Abstract:

Niflumic acid [2-((3-(trifluoromethyl)phenyl)amino)-3-pyridinecarboxylic acid, NFA] is a nonsteroidal anti-inflammatory drug that also blocks or modulates the gating of a wide spectrum of ion channels. Here we investigated the mechanism of channel activation by NFA on ether-a-go-go-related gene (ERG) K(+) channel subtypes expressed in Xenopus laevis oocytes using two-electrode voltage-clamp techniques. NFA acted from the extracellular side of the membrane to differentially enhance ERG channel currents independent of channel state. At 1 mM, NFA shifted the half-point for activation by -6, -18, and -11 mV for ERG1, ERG2, and ERG3 channels, respectively. The half-point for channel inactivation was shifted by +5 to +9 mV by NFA. The structural basis for the ERG subtype-specific response to NFA was explored with chimeric channels and site-directed mutagenesis. The molecular determinants of enhanced sensitivity of ERG2 channels to NFA were isolated to an Arg and a Thr triplet in the extracellular S3-S4 linker.

Abstract:

A 3-D reconstruction of the coronary arteries offers great advantages in the diagnosis and treatment of cardiovascular disease, compared to 2-D X-ray angiograms. Besides improved roadmapping, quantitative vessel analysis is possible. Due to the heart's motion, rotational coronary angiography typically provides only 5-10 projections for the reconstruction of each cardiac phase, which leads to a strongly undersampled reconstruction problem. Such an ill-posed problem can be approached with regularized iterative methods. The coronary arteries cover only a small fraction of the reconstruction volume. Therefore, the minimization of the mbiL(1) norm of the reconstructed image, favoring spatially sparse images, is a suitable regularization. Additional problems are overlaid background structures and projection truncation, which can be alleviated by background reduction using a morphological top-hat filter. This paper quantitatively evaluates image reconstruction based on these ideas on software phantom data, in terms of reconstructed absorption coefficients and vessel radii. Results for different algorithms and different input data sets are compared. First results for electrocardiogram-gated reconstruction from clinical catheter-based rotational X-ray coronary angiography are presented. Excellent 3-D image quality can be achieved.

Abstract:

The quality of three-dimensional (3D) reconstructions of the coronary arteries from rotational coronary angiography depends on the selected phase point. Inconsistencies in the projection data, due to heart motion, degrade the image quality. Here, a method for the automatic selection of the optimum phase points for reconstruction is presented.The method aims at determining heart phases with minimum inconsistency of the motion state in the selected projection data. This is achieved by calculating an error measure which describes the inconsistency of the vessel centerline geometry in three dimensions for all cardiac phases. The phases with minimum inconsistency are then selected as optimum reconstruction phases. The method's feasibility was tested on 22 clinical cases. One late-diastolic and one end-systolic optimum phase were determined automatically for each case. For comparison, three observers visually determined the optimum phases.Overall, 82% of the 44 automatically determined phases delivered optimum image quality, only 5% showed considerably lower quality than the visually determined optimum phase. For all 22 cases at least one of the two automatically determined phases yielded optimum quality.In a first test the method proved to robustly determine optimum reconstruction phase points.

Abstract:

Three-dimensional reconstruction of coronary arteries can be performed during x-ray-guided interventions by gated reconstruction from a rotational coronary angiography sequence. Due to imperfect gating and cardiac or breathing motion, the heart's motion state might not be the same in all projections used for the reconstruction of one cardiac phase. The motion state inconsistency causes motion artefacts and degrades the reconstruction quality. These effects can be reduced by a projection-based 2D motion compensation method. Using maximum-intensity forward projections of an initial uncompensated reconstruction as reference, the projection data are transformed elastically to improve the consistency with respect to the heart's motion state. A fast iterative closest-point algorithm working on vessel centrelines is employed for estimating the optimum transformation. Motion compensation is carried out prior to and independently from a final reconstruction. The motion compensation improves the accuracy of reconstructed vessel radii and the image contrast in a software phantom study. Reconstructions of human clinical cases are presented, in which the motion compensation substantially reduces motion blur and improves contrast and visibility of the coronary arteries.

