Remodeling of the transverse tubular system after myocardial infarction in rabbit correlates with local fibrosis: A potential role of biomechanics.

The transverse tubular system (t-system) of ventricular cardiomyocytes is essential for efficient excitation-contraction coupling. In cardiac diseases, such as heart failure, remodeling of the t-system contributes to reduced cardiac contractility. However, mechanisms of t-system remodeling are incompletely understood. Prior studies suggested an association with altered cardiac biomechanics and gene expression in disease. Since fibrosis may alter tissue biomechanics, we investigated the local microscopic association of t-system remodeling with fibrosis in a rabbit model of myocardial infarction (MI). Biopsies were taken from the MI border zone of 6 infarcted hearts and from 6 control hearts. Using confocal microscopy and automated image analysis, we quantified t-system integrity (ITT) and the local fraction of extracellular matrix (fECM). In control, fECM was 18 ± 0.3%. ITT was high and homogeneous (0.07 ± 0.006), and did not correlate with fECM (R2 = 0.05 ± 0.02). The MI border zone exhibited increased fECM within 3 mm from the infarct scar (30 ± 3.5%, p < 0.01 vs control), indicating fibrosis. Myocytes in the MI border zone exhibited significant t-system remodeling, with dilated, sheet-like components, resulting in low ITT (0.03 ± 0.008, p < 0.001 vs control). While both fECM and t-system remodeling decreased with infarct distance, ITT correlated better with decreasing fECM (R2 = 0.44) than with infarct distance (R2 = 0.24, p < 0.05). Our results show that t-system remodeling in the rabbit MI border zone resembles a phenotype previously described in human heart failure. T-system remodeling correlated with the amount of local fibrosis, which is known to stiffen cardiac tissue, but was not found in regions without fibrosis. Thus, locally altered tissue mechanics may contribute to t-system remodeling.

Cellular electrophysiological principles that modulate secretion from synovial fibroblasts.

Rheumatoid arthritis (RA) is a progressive disease that affects both pediatric and adult populations. The cellular basis for RA has been investigated extensively using animal models, human tissues and isolated cells in culture. However, many aspects of its aetiology and molecular mechanisms remain unknown. Some of the electrophysiological principles that regulate secretion of essential lubricants (hyaluronan and lubricin) and cytokines from synovial fibroblasts have been identified. Data sets describing the main types of ion channels that are expressed in human synovial fibroblast preparations have begun to provide important new insights into the interplay among: (i) ion fluxes, (ii) Ca2+ release from the endoplasmic reticulum, (iii) intercellular coupling, and (iv) both transient and longer duration changes in synovial fibroblast membrane potential. A combination of this information, knowledge of similar patterns of responses in cells that regulate the immune system, and the availability of adult human synovial fibroblasts are likely to provide new pathophysiological insights.

Analyzing Remodeling of Cardiac Tissue: A Comprehensive Approach Based on Confocal Microscopy and 3D Reconstructions.

Microstructural characterization of cardiac tissue and its remodeling in disease is a crucial step in many basic research projects. We present a comprehensive approach for three-dimensional characterization of cardiac tissue at the submicrometer scale. We developed a compression-free mounting method as well as labeling and imaging protocols that facilitate acquisition of three-dimensional image stacks with scanning confocal microscopy. We evaluated the approach with normal and infarcted ventricular tissue. We used the acquired image stacks for segmentation, quantitative analysis and visualization of important tissue components. In contrast to conventional mounting, compression-free mounting preserved cell shapes, capillary lumens and extracellular laminas. Furthermore, the new approach and imaging protocols resulted in high signal-to-noise ratios at depths up to 60 µm. This allowed extensive analyzes revealing major differences in volume fractions and distribution of cardiomyocytes, blood vessels, fibroblasts, myofibroblasts and extracellular space in control vs. infarct border zone. Our results show that the developed approach yields comprehensive data on microstructure of cardiac tissue and its remodeling in disease. In contrast to other approaches, it allows quantitative assessment of all major tissue components. Furthermore, we suggest that the approach will provide important data for physiological models of cardiac tissue at the submicrometer scale.

Minimum Information about a Cardiac Electrophysiology Experiment (MICEE): standardised reporting for model reproducibility, interoperability, and data sharing.

Cardiac experimental electrophysiology is in need of a well-defined Minimum Information Standard for recording, annotating, and reporting experimental data. As a step towards establishing this, we present a draft standard, called Minimum Information about a Cardiac Electrophysiology Experiment (MICEE). The ultimate goal is to develop a useful tool for cardiac electrophysiologists which facilitates and improves dissemination of the minimum information necessary for reproduction of cardiac electrophysiology research, allowing for easier comparison and utilisation of findings by others. It is hoped that this will enhance the integration of individual results into experimental, computational, and conceptual models. In its present form, this draft is intended for assessment and development by the research community. We invite the reader to join this effort, and, if deemed productive, implement the Minimum Information about a Cardiac Electrophysiology Experiment standard in their own work.

Models of cardiac tissue electrophysiology: progress, challenges and open questions.

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Experimental and computational studies of strain-conduction velocity relationships in cardiac tissue.

Velocity of electrical conduction in cardiac tissue is a function of mechanical strain. Although strain-modulated velocity is a well established finding in experimental cardiology, its underlying mechanisms are not well understood. In this work, we summarized potential factors contributing to strain-velocity relationships and reviewed related experimental and computational studies. We presented results from our experimental studies on rabbit papillary muscle, which supported a biphasic relationship of strain and velocity under uni-axial straining conditions. In the low strain range, the strain-velocity relationship was positive. Conduction velocity peaked with 0.59 m/s at 100% strain corresponding to maximal force development. In the high strain range, the relationship was negative. Conduction was reversibly blocked at 118+/-1.8% strain. Reversible block occurred also in the presence of streptomycin. Furthermore, our studies revealed a moderate hysteresis of conduction velocity, which was reduced by streptomycin. We reconstructed several features of the strain-velocity relationship in a computational study with a myocyte strand. The modeling included strain-modulation of intracellular conductivity and stretch-activated cation non-selective ion channels. The computational study supported our hypotheses, that the positive strain-velocity relationship at low strain is caused by strain-modulation of intracellular conductivity and the negative relationship at high strain results from activity of stretch-activated channels. Conduction block was not reconstructed in our computational studies. We concluded this work by sketching a hypothesis for strain-modulation of conduction and conduction block in papillary muscle. We suggest that this hypothesis can also explain uni-axially measured strain-conduction velocity relationships in other types of cardiac tissue, but apparently necessitates adjustments to reconstruct pressure or volume related changes of velocity in atria and ventricles.

A software framework for solving bioelectrical field problems based on finite elements.

Computational modeling and simulation can provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Commonly, the modeling is based on Maxwell's and Poisson's equations for electromagnetic and electric fields, respectively, and numerical techniques are applied for field calculation such as the finite element and finite differences methods. Focus of this work are finite element methods, which are based on an element-wise discretization of the spatial domain. These methods can be classified on the element's geometry, e.g. triangles, tetrahedrons and hexahedrons, and the underlying interpolation functions, e.g. polynomials of various order. Aim of this work is to describe finite element-based approaches and their application to extend the problem-solving environment SCIRun/BioPSE. Finite elements of various types were integrated and methods for interpolation and integration were implemented. General methods for creation of finite element system matrices and boundary conditions were incorporated. The extension provides flexible means for geometric modeling, physical simulation, and visualization with particular application in solving bioelectric field problems.

Conduction velocity in myocardium modulated by strain: measurement instrumentation and initial results.

Quantification of the relationship between strain and excitation velocity in cardiac muscle gives important insights into the significance and contribution of microstructure and several transmembrane proteins to cardiac electrophysiology. In this study we introduce a measurement and analysis system for quantification of the relationship in papillary muscle of small mammals, superfused and kept in a physiological environment. A novelty of the approach is the extensive automation and computerization of the measurement and analysis procedure. Initial results indicate that the conduction velocity is strain dependent in such a manner that several components contribute to establish this relationship. Further studies will help to quantify the relationship and importance of the components.

A software framework for solving problems of bioelectricity applying high-order finite elements.

Electrical activity in biological media can be described in a mathematical way, which is applicable to computer-based simulation. Biophysically mathematical descriptions provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Examples of these descriptions are Maxwell's and Poisson's equations for electromagnetic and electric fields. Commonly, numerical techniques are applied to calculate electrical fields, e.g. the finite element method. Finite elements can be classified on the order of the underlying Interpolation. High-order finite elements provide enhanced geometric flexibility and can increase the accuracy of a solution. The aim of this work is the design of a framework for describing and solving high-order finite elements in the SCIRun/BioPSE software system, which allows geometric modeling, simulation, and visualization for solving bioelectric field problems. Currently, only low-order elements are supported. Our design for high-order elements concerns interpolation of geometry and physical fields. The design is illustrated by an implementation of one-dimensional elements with cubic interpolation of geometry and field variables.

Hyperelastic description of elastomechanic properties of the heart: a new material law and its application.

Knowledge concerning passive mechanic cardiac properties is necessary to model behavior of whole hearts. Commonly, a continuum mechanics based description is chosen in conjunction with the finite element method. The aim of this work is to summarize, derive and evaluate hyperelastic material laws for inhomogeneous, anisotropic myocardium. Hence, different material laws were set up and their parameters were determined taking measurement data in literature into account. The material laws were compared from a theoretical and numerical point of view. Furthermore, the application of continuum mechanics based methods is evaluated concerning aspects of numerical solution and spatial discretisation. In further work the laws will be implemented and integrated in an existing software environment, which allows the calculation of deformations in complex geometries.

Modeling force development in the sarcomere in consideration of electromechanical coupling.

Models of the cellular force development simulate the contractive behavior of the sarcomere. In conjunction with electrophysiological models they can contribute to a better comprehension of physiology and pathologies. Aim of this study is to examine the coupling of cellular electrophysiological processes and force development. For that a graphical user interface was developed to simplify the parameterization and calculation of the models as well as to present the results graphically. A feedback mechanism is introduced to pay attention to close connections between force development and intracellular processes. On basis of various tests with different boundary conditions, new force models are developed, parameterized, validated and compared with models in literature. In future studies the results will be tested in multiple cell organization.

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.

Excitation propagation and force development in the left ventricle of the visible female data set.

Simulations of the electro-mechanical behavior of the heart improve the comprehension of the mechanisms of the cardiovascular system. In this study a left ventricular model including electrical excitation and force development is presented. The electrical model consists of a complex electrophysiological cell model and a monodomain excitation diffusion model. The force development bases on the intracellular calcium concentration and is calculated with a force model. It consists--like the electrophysiological model--of non-linear coupled differential equations. Simulations are obtained in a realistic and anisotropic model of the left ventricle of the Visible Female data set provided by the National Library of Medicine, USA. Effects to the mechanical behavior will be examined in future.

Comparison of regularization techniques for the reconstruction of transmembrane potentials in the heart.

Computer simulations to reconstruct the transmembrane potential distribution were performed for an anisotropic finite element model of the heart. Transmembrane potential was reconstructed in the form of 3D patches. Test patterns generated with a cellular automaton were used. Tikhonov 0-order and 2-order reconstruction techniques were compared. Tikhonov 2-order regularization was shown to deliver better solutions; this is demonstrated by the inspection of the source space of the inverse problem and by the comparison of the correlation coefficients between the reconstructed and original distributions. Time information was incorporated into the regularization.

[Computer models of the electrophysiological properties of the heart]. / Computermodelle der elektrophysiologischen Eigenschaften des Herzens.

Computer models of the heart can improve the understanding of the electrophysiological processes in healthy and diseased heart. They become more and more important for detailed diagnosis of arrhythmias and for optimization of therapy. Models of myocardium cells known today are described--they are based on the properties of all relevant ion channels in the cell membrane. Then it is demonstrated, how many cells can be joined to form a cell patch and how finally the complete heart can be modelled. A simpler approach is using a so called cellular automation that allows for a significant reduction of calculation time while sacrificing some accordance to reality. Adaptive cellular automations allow for a fast simulation with acceptable accuracy. Using them some results were gained for the simulation of typical arrhythmias, in the field of validation using an animal model and for therapy planning with RF-ablation.

Development of a human body model for numerical calculation of electrical fields.

Knowledge of the distribution of electrical fields in the human body is of importance for scientists, engineers and physicians. This paper shows one way to achieve this knowledge by numerical calculation based on macroscopic models of the human body. An anatomical model is created by preprocessing, segmentation and classification of the digital images within the Visible Man data set. Conductivity models are derived, which describe the distribution of electrical conductivity in the human body. A conductivity model is applied to solve an exemplary forward problem in electrophysiology, which consist of the calculation of the electrical field distribution arising from cardiac sources. The cardiac sources are obtained by a model of the excitation process within the heart. The calculation of electrical fields is carried out numerically by employing the finite difference method.