Optimizing distal and proximal splenic artery embolization with patient-specific computational fluid dynamics

Abstract

Splenic artery embolization (SAE) has become a favored alternative to splenectomy, offering a less invasive intervention for injured spleens while preserving spleen function. However, our understanding of the role that hemodynamics plays during embolization remains limited. In this study, we utilized patient-specific computational fluid dynamics (CFD) simulations to study distal and proximal embolization strategies commonly used in SAE. Detailed 3D computer models were constructed considering the descending aorta, various major visceral arteries, and the iliac arteries. Subsequently, the blood flow and pressure associated with different coil placement locations in proximal embolization were studied considering the collateral vessels. Coil induced variations in pressure fields were quantified and compared to baseline. The coil induced flow stagnation was also quantified with particle residence time. Distal embolization was modeled with Lagrangian particle tracking and the effect of particle size, release location, and timing on embolization outcome was studied. Our findings highlight the crucial role of collateral vessels in maintaining blood supply to the spleen following proximal embolization. It was demonstrated that coil location can affect distal pressure and that strategic coil placement guided by patient-specific CFD simulations can further reduce this pressure as desired. Additionally, the results point to the critical roles that particle size, release timing, and location play in distal embolization. Our study provides an early attempt to use patient-specific computer modeling for optimizing embolization strategies and ultimately improving patient outcomes during SAE procedures.

1. Introduction

The spleen, often underestimated in its significance, plays a multifaceted role in human physiology, contributing to immune function, hematological homeostasis, and blood filtration (Cesta, 2006). It diligently monitors the bloodstream, promptly detecting and neutralizing foreign pathogens, while also serving as a reservoir for critical blood components such as red blood cells and platelets (Lewis et al., 2019; Mebius and Kraal, 2005). Despite its vital functions, the spleen is highly vulnerable to injury, particularly in cases of blunt abdominal trauma, where it is often the most commonly affected abdominal organ (Quencer and Smith, 2019).

Historically, the standard medical response to splenic injuries has been splenectomy, the invasive surgical removal of the spleen. However, given the organ’s importance, contemporary medical practice seeks alternatives that can preserve spleen function to some extent (Cadili and de Gara, 2008). Specifically, endovascular splenic artery embolization (SAE) has been introduced as a preferred treatment choice, offering a less invasive intervention that can maintain spleen function (Bessoud et al., 2007; Olthof et al., 2014; Liu et al., 2004). SAE can be performed in a proximal or distal fashion (Quencer and Smith, 2019). In proximal SAE, plugs or coils are used to block blood supply to the spleen via the splenic artery, while ideally maintaining some level of blood flow to the spleen via collaterals. In distal SAE, embolic particles are injected to block blood flow to a local injured region in the spleen. As such, proximal and distal SAE are preferred for multifocal and focal injuries, respectively. Clinical evidence suggests that proximal embolization has less life-threatening complications and is simpler to perform (Imbrogno and Ray Jr, 2012; Rong et al., 2017).

Patient-specific blood flow patterns play a critical role in the success of different forms of embolization (Damiano et al., 2015; Taebi et al., 2021; Mahmoudi et al., 2022; Talaie et al., 2022). However, the hemodynamics of the splenic artery is understudied. Earlier computational fluid dynamics (CFD) and particle image velocimetry (PIV) models of the abdominal aorta included the splenic artery in their model as an outlet boundary (Les et al., 2010; Arzani et al., 2014; Scardulla et al., 2017). More recently, the hemodynamics of the splenic artery has been studied with more detailed models of the surrounding visceral arteries (Qin et al., 2021) with a particular focus on studying visceral artery aneurysms (Gao et al., 2022; Li et al., 2022a).

In distal SAE, successful transport of embolic particles to the desired focal region in the spleen is required. The transport of embolic particles within the bloodstream is complicated by factors such as the pulsatile nature of blood flow, the interaction between particles and flow, particle-wall collisions, and the potentially disturbed and multidirectional nature of blood flow. Blood flow mediated particle transport has been extensively studied in other organs in various applications (e.g., (Korin et al., 2012; Childress and Kleinstreuer, 2014; Mukherjee and Shadden, 2017; Amili et al., 2019; Forouzandehmehr et al., 2022)). In proximal SAE, the goal is to effectively reduce arterial pressure in the distal portion of the splenic artery where blood flow is supplied to the spleen without complete blockage (Bessoud et al., 2007; Requarth, 2010). However, we do not understand how coil placement affects blood pressure in the splenic artery, which is likely a patient-specific problem dependent on the collateral blood flow (Requarth, 2010).

