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Timetable (FHTW01)

Uncertainty quantification for cardiac models

Wednesday 5th June 2019 to Friday 7th June 2019

Wednesday 5th June 2019
09:30 to 09:50 Registration
09:50 to 10:00 Welcome from David Abrahams (Isaac Newton Institute) INI 1
10:00 to 11:00 Andrew McCulloch (University of California, San Diego)
Ventricular Remodeling: Population Variation in Congenital Heart Disease and Data Uncertainty in Systems Mechanobiology
Chair: Richard Clayton (University of Sheffield)
Congenital heart defects are the commonest class of birth defect and are associated with a wide range of anatomic lesions which are frequently life-threatening without surgery early in life. The success of these interventions means that there are now more adults than children with congenital heart disease (CHD), but many of these patients are at risk of adverse ventricular remodeling and heart failure. Managing these patients and predicting when to intervene are important clinical decisions and cardiac MRI exams every few years are common. However how to use the structural and functional data from these studies is complicated by the atypical and widely varying ventricular shapes in many CHD such as repaired Tetrology of Fallot. Here, I describe how ventricular shape atlases derived from principal component analysis of parametric shape models can be used to understand patient variation and identify potential markers of adverse ventricular remodeling in CHD.

Underlying ventricular modeling processes are myocyte signaling pathways, many of which are mechanosensitive. Genome scale data such as RNA-seq provide a way to experimentally validate the predictions of cell signaling models. In a model of myocyte mechanosignaling, we were able to correctly predict the responses over over 70% of approximately 800 genes to longitudinal and transverse stretch. However, uncertainty in underpowered transcriptomic data sets is a significant impediment to more stringent model validation and optimization.

