The dynamics of aortic blood flow have been examined as far back as the 16th century, when Leonardo da Vinci postulated that, based on its morphology, the sinus of Valsalva, a region of the aortic root, may play a crucial role in initiating retrograde blood flow and specific vortices after aortic valve closure [12]. Centuries later, in 1856, Rudolf Virchow, the German “father of pathology”, also noticed a spatial relationship between abnormal blood flow and atherosclerosis [13]. Subsequently, in the 20th century, multiple biomechanical researchers, radiologists, and surgeons conducted multi-dimensional studies on aortic blood flow and the fluid-structure interface of mechanical parameters. For instance, Friedman et al. [13] created a silicone model of an aorta, obtained from an autopsy of a 63-year-old male with moderate atherosclerosis, and used laser Doppler to measure fluid velocity and wall shear force. They found that different wall shear levels were associated with intimal thickening [13]. Another study by Chang et al. [14] used MRI to describe the flow field within both true and false lumens (FLs) of aortic dissections. Vorp et al. [15] used computer simulation technology to reconstruct two 3D models, and demonstrated that both shape and diameter were essential for predicting the progression of abdominal aortic aneurysms.

The application of CFD technology to the aorta was first facilitated by the data collected by Long et al. [16, 17, 18, 19], who successively conducted hemodynamic studies on superior arch branches, the descending aorta, and key abdominal aortic branches. Their data served as the basis for boundary setting, which was then utilized by subsequent numerical simulation studies based on CTA [16, 17, 18, 19]. Animal experiments, using pigs, were first conducted in 2000 by Angouras et al. [20], where they found that hypertensive states increased aortic medial stiffness and generated wall shear stress (WSS), eventually leading to aortic dissection. In 2009, Doyle et al. [21] developed a silicone blood vessel to simulate the elastic parameters of the human aorta, in order to define the structural properties of the wall of an aortic aneurysm. They noted that the use of wall stress was more able to accurately predict the risk of rupture for abdominal aortic aneurysms [21]. Karmonik et al. [4, 22, 23, 24, 25] conducted a series of studies on Stanford type B aortic dissections, which demonstrated the feasibility of using CFD for analyzing aortic dissection and the hydrodynamic factors contributing to type B dissection events. In addition, intraoperative simulation of the extent of tear coverage and thoracic endovascular aortic repair (TEVAR), as well as prognosis, were also studied, thereby serving as the foundation for applying CFD in decision-making under surgical simulation training [4, 22, 23, 24, 25].

There are several major steps involved in implementing CFD. The brief process is shown in Fig. 2.

Fig. 2.

Diagram of the steps for performing a CFD analysis. CFD, computational fluid dynamics; 3D, 3-dimension.

Currently, evaluating the risk of aortic rupture is mainly based on a single morphological index, namely aortic diameter; in patients without high-risk factors, such as Marfan’s syndrome or other familial genetic disorders, having a maximum diameter of $\ge$5.5 cm is an indication for surgical intervention. However, even for patients with a diameter of 5.5 cm, the probability of adverse events, such as rupture, is still 5–10% [26]. With an increased understanding of unilateral morphological indicators, it is inadequate to only use a diameter or $\ge$5.5 cm to predict the risk of aortic rupture and the necessity for surgical intervention. A combination of biomechanical factors is considered the most reliable method for determining whether an individual is at risk for developing an aortic rupture [27]. The significance of different biomechanical factors is shown in Table 1 (Ref. [5, 6, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]).

