some patients (33). Non-invasive, speckle-tracking Doppler echocardiography has been employed to evaluate LA mechanical function via myocardial strain (36, 37). This metric measures the contractility/deformation of the LA wall, which is severely impaired during AF and directly influences intracardiac blood motion, potentially leading to stasis (38).

Cardiac magnetic resonance (CMR) imaging and cardiac computed tomography (CCT) are two non-invasive alternatives to TEE for the identification of thrombi (39). A meta-analysis and systematic review of clinical trials assessing LA thrombi by CCT showed a mean sensitivity and specificity of 96 and 92%, with dual-enhanced CCT protocols able to increase the latter to 100% (27, 28). A similar meta-analysis showed that contrast-enhanced CMR angiography has a specificity of 95.2% and sensitivity of 66.7%, rising to 99.2 and 100%, respectively for delayed-enhancement CMR with long inversion time (40, 41).

Cardiac magnetic resonance and CCT allow visualisation of the LA anatomy including the PVs, which can provide useful anatomic information to guide AF ablation and LAA occlusion therapy (33). CCT has a spatial resolution of 0.5 mm in the x and y (axial) plane with slice thickness ranging between 0.5 and 0.625 mm and a maximum temporal resolution of 20 phases per cardiac cycle (83–135 ms). CMR achieves spatial resolution of 1–2 mm in the axial plane with slice thickness of up to 10 mm, however, the temporal resolution is more than double at 50 phases per cardiac cycle (20–50 ms) (42). Moreover, CMR techniques such as phase-contrast MRI enable the assessment of blood stasis by visualising blood velocity inside the LA, in either a 3D region of interest (4D Flow) or in slices (2D Flow), shown in Figure 2. However, 4D Flow suffers from challenges in spatiotemporal resolution and difficulty in measuring PV flows accurately, which currently prevent its full clinical translation (43). While CCT sequences cannot image blood flow, the superior spatial resolution enables detailed visualisation of the LAA anatomy (16). Doses of ionising radiation in CCT image acquisition have considerably decreased in recent years but remain a common limitation of this modality, alongside the administration of contrast agents, particularly in dual-enhanced imaging (33).

The extent of atrial myopathy, such as fibrotic lesions, is correlated with the perpetuation of AF and increased potential for stroke (44). Echocardiography, CCT and CMR can assess AF-related increases in LA volume, a surrogate metric associated with endothelial dysfunction and a higher stroke risk (45). Late gadolinium enhanced MRI (LGE-MRI) can generate detailed maps of LA fibrosis, with increased fibrosis levels associated with increased risk of thrombus formation (46, 47). LGE-MRI maps have also been used to validate LA strain measurements determined from echocardiographic techniques, finding an inverse relationship between strain and myocardial fibrosis, as the formation of stiff fibrotic lesions due to endothelial damage degrades the local contractility of the LA wall (48). The standard for invasive substrate characterisation in patients with AF-related myopathies is electroanatomic mapping, involving transvenous mapping of endocardial electrogram voltages, with regions of low-voltage or electrical silence linked to underlying atrial scar (44). Ex-vivo, scanning electron microscopy has been used to visualise myocardial damage in the LAA, showing that prolonged AF can lead to the creation of endothelial craters, which in turn concurred to form a thrombotic mass, comprised primarily of erythrocytes, at the location of severe endothelial damage (Figure 3) (49).

While these imaging techniques can help to reliably identify LAA thrombi, this is often after their formation. Imaging only provides snapshots of empirical biomarkers of structural changes and thrombogenic states at the time of the scan. Thus, it fails to explain the mechanisms of thrombogenesis or provide prediction of stroke risk, which are key steps in stroke prevention therapy. The most cutting-edge applications of cardiac imaging for AF-related stroke are currently restricted to research environments, limiting their impact. However, the imaging techniques currently available to clinicians have fueled the recent progress in image-based biophysical modelling, showing great promise to identify the mechanistic aspects of thrombogenesis.

Computational fluid dynamics (CFD) is an established modelling approach that has been used for decades in (bio)engineering applications (50, 51). By solving the 3D Navier-Stokes equations for fluid motion over a user-defined domain, this technology can quantify blood flow velocity and pressure noninvasively with high spatiotemporal resolution. The accuracy of the model relies on input parameters, such as the fidelity of the anatomical domain segmentation, the conditions defining the behavior of the blood velocity and/or pressure at the domain boundaries (LA wall, PV inlets and mitral valve outlet), and the constitutive parameters of blood (52). Such models can range in complexity from 0D lumped parameter models of blood flow (53, 54) to 3D patient-specific models to replicate realistic cardiac haemodynamics (7, 8, 50, 55–59). Modelling of CFD requires integration in software packages such as CRIMSON, SimVascular and ELMER to perform simulations of cardiovascular flows in 0-3D (60–64).

