1 INTRODUCTION

Congenital heart disease affects almost 1% of live births,¹ with approximately 20% of these cases involving abnormal right ventricular outflow tract (RVOT) or pulmonary valve anatomy.² These conditions include a variety of congenital heart diseases, including tetralogy of Fallot, double outlet right ventricle, isolated pulmonary valve stenosis, and truncus arteriosus.³ Typically, these conditions require surgical intervention during early childhood, involving procedures like transannular patch plasty or the implantation of valved conduits.^{4, 5} Unfortunately, degeneration of these conduits is inevitable over time and leads to RVOT dysfunction (stenosis or insufficiency or commonly a combination of both),⁶ necessitating multiple re-interventions over the life spans of these patients.

Percutaneous pulmonary valve implantation (PPVI) is a non-surgical treatment for RVOT dysfunction. During PPVI using balloon expandable valves, traditionally, the valve is delivered via catheter to replace the stenosed or leaky valve. The stented valve is anchored by expanding the stent to a diameter larger than the native vessel. The proximity of the RVOT to neighboring vessels, particularly coronary arteries (CAs) and the aortic root (AR), introduces the risk of CA compression and/or aortic valve insufficiency (AVI) due to stent oversizing (Figure 1). Torres et al.⁷ reported that approximately 14% of patients who underwent balloon test sizing before device placement (5% of total patient pool) experienced AR distortion and/or AVI. Similarly, CA compression is observed during balloon sizing in about 5% of all patients^{8, 9} and up to 21% in patients with abnormal CA anatomy.⁸ These concerns are magnified in complex congenital heart disease patients, where variable anatomy, iatrogenic distortions, and prior interventions make assessing AR or CA compression risk using existing noninvasive imaging methods challenging. If undetected before PPVI, AR, or CA compression can be disastrous or even fatal.¹⁰

The current gold standard for assessing these risks in the congenital catheterization laboratory involves balloon sizing/angioplasty before stent/valve deployment.⁸ Despite its high success rate at assessing coronary compression risk, stent/valve expansion pre-testing in the catheterization laboratory has limitations, including misinterpretation,¹¹ invasiveness, potential hemodynamic effects, and healthcare cost implications. Alternative approaches to assess PPVI risks without balloon sizing include assessing potential structural complications using computed tomography (CT),^12-14 magnetic resonance imaging,^{13, 14} and 3D printing.^{13, 15} However, these methods do not assess the complex interaction that happens during stent deployment and the resultant outcomes.

Finite element (FE) modeling is a computer-aided design and analysis tool with potential to assess PPVI risks virtually, as demonstrated by previous studies.^{16, 17} Caimi et al.¹⁶ simulated PPVI with balloon-expandable valves for three candidates, correctly identifying CA compression in one and successful PPVI in the other two. Capelli et al.¹⁷ modeled seven patients, accurately predicting outcomes in six, including one CA compression case and five patients with successful PPVIs. Neither study addressed the risk of AVI. The computational time required for complex FE analysis poses a challenge in the clinical setting. Caimi et al.'s¹⁶ models, which simulated interactions between the catheter, balloon, and stent, took ~300 h to run on 16 central processing units. Capelli et al.¹⁷ did not report timing, but their models included similar detail.

An accurate computer-based predictor of PPVI complication risk would be of clear value, and the work of Caimi and Capelli demonstrates the FE modeling's potential value. Herein, we develop a simplified, efficient computational methodology for identifying potential structural complications of PPVI using balloon expandable valves, and we test the methodology in a preliminary retrospective study.

2 METHODS

This IRB-approved retrospective study was performed at the University of Minnesota. Patients who underwent transcatheter RVOT testing using balloon (for intended balloon-expandable stent or stented valve placement) at the University of Minnesota Masonic Children's hospital (Minneapolis, MN) from 2010 to 2020 were included in the cohort if they had pre-procedural cross-sectional imaging (CT scan) of adequate resolution and quality to make 3D models and perform FE modeling (described below). Patients who only underwent cardiac MRI before the procedure were not included due to insufficient resolution of the images for 3D modeling. The technical aspects of balloon testing and transcatheter pulmonary valve replacement have been described previously.¹⁸ Pre-procedural CT scans were deidentified and used for model generation (described below) in a blinded fashion. Once models were generated, the model-predicted outcomes were compared to clinical outcomes noted in the cardiac catheterization laboratory.