Abstract:

BACKGROUND: Genetic predisposition is believed to be responsible for most clinically significant arrhythmias; however, suitable genetic animal models to study disease mechanisms and evaluate new treatment strategies are largely lacking. METHODS AND RESULTS: In search of suitable arrhythmia models, we isolated the zebrafish mutation reggae (reg), which displays clinical features of the malignant human short-QT syndrome such as accelerated cardiac repolarization accompanied by cardiac fibrillation. By positional cloning, we identified the reg mutation that resides within the voltage sensor of the zebrafish ether-à-go-go-related gene (zERG) potassium channel. The mutation causes premature zERG channel activation and defective inactivation, which results in shortened action potential duration and accelerated cardiac repolarization. Genetic and pharmacological inhibition of zERG rescues recessive reg mutant embryos, which confirms the gain-of-function effect of the reg mutation on zERG channel function in vivo. Accordingly, QT intervals in ECGs from heterozygous and homozygous reg mutant adult zebrafish are considerably shorter than in wild-type zebrafish. CONCLUSIONS: With its molecular and pathophysiological concordance to the human arrhythmia syndrome, zebrafish reg represents the first animal model for human short-QT syndrome.

Abstract:

Atrial fibrillation (AF) is a common cardiac disease of genuine clinical concern with high rates of morbidity, leading to major personal and National Health Service costs. Computer modelling of AF using biophysically detailed cellular models with realistic 3D anatomical geometry allows investigation of the underlying ionic mechanisms in far more detail than with experimental physiology. We have developed a 3D virtual human atrium that combines detailed cellular electrophysiology including ion channel kinetics and homeostasis of ionic concentrations with anatomical details. The segmented anatomical structure and the multi- variable nature of the system make the 3D simulations of AF computationally large and intensive.

Abstract:

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

Abstract:

Ablation strategies to prevent episodes of paroxysmal atrial fibrillation (AF) have been subject to many clinical studies. The issues mainly concern pattern and transmurality of the lesions. This paper investigates ten different ablation strategies on a multilayered 3-D anatomical model of the atria with respect to 23 different setups of AF initiation in a biophysical computer model. There were 495 simulations carried out showing that circumferential lesions around the pulmonary veins (PVs) yield the highest success rate if at least two additional linear lesions are carried out. The findings compare with clinical studies as well as with other computer simulations. The anatomy and the setup of ectopic beats play an important role in the initiation and maintenance of AF as well as the resulting therapy. The computer model presented in this paper is a suitable tool to investigate different ablation strategies. By including individual patient anatomy and electrophysiological measurement, the model could be parameterized to yield an effective tool for future investigation of tailored ablation strategies and their effects on atrial fibrillation.

Abstract:

With scanning confocal microscopy we obtained three-dimensional (3D) reconstructions of the transverse tubular system (t-system) of rabbit ventricular cells. We accomplished this by labeling the t-system with dextran linked to fluorescein or, alternatively, wheat-germ agglutinin conjugated to an Alexa fluor dye. Image processing and visualization techniques allowed us to reconstruct the t-system in three dimensions. In a myocyte lying flat on a coverslip, t-tubules typically progressed from its upper and lower surfaces. 3D reconstructions of the t-tubules also suggested that some of them progressed from the sides of the cell. The analysis of single t-tubules revealed novel morphological features. The average diameter of single t-tubules from six cells was estimated to 448172nm (mean SD, number of t-tubules 348, number of cross sections 5323). From reconstructions we were able to identify constrictions occurring every 1.871.09m along the principal axis of the tubule. The cross-sectional area of these constrictions was reduced to an average of 57.727.5% (number of constrictions 170) of the adjacent local maximal areas. Principal component analysis revealed flattening of t-tubular cross sections, confirming findings that we obtained from electron micrographs. Dextran- and wheat-germ agglutinin-associated signals were correlated in the t-system and are therefore equally good markers. The 3D structure of the t-system in rabbit ventricular myocytes seems to be less complex than that found in rat. Moreover, we found that t-tubules in rabbit have approximately twice the diameter of those in rat. We speculate that the constrictions (or regions between them) are sites of dyadic clefts and therefore can provide geometric markers for colocalizing dyadic proteins. In consideration of the resolution of the imaging system, we suggest that our methods permit us to obtain spatially resolved 3D reconstructions of the t-system in rabbit cells. We also propose that our methods allow us to characterize pathological defects of the t-system, e.g., its remodeling as a result of heart failure.

