Virtual Heart Models: Multi-Physics Approaches to Computational Cardiology (VHEART)

Heart disease is the number one cause of death in industrialized nations. Despite the broad class of treatment techniques such as medication, surgery and tissue-engineered therapies, heart disease remains to be one of the most frequent, disabling, and life-threatening diseases. In Europe it accounts for almost half of overall annual mortality rate. In the European Union (EU) alone, cardiovascular disease causes over 2 million deaths per year. The cost of cardiovascular disease to the EU economy is €192 billion per year. As opposed to the traditional trial-and-error based therapies, a systematic, personalized simulation-aided approach offers a great potential for understanding, diagnosing, and treating heart failure through the sound understanding of functional and structural changes in the infarcted tissue and the computational tools of multi-scale solid mechanics. The proposed research aims: (1) to develop multi-scale models of computational cardiac electrophysiology, (2) to model the fully coupled electromechanics of the heart through a novel micro-structurally based kinematic approach, (3) to couple the electromechanical computational tool with the ionic models of cardiac electrophysiology, (4) to employ the new multi-scale tools of computational cardiology to explore the underlying complex mechanisms of heart diseases and thereby guide personalized cardiac therapies. The anticipated outcomes are: (A) a multi-scale computational electrophysiological tool that incorporates multi-physics ionic models in the implicit bidomain framework, (B) a better understanding of underlying physiological reasons for electrophysiological cardiac disease such as arrhythmia, left and right bundle blocks, (C) a novel, micro-structurally based, computationally efficient, modular electromechanical computational tool, (D) a virtual test environment for the patient-specific optimization of cardiac therapies and surgical procedures.EU, Funded under :FP7-PEOPLE-2011-CI

Eşyönsüz Mikro Yapıya Sahip Kalp Dokusundaki Büyümenin Modellenmesi Üzerine

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Bu çalışma eşyönsüz mikro yapıya sahip kalp dokusunda meydana gelen fizyolojik ve patolojik büyümenin modellenmesi için geliştirilen genel bir kinematik yaklaşımı konu almaktadır. Bu amaçla, şekil değiştirme gradyanı çarpımsal olarak elastik şekil değiştirme gradyanı ve büyüme tensörlerine parçalanmıştır. Büyümenin yönü kalp dokusunun mikro yapısı tarafından kontrol edilirken, büyümenin miktarı skalar büyüme değişkeni ile belirlenmektedir. Bu büyüme değişkeninin zamanla değişimini de hipertrofinin tipine göre değişen büyüme kriteri ve onun sınırlandırılmış çarpanı tarafından kontrol edilmektedir. Büyüme tensörü elde edildikten sonra şekil değiştirme gradyanının elastik kısmı hesaplanır. Bu tensör cinsinden ifade edilmiş olan serbest enerji fonksiyonundan Doyle-Ericksen formülü yardımı ile Kirchhoff gerilme tensörü elde edilir. Anahtar Kelimeler: Biyomekanik, Kalp Mekaniği, Büyüme, HipertrofiThis work is concerned with the generalized kinematic framework for finite growth in cardiac tissue. For this purpose, the deformation gradient is multiplicatively decomposed into an elastic part and a growth part. This naturally brings about an incompatible intermediate growth configuration. While the direction of growth is dictated by the architecture of the cardiac tissue, the amount of growth is determined by a scalar growth field whose evolution is governed by a corresponding disease-dependent growth criterion function and its bounded coefficient. Once the growth tensor is known, the elastic part of the deformation gradient, which directly enters the orthotropic energy storage function, can be readily obtained and the relevant stress tensor is determined through the Doyle-Ericksen formula. Keywords: Biomechanics, Cardiac Mechanics, Growth, Hypertroph

Elastica-based strain energy functions for soft biological tissue

Continuum strain energy density functions are developed for soft biological tissues that possess slender, fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to obtain a continuum strain energy density function. Notably, we avoid solving the exact, fourth-order, non-linear, partial differential equation for deformation of the elastica by resorting to other assumptions, kinematic and energetic, on the response of individual, elastica-like fibrils. The formulation, discussion of responses of different models and comparison with experiment are presented

Computational modeling of growth: systemic and pulmonary hypertension in the heart

We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension

Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart

Background-Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or flexible bands, increase AML strains

Mikro-Makro Ansätze für gummi- und glassartige Polymere : prädiktive, mikromechanisch basierte Modelle und Simulationen