A prevailing biomechanical factor is WSS, which was found in one study to be significantly lower in dilated ascending aortic aneurysms, compared to aortas from normal individuals without aneurysms. This, coupled with peak systolic pressure load, was 18.56–23.8% higher in the dilated segment of the aorta, indicating that the combination of lower WSS and higher pressure could contribute to increased risk for further expansion and aortic aneurysm rupture [28]. This association between lower WSS and higher pressure with aortic rupture has been supported by multiple other studies, in which lower WSS or time averaged WSS (TWSS), with higher oscillatory shear index (OSI), were more prone to expansion, dissection or rupture [29, 30, 39, 40], compared to normal areas. However, most of these studies were limited by being comparative in nature, and only focusing on fluid dynamics indicators for specific patient groups, leading to selection biases. A comprehensive study was performed in 2021 by Bappoo et al. [31], which included 295 patients with an abdominal aortic aneurysm, to which CFD was applied. More importantly, a longer median follow-up period of 914 days was conducted, and additional clinical baseline data, such as age, gender, baseline diameter, blood pressure, and smoking history, were included in the prediction model. In this study, lower WSS was identified as an independent risk factor for abdominal aortic aneurysm progression, and adverse events were more prevalent (44%), compared to those with intermediate (27%) and high WSS (29%; all p = 0.010) [31]. WSS anomalies, along with higher relative residence time (RRT), was also associated with platelet aggregation and activation, which promotes thrombus formation in aneurysms [32, 33, 34]. Abnormal WSS can also affect the arrangement and morphology of endothelial cells and stimulate cytokine secretion, which can increase intercellular permeability, promote inflammatory cell adhesion and local oxidative stress, rendering the region more prone to future focal dissections [35]. In contrast, a higher WSS was associated with reduced elastin and smooth muscle cells, leading to stiffer, less compliant aortic walls, eventually resulting in thinning, dilation, and rupture [6, 36]. Based on these findings, a predictive model combining clinical baseline characteristics, along with morphological and mechanical indicators, would significantly improve the identification of individuals with a high risk for aortic aneurysm progression and rupture, especially among those with maximum aortic diameters 5 cm [5, 37].

According to the International Registry of Aortic Dissection (IRAD), the incidence of type B aortic dissection was about 33%, of which 57–63% were the uncomplicated type. The in-hospital mortality rate was approximately 10% [41]; however, it is approximately 25% among discharged patients who have undergone conservative treatment, with an approximately 66% chance of aortic-related adverse events [42]. As a result, CFD could serve as a useful tool for developing timely surgical interventional strategies, via its analyses of true/false luminal hemodynamic performance, as well as aiding in the early detection of adverse events, such as significant progression, poor organ perfusion, reverse tear to type A dissection, and threatened rupture (Table 2, Ref. [4, 9, 22, 43, 44, 45, 46, 47, 48, 49, 50, 51]). Karmonik et al. [4] conducted a series of studies on type B dissection, using CFD technology. They found, based on reconstructions and simulations of the blood flow field using MRI, that the false luminal blood flow was disordered and turbulent, particularly at the aortic location proximal to the primary rupture. Furthermore, false luminal pressure was ten times higher than the true lumen, serving as the basis for the false lumen being more at risk for further expansion. WSS was also lower in the false lumen, which favors thrombosis formation [4]. A follow-up study had shown that higher WSS was present around the primary tear, and further expansion of the false lumen resulted in decreased flow velocity and pressure, along with increased turbulence, which may serve as a self-compensatory mechanism, but at the expense of an increased risk of rupture [43]. A significant increase in pressure difference, in terms of ascending versus descending aortas, and true versus false lumens, among type B dissection patients, compared to healthy controls, was also observed in a comparative study. The study also postulated that this significant difference could serve as a marker of abnormal abdominal organ perfusion [22], which is further supported by a research group from China. This team demonstrating that significant pressure differences between true and false lumen was indicative of poor prognoses [9, 52]. These findings, however, were contradicted by the findings from Long et al. [50], who conducted CFD with finite element analysis based on CTA on 3 patients, and found that the progression of descending aortic aneurysms was not associated with pressure difference changes, but with larger WSS differences between the true and false lumen. This is due to the pressure differences between true and false lumen in the distal descending aorta being close to 0 or a negative value. Furthermore, the flaps in this region are generally thicker and less mobile, making it more difficult for the true lumen to be constricted.

In addition to pressure and WSS, higher RRT values are present near the area of the celiac artery, which was positively correlated with local thrombosis, thereby contributing to true luminal blood flow obstruction and subsequent organ hypoperfusion [51]. Dillon-Murphy et al. [49] found that distal secondary tears were critical for reducing false lumen pressure and limiting dissection progression. This is consistent with the study by Tolenaar et al. [44] showing that patients with only a single or a smaller distal tear, exhibited unfavorable long-term hemodynamics, compared with those with multiple secondary tears [45, 49]. However, a larger distal tear may be a significant risk factor for progressive aortic expansion and rupture, as observed by CFD analysis conducted by Rudenick et al. [46] on 3 silicone models with different tear conditions. Additional factors affecting type B dissection progression are primary tear size and location, in which greater false luminal blood flow is associated with larger tears, as well as tears closer to the aortic arch. Increased false luminal enlargement has also been associated with larger TWSS around the tear, and contributes to further enlargement [47]. However, this association between larger TWSS and increased false luminal size was found by Xu et al. [48] to only be applicable for 2.5 dyn/cm${}^2$. In addition, Osswald et al. [53] found that elevated WSS in the aortic wall adjacent to the left subclavian artery was a risk factor for retrograde type A aortic dissection (RTAD).

