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Learn more: PMC Disclaimer | PMC Copyright Notice NPJ Biomed Innov . 2025 Nov 7;2:40. doi: 10.1038/s44385-025-00035-9 Search in PMC Search in PubMed View in NLM Catalog Add to search The Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework predicts optimal device landing zones tailored to patient-specific anatomy Mohamed Abdelkhalek Mohamed Abdelkhalek 1 School of Biomedical Engineering, McMaster University, Hamilton, ON Canada Find articles by Mohamed Abdelkhalek 1 , Zahra Keshavarz-Motamed Zahra Keshavarz-Motamed 1 School of Biomedical Engineering, McMaster University, Hamilton, ON Canada 2 Department of Mechanical Engineering, McMaster University, Hamilton, ON Canada 3 School of Computational Science and Engineering, McMaster University, Hamilton, ON Canada Find articles by Zahra Keshavarz-Motamed 1, 2, 3, ✉ Author information Article notes Copyright and License information 1 School of Biomedical Engineering, McMaster University, Hamilton, ON Canada 2 Department of Mechanical Engineering, McMaster University, Hamilton, ON Canada 3 School of Computational Science and Engineering, McMaster University, Hamilton, ON Canada ✉ Corresponding author. Received 2025 Feb 14; Accepted 2025 Aug 5; Collection date 2025. © The Author(s) 2025 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC12594614 PMID: 41211048 Abstract VTAVR, a novel simulation for Transcatheter Aortic Valve Replacement (TAVR), optimizes device placement using routine patient-specific CT angiography data. It integrates image processing, geometric reconstruction, and centerline estimation for accurate valve deployment. The framework employs a kinematic simulator to optimize valve performance by adjusting parameters like expansion area, anchoring depth, and implantation height, aiming to reduce complications such as paravalvular leaks (PVL) and left bundle branch block (LBBB). In this retrospective study ( N = 40; pre and post TAVR), VTAVR demonstrated high fidelity with average Surface Error of pre CT simulated device versus in-vivo post CT stent frame (L2 Norm) Median: 0.633 mm; IQR= [0.216–1.37 mm]. Median post-TAVR CT device diameters were 24.4 mm [22.0–25.9 mm] at the outflow, 24.4 mm [22.5–26.0 mm] at the midflow, and 24.9 mm [22.9–26.7 mm] at the inflow, showing no significant differences compared to VTAVR simulations ( p < 0.001). Median implantation height was 8.1 mm [6.9–10.4 mm] vs 7.2 mm [6.7–8 mm], with VTAVR predicting similar heights ( p < 0.05). Additionally, VTAVR accurately predicted the area cover index, with a median of 101.4% [91.9–105.3%] closely matching post-TAVR CT ( p < 0.01). The system provides assessments of peri-procedural risk factors by quantifying geometrical “safety” margins, aiming to minimize common complications such as improper implantation depth and over-expansion. VTAVR’s simulation of various deployment scenarios allows clinicians to foresee and address potential complications effectively, marking a significant advance in personalized cardiac interventions through virtual, non-invasive pre-procedural optimization. Subject terms: Computational biology and bioinformatics, Cardiovascular diseases, Interventional cardiology Introduction Transcatheter Aortic Valve Replacement (TAVR) has emerged as a transformative procedure for patients with severe aortic stenosis, traditionally deemed high-risk and often ineligible for surgical interventions 1 , 2 . As populations age, the prevalence and necessity of TAVR continue to grow, emphasizing the need for continual advancements in procedural techniques and planning 3 , 4 . Unlike surgical aortic valve replacement, TAVR does not allow for direct inspection of the perivalvular area by the operator, and the variability in aortic valve anatomy complicates the accuracy of device sizing, optimal landing zone selection, and adequate balloon expansion 5 , 6 . These challenges are exacerbated by calcifications on the valve cusps, annulus, and left ventricular outflow tract, which vary widely between patients in density and distribution and are particularly important in the device landing zone (DLZ) 4 , 7 . These variations in aortic shapes and calcific distribution can significantly influence both short and long-term clinical outcomes 8 , 9 . Incorrect sizing of the prosthetic device, inadequate balloon expansion, and uneven expansion within the TAVR landing zone are linked to poorer outcomes, including various degrees of paravalvular leakage/regurgitation 10 . Furthermore, the proximity of the device to the membranous interventricular septum can lead to complications such as left-bundle-branch-block or complete atrioventricular block post-TAVR 11 , 12 requiring a permanent pacemaker implantation after the procedure. Factors like increased implantation depth and asymmetric calcification are critical in predicting the necessity for mitigating such consequences 4 , 13 . Regarding procedural adaptations, TAVR techniques have evolved to incorporate simpler methods that less frequently require balloon pre-dilation of the native calcified leaflets and post-dilation of the TAVR device 14 . This shift underscores the need for a more tailored approach to TAVR, where understanding the specific patterns of calcification could be crucial 15 , 16 . One of the critical challenges in TAVR is ensuring the precise deployment of the aortic valve prosthesis within a complex anatomical landscape 6 , 17 . Suboptimal deployment can lead to severe complications, such as paravalvular leaks or valve misplacement, which significantly affect patient outcomes. This necessitates highly accurate pre-procedural planning and assessment techniques to ensure optimal positioning and sizing of the valve 3 , 4 , 6 , 18 . Doppler Echocardiography (ECHO) and Cardiac Magnetic Resonance (CMR) are key tools for assessing a variety of aortic valve conditions, though both have their drawbacks 19 . ECHO, while considered the gold standard for evaluating valve function 20 , suffers from low spatial resolution, operator dependency, and its inability to effectively quantify calcification. On the other hand, CMR, despite its detailed imaging capabilities, is hindered by long acquisition times, and it cannot be used for patients with certain implants; it is also prone to motion artifacts and geometric distortions 13 , 19 . These limitations are particularly significant for cardiac valve assessments. In the context of TAVR, computed tomography (CT), particularly Cardiac Computed Tomography Angiography (CT), is preferred due to its high spatial resolution and precise ECG-gated timing, making it indispensable for detailed anatomical assessment and procedural simulation in valvular interventions or surgeries 4 , 6 , 21 . Despite these advancements, current methodologies often fall short in dynamically simulating device deployment and predicting interactions between the device and the anatomical structures in real-time suitable for a rapid action clinical setting. Recent research has highlighted the potential of integrative patient-specific computational modeling to enhance the precision of cardiovascular interventions 21 , 22 . The use of detailed structural and fluid-dynamic simulations including novel techniques for modeling complex physiological phenomena has been promising 8 , 17 , 23 – 25 , 26 – 30 . However, these models have traditionally needed vast computational resources as well as expert manual interaction for assembling the computational domain and boundary conditions, which severely limits their ability to simulate real-time device interactions during the TAVR procedure. We herein introduce Virtual Transcatheter Aortic Valve Replacement (VTAVR) system (Fig. 1 ). VTAVR integrates advanced image preprocessing with kinematic geometry to construct fast, dynamic, patient-specific simulations of the device deployment process. This system incorporates previously developed image segmentation and geometric reconstruction techniques to assemble an accurate digital representation of the patient-specific aortic valve anatomy. By employing a data driven kinematic geometry framework, VTAVR aims to predict the optimal device landing zone, anticipate potential procedural risks, and propose modifications before actual surgery. This predictive capability is built on an understanding of device-tissue interaction up until the time at which the device contacts the aortic annulus. The framework, therefore, aims to model the requirements of balloon expandable catheter prosthetic valve delivery system by modeling (1) the surrounding tissue structure (aortic root including the ascending aorta, aortic valve and left-ventricle outflow tract and calcifications). (2) The device trajectory curve which models the route taken by a typical balloon expandable device along the delivery system. (3) The device landing zone geometric settings which describe the spatial extents of an idealized device including changes in these extents depending on dynamic changes to expansion diameter and prespecified device size. (4) A novel custom simulator module that allows for manipulation of the device position, orientation, and sizing along the delivery system. (5) A novel custom interaction system that models interaction between the device landing extents and surrounding patient specific geometry and structure including a dynamic leaflet displacement module to allow for visualization and quantification of leaflet calcific migration during device deployment. (6) An optimization system for finding optimal device deployment configurations based on clinical requirements and real-time information from (4) and (5). Fig. 1. Computational workflow overview for the CT-based Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework. Open in a new tab A illustrates the initial step where a patient diagnosed with aortic stenosis (AS) undergoes clinical CT TAVR assessment, Displays the end-to-end pipeline: ( A ) patient CT segmentation using FPR; ( B ) MVGIPR-based topology reconstruction of the aortic root; and ( C ) VTAVR-specific modules including device simulation along the Frenet-Serret trajectory, landing zone optimization, and calcification displacement prediction for tailored intervention planning. VTAVR is designed for real‑time device landing zone deployment and configuration testing as an incremental add‑on tool to the current clinical workflow, supporting device landing zone, sizing and leaflet displacement evaluation without the computational cost of full structural analyses up until moment of contact with surrounding tissue. The application of VTAVR in clinical may potentially augment TAVR interventional planning by enabling the virtual testing of various deployment scenarios. This approach not only improves the safety and effectiveness of procedures but also paves the way for personalized cardiac interventions, potentially reducing the incidence of complications and enhancing patient outcomes. We note that, to achieve the high computational efficiency required for interactive clinical use, VTAVR currently represents the aortic root and leaflets as static, rigid geometries and does not account for their elastic deformation under device expansion. While this assumption is enables rapid trialing of device positions, it omits the effects of root compliance and leaflet stiffness that influence post‑deployment stresses and long‑term outcomes. Furthermore, by rapidly identifying optimal device configurations, VTAVR provides a priori initial conditions for downstream post‑deployment strain and stress analyses on the aortic annulus and native leaflets. Results The Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework was evaluated primarily on a of aortic stenosis patients ( N = 40; Male: 52.5%; Female: 47.5%; Tricuspid: 55%; Bicuspid: 45%) with demographic and baseline characteristics presented in Table 1 . The methodology was assessed by comparing VTAVR predictions to clinical CT scans and post-procedural CT and ECHO measurements. All evaluated parameters used for quantitative assessment are presented in Table 2 . Agreement between VTAVR predictions and clinical measurements was evaluated based on Spearman’s correlation coefficient (R), with values interpreted as follows: [0.5: poor; 0.5–0.75: moderate; 0.75–0.9: strong; 0.9–1: very strong]. The framework was validated by comparing VTAVR-predicted parameters such as device landing zone expansion dimensions, implantation height, orientation, and area cover index against actual post-procedural measurements. Sensitivity analysis of procedural parameters provided insights into their impact on procedural success and potential complications (Supplementary Movies 2 - 4 ). We further examined framework parameters that may indicated potential risk factors associated with procedural complications such as patient-prosthesis mismatch (PPM), left bundle branch block (LBBB), and paravalvular leakage (PVL) was also evaluated, highlighting its potential for optimizing TAVR outcomes. Additionally, the VTAVR system’s performance was compared across different patient groups, including male versus female and tricuspid versus bicuspid valve cases, to assess its robustness and adaptability in diverse clinical presentations. Table 1. Baseline patients characteristics of the retrospective aortic valve disease (AS and BAS) clinical cohort ( N = 40) Baseline Parameters Category Value Age (years)–mean + -sd 75.6 ± 6.6 Sex-n(%) Female 19 (47.5%) Male 21 (52.5%) AV Morphology-n(%) Tricuspid 22 (55%) Bicuspid (T = 1) 9 (22.5%) Bicuspid (T = 2) 6 (15%) Bicuspid (T = 3) 3 (7.5%) Valve Type Implanted Edwards Sapien 3 (23 mm) 15 (37.5%) Edwards Sapien 3 (26 mm) 16 (40%) Edwards Sapien 3 (29 mm) 9 (22.5%) Procedural Outcome / Complication (Post TAVR) Paravalvular Leakage (PVL) 8 (20%) Left Bundle Branch Block (LBBB) 8 (20%) Patient Prosthetic Mismatch (PPM) 3 (7.5%) NYHA Class-n(%) I 3 (7.5%) II 18 (45%) III 17 (42.5%) IV 2 (5%) Coronary artery disease–n(%) Yes 8 (20%) Hypertension–n(%) Yes 32 (80%) Type 2 diabetes mellitus–n(%) Yes 11 (27.5%) Dyslipidemia–n(%) Yes 28 (70%) Atrial fibrillation–n(%) Yes 5 (12.5%) Open in a new tab Baseline characteristics and procedural information presented as median [25th–75th percentile] for continuous variables and count (%) for categorical variables. Table 2. Summarized statistics for the optimized VTAVR framework device landing zone configuration parameters for the retrospective TAVR cohort ( N = 40) Simulation Framework Parameters Female Male Tricuspid Bicuspid Total Geometric Reconstruction Error - Mean (mm) −0.028 [−0.044 to −0.017] −0.024 [−0.03–−0.005] −0.025 [−0.045– −0.011] −0.027 [−0.034 to −0.01] −0.026 [−0.041 to −0.01] Geometric Reconstruction Error – Standard Deviation (mm) 0.29 [0.27–0.36] 0.32 [0.27–0.37] 0.34 [0.27–0.38] 0.3 [0.27–0.35] 0.3 [0.27–0.37] Device Landing Zone Geometric Calcific Ratio – Total (%) 14.3 [10.6–19.7] 14.8 [12.8–21.7] 13.6 [10.4–18.7] 15.3 [11.3–22.1] 14.8 [10.6–20.8] Device Landing Zone Geometric Calcific Ratio – NCC (%) 7.2 [3.2–9.6] 7.8 [5.0–10.5] 7.8 [4.7–9.6] 7.4 [5.2–10.3] 7.6 [4.8–10.0] Device Landing Zone Geometric Calcific Ratio – RCC (%) 3.7 [1.6–7.0] 4.5 [2.3–5.4] 3.5 [1.6–5.9] 5.3 [2.2–6.5] 4.5 [1.77–6.24] Device Landing Zone Geometric Calcific Ratio – LCC (%) 2.7 [1.4–7.1] 3.1 [1.5–5.7] 2.6 [1.4–6.9] 3.0 [1.5–4.2] 2.8 [1.5–6.1] VTAVR-Optimized Device Diameter – Outflow (mm) 22.2 [20.8–23.3] 25.3 [23.4–27.0] 23.2 [21.1–25.0] 24.0 [22.4–25.4] 23.4 [22.1–25.4] VTAVR-Optimized Device Diameter – Midflow (mm) 22.3 [21.1–23.5] 25.5 [23.0–26.7] 23.2 [21.2–25.2] 24.0 [22.5–25.6] 23.4 [22.1–25.6] VTAVR-Optimized Device Diameter – Inflow (mm) 22.8 [21.6–23.8] 24.3 [23.3–27.1] 23.3 [21.5–24.5] 24.3 [22.9–26.2] 23.7 [22.4–25.6] VTAVR-Optimized Device Area Cover Index (%) 91.5 [88.4–96.2] 91.8 [86.5–100.4] 91.8 [88.3–98.3] 91.6 [87.0–100.9] 91.7 [87.1–99.1] VTAVR-Optimized Device Implantation Height (mm) 6.8 [6.2–7.4] 7.7 [7.2–8.8] 7.2 [6.5–7.7] 7.32 [6.8–8.2] 7.2 [6.7–8.0] VTAVR-Optimized Device Annular Orientation Deviation (%) 0.982 [0.956–0.987] 0.976 [0.944–0.989] 0.96 [0.945–0.986] 0.984 [0.962–0.992] 0.978 [0.949–0.989] VTAVR-Euclidean Distance (L2 Norm) Mean Error (mm) 0.849 [0.243–1.24] 0.457 [0.249–1.74] 0.421 [0.152–1.31] 0.891 [0.274–1.72] 0.633 [0.216–1.37] VTAVR-Euclidean Distance (L2 Norm) Standard Deviation Error (mm) 2.1 [1.67–2.74] 2.3 [1.48–2.75] 2.14 [1.42–2.7] 2.15 [1.75–2.77] 2.14 [1.62–2.76] Open in a new tab The table presents parameter values as median[25 th –75 th percentile] comparing simulation framework output parameters based on recommended TAVR guidelines The data is grouped by valve morphology (tricuspid vs. bicuspid) and, and patient sex (Female vs Male). Including co-registered (pre CT) VTAVR deployed frame L2 norm measure against actual deployed stent frame in post-CT. Importantly, the validation presented here is retrospective and relies solely on post-deployment imaging data, thus reflecting final device positioning rather than precise intra-procedural conditions. During clinical TAVR procedures, the actual intra-procedural configuration of the deployed device may vary from the simulated optimal placement due to dynamic adjustments made by operators in real time, patient-specific anatomical responses, and procedural conditions not captured in pre-procedural imaging. Consequently, the current VTAVR results should be interpreted primarily as predictive and illustrative of potential clinical outcomes. These findings demonstrate VTAVR’s clinical utility for simulation-based procedural planning, allowing exploration of optimal device configurations and providing important quantitative insights into procedural outcomes before actual intervention. Future prospective investigations incorporating intra-procedural imaging and real-time data capture will be essential to fully validate the concordance between predicted deployment configurations and actual device positions achieved during clinical procedures. Such prospective studies would further solidify the clinical value of the VTAVR system, enabling robust prediction and real-time procedural guidance. VTAVR device landing zone configuration The VTAVR Device Landing Zone Configuration refers to the optimal spatial parameters within the aortic annulus where the transcatheter aortic valve prosthesis is to be deployed. These parameters are critical for ensuring the valve’s effective anchoring, sealing, and overall performance post-implantation. The configuration is defined by several degrees of freedom, including device expansion dimensions (diameters at various levels), implantation height, rotational orientation, and area cover index. Figure 2 , Panel A illustrates these key parameters: device diameters at the outflow, midflow, and inflow levels; the implantation height relative to the aortic annulus; and the orientation deviation, which measures the alignment of the device relative to the native annulus plane. The expansion dimensions are crucial for ensuring that the prosthesis fits snugly within the annulus without causing undue stress on the surrounding tissues. The implantation height determines the depth at which the device is anchored, influencing both hemodynamic performance and the risk of complications such as conduction disturbances. The rotational orientation ensures that the prosthesis is aligned correctly with the native aortic valve leaflets, minimizing the risk of paravalvular leakage. The area cover index indicates the percentage of the annular area covered by the prosthesis, which is essential for achieving a secure seal and preventing leakage. By optimizing these parameters through the VTAVR framework, we aim to enhance procedural planning, improve post-operative outcomes, and minimize the risk of complications. The following sections detail the correlation between VTAVR suggested optimal parameters and the corresponding measured post CT device frame settings in-vivo. Fig. 2. Validation of the VTAVR framework through comparison with post-CT device landing zone configuration. Open in a new tab A – D Compare simulated and actual device outcomes: expansion geometry, implantation depth, displaced calcifications, and mesh deviation. Visualizes collision sites and deformation, confirming VTAVR's predictive fidelity with post-procedural CT; E – F Shape variance analysis comparing the simulated ideal stent configuration to the actual deployed stent surface derived from a post-operative CT scan. The color map and vectors represent the signed Euclidean distance, indicating regions of over-expansion (positive, red) and under-expansion (negative, blue). The mean ± standard deviation of the distance for this patient was 0.25 ± 1.0 mm. Device landing zone expansion diameters The VTAVR framework demonstrated high accuracy in predicting the expansion diameters of the device within the landing zone, a parameter critical to the seating, sealing, and overall effectiveness of the transcatheter aortic valve replacement (TAVR) device. Qualitative visualizations (Figs. 3 and 4 ) showed a strong alignment between VTAVR-predicted expansion diameters and actual post-procedural CT measurements at the outflow, midflow, and inflow sections of the device. Quantitatively, the median post-TAVR CT device diameters were 24.4 mm [22.0–25.9 mm] at the outflow, 24.4 mm [22.5–26.0 mm] at the midflow, and 24.9 mm [22.9–26.7 mm] at the inflow levels, which were closely matched by the VTAVR simulations with no significant differences observed ( p < 0.001; Fig. 5 ). The framework accurately reflected sex-specific differences, where males had larger device diameters post-TAVR compared to females: males had 25.6 mm at the outflow, 25.5 mm at the midflow, and 25.8 mm at the inflow, while females had 22.3 mm, 22.7 mm, and 23.4 mm, respectively (Fig. 6 ). Similarly, it effectively captured the morphological differences between patients with bicuspid aortic stenosis and those with tricuspid aortic stenosis. Bicuspid patients had larger expansion diameters: 25.0 mm at the outflow, 25.0 mm at the midflow, and 25.1 mm at the inflow, compared to TAS patients with 23.6 mm, 24.4 mm, and 24.8 mm, respectively (Fig. 6 ). Fig. 3. Representative samples from patients with tricuspid aortic stenosis who underwent TAVR (grouped by device size). Open in a new tab Patient samples ( A – F ) ( N = 6, grouped by device size) show how VTAVR predictions align with clinical outcomes. Includes control and complicated cases (e.g., PVL, LBBB), with metrics for expansion, depth, orientation, calcific ratio, and segmentation error. Fig. 4. Representative samples from patients with bicuspid aortic stenosis who underwent TAVR (grouped by device size). Open in a new tab Patient samples ( A – F ) (N = 6, grouped by device size); Similar to Fig. 3 but for bicuspid morphologies (types 1–3). Demonstrates VTAVR’s predictive performance across variable valve anatomy and associated procedural complications (e.g., PPM, LBBB), using simulated vs. actual outcome alignment. Fig. 5. Correlation matrices highlighting the validation of the VTAVR framework through comparison with post-TAVR CT parameters and post-TAVR echocardiographic measurements. Open in a new tab A Matrix comparing VTAVR simulation outputs with post-TAVR CT metrics. B Matrix showing correlations with echocardiographic data (mean gradient, AVA, DVI). Validates VTAVR’s predictive value for both anatomical and hemodynamic outcomes. Fig. 6. Comparison of VTAVR framework simulation optimal device landing zone parameters and actual measured parameters from post-CT imaging for patients with tricuspid and bicuspid aortic stenosis who underwent TAVR. Open in a new tab Compares VTAVR-predicted vs. measured outflow ( A ), midflow ( B ) and inflow ( C ) diameters. Stratified by morphology and complications, highlighting prediction deviations in PVL, LBBB, and PPM cases. Optimization constraints based on Edwards SAPIEN 3 guidelines are annotated. Device landing zone implantation height The accuracy of the VTAVR framework in predicting the implantation height was validated through comparisons with post-procedural CT imaging data. As shown in Figs. 3 and 4 , the qualitative visualization of the device implantation height closely matched the post-procedural measurements, with a median implantation height of 8.1 mm [6.9–10.4 mm]. The VTAVR simulations predicted similar implantation heights, with no significant differences observed ( p < 0.05; Fig. 5 ). When comparing between sexes, males and females had similar implantation heights (8.1 mm), and the VTAVR framework accurately predicted these values. However, variations were observed between tricuspid and bicuspid cases, with bicuspid patients having a slightly higher implantation height (9.1 mm) compared to tricuspid patients (7.7 mm), which was also accurately reflected in the VTAVR simulations (Fig. 7B ). The simulation-optimized implantation height closely matched the actual procedural status, with high implantation heights potentially restricting nominal expansion and adversely affecting valve performance, while deep implantation heights could induce stress on the atrioventricular node, leading to post-procedural complications such as the need for pacemaker implantation due to electrical conduction issues. In our cohort, the simulation-predicted implantation heights deviated by less than 1 mm from the actual heights observed in post-procedural imaging. This high level of accuracy underscores the VTAVR system’s ability to provide reliable predictions for procedural planning, minimizing the risks associated with suboptimal device positioning. Fig. 7. Comparison of VTAVR framework simulation optimal device landing zone parameters and actual measured parameters from post-CT imaging for patients with tricuspid and bicuspid aortic stenosis who underwent TAVR. Open in a new tab A – C Plots simulated vs. actual annular area cover index, implantation height, and alignment (dot product of annular and device normals). Notes discrepancies in cases with adverse outcomes. Reinforces VTAVR’s relevance for procedural alignment prediction. Device landing zone orientation Orientation of the device within the landing zone is critical for procedural success and long-term valve performance. The VTAVR framework effectively modeled the device’s rotational orientation relative to the aortic root. Figures 3 and 4 demonstrate that the qualitative visualization of the device orientation closely matched the post-procedural CT measurements. The median post-TAVR device annular orientation deviation was 0.998 [0.996-1.0]. Variations across sex and morphology were minimal, with both male and female patients and tricuspid and bicuspid cases showing similar orientation deviations. This suggests that the VTAVR framework can reliably predict device orientation regardless of patient demographics or valve morphology (Fig. 7C ). Device landing zone area cover index The area cover index, representing the percentage of the annular area covered by the deployed device, is a crucial metric for procedural success. Figure 7A . shows the simulated and actual area cover indices, illustrating the VTAVR framework’s ability to predict this parameter accurately. The simulation-optimized device area covers closely matched the post-procedural measurements, confirming the framework’s reliability in ensuring adequate coverage of the annular area without excessive oversizing or under sizing. The area cover index, representing the percentage of the annular area covered by the deployed device, is a crucial metric for procedural success. The VTAVR framework accurately predicted the area cover index, with post-TAVR CT measurements showing a median area cover index of 101.4% [91.9–105.3%]. The VTAVR simulations closely matched these values, demonstrating strong predictive accuracy ( p < 0.01; Fig. 5 ). Sex-specific differences showed that both males and females had similar area cover indices (101.6% and 101.3%, respectively). However, bicuspid cases showed slightly lower area cover indices (98.4%) compared to tricuspid cases (101.6%), which was accurately reflected in the VTAVR simulations. This suggests that the framework can effectively predict and optimize the area cover index across different patient demographics and valve morphologies (Fig. 5 ). Device landing zone L2 surface error The L2 surface error quantifies the geometric deviation between the simulated device and the actual post-procedural deployment, serving as a direct measure of the simulation’s spatial accuracy (Fig. 2 ). The analysis showed a high degree of congruence between the simulation and the clinical result, with a total mean Euclidean distance error of 0.633 mm [IQR: 0.216–1.37 mm]. The standard deviation of this error across the cohort was 2.14 mm [IQR: 1.62–2.76 mm] (Fig. 8E ). Subgroup analysis revealed variations based on anatomy. Bicuspid valve cases resulted in a higher mean surface error (0.891 mm [IQR: 0.274–1.72]) when compared to the lower error in tricuspid cases (0.421 mm [IQR: 0.152–1.31]). A similar trend was observed between sexes, with female patients showing a mean error of 0.849 mm [IQR: 0.243–1.24], while male patients had a mean error of 0.457 mm [IQR: 0.249–1.74]. These findings suggest the framework’s predictive accuracy is robust, while also capturing patient-specific anatomical complexities. Fig. 8. Box plots for diameters and depth, highlighting significant correlations, and scatter plots comparing calcification score and calcific device landing zone area effect on device expansion. Open in a new tab A – B Box plots show significant correlations between simulated and measured diameters/depths. C – D Scatter plots reveal weak correlation between calcification metrics and expansion deviation, supporting robustness of VTAVR against calcific variability. E A boxplot of Euclidean distance (L2 Norm between optimized device landing zone and in-vivo post CT stent frame), showing a mean of 0.633 mm with an interquartile range (IQR) from 0.216 mm to 1.37 mm. Sensitivity of parameters on objective function The impact of modifying various parameters, such as expansion radius and implantation height, on the objective function was evaluated numerically. The objective function aimed to maximize valve performance by optimizing device