Despite the widespread use of splenic embolization procedures, there is still a significant lack of patient-specific models for studying proximal and distal SAE. Our paper seeks to fill this gap by examining proximal and distal splenic embolization using a detailed patient-specific CFD model. We use our model to compare different coil placement strategies in proximal SAE and evaluate success rates in distal SAE based on particle size, release location, and timing to refine the embolization process and ultimately improve its efficacy.

2. Methods

In this study, we utilized computed tomography (CT) data obtained from a male patient with a history of autoimmune hepatitis, cirrhosis, status post deceased liver donor transplant with post-transplant course complicated by portal hypertension, splenomegaly, and thrombocytopenia. The CT was obtained with intravenous contrast timed for the early arterial phase using bolus tracking technique (scan acquired approximately 18 seconds after injection of IV contrast). Helical images were acquired in the axial plane and then reformatted to provide coronal and sagittal images. CT data was anonymized and exported for analysis and CFD simulations in the open-source SimVascular software (Updegrove et al., 2017). These simulations were specifically designed to explore the effects of collateral vessels and coil placements (proximal embolization) causing full occlusion, on the hemodynamics. Subsequently, particle tracking (distal embolization) simulations were performed on the model with collaterals and without a coil.

2.1. Model Construction

The constructed models started from the supraceliac aorta and included the renal arteries, superior mesenteric artery, hepatic artery, splenic artery, and iliac arteries. The splenic artery included the distal portions feeding the spleen. The first model deliberately omitted the presence of collateral vessels, providing a baseline to assess their impact on the hemodynamics. The second model included all three collateral vessels, making it a more comprehensive representation to better understand the role of collaterals. The third model introduced a coil as well as the collaterals to examine the hemodynamic consequences of proximal embolization. Three different coil placement strategies were investigated by changing the spatial location of the coil. Given the very low permeability of coils in SAE, they were modeled as a wall (no-slip, no-penetration) boundary condition where a region representing the diameter of the coil was subtracted from the main model. An overview of the sequential process for building models and schematic shape of coil placement and collaterals arteries are shown in Fig. 1 and the three coil placement locations are shown in Fig. 2.

Figure 1:

The sequential steps in creating a 3D computational model from medical imaging data in SimVascular is shown on the left. The pulsatile flow waveform used as an inlet boundary condition together with the final model along with the three collaterals and coil are shown on the right. The average diameter of the splenic artery is 5 mm and the coil diameter is 6 mm.

Figure 2:

An overview of the distal and proximal embolization strategies is shown. The red surfaces denote the cross-sectional areas representing the five distinct locations for uniform particle release along the splenic artery (distal embolization). These locations (Loc1 to Loc5) are chosen to ensure no bifurcation interference, maintaining consistency in particle trajectory analysis. Among these locations, Loc5 is nearest to the spleen, while Loc1 is the farthest away. The green spheres show the three different places for coil placement (proximal embolization).

2.2. CFD Simulations

The CFD simulations were conducted using the finite element solver in SimVascular. A mesh independence test was performed on two models with 4.20M and 8.98M number of tetrahedral elements. The maximum difference in velocity magnitude between the two cases was less than 2%, therefore all the simulations were done on the 4.20M mesh model. All simulations were done for four cardiac cycles and the fourth cycle was used for post-processing. Each cardiac cycle was divided into 1000 time steps. The fluid was considered as Newtonian (Arzani, 2018) with ρ = 1.06 g/cm³ and μ = 0.04 P.

A pulsatile flow rate was prescribed at the supraceliac inlet based on (Les et al., 2010), which corresponds to rest condition and was mapped to a parabolic profile. Resistance boundary conditions were prescribed at the outlets to achieve physiological flow rates based on data reported in the literature (Sato et al., 1987; Les et al., 2010; Qin et al., 2021). Simvascular’s 1D blood flow solver was used for an initial tuning of the resistances. Subsequently, 3D steady simulations were performed for additional tuning and finally, the outlet flow distributions were verified with the final unsteady simulation to be within 7% of the target flow rates. The artery walls were assumed rigid in all simulations.