Abstract:

Die großen Trends der Medizintechnik Biomolekularisierung, Miniaturisierung, Computerisierung werden beschrieben und die gesellschaftlichen Rahmenbedingungen, unter denen in Zukunft Innovationen der Medizintechnik entstehen, werden analysiert. Einige Fokusthemen der Medizintechnik werden etwas detaillierter betrachtet: Was sind die interessanten Forschungsvorhaben von heute, die möglicherweise morgen Wirklichkeit werden?

Abstract:

Es wird eine Methode beschrieben, wie medizinische Bilder des Herzens modellbasiert mit EKG-Daten verknüpft werden können, um damit zu einer spezifischen Diagnostik und zu einer besseren Therapieplanung in der Kardiologie zu gelangen. Zunächst wird aus MRT- oder CT-Bildern des Patienten die Geometrie seines Herzens ermittelt. Elektrokardiographische Messungen an der Körperoberfläche (EKG oder Body Surface Potential Mapping) und aus dem Inneren des Herzens (intracardial mapping) werden aufgenommen und die Orte der Messung in den Bilddatensatz eingetragen (registration). Ein elektrophysiologisches Computermodell vom Herzen des Patienten wird mit Hilfe der elektrophysiologischen Messdaten iterativ angepasst. Schließlich entsteht im Computer ein virtuelles Herz des Patienten, welches sowohl die Geometrie als auch die Elektrophysiologie wiedergibt. Ein Modell der Vorhöfe hat beispielsweise das Potenzial, die Ursachen von Vorhofflimmern zu erkennen und die Radiofrequenz-Ablationsstrategie zu optimieren. Ein Modell der Ventrikel des Herzens kann helfen, genetisch bedingte Rhythmusstörungen besser zu verstehen oder auch die Parameter bei der kardialen Resynchronisationstherapie zu optimieren. Die Modellierung des Herzens mit einem Infarktgebiet könnte die elektrophysiologischen Auswirkungen des Infarktes beschreiben und die Risikostratifizierung für gefährliche ventrikuläre Arrhythmien unterstützen oder die Erfolgsrate bei ventrikulären Ablationen erhöhen.

Abstract:

The modelling of the relationship between QT and RR intervals is an important issue for pharmaceuticalresearch on the way to new drugs. Pharmaceutical industries have to thoroughly investigate potential effects of their medicines on QT intervals since QT prolongation is considered as a marker of the proarrhythmia risk. As QT intervals depend on RR intervals there is an obvious interest in modelling the QT-RR relationship. Static formulas to correct QT for RR are well known, but a dynamic dependencyis mainly observed.Two models of dynamic QT-RR relationships are introduced to eliminate the heart rate dependent part out of the QT interval. These models are based on heart cell measurements and simulations and are validated by Holter ECG data.

Abstract:

Numerous studies about the effects in human body of high frequency magnetic fields on the one hand and extremely low frequency fields on the other hand have been carried out. This is not the case for the mid frequency range around 100 kHz. When applying external magnetic fields to the human body in this frequency range both electric stimulation and thermal heating effects have to be considered. Magnetic Particle Imaging (MPI), a new imaging technique, and Hyperthermia, a tumor treatment therapy, both apply magnetic fields in a frequency range around 100 kHz. In MPI thermal heating of the body has to be prevented, whereas in Hyperthermia a temperature increase of about 4 K in the target region is desirable. Induced currents may lead to muscle stimulation which is not acceptable above a certain threshold. This paper presents the results of induced current densities and SAR in a numeric field calculation simulation. For the model of the human body the torso of the Visible Man Dataset has been employed, along with the dielectric properties of biological tissues investigated by Gabriel & Gabriel. The model has been exposed to a sinusoidal magnetic field with an amplitude of 10 mT. The results of the induced current densities and SAR values have been compared with the currently valid official guidelines for limiting exposure to time-varying electric, magnetic and electromagnetic fields by the International Commission on Non-Ionizing Radiation Protection (ICNIRP). It turns out that limits of induced current densities are reached by applying a magnetic flux density of 10 mT and the SAR limit even is exceeded.