placement within the patient-specific anatomical constraints. Supplementary Movie 2 – 4 illustrate the sensitivity of these parameters, showing how changes in expansion radius, implantation height and shape of the catheter trajectory curve affect the annular area cover index and overall procedural success. Expansion radius The effect of modifying the expansion radius on the objective function was numerically evaluated (Supplementary Movie 2 ). The simulation results indicated that an optimal expansion radius maximized the area cover index while minimizing stress on the annular structures. Based on geometric analysis deviations from the optimal radius may result in reduced performance, either through under expansion, which limited leaflet coaptation and effective hemodynamic function, or overexpansion, which increased the risk of annular rupture and calcific embolization. Implantation height Similarly, the effect of implantation height on the objective function was evaluated. The results showed that an optimal implantation height ensured adequate expansion and anchoring of the device, while minimizing the risk of inducing electrical conduction issues and the need for pacemaker implantation. High implantation heights restricted nominal expansion, adversely affecting valve performance, while deep implantation heights stressed the atrioventricular node, leading to potential complications. Catheter trajectory curvature (geometric symmetrisation) The catheter trajectory curvature significantly influences the VTAVR framework’s objective function, particularly the annular area cover index (ACI). By adjusting the tolerance of the centerline curve, which mimics the deployment wire, the framework can optimize the device trajectory for patient-specific anatomical features. This adjustment modifies the device’s orientation and initiation site, aligning the deployment path optimally with the patient’s anatomy. Supplementary Movie 3 illustrates how this parameter reduces the search space of the affine matrix for device configuration, including rotation and translation. By fine-tuning the trajectory curve tolerance, the VTAVR framework narrows down the possible configurations to a small set of optimal solutions that best match the shape of the deployment site. This approach ensures better alignment and fit of the valve, enhancing procedural success. By modeling straight trajectories for simpler cases or highly curved paths for complex anatomies, the VTAVR framework adapts to patient-specific shapes and features, improving overall procedural outcomes and reducing the risk of complications. This tailored approach allows for precise navigation around anatomical obstacles, ensuring optimal device placement. TAVR procedural outcomes in the context of the VTAVR framework Transcatheter Aortic Valve Replacement (TAVR) procedures, while transformative for patients with severe aortic stenosis, are not without peri-procedural events and complications. Common complications include paravalvular leakage (PVL), left bundle branch block (LBBB), and patient-prosthesis mismatch (PPM). These events can adversely affect patient outcomes, leading to prolonged recovery times and additional interventions. Traditional clinical intervention planning, which relies primarily on pre-procedural CT planimetry, may not fully account for the dynamic and complex interactions between the deployed device and the anatomical structures. This limitation often results in suboptimal device placement and unforeseen complications. The VTAVR device landing zone simulator addresses these limitations by allowing clinicians to try and simulate different device configurations in an interactive and highly quantitative manner. This approach leverages advanced computational modeling to predict the optimal device parameters, thereby minimizing the risk of complications. The simulations include detailed visualizations and analyses, such as those shown in Supplementary Movies 1 – 3 and Figs. 3 – 7 , which provide comprehensive insights into how the device interacts with the patient-specific geometry. Device landing zone and paravalvular leakage (PVL) Paravalvular leakage (PVL) occurs when the prosthetic valve does not completely seal against the aortic annulus, allowing blood to flow around rather than through the valve. This can lead to significant hemodynamic inefficiencies and increase the risk of endocarditis. Figures 3 and 4 highlight specific cases from our cohort, such as Patient #8 (F, PVL, 23 mm), where the VTAVR framework showed a potential for PVL due to suboptimal device expansion and alignment. The VTAVR simulations provided detailed predictions of the device landing zone parameters, revealing areas where the device might not fully appose to the annulus. By comparing these predictions with post-procedural CT measurements, it was evident that the VTAVR framework can potentially identify sites of PVL and suggest alternative device configurations to achieve better sealing. Figures 6 and 7 show bar plots of the device landing zone parameters across all patients, indicating which cases had higher risks of PVL. Device landing zone and left bundle branch block (LBBB) Left bundle branch block (LBBB) is a conduction disturbance that can occur post-TAVR when the prosthetic valve impinges on the left bundle branch of the heart’s electrical conduction system. This can necessitate the implantation of a permanent pacemaker. Figures 3 and 4 detail cases like patient #14 (M, LBBB, 29 mm), where the VTAVR framework suggest contact interactions between the device and the atrioventricular node at regions towards the left ventricle outflow tract. The VTAVR simulations suggest that optimizing the implantation height and orientation could potentially be a viable option for these patients. By adjusting these parameters pre-operatively, clinicians could simulate different scenarios that may help minimize the risk of inducing LBBB and consequently a permanent pacemaker implantation. In our cohort Fig. 7B patients with higher implantation heights had a greater incidence of LBBB. Device landing zone and patient prosthetic mismatch (PPM) Patient-prosthesis mismatch (PPM) occurs when the effective orifice area of the implanted valve is too small relative to the patient’s body size, leading to higher residual gradients and suboptimal hemodynamic performance. Figures 3 and 4 include examples such as Patient #3 (M, Control, 23 mm), where the VTAVR framework accurately predicted optimal device sizes to avoid PPM. The VTAVR simulations provided valuable insights into the appropriate device sizes and configurations to match the patient’s anatomical and physiological characteristics. Corresponding bar plots in Figs. 6 and 7 show that for our cohort patients with optimized device dimensions had lower incidences of PPM. Device landing zone configuration and calcification Accurate modeling of calcification and its migration is crucial for optimizing TAVR outcomes. The VTAVR system’s ability to simulate calcific displacement and interaction with the device suggests its potential to predict long-term calcific-related complications and optimize procedural planning to mitigate these risks. The VTAVR framework provides a fast and powerful tool for simulating calcific migration during TAVR procedures, which correlates well with visual inspections of post-procedural CT calcification. One major challenge in current TAVR procedures is the inability to detect calcification post-intervention due to the blooming effect caused by stent metal. This limitation hinders our understanding of calcification’s impact on device performance and patient outcomes. Simulating calcific migration The VTAVR framework can simulate the movement of calcific deposits during device deployment, providing a detailed prediction of how calcification will interact with the prosthetic valve. This simulation capability is crucial because leaflet calcification does not primarily hinder device expansion; instead, the balloon pressure during deployment displaces the thin leaflets along with the calcific deposits 4 . This behavior was observed by comparing the regression of calcification against deviations from nominal expansion (Fig. 8C–D ), both using standard clinical calcification scores and geometrically derived landing zone calcific areas 31 . The MVGIPR technique quantifies the surface area in the device landing zone that is calcified, providing a precise measure of calcification burden that is invariant to shape uncertainty due to curvature and morphology 31 . Impact of calcification on device expansion Our analysis revealed that leaflet calcification did not significantly obstruct device expansion. Figures 3 and 4 show that the presence of calcification on the leaflets did not prevent the prosthesis from achieving the intended expansion dimensions. However, calcification remains clinically important because its regional distribution and density correlate with key procedural risks. For example, pronounced focal calcification can create asymmetric anchoring, elevate radial stress at the membranous septum, and increase the risk of paravalvular leakage or conduction disturbances 32 , 33 . Importantly, although calcification has only a modest effect on the mechanical expansion geometry, its inclusion is essential for risk stratification and procedural planning. In our separate validation study 4 , intensity‑weighted regional calcification scores improved prediction of paravalvular leakage (AUC = 0.80), left bundle branch block (AUC = 0.748), and the need for balloon pre‑dilation (AUC = 0.907) and post‑dilation (AUC = 0.75). These results demonstrate that calcification density and asymmetry critically influence device sealing, anchoring, and conduction risk, justifying its continued inclusion in VTAVR despite limited mechanical obstruction as previously stated. Discussion Current clinical processes for TAVR intervention planning predominantly rely on pre-procedural CT planimetry to estimate anatomical dimensions and guide device selection 6 , 34 , 35 . However, this approach often falls short in dynamically simulating the device deployment and predicting interactions between the device and the anatomical structures, which are crucial for minimizing peri-procedural complications such as paravalvular leakage (PVL), left bundle branch block (LBBB), and patient-prosthesis mismatch (PPM) 4 , 7 . There is a growing need for fast, accurate, and robust procedural planning and optimization frameworks that can provide patient-specific insights and improve procedural outcomes 36 . Our VTAVR framework presents a significant advancement over typical CT planimetric TAVR procedural planning by integrating detailed geometric modeling and simulation capabilities. Unlike traditional methods, which may not fully capture the complexities of device behavior and anatomical interactions, the VTAVR framework offers a highly interactive and quantitative approach to procedural planning. Compared to expensive finite element modeling, which requires substantial computational resources and time, the VTAVR framework is extremely fast and efficient 17 , 25 , 37 , 38 . The assumptions made to build this purely kinematic geometric framework align with existing knowledge on device behavior up until the point of contact with surrounding structures, ensuring accuracy and reliability. Importantly, the VTAVR framework leverages only information directly gleaned from routine TAVR clinical data, including CT angiograms and procedural information such as device type and size. Simulation optimization bounds are based on existing recommended guidelines for balloon-expandable SAPIEN devices 39 , 40 , making this framework both practical and easily integrable into current clinical workflows. The following sections detail the specific benefits and implications of using the VTAVR framework for TAVR procedural planning, highlighting its potential to enhance procedural success and improve patient outcomes. The precise predictions of the VTAVR system for device landing zone parameters underscore its potential for enhancing procedural success. Accurate modeling of expansion dimensions and implantation height, as demonstrated by the close alignment with post-procedural measurements, suggests that clinicians can rely on VTAVR for better pre-procedural planning. This can lead to more accurate sizing and positioning of the TAVR device, thereby reducing the risks associated with under expansion, overexpansion, and suboptimal implantation heights 14 , 40 , 41 . The sensitivity analyses of parameters such as expansion radius and implantation height provided valuable insights into their impact on procedural success. The observed correlations between these parameters and the objective function emphasize the need for precise optimization to maximize valve performance. This detailed understanding can guide clinicians in tailoring TAVR procedures to individual patient anatomies, potentially improving procedural outcomes and reducing complications. The VTAVR framework may offer significant benefits in predicting and mitigating common TAVR-related complications, including patient-prosthesis mismatch (PPM), left bundle branch block (LBBB), and paravalvular leakage (PVL). The observed deviations between optimized VTAVR simulator predictions and actual device measurements in patients with these complications hint that these patients might have benefited from the VTAVR-recommended procedural strategy. This framework can be instrumental in designing procedural plans that account for complex geometries and dense calcification profiles, which represent significant challenges in routine intervention planning 4 , 13 , 18 , 33 . For instance, in cases of PPM and PVL, the detailed geometric model and simulation capabilities of VTAVR can help identify optimal device sizes and implantation strategies that minimize the risk of these complications. The ability to model the surface interfaces between the device and anatomical structures in real-time can provide clinicians with a better understanding of potential risks and enable them to adjust their strategies accordingly. Regarding conduction disturbances such as left bundle branch block (LBBB), our virtual deployment model assesses risk indirectly based on anatomical proximity rather than predicting electrical conduction effects directly. In the VTAVR simulation, we evaluate how close the prosthetic valve comes to critical anatomical landmarks of the cardiac conduction system (for example, the membranous septum housing the atrioventricular node and bundle branches). If the virtual device impinges on or lies very near the septal region, the model flags an elevated risk of conduction interference. However, VTAVR currently does not simulate the mechanical forces on or the electrophysiological response of the conduction tissue itself; therefore, any predicted “LBBB risk” from our framework should be interpreted as indicating increased anatomical likelihood of LBBB, rather than a definitive prediction of conduction block onset. In other words, VTAVR identifies cases where the implant’s position is