23 Oct Complete device level Hierarchical VVUQ Strategy
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Device Assembly Level in Hierarchical VVUQ Strategy for Biodegradable Pulmonary Heart Valve Development
Welcome to the fourth installment of our blog series on the Hierarchical VVUQ Strategy for the development of biodegradable pulmonary heart valves within the EU-funded SimInSitu project. In this post, we focus on the Device Assembly Level, detailing the process of modeling, verification, and validation of the entire pulmonary valve (PV) device.
Read the first blog post: Hierarchical VVUQ Strategy
Read the second blog post: Material level Hierarchical VVUQ Strategy
Read the third blog post: Single device level Hierarchical VVUQ Strategy
Device Assembly Modeling
The assembly of the PV device involves connecting the leaflets and conduit using tie-constraints. The interface between the leaflets and the conduit is defined as frictionless penalty contact, and self-contact for all components is included to accurately simulate real-life interactions. Since the PV model will eventually be integrated into a patient-specific model of the right heart (right ventricle outflow tract and pulmonary artery), the free end of the conduit will be connected to the corresponding native counterparts. For now, as a stand-alone model, the free ends of the conduit are displacement-constrained in both the axial and circumferential directions.
To simulate in-vivo conditions, transient pressure loads are applied at the right-ventricle side and pulmonary outflow side. All simulations are conducted using Abaqus Explicit.
Verification
For the assembly level verification, additional factors such as time-discretization and solver errors (e.g., contact parameters, mass scaling, bulk viscosity, or viscous pressure) were investigated. These parameters were adjusted to achieve a relative error smaller than 1%.
Below you can see the transient leaflet motion (radial position: 0.0 = centre position) of a leaflet-tip as a result of varying degree of viscous pressure (left) and contact stiffness (right).
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Model Validation and Uncertainty Quantification
Two primary comparators were defined to validate the structural response of the PV model:
1 Leaflet Opening Resistance: Chosen as a surrogate for Pressure Gradient.
2 Parallel-Plate Compression Stiffness: Used as an indicator for crush-resistance.
Uncertainty quantification was initiated through a comprehensive review of all relevant uncertainty parameters, including device dimensions, material properties, and loading conditions. Meta-models (response surfaces) were constructed from simulation outputs and used in Monte Carlo simulations to compute propagated output uncertainty. Global probabilistic sensitivity factors were assessed using the obtained data points.
Leaflet Opening Resistance
The opening resistance was measured by pushing a smooth cylindrical rod into the device, causing the leaflets to open and recording the axial reaction force. This was done for the FEM model and corresponding experimental tests across all three device sizes (16mm, 18mm, and 20mm), with five samples/tests per size. Uncertainty quantification considered sample alignment deviations.
Experimental and simulation Cumulative Distribution Functions (CDFs) were compared using a normalized area metric. For peak resistance force, area metric values of 24.3%, 29.3%, and 26.8% were obtained for sizes 16, 18, and 20, respectively. These values, higher than the target of 10%, were mainly driven by differences in distribution width, with simulation CDFs showing higher scatter.
The Leaflet Opening Resistance Test can be seen below.
Parallel-Plate Compression
This test (shown below) involved placing the PV device between two parallel plates and compressing it by a predefined amount while recording the vertical reaction force. The compression resistance was measured at a given compression level, with five samples tested for each device size. Experimental uncertainty factors such as rotational placement were considered.
For this validation, area metric values ranged from 51% to 63%, which was unacceptably high.
Below you can see exemplary reaction forces as simulated for the leaflet opening resistance (left) and parallel plate compression (right). Dashed lines indicate the evaluation region.
Furthermore you can see the Leaflet Peak Resistance (left) and Conduit Compression Resistance (right) showing the area metric as the grey are between the simulation and experimental CDF, respectively.
Recalibration and Revalidation
Due to the large discrepancy in validation metrics, an extensive root-cause analysis was conducted following a top-to-bottom hierarchical approach. The scaffold test-coupons were identified as the main source of deviation. Despite similar manufacturing processes (electro-spinning), the scaffold behavior of the final device conduit showed significantly different material properties than the test coupons. After recalibrating the material models, validation simulations were repeated, resulting in acceptable validation metrics.
Conclusion
The Device Assembly Level is crucial in our hierarchical VVUQ strategy, encompassing detailed modeling, rigorous verification, and thorough validation of the entire PV device. In our next post, we will delve into the Complete Device Level, focusing on the assembly of the entire device and the extensive testing involved to ensure its functionality and reliability. Stay tuned for more insights into our journey to develop a credible, patient-specific in-silico FEM model for biodegradable pulmonary heart valves.
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