FOMICSDADSI WINTER SCHOOL ON CARDIAC SIMULATIONs 2020
Geometry Modeling and Mesh Generation of the Cardiac Geometry
SpaceTime Approaches in Cardiac Electrophysiology
Electromechanics
Optimization and Inversion Problems Applied to Electrophysiology
FluidStructure Interaction and Heart Valves
Lecture I  Lecture II  
Monday  15:0016:30 (CET) 
16:3017:30 (CET) 
Tuesday 
16:0017:00 (CET) 
17:0018:30 (CET) 
Wednesday 
17:0018:30 (CET) 

Thursday 
17:0018:30 (CET) 

Friday 
17:0018:30 (CET) 
Speaker  
Monday 
Lecture I: Prof. Gernot Plank (Med Uni Gratz) Lecture II: Dr. Suzanne M. Shontz (Kansas University/USI) 
Tuesday 
Lecture I: Dr. Suzanne M. Shontz (Kansas University/USI)
Lecture II: Dr. Simone Pezzuto (USI/ICS/CCMC) 
Wednesday 
Lecture II: Prof. Rolf Krause/Dr. Benedusi Pietro (USI/ICS/CCMC) Dr. Ali Gharaviri (USI/ICS/CCMC) 
Thursday 
Lecture II: Dr. Martin Weiser (Zuse Institute of Berlin, ZIB) 
Friday 
Lecture II: Dr. Maria Nestola (USI/ICS/CCMC/ETHZ) 
Personalized computational model of total electromechanofluidic function of the heart
Using computational models of total heart function that are based on clinical images and parameterized to reflect a given patient's physiology, are a highly promising approach to comprehensively and quantitatively characterize cardiovascular physiology in a given patient. Such models are anticipated to play a pivotal role in future precision medicine as a method to stratify therapies, optimize therapeutic procedures, predict outcomes and thus better inform clinical decision making.
However, translating modeling into a clinically applicable modality a number of key challenges have to be addressed. In particular, expensive computational models must be made efficient enough to be compatible with clinical time frames. As the etiology of most cardiac pathologies comprises multiphysics aspects, requiring the coupling of various physics characterized by very different space and time scales, robust coupling schemes must be conceived. Finally and most importantly, to be of clinical utility generic models must be specialized based on clinical data, which requires complex parameterization and data assimilation procedures to match model behavior with clinical observations.
In this talk our latest advances in building computationally efficient multiphysics models and techniques for their patientspecific parameterization will be presented.
Geometric Modeling and Mesh Generation for Computational Cardiology Simulations
Patientspecific computational cardiology simulations require both geometric model which describes the shape of the heart and a computational mesh on the heart on which the associated PDEs can be solved numerically. Geometric models of the heart are typically generated from the patient’s medical images using the marching cubes method which extracts isosurfaces in order to generate a triangular surface mesh. Alternatively, a parametric representation of the heart’s surface can be generated using spline surfaces. For example, spline surfaces based on Bezier patches or triangles can be generated using the de Casteljau algorithm (or one of its variants). Once the geometric model is created, a computational mesh can then be generated using the boundary surface representation as input. For example, Delaunay or advancing frontbased approaches can be used to generate volume meshes. Finally, the deformations of the heart can be simulated using mesh warping approaches based on the geometry and mechanics of the heart. This talk will be arranged in two parts. In the first part of the talk, we will cover geometric modeling of the cardiac geometry. Generation of static and dynamic computational meshes of the heart will be presented in the second part of the talk. Recent research results will also be presented.
Speaker: Simone Pezzuto (USI/ICS/CCMC)
The pumping function of the heart emerges from a finetuned coupling of electric wave propagation and mechanical contraction. The goal of this lecture is to introduce their mathematical formulation, numerical discretization and efficient implementation.
We will study the bidomain model of cardiac electrophysiology and its application to atrial fibrillation. The bidomain model is a coupled system of a parabolic equation, an elliptic constraint and a large set of ordinary differential equation. It poses significant challenges from a numerical viewpoint, due to the type of solutions. We will also consider simplified models, such as the eikonal equation, which can be quite effective for the personalization of cardiac models. We will present some clinical applications in this respect, including a fast ECG simulator and multifidelity uncertainty quantification.