anatomically close to the conduction system—a scenario known to correlate with LBBB in clinical practice—but it does not calculate the actual stress or damage to the conduction fibers. This limitation means the simulation’s output on LBBB risk is suggestive rather than conclusive. Future enhancements would be needed to model the biomechanical impact on the conduction system to directly predict conduction disturbances. For now, our interpretation of LBBB risk in VTAVR is cautious: a close spatial relationship between the device and septal wall serves as a warning for potential LBBB, guiding clinicians to consider implant depth or positioning adjustments to preserve conduction, even though the model does not quantify conduction force or injury. The comparison between tricuspid and bicuspid valve cases demonstrated the VTAVR framework’s robustness in handling anatomical variability. By accurately modeling both symmetrical and asymmetrical anatomies, the framework can provide tailored predictions that match post-procedural outcomes across different valve morphologies. This flexibility is crucial for ensuring reliable procedural planning and optimizing outcomes in a diverse patient population 42 , 43 . The detailed modeling of calcification and its migration is another significant advantage of the VTAVR framework. Accurate quantification of calcification volume and the ability to predict its interaction with the TAVR device can help clinicians anticipate and mitigate long-term complications related to calcific embolization and device malfunction 4 , 9 , 18 . The framework’s capability to simulate calcific displacement and identify potential collision sites during device deployment underscores its potential to enhance procedural planning and improve long-term valve performance. The VTAVR framework’s ability to detect potential contact sites between the device and the calcified anatomical structures is a significant innovation. By post-processing collision detection between the final device landing zone geometry and the patient-specific anatomy, VTAVR can identify precise locations where contact occurs. This capability extends beyond merely identifying affected topographical regions; it provides exact regional and parametric coordinates of contact sites. Using a novel parametric geometric reconstruction technique 31 , these coordinates are expressed in a geometric invariant way, making the framework robust against both natural and pathological physiological variations in the aortic shape. This detailed collision detection has potential prognostic implications for long-term procedural outcomes. By identifying regions of potential residual stress or thrombosis 6 , 44 , the VTAVR framework can potentially help clinicians anticipate and mitigate complications. Furthermore, this information can guide patient-specific and population-specific intervention strategies, tailoring TAVR procedures to individual anatomical variations and improving overall procedural success rates. The VTAVR framework represents a promising tool for advancing TAVR procedural planning and execution. VTAVR is designed to fit seamlessly into the pre-procedural planning routine for TAVR. In practice, after obtaining the patient’s CT angiography, the imaging data would be fed into the VTAVR software, which automatically performs segmentation and geometric reconstruction using our established pipeline. A clinician or technician can then interact with the patient-specific 3D model via a user-friendly interface – for example, virtually adjusting the prosthetic valve’s size, depth, and orientation within the aortic root. The simulation updates in real time (within seconds) as these parameters are changed, providing immediate feedback on how the device would deploy in the given anatomy. The entire VTAVR analysis, from CT input to optimal deployment recommendation, can be completed on a standard computer in a clinically acceptable timeframe (on the order of minutes). This allows the heart team to iterate through multiple “what-if” deployment scenarios before the actual procedure, enhancing decision-making without delaying care. By integrating VTAVR results into the workflow (e.g., during heart team meetings or pre-procedure planning sessions), clinicians can better anticipate challenges such as difficult anatomies or high-risk positioning, and refine their strategy (device selection, sizing, implantation technique) accordingly 6 . A number of computational planning frameworks have been developed over the past decade to simulate and optimize TAVR procedures. These platforms differ significantly in their underlying modeling philosophies, data dependencies, execution speed, and clinical applicability. Broadly, they fall into three classes: high-fidelity finite element analysis (FEA) and computational fluid dynamics (CFD) pipelines; regulated patient-specific commercial simulators; and AI-based surrogate models trained on empirical data. VTAVR, by contrast, introduces a kinematic-geometric optimization paradigm grounded in patient-specific imaging data and deterministic mathematical models. High-fidelity FEA/CFD workflows (full physics) These systems are primarily research-oriented and simulate the mechanical behavior of the stent–aortic root system under patient-specific loading conditions using full continuum mechanics and fluid–structure interaction. Implementations are often built around commercial solvers like Abaqus®, ANSYS®, or open-source platforms with high mesh resolution, complex boundary conditions, and nonlinear material laws 45 . Such simulations require between 6–48 h of computation per patient and necessitate significant manual pre-processing including mesh preparation, contact definitions, and valve modeling. Outputs include detailed spatiotemporal maps of plastic deformation, wall stress, leaflet stress distributions, and flow velocity fields that offer exceptional biomechanical insight. However, these workflows are too computationally intensive for real-time planning and require technical personnel for setup and interpretation, limiting their role to retrospective analysis or complex research applications. Regulated commercial simulators These platforms offer cloud-based FEA simulations of transcatheter valve deployment tailored to individual patient anatomies 46 . They are FDA-cleared and CE-marked, enabling integration into clinical workflows under regulatory frameworks. Users upload CT data to a secure server, where the simulation is run by the provider. Within 30–90 min, a report is returned detailing expected frame apposition, oversizing metrics, paravalvular leak risk, and suggested device configurations. These tools typically provide a user-friendly web interface, allow standardized comparison across multiple valve sizes, and are trusted due to regulatory compliance. However, the simulations remain opaque (“black-box”) to the clinician, with no ability to modify simulation parameters, inspect intermediate calculations, or simulate off-label deployment configurations. Furthermore, the need for off-site processing and data-sharing agreements may be a barrier in institutions with strict data governance. Finally, as it currently stands FEOPS only supports certain types of valves (self-expandable: NEO and EVOLUT) 46 . AI-based surrogate models (e.g., DASI simulations, neural emulators) Recent approaches have focused on constructing surrogate models trained on large datasets of FEA/CFD simulations and real-world outcomes. DASI Simulations 37 , for instance, employs deep learning to predict optimal valve size, implantation depth, and hemodynamic parameters based on preoperative CT inputs. These models can generate results in 2–10 min and present them via accessible desktop or tablet interfaces. Their key advantage lies in speed and ease of use, with minimal user input required. However, they inherit the biases and coverage gaps of their training data. For example, if rare bicuspid morphologies or extreme calcific burden were underrepresented during training, predictions may extrapolate poorly 37 , 38 . Importantly, the clinician cannot directly inspect or adjust internal model logic, and decision rationale remains implicit. Geometrically constrained kinematic simulator (VTAVR: proposed approach) Compared to these methods, VTAVR offers a unique middle-ground solution: it avoids the computational and interpretive burdens of full-physics FEA/CFD pipelines and does not inherit the biases or generalization risks associated with surrogate machine learning models. Its transparent, geometry-driven approach enables simulation of deployment behavior in under a minute using standard imaging inputs and local computing resources. The VTAVR framework’s novel kinematic approach confers several practical advantages over traditional computational methods for simulating TAVR outcomes. Finite Element (FE) and Fluid–Structure Interaction (FSI) models, while capable of detailed stress and flow analysis, require extensive meshing, definition of material properties, and often multi-hour simulation runtimes 37 , 38 . These approaches, though informative, are limited to academic or retrospective applications and remain impractical for routine clinical workflows. In contrast, VTAVR achieves rapid simulation and optimization by modeling device deployment as a constrained geometric process. Its use of symmetric, parameterized primitives (e.g., conical frustums) eliminates the need for complex meshing, enabling faster execution without sacrificing core performance metrics such as device expansion profile, implantation depth, and annular fit 13 , 39 . Unlike FEA systems that often require domain-specific knowledge to interpret results, VTAVR’s visual outputs—collision maps, area-cover indices, and geometric overlays—are immediately comprehensible to interventional cardiologists and imaging specialists, supporting real-time planning in multidisciplinary meetings. Furthermore, VTAVR leverages standard clinical imaging inputs (e.g., gated CT angiography) and is designed to integrate into existing decision-making protocols with minimal additional overhead 6 , 35 . While recent surrogate-model platforms aim to accelerate FE workflows using AI, they still depend on large training databases and may extrapolate poorly when applied to outlier anatomies or complex calcification patterns. This limitation is critical in TAVR populations where patient-specific variation is high and generalization errors can have significant clinical consequences 21 . VTAVR, in contrast, derives its predictions from mathematical and anatomical first principles. It remains robust across tricuspid and bicuspid phenotypes and provides real-time interactivity: the user can iteratively adjust deployment parameters (e.g., device size, orientation, depth) and visualize outcomes immediately. This flexibility facilitates “what-if” scenario testing and increases the clinician’s ability to adapt the intervention plan to each patient’s unique morphology. An additional and distinguishing strength of VTAVR is its ability to detect and localize device–calcium contact sites. By comparing the final deployed geometry against the segmented anatomical model, VTAVR computes the precise parametric coordinates of all regions where the prosthetic frame intersects or impinges on calcific nodules. This offers a unique prognostic tool to anticipate risks of malposition, residual stress, conduction disturbance, or thrombosis—features not readily accessible in black-box surrogates or conventional sizing methods. In summary, VTAVR occupies a clinically pragmatic niche: it is transparent, adaptable, fast enough for real-time use, and interpretable by the end-user. It may be used as a primary planning tool, a complement to existing surrogates, or as a “first-pass” deployment simulator prior to more detailed FE validation. Its integration into routine planning could improve outcomes by promoting evidence-based, anatomy-specific procedural strategies. The VTAVR system offers a new approach to real-time patient-specific transcatheter aortic valve replacement by incorporating a novel kinematic geometry optimization framework. This study demonstrates how VTAVR can reliably simulate and predict the optimal device landing zone, accounting for complex anatomical variability, calcific deposits, and dynamic interactions between the device and the aortic root. By optimizing key deployment parameters such as expansion dimensions and implantation height, VTAVR enhances procedural planning and mitigates risks associated with device misplacement, paravalvular leakage, and conduction disturbances. Our results, validated through retrospective comparisons with post-procedural CT images and post-procedural ECHO findings show that the system can reliably predict key decision-making parameters such as device expansion diameters, implantation height, and orientation with high fidelity. Furthermore, the ability to simulate and adjust the framework decision models (catheter trajectory curve, device settings and optimization parameters) facilitate the interactivity and applicability of the model in a diverse set of clinical scenarios. We demonstrated the potential ability of the framework in predicting and mitigating common TAVR-related complications, such as paravalvular leakage (PVL), left bundle branch block (LBBB), and patient-prosthesis mismatch (PPM). Overall, our results suggest that fast kinematic-geometry simulation techniques offer a practical and highly accurate tool for clinicians in pre-procedural planning. This study presents a first-in-class approach that integrates image processing, computational geometry, and parametric optimization in a clinically relevant workflow, ultimately paving the way for real-time personalized interventions in TAVR. Looking ahead, several developments are planned to broaden VTAVR’s clinical applicability and real-time utility. First, prospective validation studies will be essential. Instead of relying solely on retrospective post-CT comparisons, we aim to test VTAVR predictions in a prospective manner, during actual TAVR cases. This would involve comparing the simulation’s guidance with the intra-procedural results and assessing how well VTAVR can predict and potentially improve outcomes in real time. Early integration of VTAVR into the procedural workflow – for instance, by incorporating intra-procedural imaging feedback from fluoroscopy or transesophageal echocardiography – could enable the simulation to update or refine its predictions during the deployment process. Such an approach would transform VTAVR from an offline planning tool into an interactive, intra-operative decision support system, providing real-time guidance to the heart team. Achieving this will require a user-friendly interface and seamless compatibility with existing clinical imaging and navigation tools. Work is underway to streamline the software for use in the Cath lab environment, leveraging interfaces that can rapidly import imaging data and display VTAVR outputs without disrupting the clinical workflow 5 , 6 , 47 . Another important future direction is coupling the