M.B. Mohr

Modelling and Imaging Electrophysiology and Contraction of the Heart

A computer model of the human heart is presented, that starts with the electrophysiology of single myocardial cells including all relevant ion channels, spans the de- and repolarization of the heart including the generation of the Electrocardiogram (ECG) and ends with the contraction of the heart that can be measured using 4D Magnetic Resonance Imaging (MRI). The model can be used to better understand physiology and pathophysiology of the heart, to improve diagnostics of infarction and arrhythmia and to enable quantitative therapy planning. It can also be used as a regularization tool to gain better solutions of the ill-posed inverse problem of ECG. Movies of the evolution of electrophysiology of the heart can be reconstructed from Body Surface Potential Maps (BSPM) and MRI, leading to a new non-invasive medical imaging technique.

Modeling of electro-mechanics of human cardiac myocytes: parameterization with numerical minimization techniques

Knowledge of cardiac electro-mechanical phenomena can be achieved by mathematical modeling and numerical simulation. Topic of the work is the assembly and parameterization of an electro-mechanical model of human cardiac myocytes. The model integrates an electrophysiological and a tension development model. This integration and additional adaptation to studies of human myocardium necessitated re-parameterization of several components, which was performed applying different numerical optimization techniques. Results and characteristics of the parameterization are illustrated by numerical experiments. Simulations with the electro-mechanical model show characteristic shapes of the courses of transmembrane voltage, concentration of intracellular calcium, and developed tension.

MATHEMATICAL MODELING OF CARDIAC ELECTRO-MECHANICS: FROM PROTEIN TO ORGAN

Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models. In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively. The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.

Deformation simulation in an elastomechanical ventricular model

The hearts pumping function is dependent on the vitality of the heart muscle, which is mostly composed of contractile cells, so-called myocytes. The orientation of these myocytes throughout the muscle results in a unique profile of contraction allowing the pumping process to be possible. Knowledge of arrangement and physiological properties of these cells permits the creation of realistic computer models. Simulations with computer models can be used e. g. for pre-interventional planning and for educational purposes. The utilized elastomechanical model is based on a spring mass system enhanced by continuum mechanics based methods. A truncated ellipsoid is chosen to represent a ventricle. Three simulation scenarios were chosen, in which parameters varied to simulate behavior of normal dilated, and necrotic tissue. The results of these three studies are discussed with focus on change of inner ventricular volume, tissue volume, and suitability of the elastomechanical ventricular model for pathologic tissue modeling. As deformation results show, the presented model is able to reconstruct pathologic and nonpathologic mechanical properties of myocardium.

Hybrid deformation model of myocardium

Computer models of the heart lead to a better understanding of the physiological and physical processes underlying each heart beat. Various models exist for simulating electrophysiology, excitation propagation, force development and deformation. Simulations can be used to support medical doctors in diagnostics, surgery planning and serve educational purposes. This work focuses on simulating mechanical aspects of a heart. Simulations with electrophysiological, excitation propagation and force development models were carried out. Force development was utilized as input to the mechanical model. A hybrid myocardial deformation model is introduced merging a spring mass system and a continuum mechanical model. Simulations with simple geometries and fiber orientation were conducted to display the models capabilities. Detailed analysis of the deformations of a patch yielded the expected behavior.

Comparison of macroscopic models of excitation and force propagation in the heart.

Computer aided simulations of the heart provide knowledge of phenomena, which are commonly neither visible nor measurable with current techniques. This knowledge can be applied e.g. in cardiologic diagnosis and therapy. A variety of models was created to reconstruct cardiac processes, e.g. electrical propagation and force development. In this work different macroscopic models were compared, i.e. models based on excitation-diffusion equations and cellular automata. The comparison was carried out concerning reconstruct-ability of cardiac phenomena, mathematical and biophysical foundation as well as computational expense. Particularly, the reconstruct-ability of electromechanic feedback mechanisms was examined. Perspectives for further developments and improvements of models were given.

Models of the human heart for simulation of clinical interventions

Detailed models of the human heart are introduced which can serve in conjunction with virtual reality techniques as basis for the simulation of cardiac interventions. The models describe the anatomy, electrical excitation propagation and force development. The anatomical models were constructed with methods of digital image processing basing on photographic images delivered by the Visible Human Project, National Library of Medicine, USA. Appropriate models of electrophysiology and force development are chosen subject to the tissue types. The models are applied to simulate electrical and mechanical processes in the heart.

Electro-mechanics in biventricular models

Cardiac electro-mechanical models are valuable tools to gain insights in physiology and pathophysiology of the heart. Progressive models can be created by fusion of various basic models. In this work biventricular models of cardiac electro-mechanics were developed by fusion of anatomical, electrical, and mechanical models. The importance of anatomical modeling was researched by inclusion of two different anatomical models, i.e. an analytical and a magnetic resonance diffusion tensor imaging based model. The fused models were applied in simulations of physiological behavior and results of these were analyzed. Significant difference of deformation were found, which can be attributed to the anatomical models. The analysis emphasized the importance of appropriate anatomical modeling for simulations of cardiac mechanics.

Incorporating blood pressure load into an elastomechanical ventricular mod

Elastomechanical modeling constitutes an essential step for realistic computer simulations of the cardiac system. The deformation of tissue effects e.g. cellular electrophysiology, which is commonly neglected in electrophysiological simulations due to the lack of efficient mechanical models. This work focuses on extending a mechanical deformation model by including blood pressure as endocardial boundary condition. Four phases are distinguished in a normal heart cycle: isovolumic contraction, isotonic contraction, isometric relaxation, and isotonic relaxation. The first three phases were modeled. The methods modeling intraventricular pressure corresponding to contraction phases are illustrated, applied, and discussed. Simulation results show that the mechanical model is capable of incorporating a pressure load leading to a more realistic contraction behavior. Furthermore, the ejection curve resembles in closer detail measured data

Volumenbasierte Modellierung der Deformation im Myokard ausgehend von Modellen der Kraftentwicklung.

Die computergestützte Simulation der Deformation im Myokard eröffnet der Medizin und Technik Möglichkeiten, das mechanische Verhalten des Herzens zu untersuchen. In dieser Arbeit wird ein Feder-Masse-Dämpfer Modell zur Simulation der Deformation im Myokard vorgestellt, das anhand eines kontinuumsmechanischen Deformationsmodells parametrisiert wurde. Die zur Deformation notwendige Kraftkomponente wird mit Hilfe eines zellulären Automaten berechnet, der durch mikroskopische Kraftmodelle parametrisiert wird. Es werden Simulationen in Myokardausschnitten durchgeführt und die Ergebnisse diskutiert. Keywords— Volumenbasierte Modellierung, Deformation, Myokard, Feder-Masse-Dämpfer Modell