Preclinical Validation of a Patient-Specific Patch-Planning Workflow for Congenital Cardiovascular Reconstruction

Abstract

Purpose

Branch pulmonary artery (BPA) reconstruction is associated with high reintervention rates. We present in vitro validation of a patch-planning workflow accounting for vessel prestretch, tissue properties, and suture uptake, to achieve targeted reconstructed dimensions.

Methods

Two physiologically compliant, centrally stenosed BPA silicone models were created to represent neonatal and child-age repairs. Preoperative CTs were segmented to create 3D models for virtual planning. Patches were designed to restore stenotic regions to target diameters under two physiological pressure extremes, accounting for model and patch material distensibility. Finite-element simulation determined the loaded flat patch configuration. Analytical transformation produced unloaded designs for patches planned at high pressure. Designs were laser projected onto patch surfaces, patches sutured, and postoperative CTs acquired (n ≥ 3 per model/pressure/material). Virtual model credibility was evaluated following a recent credibility assessment framework.

Results

Patches designed for low vs. high pressure differed in size by up to 25%. All samples were reconstructed to within 0.8 mm of the target diameter (n = 45), and all but three were within z-score ± 0.5. Through credibility assessment, we verified that simulations introduced < 3% error versus the analytical solution. Patch size was most sensitive to one standard deviation change in patch stiffness. From experiments, suture uptake exhibited highest variability from allocated offset.

Conclusion

Preclinical evaluation of a patch-planning workflow demonstrated accurate reconstruction of BPA stenosis. Incorporation of material properties is essential to achieve targeted reconstructed dimensions under physiological conditions. Model credibility assessment and in vitro validation of more complex patient-specific anatomy will precede prospective clinical trials.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10439-025-03870-4.

1. Introduction

Patch augmentation of hypoplastic or stenosed vessels is a common type of procedure within the field of congenital cardiovascular surgery. Adequacy of reconstruction of the aortic arch and the pulmonary arteries (PAs) during the newborn and infant periods can have significant impact on long-term outcomes and survival. Patients who undergo patch augmentation for PA stenosis have a high burden of reintervention, with reports ranging from 16 to 64% [1–7]. Commonly identified risk factors for PA restenosis are younger age at primary repair, bilateral disease, and complex native anatomy [1–3]. Patch augmentation for hypoplastic aortic arch is associated with a reintervention rate of 11–21% in biventricular patients [8–10] and 10–30% in single ventricle patients following the Norwood procedure [9, 11–14]. Risk factors for recurrent aortic arch obstruction include age and weight at initial surgery, high post-repair arch gradient, and small pre- and postoperative aortic size [10, 15–19]. Placing a patch that achieves the targeted reconstruction dimensions is essential to reducing the burden of reintervention [10], but several intraoperative factors make this difficult to accomplish. Key technical challenges include visualizing the native anatomy, estimating dimensional changes between physiological pressure and the depressurized operative conditions based on mechanical properties of the patch and native tissue, and tailoring the flat patch material to achieve the desired 3D reconstruction following the natural multi-planar curvature of the PAs and aortic arch.

Standard practice is for patches to be shaped intraoperatively with reference to the unpressurized native vessel dimensions, which limits the ability to achieve precise reconstructed geometry under physiologic loads. A patient-specific preoperative planning workflow would give surgeons access to patches that have been designed to achieve the targeted reconstruction with consideration of local hemodynamics, vessel and patch mechanical properties, surgical approach, and other relevant factors. A handful of groups have previously reported efforts to prospectively design patches and other surgical reconstructions using preoperative imaging and various computational tools. The most prevalent strategy is to optimize (manually or automatically) reconstructed geometry through patient-specific computational fluid dynamics (CFD) simulations of blood flow. This technique has been demonstrated pre-clinically for aortic arch reconstruction [20–22], PA plasty [23], and modified Blalock–Taussig–Thomas shunt placement [24, 25], and applied clinically in a case report for aortic reconstruction for Williams Syndrome [26] and systematically for Fontan surgery [27, 28] and coronary artery bypass grafting [29]. A CFD-based approach is most appropriate for structures that undergo minimal deformation under physiological loading since the models normally assume rigid wall boundaries. Another approach to virtual surgical planning relies on finite-element analysis (FEA) of the anatomy. In FEA-based simulation, the cardiovascular structures are the subject of study, with questions focused on how they bear loads and deform under physiological pressures. This technique is most commonly applied to valve structures in order to inform surgical repair [30, 31]. Meoli et al. [32] combined cardiac FEA with lumped parameter modeling to predict postoperative hemodynamics in single ventricle patients across palliative stages. Vascular patching has been simulated with FEA to assess how patch size, material, and incision location affect geometry and stresses of the reconstructed vessel and patch [33, 34]. Yet another category of virtual surgical planning tools is focused primarily on model visualization and manipulation for the surgeon to interactively plan their reconstruction; these tools often output a flattened patch template that the surgeon can use to reproduce the virtual reconstruction intraoperatively [35–38]. As prospective planning tools become more sophisticated and clinically viable, it is critical that they are rigorously and systematically evaluated prior to clinical implementation.

In this paper, we introduce a model-based vascular patch-planning workflow for generating patient-specific flat patch templates to achieve a targeted 3D reconstructed geometry under physiological loads. Incorporating the advantages of prior tools, our hybrid FEA/analytical model combines surgeon input with objective, population-based statistical data of cardiovascular allometric relationships and tissue mechanical properties to produce a surgically viable patch design. The workflow accounts for axial prestretch of the native vessel and material uptake at the suture line, both of which have significant impact on patch design. We additionally present a pre-clinical evaluation of this patch-planning workflow using in vitro silicone models of pediatric branch pulmonary artery (BPA) stenosis. Since computational modeling is a key component of our patch-planning workflow, rigorous credibility assessment of FEA/analytical models is an essential task in evaluating the workflow. We use a recent credibility assessment framework [39] to evaluate the computational modeling stages in a manner that accounts for unique considerations of computational modeling within a surgical planning workflow.

2. Materials and Methods

2.1. Virtual Workflow

Figure 1 shows the steps of the virtual workflow approach and how they fit into the proposed clinical workflow. The approach combines finite-element models in the 3DEXPERIENCE software platform (Dassault Systèmes, Vélizy-Villacoublay, France) to define the geometry of the pressurized patch (“Define Anatomy of Patient Model” through “Extract and Flatten Patch” Sects.), followed by an analytical model to transform the patch to its unloaded configuration (“Transform Patch to Unloaded State” Sect.). While the FEA environment has advantages for handling geometric complexity, the unloading transformation is performed analytically to enable faster incorporation of patch-specific mechanical test data. Performing the transformation with an analytical model also obviates the need for a computationally intensive finite-element inverse problem, which would need to be executed iteratively as the guess for an appropriate material model for the Target geometry is not obvious and will depend on the size of the patch (see Fig. S11, Supplemental Material). The following subsections provide descriptions of each virtual workflow step as they would broadly apply to vascular reconstructions. “Silicone Branch Pulmonary Artery Models for Patch-Planning Validation” through “Virtual Workflow Credibility Assessment” Sects. describe the specific validation case of isolated branch PA reconstruction.