VTAVR platform with comprehensive cardiovascular models, including patient-specific ventricular dynamics. By integrating the left ventricle and possibly the circulatory system into the simulation, we can begin to evaluate the hemodynamic consequences of a given TAVR deployment. For example, coupling VTAVR to a ventricular model would allow assessment of how changes in outflow geometry might affect metrics like cardiac output, pressure gradients, or ventricular strain. This extension moves VTAVR closer to a full digital twin of the patient’s heart, where both the device geometry and the blood flow/ventricular function are simulated together. Early studies in computational TAVR have shown the value of such integrated modeling for predicting post-TAVR valve performance and ventricular load. However, those high-fidelity FEA or fluid–structure interaction approaches often require long computation times and expert oversight 48 – 50 . In contrast, VTAVR’s strength is speed and automation; thus, the challenge for future research will be to incorporate richer physiology (e.g., real-time pressure-flow feedback) while maintaining near-real-time simulation capability. Continued collaboration with cardiovascular modeling efforts (e.g., coupling with lumped-parameter or reduced-order ventricular models) and further validation in larger, more diverse patient cohorts are planned to ensure that VTAVR evolves into a robust predictive tool for a wide range of clinical scenarios. Ultimately, by prospectively validating VTAVR in clinical trials and enhancing it with intra-procedural imaging integration and ventricular coupling, we aim to solidify its role in improving TAVR planning and execution for better patient outcomes. Despite its promising performance and real-time capabilities, the VTAVR framework has inherent limitations arising from its deliberately simplified modeling assumptions—chiefly made to enable sub-minute runtimes and full clinical interactivity. These simplifications distinguish VTAVR from traditional finite element analysis (FEA) and fluid–structure interaction (FSI) models, which offer deeper biomechanical fidelity at the cost of computational complexity and practical clinical deployment. First, the framework currently lacks modeling of tissue deformation or elastic recoil. The aortic root, annulus, and valve leaflets are treated as rigid, non-compliant structures, and the prosthetic device expands kinematically until it geometrically intersects with the anatomy. While this approach suffices for simulating deployment up to initial contact, it does not account for post-contact interactions such as stent recoil, elastic recoil of the annulus, or deformation of leaflet tissue. Therefore, important phenomena like frame under-expansion due to asymmetric calcific resistance, or annular injury from radial overstress, are not explicitly predicted. In clinical cases with severe or eccentric calcification, this may lead to overestimation of deployment uniformity or annular conformity. Second, VTAVR does not incorporate hemodynamic modeling 51 , 52 . The framework does not simulate blood flow, pressure gradients, shear stresses, or vortex shedding through the implanted valve. Consequently, it cannot directly estimate important clinical indices such as residual transvalvular gradients, paravalvular leak risk, or leaflet thrombosis potential. Instead, VTAVR relies on geometric surrogates—such as annular area coverage, radial clearance, and contact maps—as proxies for evaluating procedural quality. While informative, these proxies may not fully capture post-implantation flow behavior, particularly in borderline anatomical configurations. Third, the expansion model assumes radial symmetry of the prosthesis. The device is modeled as an idealized, conical-frustum structure whose expansion is uniform across all cross-sections. In reality, frame distortion, elliptical deformation, or asymmetric crimping can occur due to localized calcium deposits or variations in annular compliance. VTAVR currently cannot replicate such asymmetric deformation patterns, which may affect valve sealing, device durability, or conduction system interaction. Fourth, the framework does not currently simulate post-deployment leaflet dynamics. Leaflet coaptation is modeled in static diastolic closure based on CTA segmentation, but leaflet flutter, cyclic fatigue, or thrombosis-inducing stasis regions are not accounted for. These phenomena require transient simulations with pressure-driven leaflet motion or at least reduced-order dynamical models, which are under investigation for future VTAVR versions. Taken together, these limitations illustrate the essential trade-off VTAVR makes sacrificing high-resolution mechanical and hemodynamic details in favor of real-time interactivity and user transparency. This makes VTAVR well suited as a fast, geometry-informed pre-procedural planning tool, particularly in multidisciplinary settings where time, interpretability, and data governance constraints exist. Nonetheless, its outputs should be interpreted in context. VTAVR provides accurate predictions of device–anatomy geometric fit, contact regions, and relative performance across multiple deployment scenarios within the same patient. However, clinicians should complement its use with clinical judgment and, where needed, high-fidelity FEA or FSI analyses to fully evaluate patient-specific mechanical and hemodynamic risks. To address current limitations, future versions of VTAVR aim to incorporate reduced-order biomechanical models (e.g., ring-wise compliance, frame–annulus force equilibrium, soft body deformation), lumped-parameter fluid dynamics, or hybrid optimization loops that blend the speed of geometric models with selected aspects of tissue and flow behavior. These enhancements will need to preserve the framework’s hallmark efficiency while increasing its predictive depth. VTAVR outputs may also serve as initialization or boundary conditions for full-physics simulations, enabling a two-stage pipeline in which clinicians first screen multiple configurations rapidly and then subject high-risk cases to detailed physical modeling. This hybrid workflow could deliver the best of both worlds: speed, precision, and clinical confidence. Methods In this study, we developed a novel geometric simulation framework to simulate and predict optimal device landing zone deployment configuration using routine high-resolution computed tomography imaging data, employing a novel approach termed Virtual Transcatheter Aortic Valve Replacement (VTAVR). Our methodology integrated advanced image processing techniques to create a detailed geometric model of the aortic valve, adapted for both healthy and pathologically altered structures due to calcific disease (Fig. 1 , Supplementary Fig. 1 , Supplementary Movie 1 ). The VTAVR framework adeptly accommodates the anatomical, morphological, and pathological variability among patients, effectively addressing both normal and pathologically altered structures due to aortic stenosis and bicuspid aortic stenosis. A key feature of the VTAVR framework is its ability to minimize operator sensitivity and the need for specialized knowledge through a semi-automatic image preprocessing workflow and a fully automatic geometric reconstruction pipeline based on previously developed geometric reconstruction 31 and segmentation techniques 13 , 15 . This enhances its utility in a clinical setting by providing precise and reproducible simulations with minimal manual intervention. The framework leverages geometric shape optimization to adapt to imaging uncertainties and limited a priori information, ensuring a consistent and accurate representation of the aortic valve and surrounding structures. The VTAVR framework uses advanced image processing techniques to segment patient-specific anatomical structures, including the aortic root and calcifications, from CT angiograms. The integration of these detailed anatomical models into the simulation environment allows for the precise prediction of device behavior and interactions during deployment. By adjusting parameters such as device geometrical specifications, expansion behavior, catheter trajectory curve, and implantation height, the framework ensures an accurate representation of the device landing zone (Fig. 9 , Supplementary Movie 1 ; Fig. 2 ). Modeling transparency and interactivity are further facilitated by the system’s capacity for interventionists to freely manipulate the simulator settings and fine tune the device route, positioning, and sizing. This allows for dynamic interaction with the simulation process, enabling clinicians to explore the model according to specific clinical requirements or research objectives. Fig. 9. Computational workflow details for the CT-based Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework. Open in a new tab A Shows parametric centerline computation and Frenet-Serret frame definition for guiding device trajectory. B Presents the idealized conical-frustum device geometry with statistical sizing models. C Explains the optimization scheme adjusting position, orientation, and expansion radius under procedural constraints, including contact detection with patient anatomy. The framework was assessed on a retrospective data acquisition from high-resolution Cardiac Computed Tomography Angiography (CCTA) ( N = 40). The pipeline consists of an image pre-processing workflow to segment the patient-specific aortic root and calcification, delineate anatomical landmarks, and reconstruct the geometry optimized for the simulation procedure (Fig. 9 ). The developed framework is based on ITK 5.3 (ref. 53 ), VTK 9.1.0 (ref. 54 ) and ParaView 5.10 (ref. 55 ). Subsequently, with we developed a novel fully automatic kinematic geometry simulation framework that models the catheter trajectory curve, the device landing environment and an idealized device model (Fig. 9 ). The simulator can represent the position, pose and spatial bounds of the device and allows for an efficient and reproducible digital environment to mimic the actual procedural environment and interventional parameters. Finally, a mathematical optimization scheme is incorporated that represents interventional and patient-specific anatomical and procedural characteristics as initial conditions, decision variable ranges as well as constraints and penalties. Aimed to find an optimal device landing zone configuration based on established clinical endpoints for procedural outcomes (Figs. 1 , 9 ). Following is the description of the methods employed in the development of the VTAVR framework detailed and visualized across Figs. 1 to 9 , Supplementary Movies 1 – 4 . Details on dataset attributes, simulation parameters and summary data analysis comparing simulated versus actual interventional outcomes is documented across Tables 1 – 3 . Framework flowchart diagram is presented in Supplemental Fig. 2 . Table 3. Summarized statistics for clinical CT device landing zone measured settings and functional clinical parameters for the retrospective TAVR cohort ( N = 40) Clinical Evaluation Parameter Female Male Tricuspid Bicuspid Total Pre TAVR-CT Annular Area (mm 2 ) 430 [386–490] 504 [485–595] 479 [402–515] 499 [431–549] 491 [420–527] Pre TAVR-CT Valve Height (mm) 13.3 [12.7–14.5] 15.2 [14.0–17.4] 14.3 [13.0–15.7] 14.1 [12.8–16.1] 14.3 [12.8–16.0] Pre TAVR-CT Calcification Score (Agatston Units) 2194 [2560–3271] 3384 [2560–4284] 2557 [2263–3503] 3229 [2724–3799] 2890 [2431–3576] Post TAVR-CT Device Diameter - Outflow (mm) 22.3 [21.7–25.2] 25.6 [23.9–27.9] 23.6 [22.0–25.8] 25.0 [22.2–25.9] 24.4 [22.0–25.9] Post TAVR-CT Device Diameter - Midflow (mm) 22.7 [22.1–25.1] 25.5 [23.3–27.8] 24.4 [22.3–25.9] 25.0 [22.7–26.7] 24.4 [22.5–26.0] Post TAVR-CT Device Diameter - Inflow (mm) 23.4 [22.7–25.4] 25.8 [23.2–28.5] 24.8 [22.7–26.0] 25.1 [23.2–28.0] 24.9 [22.9–26.7] Post TAVR-CT Device Area Cover Index (%) 101.3 [92.6–105.8] 101.6 [91.9–104.4] 101.6 [93.0–104.8] 98.4 [92.3–105.9] 101.4 [91.9–105.3] Post TAVR-CT Device Implantation Height (mm) 8.1 [6.8–10.2] 8.1 [7.4–10.5] 7.7 [6.9–10.2] 9.1 [7.1–10.3] 8.1 [6.9–10.4] Post TAVR-CT Device Annular Orientation Deviation (%) 0.997 [0.996–0.999] 0.999 [0.997–1.0] 0.997 [0.995–0.999] 0.999 [0.997–1.0] 0.998 [0.996–1.0] Post TAVR ECHO Aortic Valve Area (cm 2 ) 1.79 [1.4–2.17] 1.79 [1.58–2.0] 1.79 [1.38–2.0] 1.84 [1.7–2.2] 1.79 [1.5–2.1] Post TAVR ECHO Mean Gradient (mmHg) 11 [7.5–13] 8 [6–13] 10.5 [6.3–13.8] 10.0 [6.3–11.0] 10.0 [6.0–13.0] Post TAVR ECHO Doppler Velocity Index (%) 0.56 [0.51–0.65] 0.52 [0.46–0.63] 0.52 [0.49–0.62] 0.58 [0.55–0.65] 0.55 [0.49–0.64] Open in a new tab The table presents parameter values as median[25 th –75 th percentile] comparing independently measured clinical shape (geometric) measurements, structural (calcification) calcification indices of the aortic valve complex and echocardiographic indices measured post TAVR. The data is grouped by valve morphology (tricuspid vs. bicuspid) and, patient sex (Female vs Male). Data acquisition This retrospective study reviewed clinical and CT data of patients who underwent TAVR with a balloon-expandable Sapien 3 transcatheter heart valve (THV) (Edwards Lifesciences, Irvine, California). Data was acquired from three medical centers affiliated with McMaster University (Hamilton General Hospital; McMaster Children Hospital and St. Joseph’s Hospital; Hamilton Ontario, Canada, N = 40 between 2020–2022). Patients included in the analysis were required to have undergone gated contrast CT and 2D Doppler echocardiography assessment before and after intervention. After a review of 251 patients evaluated for TAVR, 40 patients with complete pre-post follow-up data were included in the study (Bicuspid: 45%; Tricuspid: 55%), sex (Male: 52.5%; Female: 47.5%). Patients with self-expandable devices, those treated for surgical aortic bio prosthesis degeneration (i.e., valve‐in‐valve) and those with unsuccessful devices as per VARC‐3 (Valve Academic Research Consortium 3) criteria were excluded 56 . No patients were excluded based on image quality. The procedural access route, THV type and sizing was determined by the local heart teams on basis of annular area and qualitative calcification grade as per recommended SCCT guidelines 6 . Waiver of informed consent and data transfer was approved by the institutional review board (HiREB). Data collection and clinical measurements were performed by operators blinded to the objectives and contents of this study. Standard measurements were performed per relevant guidelines and regulations including guidelines of the American College of Cardiology and American Heart Association. Demographic and peri-procedural notes were collected from the patients’ medical records (see Table 1 for patient characteristics). The development and validation of the VTAVR framework was conducted in a blinded fashion with respect to the patient data. An initial prototype was created and refined using a single patient case (Fig. 2 ). After this development phase, the finalized VTAVR pipeline was applied to the 40-patient retrospective cohort as an unseen test