2.1 Clinical statistics: Enrolled patients
This study is a retrospective multi-center trial study. We counted 150 stenosis vessels of 136 patients who underwent FFR catheter surgery in Peking University People's Hospital, Beijing An Zhen Hospital of the Capital University of Medical Sciences and The Second Affiliated Hospital of Zhejiang University from 2017 to 2020. All patients underwent CTA scanning. Every central institution has undergone an ethical review, all patients signed informed consent forms. We confirmed that all experiments were performed in accordance with relevant guidelines and regulations. The exclusion criteria of the clinical trial in this study included poor CTA image quality, coronary artery occlusion, and patients undergoing thoracotomy with Tavi, as shown in Fig. 2 for the inclusion process.
We need to conduct THREE-DIMENSIONAL reconstruction of patients' CTA images, obtain personalized coronary artery vascular structure of patients, and measure the coronary artery vessel diameter of each patient. The resolution of CTA image was 512*512 pixels, the adjacent slice layer was 1mm and the pixel quality of each slice was 0.5mm*0.5mm. Mimics 20.0, an interactive medical image control system, was used for image reconstruction in this study, and the diameter of vessel stenosis was measured in the software, as shown in Fig. 3. All patients' clinical data were processed by the Statistical software IBM SPSS Statistics. We compared differences between the ischemic group and the non-ischemic group by one-way ANOVA using the F-test for diameter.
2.2 Numerical simulation experiment: Idealized construction of the three-vessel model of coronary artery
According to the standard structure of the patient's coronary artery model, we established 8 idealized coronary artery models (1, 2, 3, 4, 5, 6, 7 and 8) containing three vessels (right coronary artery, left anterior descending branch (LAD) and left circumflex artery (LCX)). For the 3D model of the coronary artery, it was assumed that the vessel wall was rigid . Models of coronary artery stenosis were divided into two groups based on the diameter.
The stenosis of models 1, 2, 3 and 4 were located in the LAD (diameter 4 mm), and the stenosis rate was 40%, 50%, 60% and 70%, respectively. The stenosis of models 5, 6, 7 and 8 were located in LCX (diameter 3 mm), and the stenosis rate was 40%, 50%, 60% and 70%, respectively. The rate of narrowing was calculated from the diameter of the narrowing. as shown in Fig. 4.
The above models were divided into tetrahedral meshes by ANSYS ICEM CFD software. As shown in Fig. 5. the meshes of all models were analyzed with mesh sensitivity. Through ANSYS CFX finite element simulation, we assumed that the vascular wall was rigid and impermeable without slippage, the blood material property was adiabatic and comprised of incompressible viscous Newtonian fluid, and its flow was unsteady laminar flow. The density of blood flow was set at 1050 kg/m^3, and the viscosity of blood was set at 0.0035 Pa •s.
2.2 Geometric multi-scale coupling calculation method
In this study, coronary artery geometric multi-scale methodology  was used to calculate FFR CT. The 0D/3D coupled geometric multi-scale model is composed of two parts, one is the three-dimensional model composed of three vessels of the aortic root and coronary artery, and the other is the local standard coronary artery lumped parameter model, which provides boundary conditions for the three-dimensional model.
As shown in Fig. 6. The entrance of the 3D model of coronary artery is connected with a lumped parameter model simulating a human heart module, and the exit is connected with a lumped parameter model simulating an aorta module and coronary microcirculation model, respectively. The lumped parameter module provides boundary conditions for the hemodynamic solution of the 3D model of coronary artery.
In the centralized model of multi-scale cardiac modules, the power source cardiac contraction is represented by time-varying capacitance, which can simulate the periodicity of the ventricle. Suga and Sagawa et al.  established the relationship between ventricular pressure and volume through animal experiments. The pressure-volume relationship is represented by the time-varying function E(t) ,
Emax and Emin respectively represent end-diastolic and end-systolic ventricular pressures. En(tn)  is the elastic modulus varying with time and refers to the time of a cardiac cycle. Besides, in the lumped parameter model, we adopted the optimization algorithm (simulated annealing method) to optimize the model's pressure and flow waveform, capacitive inductance and other parameters .
2.3 Calculation of FFR CT
Estimation of FFR based on coronary CTA image comprises five necessary steps: . (1) an accurate personalized epicardium coronary artery anatomical model was constructed based on CTA images; (2) determination of the total coronary artery vessel flow and each branch flow under normal (assuming no vascular stenosis) resting state; (3) determination of the resistance of coronary microcirculation in resting-state; (4) quantification of the change of microcirculation resistance under maximum hyperemia; and (5) the governing equation (N-S equation) of the fluid in the coronary arteries was numerically calculated to obtain the flow rate and pressure in the coronary arteries in resting and congested states, and then FFR was calculated.
2.4 Design of the experiments
According to Kim et al, the total coronary artery flow accounts for 4% of the cardiac output . So, the flow in each branch of the coronary artery can be changed in different models by changing the value of cardiac output. Experiment 1 explored the changes of FFR CT with vessel diameters of 4 mm and 3 mm under different stenosis rates at a specific cardiac output. We used the physiological parameters of standard patients as the initial conditions for multi-scale calculation: heart rate 75 per min, systolic diastolic pressure:120/80 and cardiac output: 5L/min. We calculated FFRCT value and FFRCT rate of change of eight models. Experiment 2 explored the changes of FFR CT with vessel diameters of 4 mm and 3 mm under the same stenosis rate but different cardiac outputs. We took 50% stenosis in the moderate degree as an example, and calculated FFR CT value and rate of change under the condition of model 2 and 6 with a cardiac output of 4 L/min, 5 L/min, 6 L/min and 7 L/min, respectively.