2.3. Particle Tracking

To model distal embolization, we utilized Lagrangian particle tracking based on the velocity results obtained from the CFD simulations. Specifically, the Maxey-Riley equation was solved for inertial spherical particles using FlowVC, an in-house code used in prior studies (Shadden and Arzani, 2015; Mukherjee et al., 2016a; Farghadan et al., 2019; Mahmoudi et al., 2022)

$$\left({\rho }_p+\frac{1}{2}{\rho }_f\right)\frac{d\mathbf{v}(\mathbf{\text{x}}(t))}{dt}=\left({\rho }_p-{\rho }_f\right)\mathbf{\text{g}}+\frac{3{\rho }_f}{2}\frac{D\mathbf{u}(\mathbf{\text{x}},t)}{Dt}-\frac{18{\mu }_f}{d_p^2}(\mathbf{\text{v}}(\mathbf{\text{x}}(t))-\mathbf{u}(\mathbf{\text{x}},t)),$$ (1)

where g represents gravity, v and u represent the velocities of particles and fluid, respectively, μ_f is fluid viscosity, and ρ_f and ρ_p denote fluid and particle densities, respectively. Neutrally buoyant particles were assumed eliminating the effect of gravity.

Particles were released uniformly at five distinct cross-sectional locations along the splenic artery as shown in Fig. 2 to understand how altering the release location in the absence of bifurcations can alter successful particle delivery. The number of released particles ranged from 1100 to 1500 for different release locations and convergence was studied where success rates changed less than 1% by increasing the number of particles by a factor of four. Additionally, particles were released at five different time-steps evenly distributed throughout the cardiac cycle.

Embolic particle radii investigated included sizes of 1, 50, 100, 200, and 400 micrometers, corresponding to Stokes numbers of 3.05e-6, 7.64e-3, 3.05e-2, 0.12, and 0.49, respectively, enabling thorough examination of size-dependent effects on distal embolization. The Stokes number is defined as $St=\frac{{\rho }_p{d}_p^{2}U}{18{\mu }_{f}D}$ where ρ_p and d_p represent the density and diameter of the particles, respectively, U is the mean velocity of blood flow in the splenic artery, D represents the diameter of the splenic artery, and μ_f is blood dynamic viscosity. The distal part of the splenic artery has an approximate diameter of 4 mm, resulting in particle-to-artery diameter ratios ranging from 2.5e-4 to 0.1.

3. Results

3.1. Hemodynamics

A comparison of the three models (baseline without collaterals, baseline with collaterals, and second coil placement) in Fig. 3 shows that the presence of collateral vessels does not significantly alter pressure distribution when a coil is absent. This can be attributed to their relatively small diameter, typically ranging between 1 to 1.5 mm. However, upon introducing a coil, the hemodynamic environment undergoes a transformation and the collaterals become essential in maintaining blood supply to the spleen. Notably, in the third case with a coil, the upstream pressure is elevated and the downstream pressure is much lower compared to other cases. Application of a coil leads to a substantial increase in flow rate within the collaterals by up to an order of magnitude. As shown in Table 1, the collateral that initially exhibited the lowest flow rate demonstrates more comparable flow rates to other collaterals when a coil is utilized. Another interesting point about collaterals in case 2 (model without a coil) is that two collaterals show a reverse flow direction (from the splenic artery to the celiac truck), while all three sustain forward flow (from celiac trunk to the spleen) in case 3 where a coil is placed (shown in Fig 3). The flow rate in the collaterals for the different models are listed in Table 1 and the time-average wall shear stress and blood flow streamlines are shown in Fig. 4.

Figure 3:

Static pressure on the wall for three models at peak systole. Case 1 depicts the baseline model without collateral vessels, while Case 2 incorporates collateral vessels. In Case 3, collateral vessels are considered alongside the second coil placement location. Despite collaterals supplying blood flow to the spleen after placing the coil, a significant pressure drop occurs. Moreover, time-averaged velocity magnitude and directions are shown for case 2 and case 3 with second coil placement. As shown, in case 2, the collateral 1 and 3 have inverse flow direction.

Table 1:

The flow rate in collaterals for different cases. The negative flow rate implies that the collateral is transferring blood flow from the spleen to the celiac trunk and positive flow rate implies the opposite.

