### Simulation study methods

#### Geometric model and meshing

Utilizing a prototype of a Greenfield VCF [3, 17], and vena cava structure sizes extracted from [18], we used Pro/Engineer (version Wildfire 4.0, Parametric Technology Co., USA) and created a cone-shaped filter. The cone-shaped filter was simplified into six symmetrical circular struts each, with a diameter of 0.5 mm. The length of the filter was 30 mm. Figure 3I shows four cases that represent a traditional deployment and a reverse deployment with or without a thrombus, which were investigated using numerical simulations. The volume of the cone thrombus used in the numerical simulation was 0.565 cm^{3}, which is consistent with the volume reported by Wang et al. [16, 19]. The vena cava model, as shown in Fig. 3I, was reconstructed based on computed tomographic images from a healthy male volunteer aged 58 years. The volunteer provided written informed consent to this study, which was approved by the Ethical Committee of the General Hospital of the People’s Liberation Army and carried out in accordance with the regulations of the hospital. We reconstructed the vena cava model images using the commercial three-dimensional reconstruction software Mimics (Materialize, Belgium). Next, Geomagic (Geomagic, USA) was used to improve the quality of the model surface. The vena cava model was 109 mm long.

In each case, all computational models were meshed using tetrahedral and hexahedral elements using ANSYS ICEM (ANSYS Inc., Canonsburg, PA). To ensure that the results were mesh-independent and validated, a grid-adaptation technique was used, which refined the grid based on the geometric and numerical solution data. Boundary layers near the vessel wall were also applied, which were set to 3; the height ratio was set to 1.2, and the total height was set to 0.2 mm. High-density mesh elements were applied close to filters, and the maximum size of the filter was set to 0.15 mm. The final volumes of the meshes corresponded to 3 298 245, 3 838 665, 3 318 325, and 3 798 220 for Case 1, 2, 3, and 4, respectively. In particular, the mesh distribution for Case 4 is presented in Fig. 9.

#### Assumptions

In this study, simulations were performed assuming laminar flow conditions [20]. Blood was assumed to be a homogeneous and incompressible non-Newtonian fluid. Notably, our previous study showed a similar difference in the flow features between the Newtonian numerical simulations and Carreau model simulations in the vena cava [21]. Therefore, only the Carreau model simulation results are provided in this study.

#### Governing equations

Flow simulations were performed based on the three-dimensional, incompressible Navier–Stokes and the continuity equations as follows [22]:

$$\rho ((\partial \upsilon /\partial t) + (\upsilon \cdot \nabla )\upsilon ) = - \nabla p + \nabla \cdot \tau ,$$

(2)

$$\nabla \cdot \upsilon = 0,$$

(3)

where \(\upsilon\) and *p* are the fluid velocity vector and pressure, respectively; *ρ* = 1050 kg/m^{3} is the blood density; and \(\tau\) is the tension tensor, which is expressed as follows:

$$\tau = 2\eta (\dot{\gamma })D.$$

(4)

Here, *D* and \(\dot{\gamma }\) are the respective deformation rate tensor and shear rate, respectively, and \(\eta\) is the viscosity, which is a function of the shear rate.

The Carreau model is used to calculate the viscosity of blood as follows:

$$\eta (\dot{\gamma }) = \eta_{\infty } + (\eta_{0} - \eta_{\infty } )[1 + (\lambda \dot{\gamma })^{2} ]^{((n - 1)/2)} ,$$

(5)

where \(\eta_{\infty }\) = 3.45 \(\times\) 10^{−3} kg/(m s), \(\eta_{0}\) = 5.6 \(\times\) 10^{–2} kg/(m s), *n* = 0.3568, and \(\lambda\) = 3.313 s [23].

#### Hemodynamic parameters

The shear stress on the vessel wall throughout a cardiac cycle was evaluated by using the TAWSS, which is expressed as follows:

$$\mathrm{TAWSS}=\frac{1}{\mathrm{T}}{\int }_{0}^{\mathrm{T}}\left|\mathrm{WSS}\left(\mathrm{s},\mathrm{t}\right)\right|\mathrm{dt},$$

(6)

where *T* is the cardiac cycle period, WSS is the instantaneous wall shear stress vector, and s is the position on the caval wall. The OSI indicates the changing frequency of the wall shear-stress direction as follows [24]:

$$\mathrm{OSI}=\frac{1}{2}\left[1-\left(\frac{\frac{1}{\mathrm{T}}\left|{\int }_{0}^{\mathrm{T}}\mathrm{WSS}\left(\mathrm{s},\mathrm{t}\right)\cdot \mathrm{dt}\right|}{\frac{1}{\mathrm{T}}{\int }_{0}^{\mathrm{T}}\left|\mathrm{WSS}\left(\mathrm{s},\mathrm{t}\right)\right|\mathrm{dt}}\right)\right],$$

(7)

$$0\le \mathrm{OSI}\le \frac{1}{2}.$$

A zero OSI value corresponds to a unidirectional shear flow, and the OSI value is 1/2 when a purely oscillatory shear case occurs [25].