Abstract:

After mathematical modeling of the healthy heart now modeling of diseases comes into the focus of research. Modeling of arrhythmias already shows a large degree of realism. This offers the chance of more detailed diagnosis and computer assisted therapy planning. Options for genetic diseases (channelopathies like Long-QT-syndrome), infarction and infarction-induced ventricular fibrillation, atrial fibrillation (AF) and cardiac resynchronization therapy are demonstrated.

Abstract:

Three-dimensional (3-D) reconstruction of the coronary arteries from a rotational X-ray angiography sequence can support diagnosis of coronary artery disease, treatment planning, and intervention guidance during catheter interventions. 3-D reconstruction enables quantitative vessel analysis, including vessel dynamics from a time-series of reconstructions. This contribution presents a method for reconstructing coronary arteries with high contrast and high level of detail. It employs an iterative reconstruction algorithm in combination with projection-based motion compensation. An efficient implementation using a graphics processing unit delivers reconstruction times close to clinically acceptable values. Reconstructions from clinical human cases, acquired on an interventional C-arm system, are presented. Excellent image quality is achieved.

Abstract:

Image registration is used to reduce movement artifacts caused by contracting heart muscle in transmembrane voltage measurements using fluorescence microscopy. The applied registration methods include Thin-Plate Splines (TPS) and Gaussian Elastic Body Splines (GEBS). Landmarks are established automatically using regional cross-correlation. Then these landmarks are filtered for meaningful correspondences by requiring a minimum correlation coefficient and clustering adjacent and identical displacements. Registration of an image sequence showing a contracting muscle is realized by spatially aligning the images at maximum contraction and at rest. For the other images the movement of the muscle is interpolated using an analytical description of the contraction of heart muscle.TPS cause amplification of displacements at the image border, while GEBS restrict landmarks influence to a local region. Over a set of 81 images GEBS are shown to register images better and more robust than TPS, which in some cases cannot reduce movements. Validation through visualization of transmembrane voltages on contracting muscle reveals that GEBS registration removes movement artifacts better than TPS. Image regions with prominent structures are successfully tackled by GEBS registration.

Abstract:

Ventricular premature beats (VPB) occur when a cardiac depolarization is initiated from a focus in the ventricle instead of the sinoatrial node. Because the ventricular electrical excitation is not started from the intraventriclular conduction system, the excitation propagation in the ventricles behaves in an abnormal manner. This results in an extra asynchronous contraction of the ventricles. In addition VPBs can trigger life-threatening heart arrhythmias. Applying catheter ablation can cure VPB. Therefore it is of importance to localize the origin of VPB using a non-invasive approach before interventional treatment. In this work the inverse problem of electrocardiography is deployed to reconstruct electrical sources in the ventricles, from which the origin of VPB can be identified. By using a spatiotemporal maximum a posteriori (MAP) based regularization the quality of reconstructions is improved. In this work forward calculations with various VPBs are employed to construct a statistical a priori information.

Abstract:

Solving the forward problem of electrocardiography provides a better understanding of electrical activities in the heart. The inverse problem of electrocardiography enables a direct view of cardiac sources without catheter interventions. Today the forward and inverse computation is most often performed in a static model, which doesn't take into account the heart motion and may result in considerable errors in both forward and inverse solutions. In this work a dynamic heart model is developed. With this model the effect of the heart motion on the forward and inverse solutions is investigated.

Abstract:

Computer simulations can significantly improve comprehension of cardiac electrophysiology. A mathematical model for the simulation of complex cardiac electrophysiology is the bidomain model. A new tool, acCELLerate, was developed using the PETSc library [1] for a parallel time and memory efficient implementation of the bidomain equations enabling the computation of large scale cardiac simulations. It offers an extensible modular structure. The optimization of the cost-intensive solution of the elliptical part of the bidomain equation was achieved by analyzing several iterative Krylov subspace methods and preconditioners provided by PETSc. Best performance results were achieved by using a combination of minimal residual method (MinRes), conjugate residual method (CR) or conjugate grandient method (CG) as solver with adjusted successive over-relaxation preconditioning (SOR). A validation proved the authenticity of the new tool.