Case	Case 2 (baseline with collaterals)	Case 3 (first coil place)	Case 3 (second coil place)	Case3 (third coil Place)
Collateral 1	−0.81 ml/min	21.1 ml/min	23.3 ml/min	17.7 ml/min
Collateral 2	3.71 ml/min	18.0 ml/min	19.2 ml/min	15.6 ml/min
Collateral 3	−3.66ml/min	42.65 ml/min	43.9 ml/min	36.7 ml/min

Figure 4:

Velocity streamlines are shown for case 2 (baseline with collaterals). a) peak systole, b) early diastole, and c) mid diastole results are depicted. d) Time-average wall shear stress (TAWSS) streamlines are shown.

3.2. Proximal Embolization

The goal of proximal embolization is to reduce the pressure at distal splenic arteries where blood is supplied to the spleen without fully eliminating blood flow. Various pressure drop and flow rate results following the three different coil placement locations (Fig. 2) are listed in Table 2. Our findings reveal a significant reduction in pressure right after the coil compared to baseline (${\text{P}}_{\text{After}}^{\text{Coil}}-{\text{P}}^{\text{Base}}$) ranging between −39 mmHg to −42 mmHg. The pressure right before the coil also increased but to a lesser degree (4–10 mmHg). Interestingly, the difference between pressure right after and before the coil $\left({\text{P}}_{\text{Before}}^{\text{Coil}}-{\text{P}}_{\text{After}}^{\text{Coil}}\right)$ was much less variable for different coil placement locations and varied between 46–50 mmHg. Pressures at the distal portion of the splenic artery P_Distal are also reported. The coil placement reduced this pressure compared to baseline between 36–40 mmHg with the highest reduction achieved by the third placement. This pressure drop is crucial for promoting healing by preventing spleen rupture. The pressure pulse at this distal location was also lowest for the third placement (11 mmHg). The flow rate to the spleen in case 2 (baseline with collaterals) was 166 ml/min, and coil placement based on its location can reduce this flow to 54.4–70.1 ml/min.

Table 2:

Pressure, stagnant blood volume, and spleen flow rate results are compared between three coil placement strategies. P^Base represents the baseline pressure in case 2 without coil. ${\text{P}}_{\text{Before}}^{\text{Coil}}$ and ${\text{P}}_{\text{After}}^{\text{Coil}}$ indicate the pressure immediately before and after the coil, respectively. P_Distal is the pressure at the distal part of the splenic artery before the bifurcations to the spleen and its baseline value in case 2 is ${\text{P}}_{\text{Distal}}^{\text{Base}}=116\text{mmHg}$. $\Delta P_{\text{Distal}}$ denotes the difference between maximum and minimum pressure in the cardiac cycle (pressure pulse) for the distal part of splenic artery and its baseline value for case 2 is 47.5 mmHg. The blood flow rate to the spleen is 166 ml/min during baseline (case 2) and its alteration for various coil placements is listed. Stagnant blood volume listed in the table refers to the volume of blood with PRT>20s (ensuring full stagnation). Stagnant blood flow volumes before and after coil placement were separately calculated.

Coil place	First place	Second place	Third place
${\text{P}}_{\text{Before}}^{\text{Coil}}-{\text{P}}^{\text{Base}}$	+8 mmHg	+10 mmHg	+4 mmHg
${\text{P}}_{\text{After}}^{\text{Coil}}-{\text{P}}^{\text{Base}}$	−42 mmHg	−39 mmHg	−42 mmHg
${\text{P}}_{\text{Before}}^{\text{Coil}}-{\text{P}}_{\text{After}}^{\text{Coil}}$	+50 mmHg	+49 mmHg	+46 mmHg
${\text{P}}_{\text{Distal}}^{\text{Coil}}$	80 mmHg	80 mmHg	76 mmHg
${\text{P}}_{\text{Distal}}^{\text{Coil}}-{\text{P}}_{\text{Distal}}^{\text{Base}}$	−36 mmHg	−36 mmHg	−40 mmHg
$\Delta P_{\text{Distal}}$	14.5 mmHg	14.5 mmHg	11 mmHg
Flow rate to spleen	66.4 ml/min	70.1 ml/min	54.4 ml/min
Stagnant blood volume before the coil	0 mL	0.42 mL	1.08 mL
Stagnant blood volume after the coil	2.52 mL	2.06 mL	1.28 mL
Total stagnant blood flow	2.52mL	2.48 mL	2.36 mL