Fig. 1.

Proposed patient-specific patch-planning workflow centered around a virtual patch design workflow (dashed light-blue box). Parenthetical numbers denote text sections that describe each step. Boxes pointing into the virtual workflow box represent software inputs, with dashed red outlines denoting patient-specific inputs and solid gold outlines denoting generic inputs. The output of the virtual workflow is an annotated patch template that can be printed or displayed with a laser projector. Note that both the Patient and Target models (2.1.1 and 2.1.2) are defined in the physiological loading state

2.1.1. Define Anatomy of Patient Model

Preoperative cross-sectional imaging is the first input to the virtual workflow, from which a model of the lumen of the relevant stenosed or hypoplastic patient anatomy is segmented. Segmentation should be performed systematically with reference to cardiologist-reported measurements to ensure that the segmented model accurately reflects the true anatomic dimensions. Our team employs AI-enabled semi-automatic segmentation, with each clinical model undergoing peer review prior to utilization. It is important to note the cardiac phase from the imaging and an estimate of the blood pressure within the vessel of interest at the time of acquisition, as these will be needed to calculate the patch unloaded configuration (“Transform Patch to Unloaded State” Sect.). For systemic vasculature, this estimate can be taken from an invasive arterial/venous line or non-invasive cuff measurement recorded at the time of imaging acquisition. If the intervention is on the pulmonary vasculature, the pressure may need to be estimated based on normative values unless pulmonary pressure measurements are available from invasive PA catheter placement, right/left heart catheterization, or estimated by tricuspid valve regurgitation jet. The segmented lumen surface model of the pressurized preoperative anatomy, herein referred to as the Patient model, is then imported in STL format into the 3DEXPERIENCE software platform. With guidance from the surgeon, an incision line is drawn on the model surface to virtually mark the location and extent of planned patch augmentation. The incision line is assigned a finite thickness of 0.05 mm and used to virtually cut the Patient model.

2.1.2. Define Anatomy of Target Model

Next, the targeted 3D reconstructed geometry, or the Target model, must be defined. Our group uses population-based statistical data to set diameter targets of + 0.5 z-score (i.e., half a standard deviation greater than the mean) at each anatomical segment. In prior studies about patch augmentation of the aortic arch, we found that initial arch reconstruction to z-score of ± 1 resulted in normal aortic longitudinal growth and that aortic undersizing (defined as z-score ≤ − 2) predicted arch reintervention [10, 40]. Therefore, our team targets a z-score of + 0.5 to maintain adequate growth and avoid known serious complications. If z-score data are not available or conflict with dimensions of proximal/distal regions that will not be augmented, we create a smooth loft across the incision line to meet the native anatomy at either end. The Target model instead may be defined based on surgeon preference, with the only requirement being that it matches the Patient model beyond the limits of the incision line. It is important to remember that the Target must be defined at the same blood pressure level as the Patient model. If it makes more sense to define the Target at a different pressure (e.g., pulmonary pressure is expected to be much higher following surgery in the case of Tetralogy of Fallot repair), then the Patient model must be resized to accurately reflect its dimensions at the targeted pressure level. This resizing would require use of the vessel’s known or estimated mechanical properties.

2.1.3. Map Patient Model to Target to Define Patch

To determine the extent of patching required at the region of stenosis or hypoplasia, we perform a finite-element contact simulation to open the Patient model along the incision line until it is pushed out against the Target model. For the simulation, the Target model is duplicated, and the new copy is uniformly expanded out by 0.1 mm radially along surface normals to eliminate potential areas of overlap with the Patient model. A smaller offset may be applied as long as the resulting model fully encloses the Patient model without intersection. This offset model is used in the contact simulation as a fixed rigid body with an arbitrary linear elastic material assignment and 0.01 mm wall thickness. At this stage, the Patient model is treated as a deformable but inextensible shell to maintain constant surface area as it opens to meet the Target. A nearly incompressible Ogden material model is assigned, and the wall thickness is set to 3–5% of the narrowest diameter to balance bending stiffness and buckling risk. Contact is prescribed between the Patient and offset Target models with Coulomb type friction and a coefficient of 0.1. The Patient model is fixed at its ends, and an outward pressure load is applied to the inner surface. The simulation is run as an explicit dynamic step with the pressure load ramped up over 0.25 seconds. The pressure magnitude is iteratively adjusted and the simulation re-evaluated until the Patient model fully opens to the offset Target surface with negligible (<2%) material stretch in the stenosed region.

2.1.4. Extract and Flatten Patch

From the inflation simulation, the edge of the open incision on the deformed Patient model is extracted and projected onto the non-offset Target model surface to account for incomplete contact from the simulation. The projected incision outline is used to cut the Target model, leaving only the bounded section that defines the required patch shape. Next, the Composites Fiber Modeling FEFlatten tool in 3DEXPERIENCE is used to convert the three-dimensional patch surface into its equivalent planar shape. For this simulation, the patch is assigned the same material model as used for the mapping simulation in “Map Patient Model to Target to Define Patch” Sect. The length, width, and area of the patch before and after flattening are compared to ensure that no erroneous strains are accumulated. Error tolerance will depend on the degree of precision required for the application; we chose to tolerate up to 0.1 mm (0.5%) change in patch width or length from flattening, which is the expected precision achievable during subsequent surgical steps. For patches with elliptical or saddle-like curvature that cannot be directly flattened, darts (triangular cutouts) would need to be added to the design. All patches designed for this validation study were developable and therefore did not require darting.

2.1.5. Transform Patch to Unloaded State

Because the patch shape is extracted from the physiologically pressurized Patient and Target models, it must undergo a series of transformations to generate a template that accurately represents the unloaded patch design. After flattening, the patch is imported into MATLAB (R2021b, The MathWorks, Natick, MA) as a list of x-y coordinates to perform two sequential transformation steps:

• Step #1: Reduce patch width to account for change in vessel circumferential stretch caused by stress increase from preoperative to postoperative diameter increase.

• Step #2: Scale patch from physiological loading state to unloaded configuration.

For both of these steps, the thickness and mechanical properties of the vessel and patch materials must be known or estimated. For our proposed clinical workflow, average mechanical properties for each material of interest are used as there is not yet an established process to sterilely test individual vessel and patch material samples prior to use in vivo. To acquire average properties for a given material, we perform displacement-controlled biaxial testing using the BioTester 5000 (CellScale, Waterloo, ON) following [41] to obtain data across a range of loading conditions. Samples are mounted along the principal fiber axes, when applicable and known. Sample thickness is measured with the Litematic VL-50-B Measuring Unit (Mitutoyo, Aurora, Illinois). Cauchy stresses ($\sigma$) across samples are interpolated to standard stretch ($\lambda$) intervals to facilitate averaging. Linear interpolation is used to create $\sigma \left({\lambda }_{\theta },,,{\lambda }_Z\right)$ response surfaces, equating the planar biaxial test data to cylindrical circumferential ($\theta$) and axial ($Z$) directions.