Abstract:

Many studies conducted on patients suffering from congestive heart failure have shown the efficacy of cardiac resynchronization therapy (CRT). The presented research investigates an off-line optimization algorithm based on different electrode positioning and timing delays. A computer model of the heart was used to simulate left bundle branch block (LBBB), myocardial infarction (MI) and reduction of intraventricular conduction velocity in order to customize the patient symptom. The optimization method evaluates the error between the healthy heart and pathology with/without pacing in terms of activation time and QRS length. Additionally, a torso model of the patient is extracted to compute the body surface potential map (BSPM) and to simulate the ECG with Wilson leads to validate the results obtained by the electrophysiological heart model optimization.

Abstract:

The treatment of ventricular arrhythmia often requires detailed information about the location of ectopic beats. A noninvasive procedure is adopted to achieve this purpose. The aim of this work is the reconstruction of ectopic foci by using the critical point theory introduced by Greensite and Huiskamp [1]. The reliability and adaptability of the obtained simulation results are evaluated with regard to the reconstruction error.The reconstruction of bioelectrical sources from measured body surface potentials is an ill-posed problem and requires regularization. The advantage of the presented method is to deal with a well-posed formulation of the problem. Locations of ectopic beats can be detected by the critical point theorem. Four simulated ectopic centers have been localized to evaluate the method. The influence of Gaussian noise is considered.The reconstruction depends on the effective rank of a singular value decomposition (SVD) of the multi-channel ECG matrix. Regarding lower ranks, many critical points presenting ectopic foci can be observed. For higher ranks, the detection leads more and more to a stable estimation of ectopic locations. The detected critical points are shown to be reliable approximations of the simulated ectopic foci.

Abstract:

Multi-scale, multi-physical heart models have not yet been able to include a high degree of accuracy and resolution with respect to model detail and spatial resolution due to computational limitations of current systems. We propose a framework to compute large scale cardiac models. Decomposition of anatomical data in segments to be distributed on a parallel computer is carried out by optimal recursive bisection (ORB). The algorithm takes into account a computational load parameter which has to be adjusted according to the cell models used. The diffusion term is realized by the monodomain equations. The anatomical data-set was given by both ventricles of the Visible Female data-set in a 0.2 mm resolution. Heterogeneous anisotropy was included in the computation. Model weights as input for the decomposition and load balancing were set to (a) 1 for tissue and 0 for non-tissue elements; (b) 10 for tissue and 1 for non-tissue elements. Scaling results for 512, 1024, 2048, 4096 and 8192 computational nodes were obtained for 10 ms simulation time. The simulations were carried out on an IBM Blue Gene/L parallel computer. A 1 s simulation was then carried out on 2048 nodes for the optimal model load. Load balances did not differ significantly across computational nodes even if the number of data elements distributed to each node differed greatly. Since the ORB algorithm did not take into account computational load due to communication cycles, the speedup is close to optimal for the computation time but not optimal overall due to the communication overhead. However, the simulation times were reduced form 87 minutes on 512 to 11 minutes on 8192 nodes. This work demonstrates that it is possible to run simulations of the presented detailed cardiac model within hours for the simulation of a heart beat.

Abstract:

Increasing biophysical detail in multi physical, multiscale cardiac model will demand higher levels of parallelism in multi-core approaches to obtain fast simulation times. As an example of such a highly parallel multi-core approaches, we develop a completely distributed bidomain cardiac model implemented on the IBM Blue Gene/L architecture. A tissue block of size 50 times 50 times 100 cubic elements based on ten Tusscher et al. (2004) cell model is distributed on 512 computational nodes. The extracellular potential is calculated by the Gauss-Seidel (GS) iterative method that typically requires high levels of inter-processor communication. Specifically, the GS method requires knowledge of all cellular potentials at each of it iterative step. In the absence of shared memory, the values are communicated with substantial overhead. We attempted to reduce communication overhead by computing the extracellular potential only every 5th time step for the integration of the cell models. We also investigated the effects of reducing inter-processor communication to every 5th, 10th, 50th iteration or no communication within the GS iteration. While technically incorrect, these approximation had little impact on numerical convergence or accuracy for the simulations tested. The results suggest some heuristic approaches may further reduce the inter-processor communication to improve the execution time of large-scale simulations.

