Vascular calcification is the abnormal deposition of pathological mineral components in the vascular system, which is closely related to numerous cardiovascular diseases and is regarded as an important risk factor for adverse cardiovascular events [1]. Clinical and epidemiological data show that vascular calcification is a common pathological manifestation prevalent in patients with atherosclerosis, chronic kidney disease (CKD), hypertension, etc. ^[2][3][4][2,3,4]. Additionally, vascular calcification can be found in about 80% of vascular injuries and 90% of coronary artery diseases. Previous studies believed that vascular calcification was a passive process of calcium phosphate deposition, but subsequent studies confirmed that vascular calcification was an active and controllable process similar to osteogenesis. This process encompasses the activation of osteogenic signaling, the osteogenic transformation of vascular smooth muscle cells (VSMCs), and other effectors mediating abnormal vascular calcification ^[5][6][5,6].

Flowing blood can exert a frictional force called shear stress on the vessel wall, but its effect can vary in hydrodynamic properties depending on the geometry and location of the vascular tree [7]. In complex blood flow environments, such as arterial branches and vascular bends, the shear stress acting on the vascular wall is different from the physiological magnitude [8]. Through the signal transduction of endothelial cells (ECs) and VSMCs, mechanical signals are converted into electrical and chemical signals, and thus the “switch” of vascular calcification is turned on [9]. During the process of vascular calcification, ECs and VSMCs play crucial roles. They not only activate osteogenic signals but also engage in crosstalk, jointly mediating calcification. Given the significant influence of fluid mechanics on cardiovascular diseases, emerging imaging technologies such as 4D Flow MRI and computational fluid dynamics (CFD) have emerged, greatly enhancing the diagnostic and treatment capabilities of related diseases.

In recent years, technological advances in computer science and imaging have significantly propelled the field of cardiovascular imaging. Traditional cardiovascular imaging primarily focuses on depicting the geometric characteristics of the cardiovascular lumen and its changes during the cardiac cycle. However, blood flow imaging techniques, which are rooted in fluid dynamics, have expanded the scope of cardiovascular imaging. In addition to conventional vessel morphology, these techniques encompass the physical properties of the fluid, such as flow velocity and pressure distribution, at any given time. The laws governing blood flow are governed by mass and momentum conservation equations ^[10][116]. The mass conservation equation states that the sum of inflow and outflow rates in a small space is equal to zero. On the other hand, the momentum conservation equation describes the balance of forces acting on the fluid, including convective or “swirling” flow, pressure gradient, and friction due to viscosity. The mechanical stress information derived from blood flow is often indicative of potential adverse cardiovascular events. For instance, excessive WSS in coronary arteries can increase the likelihood of plaque rupture, whereas too-low WSS can lead to plaque progression ^[11][117]. Capturing the fluctuation or oscillation information of WSS is crucial for assessing the occurrence and progression of diseases such as vascular calcification or atherosclerosis. Flow energy loss (EL) is defined as the energy dissipation caused by turbulent flow in diseased conditions ^[10][116]. A significant increase in flow energy loss can not only indicate ventricular function overload but also serve as an effective predictor of heart failure occurrence ^[12][13][118,119]. Surgical interventions aimed at effectively reducing flow energy loss can lead to improved long-term cardiac function while reducing cardiac workload.

A prominent emerging technology, 4D Flow MRI, introduces an innovative in vivo approach to assess fluid mechanics parameters. Technically, 4D Flow MRI builds upon phase-contrast magnetic resonance imaging (PC MRI) by incorporating three-directional flow velocity encoding and time-resolved capabilities ^[14][120]. It empowers the comprehensive measurement of fluid mechanics parameters within the heart and major vessels, providing full volumetric coverage throughout the entire cardiac cycle. The resulting data (3D + time + three velocity directions) facilitates the calculation of a multitude of derived fluid mechanics parameters, encompassing wall WSS, EL, pressure gradient, and pulse wave velocity, among others, significantly enhancing the evaluation of 3D fluid mechanics in vivo ^[15][121]. Furthermore, 4D Flow MRI excels in precision measurements of intricate blood flow patterns, exemplified by its ability to accurately assess false lumen flow in aortic dissections or entry/re-entry flow in cardiac valve diseases ^[16][17][122,123]. In addition, 4D flow MRI data are typically acquired during free breathing, utilizing retrospective electrocardiogram (ECG) gating with an end-expiratory navigation gate to synchronize the cross three-way blood flow coding gradient-echo pulse sequence ^[18][124]. This technique enables the retrospective evaluation of flow information across the entire vascular system from any image plane, as both anatomical and flow information are incorporated for every pixel in a 3D volume. Moreover, 4D flow MRI allows for time-resolved cine velocity acquisition. However, it is important to note that the time dimension in this context does not represent real time but is an effective average derived from multiple heart cycles. Consequently, any fluctuating or pulsatile changes in blood flow have a minimal impact. To visualize 4D flow MRI data, various techniques are employed, including streamline, isosurface, vector field, and volume rendering. Furthermore, the volumetric acquisition enhances the ability to accurately quantify complex cardiac blood flow ^[19][125]. With the rapid advancement of highly accelerated imaging and cutting-edge technologies, including artificial intelligence, 4D Flow MRI is expected to achieve higher speeds at a lower cost ^[20][126]. Given its ability to provide comprehensive spatiotemporal velocity vector data closely related to vascular pathophysiology, 4D Flow MRI has been applied in intracranial and cardiac vascular imaging. In the cardiovascular domain, 4D blood flow MRI is predominantly used for congenital heart diseases, but it also holds significant importance in other cardiovascular conditions, such as aortic aneurysms, aortic stenosis, pulmonary hypertension, and heart valve diseases ^[21][127].

However, there is still a lot of room for the development of 4D Flow MRI. Plenty of recent studies have explored the basis of it. 18F-sodium fluoride (18F-NaF) is a marker of calcification activity that identifies active regions of vascular calcification, the levels of which correlate with future disease progression and adverse events ^[22][128]. Minderhoud et al. ^[23][129] developed a software to explore the correlation between WSS and 18F-NaF PET uptake through precise co-registration of 4D flow MRI and 18F-NaF PET data. It can analyze the potential link between WSS and bicuspid aortic valve. However, 4D Flow MRI technology is slightly insufficient in time and space resolution, and the quantitative determination of fluid dynamics parameters takes a long time. Winter et al. ^[24][130] developed a set of post-processing algorithms based on a flexible reconstruction framework. It can greatly shorten the evaluation time of global pulse wave velocity and 3D-WSS, and significantly improve the analysis efficiency of in vivo measurements. Garrido-Oliver et al. ^[25][131] developed and tested a fully automatic aortic 4D flow MRI analysis process based on machine learning. Its automatic blood flow assessment results are in excellent agreement with manually measured in-plane and through-plane rotational flow descriptors, and axial and circumferential WSS, greatly improving the quantification efficiency of blood flow velocity.