In Step #1, we are correcting the erroneous assumption from “Map Patient Model to Target to Define Patch” Sect. that the pressurized Patient model would maintain a fixed surface area when opening from the preoperative, stenosed radius $r_{\mathit{pre}}$ to the targeted postoperative size $r_{\mathit{post}}$. Because ${\sigma }_{\theta }$ in a cylindrical pressure vessel is proportional to radius, the change from $r_{\mathit{pre}}$ to $r_{\mathit{post}}$ induces a higher stress, which will correspond to an increase in circumferential stretch. Given the anatomic constraints of most vasculature, we assume that the modeled vessel segment is held at a fixed axial prestretch ${\lambda }_Z^{\mathit{vessel}}$. Under this assumption, the mechanical response of the Patient model is constrained to a unique pair of curves ${\sigma }_{\theta }^{\mathit{vessel}}\left({\lambda }_{\theta }^{\mathit{vessel}}\right)$ and ${\sigma }_Z^{\mathit{vessel}}\left({\lambda }_{\theta }^{\mathit{vessel}}\right)$ from the biaxial response surfaces. Using Lamé’s equations for a thick-walled cylindrical pressure vessel, the circumferential stresses before $\left({\sigma }_{\theta ,pre}^{\mathit{vessel}}\right)$ and after $\left({\sigma }_{\theta ,post}^{\mathit{vessel}}\right)$ patch placement are calculated to find the corresponding stretches ${\lambda }_{\theta ,pre}^{\mathit{vessel}}$ and ${\lambda }_{\theta ,post}^{\mathit{vessel}}$. The increase in Patient model circumference ${\lambda }_{\theta ,post}^{\mathit{vessel}}-{\lambda }_{\theta ,pre}^{\mathit{vessel}}$ from the stenosed to the target diameter, which was neglected from the simulation in “Map Patient Model to Target to Define Patch” Sect., must now be subtracted from the patch width. The result of this step is the true pressurized patch size.

In Step #2, the pressurized patch is transformed into its unloaded state by estimating its loaded stretch state. An implicit assumption within the virtual workflow is that placement of the patch into the open incision in the pressurized Patient model does not cause any change to the axial extent of the incision. This assumption is equivalent to setting the axial stress of the patch ${\sigma }_Z^{\mathit{patch}}=0$ at the target pressure. Under this constraint, and using Lamé’s equations to calculate the circumferential stress ${\sigma }_{\theta }^{\mathit{patch}}$, the stretches ${\lambda }_{\theta }^{\mathit{patch}}$ and ${\lambda }_Z^{\mathit{patch}}$ can be determined based on the material properties. The circumferential and axial coordinates of the patch are divided by their respective stretches to produce the unloaded patch configuration. Additional details about the code structure used to implement both of these transformation steps are available in Section S1.4.3 (Supplemental Material).

2.1.6. Create Surgical Template

The final modification to the patch design is the addition of a suture bite offset. A uniform offset is added to the flattened, unloaded patch boundary to account for material that will be taken up in the suture line when securing the patch to the vasculature of interest. Preliminary testing between different material pairs (vessel and patch) showed that the uptake was consistently 1–1.25 mm for the standard suture material (7-0 Prolene) and bite depth (1–1.5 mm), with a pair of thinner, more compliant materials tending to have slightly larger uptake than two thicker, stiffer materials. The final patch design is exported as coordinates in a text file formatted for projection by the microLASERGUIDE system (Aligned Vision, Chelmsford, MA). The LASERGUIDE software is used to add annotations regarding the patient ID, procedure details, patch orientation, and overall patch size for intraoperative verification. The primary output of the virtual workflow (“Virtual Workflow” Sect.) is the laser template of a patch design with sub-millimeter geometric detail based on patient-specific anatomy, orientation markers, and suture bite offset to allow for accurate intraoperative reconstruction of congenital cardiovascular defects.

2.2. Silicone Branch Pulmonary Artery Models for Patch-Planning Validation

2.2.1. Model Selection

Branch pulmonary arterioplasty is typically performed in infant- and toddler-aged patients, most commonly at 0.5–1.5 years of age [1–4, 1–4]. However, there is a small percentage of patients in which repair is performed in the neonatal or child stages of development, ranging from 1 month to 12 years old. Given the drastic differences in anatomical size between these age groups, we developed two silicone models of BPA stenosis to represent the relative size extrema at which reconstructions are conducted clinically. In both cases, the isolated BPA anatomy was represented as a straight tube with a centrally located region of stenosis (Fig. 2a). Design of both models was based on inner diameter measurements taken at an inflation pressure of 15 ± 1 mmHg, normal mean PA pressure for this patient population [42], and a physiologic axial prestretch of ${\lambda }_Z^{\mathit{vessel}}=1.31\pm 0.02$ [43]. For the neonatal-sized silicone model, the non-stenosed region measured 5.0 ± 0.1 mm in diameter (n = 27), corresponding to z-score zero (i.e., mean) right pulmonary artery diameter for a 1-day-old patient with body surface area of 0.20 m² [44]. The stenosed region measured 2.3 ± 0.1 mm, corresponding to an average diameter z-score of − 3.0. For the child-sized silicone model, the non-stenosed region measured 10.1 ± 0.1 mm in diameter (n = 18), corresponding to a 5-year-old patient with a body surface area of 0.80 m² [44]. The stenosed diameter measured 5.3 ± 0.2 mm, corresponding to an average diameter z-score of − 3.3. Of note, surgical correction of BPA stenosis via patch augmentation is usually performed when the diameter z-score of either branch is ≤ − 2, with an average of − 3.4 ± 1.3 [6].

Fig. 2.

Procedure for in vitro validation of the clinical patch-planning workflow using silicone branch pulmonary artery models. The central “Clinical patch-planning workflow” box refers to the steps outlined in Fig. 1. Rectangular boxes (yellow) denote additional measurements taken during the in vitro validation study for error analysis

2.2.2. Fabrication

Due to difficulties in acquiring and maintaining tissue-based vascular models, silicone replicas of BPA stenosis were fabricated. In addition to the diameter targets detailed in “Model Selection” Sect., we wanted to achieve physiologic diameter change (20–40%) from zero pressure to the targeted high pressure of 30 mmHg [42] under 30% prestretch (“Loading Fixture and Measurements” Sect.). To guide silicone selection for achieving these targets, biaxial mechanical testing was performed on various EcoFlex silicones (Smooth-On, Macungie, PA). Silicone type was selected, and the required thickness was estimated for each model (neonatal and child) using cylindrical pressure vessel equations to best fit the targeted diameters and distensibility (Fig. 2b). For the neonatal model, EcoFlex 00-20 (EF20) with 2 mm thickness best matched porcine BPA tissue properties. For the child model, EcoFlex 00-50 (EF50) with thickness 1.1 mm was selected. Three-part molds were printed (Form 3 + , FormLabs, Somerville, MA) and silicone injected via syringe to create samples meeting these specifications (Fig. 2c). The non-stenosed inner diameter was molded to 5.0 mm in the neonatal model and 10.4 mm in the child model. The stenosed segments were molded to 2.5 mm in the neonatal model and 5.7 mm in the child model.