Endovascular surgeries, in the form of TEVAR or endovascular aneurysm repair (EVAR), have become an important treatment for type B aortic dissection and thoracic aortic aneurysms. However, TEVAR/EVAR has multiple complications, such as endoleaks, stent displacement/collapse, and RTAD. The occurrence of these complications had been related to the anatomical complexity of the dissection, aortic curvature, anchoring site conditions, and various other biomechanical indicators, all of which could be identified by CFD to aid in predicting their occurrence (Table 3, Ref. [7, 8, 9, 10, 23, 24, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64]). As a result, CFD technology could be a useful tool to evaluate the likelihood of complications from TEVAR/EVAR.

One example regarding the application of CFD was performed in 2006, when Frauenfelder et al. [54] established a silicone model, based on CTA data from 11 aortic aneurysm patients, to develop CFD simulation using the fluid-structure interaction method (FSI). The quantitative results indicated that the blood flow in the descending aorta and the iliac arteries were more uniform, the flow field was smoother, and the size and number of eddy currents were reduced after stent implantation [54]. In addition to the characterization of the general flow field after stent implantation, other studies have suggested that short, rigid, and strong branch stents were able to transmit forces from the stent bifurcation to the aortic bifurcation, which was impossible with long, flexible stents. Therefore, all displacement forces at the bifurcation must be borne by the stent trunk and the infrarenal aneurysm neck anchoring this area, leading to higher wall stress and shear stress around the stent bifurcation area, which may serve as the mechanical basis behind long-term stent displacement and endoleaks [54].

Karmonik et al. [24], using MRI-based CFD to simulate proximal and distal tear closure for type B dissection, found that TEVAR was able to effectively reduce false luminal antegrade blood flow. The total false lumen pressure decreased significantly (by approximately 97%), and the maximum WSS in the false lumen was reduced, all of which could lower the incidence of long-term complications. However, it was found that a short-term reversal of the pressure difference between the true and false lumens occurred at the end of systole, in which the pressure in the false lumen was higher than that in the true lumen. This may serve as the basis for some type B dissections, with weak flaps, being associated with the long-term risks of stent rupture, displacement, and endoleaks [23, 24, 55]. In contrast, distal tear closure or thrombosis could result in increased false lumen pressure, thus increasing the long-term risk of rupture [45, 56]. Chen et al. [9] found in a follow-up simulation study, conducted on a type B dissection patient, that separate closures of either the proximal or distal tear were unable to reduce false luminal perfusion, and that stent coverage was required. The requirement for stent coverage was further supported by Alimohammadi et al. [57], who found that compared to having a single stent covering the proximal rupture, double stents covering both proximal tears reduced descending aorta flow resistance by 40%, and significantly attenuated elevated WSS in that area. The number of distal tears was determined to be a key factor for occurrence of false lumen thrombosis. Therefore, to promote thrombosis, it is recommended to selectively perform a one-stage repair of distal tears with large areas, and those located in non-visceral arterial branches [58].

Xu et al. [59] conducted a study on the risk factors for further FL expansion after TEVAR. They found that the stable and progressive patients after TEVAR had significant differences in WSS, RRT, and true and false lumen pressure. A significant increase in the true-false lumen pressure difference suggests a potential expansion of the FL. Therefore, early monitoring of the pressure differences, identifying the false lumen entrance location, and measuring maximal pressure difference could aid in predicting the onset of false luminal expansion [59]. The positioning of the TEVAR stent could also affect the occurrence of endoleaks, in which it is often anchored at the proximal end of the aortic arch, when the tear position is high and close to the orifice of the left subclavian artery. This results in the left subclavian artery blood supply being sacrificed, though it did not significantly increase abnormal aortic arch blood flow, as documented by Van Bogerijen et al. [60]. However, this “bird-beak” change increased the risk of poor distal organ perfusion, proximal aortic hypertension, long-term stent collapse, and type I endoleaks [60, 61]. These findings were supported by a follow-up study by Prasad et al. [62] on a patient who developed long-term type III endoleaks after receiving two TEVAR stents. It was observed that the highest stress was located at the junction between the two stents. Furthermore, tribological stability testing showed that most of the surface area (53% of this region) had unstable contacts, corresponding to the location of the Type III endoleaks [62].