2.1 3D computer model generation

The RVOT, AR, and CAs were segmented using Seg3D¹⁹ from CT angiograms obtained before catheterization lab intervention. Using Meshmixer (Autodesk), the 3D vessels were smoothed and extruded to thicknesses of 1.5 mm for RVOT,²⁰ 1.8 mm for AR,²¹ and 0.7 mm for the CAs,²² assumed constant along the vessel length (Figure 2B). The volume surrounding the vessels, identified by Boolean subtracting the vessels from a larger block of material, was filled with homogeneous adipose tissue. To simplify the model characteristics, adipose tissue heterogeneity and tissue calcification were not considered in the current model.

All 3D model components were discretized by tetrahedral meshes. An appropriate mesh density was considered to be fine enough to capture the vessel shape but coarse enough to run efficiently. Blood vessels were described by finer meshes than adipose tissue, with average element volumes of 0.11 and 1.14 mm³, respectively. A mesh convergence study (Supporting Information Methods) confirmed that the selected mesh densities yielded accurate solutions.

3 RESULTS

3.2 Patient-specific analysis

We provide examples of three patients, one in each category: (1) no AR distortion or CA compression, (2) AR distortion and (3) CA compression.

• (1)

  Figure 2 provides an example of a simulation in which stent expansion did not significantly reduce the lumen diameter of any vessels of interest (AR or CAs). The aortic sinus wall displaced slightly (Figure 2D–F), but the reduction in AR diameter was less than 2%. The CAs were not compressed by simulated stenting. The model prediction was retrospectively confirmed to agree with clinical observations; this patient safely received a stented valve after a negative pre-test in the catheterization lab.

• (2)

  In contrast to Figure 2, Figure 3 shows simulation of a PPVI candidate who experienced AVI during balloon angioplasty in the catheterization lab. The model estimated a 30% reduction in lumen diameter due to RVOT expansion (Figure 3D–F). The CAs were undisturbed. During balloon sizing in the catheterization laboratory, AVI was observed in this patient. Due to the risk of AR distortion and AVI, this patient did not receive a stented valve.

• (3)

  Finally, Figure 4 shows a case in which a CA was compressed during balloon angioplasty. The left CA was near the RVOT (Figure 4B), and simulated RVOT expansion pressed against the left CA (Figure 4C). The pressure from the RVOT caused significant displacement of the AR and left CA (Figure 4D), as well as a 31.2% loss in CA lumen diameter (Figure 4E,F). While the AR experienced significant displacement, the lumen diameter dropped by only 17.4%. This reduction was less than the four patients who experienced AVI clinically. In the catheterization lab, left CA compression had been observed during balloon angioplasty, and, therefore, this patient did not receive a stented valve.

3.3 Comparison between model and PPVI clinical outcomes

Table 2 summarizes clinical outcomes and model outputs, and Figure 5 plots the model-predicted reduction in left CA diameter versus the model-predicted reduction in aortic sinus diameter. The most striking result is that patients whose simulated stent expansion induced only low or moderate vessel compression (<20% diameter change in all vessels) had experienced no aortic insufficiency or coronary artery compression in the catheterization lab. For the right CA, all simulations were in the low-to moderate compression range, and no right CA compression was observed in any retrospective case Central Illustration 1.

The four patients that experienced AVI clinically had models with large (>20%) AR lumen diameter reductions. These reductions exceeded all AR lumen reductions in simulations of cases where AVI was not observed clinically, and six of the eight patients that did not experience AVI had models with small (<10%) AR reductions. Two patients (#7 and #12) experienced moderate reductions (10%–20%) to AR diameter in the simulations, but no significant AVI was observed on balloon sizing in the cardiac catheterization laboratory (Table 2).

The two patients who experienced left CA compression clinically had high (>20%) model-predicted left CA lumen reductions, while patients without left CA compression during balloon sizing had simulated left CA compression in the low (<10%) range. For both high-compression simulations, oversizing the stent by 30% created conflicting boundary conditions between the stented vessel and the fixed underside of the left CA where it is embedded in heart tissue. This error was an indication of severe left CA compression, but to achieve model convergence, the stent oversizing condition was lowered to 20%, making the reported lumen diameter reductions underestimates of what one might expect in the clinic.

4 DISCUSSION

In our small retrospective cohort of 12 patients (for both native RVOT and RV-PA conduits), we were able to classify high versus low potential risks of AVI and/or CA compression during placement of balloon-expandable pulmonary valves using a simplified FE stent expansion model, with our classifications of high versus low risk agreeing with the clinical decision that had been made. Our simulations have run times of 2–6 min, which is much faster than previously reported¹⁶ and eliminates the need for supercomputing capabilities. The greater computational efficiency and retained clinical accuracy improve the outlook for pre-procedural FE-based PPVI risk assessment in our preliminary study.

We found lumen diameter change to be an excellent classifier for estimating patient risk in our small cohort (Figure 5). However, in four cases (# 3, 7, 10, and 12 in Table 2), 10%–20% lumen diameter reductions did not correlate with significant aortic insufficiency or coronary artery compression during balloon sizing in the cardiac catheterization laboratory. Lumen reductions of this magnitude may not have a substantial impact on aortic valve function or CA blood flow, or it could be that our FE model overestimates the extent of diameter loss. It is also possible that other metrics of lumen reduction, such as cross-sectional area or hydraulic radius, would be of comparable or even better predictive value; in the extreme limit of this argument, one could perform FEM simulations of flow in the compressed versus uncompressed vessel, including the mechanics of the aortic valve, but the computational cost of such simulations would be inconsistent with our goal of a simplified model.

Our model's clinical relevance is most pronounced at the two extremes of simulation outcomes: either when it predicts very small lumen reductions, indicating that PPVI may be a safe and effective treatment, or when it predicts substantial lumen reductions, signaling a higher risk associated with PPVI for the patient. In cases such as those between 15% and 25% aortic sinus lumen diameter reduction (see Figure 5 above), although the model classifications were consistent with the clinical decision in the cases studied, one would expect there to be a range of model-predicted diameter reductions for which uncertainty in the classification would arise over a larger patient pool. Catheterization laboratory testing would be required for patients in the borderline region.

Our scope was a single, specific question: Can anatomical information alone be used to predict the risk of compressing nearby vessels? With that narrow focus, we simplified the model and improved run times dramatically over previous studies. More detailed CA-compression risk assessment models developed by others,^{16, 17} which required hundreds to thousands of CPU hours in contrast to our few-minute simulations, have allowed for the analysis of stent-tissue interactions, stent deformation, stress distributions in the stents, asymmetric expansion due to calcifications and RVOT curvature, and comparison of specific stents (Melody vs. Sapien). Additionally, there are several studies that model patient-specific PPVI procedures to assess other risks (i.e., stent fracture),³⁰ compare different devices (i.e., balloon-expandable vs. self-expandable),³¹ and estimate stresses in the stent and RVOT wall.³² Our procedure provides an accurate risk assessment of AVI or CA compression but is not intended to perform any of those other calculations. Despite the use of uniform, non-patient-specific mechanical properties, our simplified model enabled accurate predictions of the clinical outcomes even in patients with RVOT conduits and asymmetrical anatomies; again, if one wished to answer more specific questions, a more detailed model might be necessary.

While our models have significantly faster run times than previous studies, image segmentation and model generation are still relatively slow and tedious processes. Improving the efficiency of image segmentation is the aim of many advanced computational studies that utilize machine learning and artificial intelligence tools.^33-36 Combining our FE workflow with automatic image segmentation would result in an improved clinical tool for assessing the risks of PPVI.

Despite its limitations, our preliminary study demonstrates the potential for a simplified FE modeling approach to assess possible risk of AVI and CA compression during PPVI provides impetus for further study, and lays the foundation for potential development of a new tool for pre-procedural risk assessment. A computationally efficient method, which would significantly reduce simulation time when compared to existing PPVI simulations, would be advantageous if it can be developed and validated across a larger patient population. The approach presented herein complements more detailed computational strategies and is part of the growing body of research aimed at improving the safety and effectiveness of PPVI, ultimately benefiting patients with congenital heart diseases.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.