A consideration regarding coil implementation pertains to stagnant flow within the celiac trunk and splenic artery, which may potentially lead to clot formation. To study this, we calculated the particle residence time (PRT) (Reza and Arzani, 2019) by tracking tracers over 20 cardiac cycles. PRT denotes the duration required for a particle to exit a particular region of interest. Here, the region of interest is defined as a segment of the splenic artery where we placed the coil up to the next bifurcation region (downstream or upstream). The PRT results for the three coil placement locations are shown in Fig. 5 demonstrating high flow stagnation before and after the coil. The first placement location was immediately after a bifurcation, therefore PRT was close to zero before the coil (Fig. 5a). The volume of stagnant flow (defined as the region with PRT > 20s) before and after coil placement is presented in Table 2 demonstrating stagnation variability before or after the coil based on coil positioning and a more consistent total stagnation volume between the cases.

Figure 5:

Particle residence time (PRT) for three coil placements. a) First coil placement, immediately after the last bifurcation, b) second coil placement, and c) third coil placement along the splenic artery are shown. The coil is depicted as a green sphere.

3.3. Distal Embolization

Distal embolization involves the release of particles (emboli) that can accumulate downstream, potentially obstructing arteries supplying blood to the spleen. The efficacy of distal embolization depends on the release time and location of these particles. In cases where the catheter can be maneuvered close to the target, delivery efficiency is higher. However, in scenarios with arteries exhibiting high curvature, such as the case here, navigating very close to the target can be challenging for interventional radiologists.

Here, we considered five distinct locations along the splenic artery where no bifurcations occur as shown in Fig. 2. Additionally, we selected five equally distributed release times throughout the cardiac cycle (t=0, 0.2T, 0.4T, 0.6T, and 0.8T). A snapshot of the particle locations at different times for a representative case (100 μm diameter) is depicted in Fig. 6.

Figure 6:

Snapshot of particle trajectories based on five different release locations and initial times. Representative results for 100 μm diameter (St=3.05e-2) are shown. Particles are represented larger than their actual size for visualization purposes.

The average success rate across all releasing times for different locations and particle diameters are shown in Fig. 7, with the fifth location being the closest to the spleen and the first location being the farthest. The results indicate that particles with diameters of 50 and 100 μm exhibit a higher likelihood of delivery to the spleen. Furthermore, as the catheter advances within the splenic artery, particles with a diameter of 100 μm demonstrate an increasing success rate compared to those with a diameter of 50 μm. To further explore the impact of release timing and location, figure 8 depicts the success rate for particles with a diameter of 100 μm across different locations and release times. The results show that for particles released downstream (loc5), early diastole release is optimal, whereas for particles released farther away from the spleen (loc1) peak systole release achieves the highest success rate. As shown in figure 8, for particles released at peak systole (t=0.2), advancing the catheter decreases the success rate. In contrast, for particles released at early diastole (t=0.4), advancing the catheter increases the success rate. This difference is due to the flow dynamics at the bifurcation where particles reaching the bifurcation during peak systole are more likely to follow the straight daughter branch, whereas particles reaching the bifurcation during diastole are more likely to follow the side daughter branch. Notably, in this patient, the spleen is located downstream of the side daughter branches.

Figure 7:

The success rate for emboli transport to the spleen averaged across all releasing time points and in different locations for different particle diameters is shown. Success rate is defined as the percentage of particles reaching the spleen.

Figure 8:

The success rate for particles with 100 μm diameter (St=1.49e-4) based on different locations and releasing time is shown. Success rate is defined as the percentage of particles reaching the spleen.

4. Discussion

The present study offers valuable insights into the hemodynamic characteristics and embolization outcomes associated with the SAE procedures. By utilizing patient-specific CFD modeling, we were able to uncover the interplay between the hemodynamics and embolization strategies. One of the key findings was the significant impact of collateral vessels on hemodynamic changes during proximal embolization. While under normal conditions the presence of collateral vessels may not significantly influence the hemodynamics, following proximal embolization, these vessels play a crucial role in keeping the blood supply to the spleen. This highlights the importance of considering post-embolization collateral flow patterns to minimize the risk of ischemic complications. Additionally, we observed a notable pressure drop of approximately 46–50 mmHg on the two sides of the coil for all three coil placements where the pressure upstream was elevated and the pressure downstream was decreased. Pressure reduction at the distal part of the splenic artery is a crucial parameter in proximal embolization success, and our results demonstrated that the third coil placement can achieve the greatest reduction, likely due to the proximity to collateral arteries.

