Advances in computational medicine have made mathematical modeling of hemodynamics a key area of scientific research. Innovations in high performance computing and high-fidelity models allows for sophisticated approximations of in-vivo cardiovascular dynamics. To this end, a variety of models including system level 0D models, 1D fluid dynamics network models, and 3D fluid structure interaction models, can be used to investigate structure-function relation of the cardiovascular system, on a local, global, or multiscale level. However, these computational models are susceptible to both model discrepancy and uncertainty in model inputs, and predictions. Cardiovascular models are calibrated to sparse data, i.e. they contain parameters unmeasurable in-vivo, making parameter estimation and forward uncertainty propagation difficult. This minisymposium will focus on cardiovascular inverse problems and statistical inference methodology including:
• Parameter estimation techniques for complex ODE-PDE coupled models
• Novel emulation and metamodeling procedures for high-fidelity models
• Advances in surrogate and low-fidelity model construction
• Quantification of model consistency using machine-learning
• Efficient uncertainty propagation and quantification
• Innovative numerical and analytical sensitivity techniques
16:30
Sensitivity analysis informed cardiovascular modelling for clinical applications
Jacob Sturdy | Norwegian University of Science and Technology | Norway
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Authors:
Jacob Sturdy | Norwegian University of Science and Technology | Norway
Fredrik Fossan | Norwegian University of Science and Technology | Norway
Nikolai Bjørdalsbakke | Norwegian University of Science and Technology | Norway
Lucas Mueller | University of Trento | Italy
Leif Hellevik | Norwegian University of Science and Technology | Norway
The process of developing reliable cardiovascular models has at least three facets. First, the models may be applied to provide an integrated understanding of the relevant physiology in general. Second, the clinical usage context must be considered with the associated issues of pre-processing measurement data which may have considerable uncertainty relative to corresponding the inputs for a physiological model. Finally, robustness requires that the model performance is understood for cases across the population of interest. The uncertainty of the model must weighed against the risk of wrong decisions based on model predictions. These aspects of model development all require solving inverse problems and quantifying the sensitivity of model outputs to input uncertainties. We will present some insights from non-invasive prediction of coronary hemodynamics where sensitivity analysis enabled to solution of an inverse problem related to pre-processing imaging data. Further, these results have led us to pursue machine learning approaches for correcting model discrepancy when our reduced order model is expected to disagree with full computational fluid dynamics (CFD) simulations. In addition, we have investigated the reliability of various inverse problem formulations for prediction of individual hemodynamic and biomechanical quantities predicted from personalized models of the systemic circulation that have been calibrated against non-invasive clinical measurements.
17:00
- CANCELED - Uncertainty Quantification in Numerical Simulations of the Hemodynamics of the Aorta
Huijuan Xu | Georgia Institute of Technology | United States
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Authors:
Huijuan Xu | Georgia Institute of Technology | United States
Davide Baroli | Aachen Institute for Advanced Study in Computational Engineering Science | Germany
Alessandro Veneziani | Emory University | United States
Modeling and propagating sources of uncertainty in hemodynamics modeling raises challenges due to the intrinsic complexity of the problem. Different factors introduce uncertainty in the final clinical-relevant results, including the boundary condition (e.g. pulsatile inflow), spatial variability of material parameter and the anatomy of the vessel due to the potential acquisition, segmentation and reconstruction errors.
In aortic simulations, the nature of the fluid is highly disturbed and therefore introduces additional troubles to the numerical model. As a matter of fact, turbulence models are sometimes required to contain the computational costs of a Direct Numerical Simulation. These models, in turn, feature parameters whose tuning has generally an impact on the solution.
In this talk, we present a UQ analysis combining the uncertainty induced by the geometry, the boundary condition and the parameter of a Large Eddy Simulation (LES) modeling. We perform polynomial chaos expansion with Leja nested sparse grid and global sensitivity analysis based on Sobol’ index to identify the most relevant parameters in relation with the choice of hemodynamic indexes of clinical relevance. The simulations are performed on a 3D simplified aortic arch and 3D patient-specific setup with the abdominal aortic aneurysm.
17:30
Parameter identifiability and estimation in a 1D cardiovascular fluid dynamics model
Mitchel Colebank | North Carolina State University | United States
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Authors:
Mitchel Colebank | North Carolina State University | United States
Mette Olufsen | North Carolina State University | United States
One-dimensional (1D) fluid dynamics models can be used to describe network dynamics in a system of branching blood vessels. This is a promising tool for clinical diagnostics, as data cannot be measured in all of the downstream vasculature. Moreover, imaging practices have limited resolution for detecting in-vivo patient geometry, thus limiting the number of vessels captured for subject-specific modeling. To combat this, researchers will employ 0D boundary conditions, such as 3 element Windkessel models, or try to capture the downstream branching properties of the network using fractal surrogates, such as the structured tree model. Determining the parameters that describe distal vascular resistance and compliance are especially important in the case of Pulmonary Hypertension (PH), where pulmonary vessels branch rapidly to supply blood to the lungs for oxygenation and are suspected to play the largest role in disease progression. However, a lack of data distal to the proximal arteries can lead to issues with parameter identifiability, as parameters may not be uniquely informed from the data. This talk will focus on determining parameter identifiability via the use of profile likelihood calculation. In addition, we consider the adjoint PDE system, which is used to expedite parameter inference via rapid calculation of the objective function gradient.
18:00
Anatomic Model Uncertainty through Convolutional Bayesian Dropout Networks
Gabriel Maher | Stanford University | United States
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Authors:
Alison Marsden | Stanford University | United States
Daniele Schiavazzi | Notre Dame University | United States
Gabriel Maher | Stanford University | United States
Casey Fleeter | Stanford University | United States
Cardiovascular simulation is gaining increasing momentum in non-invasive diagnostics, but further adoption is hindered by lack of robustness due to uncertainty from various sources including image segmentation and vascular tissue histology. Thus, research in efficient uncertainty quantification approaches is key to further improve model-based diagnostics. While prior work has examined uncertainties stemming from vascular material properties and physiologic boundary conditions, the impact of image data uncertainty remains underexplored. In part due to the time and manual effort required to produce patient-specific models, and the complexity of approaches to parameterize their geometry, it is still unclear how noise in the clinical image translates onto distributions of segmented patient-specific anatomies. In this work, we propose a novel approach to sample from a distribution of patient-specific models for a given image volume. Our method uses convolutional neural networks, trained to predict 2D vessel lumen cross-sections, combined with dropout layers, to enable Bayesian sampling of vessel geometries. A path-planning patient-specific modeling pipeline is then used to generate families of cardiovascular models. A key innovation of our method is the ability to learn geometric uncertainty directly during training. We apply this method to quantify geometric uncertainty for clinically relevant anatomies, and provide detailed analysis on its effects on simulation results.