Supported by NIH grants
INI 1
11:00 to 11:30 Morning coffee and poster session
11:30 to 12:00 Alexander Panfilov (Universiteit Gent); (Universiteit Leiden)
In silico–in vitro approach to study the mechanisms of cardiac arrhythmias
Chair: Tammo Delhaas (Maastricht University)
In my talk I will present results of research which combine usage of modelling and experimental techniques. In particular, I will report on studies in which properties of cardiac tissue were manipulated using optogenetics and show how this technology can be used to study basic properties of cardiac propagation, be applied for reversible ablations, studies of ectopic activity and can result in novel methods to arrhythmias elimination using Attract-Anchor-Drag method.
INI 1
12:00 to 12:30 Wouter Huberts (University of Maastricht); (Technische Universiteit Eindhoven)
The role of uncertainty and sensitivity analysis in patient-tailored cardiovascular models
Chair: Tammo Delhaas (Maastricht University)
Physics-based patient-specific models have the potential to support physicians in decision-making during diagnosis and intervention planning.To adapt these models to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a global variance-based sensitivity analysis it can be assessed which uncertain input parameters are most rewarding to measure more accurately for reducing output uncertainty (parameter prioritization) and which irrelevant model parameters can be fixed within their uncertainty domain (parameter fixing). Such an analysis can therefore give directions for input measurement improvement.
In this work, we will discuss the role of uncertainty and sensitivity analysis in patient-tailored modeling. In addition, we will present a two-step variance-based sensitivity analysis method for a cardiovascular model with many model parameters. In the first step, we perform a screening method to reduce the parameter input space, followed by generalized polynomial chaos expansion. Furthermore, we will introduce an adaptive generalized polynomial chaos expansion method which is an efficient variance-based sensitivity analysis approach for computationally expensive models and was first introduced by Blatman et al. in the field of structural reliability engineering.
INI 1
12:30 to 14:00 Lunch at Westminster College
14:00 to 15:00 Chris Holmes (University of Oxford)
Quantification of Model Uncertainty
Chair: Gary Mirams (University of Nottingham)
Statistical estimation and uncertainty quantification of parameter values within models is fairly well established, where Bayesian and non-Bayesian approaches typically show broad agreement. In contrast, quantification of uncertainty around issues of model choice or parameter selection is much more contentious. We will review some of the distinctive features of statistical approaches to model evaluation with a focus on the foundations of Bayesian inference and robustness to model misspecification.
INI 1
15:00 to 15:30 Samuel Coveney (University of Sheffield)
Probabilistic Interpolation of Uncertain Local Activation Times
Chair: Gary Mirams (University of Nottingham)
Local Activation Time (LAT) measurements on the left atrium are subject to uncertainty due to electrogram analysis and the assignment of measurements to an anatomical mesh. Interpolation of LAT measurements to provide LAT maps also introduces prediction uncertainty. Using Gaussian Markov Random Fields, it is possible to perform probabilistic interpolation of uncertain LAT measurements directly on the left atrium. This produces a probabilistic LAT map which can be viewed as a mean and standard deviation of LAT at every mesh location.
INI 1
15:30 to 16:00 Dirk Husmeier (University of Glasgow)
Statistical inference in soft-tissue mechanics and fluid dynamics with an application to prognostication of myocardial infarction and pulmonary hypertension
Chair: Gary Mirams (University of Nottingham)
A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is estimating the material properties from in-vivo clinical 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 treatment. However, finding a solution to the differential equations which describe the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of statistical emulation to infer the myocardium properties in a viable clinical time frame using in-vivo MRI data. Emulation methods avoid computationally expensive simulations from the LV model by replacing it with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving efficiency at the clinic. In the talk I will compare and contrast various emulation strategies, discuss uncertainty quantification and (it time permits) discuss an extension of this framework to fluid dynamics in the pulmonary blood circulation system for prognostication of pulmonary hypertension.
INI 1
16:00 to 16:30 Afternoon tea and poster session
16:30 to 17:00 Leif Rune Hellevik (Norwegian University of Science and Technology); (NTNU)
Applications of uncertainty quantification and sensitivity analysis for cardiovascular models
Chair: Pras Pathmanathan (US Food and Drug Administration)
INI 1
17:00 to 17:30 Simone Pezzuto (Università della Svizzera italiana)
Enabling high-dimensional uncertainty quantification for cardiac electrophysiology via multifidelity techniques
Chair: Pras Pathmanathan (US Food and Drug Administration)
Mathematical modeling of the heart, as many other models in biomedical sciences, involves a large number of parameters and simplifying approximations. Uncertainties for cardiac models are ubiquitous, including anatomy, fiber direction, and electric and mechanical properties of the tissue. Hence, both UQ and parameter sensitivity naturally arise during modeling, and they shall become fundamental in view of clinical applications.

For high-dimensional input uncertainties, e.g., substrate heterogeneity or cardiac fibers orientation, and high-dimensional output quantities of interest, e.g., the activation map, the method of choice for UQ is the classic Monte Carlo (MC) method. MC convergence rate does not suffer from the curse of dimensionality, but it is notoriously slow. While sampling a random field can be done very efficiently via the pivoted Cholesky decomposition, computing the cardiac activation from the bidomain equation is a computational demanding task. A single patient-tailored simulation can take several CPU-hours even on a large cluster. This makes uncertainty quantification (UQ) unfeasible, unless modeling reduction strategies are employed.

One such strategy is represented by multifidelity methods [1]. A key ingredient of the multifidelity approach is the choice of low-fidelity models. Typical strategies are projection-based or data-fit surrogates, which however need to be trained anew for each patient and may become inefficient for a large dimensionality of the input, as in the case under consideration. Instead, a more physics-based approach is to take advantage of the natural hierarchy of available models. These include different cellular models for the monodomain equation, the time-independent eikonal equation, and the 1D geodesic point activation [2,3]. By exploiting statistical correlations in this hierarchy, we observed a reduction of the computational cost by at least two orders of magnitude, enabling to perform a full analysis within a reasonable time frame. Moreover, we incorporate Bayesian techniques, which provide confidence intervals and full probability distributions at selected points, thus augmenting the information provided by standard frequentist approaches.