Our investigation revealed that particle size, release location, and release timing are all critical factors influencing the success rate of delivery to the spleen. Namely, the particles tend to follow the straight major daughter vessel after the bifurcation if they reach the bifurcation during systole and move towards the side branch that leads to the spleen if they reach the bifurcation during diastole. If particles are released at a distance away from the spleen, their trajectories vary, leading to some particles reaching bifurcations sooner while others arrive at another time. Consequently, if the release strategy leads to more particles encountering the bifurcations during systole, the success delivery rate during distal embolization will be decreased. Experimental studies have also shown the importance of bifurcation flows in emboli transport (Li et al., 2022b).

Our CFD simulations yielded blood flow distributions that align with reported values in the literature (Les et al., 2010; Sato et al., 1987; Qin et al., 2021; Wang et al., 2021), as we adjusted our boundary conditions to match physiological values. The maximum flow rate error at the outlets was 6.5% compared to the flow rates reported in the literature. The flow rate to the spleen in our simulation was calculated at 166 ml/min during baseline (case 2). In (Sato et al., 1987), this flow rate is reported at 179 ± 37 ml/min for a group of 24 subjects, while in (Wang et al., 2021) it is reported that spleen flow rate is 100–300 ml/min in a healthy adult.

In the comparison between proximal and distal embolization strategies for splenic artery embolization, our study unveils distinctive yet complementary approaches to achieving therapeutic efficacy. Indeed, combined proximal and distal embolization strategies have been attempted (Sato et al., 1987). Proximal embolization, characterized by coil placement to reduce blood flow into the splenic artery, offers a direct and targeted method for reducing spleen size. Our results demonstrate that the precise positioning of the coils can have an influence on the outcome. Specifically, it is desired to achieve significant reductions in distal pressure, while maintaining a reasonable amount of blood flow through collateral perfusion. The results in Table 2 show that between 33% and 42% of the baseline blood flow to the spleen could be maintained with the collaterals, while significantly reducing the distal pressure (36-40 mmHg). The precise amount of blood flow and distal pressure reduction could be optimized by patient-specific variation in coil placement with our patient-specific CFD model. Interestingly, it has been reported that an average systolic pressure drop of 40 mmHg in the splenic artery after using coils contributes to the healing process (Thony, 2016), which matches the pressure drops observed in our study.

On the other hand, distal embolization involves the release of embolic particles into the splenic artery, where their trajectories are influenced by blood flow dynamics and arterial geometry. Our prior similar studies in other applications have shown a significant role for flow topology in the emboli trajectory (Farghadan et al., 2019; Meschi et al., 2021). Specifically, particle release maps can be computed to identify precise release locations within a cross-section to achieve complete success (Farghadan et al., 2019; Childress and Kleinstreuer, 2014). However, in practice, the precise cross-sectional release location is not easily controlled by clinicians. Therefore, in this study, we assumed a uniform probability of release within a cross-section and calculated the success rate. Overall, our findings indicate that proximal embolization has the potential to provide higher efficiency, which is also supported by previous clinical studies (Imbrogno and Ray Jr, 2012; Rong et al., 2017).

Despite insightful results, several limitations of our work should be acknowledged. First, while we compared some of our overall results with the literature, a more detailed validation is necessary. Experimental validations are crucial for final implementation in clinical settings. Additionally, our study utilized one-way coupled equations for particle tracking and two-way coupling between blood flow and particle dynamics can become important for larger particles (Mukherjee et al., 2016b), particularly as one approaches the smaller distal vessels. Future studies should investigate two-way and four-way interactions between the flow and particles. The effect of wall compliance on embolization results remains to be investigated. The coil in proximal embolization was modeled as a wall, while porous media models can provide a more accurate representation. However, coil permeability in proximal embolization is very low and therefore we anticipate a small effect. The study is based on a single patient-specific anatomy, combined with another patien’s cardiac waveform from a separate published study, therefore the conclusions need to be verified under more controlled conditions in a cohort of patients.

In conclusion, our study provides valuable insights into the hemodynamic factors influencing splenic artery embolization procedures. By elucidating the impact of collateral vessels, particle size, and release location and timing on embolization outcomes, our findings contribute to the ongoing efforts to optimize embolization strategies and improve patient care. Our results suggest patient-specific investigation of embolization strategies before clinical implementation to minimize complications.