set, running in fully automated batch mode with no manual parameter tuning for individual cases. All optimization parameters remained fixed prior to processing the cohort, ensuring that performance metrics reflect true predictive capability rather than case-specific adjustments. Aorta segmentation and calcification detection (FPR) The initial step in the VTAVR simulation involves the application of advanced image segmentation techniques on high-resolution computed tomography angiograms (CTA). These techniques delineate the aortic root and valve leaflets, crucial for identifying and quantifying associated calcifications (Fig. 1A ). The segmentation process, which is foundational for creating a detailed anatomical framework for further analysis and simulation by the VTAVR system, employs algorithms designed to identify calcific deposits based on their intensity and distribution based on the previously developed (FPR) method 13 , 15 . This method provides a refined assessment of calcific deposits, leveraging contrast-enhanced CT’s superior spatial and contrast resolution to offer better descriptors of calcific lesions on the leaflets 13 , 15 . Together, these processes form an integral part of the VTAVR simulation, ensuring that the virtual modeling and subsequent device deployment simulations are based on an accurate and detailed image segmentation which includes both the aortic lumen and calcification in the region of interest. Aortic root geometric reconstruction (MVGIPR) Following the segmentation of the aortic root, valve leaflets, and calcifications (Fig. 1A ), the previously developed Minimal Variation Geometry Invariant Parametric Reconstruction (MVGIPR) method is employed 31 . This method leverages sophisticated image processing pipelines and automatic computer-aided design algorithms to reconstruct the intricate geometry of the aortic valve (Fig. 1B ). MVGIPR ensures that the model retains anatomical accuracy by minimizing geometric variations, closely adhering to the patient’s actual physiological structure, which is crucial for successful simulation and intervention planning. The MVGIPR framework is designed to adapt to the anatomical, morphological, and pathological variability among patients, which is particularly important for conditions like aortic stenosis (AS) and bicuspid aortic stenosis (BAS). This process involves generating edge and face networks using B-Spline curve and surface approximation algorithms, ensuring high fidelity to anatomical features. The framework incorporates shape optimization techniques to handle variations in aortic geometry due to natural or pathological conditions, enhancing robustness against poor signal-to-noise ratios. This step adjusts fundamental geometric quantities like curvature and torsion to optimize the anatomical representation. MVGIPR’s patient-specific parametric model offers fast and automatic geometric reconstruction while maintaining clinical interpretability using standardized anatomical landmarks (Fig. 9 ). To validate robustness, MVGIPR was tested on phantom spherical nodule CT datasets. To validate robustness, MVGIPR was tested on phantom spherical nodule CT datasets with varied slice thickness (up to 3 mm) with landmark input perturbations simulating inter-observer segmentation variability. In these sensitivity studies, reconstructed surfaces deviated by <0.05 mm (mean) from high-resolution references, and key annular landmark annotation exhibited intraclass correlation coefficients of 0.90–0.97 with minimal effect on surface reconstruction. Furthermore, comparison against clinical segmentations and ex vivo micro-CT scans of the aortic valve yielded sub-millimeter mean errors ( ~ 0.1–0.2 mm) and phantom tests (spherical nodules) achieved 0.003 ± 0.04 mm accuracy, underscoring MVGIPR’s noise-resilience and fidelity. MVGIPR’s parametric representation not only enhances stability but also reduces mesh complexity relative to raw voxel-based models, striking an optimal balance between detail and computational efficiency—a necessary requirement for rapid clinical application of VTAVR kinematic simulations. Once the clean surface model of the aortic root is extracted, a parametric space of the patient-specific aortic root surface is generated as follows: The parametric geometry representation allows traversal of the geometric domain in a manner that is invariant to natural, pathological, or congenital variations in anatomy, making it ideal for integration with kinematic based device simulator. Once the surface model that covers the entire aortic root is extracted a parametric space of the patient-specific aortic root surface is generated: S ( u , v ) ;u ∈ U : [ 0 , 1 ] ;v ∈ V : [ 0 , 1 ] 1 where U defines a circumferential periodic boundary encircling the aortic annulus and V defines an open longitudinal boundary starting from the ascending aorta towards the left ventricle outflow tract (Fig. 9 ). Virtual transcatheter aortic valve replacement system (VTAVR) The VTAVR module integrates advanced computational models and simulation frameworks to support the planning and execution of aortic valve replacements. The system leverages parametric modeling and virtual simulation techniques to predict and optimize device deployment within the complex geometry of the aortic root. Below are the core components of the VTAVR system as described in the provided Fig. 9 . Aortic root minimal variation center line (Catheter trajectory curve) The VTAVR system calculates the minimal variation center line of the aortic root using the reconstructed parametric surface model (Section “Device landing zone implantation height”). This center line is crucial for determining the optimal path for device deployment, taking into account the unique twists and turns of the patient’s aortic anatomy (Fig. 9 , Supplementary Movie 1 ). The idealized device model is adapted based on the parametric dimensions of the aortic root, ensuring a tailored fit and minimizing adaptation errors during deployment. In the VTAVR system, the centerline of the aortic root is defined within a parametric space of the patient-specific aortic root surface (See Section “Device landing zone implantation height”, Eq. 1 ). The centerline curve, C(s), is determined by first averaging points circumferentially at intervals along the longitudinal dimension V, resulting in data points p j . These are mathematically represented as: p j = 1 n j ∑ i = 1 n j C i u , v j 2 n j here is the number of circumferential samples (across the circumferential boundary U) at each longitudinal position v j . The centerline is then approximated using a B-spline curve that minimizes the distance to these data points, subject to a tolerance that simulates the flexibility of the TAVR guide wire. The curve is given by: C s = ∑ j = 0 m N j , k v ⋅ p j 3 where are the B-spline basis functions of degree and the optimization criterion is? min ∑ j = 0 m ∣ C v j − p j ∣ 2 4 This optimization criterion minimizes the sum of squared distances between the B-spline curve and the data points at parameter values p j . This parametric setup is critical for accurately modeling the complex anatomy of the aortic root. The minimal variation center line, calculated through interpolating sets of periodic circumferential curves along the V direction, closely aligns with the line of symmetry within the aortic root. This center line is vital not only for determining the optimal path for device deployment but also for simulating the behavior of the transcatheter aortic valve replacement (TAVR) guide metallic wire. This simulation is crucial as it incorporates the flexibility and responsiveness of the interventional guide wire into the VTAVR system, allowing the center line’s sensitivity and degree of freedom to be calibrated to match that of the actual guide wire used during interventions. Such calibration ensures that the center line can realistically mimic the guide wire’s behavior within the patient-specific aortic anatomy, enhancing the procedural planning and execution. Virtual intervention simulator Device geometry To mathematically model the idealized device for balloon-expandable devices in the VTAVR system, we utilize the geometric concept of conical frustums 18 . These are particularly relevant due to their ability to effectively represent the shape and spatial bounds of balloon-expandable stents. The model consists of two connected conical frustums: a top frustum and a bottom frustum (Fig. 9 ). Each frustum can be individually described and adjusted based on specific requirements related to the device’s deployment and expansion dynamics. A conical frustum is a portion of a cone that remains after its top is cut off with a plane parallel to its base. For each frustum (top and bottom), the parameters are the radii in each section (rT, rM, rB) and the height (h) (Fig. 5 ). The three radii play crucial roles in modeling the dynamics of the device’s expansion. The device’s initial configuration can be precisely set by prescribing the values of the crimped TAVR device (r and h). During the expansion process, the changes in the radii, particularly allow for simulation of the stent’s behavior as it adapts symmetric balloon expansion pressure. The ability to vary the three radii further enhances this model by providing a realistic depiction of how the stent can expand or contract at different points, influenced by both internal balloon pressure and external anatomical constraints. By modeling the balloon-expandable device as two connected conical frustums, the VTAVR system can simulate both the initial deployment configuration and the subsequent expansion dynamics with high precision. This dual capability of setting initial geometrical parameters and dynamically adjusting them allows for an in-depth exploration of various deployment scenarios, enhancing procedural planning and potential outcomes for TAVR procedures. CFP ( rT , rM , rB , h ) = rT rM rB h 5 To further refine the device landing zone model, we built a statistical linear regression model based on ex-vivo experiments of device expansion behavior 40 . This regression model explicitly includes nominal expansion dynamics as well as under- and over-expansion scenarios. In other words, the nominal (normal) expansion behavior of the device—used as the default simulation scenario—is derived directly from experimentally measured nominal expansion dimensions and corresponding foreshortening behavior. The regression relationships established from ex vivo experiments allow the VTAVR framework to accurately predict how each radius (inflow, midflow, and outflow) and device height evolve through the entire spectrum from under- to nominal to over-expansion conditions, consistent with expert recommendations on device sizing and deployment dynamics 39 . The ex-vivo study demonstrated that the Sapien 3 valves could be incrementally overexpanded beyond their nominal dimensions, providing critical data on the physical limits and performance characteristics of the valve under varying expansion scenarios. These findings informed the regression model, enabling it to predict device behavior accurately under different procedural conditions. The OLS regression model incorporates key parameters such as the midvalve diameters achieved through overexpansion and the corresponding changes in device height (Fig. 9 – Table showing the spatial extents of the device model in different settings). This statistical approach allows the VTAVR framework to simulate a wide range of deployment scenarios, including those involving overexpansion and under expansion, thereby providing clinicians with comprehensive planning tools that account for the dynamic nature of device deployment. Although our current validation and analysis specifically address balloon-expandable devices, the VTAVR framework is designed for adaptability to other TAVR device types. By simply modifying the initial conical frustum dimensions and adjusting the expansion rates and dynamics parameters, the same geometric modeling approach can accommodate self-expanding valve designs. For instance, simulating self-expanding devices could involve specifying distinct initial radii and expansion characteristics consistent with the mechanical and material properties of these devices. This inherent flexibility enhances VTAVR’s broader clinical applicability and positions it effectively for future validation across a wider range of transcatheter heart valve technologies. Device kinematics Employing the principles of differential geometry, the VTAVR system uses the Frenet-Serret apparatus to compute the trajectory for the aortic valve replacement device. This involves defining a set of frames along the center line that describe the natural curvature and torsion of the aortic passage. These frames are critical for planning the device’s navigational path and ensuring that the trajectory adheres to the safest and most effective route through the aortic anatomy (Fig. 9 , Supplementary Movie 1 ). To define the device trajectory using the Frenet-Serret apparatus in the Virtual Intervention Simulator section of the VTAVR system, we’ll utilize the parametric centerline curve C(s), calculated previously. The Frenet-Serret formulas provide a method to calculate an orthonormal frame at each point on this curve, which is crucial for defining the trajectory and orientation of the device during deployment. Let C(s) be a smooth, regular parametric curve representing the centerline of the aortic root, where v is the parameter along the curve. C(v) should be sufficiently smooth such that its first and second derivatives exist and are continuous. An orthonormal frame is defined along the parameter of the curve as the tangent, normal and binormal vectors, respectively, as follows: T s = C ′ s | C ′ s | ;N s = C ′ ′ s | C ′ ′ s | ;B s = T s × N s 6 Where the tangent vector T s at each point in the curve is defined as the normalized derivative of C(s). The normal vector N s derived as the derivative of the tangent vector and points in the direction of the curve’s principal normal. The binormal vector is the cross product of the tangent and normal vectors, respectively, completing the right-handed coordinate system. Using the Frenet-Serret frame (T, N, B) at each interval along the parametric curve C(s), the pose of the TAVR device during motion is uniquely determined (see Fig. 2 ). This local coordinate system (T, N, B) provides the axes for aligning the device correctly with respect to the aortic root’s geometry. The parametric centerline curve C(s) describes the spatial path of the centerline through the aortic root, with s parameterizing the curve from the ascending aorta towards the left ventricle. Each point on C(s) is can be represented in real coordinates as (x, y, z) coordinates in 3D space which allows for precise spatial positioning of the device at any given point along the trajectory defined by the parametric curve. To fully integrate the idealized device model parameters into the virtual device simulator of the VTAVR system, we can express the complete kinematics of the device deployment using a matrix representation. This