References:
[1] Peherstorfer, B., Willcox, K., & Gunzburger, M. (2018). Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review, 60(3), 550-591.
[2] Quaglino, A., Pezzuto, S., Koutsourelakis, P.S., Auricchio, A., Krause, R. (2018). Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints. Int J Numer Meth Biomed Engng, e2985.
[3] Quaglino, A., Pezzuto, S., Krause, R. (2018). Generalized Multifidelity Monte Carlo Estimators. Submitted to J Comp Phys. ArXiv: 1807.10521
INI 1
19:30 to 22:00 Formal Dinner at Clare College (Garden Room)



LOCATION
Clare College (Garden Room) - on the ground floor of the Gillespie Centre, Memorial Court.
Queen's Road, Cambridge, CB3 9AJ

DRESS CODE
Smart casual

MENU

Starters
Corn fed chicken, ham hock and white bean terrine - smoked white bean hummus, parsley oil, crispy potato
Braised and roasted baby carrots (v) - dukkah, hung goats’ curd, curried emulsion, wild rice, pickled carrots, coriander cress
Main course
Honey and szechuan duck breast - braised leg pastille, poached baby fennel, black bean and hoisin bonbon, anise carrot purée, pak choi, fig jus  
Dauphinoise, caramelised onion and comté pithivier (v) - roasted shallot purée, celeriac fondant, trompette and spring vegetable fricassee 
Dessert
Chocolate and hazelnut fondant (v) - espresso, hazelnut, salted pear and rosemary ice cream


Thursday 6th June 2019
09:00 to 10:00 Tony O'Hagan (University of Sheffield)
Model uncertainty - and the consequences of ignoring it
Chair: Richard Wilkinson (University of Sheffield)
INI 1
10:00 to 10:30 Wolfgang Giese (Max Delbrück Center for Molecular Medicine)
Characterizing parameter sensitivity and uncertainty in dyadic structure-function relationships by using a multiscale model of ventricular cardiac myocytes
Chair: Richard Wilkinson (University of Sheffield)
The heart is an electromechanical pump and its functioning is based on the precisely controlled contraction of its cardiac myocytes in a process that is called excitation-contraction-coupling (ECC). The heart rhythm is set by waves of electrical action potentials emanating from the sinoatrial node. Mathematical models of cardiac myocytes are valuable research tools as they express quantitatively the knowledge of the biophysical processes that generate the cardiac action potential.

Cardiovascular disease is often related to defects in molecular and sub-cellular components in cardiac myocytes, specifically in the dyadic cleft. We use a multiscale model to create dyadic structure-function relationships in order to explore the impact of molecular changes on whole cell electrophysiology. This multiscale model incorporates stochastic simulation of individual L-type calcium channels (LCC) and ryanodine receptor (RyRs), spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell.