Mechanically, the heart is an active soft tissue. We will model it as a hyperelastic material with an external active stress determined by the electrophysiology. A number of challenges arise on the computational side: boundary conditions, incompressibility, the role of cardiac fibers and the coupling to systemic circulation. The final part of the lecture is devoted to them, with a brief outlook in terms of applications.
SpaceTime Approaches in Cardiac Electrophysiology
The simulation of the electrical activation of the human heart requires the solution of a timedependent PDE, such as the monodomain model. Traditionally, timestepping methods are used to advance the solution of evolutionary PDEs in time, but these techniques are inherently sequential and therefore they introduce a bottleneck in the overall computational scalability. To achieve parallel efficiency in both space and time, a multilevel spacetime finite element discretization can be employed. The multilevel discretization in time needs special care, that will be discussed in the course. The spacetime discretization gives rise to a large, nonlinear system that can be conveniently distributed among many processors and solved on massively parallel machines. We present novel approaches for the parallel solution and preconditioning of the spacetime systems, which are based on multilevel and domain decomposition ideas as well as on the spectral analysis of the discrete operators of interest. Moreover, since the relevant dynamics of the monodomain solution takes place in a limited region of the spacetime domain, we discuss the usage of an adaptive approach, in both space and time, to reduce the overall time to solution.
Speaker: Ali Gharaviri (USI/ICS/CCMC)
Computer Models as Tools for Personalized Therapy of Atrial Fibrilation
Atrial fibrillation (AF) is a heterogenous cardiac rhythm disorder related to an expansive spectrum of etiologies. Mechanisms underlying AF entails complex interactions among triggers, substrate, and modulators including genetic predisposition, channelopathies, ionic remodeling, and neurohormonal. Despite, extensive research performed so far on AF, little is known about the interaction among these different aspects of the pathophysiology of AF and the relation between individual disease mechanisms and the clinical presentation of the patients. Therefore, the treatment of AF remained far from satisfactory.
Computational models can be used as a surrogate method to understand better the mechanisms underlying AF initiation, perpetuation. These models, which are based on physiology and physics, enable computational simulations to reveal mechanistical and diagnostic information that give us significant insight into better AF treatment.
Speaker: Martin Weiser (ZIB)
Optimization and Inversion in Computational Cardiac Electrophysiology
Reliable predictions of cardiac excitation depend not only on good geometric and physiology models and our ability to simulate them faithfully, but also on the correct parametrization of the models. Given actual measurement data, parameter identification techniques can be used for model personalization. We will formulate the inverse problem of identifying conductivities and scar tissue as an optimization problem and cover aspects of quasiNewton methods, adjoint gradient computation, trajectory storage, multilevel acceleration, and regularization.
Once wellparametrized models are at hand, not only reliable predictions, but also planning of therapies are to some extent possible. Often, this leads to optimization problems of a similar structure as the inverse problem above. Here, we consider a conceptual problem of defibrillation.
Speaker: Maria Nestola (USI/ICS/CCMC/ETH Zurich)
NonFitted Boundary Methods for FluidStructure Interaction Simulations of Prosthetic Aortic Valves
In the last years, the role of the Fluid Structure Interaction (FSI) simulations in the analysis of the cardiovascular system has become the gold standard for assessing the haemodynamic risk in physiological and pathological conditions. To this aim, several approaches have been developed to reproduce the interaction between the blood and the surrounding solid structure, which can be classified in the boundaryfitted and not boundaryfitted method.
In this talk we first present a basic knowledge about fluid dynamics and elastodynamics equations.
Then we give some details about fluid structure intercation modelling. In particular, we present a new framework for the FSI simulations. By taking inspiration from the immersed boundary technique introduced by Peskin and from the Fictitious domain method introduced by Glowinski, we employed the finiteelement method for discretizing the equations of the solid structure and the finitedifference method for simulating the fluid flow. The two codes are coupled by using a variational approach to transfer the data from the fluid to the solid domain and viceversa. For validation and evaluation of the accuracy of the proposed methodology, we present results for an FSI benchmarking configuration which describes the selfinduced oscillating deformations of an elastic beam in a flow channel. Moreover, applications to the FSI simulationsof the bioprosthetic aortic valve are presented.