Abstract:

The classic tool of assessing learning progress are written tests and assignments. In large groups of students the workload often does not allow in depth evaluation during the course. Thus our aim was to modify the course to include active learning methods and student centered teaching. We changed the course structure only slightly and established new assessment methods like minute papers, short tests, mini-projects and a group project at the end of the semester. The focus was to monitor the learning progress during the course so that problematic issues could be addressed immediately. The year before the changes 26.76 % of the class failed the course with a grade average of 3.66 (Pass grade is 4.0/30 % of achievable marks). After introducing student centered teaching, only 14 % of students failed the course and the average grade was 3.01. Grades were also distributed more evenly with more students achieving better results. We have shown that even in large groups of students with > 100 participants student centered and active learning is possible. Although it requires a great work overhead on the behalf of the teaching staff, the quality of teaching and the motivation of the students is increased leading to a better learning environment.

Abstract:

We describe an approach to develop anatomical models of cardiac cells. The approach is based on confocal imaging of living ventricular myocytes with submicrometer resolution, digital image processing of three-dimensional stacks with high data volume, and generation of dense triangular surface meshes representing the sarcolemma including the transverse tubular system. The image processing includes methods for deconvolution, filtering and segmentation. We introduce and visualize models of the sarcolemma of whole ventricular myocytes and single transversal tubules. These models can be applied for computational studies of cell and sub-cellular physical behavior and physiology, in particular cell signaling. Furthermore, the approach is applicable for studying effects of cardiac development, aging and diseases, which are associated with changes of cell anatomy and protein distributions.

Abstract:

While chloroquine remains an important therapeutic agent for treatment of malaria in many parts of the world, its safety margin is very narrow. Chloroquine inhibits the cardiac inward rectifier K+ current IK1 and can induce lethal ventricular arrhythmias. In this study, we characterized the biophysical and molecular basis of chloroquine block of Kir2.1 channels that underlie cardiac IK1. The voltage- and K+-dependence of chloroquine block implied that the binding site was located within the ion conduction pathway. Site-directed mutagenesis revealed the location of the chloroquine binding site within the cytoplasmic pore domain, rather than within the transmembrane pore. Molecular modeling suggested that chloroquine blocks Kir2.1 channels by plugging the cytoplasmic conduction pathway, stabilized by negatively charged and aromatic amino acids within a central pocket. Unlike most ion channel blockers, chloroquine does not bind within the transmembrane pore. These findings explain how a relatively low-affinity blocker like chloroquine can effectively block IK1 even in the presence of high affinity endogenous blockers. Moreover, our findings provide the structural framework for the design of safer, alternative compounds that are devoid of Kir2.1 blocking properties.

Abstract:

Electrophysiological modeling of the heart enable quantitative description of electrical processes during normal and abnormal excitation. Cell models describe e.g. the properties of the cell membrane and the gating process of ionic channels. New measurement data is available for these channels for physiological and some pathological states. These data should be included in the models to enhance their features. In this work we describe a framework adapting ion channel models to measurement data by using a particle swarm optimization (PSO). Models of ion channels can be described by Hogdkin-Huxley equations or by Markovian models. They consider rate constants that are complex functions depending on the transmembrane voltage. Each transition has two rate constants described by several parameters. These parameters need to be varied in order to minimize the difference between measured and simulated ion channel kinetics. Since this minimization procedure is multidimensional and the function can have several local minima, conventional optimization strategies like Powells algorithm and conjugate gradient do not ensure to find the global minimum. To overcome this, a PSO was implemented that inserts several dependent particles randomly into the search space. It is based on the social behavior of swarms. As the particles are independent during each iteration the procedure can be calculated in parallel. The measurement data used for this work were current traces of a voltage-clamp protocol of reggae mutant hERG channels. The same protocol as for the measurement was assigned to the model of Lu et al. describing hERG function with a Markovian model. The value to be minimized was the sum of mean square errors between measured and simulated currents at certain time instances. Both Powell and PSO were started several times with random starting values. In 94% of the cases PSO found the minimum compared to 16% for Powell. On the other hand PSO needed approximately 100 times more function evaluations. The parallelization decreased the overall time needed by the PSO to about the same amount Powell needed. Therefore, the parallel PSO is a fast and reliable approach for adapting ion channel models to measured data.