We created a population of models with changes of crucial dyadic cleft properties, such as RyR and LCC clustering properties, stochastic opening and closing rates as well as changes in LCC  and RyR calcium currents. We investigated commonly used biomarkers describing action potential, Ca(2+) transient and Ca(2+) spark dynamics. By using surrogate models we are able to quantify sensitivity and parameter uncertainty in order to derive functional implications from molecular level properties.
INI 1
10:30 to 11:00 Andrea Manzoni (Politecnico di Milano)
Reduced order modeling for uncertainty quantification in cardiac electrophysiology
Chair: Richard Wilkinson (University of Sheffield)
We present a new, computationally efficient framework to perform both forward and inverse uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in a subject-specific left ventricle geometry, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We take into account relevant inputs related to both models, such as electrical conductivities, pacing times, and coefficients affecting the ionic models. We address a complete UQ pipeline, including: (i) a variance-based sensitivity analysis for the selection of the most relevant input parameters; (ii) forward UQ to investigate the impact of intra-subject variability on clinically relevant outputs related to the cardiac action potential, and (iii) inverse UQ for the sake of parameter and state estimation within a Bayesian framework. All these stages exploit stochastic (Monte Carlo) sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order coupled PDE-ODEs model. To mitigate this computational burden, we replace the high-fidelity model with computationally inexpensive projection-based reduced-order models aimed at reducing the state-space dimensionality. ROM approximation errors on the outputs of interest are finally taken into account by means of statistical error models built through Gaussian process regression, enhancing the accuracy of the whole UQ pipeline.
INI 1
11:00 to 11:30 Morning coffee and poster session
11:30 to 12:00 Boyce Griffith (University of North Carolina)
In vitro and in vivo computational models of heart valve dynamics
Chair: Pablo Lamata (King’s College London)
Heart valves are thin elastic structures that move with the blood flow, but at the same time, they apply forces to the flow that alter the fluid motion. Simulating heart valve performance across the full cardiac cycle requires a fluid-structure interaction approach. This talk will describe work to develop and to validate fluid-structure interaction (FSI) models of native and bioprosthetic heart valves. We consider models of in vitro systems that can provide detailed experimental data in a controlled, reproducible environment as well as subject-specific models of the heart. Initial validation results show excellent agreement between simulated and experimental flow, pressure, and valve kinematics data acquired from the experimental system. We also will present recent work that is developing a complete fluid-structure interaction model of the heart that includes anatomically and biomechanically realistic descriptions of the atria, ventricles, the four cardiac valves, and the nearby great vessels.
INI 1
12:00 to 12:30 Brian Hong (None / Other)
Efficient Quantification of Left Ventricular Function During the Full Cardiac Cycle Using a Characteristic Deformation Model
Chair: Pablo Lamata (King’s College London)
Heart failure is a significant source of morbidity and the prevalence of heart failure continues to rise. Quantification of cardiac function beyond standard clinical indices is essential to improving heart failure diagnosis specificity. Patient-specific computational models of the heart offer detailed descriptions of cardiac function suitable for this purpose. Such models are typically constructed using 0D “varying elastance” or 3D Finite element method (FEM) approaches. While both methods have been successfully applied to many patient-specific applications, each has limitations. Varying elastance models are limited by their simplified representation of the myocardium while FEM models have a high computational cost that is restrictive in applications that require the simulation of many cardiac cycles. As an alternative to these approaches, we describe a computationally efficient method for simulating the dynamics of the left ventricle (LV) in three dimensions using characteristic deformation modes (CDM). In the CDM-LV model, LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions. A variational approach is used to incorporate a mechanical model of the myocardium. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length-tension and force-velocity properties of cardiac muscle.