Different from the direct measurement data of 4D flow MRI, CFD calculates hydrodynamic parameters through computer simulation of a fluid model. This imaging technology can provide extremely high temporal and spatial resolution, and can be effectively applied to small blood vessels such as coronary arteries that cannot be detected by MRI ^[26][132]. Meanwhile, in some highly diseased flow with extremely high-velocity turbulent jets, the hydrodynamic parameters including WSS and EL can still maintain accuracy. For patients with coronary calcification, the diagnostic performance of coronary computed tomography angiography (CCTA) is often affected by calcification artifacts ^[27][133]. Compared with invasively measured fractional flow reserve (FFR), CFD model-based CT-FFR showed very high diagnostic performance in all lesions suspected of coronary artery disease (CAD), according to a Chinese multicenter study. In particular, the high specificity, sensitivity, and accuracy of CT-FFR, even in patients with calcifications, are significantly superior to previous CCTA assessments ^[28][134]. In addition, CFD modeling can also generate equations of fluid dynamics based on the geometry and fluid parameters of the patient’s vessels ^[10][116]. By combining “virtual surgery” with computer graphics simulations, CFD can guide optimal surgical decision making. However, CFD also has the disadvantage of being time-consuming. The high cost of modeling cardiovascular hemodynamics with available resources has also hindered the incorporation of CFD into clinical practice ^[29][135]. Acquiring accurate blood flow parameters in a low-cost and efficient manner is crucial for the diagnosis of cardiovascular diseases. AI, especially computer deep learning technology, makes it possible to achieve the above goals. Machine learning enables instantaneous or fast predictive outcomes. Su et al. ^[30][136] incorporated the blood flow WSS values of 2000 ideal coronary arteries calculated by CFD simulation into the machine learning model. By adopting multivariate linear regression, multi-layer perceptron, and convolutional neural network architectures, it is possible to directly generate WSS values within 1 s without using CFD. Through comparing the computational accuracy, the convolutional neural network outperforms other architectures, with a normalized mean absolute error of 2.5%. Lv et al. ^[31][137] designed a fast, end-to-end, pixel-wise AI-based platform, including an automatic segmentation platform for aortic segments and a time-averaged wall shear stress (TAWSS) computing platform. By incorporating the CFD data set to train the AI model, it can automatically estimate the value and distribution of the ascending aorta TAWSS, with an ideal clinical application prospect. Gharleghi et al. ^[32][138] used computer deep learning technology to predict the luminal WSS magnitude of coronary artery bifurcations throughout the cardiac cycle based on steady-state solution, vessel geometry, and additional global features. Compared with CFD-derived values, the model has a deviation of <5% and an average calculation time of <2 min, which ensures high-fidelity predictions while achieving fast calculations. Computational deep learning techniques have significantly reduced the computational cost of large-scale population-based studies involving coronary hemodynamic metrics, and may open the way for future clinical integration.

Hemodynamic modeling based on three-dimensional quantitative coronary angiography (3D-QCA) has potential value in detecting obstructive lesions or lesions with a vulnerable phenotype. The model can reconstruct coronary anatomy and assess lesion severity in real time, thus providing another attractive option for WSS calculations ^[33][139]. The 3D-QCA-derived WSS correlates well with the WSS estimated by models reconstructed by intravascular imaging data ^[34][140]. Additionally, 3D-QCA-derived WSS can also identify vulnerable plaque and stratify cardiovascular risk in patients with a borderline negative FFR (FFR: 0.81–0.85) ^[35][141]. Assessment of WSS along plaques will help to better characterize vulnerable plaques, defining individualized risk of plaque rupture and stroke. Quantitative flow ratio (QFR) is a technique for calculating FFR based on 3D-QCA and CFD. Without pressure guide wire and hyperemia induction, it is superior to angiographic guidance in terms of the number of stents implanted, the dose of contrast agent applied, and the operation time. In a large-sample, multicenter, randomized, controlled clinical trial (FAVOR III China) conducted by Xu et al. ^[36][142], compared with angiography-guided percutaneous coronary intervention (PCI), QFR-guided PCI significantly improved the 1-year clinical endpoints of patients, with less myocardial infarction and ischemia-driven revascularization, showing a better prospect of broad clinical application of QFR. Conventional ultrasound imaging cannot accurately assess flow velocity in contact with the arterial wall. Ultrafast vector Doppler can calculate WSS by measuring the velocity vector of the entire 2D image. The setup for measuring WSS has been validated in vitro on a linear flow phantom by comparing measured values with in silico calculations ^[37][143]. The method provides a means of delineating the hemodynamic constraints of arterial plaques. The use of deep-learning-based ultrasound imaging for flow-vessel dynamics (DL-UFV) has the opportunity to improve the measurement accuracy of vascular properties and hemodynamics. Park et al. ^[38][144] designed an integrated neural network for super-resolved localization and vessel wall segmentation. It can be used to measure velocity field information of blood flow by combining with tissue motion estimation and flow measurement techniques. Through validating the evaluation results in mouse carotid arteries of different pathological types (aging and diabetes), DL-UFV is demonstrated to outperform conventional ultrasound flow and strain measurement techniques in measuring vessel stiffness and complex flow-vascular dynamics.