2.2.3. Loading Fixture and Measurements

To impose the target prestretch and inflation pressures, a custom fixture was fabricated (Fig. 2d). The fixture consisted of custom end caps printed in Tough PLA (UltiMaker S7, Utrecht, Netherlands) with sliding attachment to a central acrylic post. Each end cap had four holes for Luer lock connectors to attach four different silicone BPA samples. The four samples were mounted in parallel and connected to a pneumatic line with 1/4″ tubing. Prior to mounting each sample in the fixture, paired reference markers were drawn at three locations along the length, at the proximal and distal non-stenosed segments, and at the central stenosed region. The distance between these marker pairs was measured with digital calipers. These markers were used to calculate the prestretch at these three locations. Additionally, distance between the barbed fittings at either end of the model was measured to calculate the average prestretch along the sample. The samples were then secured into the fixture and its end caps were adjusted to apply a targeted average prestretch of 30%. After the sample was secured in the fixture, the distance between each pair of reference markers was remeasured. Inflation was achieved using the wall air supply regulated by an Arduino Uno microcontroller board (Arduino, Monza, Italy) with pressure sensors (Honeywell Microstructure Pressure Sensor SCX05DN).

2.3. In Vitro Validation of the Clinical Patch-Planning Workflow

The BPA silicone models were used to validate the proposed clinical workflow. Following the steps outlined in “Virtual Workflow” Sect., patch designs were generated for three different patch materials: EF20 silicone, CardioCel Neo (CN) bovine pericardium (LeMaitre Vascular, Burlington, MA), and porcine BPA (pBPA) tissue (Lampire Biological Laboratories, Pipersville, PA). The EF20 patch, while not used clinically, was chosen for its low variability in thickness and stiffness, which facilitated direct assessment of any systematic errors in the workflow. CN, among other pericardial tissues, is a commonly used material for BPA plasty and undergoes minimal stretch under pulmonary pressure loads. The pBPA tissue was selected as a surrogate for BPA homograft tissue, which is the most distensible material used clinically. Using the CN and pBPA materials for in vitro validation allowed for assessment of the extremes of patch mechanical properties seen clinically.

To provide contrast from the silicone models in postoperative CT scans, the EF20 patches were dyed with barium sulfate (1.5%) during the fabrication process. For each patch material, in both the neonatal and child BPA models, two patches were designed to achieve consistent reconstructed diameter at two distinct pressure targets. Targets at (1) zero (“low”) pressure and (2) 30 mmHg (“high”) pressure were chosen to represent the relative extremes of pressure at which patients would recover after reconstruction. The low-pressure condition also reflected the scenario of sizing a patch for intraoperative (unpressurized) conditions. Axial prestretch was kept constant across all cases. Figure 3 summarizes the patches designed and number of samples tested across both BPA models. For a set of conditions (patient size, patch type, and target pressure), at least n = 3 patches were sewn. CN (low and high pressure) and pBPA (low pressure) in the neonatal model required initial troubleshooting as these were the first experiments with biologic materials; therefore, n = 5–7 samples were patched.

Fig. 3.

Summary of patches designed and tested in the neonatal and child branch pulmonary artery (BPA) silicone models. For each patch material, two different patches were designed to reach target diameters at low (0 mmHg) or high (30 mmHg) pressurization levels. Photos depict example reconstructions with each patch material at 30 mmHg

2.3.1. Patient and Target Model Definition

After mounting the silicone BPA models (“Loading Fixture and Measurements” Sect.), a preoperative CT scan was acquired using an Albira SI PET/SPECT/CT system (Bruker, Billerica, MA). The models were scanned at 15 mmHg to confirm our targeted dimensions (“Model Selection” Sect.) and at 0 and 30 mmHg for use in the virtual workflow. Table 1 summarizes the measured non-stenosed and stenosed diameters across all molded samples. The DICOM files were batch segmented using SimVascular [45] with 6-node splines at a fixed threshold of 60 Hounsfield units, which was found in preliminary testing to best capture the true dimensions of the silicone models. The resulting contour group files were imported into MATLAB to evaluate diameters at 0.5 mm increments along the length of each model. The segmented lumen surface model of the preoperative anatomy at target pressure (Patient model) was then imported as an STL into 3DEXPERIENCE, and the Virtual Workflow was followed (“Virtual Workflow” Sect.). In brief, an incision line was drawn extending across the area of central stenosis. Next, the Target model was defined as a straight cylindrical segment that matched the diameter of the non-stenosed segments of the Patient model. Target diameters for the neonatal model were 4.5 mm (low pressure) and 5.8 mm (high pressure) and those for the child model were 9.4 and 11.3 mm for the low- and high-pressure conditions, respectively. Note that these diameters are similar but not necessarily identical to the median across all tubes, since the virtual modeling for each model type was performed with one representative segmented sample. The Patient model was then mapped to the offset Target model, the patch design was extracted, the 3D patch surface was converted into its equivalent planar dimensions, and the flattened design was transformed to its unloaded configuration. Patches designed under low (zero) pressure did not require any transformation.

Table 1.

Silicone BPA preoperative diameter measurements at low (0 mmHg), nominal (15 mmHg), and high (30 mmHg) pressure levels

	Diameter at 0 mmHg (mm)	Diameter at 15 mmHg (mm)	Diameter at 30 mmHg (mm)
Neonatal model (n = 27)
Non-stenosed	4.5 [4.4, 4.6]	5.0 [4.9, 5.1]	5.8 [5.6, 6.0]
Stenosed	2.1 [2.0, 2.1]	2.3 [2.2, 2.4]	2.6 [2.5, 2.7]
Child model (n = 18)
Non-stenosed	9.3 [9.1, 9.5]	10.1 [10.0, 10.3]	11.2 [10.9, 11.7]
Stenosed	5.0 [4.8, 5.3]	5.3 [5.0, 5.6]	5.7 [5.4, 6.0]

Values presented as median [range]

2.3.2. Patch Unloaded Configuration and Surgical Template Creation

The scaling process incorporated material properties from biaxial testing of both the silicone BPA model and patch materials. Thicknesses of the vessel (2 mm for the neonatal model and 1.1 mm for the child model) and patch (2 mm for EF20, 0.3 mm for CN, and patch-specific for pBPA) were also incorporated. Given that the silicone tubes and patches were created from a closed mold and CN patches were commercially sourced with reported thickness, the variation in thickness in these materials (<0.05 mm) was neglected. The pBPA patch median thickness was 1.03 mm, ranging from 0.78 to 1.16 mm across samples. Using these inputs, the unpressurized patch geometry was calculated as described in “Transform Patch to Unloaded State” Sect. Given the expected variability across different specimens of the tissue-based CN and pBPA patch materials, biaxial testing was conducted on n = 5 samples from each new specimen, and specimen-specific properties were used for the unloading analysis.