We apply this model to quantify LV function in two cases.  First, we quantify the passive stiffness of a mouse heart. The stiffness parameters of the mouse LV calculated with the CDM model are similar to those identified using a FEM approach. Second, we quantify LV function during the full cardiac cycle from 3D echocardiogram data. We estimate parameters for the myocardial passive stiffness and active contractile function using a bounded quasi-newton numerical optimization algorithm. We demonstrate that this method is capable of recapitulating the observed aggregated motion of the LV and provides reasonable estimates for the mechanical parameters. The problem of estimating LV functional parameters has numerous sources of uncertainty. Errors arise from the limitations of the imaging method, insufficiency of the data to fully characterize the mechanical system, and from simplifications present in the mathematical model. We present a preliminary analysis of the uncertainty resulting from these three sources. Overall, this approach provides reasonable estimates for the mechanical parameters that determine LV function on a clinically relevant time-scale.
INI 1
12:30 to 14:00 Lunch at Westminster College
14:00 to 15:00 Michael Goldstein (Durham University)
The Bayes linear approach to emulation and history matching for complex computer simulators
Chair: Keith Worden (University of Sheffield)
This talk gives an overview of the Bayes linear approach for
uncertainty quantification for complex computer models. The approach is
based around careful structural model discrepancy analysis and Bayes
linear emulation as a basis for history matching against real system
data. The approach will be illustrated in the context of monitoring
post-operative complications following cardiac surgery.
INI 1
15:00 to 15:30 Richard Wilkinson (University of Sheffield)
Hunting for tigers: which uncertainties matter?
Chair: Keith Worden (University of Sheffield)
I will talk about on-going work on developing patient specific biophysical heart models for predicting atrial tachycardia (AT) recurrence and pathway in patients undergoing ablation for atrial fibrillation. There are many sources of uncertainty when using personalised models to make predictions. The aim of this project is to characterise these uncertainties and to thus determine which of them are most important, so that data collection can be targeted accordingly.
measurements.
INI 1
15:30 to 16:00 Samuel Wall (Simula Research Laboratory)
Uncertainty Quantification in the Parameterization of Cardiac Action Potential Models Through the Singular Value Decomposition
Chair: Keith Worden (University of Sheffield)
Mathematical models describing cardiac action potential dynamics are highly used to understand processes that may disrupt the normal electrical activity of the heart.  However, these models, consisting of biophysical descriptions of ion flux and transport across membranes and through the cell, are heavily, heterogeneously, and non-uniquely parameterized, leading to significant uncertainty in their predictions.  Here we investigate this uncertainty, in the context of model parameterization through adjustment of the maximum conductances of the individual contributing ionic cellular currents.  It has been well described that non-unique solutions exist for given action potential dynamics using this approach, and we present a method for quantifying the uncertainty in this framework.  Our key question is this: How can the maximum conductances of a model be changed without giving appreciable changes to a given action potential? We probe this question using a method founded on the singular value decomposition of a matrix built from the contribution from all the individual ion currents over the time course of an action potential. When small singular values of this matrix are present, there exist identifiable combinations of currents that will lead to no or minimal change to the overall voltage waveform.  We test this method across a range of cardiac models, quantifying parameter uniqueness in each case, and testing whether the conclusion from linear analysis of the matrix of currents carries over to provide insight in the uniqueness of the parameters in the non-linear case.
INI 1
16:00 to 16:30 Afternoon tea and poster session
16:30 to 17:00 Seiryo Sugiura (University of Tokyo)
Uncertainty in the prediction of drug-induced arrhythmogenic risk assessed by a multi-dimensional hazard map
Chair: Kylie Beattie (GlaxoSmithKline)
Arrhythmogenicity of drugs involves multi-scale events taking place at molecular, cellular, tissue and organ levels. In order to understand the mechanism behind this complex phenomena, we developed a multi-scale 3D heart simulator, with which we can evaluate the arrhythmogenicity of drugs based on their inhibitory actions on multiple ionic currents. Recently, we extended this approach to create a hazard map of drug-induced arrhythmia identifying the region at risk in a multi-dimensional space, each co-ordinate of which represents the inhibition of specific ionic current. This hazard map can also be used to assess the two major uncertainties we encounter in the evaluation of arrhythmogenic risk. One is the uncertainty in experimentally determining the inhibitory action of drugs on ionic currents. The other is the individual variability in the sensitivity to drugs possibly caused by the polymorphism in genes coding ion channels or enzymes responsible for the drug metabolism. These uncertainties can also be identified by a region of drug effects in this hazard map and the distance from its border to the region at risk can be taken to indicate the safety margin.
INI 1
17:00 to 17:30 Francisco Sahli Costabal (Stanford University); (Pontificia Universidad Católica de Chile)
Classifying drugs by their arrhythmogenic risk using multiscale modeling and machine learning
Chair: Kylie Beattie (GlaxoSmithKline)
