The chronic animal experiments were conducted at the animal research facilities at the Charité - Universitätsmedizin Berlin from April until October 2022. They were approved by the ethics committee of the responsible veterinary department for animal protection at the relevant competent authority, the Regional Office for Health and Social Affairs Berlin (registration number G 0091/21). The animals were treated, fed and cared for according to the guidelines of the European and German Society for Laboratory Animal Science (FELASA, GV-SOLAS), as well as standard operating procedures established at the animal research facilities.

Device implantation was performed in 10 pigs, with an approximate weight of 60 kg at the day of device implantation. For each animal CT acquisition was performed seven days before and immediately after device implantation, as well as at 30 and approximately 60 days after implantation, resulting in 4 acquisitions per animal. Two sensors were implanted into each of the 10 animals, one into the left and right pulmonary artery, respectively. Thus, the number of required animals could be halved. This approach was chosen as the hemodynamic interaction between the sensors implanted into each side of the pulmonary artery are neglectable. One animal died after implantation.

During the animal experiments following steps were conducted for each animal following the general procedure: (1) sedation and anaesthesia, (2) pre-treatment CT, (3) device implantation including establishing a venous access, guidewire placement with PA visualization via angiography, implantation site identification and finally sensor implantation followed by (4) post-treatment as well as follow-up CTs, and finally (5) euthanasia and device explantation. For general anesthesia, which was performed in total four times, the animals were sedated with a mixture of atropine, ketamine, xylazine, and midazolam and were intubated, if necessary, with propofol administration and connected to inhalation anaesthesia (low dosis isoflurane 0.4–1% and oxygen) to maintain anaesthesia. In addition, the animals received midazolam via a perfusor (0.1 mg/kg/h). For analgesia, they also received fentanyl (1–4 μg/kg/h) via a perfusor as well as heparin diluted in NaCl via a continous infusion rate of 2 mL/h. To avoid infection they recieved intra-venous antibiotics. The implants were placed using jugular access (via vena jugularis externa). The access was established via a 21 F sheath by venae sectio. The 21 F sheath was a prototype developed for the PAPS. First, a 12 F introducer was used to widen the vein, followed by the 21 F sheath. As the main focus of the experiments was to obtain information for subsequent validation of models for device implantation and device effect simulation, devices were not only placed in the ideal arterial diameter range of 11–14 mm, but also in proximal parts of the left and right pulmonary artery. This approach was chosen to increase the number of occurrences of device migration and thus hemodynamic disturbances that might cause device thrombosis. Respectively, implanted devices were later subdivided into the optimally and sub-optimally implanted devices for further analysis. Euthanasia was performed by injection at least 60 mL KCL under general anaesthesia.

CT image data was acquired using a dual-source multi-slice spiral CT scanner (SOMATOM Definition Flash, Siemens Healthineers, Erlangen, Germany) with a tube voltage of 100 kV, an in-plane resolution of 0.67mm×0.67mm, and a slice-thickness of 0.7 mm. Acquisitions were triggered using electrocardiographic information to facilitate averaging over several heartbeats and reconstructions of temporally resolved images at a temporal resolution of 10 phases per heartbeat. Contrast agents were administered to better visualize the blood pool (Imeron 300, 2–5 mL/kg).

CT image data was used to reconstruct the end-diastolic 3D geometry of the PA including main, left and right PA. The entire pulmonary artery in the field of view was reconstructed. During image acquisition, the aim was to assess at least 80 mm of length of the left and right PA, to ensure that the targeted implantation site, which features relatively small diameters and can be located far downstream to the main bifurcation, was included in the field of view. The reconstruction was performed using ZIBAmira (v. 2015.28, Zuse Institute Berlin, Germany). Mostly manual procedures and few semi-automatic methods were used to reconstruct the 3D anatomy of the PA. In general, all image voxels above a specific Hounsfield Unit (HU) threshold were considered to be potential candidates of the PA lumen. No fixed threshold could be defined for all 40 data sets, as high variations in the contrast agent concentration were observed. Overall, the individual HU thresholds chosen for reconstruction varied between 100 and 250. The PA lumen was reconstructed slice by slice, beginning from the right ventricular outflow tract (RVOT), using different tools implemented in ZIBAmira, such as brushes, flood fill, as well as region-grown algorithms. The reconstruction was corrected by slicing through the data stack in all three directions. The voxel label field was then used to generate initial triangulated surface meshes, which were subsequently smoothed. Finally, centrelines were generated and used to automatically calculate major geometric parameters, such as the length and mean diameters of vessel segments of the main, left and right pulmonary artery, as well as the bifurcation angle between LPA and RPA.