For both the low- and high-pressure planned designs, a material-specific suture bite offset was added. A single orientation marker was added to indicate the proximal end of the patch with respect to BPA orientation in the CT scanner. The final patch template was uploaded to the LASERGUIDE software and projected onto the desired material (“Create Surgical Template” Sect.).

2.3.3. Patch Placement

All steps of the patch placement procedure were performed by a trained surgeon. The patch was traced from the laser-projected template and cut out as previously reported [47]. Patch width and length were measured with digital calipers (Mitutoyo, Aurora, IL). Preoperatively, four reference markers were placed on each silicone model and patch (two along the length and two along the width) in order to calculate the amount of material taken up at the suture line after BPA reconstruction (Fig. 3). The distance of each marker from the model/patch edge was measured using ImageJ [48].

With the silicone BPA sample mounted and under target pressure, the endpoints of the incision line were marked to match the length and location of the incision in the virtual model. The incision line was opened using a #11 blade, ensuring not to puncture the back wall of the sample (Fig. 2e). Each patch was initially secured at the proximal and distal ends using a double-armed 7-0 Prolene suture. Then, one arm of each suture was run down each side of the patch and tied in the center (Fig. 2f). The surgeon attempted to take 1–1.5 mm bites into the patch and BPA sample with a similar bite spacing along the length of the suture line. Postoperatively, distances between the reference makers on the patch and BPA were measured using ImageJ, and material uptake was calculated by subtraction from the preoperative measurements. Prior to postoperative scanning, prestretch measurements were repeated to confirm that manipulation of the fixture during reconstruction did not affect sample prestretch. The overall postoperative prestretch was within 4% of the target.

2.3.4. Postoperative Evaluation

Postoperative CT scans were acquired for each reconstructed sample at low and high pressure (Fig. 2g). The resulting DICOM files were again segmented in SimVascular, with manual segmentation required for many of the low-pressure scans due to folding of the unpressurized patch. The postoperative diameter was defined as the average diameter across the central 10 mm of the repaired stenotic region. Effective diameter of non-circular cross sections was calculated from perimeter measurements. The primary output of the in vitro validation was postoperative diameter at the region of the reconstructed stenosis. Error was calculated for each model between the measured diameter and the corresponding virtual target (Fig. 2h).

2.4. Virtual Workflow Credibility Assessment

2.4.1. Overview

Various activities can be performed for model credibility assessment, including code verification, calculation verification, validation, uncertainty quantification, model form assessment, and sensitivity analysis. In addition, a credibility assessment framework such as [39, 49] can be used to systematically justify that the activities and results are sufficient. We followed the credibility assessment framework of [39], which generalizes the process outlined in ASME V&V40-2018 [49]. A detailed description of the methods and results for code and calculation verification and model form assessment is provided in Section S2.5.1 (Supplemental Material). A brief summary of the results of these activities is provided in “Credibility Assessment” Sect. Sensitivity analysis is discussed in detail in “Sensitivity Analysis” (Methods) and “Model Form Assessment and Sensitivity Analysis” Sects. (Results). For validation, one option is to perform validation of the FEA and analytical model in isolation, that is, outside of the overall workflow. This is challenging in practice for this case; instead, we relied upon the workflow validation described in “In Vitro Validation of the Clinical Patch-Planning Workflow” Sect., which tested all aspects of the workflow including the FEA and analytical models. This was a non-traditional approach to validation of a computational model (Fig. S1, Supplemental Material), and to follow the process outlined in [39], we defined a new category of credibility evidence and new ASME V&V 40-2018 [49] credibility factors. All details can be found in Section S2 (Supplemental Material).

2.4.2. Sensitivity Analysis

As part of the credibility assessment, a sensitivity analysis was performed on the virtual workflow for the validation model to assess how known variability of the inputs affects the output of patch size. The analysis focused on the analytical portion of the virtual model given that the FEA inputs (preoperative vessel and target dimensions) for the simple silicone BPA geometry have a trivially predictable impact on the output (e.g., a 1 mm increase in target diameter will cause a 3.14 mm increase in loaded patch width). Given that the low-pressure patches did not require unloading analysis, only the high-pressure patch designs were evaluated. The inputs of silicone BPA prestretch, thickness, and stiffness were evaluated, as well as internal pressure, patch orientation, thickness, and stiffness. The silicone patch material was excluded given its low variability in both thickness and stiffness. For both of the remaining patch materials (CN and pBPA) for both patient sizes (neonate and child), each input was tested at one standard deviation above and below the nominal value. Patch orientation was tested by assuming the long axis of the CN patch or the axial direction of the pBPA patch was oriented circumferentially within the BPA model rather than in the typical axial orientation. Molded BPA wall thickness and inflation pressure were not recorded for most samples, so a conservative estimate of 10% variation from the mean was used for both. Change in patch area was reported as a percent difference from the nominal value.

3. Results

3.1. Patch Designs

Figure 4 shows the patches designed for the silicone BPA models using the virtual workflow. In both the neonatal and child models, the patches planned for low pressure were 15–25% shorter axially than those planned for high-pressure reconstruction. In the neonatal model, EF20 and CN patch materials both required a suture bite offset of 1 mm, meaning they shared the same low-pressure patch designs, while the pBPA required 1.25 mm suture offset, leading to 0.5 mm larger patch dimensions. In the child model, CN suture offset increased from 1 to 1.25 mm, while the other two materials maintained the same offset, causing CN and pBPA to share the same low-pressure patch design.

Fig. 4.

Patch designs generated for each of the a neonatal and b child model cases defined in Fig. 3. All of the patches designed for the low-pressure state for a given model were identical aside from differences in the suture offset across patch materials (1 vs. 1.25 mm), leading to only two designs per model. For the high-pressure state, all EcoFlex 00-20 silicone (EF20) samples for a given model used the same patch design (n = 1), while CardioCel Neo (CN) and porcine branch pulmonary artery (pBPA) designs were created with specimen-specific material properties (n = 2 and n = 3 per model, respectively)

Among the high-pressure designs, EF20 patches were the longest axially and narrowest circumferentially, decreasing in width by 20% in the neonatal and 28% in the child model from the planned pressurized state to the unloaded configuration. For the CN and pBPA patches, specimen-specific material properties were used for each high-pressure patch design, resulting in two unique CN patch designs and three pBPA designs per patient model. The stiff CN material produced the shortest and widest patches after exhibiting 12 and 16% change from pressurized to unloaded states in the neonatal and child models, respectively. In the neonatal model, one of the three pBPA designs was wider than both CN patches, resulting from its greater thickness (0.97 ± 0.34 mm) compared to the other pBPA patches (0.70 ± 0.12 and 0.73 ± 0.06 mm).