The most successful applications of CFD to LA flow modelling use 3D patient-specific anatomies and boundary conditions from imaging data, and average values for blood density and viscosity (Figure 4). For example, models can account for the patient-specific myocardial contractility by prescribing the LA wall deformation based on the wall motion tracked from temporally varying imaging data such as Cine-MRI or 4D CCT sequences (Figure 4A). The choice of boundary conditions to personalise the model depends on the availability and quality of the imaging data. 4D CCT series allow for a detailed segmentation of the LA and LAA anatomies at the cost of a low temporal resolution, potentially introducing inaccuracies in wall motion tracking (7, 65), whereas the reverse is true for Cine-MRI sequences (57, 66). Hence, quantitative analyses of shape-dependent LAA haemodynamics are often performed using CCT-based models (56, 67–69). CCT-based CFD studies of the LAA in sinus rhythm (SR) and AF were able to quantify blood stasis by computing the blood residence time inside the LAA, either by releasing a dummy agent concentration in the LAA as a surrogate for SEC (65), or by particle tracking and computation of blood velocity at the LAA entrance (5, 56, 67).

Computational fluid dynamics analyses based on Cine-MRI data yield more accurate measurements of LA cavity flow and motion, but due to poor LAA imaging with this modality, idealised shapes are often used (8, 57, 66). The inflow and outflow conditions are generally treated by prescribing mass flow rates through the PVs and the MV (QPV and QMV in Figure 4B) derived from Doppler echocardiography or 2D Flow data at the valve planes, where available (57, 66, 70). However, the latter is not routinely acquired, and Doppler data is rarely obtained simultaneously with MRI sequences, possibly leading to a mismatch between flow patterns observed in SR or AF using different modalities (6). Several CFD studies achieved successful validation against Doppler echocardiography and 4D Flow data, demonstrating the effectiveness of this approach (7, 43, 65, 70). Currently, all LA flow modelling studies, as summarised in Table 1, have been restricted to small patient cohorts due to the time- and resource-intensive nature of CFD simulations. This limitation, in addition to the lack of a unified validation protocol, has prevented these models from full deployment in the clinical environment.

However, CFD technology is gaining momentum as a clinical tool, with the HeartFlow software package for assessment of coronary artery disease receiving FDA approval, which demonstrates the potential for clinical translation of this approach (71).

AF increases the risk of LA thrombogenesis by inducing a hypercoagulable state due to presence of abnormal thrombogenic protein concentrations (11). Clinical assessment of coagulation function in AF patients relies on the detection of abnormal clotting times, e.g., prothrombin time and international normalised ratio. Coagulability is also evaluated by blood samples to identify biomarkers of elevated coagulation, such as vWf, prothrombin fragment 1+2 and D-dimer (72). Recently, thrombin generation assays have been proposed to reproduce blood coagulation in vitro, yet issues with standardisation between centres and lack of clinical validation prompt the search for more robust approaches (73). Blood coagulation is a complex multifactorial process and the metrics derived from these techniques can only provide an indication of underlying abnormalities, without explicitly quantifying the key factors and mechanisms.

In-silico modelling of the coagulation cascade can address some of these limitations by developing a standardised framework to capture the spatiotemporal dynamics of thrombogenic protein concentrations. Such models can also be used to understand the most important parameters responsible for coagulation disorders using sensitivity analyses (74). The complexity of the cascade requires simplifications to strike a balance between practicality and physiological accuracy of the models (75). To achieve this, most studies focus on the final stages of coagulation, where fibrin is generated by the enzymatic cleaving of fibrinogen in blood (76–81). Unlike white thrombi, which form in higher pressure arterial systems and consist mostly of fibrin and platelets, LA thrombi are primarily comprised of fibrin and red blood cells (82). Although platelets are frequently included in extra-cardiac coagulation models, their role in AF-related thrombi and the need to explicitly model them remains unclear. In this case, the effect of red blood cells is accounted for by modelling the spatiotemporal evolution of protein concentrations.

The behavior of clotting factors is commonly modelled by partial differential equations, known as the reaction-diffusion-convection (RDC) equations, which are easy to integrate with CFD models (Figure 4). Two aspects of Virchow’s triad, hypercoagulability and blood stasis, are reflected in the RDC equations. Hypercoagulability is associated with the RD terms, which model the biochemical reactions of thrombin generation and the subsequent stages of coagulation. Blood stasis is represented by the convective term in the RDC equation, with the blood velocity coming directly from the CFD model.

Early studies on coagulability focused on the reactions in the coagulation cascade in the absence of blood flow (79, 83), followed by increasingly complex models with multiple kinetic equations for various proteins in the cascade (77, 78). While reaction equations alone can describe the chemical interactions between proteins at one spatial point, reaction-diffusion models are needed to describe their interplay in space and thrombus growth (83, 84). The more complex reaction-diffusion models include up to 76 equations to capture thrombus formation from initiation to stabilisation, with emphasis on understanding the impact of various proteins on thrombin generation and spatial growth of thrombi (79–81).

The complete RDC equations enable the most physiologically accurate representation of in-vivo coagulation by coupling blood flow with the biochemical reactions of the cascade, demonstrating that coagulation under flow conditions indicates an increased threshold for thrombus formation (84). This makes clot solidification less likely to occur without significant thrombin generation due to the surrounding blood flow washing thrombogenic proteins away from site of injury. A pioneering study investigated clot formation using a system of 15 coagulation proteins and platelets linked with CFD simulation of blood flow in a 2D channel setting (77). The polymerisation of fibrin was modelled to create the first two-way coupling between blood flow and thrombus growth, which introduced a resistance to flow local to the clot (Figure 5A). This novel approach has informed subsequent studies in which thrombus growth influences blood flow velocity (78, 85, 86). The study of fibrin and thrombus growth dynamics is a continually growing area of interest in both clinical and engineering research fields (87–89).

More recent studies coupled CFD with the RDC equations, advancing from simple 2D channel flows (Figure 5A) to semi-realistic LAA geometries in AF and SR conditions (Figure 5B) and finally to patient-specific 3D models of the LA in an effort to achieve clinical translation (Figure 5C). Rigid-wall CFD models of the LA based on CCT and Doppler echocardiography data were deployed to assess the thrombogenic role of AF using bound platelets at the area of injury as a biomarker of thrombus formation (90). A similar approach was also used on 3D patient-specific models of the LA in both SR and in AF derived from Cine-MRI data (8, 83, 91) where coagulation dynamics were modelled by initiating a thrombin concentration in two locations (near the PVs and LAA) and the accumulation of thrombin was compared between SR and AF in each case.

After the endothelial injury is repaired in regular hemostasis, the clot is broken down in a process known as fibrinolysis, mediated by tissue plasminogen activator. This essential process dissolves the solid thrombotic mass from the endothelial lining (2). However, this aspect of coagulation, often impaired in AF owing to unregulated thrombus growth, has been represented by RDC equations in general channel flow simulations but remains to be modelled in the fibrillating LA (92).

The modelling of various characteristics of coagulation, summarised in Table 2, has significantly improved knowledge of this complex process. The critical next stage is development of patient-specific coagulation modelling by deriving parameters for the RDC equations. With current technology, these values are measured using thrombin generation assays and mathematical approximations, however significant variability between patients and expensive testing prohibits this from widespread use (93). Furthermore, the precise changes to coagulation mechanisms in AF have not been fully addressed yet (75). Future studies should focus of identifying a small number of key parameters that can be derived from patient measurements, and how these parameters change in AF.

In healthy tissue, the lining of endothelial cells has anticoagulant properties which regulate haemostasis. However, structural remodelling of the LA myocardium in AF exposes sub-endothelial TF, triggering coagulation mechanisms. Identification of LA dysfunction in clinic is primarily based on the presence of increased concentrations of proteins in blood samples, such as vWf and asymmetric dimethylarginine (11).

Computational models of endothelial dysfunction may provide a significant advantage in predicting locations that are prone to thrombus formation. Although this area of research is still in its infancy, existing approaches for personalised identification of cellular remodelling may be translated to thrombogenicity in AF patients (94). The most common approaches for identifying regions of endothelial injury through computational modelling use CFD simulations to assess the time averaged wall shear stress (TAWSS) and oscillatory shear index (OSI), Eqs. 1 and 2. These are indirect metrics for identifying locations where endothelial cellular processes may be altered due to abnormal flow patterns (95, 96). An extension to these metrics proposed a new measurement, known as the endothelial cell activation potential (ECAP), based on the ratio of OSI to TAWSS, with higher ECAP values corresponding to greater risk of endothelial susceptibility, Eq. 3 (97). This was then taken further to calculate a platelet activation potential (PLAP) in Eq. 4 which represents the magnitude of shear rates that a fluid particle accumulates travelling through the fluid domain, and ultimately a metric for thrombus formation potential (TFP) defined as the product of ECAP and PLAP. These measures were then used to assess the thrombogenic risk of different regions in a patient-specific anatomy based on their magnitude and spatial distribution (98). While these methods have primarily been tested on a series of carotid arteries with ECAP with expected orders of magnitude ranging from 0.1 to 10 Pa^–1 for the ECAP, with further validation, they may also have potential application to the LA in AF. Combining such approaches with the image-based myocardial wall models outlined in Section 3.1 may provide a powerful tool for the prediction of thrombus formation (9, 99, 100).