This work is concerned with the development of physically motivated constitutive models for the description of the material behavior of rubbery and glassy polymers. The particular focus of the thesis is placed on elasticity, finite viscoelasticity, deformation-induced Mullins-type damage in rubbery polymers, and finite viscoplasticity of amorphous glassy polymers. The models developed possess the intrinsic character of a micro-macro transition that, in turn, allows us to incorporate the physical mechanisms stemming from a micro-structure of the material through geometrically well defined kinematic measures and in terms of physically motivated material parameters. The proposed approaches make use of a micro-structure that is symbolized by a unit sphere, the so-called micro-sphere. The surface of the micro-sphere represents a continuous distribution of chain orientations in space. A key idea of the proposed constitutive framework may be considered as a two-step procedure that incorporates the set up of micromechanically-based constitutive models for a single chain orientation and the definition of the macroscopic stress response through a directly evaluated homogenization of state variables. The disribution of micro-state variables are defined on the micro-sphere of space orientations in a discrete manner. The proposed models are further furnished with the associated algorithmic procedures that perform the update of internal variables and computation of stresses and tangent moduli in a way consistent with the employed integration scheme. The modeling performance of the models is tested against broad range of homogeneous and inhomogeneous experimental data with particular regard to their predictive simulation capabilities.Die vorliegende Arbeit befasst sich mit der Entwicklung von physikalisch motivierten Modellen für die Beschreibung des Materialverhaltens von gummi- und glasartigen Polymeren. Ein besonderer Fokus dieser Arbeit liegt auf der Elastizität, finiten Viskoelastizität, deformationsinduzierten Mullins-Typ Schädigung in gummiartigen Polymeren sowie auf der Viskoplastizität amorpher glasartiger Polymere bei finiten Deformationen. Die entwickelten Modelle besitzen intrinsische mikro-makro Übergangseigenschaften die uns erlauben Mechanismen der Mikrostruktur zu berücksichtigen. Physikalisch motivierte Materialparameter folgen aus der geometrischen Betrachtung diese Mechanismen. Vorgeschlagen wird eine Mikrostruktur, die durch eine sogenannte Mikrokugel charakterisiert ist. Die Oberfläche der Mikrokugel stellt die stetige Verteilung der räumlichen Orientierung der Polymerketten dar. Die Hauptidee des vorgeschlagenen konstitutiven Rahmens beruht auf zwei Schritten: der Entwicklung eines mikromechanisch motivierten konstitutiven Modells einer einzelnen Polymerkette und der Definition der makroskopischen Spannungen die aus einem homogenisierungsverfahren der Zustandesvariablen folgen. Die Verteilung und die räumliche Orientierung der mikroskopischen Zustandsvariablen werden in diskreter Weise auf der Mikrokugel definiert. Die diskutierten Modelle werden weiter mit den zugehörigen algorithmischen Verfahren ausgestattet, die einerseits die Aktualisierung der internen Variablen durchführt und andererseits die Berechnung von Spannungen und konsistenten Tangentenmodulen bereitstellt. Die Leistungsfähigkeit der Modelle wird anhand zahlreicher Vergleiche homogener und inhomogener Experimente mit den entsprechenden Simulationen gezeigt

Fitzhugh–Nagumo Equation

The Fitzhugh–Nagumo equation (FHN) is a set of nonlinear differential equations that efficiently describes the excitation of cells through two variables

Electromechanics of the heart: a unified approach to the strongly coupled excitation-contraction problem

This manuscript is concerned with a novel, unified finite element approach to fully coupled cardiac electromechanics. The intrinsic coupling arises from both the excitation-induced contraction of cardiac cells and the deformation-induced generation of current due to the opening of ion channels. In contrast to the existing numerical approaches suggested in the literature, which devise staggered algorithms through distinct numerical methods for the respective electrical and mechanical problems, we propose a fully implicit, entirely finite element-based modular approach. To this end, the governing differential equations that are coupled through constitutive equations are recast into the corresponding weak forms through the conventional isoparametric Galerkin method. The resultant non-linear weighted residual terms are then consistently linearized. The system of coupled algebraic equations obtained through discretization is solved monolithically. The put-forward modular algorithmic setting leads to an unconditionally stable and geometrically flexible framework that lays a firm foundation for the extension of constitutive equations towards more complex ionic models of cardiac electrophysiology and the strain energy functions of cardiac mechanics. The performance of the proposed approach is demonstrated through three-dimensional illustrative initial boundary-value problems that include a coupled electromechanical analysis of a biventricular generic heart model