3.2. Reconstructed Dimensions of the Silicone Branch Pulmonary Artery Models

After patch placement, the diameter of each reconstructed silicone sample was compared against the corresponding target diameter. The postoperative diameter for each sample was defined as the average diameter across the central 10 mm of the repaired stenotic region taken at 0.5 mm spacings. Results for all models are summarized in Table 2. In the low-pressure models, which targeted a zero-pressure diameter, material property data were not required during patch design (Fig. 5a and c). For the high-pressure models, in which we aimed to achieve a target diameter under 30 mmHg inflation, patch designs were transformed into their unloaded state for cutting and sewing, but the reconstructed sample dimensions were evaluated under pressure (Fig. 5b and d). Overall, the central region of each sample was reconstructed to within 0.8 mm (n = 45) and 10% (except n = 3 in the neonatal model) of the target diameter.

Table 2.

Patch-augmented silicone BPA postoperative diameter measurements at the reconstructed central stenosed region at low (0 mmHg) and high (30 mmHg) pressure levels

	Diameter at 0 mmHg (mm)	Diameter at 30 mmHg (mm)
Neonatal model
Target size	4.5	5.8
EcoFlex 00-20 (n = 3,3)	4.3 [4.3, 4.4]	5.6 [5.5, 5.8]
CardioCel Neo (n = 7,6)	4.5 [4.1, 5.0]	6.1 [6.0, 6.4]
Porcine BPA (n = 5,3)	4.6 [4.2, 5.3]	6.2 [6.0, 6.2]
Child model
Target size	9.4	11.3
EcoFlex 00-20 (n = 3,3)	9.1 [8.7, 9.1]	10.7 [10.7, 11.1]
CardioCel Neo (n = 3,3)	8.8 [8.8, 8.9]	10.9 [10.7, 11.7]
Porcine BPA (n = 3,3)	9.6 [9.3, 9.7]	11.7 [11.2, 11.7]

Values presented as median [range]

Fig. 5.

Reconstructed dimensions of the silicone branch pulmonary artery (BPA) for the a and b neonatal and d–e child models after patch placement. Each curve represents the median diameter achieved across samples, and the shaded regions show the range. Yellow shaded bars depict targeted zones of z-score ± 0.5. Note that the x-axes are compressed to highlight overall variation in diameter. Percent difference between the achieved and targeted diameter is shown in c and f for the neonatal and child models, respectively. EF20 EcoFlex 00-20 silicone, CN CardioCel Neo, pBPA porcine BPA

Figure 5c and f shows the percent error in reconstructed diameter for each of the samples. All 12 EF20 patch reconstructions were undersized, with median diameter error of − 4.8[− 7.1, − 1.3]%, while 11/14 pBPA reconstructions were oversized (3.2[− 5.4,18.6]%). For CN, 9/13 neonatal samples were oversized (3.2[− 9.7, 11.1]%), while 5/6 child samples were undersized (− 5.4[− 5.8,2.9]%). We observed greatest nonuniformity in diameter of pBPA reconstructions, with one model appearing to have tethering of connective tissue to the back wall of the silicone model, and another exhibiting local bulging under pressure where the wall was likely damaged during adventitial removal. Across the child models, a consistent behavior of diameter reduction near either end of the patched region was observed.

For clinical context, the achieved diameters were compared to an acceptable targeted range used during actual BPA reconstruction. Typically, surgeons attempt to repair hypoplastic or stenosed BPAs to a diameter that is as close to z-score 0 as possible, usually within ± 1.0. We hypothesized that our clinical patch-planning workflow would be able to generate reconstructed geometries in a more precise and accurate manner than current practice. Therefore, we sought to achieve a postoperative diameter within ± 0.5 of the targeted value. For the neonatal models, this translated to a diameter within 0.5 mm from the target, and for the child models, it was ± 0.7 mm. All samples for the child model and all but three samples for the neonatal model (n = 2 pBPA and n = 1 CN low pressure) were reconstructed to a z-score ± 0.5 from the respective targets, and all were within z-score ± 1.0. For context, standard practice would allow for reconstructed variability up to 1.0 mm (neonate) and 1.5 mm (child) from the targeted diameters (z-score ± 1.0).

3.3. Evaluation of Error Sources

Measurements at each stage of the in vitro validation procedure facilitated evaluation of error sources (Fig. 6). Despite variability in mounting of the silicone models (19% maximum error between achieved and targeted model overall prestretch), the resulting preoperative diameters across models were consistent with median error in stenosed diameter 0.1[range − 4.7, 6.1]%. Minimal error was accumulated during the virtual modeling steps, with a maximum of 3% increase in the incision line length resulting from the mapping simulation. All patches were cut to within 3.8% of the templated size, with median errors of 0.2 and − 0.2% in cut width and length, respectively. Comparison between measured material uptake at the suture line and allocated suture offset yielded significant variability, with median errors of 41.0[− 43.3, 134.8]% and 15.4[− 78.0, 139.0]% in the circumferential and axial directions, respectively. Large error magnitudes here are partially attributable to limited precision in making these small measurements (median circumferential uptake error was 0.5 mm, and maximum error was < 1.5 mm), though the positive medians suggest that uptake measurements were systematically greater than expected.

Fig. 6.

Boxplot summary of error measurements for each stage of the in vitro validation procedure. Error is reported as the difference between the measured value and the targeted/expected value, and the corresponding percent error median [range] is listed next to each bar. *All boxes have units of mm other than patch area, which has units of mm²

3.4. Credibility Assessment

A detailed description of the model credibility assessment, including our modeling and verification approaches and how to account for unique considerations of computational modeling within a surgical planning workflow, are found in Section S2 (Supplemental Material). Here, we provide brief results on key elements. Our Question of Interest was framed as “Given preoperative imaging of a patient’s anatomy and a selected patch material, what patch size and shape will produce the target reconstruction dimensions?” (Section S2.2) in the context of targeted reconstruction of isolated BPA stenosis (Section S2.3). Based on the Question of Interest and Context of Use, Model Risk was assessed to be Low-Medium. This is the result of a Low Model Influence and Medium Decision Consequence (Section S2.4).

Verification, validation, and related activities were performed (Section S2.5). For code verification, software quality assurance was investigated, and numerical code verification results for the simulation software are referenced (“Code and Calculation Verification” Sect.). For model validation, the full workflow was applied using an in vitro experimental system and performance of the model-based workflow was assessed (“Patch Designs” through “Evaluation of Error Sources” Sects.). Calculation verification, investigation of modeling assumptions, and sensitivity analysis were all performed using validation model simulations, and results are summarized below (“Code and Calculation Verification” and “Model Form Assessment and Sensitivity Analysis” Sects.). A post-study adequacy assessment was conducted, and the achieved credibility levels are reported in Section S2.6 (Supplemental Material), while a summary of the results is given below in “Adequacy of the Credibility Assessment Results” Sect.

3.4.1. Code and Calculation Verification

3DEXPERIENCE and MATLAB documentation was reviewed and no relevant issues were identified in the quality assurance practices. Internal peer review of the MATLAB script was performed, and unit testing was conducted on key functions (Table S1) to ensure functionality. No major or obvious errors were detected (Section S2.5.1.1). For numerical code verification, nominal stress from simulated equibiaxial pull of an element was compared to the exact solution using the material model that was employed for both mapping and flattening simulations. Comparison resulted in zero percent error for each stretch level (Section S2.5.1.2).

