Physics-based and data-driven reduced order models: applications to coronary artery disease diagnostics
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In this thesis we have developed reduced-order models for the prediction of pressure and flow in the arterial system and for the diagnosis of coronary artery disease. By reduced-order model we refer to a reduction of dimensionality, i.e. the conversion of a 3D problem to a 1D problem, or a 1D problem to a 0D problem. The reductions in dimensionality require simplifications of the problem, which are associated with a range of assumptions. These simplifications and assumptions lead to computationally affordable, and thereby clinically relevant models, which may be used for diagnosis, treatment and decision support. However, these benefits have to be counterweighted with the model errors introduced by the simplifications and assumptions, to maintain the clinically relevant predictability of the models. We have developed a framework for optimizing the number of segments to be included in arterial 1D blood flow models. We found that a model where all aortic segments are represented, but with a minimal description of other parts of the cardiovascular system (head and extremities), is sufficient to capture important features of the aortic pressure waveform. Furthermore, we have developed a noninvasive reduced-order model for the estimation of the hemodynamic significance of coronary artery disease, based on coronary computed tomography angiography (CCTA) imaging and computational fluid dynamics. We demonstrated how global sensitivity analysis can be used as a part of model validation and assist in parameter estimation to reduce errors with respect to a corresponding, more detailed 3D model. Moreover, the errors related to the reduced-order model were further reduced by application of neural networks for prediction of pressure loss in coronary segments. We evaluated the effect of incorporating prior physics-based knowledge in the learning process. This modification resulted in significantly improved predictions by the neural networks and also reduced the amount of training data required to achieve a specific accuracy. We characterized the diagnostic accuracy of the reduced-order model to classify ischemia using invasive Fractional Flow Reserve (FFR) measurements as reference. Our model predictions of FFR obtained an accuracy, sensitivity and specificity of 89%, 79% and 93% respectively, in an unblinded study on 63 patients. Moreover, we found that the estimation and distribution of baseline coronary flow had a significant impact on diagnostic performance. However, even imposition of the correct baseline flow would still lead to high uncertainty in predicted FFR due to uncertainties related to geometry and the effect of hyperemic inducing drugs.
Består avPaper 1: Fossan, Fredrik Eikeland; Mariscal-Harana, Jorge; Alastruey, Jordi; Hellevik, Leif Rune. Optimization of topological complexity for one-dimensional arterial blood flow models. Journal of the Royal Society Interface 2018 ;Volum 15:20180546.(149) s. 1-16 https://doi.org/10.1098/rsif.2018.0546 Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, (CC BY 4.0)
Paper 2: Fossan, Fredrik Eikeland; Sturdy, Jacob; Muller, Lucas Omar; Strand, Andreas; Bråten, Anders Tjellaug; Jørgensen, Arve; Wiseth, Rune; Hellevik, Leif Rune. Uncertainty quantification and sensitivity analysis for computational FFR estimation in stable coronary artery disease. Cardiovascular Engineering and Technology 2018 ;Volum 9.(4) s. 597-622 https://doi.org/10.1007/s13239-018-00388-w
Paper 3: Muller, Lucas Omar; Fossan, Fredrik Eikeland; Bråten, Anders Tjellaug; Jørgensen, Arve; Wiseth, Rune; Hellevik, Leif Rune. Impact of baseline coronary flow and its distribution on Fractional Flow Reserve prediction. International Journal for Numerical Methods in Biomedical Engineering 2019 ;Volum e3246. https://doi.org/10.1002/cnm.3246| This is an open access article under the terms of the Creative Commons Attribution License (CC BY 4.0)
Paper 4: F.E. Fossan, L.O. Müller, J. Sturdy, A. Bråten, A. Jørgensen, R. Wiseth, L.R. Hellevik Machine learning augmented reduced order models for FFR-prediction