Publication
Numerical Calibration of Windkessel Boundary Conditions In Ascending Thoracic Aortic Aneurysms. An Adjoint-Based Optimisation Algorithm
| Summary: | An Ascending Thoracic Aortic Aneurysm (ATAA) is a permanent and abnormal dilation of the aorta. This condition is often associated with tissue degeneration driven by disturbed hemodynamics, genetic predispositions and environmental factors. Two major aspects influencing numerical simulations are the geometry and the def- inition of boundary conditions. While geometric reconstruction has seen significant advances, the prescription of physiologically accurate boundary conditions remains a critical and challenging aspect, particularly at the outlet sections of the model. Among the commonly used boundary conditions, the Three-Element Windkessel (3WK) model is widely adopted to approximate the effect of the downstream vasculature. Often referred to as a Resistance-Capacitor-Resistance (RCR) boundary condition, the model consists of a simple lumped-parameter circuit comprising a systemic resistance ( ), a peripheral resistance ( ) and a capacitor (). In this context, the primary objectives of this dissertation are: (i) to develop an algorithm that automates the calibration of RCR boundary conditions across all outlets of patient-specific ATAAs; and (ii) to validate the proposed numerical tool. To achieve these objectives, an in-depth analysis of various techniques for estimating boundary conditions was first conducted, with the goal of identifying their limitations and assessing their applicability. Based on this analysis, the adjoint-based method was selected and adapted to better suit the specific requirements of the problem at hand. Numerical implementation was carried out by developing an optimisation algorithm that iteratively executes multiple Reduced Order Model (ROM) simulations, adjusting boundary conditions until the simulated pressures match the target values. Once conver- gence is achieved, the calibration is deemed complete. In the absence of experimental data, numerical validation was performed by comparing the calibrated pressure curve to normalised pressure waveforms reported in the literature. Calibration was conducted on three 1D geometries: a straight single vessel, a bifur- cated vessel and a patient-specific ATAA. The calibrated RCR values were subsequently implemented in a Fluid-Structure Interaction (FSI) simulation of the corresponding 3D ATAA geometry, to assess accuracy of the adjoint-based calibration. The results demonstrate that the developed numerical optimisation tool successfully calibrates RCR boundary conditions. The method accurately reproduces simulated pres- sures within tolerance, with parameter sensitivity analyses highlighting the strong influ- ence of initial estimates on waveform morphology. Extension to bifurcated and aneurysmal geometries demonstrates robustness, though non-uniqueness of parameter sets and wave- form fidelity remain as limitations. When implemented in FSI simulations, the calibrated values yield results consistent with a manually-guided iterative approach. Only minor differences in displacement fields, velocity profiles and stress distributions are observed. Despite the lack of experimental data for direct validation, comparisons with reference waveforms confirm physiological plausibility. The proposed calibration algorithm is able to generate physiologically consistent RCR parameters that yield pressure waveforms comparable to those obtained through conventional iterative methods. This underscores its potential as a reliable and automated alternative for prescribing outlet boundary conditions in patient-specific cardiovascular simulations. |
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| Main Authors: | Candeias, Sofia de Almeida |
| Subject: | Ascending Thoracic Aorta Aneurysm (ATAA) Boundary conditions Three- Element Windkessel (3WK) Reduced-Order Model (ROM) Fluid-Structure Interaction (FSI) Calibration algorithm |
| Year: | 2025 |
| Country: | Portugal |
| Document type: | master thesis |
| Access type: | open access |
| Associated institution: | Universidade Nova de Lisboa |
| Language: | English |
| Origin: | Repositório Institucional da UNL |
| Summary: | An Ascending Thoracic Aortic Aneurysm (ATAA) is a permanent and abnormal dilation of the aorta. This condition is often associated with tissue degeneration driven by disturbed hemodynamics, genetic predispositions and environmental factors. Two major aspects influencing numerical simulations are the geometry and the def- inition of boundary conditions. While geometric reconstruction has seen significant advances, the prescription of physiologically accurate boundary conditions remains a critical and challenging aspect, particularly at the outlet sections of the model. Among the commonly used boundary conditions, the Three-Element Windkessel (3WK) model is widely adopted to approximate the effect of the downstream vasculature. Often referred to as a Resistance-Capacitor-Resistance (RCR) boundary condition, the model consists of a simple lumped-parameter circuit comprising a systemic resistance ( ), a peripheral resistance ( ) and a capacitor (). In this context, the primary objectives of this dissertation are: (i) to develop an algorithm that automates the calibration of RCR boundary conditions across all outlets of patient-specific ATAAs; and (ii) to validate the proposed numerical tool. To achieve these objectives, an in-depth analysis of various techniques for estimating boundary conditions was first conducted, with the goal of identifying their limitations and assessing their applicability. Based on this analysis, the adjoint-based method was selected and adapted to better suit the specific requirements of the problem at hand. Numerical implementation was carried out by developing an optimisation algorithm that iteratively executes multiple Reduced Order Model (ROM) simulations, adjusting boundary conditions until the simulated pressures match the target values. Once conver- gence is achieved, the calibration is deemed complete. In the absence of experimental data, numerical validation was performed by comparing the calibrated pressure curve to normalised pressure waveforms reported in the literature. Calibration was conducted on three 1D geometries: a straight single vessel, a bifur- cated vessel and a patient-specific ATAA. The calibrated RCR values were subsequently implemented in a Fluid-Structure Interaction (FSI) simulation of the corresponding 3D ATAA geometry, to assess accuracy of the adjoint-based calibration. The results demonstrate that the developed numerical optimisation tool successfully calibrates RCR boundary conditions. The method accurately reproduces simulated pres- sures within tolerance, with parameter sensitivity analyses highlighting the strong influ- ence of initial estimates on waveform morphology. Extension to bifurcated and aneurysmal geometries demonstrates robustness, though non-uniqueness of parameter sets and wave- form fidelity remain as limitations. When implemented in FSI simulations, the calibrated values yield results consistent with a manually-guided iterative approach. Only minor differences in displacement fields, velocity profiles and stress distributions are observed. Despite the lack of experimental data for direct validation, comparisons with reference waveforms confirm physiological plausibility. The proposed calibration algorithm is able to generate physiologically consistent RCR parameters that yield pressure waveforms comparable to those obtained through conventional iterative methods. This underscores its potential as a reliable and automated alternative for prescribing outlet boundary conditions in patient-specific cardiovascular simulations. |
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