Endothelial dysfunction is the most under-explored factor in the modelling of Virchow’s triad. Our incomplete understanding of thrombus formation in AF prompts fundamental questions, such as whether blood stasis or the hypercoagulable state alone would lead to thrombus formation if the endothelium was not compromised, or if the endothelial injury is essential for initiating coagulation in AF. With a lack of consensus on the relative importance of the three factors in Virchow’s triad, further research is required to quantify the role of each factor in thrombogenesis.

Some of these limitations can be overcome by incorporation of machine/deep learning methods to infer prothrombotic biomarkers using image-based biophysical models to accelerate aspects of patient-specific functional assessment (Figure 7) (9, 104–112). An example of this approach is the advent of physics informed neural networks (PINNs) which integrate the PDEs discussed in Section 3.2 as part of the loss function to enable more correct approximations of the solution than earlier forms of machine learning, even with limited data availability (104, 113–115). This development is in line with the Digital Twin vision for precision cardiology which involves creation of a digital representation of the heart updated in real time using data harnessed from electronic health records, imaging data, and wearable technology (116). Combining these approaches by integrating advanced machine learning techniques directly into medical imaging technologies (MRI, CT and Echocardiography devices) to automatically update the in-silico Digital Twin may provide the greatest benefit to the patient. With rapid artificial intelligence inference times enabling simulation results in mere seconds directly from patient scans, clinicians may be able to monitor changes in vital patient information to aid in decision making. This approach has grown in availability, with clinically-validated commercial machine learning algorithms (e.g., Brainomix^® and RapidAI^®) frequently being employed in highly time-sensitive evolving stroke cases to optimise triaging and treatment, showing a potential for translation to stroke-prevention for AF patients (Figure 7, right panels) (117–120). Ultimately, combining biophysical modelling accelerated by deep learning approaches in a similar manner may allow for mechanism-based treatment to be tailored to the patient prior to the occurrence of stroke, massively improving patient outcomes and reducing healthcare costs as proposed in Figure 7 (left panels). However, both in-silico modelling and machine learning for cardiac thrombogenesis prediction must be developed within a rigorous framework of verification, validation and uncertainty quantification to fulfil regulatory evaluation and become applicable in clinics as a reliable approach to stroke risk assessment (121, 122). A proposed approach for validation of these cutting-edge techniques in a clinical setting may require funding for prospective research studies under controlled conditions with sizeable AF patient cohorts. Parameters from imaging techniques such as Cine MRI, CCT, TEE, Doppler flow, and blood samples would be measured prospectively and used to build computational models. The results of such models can be compared with the patient outcomes and the CHA₂DS₂-VASc scores to quantify the accuracy and reliability of in-silico technologies for the assessment of patient stroke risk (112).

Further to the proposed improvements to patient stroke risk stratification, in-silico and imaging techniques can also be used to improve current stroke prevention approaches. Primary treatments for patients at risk of stroke due to AF include prescription of OACs, cardioversion and LAA occlusion therapy. Development of novel OAC’s can be challenging and expensive, however, modelling tools are often employed in the early stages of pharmacological studies using RDC equations (75). Studies have investigated the patient-specific effects of warfarin and heparin on coagulation mechanisms, providing the scope for these tools to be extended to the most recent range of OACs, and development of new drugs for AF patients (93). The choice of whether to cardiovert is based on detection of an LAA thrombus, which can possibly be predicted using the modelling techniques outlined in this Review and ultimately identified by means of routinely available imaging techniques such as TEE. Finally, LAA occlusion (LAAO) is a challenging surgical procedure which involves closing of the LAA entrance to prevent thrombogenesis and is performed when patients are contraindicated to OACs. This technique has warranted pre-surgery virtual implantation using in-silico tools which leverage the patient-specific geometries derived from imaging data. Such interactive modelling can be used to guide and optimise pre-implant planning for clinicians and has shown promising results to reduce risk of device-induced thrombus formation (99, 100).

The field of image-based biophysical modelling is rapidly growing, and novel technologies are continuously being proposed to tackle the greatest challenges facing AF and its associated risk of stroke. The recent developments covered in this Review lay the foundation for the future of this field and eventually, with wider adoption and development, can lead to the translation of such techniques into the clinic for the betterment of the large and growing AF patient population.