For simulation of the hemodynamics after device implantation, the PAPS devices had to be virtually implanted into the reconstructed PA geometries while ensuring that the device position mimics that of the real post-implantation situation. First, the PA geometry that was reconstructed from pre-interventional CT following the description of the previous section was used as baseline (see Figure 1A). Subsequently, the CT data acquired 30 days after implantation was assessed to identify the subject-specific location of the sensors (Figure 1B). The scan 30 days after implantation was used instead of the immediate post-procedural CT, as the animals did not awake and move before the latter one, meaning that device dislocation due to the animals’ movement could not yet have occurred. 3D geometries of the sensor body provided by the manufacturer were then virtually implanted into the PA.

First, the two CT data sets had to be registered, to account for differences in the animal position and scanner coordinates. To facilitate this, a partial reconstruction of the PA bifurcation region was performed (Figure 1C). Then, the sensor bodies were automatically reconstructed in the post-interventional CT data set using (Figure 1D, red) a high HU threshold of 1200. Subsequently, the sensor geometries are registered with these automatic reconstructions of the real sensor positions in the follow-up data, using ZIBAmira, by minimizing the root mean square of the distances between both geometries. Figure 1D shows the superposition of the PAPS geometries (yellow) and the image-based reconstructions of the implanted devices (red). Similarly, the pre-interventional surface geometry of the PA is registered with the rough PA reconstruction performed using the follow-up CT data, as shown in Figure 1E. In individual cases, slight corrections of the sensor position were necessary to align the sensor surface with the vessel wall and in order to compensate smaller changes in the PA geometry due to somatic growth, or caused by the implantation procedure.

Finally, the sensor geometries are positioned within the PA at the exact locations as indicated in the follow-up CT data (see Figure 1F). To obtain a connected surface geometry enclosing the entire blood pool, the sensor body is subtracted from the PA lumen using the Boolean domain operations provided by STAR-CCM+ (15.04, Siemens PLM, Plano, Texas). While the result is a joint fluid domain, separate surfaces for the sensor body and the PA surface are retained. This procedure was chosen over reconstruction of the PA geometry from the follow-up CT data, as the metallic sensor bodies caused artifacts that rendered reconstruction of the intricate details of the PA, especially smaller branching vessels, impossible. The fixation wires of the sensor were not considered in its geometric model.

Blood flow simulations were performed using STAR-CCM+ (15.04, Siemens PLM, Plano, Texas). The software provides both meshing algorithms to construct the computational mesh and finite-volume solvers for calculation of the intra-arterial hemodynamics. The fluid domain is discretized using polyhedral cells. In addition, six prism layers are introduced at at the vessel and sensor wall to resolve near-wall flows accurately. This information is required to accurately calculate hemodynamic parameters such as the wall shear stress (WSS, τ) and the oscillating shear index (OSI). Exemplary cross-sections of the numerical meshes are shown in Figure 2 for a configuration with and without implanted sensor body.

A mesh independence study found that meshes with approximately 1 million cells (2.5 million vertices) generated with a base size of 0.75 mm allows accurate calculation of OSI and time-averaged WSS (TAWSS) with errors below 3% compared to simulations with very fine meshes (4 million cells), while simultaneously reducing the computational costs (see Supplemental Material). Furthermore, the chosen cell size ensured a wall y+ at the order of one throughout the whole vessel/sensor wall.

Blood was modelled as an incompressible fluid with a density of 1050 kg/m3 and a shear-rate dependent viscosity following a Carreau-Yasuda model with coefficients described by Abraham et al. (17). Given the high Reynolds numbers (>2000) expected at peak systolic flow rates, a k-omega SST turbulence model is used to account for turbulent effects. The vessel wall was assumed to be rigid and a no-slip boundary condition was applied. Each simulation included two consecutive cardiac cycles with the second cycle being used for post-processing of results. Simulation of two cycles was considered sufficient to obtain converged results, as errors between OSI and TAWSS calculated in the second and fifth cycle were less then one percent (see Supplemental Material). A constant time step of Δt=1 ms was used for all simulations. At the main PA (MPA) inlet, a time dependent volumetric flow waveform with a constant velocity profile was prescribed while a constant pressure boundary condition was used at all outlets.

Furthermore, a constant low turbulence intensity of 5% was assumed at the inlet. Flow rate curves at the MPA were generated synthetically using a hybrid approach. First, cardiac outputs (CO) and heart rates (HR) were estimated (see Table 1) based on the animals’ weights, according to scaling laws for pigs (18). Next, flow rates were synthetically generated based on principal component analysis of MRI-measured MPA flow waveforms in pigs, which were published earlier (19). Figure 3 shows all 10 simulated MPA flow rate waveforms with different heart rates, stroke volumes and curve shapes including different peak systolic volume flow rates. Pre- and post-treatment simulations were performed using the same boundary conditions.

Table 1 summarizes demographic and hemodynamic information of the animals as well as the inflow boundary conditions used for the CFD simulations.

Simulation results were post-processed using Matlab R2021a (MathWorks, Natick, MA, USA). Three parameters were evaluated: TAWSS, OSI, and static pressure. TAWSS computes the temporal mean of local WSS as defined in the Equation 1:(1)TAWSS=1N∑t=1NWSSXt2+WSSYt2+WSSZt2where WSSXt is the local WSS in x-direction at a time step t and N is the number of equidistant time steps describing the whole heart cycle. OSI is a measure of directional change of the WSS over time ranged between 0 and 0.5. It is defined in the Equation 2:(2)OSI=12(1−(∑t=1NWSSXt)2+(∑t=1NWSSYt)2+(∑t=1NWSSZt)2∑t=1NWSSXt2+WSSYt2+WSSZt2)whereas no direction change of the WSS vector over time means that the value for OSI becomes zero while a harmonic oscillation of the WSS vector results in the OSI of 0.5. Beside surface averaged values for the TAWSS and OSI, we also calculated areas with low WSS (WSS<0.5 Pa) as well as areas with high OSI (OSI>0.2). Finally the pressure drop caused by the sensor was calculated as a difference between cross-section averaged static pressure measured 10 mm downstream and 10 mm upstream of the sensor. Statistical analysis was performed using IBM SPSS Statistics 28 (IBM, USA). Mean and standard deviation were reported for normally distributed parameters. Normality of distribution was assessed using a Shapiro-Wilk test. For non-normally distributed parameters, median and interquartile [IQR] range were used to report parameter distributions. All tests used a standard significance level of 0.05.

The geometries of all 10 porcine PA reconstructed from the pre-interventional CT images are shown in Figure 4. All geometric parameters evaluated for these geometries are summarised in Table 2. The average lengths of the MPA, RPA, and LPA were 66.5±11.2 mm, 114.1±14.3 mm, and 101.9±12.2 mm, respectively. The average and standard deviations of these vessels’ diameters were 23.8±2.2 mm, 14.9±2.0 mm, and 13.6±1.7 mm. The bifurcation angle between LPA and RPA was on average 80±7 degrees. Average and standard deviations of the number of side branches were 7±1.3 and 6±1.1 in the LPA and RPA, respectively. RPA length was not significantly different then the LPA (p=0.059, Wilcoxon test), however the RPA diameter was significantly larger then the LPA diameter (p=0.047, Wilcoxon test).

The implantation sites of all 20 devices were analyzed with respect to the device position and the vessel diameter. In 12 cases, the device was located in an optimal position regarding hemodynamics. The remaining 8 cases, i.e., both devices in Cases 1 and 3, the RPA devices in Cases 5, 6, and 9, as well as a sensor located in the MPA in redCase 7, were considered to be non-optimal. The position of all devices within the respective PA anatomy are illustrated in Figure 5. Optimal implantation was present, when the entire device is pressed against the vessel wall, causing a minimal flow disturbance and blocking of the vessel. In contrast, a sub-optimal implantation was present, when the device was skewed, reaching from one vessel wall to the other, was located within a side branch (e.g., in Case 3), or was covering a side branch. An example of a skewed device and the resulting hemodynamics is illustrated in Figure 6. In addition to this classification in optimal and non-optimal position, three devices (each one in Cases 1, 4, and 7) were located in the MPA instead of the LPA or RPA, meaning that the vessel diameter at the final implantation site was much larger than the recommended one.

Spatial distributions of TAWSS and OSI for all 10 pre-interventional geometries are shown in Figures 7 and 8, respectively. The averaged surface-averaged TAWSS was 2.35±0.47 Pa, whereas the surface-averaged OSI was 0.08±0.17. Areas affected by low WSS magnitudes were on average 2.5±2.7 cm2, whereas the areas affected by high OSI were 18.1±6.3 cm2. The overall surface area of the PA geometries was on average 152.0±13.2 cm2. The individual values for TAWSS, OSI, as well as the corresponding surface areas are provided in Table 3.

Spatial distributions of TAWSS and OSI for all 10 geometries after virtual device implantation are shown in the lower rows of Figures 7 and 8, respectively. As the devices reduce the cross-section of the lumen and thus act as an obstacle, they might cause flow disturbances resulting in changes of WSS and OSI. On average, TAWSS and OSI after device implantation were 2.45±0.49 Pa and 0.08±0.16, respectively. While both TAWSS and OSI were significantly larger after device implantion compared to the pre-interventional state (p=0.001 and p<0.001, paired Student’s t-test) the respective effect sizes of these changes were 0.22 and 0.01 and are therefore not relevant. In addition to these parameters that are associated with thrombus formation, the static pressure drop across the vessel segments in which the devices were implanted were quantified. On average, the pressure drop was 0.7±1.1 mmHg. In some cases, calculated pressure drops are negative, indicating an increase in static pressure. This is caused by an increase in the cross-sectional area of the PA across the device. Finally, the surface areas affected by low TAWSS and high OSI after sensor implantation were 2.9±2.7 cm2, and 18.4±6.1 cm2, respectively. A significant increase in the surface area affected by low TAWSS (p=0.005, Wilcoxon signed rank test), was observed, however the absolute different was only 0.48±0.22 cm2, which roughly equals 0.3% of the overall PA surface, and is therefore negligible. All individual parameters are provided in Table 3.

In addition to the hemodynamics at the PA surfaces, the device bodies were investigated separately. TAWSS averaged over all 20 devices was 3.07±0.89 Pa and therefore slightly larger than the values observed at the vessel wall, while still being in the same range. No significant difference for TAWSS values at the device surface was found between sensors implanted in the LPA and RPA (3.13±0.93 Pa vs. 3.00±0.90 Pa, p=0.707, paired Student’s t-test). The difference in TAWSS for PAPS and PA surfaces were significant for sensors implanted in the LPA and the RPA (p=0.05 and (p=0.035, respectively, paired Student’s t-test). Similarly, OSI calculated at the device surface was 0.11±0.06 and thus slightly larger than the averages at the vessel wall. However in contrast to the TAWSS, differences for OSI between PAPS and PA surfaces were not significant for LPA and RPA (paired t-Student test). Furthermore, no significant difference for OSI values at the device surface was found between sensors implanted in the LPA and RPA (0.11±0.07 vs. 0.11±0.06, p=0.964, paired Student’s t-test). The individual values for OSI, TAWSS, and the pressure drop for all 20 devices are provided in Table 4.