augmented 4×4 matrix will incorporate the device’s position, and pose aligning with the local Frenet-Serret frame derived from the catheter trajectory curve C(s). M C ( i ) = T 1 N 1 B 1 C ( i ) 1 T 2 N 2 B 2 C ( i ) 2 T 3 N 3 B 3 C ( i ) 3 0 0 0 1 7 This transformation matrix M , combined with the external geometric parameters of height and radii, fully describes the kinematics of device deployment within the context of the device landing zone. Within the VTAVR system, this transformation matrix is crucial for simulating the deployment kinematics of the balloon-expandable device, offering a clear and effective way to visualize and manage the device’s interaction with the aortic root’s morphology during the procedure (Fig. 9 , Supplementary Movie 1 ). Device landing zone optimization Using the digital representations of the patient-specific environment (Sections “VTAVR device landing zone configuration”, “Device landing zone expansion diameters”, and “Device landing zone implantation height”) and the computational simulation definitions (Section. “Aortic root minimal variation center line (Catheter trajectory curve)”) we proceed in describing the optimization scheme for the deployment of the idealized device within the anatomically specific aortic root environment (Fig. 2 ). This process leverages both the detailed geometric data and the dynamic capabilities of the simulator to ensure precise placement and maximum efficacy of the device. The following details the components of the optimization algorithm: Input parameters Parametric Surface Domain: This is the geometric model of the aortic root (See Section“VTAVR device landing zone configuration”; Eq. 1 ; Fig. 1B ), which provides the anatomical boundaries and features relevant for device deployment. Catheter Trajectory Curve: Defined by the Frenet-Serret apparatus as described previously (See Section. “Aortic root minimal variation center line (Catheter trajectory curve)” ; Eq. 3 ; Fig. 9 ), which describes the path along which the device will travel during deployment. Idealized Device Model: Utilizes two conical frustums with adjustable radii (top, middle, bottom) and a single height parameter, providing a model that is representative of the physical stent deployed in TAVR procedures (See Section. “Virtual intervention simulator: Device geometry” ; Eq. 5 ; Fig. 9 ). Patient-specific virtual intervention simulation configuration The device is positioned along the wire trajectory between two critical anatomical planes: the Sinotubular junction (start of the valve complex) and the annulus plane (end of the valve complex/start of LVOT) (Fig. 1C ). The spatial coordinates of these planes are encoded and automatically determined via point projections of landmark points onto the catheter trajectory curve. Position and pose transformations are applied to the device based on traversing the 1D parametric space of the catheter trajectory curve (See Equation 3 ) and following the natural orthonormal Frenet-Serret frame at each interval of the curve. Once the device is moved to the optimal deployment site between the specified anatomical planes. Adjustments to the affine transformation matrix (See Equation 7 ) and external geometric parameterization of the idealized device model (See Equation 5 ) allow for simulating the device landing zone deployment kinematics. The transformation matrix is applied to the device model to position and orient the device according to the local frame of the catheter trajectory curve. The mathematical representation of this process can be given by: D L Z = M C ( i ) ⋅ C F P ( r T , r M , r B , h ) 8 Here, DLZ represents the current device landing zone configuration, which includes the current position, pose, and dimensions of the device (the top, middle, bottom radii, and height are outputs of the Sapien 3 parametric model based on ex-vivo studies 39 , 40 ) controlled only by the expansion radius across the middle plane of the device. Patient-specific virtual intervention simulation configuration Additional components are required for allowing the simulator to interact with the external environment (i.e., the patient specific surface domain) for tailoring the simulation to the individual’s anatomical and pathological conditions, ensuring precision and efficacy in the deployment of the transcatheter aortic valve replacement device. A dynamic slicing mechanism follows the device trajectory along the catheter path, defined by the Frenet-Serret apparatus {T, N, B} of the catheter trajectory curve C(s) (Section. “Aortic root minimal variation center line (Catheter trajectory curve)”; Fig. 9 ; Fig. 2 ). At each point along this trajectory, a slice plane Π i is defined, which moves with the trajectory and is perpendicular to the tangent vector T (See Eq. 6 ) at that point: Π i : T ⋅ X − P i = 0 9 where X is a point on the plane, and P i is the corresponding point on the curve C(s). Following this description of the slicing mechanism. We proceed to describe the environment interaction components between the device and geometric domain (patient anatomy) as follows: Multiplanar Area Cover Index Calculator: This component of the optimizer system calculates a scalar variable representing the percentage of area covered by the idealized device at various planes of intersection with the patient’s aortic root. These intersection planes are slices of the parametric surface domain. The area calculations are performed using fast Delaunay 2D triangulation, which efficiently handles complex geometric shapes and topologies, providing a precise measure of coverage that is crucial for assessing the suitability and effectiveness of the device fit within the aortic root. This component calculates the area of the device that covers the aortic root at various slices along the trajectory: A slice , i = Sum of areas of Delaunay triangles 10 AC I i , j = π r j 2 A slice , i × 100 % 11 Here j indexes the device sections (top, middle, bottom) Fig. 9 , and i indexes the intervals along the trajectory. Multi-planar Collision Detector: The collision detector is a key feature that ensures the device’s deployment does not adversely interact with the surrounding anatomical structures. It detects collisions between the device frame model and the patient-specific surface domain using a fast polygon intersection method. This detector not only identifies the points of collision but also extracts these points in both real coordinates (x, y, z) and parametric coordinates (u, v), offering detailed insights into the spatial relationships and potential interference points during device deployment. This detector identifies points of intersection between the device and the aortic surface within the slicing plane, indicating potential collision points: Collision Points i = Intersect ( P device , i , S u , v ∩ Π i ) 12 A non-empty set of signals the presence of a collision at interval i of the local frame of device motion (Fig. 2 ). Calcification Site Detector: An integral part of the simulation involves mapping calcification within the aortic root, which can significantly impact the procedure’s outcome. The parametric surface model incorporates projection sites for calcifications, plotted onto the 3D embedded 2D parametric surface at specific (u, v) coordinates where calcification is present. This mapping is particularly important for adjusting the device expansion’s sensitivity based on proximity to potential sites of calcification in critical areas such as the left ventricular outflow tract (LVOT), commissures, or the Sinotubular junction. By considering these calcification sites, the simulator can optimize device placement and expansion to minimize risks and improve procedural success. This map plots the calcification points detected within the 3D aortic root onto the 2D parametric surface at specific (u, v) coordinates: Calcification Points i = Project Calcification 3 D ∩ Π i , S u , v 13 This projection aids in evaluating the sensitivity of the device expansion to areas with high calcification density. DL Z Interaction = DL Z ACI , DL Z Collision , DL Z Calcification 13 Where DL Z ACI represents the set of area cover indices. DL Z Collision encodes information on the collision points detected. DL Z Calcification encodes information on the calcification projection regions (Fig. 2 ). This patient-specific environment interaction framework allows for dynamic assessment and adjustment of the device deployment strategy, while considering the complex geometrical and pathological features of the patient-specific aortic root. This capability enhances the safety and efficacy of the TAVR procedure, ensuring optimal outcomes tailored to individual patient anatomy. Mathematical optimization scheme Optimization Algorithm: The Nelder-Mead simplex method, a popular direct search method used for multidimensional unconstrained optimization, is employed. This method does not require derivatives and is well-suited for non-linear optimization problems. Decision Variables: Include the device’s position offsets from the initial position defined in (Eq. 7 ) in TNB coordinates and the mid-flow expansion diameter of the idealized device model to simulate the expanded device extents (Eq. 5 ). Objective Function: The goal is to maximize the area cover index of the device symmetry plane (Eq. 11 ), which represents the percentage of the aortic root’s surface area that is covered by the expanded frame of the device at the intersection plane with the patient-specific annulus plane which represents the geometric interface between the left ventricle blood inflow and the aorta outflow. Maximize : ACI i , At the annulus plane 14 This scalar parameter determines how well a specific device perimeter as well as expansion volume fits within the aortic annulus to facilitate regular valve hemodynamics after the intervention. Constraints and Penalties: Additional operational constraints are imposed to prevent the device from positioning in anatomically hazardous locations (like high calcification areas, atrioventricular wall), and penalties are applied for non-optimal deployment such as low or high implantation depth, which can lead to sealing issues or aortic damage. Integrating the patient-specific environment models (See Section “Virtual intervention simulator: Device Geometry”) into the optimization framework for device landing zone optimization enhances the process by incorporating dynamic, real-time feedback on device placement, expansion, and interaction with the anatomical structure. This will refine the decision variables and constraints to ensure that the device deployment is both efficient, safe and physiologically plausible. The list of constraints and penalties are herein defined as follows: Implantation height bounds: The device must be positioned within the anatomical boundaries defined by the Sinotubular junction and the annulus plane. Expansion Bounds: Device expansion should not exceed the constraints imposed by the patient-specific dimensions of the aortic root. Orientation Bounds: Device expansion should not deviate from the annular orientation in pre intervention diastolic phase by more than 10%. The optimization algorithm was applied to a cohort of patients with tricuspid and bicuspid aortic stenosis undergoing the TAVR procedure with the Edwards SAPIEN 3 balloon-expandable device. The constraints for optimization were designed based on recommended TAVR guidelines and expert consensus, allowing for a −10% to +10% range for under or overexpansion, 20% intrusion of the device beyond the annulus plane, and a maximum deviation from the annular normal orientation by 10%. These boundary conditions were implemented to faithfully reproduce typical TAVR procedural guidelines. The optimization was performed twice for each patient: once without collision detection and once with collision detection. The final expansion diameter was averaged from both optimized expansion diameters to account for the relative error in modeling structures as zero-thickness surface meshes, considering that the aortic tissue and the device stent have thickness. The final expansion diameter was taken as the average of the optimized expansion diameters from both the collision detection on and off runs to address several factors inherent in the modeling and simulation process. The limits of CT resolution can affect geometric fidelity, leading to uncertainties in defining precise anatomical boundaries. Given these uncertainties, using collision detection based on polygonal intersection can be overly conservative. This conservatism arises because the method might restrict device sizing excessively to avoid any potential collisions, possibly underestimating the device’s actual safe expansion capacity. Conversely, optimizing without collision detection, while focusing solely on maximizing the area cover ratio (ACI), may be under conservative. This approach might lead to recommendations for larger device expansions that do not adequately account for the risk of contact with critical anatomical structures, such as calcified areas or the atrioventricular wall. By averaging the results from both optimization runs, we balance these two approaches. This averaging accounts for the geometric uncertainties and potential conservatism of collision detection while also ensuring that the area cover ratio is optimized without risking excessive expansion. This method provides a more robust and reliable estimate of the optimal expansion diameter, enhancing the overall safety and efficacy of the TAVR procedure. In essence, this dual optimization and averaging strategy helps mitigate the limitations of each individual approach, providing a more comprehensive and balanced solution that takes into consideration both the geometric uncertainties and the practical constraints of device deployment. This ensures that the VTAVR framework offers realistic and safe recommendations for device sizing and positioning, ultimately improving patient outcomes. Calcific displacement module An integral part of the VTAVR method is mapping aortic calcifications onto the reconstructed geometry, even though calcifications in our model do not physically impede the stent’s expansion (which matches previously measured conditions 4 . This mapping is particularly important for comprehensive risk assessment and device optimization. By projecting patient-specific calcific deposits onto the aortic root surface, VTAVR can identify where the expanding device would contact or come in close proximity to bulky calcium, especially in critical regions such as the left ventricular outflow tract (LVOT), commissures, or the Sinotubular junction. Incorporating this information allows the simulator to flag high-risk interaction sites and adjust the interpreted deployment “safety margins”. In other words, even if the overall final diameters of the device are not significantly altered by calcium in the purely geometric model, the calcification map highlights areas prone to complications. This is crucial for anticipating issues like incomplete stent apposition, calcific embolization, or paravalvular leak that might arise due