Increased intrahepatic vascular resistance or hepatic disease such as cirrhosis and hepatic fibrosis can result in a condition known as portal hypertension (PH), which is characterized abnormally elevated pressure in the portal vein system (Fei et al., 2017, Karagul et al., 2016). It is clinically necessary to classify patients with PH according to their portacaval pressure gradient (PCG), a value by subtracting inferior vena cava pressure from portal vein pressure, for appropriate treatment plans (de Franchis et al., 2022, Dong et al., 2023, Lv et al., 2023). Rapid and accurate measurement of patients' PCG is essential for precise and scientific treatment. Additionally, transjugular intrahepatic portosystemic shunt (TIPS), an interventional therapy that involves creating a shunt channel in the liver between the hepatic vein (HV) and the portal vein (PV) to divert a portion of the PV blood directly into the HV, thereby reducing the portal vein pressure (Simpson et al., 1993, Zheng et al., 2021), is currently the most widely used clinical technique in PH therapy due to its high success rate in immediately reducing post-TIPS PCG (Bosch, 2021). However, during the follow-up period after TIPS, more than 15 % of patients have been reported to experience an increase in PCG, which can lead to severe complications like intra-abdominal hemorrhage, posing a significant risk to patient’ life and health (Pitton et al., 2022). Therefore, obtaining accurate PCG is of utmost importance for patients with PH, both before and after TIPS.

Currently, the only accurate way to acquire PCG is through the invasive placement of pressure catheters in the portal vein (Xu, Li, & Mao, 2019). However, this invasive measurement not only causes continuous physiological and psychological burden on patients but also have limitations in its application and poses a risk of vascular injury. Although there are some alternative methods to assess PCG in clinics including spleen stiffness evaluation and hepatic venous pressure gradient (HVPG), these methods have their limitations. Spleen stiffness can only provide qualitatively evaluation of PCG (Song et al., 2023)，while HVPG measurement may significantly deviate from the actual PCG (Qi et al., 2019). Therefore, the development and adoption of a widely-used noninvasive method to assess PCG could greatly enhance the clinical diagnosis and treatment of patients with PH.

The advancement of computer technology has considerably increased the use of patient-specific image-based computational fluid dynamics (CFD) simulation in assessing clinical outcomes for patients with cardiovascular disease (Li et al., 2015, Xiong et al., 2021). One notable application of this technology is the evaluation of the fraction flow reserve (FFR), an important indicator of coronary artery stenosis. Traditional, FFR is determined through invasive measurements, however, the wider utilization of computer numerical simulation has allowed for noninvasive FFR measurements based on CFD technology (J. P. Li et al., 2020). This noninvasive approach significant reduces the risk of coronary injury compared to the conventional method, without compromising the accuracy of clinical diagnosis, resulting in its extensive use in clinical practice (J. P. Li et al., 2020).

The replacement of traditional invasive FFR with noninvasive measurements in patients with coronary artery disease suggests that CFD can be used to noninvasively determine patient-specific PCG. Over the years, numerical simulations of portal vein system hemodynamics have significantly advanced. Initially, researchers used the lumped-model (“0 dimension” electrical models) to study changes in PCG after hepatectomy or TIPS procedure (Golse et al., 2021, Golse et al., 2020, Ho et al., 2013). Subsequently, three dimension (3D) numerical simulation of hepatic circulation became popular (Qiu et al., 2023, Rutkowski et al., 2018). However, the 0D model could not accurately account for the impact of patient-specific anatomic geometry on PCG values, while the previous 3D model simulations only adopted simplified pressure outlet boundary conditions, neglecting the influence of downstream intrahepatic branch vessels and resulting in an imprecise flow field (Golse et al., 2021, Qiu et al., 2023). Therefore, this study proposes a new multiscale model that combines of a 0D model and a 3D model based on the well-established studies and utilizes CFD to calculate patient-specific PCG before and after TIPS. The aim is to establish a noninvasive method to assess PCG, which can aid clinicians in guiding personalized post-TIPS observation for PH patients, reduce the occurrence of post-TIPS complications, and ultimately enhance the quality of life for these patients.