The aim of calculation verification is to estimate the numerical error in the specific simulations and calculations performed as part of the workflow validation (Section S2.5.1.3). For the mapping simulation, mesh resolution was doubled 3×, and the target time step was halved twice. For the flattening simulation, the mesh was refined by 85% over seven increments. Circumference of the Patient model at its central cross-section and the surface area of the resulting patch were compared. Discretization and time step errors were very small, with < 1% change in open model circumference and < 0.3% change in patch surface area across all conditions. For the MATLAB script used to perform the unloading analysis, convergence was evaluated within key functions with tolerance levels 2× and 4× the nominal values, and the resulting patch area was tracked. Less than 0.4% change in patch surface area was observed. To minimize use error within the virtual workflow steps, several standard procedures were implemented around CT segmentation, and Target model and incision line creation (Section S2.5.1.4).

3.4.2. Model Form Assessment and Sensitivity Analysis

Full description of the selected virtual model configuration and assumptions is available in Section S2.5.1.5. To evaluate the interpolation function and use of Lamé’s equation, we compared calculated pressure–diameter curves for the child model EF50 silicone tubes to experimental CT measurements, with diameter error < 5%. To calculate change in wall thickness with inflation, incompressibility was assumed, and the quadratic equation for a thick-walled cylinder was used. The incompressible wall thickness assumption was validated against CT measurements of non-stenosed silicone tubes, with differences between calculated and measured wall thickness < 0.1 mm.

Results of the sensitivity analysis are summarized in Fig. 7. Change in patch area was measured for increases and decreases of one standard deviation in each input parameter value. Internal pressure and silicone BPA wall thickness were varied by 10% of the mean value. All perturbations caused less than 7% change in patch area. Patch stiffness had the greatest impact for both CN and pBPA materials, with a decrease in stiffness for either material causing a 6.5–6.8% decrease in patch area for the neonatal model. Impact of pBPA patch stiffness was similar in the child model, while a decrease in CN stiffness only led to a 3.8% decrease in patch area. For both materials in both model sizes, patch area was more sensitive to a decrease in patch stiffness than an increase. In the neonatal model, all inputs relating to the silicone BPA (prestretch, stiffness, thickness) caused < 1% change in patch area. Although the impact remained small in the child model, a 10% change in model thickness produced just over 1% change in patch area.

Fig. 7.

Results of sensitivity analysis for high-pressure patches in the silicone branch pulmonary artery (BPA) a neonatal and b child models. The patch surface area for each test case is compared to the patch area achieved with nominal input values. Triangles pointing up vs. down denote an increase vs. decrease in each input parameter. Red triangles with solid lines represent the CardioCel Neo (CN) patch material, and blue triangles with dashed lines represent porcine BPA patch (pBPA). σ: standard deviation

3.4.3. Adequacy of the Credibility Assessment Results

Complete details related to the post-study adequacy assessment are found in Section S2.6 (Supplemental Material). In brief, all achieved credibility levels were at or above medium (Fig. S12), with all factors exceeding a level commensurate with the assessed overall model risk (Low-Medium). Additionally, the virtual model context of use (COU) encompassed most of the validation points, with one notable difference—the COU was for repair of isolated BPA stenosis, which may exhibit more complex geometry and characteristics (i.e., curvature, heterogeneous tissue properties, etc.) compared to the simplified straight-tube models used in our validation studies. Collectively, the validation activities and achieved credibility levels were considered sufficient and relevant to the COU. The maximum diameter error demonstrated in both the virtual modeling (0.6 mm) and in vitro surgical procedure (0.8 mm) was less than the variability accepted with standard clinical practice, up to 1.0–1.5 mm from the targeted diameter (z-score ± 1.0). Refinements to the model form and clinical workflow (detailed in the Discussion) may further improve repair precision. Overall, the degree of agreement between the model target and in vitro validation results, as well as the reliability of the independent software elements, was deemed satisfactory for using the virtual workflow and its model-based constituents to answer the question of interest for the stated COU.

4. Discussion

We have demonstrated accuracy of a patch-planning workflow designed for isolated BPA stenosis reconstruction through verification and in vitro validation activities. The workflow incorporates clinically relevant factors including patient-specific anatomy, surgeon-guided incision location, evidence-based dimensional targets, vessel and patch mechanical properties and physiologic loading states, material-specific suture bite offset, and 2D transformed patch templates. The workflow validation was designed to account for all of these factors to maximize applicability to the clinical context of use. Silicone BPAs were molded to reflect physiological size and distensibility under physiologic prestretch and pressure. Two patient model sizes were chosen to span the typical age range at which stenosed BPA repairs are conducted clinically. Three different patch materials were evaluated to cover a range of surgeon preferences, and designs were created for target dimensions defined at both low and high pressure to represent the relative extremes at which patients would recover after repair.

By incorporating these elements, we were able to accurately and precisely repair the stenosed BPA silicone replicas across all test conditions. Across two patient model sizes, three patch materials, and two pressure loads, all but three samples (n = 42/45) were repaired to diameters within z-score ± 0.5 and 10% from the respective targets, all within z-score ± 1.0. We identified two key steps in the patch-planning workflow that contributed most to error: (1) assigning appropriate suture bite offset to account for material uptake at the suture line, and (2) computing patch transformation from loaded to unloaded states based on mechanical properties. The low-pressure patch designs, which did not undergo the unloading step, only varied by differences in suture bite offset. Even so, a majority of EF20 and CN patch reconstructions were undersized, while most pBPA models were oversized. We found that material uptake was difficult to measure due to its small magnitude and curvature of the model surface, demonstrated by a deviation of up to 135% (1.3 mm) from the expected value when evaluating error sources. Due to unreliable measurements, we were unable to identify a correlation between suture bite offset, material uptake, and the ability to predict an over- or undersized reconstruction. Despite this uncertainty, the largest deviation in material uptake would lead to 0.8 mm diameter error.

In normal and high-pressure scenarios, vessel and patch mechanical properties play a significant role in patch design. Patch designs based on preoperative imaging must be scaled down to account for the blood pressure and vessel prestretch reflected in the imaging. High-pressure EF20 patches were the longest axially and narrowest circumferentially in both model sizes, reflecting the predicted 20–28% circumferential stretch that the vessel and patch would undergo when reperfused postoperatively. CN, a stiffer material, tended to be shortest and widest with only 12–16% predicted diameter change under pressure, largely attributable to vessel stretch. Patch stiffness was shown to have the greatest impact in sensitivity analysis, causing up to 6.8% change in patch area when varied by one standard deviation for pBPA. Furthermore, in the neonatal model, one high-pressure pBPA design was wider than both CN patches, likely resulting from its greater thickness compared to the other two pBPA patches. However, for all patch materials, we found that the unloading analysis tended to oversize high-pressure patches due to underestimation of distensibility, likely contributing to the degree of oversizing noted with several pBPA and CN high-pressure patches. This discrepancy may be partially attributable to stress shielding that can be induced by our rake-based biaxial test setup [50].