An undesirable side effect of drugs are cardiac arrhythmias, in particular a condition called torsades de pointes. Current paradigms for drug safety evaluation are costly, lengthy, and conservative, and impede efficient drug development. Here we combine multiscale experiment and simulation, high-performance computing, and machine learning to create an easy-to-use risk assessment diagram to quickly and reliable stratify the pro-arrhythmic potential of new and existing drugs. We capitalize on recent developments in machine learning and integrate information across ten orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay of two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 23 common drugs, exclusively on the basis of their concentrations at 50% current block. Our new risk assessment diagram explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the pro-arrhythmic potential of new drugs. Our study shapes the way towards establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.
INI 1
17:30 to 19:00 Poster session and drinks reception at the INI
Friday 7th June 2019
09:00 to 09:30 David Christini (Cornell University)
Embracing uncertainty and variabiilty in the design of cardiac computational models
Chair: Martin Bishop (King’s College London)
The traditional paradigm for developing cardiac computational cell models utilizes data from multiple cell types, species, laboratories, and experimental conditions to create a composite model. While such models can accurately represent data in limited biological scenarios, their ability to predict behavior outside of a narrow dynamic window is limited. This talk will describe the rationale behind using novel electrophysiological protocols that aim to densely sample the dynamics of intact cardiac myocytes. The cell-specific  information-rich data from such protocols are then fit using global parameter optimization algorithms to tune multiple model parameters simultaneously. By so doing, this approach yields cell models that fit wide-ranging and variable cellular behavior, making them better suited for physiological and pathophysiological predictions.
INI 1
09:30 to 10:00 Jichao Zhao (University of Auckland)
Application of Deep Learning on Reducing Uncertainty in the Atrial Structure from Contrast-enhanced MRIs
Chair: Martin Bishop (King’s College London)
INI 1
10:00 to 10:30 Pablo Lamata (King's College London)
The PIC experience towards the vision of the Digital Twin
Chair: Martin Bishop (King’s College London)
Providing therapy options that are tailored to each patient is the vision of the precision medicine, created by the increasing ability to capture exquisite data about the patient. In this talk it is argued that the a second enabling pillar towards this vision is the increasing ability of computers to reason with data and to build the “digital twin” of the patient, defined as the coherent representation of both its individual data and the knowledge of human physiology. This talk will review early steps of the “digital twin” in the area of cardiovascular medicine, from the perspective of the Personalised In-silico Cardiology (PIC) EU project, together with a critical discussion of the challenges and opportunities ahead. A special emphasis is given on the synergies between mechanistic and statistic models in cardiology, how they are accelerating research, and how they will enable the vision of precision medicine.
INI 1
10:30 to 11:00 Ingelin Steinsland (Norwegian University of Science and Technology)
Learning between digital twins
Chair: Martin Bishop (King’s College London)
This work is motivated by, and is part of, a project that aim to develop digital twins for essential hypertension management and treatment through physically based computer models,  new sensor data and traditional population based data. Our approach is that the individual digital twins should learn from each other. We explore doing this by combining Bayesian model calibration and mixed models for simplified models. This is work in progress.
INI 1
11:00 to 11:30 Morning coffee and poster session
11:30 to 12:00 Benjamin Meder (Ruprecht-Karls-Universität Heidelberg)
Systems Cardiology of Heart Failure
Chair: Richard Clayton (University of Sheffield)
INI 1
12:00 to 12:30 Daniele Schiavazzi (University of Notre Dame)
Quantifying uncertainty in cardiovascular digital twins through model reduction, Bayesian inference and propagation of model ensembles
Chair: Richard Clayton (University of Sheffield)
Cardiovascular disease is one of the leading cause of death in humans, affecting the life of millions of people in the US and abroad. This motivates research in numerical approaches for personalized hemodynamics with the aim of improving early diagnosis, treatment and medical device design. In this context, cardiovascular models are experiencing an increasing recent interest, with the first FDA-approved technologies becoming a market reality, creating new demand for such tools and pushing forward their clinical adoption. However, deterministic analysis of cardiovascular flow is simply inadequate to provide an accurate characterization of the patient physiology and new stochastic approaches need to be developed to efficiently quantify the effects of uncertainty from various sources, e.g., errors and inconsistency in clinical measurements, histological variability in vascular tissue and operator-dependent anatomical segmentation. In this talk, recent efforts to quantify the confidence in predicted clinical indicators from personalized hemodynamic models will be discussed, starting with the construction of zero-, one- and three-dimensional representations of the cardiovascular system. I will discuss the use of parallel adaptive Markov chain Monte Carlo for estimating the parameters of reduced order compartmental models and how improved estimators can be constructed using Bayesian updates at the compartment level. Approaches for uncertainty propagation will also be discussed using estimators constructed from a multi-resolution stochastic expansion of the quantities of interested as well as a multilevel/multifidelity Monte Carlo estimators. Applications will be presented in the context of coronary artery disease, congenital heart disease and detection of pulmonary hypertension in patients affected by heart failure with preserved ejection fraction (also known as diastolic heart failure).
INI 1
12:30 to 13:30 Lunch at Westminster College
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons