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
14:00
Statistical inference in soft-tissue mechanics with an application to prognostication of myocardial infarction
Dirk Husmeier | University of Glasgow | United Kingdom
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Dirk Husmeier | University of Glasgow | United Kingdom
A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is estimating the material properties from in-vivo clinical magnetic resonance imaging (MRI) measurements in a time frame suitable for use in the clinic. Understanding these properties can provide insight into heart function or dysfunction and help inform personalised diagnosis and treatment, including predicting the risk of myocardial infarction (heart attack). However, finding a solution to the coupled partial differential equations which describe the myocardium dynamics through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of statistical emulation to infer the myocardium properties of a healthy volunteer in a viable clinical time frame using in-vivo LV data from MRI scans. Emulation methods avoid computationally expensive simulations from the LV cardio-mechanic model by replacing it with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving efficiency at the clinic. I will compare and contrast various emulation strategies, discuss uncertainty quantification and talk about the particular challenges we are facing on the pathway to impact in personalised medicine.
14:30
Emulating cardiac cell models with Gaussian processes
Richard Clayton | The University of Sheffield | United Kingdom
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Richard Clayton | The University of Sheffield | United Kingdom
The heart is an electromechanical pump, where propagating waves of electrical activation act to initiate and synchronise contraction. Cardiac cell models aim to reconstruct the electrical activation and recovery of individual cardiac cells. They are typically composed of stiff and nonlinear ODEs, which represent the current flow through ion channels, pumps and exchangers in the cell membrane. Cardiac cell models are important research tools, and are beginning to replace experiments for applications such as drug safety testing.
Cardiac cell models have large numbers of parameters, which describe the magnitude and kinetics of each transmembrane current. They are generally intractable analytically, and so conventional sensitivity analysis is difficult. We have used Gaussian processes to emulate models of cells in different parts of the heart, and in different species. The emulators have been used to calculate first order and total effect sensitivity indices, which have yielded new insights into the models. The next step is extension of these ideas into tissue models where cell models are coupled via a PDE. We have also used emulators for history matching cardiac cell models to experimental data, which has raised important questions about model identifiability. One of the reasons for this finding is the redundancy and compensatory mechanisms which are an important feature of many biological systems.
15:00
State of the art and perspectives in patient-specific reduced order modelling for cardiovascular problems
Martin Hess | SISSA International School for Advanced Studies | Italy
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Gianluigi Rozza | SISSA Trieste | Italy
Francesco Ballarin | SISSA Trieste | Italy
Martin Hess | SISSA International School for Advanced Studies | Italy
Zakia Zainib | TU Eindhoven | Netherlands
We provide the state of the art of Reduced Order Methods (ROM) focusing in parametric problems arising in offline-online Computational Fluid Dynamics (CFD) and applications for cardiovascular flows. Efficient parametrizations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances, especially for real time computing in complex parametric biomedical flow problems, even in a flow control setting. Model flow problems will focus on few benchmarks, as well as on simple fluid-structure interaction problems, instabilities and bifurcations due to Coanda effect in Mitral valves regurgitation, as well as flows in carotid arteries properly parametrised to allow patient specific simulations. The most significant application is related with aorto-coronaric bypasses by means of optimal flow control techniques.
15:30
Parameter estimation and uncertainty quantification for the pulmonary circulation system
Mihaela Paun | University of Glasgow | United Kingdom
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Mihaela Paun | University of Glasgow | United Kingdom
Parameter estimation, uncertainty quantification and model selection are important in cardiovascular modelling, but computationally challenging due to the need to numerically integrate a system of coupled partial differential equations in every step of an iterative parameter adaption procedure. In the present talk, we present a Bayesian approach, aiming to sample the parameters from the posterior distribution with MCMC. Besides the fact that this naturally addresses the problem of uncertainty quantification, it allows the computation of state-of-the-art information criteria (WAIC and WBIC) for model selection. However, a naive implementation of MCMC incurs excessive computational costs. The centerpiece of our work, thus, is to demonstrate that a substantial improvement in computational efficiency can be achieved by combining MCMC with statistical emulation. The emulator needs to take into consideration invalid regions in parameter space, where the physical model assumptions break down, and we address this issue by automatically learning the critical regions with a multivariate classifier. We also address the challenges of a heteroscedastic noise structure with longitudinal dependencies, which we model with a Gaussian process (GP). We demonstrate that our uncertainty quantification and model selection techniques can be successfully and simultaneously applied to select both the kernel of the GP and the physical model that are most consistent with the data.