Finally, the surface areas of the device affected by low TAWSS and high OSI were analyzed. The average device area with low WSS was 0.2±0.1cm2 and therefore 10 times smaller than the area with low WSS measured at the PA surface. In relative measures, less than 7 % of the device surface were affected by low WSS. The device surface affected by high OSI was with median of 0.49cm2 and IQR of [0.29−1.06]cm2 more than 30 times smaller compared to the vessel area affected by high OSI. In relative measures, less than 17 % of the device surfaces were affected by high OSI.

To compare, whether non-optimal device position results in hemodynamic differences, the above-mentioned parameters were also compared between the 12 optimally and 8 non-optimally positioned devices. First, the device area in contact with blood was significantly larger in the non-optimally positioned devices (3.8±0.6 cm2 vs. 2.7±0.3 cm2 vs. p=0.001, Student’s t-test). TAWSS at the device surface was significantly smaller in the optimal compared to the non-optimal cases (2.55±0.56 Pa vs. 3.85±0.71 Pa, p<0.001, Student’s t-test). No significant differences were found for OSI at the device surface (0.12±0.08 vs. 0.09±0.03, p=0.263). Similarly, the comparison of areas with low WSS and high OSI showed no significant differences between optimally and non-optimally implanted PAPS. No differences were found for the device area affected by low WSS (0.23±0.11 cm2 vs. 0.16±0.11 cm2, p=0.188, Student’s t-test) or high OSI (0.70±0.55 cm2 vs. 0.63±0.37 cm2, p=0.744, Student’s t-test). Finally no significant difference was found between pressure drop caused by optimally and non-optimally positioned devices (0.9±1.3 mmHg vs. 0.4±0.6 mmHg, p=0.264, Student’s t-test).

This study is associated with some limitations that should be noted. First, flow rate waveforms used as inlet boundary conditions were generated synthetically, as no subject-specific measurements were available. Second, simulation were performed assuming rigid walls, neglecting the vessel distensibility. Studies using fluid structure interaction to asses hemodynamics in healthy PA reported overestimated WSS when using rigid walls (29). However, PAPS are used in HF patients, which are associated with significantly stiffer PA (30). Furthermore, the recently published work of Kong et al. regarding fluid-structure interaction (FSI) simulations of the PA tree reported only slight differences in wall shear stress calculated using FSI compared against simulations with rigid walls (22). As the main focus of this study was assessing the hemodynamic changes caused by the device, the effects of these assumptions are assumed to be minimal.

Additionally, two sensors were implanted in each animal to reduce the sample size, adhering to the 3R principles. The intended use for the sensor, however, is only one sensor to be implanted into one side of the pulmonary artery. As the pressure gradients across the sensor were approximately 1.0 mmHg and therefore are smaller than the PA pressure, no relevant change in resistance and therefore in flow distribution is to be expected. Implantation of a second device might result in dislocation of the first device.

In this study, only OSI and TAWSS were calculated to assess thrombosis risk as well as occurence of flow disturbances, even though a large number of potential parameters are discussed. These parameters have been selected as they are the most commonly used parameters, common thresholds for them are suggested, and they are applied to a wide range of applications, such as abdominal aortic aneurysms (31, 32), left atrial appendage thrombus formation (33), and medical device thrombosis (34). Another commonly evaluated parameter, the relative residence time (RRT) can be calculated from TAWSS and OSI and was therefore considered redundant for the purpose of this study. Additionally, only wall-bound parameters but no intra-vascular hemodynamics, such as shear rates and recirculation regions were investigated.

Finally, the chronic animal experiment were only run for three months and thrombosis is known to be a long-term effect. However, acute thrombosis, which occurs within 24 h of initial placement as well as subacute or earlier thrombosis, which occurs between 24 h to one month of initial placement are assessed in our animal study. Thus, chances for thrombus formation might have increased with longer study duration. These however, were not possible due to constraints arising from the animals’ growth.