Low-pressure patch designs represent intraoperative patch sizing, wherein the surgeon tailors the patch to smoothly reconstruct the depressurized vessel. Across all materials, the patches planned under low pressure were 15–25% shorter axially and up to 10% narrower or wider than those planned for a high-pressure target. This reflects an important point as intraoperative patch sizing is likely not accounting for changes to the vessel and patch geometry under postoperative physiological loads. Since the target diameter was much larger at higher pressure, and the stenosed region was more elongated, this resulted in longer patches for the high-pressure cases, but the width of the patches was highly dependent on mechanical properties. One must appreciate that, with currently available tools, achieving targeted geometry during BPA repair is technically challenging for the operator due to small size of native structures, anatomic distortion with intraoperative depressurization, and formation of flat patches into complex 3D shapes. Our data would suggest that, if patches are sized only based on intraoperative measurements, then patch length could be underestimated by as much as 25%. Surgeons have attempted to perform calculations to achieve predetermined postoperative target diameters based on preoperative imaging, but this practice is both tedious and unreliable due to lack of incorporation of essential elements included in the proposed clinical patch-planning workflow, such as specified incision line placement, consideration of physiologic loading states and tissue mechanical properties, and 3D to 2D patch shape transformation.

Surgical technique also appeared to contribute significantly to the repaired geometric outcome. We observed the greatest diameter nonuniformity across the length of each sample in pBPA reconstructions due to tethering of connective tissue and local wall damage. These are issues in the surgical technique that can be corrected with meticulous attention and additional planning steps. Since the overall scale of the anatomy in these cases is on the millimeter level, even sub-millimeter discrepancies are relevant. These seemingly small differences accumulate and account for a large portion of the error observed between the reconstructed and target diameters. We therefore emphasize the importance of incorporating all known variables into the design of surgical patches used for anatomic repairs in which the geometric outcome translates to patient impact. The analysis also highlights the potential for suture bite depth to significantly impact the reconstructed dimensions. This highlights an opportunity to introduce additional controls to assist the surgeon in accurate bite placement including potentially marking planned suture entry points on the patch with the laser guide during patch marking and cutting.

Due to the stringent nature of the question of interest related to pediatric-isolated BPA reconstruction, we sought to perform a model credibility assessment of the proposed virtual patch-planning workflow. Early in the process, we observed that the proposed workflow did not align with a traditional ASME V&V40 bench test validation. Typically, there would be independent experimental and model systems with common inputs, and comparison would be made between the measured and simulated outputs (Fig. S1, Supplemental Material). In contrast, our workflow uses the output of the model to inform the experimental system and then compares the measured quantity to the virtual target. We defined a new category of credibility evidence (using the terminology of [39]) for this type of validation and adapted ASME V&V40 credibility factors accordingly. Importantly, through the credibility assessment, we verified that simulations within the virtual models introduced less than 3% error compared to analytical calculations, and changes to simulation parameters led to less than 1% change in patch size. In the sensitivity analysis, all inputs besides patch stiffness led to < 4% change in patch area. Through rigorous evaluation of the virtual workflow and in vitro validation, we were able to identify potential sources of significant error that can be targeted prior to application to other anatomies. Patient-specific modeling and patch-planning workflows are relatively new areas in medicine, for which performing a credibility assessment is essential prior to clinical implementation to develop trust in the predictive capability of the simulations and to mitigate risk. We sought not only to demonstrate the utility of our patch-planning workflow through in vitro validation but also to provide an example of systematic model credibility assessment (Supplemental Material) for future reference by other groups in the surgical and modeling communities. This work will hopefully provide insight into the elements necessary to establish credibility in computational modeling related to patient-specific surgical planning.

Patch augmentation of hypoplastic or stenosed vasculature is common in congenital cardiac surgery. Arch reconstruction, Damus-Kaye-Stansel anastomosis, Tetralogy of Fallot transannular patching, intra-cardiac baffling, ventricular septal defect closure, branch pulmonary arterioplasty with Glenn palliation, and isolated BPA reconstruction are only a few procedures in which patches of various shapes and sizes are necessary to achieve an acceptable surgical outcome. Although the goal of these procedures is to restore underdeveloped structures to adequate dimensions, vessel mis-sizing due to inadequate initial repair results in well-known postoperative consequences, including residual stenosis, increased afterload, inefficient blood flow, impedance mismatch, and high reintervention rates [1, 12, 45, 51–53]. In fact, reintervention rates due to residual obstruction and/or restenosis are as high as 60% for BPA reconstruction, in part due to technical challenges with intraoperative patch sizing. Therefore, we developed a prospective patch-planning workflow utilizing computational software for design of patient-specific patches to achieve targeted reconstructed geometry. We focused on isolated BPA stenosis in our first validation series due to the more simplified geometry. With feasibility established, we will now use the validation platform to test more complex patient-specific anatomic models for BPA plasty prior to initiation of prospective clinical trials. We suspect that, by achieving normal repaired dimensions through this patch-planning workflow, reintervention rates along with other adverse events will decrease.

Additionally, this workflow could allow for the equalization of outcomes across centers by minimizing intraoperative “guesswork” currently performed by the surgeon, biased by their training experience. Through this detailed report of our modeling and validation approaches, we hope that other centers can consider implementing their own patch-planning programs. The largest investment required for such a program is a dedicated engineering team that would perform or oversee all aspects of the workflow. Once the workflow is fully established, each clinical case will require about 10–15 h of engineering time, as well as 1 h of the surgeon’s time to discuss the planned approach and to review the patch design with the engineer. As their value becomes more widely recognized, we anticipate that surgical planning workflows have the potential for medical insurance reimbursement, facilitating the development of sustainable programs within Heart Centers across the nation. We envision applying this framework to develop workflows to assist surgeons with reconstructions for numerous cardiac anomalies requiring patch augmentation, achieving targeted dimensions with high reproducibility, thereby, ultimately, improving patient outcomes.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

BPA

Branch pulmonary artery

CFD

Computational fluid dynamics

CN

CardioCel Neo

COU

Context of Use

EF20

EcoFlex 00-20 silicone

EF50

EcoFlex 00-50 silicone

FDA

US Food and Drug Administration

FEA

Finite-element analysis

pBPA

Porcine branch pulmonary artery

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Shannen B. Kizilski, Dominic P. Recco, Jocelyn M. Davee, Ashley Masterson, Jiang Yao, Patrick D. Earley, Nicholas E. Kneier, Kenneth I. Aycock, Brent A. Craven, and Pras Pathmanathan. The first draft of the manuscript was written by Shannen B. Kizilski and Dominic P. Recco; and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

This work was supported by the Additional Ventures Catalyst to Independence Award (SBK) and the National Institutes of Health T32HD104582 (DPR).

Declarations

Competing interests

The authors have no competing interest to declare.