Another useful parameter, the RRT, was also calculated. Specifically, RRT reflects the residence time of flow particles near the caval wall, and it is also recommended as a single metric of low and oscillating shear stress [26]. Thus, RRT is defined as follows [27]:

$$\mathrm{RRT}=\frac{1}{\left(1-2\cdot \mathrm{OSI}\right)\cdot \mathrm{TAWSS}}.$$

(8)

The OSI does not distinguish well between uniaxial pulsatile flow and multidirectional flow. Therefore, the parameter, namely, transWSS, was also introduced. It is expressed as follows [28]:

$$\mathrm{transWSS}=\frac{1}{\mathrm{T}}{\int }_{0}^{\mathrm{T}}\left|\mathrm{WSS}\cdot \left[n\times \frac{\frac{1}{\mathrm{T}}{\int }_{0}^{\mathrm{T}}\mathrm{WSS}\left(\mathrm{s},\mathrm{t}\right)\cdot \mathrm{dt}}{\left|\frac{1}{\mathrm{T}}{\int }_{0}^{\mathrm{T}}\mathrm{WSS}\left(\mathrm{s},\mathrm{t}\right)\cdot \mathrm{dt}\right|}\right]\right|\mathrm{dt},$$

(9)

where *n* is normal to the vessel surface. This new metric has clear advantages over other parameters that have attempted to capture multidirectional aspects. It also appears to be more sensitive to changes in the velocity waveform [29]. Thus, it complements TAWSS and OSI as opposed to replacing them.

#### Boundary conditions and computation

In all cases, a steady-flow simulation was first performed. The solution obtained from this simulation was then used as the initial iteration data for further pulsatile flow simulations. With respect to the steady-flow simulation, a uniform inflow velocity profile with an axial velocity component of 0.1 m/s and a transverse velocity component equal to zero were used at the inlet [30]. We set the outlet as the outflow. The caval wall was assumed to be rigid and non-slippery.

For the pulsatile flow simulation, the time-dependent parabolic flow velocity waveform based on the measurement performed by Zhang et al. (as shown in Fig. 10) was set at the inlet [31]. The other boundary conditions were identical to those in the steady computation.

The finite volume method was adopted to solve the mass and momentum conservation equations using ANSYS Fluent 14.0 computational fluid dynamics solver (ANSYS Inc., Canonsburg, PA). The residual continuity and velocity were assigned a value of 1.0 × 10^{–5}. Six cycles were required to obtain convergence for the transient analysis, with 200 steps in each cycle (time = 1 s). The pulsatile calculation was performed on a computer equipped with a 2.20 GHz Intel(R) Xeon(R) CPU processor and 64 GB of random access memory (RAM). The computational time-span approached a week for each scenario.

### Animal experiment methods

#### Animal experimental setup

The use of animals in the present study was approved by the local ethical committee (Guizhou Institute of Animal Husbandry and Veterinary Science, Guiyang, China) and was based on the laboratory animal administration rules of China. A healthy adult male goat weighing 51.2 kg was used for the experiment. The goat was anesthetized through an intramuscular injection of a general anesthesia agent of QMB (a product of the Department of Veterinary Surgery, Northeast Agricultural University, China.) at 0.1 mL/kg body weight. Initially, an attempt was made to deploy the VCF in an inferior vena cava from the femoral vein. However, the results indicate that the femoral vein of the goat was excessively thin to allow it to separate from the vessels, thereby making it difficult to insert the filter. The filter was deployed in the superior vena cava from the jugular vein of the goat.

Option™ VCF, a commercially available filter, is cone-shaped and in wide clinical use. In this study, the Option™ VCF (Argon Medical Devices, Frisco, Texas, USA) was inserted into the superior vena cava via the jugular vein of the goat using B-mode ultrasound guidance.

The goat did not exhibit any abnormalities under the preoperative B-mode ultrasound guidance. After anesthesia, the goat was placed in a left lateral decubitus position. The left jugular vein of the goat was fixed. The skin at the surgical site was disinfected as per the standard. The jugular vein was approached using a longitudinal incision in the middle of the neck with adequate vessel separation, and the vessel was subsequently punctured using a puncture needle. The Option™ VCF was then deployed in the superior vena cava according to the routine procedure of VCF deployment.

After deployment, computed radiography (CR; Carestream Vita CR System, Rui Ke Medical Shanghai Co., Ltd.) was used to determine the VCF location. The CR image display showed that VCF was present in the superior vena cava (Fig. 8II).

Eleven days after the VCF deployment, 10 mL off-venous blood was drawn from the goat with the help of a syringe. The blood sample in the syringe was maintained for 30 min at room temperature, and the syringe was then depressed to form cylindrical thrombi on sterile gauze. A cylindrical thrombus of 2–6 mm in length was selected. Autologous thrombi were flushed using physiological saline. Subsequently, a mixed suspension containing at least three clots per 1 mL of physiological saline was prepared. Next, 20 mL of the mixed solution of autologous thrombi was injected into the left jugular vein of the goat (Fig. 8I). Although collagen proteins or other coagulation factors could also simulate a thrombus, these invaders may cause an immune response [32]. Therefore, autologous blood clots are more favorable than other coagulation factors. To develop a canine model of an acuter PE model, extant studies have also considered using autologous blood clots as simulated thrombin [33]. Previous studies revealed that placing a filter in the vena cava for longer than 2 weeks leads to intimal hyperplasia and vascular adhesion [34, 35]. Therefore, 14 days after the VCF deployment, the goat was euthanized through an overdose of anesthesia, and the filter was removed to observe thrombosis capture on the spot.