The cross-limb EVAR stent has higher helical blood flow and is able to reduce stent thrombosis. However, EVAR stents are associated with higher stress fluctuations, which may cause stent fatigue and subsequent long-term device failure [8]. Due to these limitations for EVAR, open surgery may be considered for abdominal aortic aneurysms with short necks and lesions close to the renal artery orifice. Open surgery was found by CFD simulations to significantly reduce abdominal aortic false luminal retrograde blood flow, compared to EVAR. However, iliac arterial retrograde blood flow, flow rate, and WSS were all significantly increased [63]. Additionally, after replacing the ascending aorta and total arch replacement with the frozen elephant trunk technique, distortion of the graft is the main factor affecting ascending aorta hemodynamics and thrombosis. Studies have shown that the platelet activation potential index could be significantly reduced if the artificial vessel maintained its proper shape and surface smoothness [64].

Independent risk factors for predicting early mortality from type A aortic dissections include age, previous cardiac surgery, hypotension/shock, cardiac tamponade, pulselessness and myocardial ischemia/infarction. CFD has proven to be useful for obtaining hemodynamic indices, which have provided new directions for developing prediction models of adverse events associated with type A dissections (Table 4, Ref. [3, 65, 66, 67]). Table 4 summarizes the characteristics of individual studies associated with type A aortic dissection (TAAD).

Due to type A aortic dissections being associated with profound pathological changes and complex morphological variations, particularly with respect to multiple irregular ruptures, as well as the involvement of the aortic sinus and branch vessels above the arch, it has been extremely difficult to construct a 3D model suitable for CFD simulation. This is further complicated by the fact that most type A dissection patients cannot undergo MRI examination due to the acuteness and instability of their conditions. As a result, the application of CFD approaches for this disease has been hampered, owing to complicating factors, such as the large number of branch outlets and errors in the setting of the outlet boundary, adding another layer of complexity to the development of a CFD model.

Nevertheless, systematic hemodynamic analyses of type A aortic dissection, using CFD techniques, have been conducted. Malvindi et al. [3] used a simple CFD technique as part of their follow-up of a patient who initially presented with an ascending aortic aneurysm and later developed type A dissection to perform transient peak simulations of pre- and post-dissection conditions. The results of these simulations showed that abnormal spiral flow was present in the ascending aortic aneurysm, along with significant increases in wall stress and WSS for the right posterior portion of the ascending aorta, both of which corresponded with the site of the dissection flap. This suggests that regions with high wall stress and WSS are the most prone to developing intimal damage and tears in type A aortic dissections [3].

In another analysis, Chi et al. [65] used CFD for type A aortic dissections in five patients, in which the dissecting flap was artificially removed to simulate pre-dissection conditions. They found that increases in ascending aortic diameter corresponded to increased mean WSS, and the area was related to the actual tear site [65]. Furthermore, the progression of the ascending aortic diameter was still a risk factor for predicting long-term dissection in aortic aneurysm patients. These findings were further supported by Ma et al. [66], who found that the mean wall pressure, mean WSS, mean vortex strength, and mean eddy viscosity of patients who died from type A dissection were significantly higher than those who survived. Mean eddy viscosity was found under multivariate logistic regression analysis to be an independent predictor of in-hospital mortality (p = 0.037, AUC = 0.94) [66]. CFD simulation was used by Xiao et al. [67] to study the problem of poor liver and kidney perfusion in post-type A aortic dissections, and showed that increased branch vessel flow velocity and higher branch vessel wall WSS were associated with lower probabilities of poor organ perfusion post-surgery.

Even though few studies exist for type A aortic dissection CFD hemodynamics, these studies have proven the feasibility of CFD for studying the type A aortic dissection, which could reflect blood flow field characteristics, both pre- and post-dissection, as well as providing quantitative calculations for biomechanical indicators, which can provide assistance in developing risk prediction approaches for type A aortic dissections in the future.

CFD is a very promising analysis method. It can transform the complexity of human vessels and blood flow into a simplification of mathematical models, giving computational fluid dynamics the potential to enhance standard medical images and thus aid in treatment decisions. However, at the present stage, it requires a lot of labor and computing time, making it difficult to calculate the results in a short time and immediately put into a wide range of clinical application. Another major disadvantage is that the biomechanical data obtained can only be used for intra-group comparison because the early boundary conditions were set differently across teams. In the future, with the further improvement and consensus of the algorithm and branch vessel outlet pressure, rate and resistance, unified calculation can be completed for mutual comparison and evaluation.