to heavy calcification. Thus, including calcification mapping in the simulation enhances its clinical relevance by ensuring that calcified anatomy is accounted for in deployment planning, helping clinicians mitigate potential calcium-related complications. Once the final configuration of the device is reached via the optimization scheme, the VTAVR framework proceeds to simulate the displacement of calcific deposits. This process involves the following steps: Contact simulation with parametric leaflets The simulation is repeated with the parametric leaflets coapted against the crimped device. This step models the interaction between the leaflets and the device during the expansion process. The coaptation of the leaflets against the crimped device allows for a more accurate representation of the leaflet dynamics as they are displaced by the expanding stent. As part of our modeling approach, the coapted (closed) geometry of the aortic valve leaflets was derived directly from patient imaging data rather than through a dynamic simulation. Specifically, we utilized late-diastolic phase cardiac CT images (when the aortic valve is fully closed) to reconstruct the leaflets in their coapted configuration. This strategy obviates the need for an explicit simulation of diastolic leaflet closure and loading, simplifying the workflow while preserving anatomical realism. Using the MVGIPR pipeline (Fig. 1B ) for surface reconstruction, we obtained a high-fidelity parametric model of the closed leaflets that closely matches the true anatomy (demonstrating sub-millimeter surface accuracy in validation). Importantly, this image-based reconstruction is robust to valve morphology variations, enabling accurate representation of both tricuspid and bicuspid valve leaflets in the sealed state. By initializing the simulation with anatomically realistic coapted leaflets, the framework ensures that subsequent device–leaflet interactions (during expansion and calcific displacement) start from a physiologically appropriate geometry, without incurring the computational expense of simulating the entire diastolic loading process. Projection map of calcification A projection map of calcification in the late diastolic phase (valve closure) is taken. This map captures the spatial distribution and density of calcific deposits on the leaflets when the valve is closed. This phase is critical because it represents the maximal overlap and contact between the leaflets and the device, providing a comprehensive view of the calcific landscape. Contact algorithm A contact algorithm is employed to reproduce how the leaflet belly curve will bend following device expansion. This algorithm models the mechanical interaction between the expanding device and the leaflets, predicting how the leaflets will deform and adapt to the new geometry imposed by the device. The contact points and the resulting bending curves are calculated iteratively as the device expands. Reconstruction of leaflet surfaces At each step of the device expansion, the leaflet surfaces are reconstructed with the original projection map when the leaflets were closed. This reconstruction ensures that the calcific deposits are accurately mapped onto the deformed leaflet surfaces, preserving their original spatial distribution and density. The iterative reconstruction process allows for the dynamic visualization of calcific displacement as the device expands. Visualization and analysis The final step involves generating detailed visualizations of the calcific displacement. These visualizations include maps showing the new positions of calcific deposits on the leaflets and the extent of displacement caused by the device expansion. By comparing these maps with the initial projection map, clinicians can assess the impact of the device on calcific displacement and potential areas of concern for post-procedural complications. This methodology provides a comprehensive and dynamic model of calcific displacement, offering valuable insights into how calcific deposits interact with the expanding device. By accurately simulating these interactions, the VTAVR framework enhances the understanding of the mechanical behavior of calcified leaflets during TAVR procedures, potentially improving procedural planning and patient outcomes. Evaluation and analysis of the VTAVR framework To evaluate the accuracy and effectiveness of the VTAVR framework, we conducted both qualitative and quantitative comparisons with post-TAVR intervention CT data as well as CT and echocardiographic clinical parameters. This comprehensive evaluation aimed to validate the framework’s ability to predict key dimensions and configurations of the device landing zone, its ability to predict calcification patterns after device deployment and relation to function echocardiographic indices after the procedure. Appropriate statistical tests were performed using Jamovi v.1.8. Summaries of the variables and tests performed in (Figs. 5 – 8 , Tables 2 and 3 ) are outlined as follows. Correlations and comparisons between the variables were performed using Spearman’s rank correlation test. Values were reported as median [25th-75th percentile], mean ± standard deviation where applicable. In evaluating the VTAVR model’s accuracy, we prioritized clinically relevant scalar metrics rather than a global surface-to-surface overlap error. Notably, a direct L2-norm surface error between the simulated deployment geometry and the post-TAVR CT anatomy was not calculated, due to frame mismatches and alignment challenges between the simulation output and imaging data. The optimal deployment state produced by the simulation does not correspond to a specific instantaneous CT phase, making point-by-point geometric comparison unreliable. Instead, our validation focuses on key quantitative parameters with established clinical significance. For example, we compared the VTAVR-predicted and actual post-procedure values for device expansion diameters at the outflow, midflow, and inflow levels, the implantation depth within the annulus, the device’s rotational orientation, and the annular area cover index—each of these metrics directly relates to valve seating, sealing, and performance (e.g., adequate expansion helps prevent paravalvular leak, proper depth minimizes conduction disturbance risk). We also examined correlations between the simulation outputs and echocardiographic indicators of valve function (such as transvalvular pressure gradients and effective orifice area) to ensure the virtual deployment reflects real-world hemodynamic outcomes. Since the simulation is performed using the patient’s pre-operative CT scan, placing the results in that initial coordinate system. The validation data, however, comes from a separate post-operative CT scan. Due to minor changes in patient positioning between scans, there are slight rotational and translational differences between the two datasets. Therefore, a robust alignment step is required before calculating direct surface-to-surface error measure between simulated and in-vivo detected device frame. This co-registration eliminates the positional discrepancies, ensuring that the L2 norm measures only the true geometric error of the simulation itself, not artificial error caused by the misalignment of the two scans. This analysis is necessary because simpler validation metrics, such as diameters or area coverage, do not capture the full three-dimensional complexity of the device’s final shape. The L2 surface norm provides a comprehensive, point-by-point quantification of geometric error across the entire device. This offers a more robust and objective assessment of the simulation’s spatial accuracy. Device landing zone configuration The qualitative comparison involved visual inspections of the device landing zone configuration as predicted by the VTAVR framework against the actual configurations observed in post-TAVR CT scans (see Fig. 2 ). Key dimensions that fully describe the device landing zone, such as expansion diameters at various levels (outflow, midflow, inflow), implantation height, and rotational orientation, were evaluated. Figure 2 left panel shows the VTAVR predicted configuration, while Fig. 2 right panel presents the corresponding post-TAVR CT configuration. These comparisons highlighted the framework’s precision in simulating the geometrical attributes of the deployed device. We also qualitatively compared the calcification patterns predicted by the VTAVR framework with those observed in post-TAVR CT scans (see Fig. 2 ). The framework’s ability to simulate the displacement and interaction of calcific deposits during device deployment was assessed. Figures 3 and 4 illustrate the VTAVR-predicted calcification distribution in representative patient samples, showing detailed maps of calcific deposits and their displacement. These were compared to post-TAVR CT images to evaluate the accuracy of the framework’s predictions. Quantitative analysis (Figs. 4 , 6 ) focused on comparing the VTAVR-predicted key dimensions of the device landing zone with the actual measurements from post-TAVR CT scans or echocardiographic functional parameters measured after the procedure was performed. These dimensions included: Clinical post TAVR CT Expansion diameters The final expanded diameters at the outflow, midflow, and inflow levels. Implantation height The vertical distance from the device origin (at the midflow plane) to the aortic annulus. Deviation from annular orientation The angular deviation of the device relative to the native annulus plane calculated as the dot product of the normal vector pointing towards the en-face view of the valve and the normal vector of the device at the midflow plane. Area cover index The percentage of the annular area covered by the deployed device. These measurements were compared to assess the framework’s predictive accuracy. Clinical post TAVR ECHO The clinical evaluation of post-TAVR outcomes involves several key echocardiographic measurements that are crucial for assessing the success of the procedure. Aortic valve area The Aortic Valve Area is a measure of the effective orifice area of the aortic valve, typically assessed using Doppler echocardiography and the continuity equation. It is calculated by measuring the flow of blood through the aortic valve and the cross-sectional area of the left ventricular outflow tract (LVOT). A higher AVA post-TAVR indicates a successful procedure, as it reflects an unobstructed and adequately opened valve, facilitating improved blood flow. Mean pressure gradient The Mean Pressure Gradient (MPG) across the aortic valve is measured using Doppler echocardiography and reflects the average pressure difference between the left ventricle and the aorta during systole. It is calculated by integrating the instantaneous gradients over the ejection period. A gradient MPG post-TAVR is desirable and indicates successful valve function, as it suggests reduced resistance to blood flow across the valve. Doppler velocity index The Doppler Velocity Index is a dimensionless index that compares the velocity of blood flow in the LVOT to the velocity of blood flow through the aortic valve. Geometric reconstruction error We quantified the geometric reconstruction error between our surface domain (aortic root) and the original aortic root segmentation from CT images. This evaluation involved comparing the segmented isosurface from the CT images with the patient-specific surface model used in the VTAVR simulator. The error was quantified using a mesh surface error map, which indicated the deviation between the two surfaces. Figure 3D shows the error distribution on a sample patient, highlighting areas with minimal deviation and those requiring further refinement. And the summary average / standard deviation of mesh error over the entire surface grouped by sex and morphology is presented in Table 2 . Euclidean distance error (L2 Norm) A co-registration step was performed to spatially align the simulated device geometry with the ground-truth stent geometry in the post-operative reference frame (Fig. 3E,F ). This registration utilized the aortic annulus as a stable and anatomically consistent landmark (Fig. 3A ) common to both the simulation and the clinical image, ensuring a direct and meaningful comparison. Following registration, the L2 norm (point-to-surface Euclidean distance) was calculated to quantify the geometric deviation between the predicted and actual stent surfaces. This provides a robust and unambiguous measure of spatial accuracy at thousands of points across the entire device. These distance metrics were computed for all patients in the cohort ( N = 40) to evaluate the framework’s overall performance and local predictive accuracy and statistical summaries are presented in (Fig. 8E ; Table 2 ). Supplementary information Supplementary Information (1.4MB, pdf) Supplementary Information (1.4MB, mp4) Supplementary Information (1.2MB, mp4) Supplementary Information (1.7MB, mp4) Supplementary Information (2MB, mp4) Acknowledgements This work was supported by NSERC Discovery Grant (RGPIN-2017-05349). NSERC ( https://www.nserc-crsng.gc.ca/index_eng.asp ) as the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author contributions The Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework, which predicts optimal device landing zones tailored to patient-specific anatomy, was developed by Mohamed Abdelkhalek and Zahra Keshavarz-Motamed. Mohamed Abdelkhalek: Investigation, Methodology, Software, Writing, Review & Editing, Zahra Keshavarz-Motamed: Review & Editing, Funding acquisition, Supervision. Data availability The VTAVR simulation framework may be made available upon reasonable request from the correspondence author (ZKM), in accordance with institutional and patient confidentiality guidelines. Due to an ongoing patent submission process, the source code and data cannot be publicly released at this time. As per McMaster University’s Intellectual Property (IP) policy, disclosure of materials related to innovations under patent consideration is restricted to ensure the confidentiality and integrity of the application process. 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J. Cardio. Thorac. Surg. 42 , S45–S60 (2012). [ DOI ] [ PubMed ] [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Supplementary Materials Supplementary Information (1.4MB, pdf) Supplementary Information (1.4MB, mp4) Supplementary Information (1.2MB, mp4) Supplementary Information (1.7MB, mp4) Supplementary Information (2MB, mp4) Data Availability Statement The VTAVR simulation framework may be made available upon reasonable request from the correspondence author (ZKM), in accordance with institutional and patient confidentiality guidelines. Due to an ongoing patent submission process, the source code and data cannot be publicly released at this time. As per McMaster University’s Intellectual Property (IP) policy, disclosure of materials related to innovations under patent consideration is restricted to ensure the confidentiality and integrity of the application process. 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