Abstract:

The sinus node (SN) is the primary pacemaker of the heart. It is a heterogeneous structure in the right atrium composed of two types of cells with different electrophysiological properties. One type is distributed more densely in the periphery the other in the center. Different gap junction types and densities exist leading to a heterogeneity in conduction. It is supposed that this complex interplay of heterogeneities is the basic mechanism that the small SN is able to electrically drive the surrounding atrial muscle. If this interplay is disturbed, the function of the SN can be effected massively. In this simulation study we want to demonstrate the effects of the L532P mutation in hERG called reggae on SN electrophysiology.Mutant hERG channels were expressed in xenopus oocytes and the channel properties were measured with voltage-clamp technique. The data showed mainly a shift of the steady-state inactivation to more positive potentials. This leads to an increase of the ionic current during the depolarized phase. The data was integrated in the heterogeneous rabbit SN model of Zhang et al. by adapting the parameters of the IKr channel with aid of optimization methods using the same stimulation protocol as in the measurements.The most sensitive parameter was the shift voltage of the steady-state inactivation from -19.2 mV in the physiological case to 10.1 mV in the mutant model. When inserting this mutant IKr in the central SN model the ability of the central cells to depolarize spontaneously was eliminated. Peripheral cell still beat but are affected by the mutation. The slope of the pre-potential and the upstroke velocity were not changed. The maximum diastolic potential was increased by 2 mV and the maximum systolic potential decreased by 1.5 mV. The diastolic interval was shortened slightly by 3 ms. The main effect was a reduction of the action potential duration from 108 ms to 84 ms leading to a frequency increase from 6.37 Hz to 7.62 Hz.These effects lead to a changing SN function. The increase of the shift voltage is in good agreement with the measured changes. Especially the loss of auto-rhythmicity in the central zone is expected to change the overall SN activity. Although peripheral SN cells beat faster we expect a bradycardial function of the complete SN because of electrotonic interactions with the silent central SN cells and the low resting membrane voltage of surrounding atrial muscle cells. In a further study this suggestion has to be investigated in an anisotropic and heterogeneous 3D model.

Abstract:

The number of implanted cardiac pacemakers and defibrillators is constantly increasing. At the same time, more and more of those patients use wireless mobile communication devices.Aim of this work was the development of a pacemaker-electrode model and its “implantation” into a detailed anatomical correct voxel model. Additionally generic body models were examined. It consists of several layers with varying thickness and conductivity/permittivity values corresponding to different tissue types. This approach was chosen to avoid numerical errors at tilted boundaries. The excitation sources were modeled as generic dipoles and as plane waves operating at the frequency range normally used by cellular phones and wireless networks (900 to 2450 MHz). The dipoles were designed to provide maximum radiation efficiency at the frequencies of interest. Finally numerical calculation of induced fields by external signal sources were conducted. The results were then evaluated regarding the compliance to the guidelines of ICNIRP and a draft by DIN/VDE.For the Visible Man model, the computed specific absorption rate (SAR) values were well below the thresholds both for single and multi-antenna setups and for all frequencies of interest if the power did not exceed the regulatory specifications. The same results were obtained for the electrical field values determined at commonly used implantation sites for pacemakers. For some tissue configurations in the generic model, higher SAR values than allowed by regulations could be observed.

Abstract:

The development of new devices used for defibrillation and cardioversion is often supported by numerical simulations of the induced electric potentials and current distributions. The commonly used tools incorporate isotropic models of the tissue properties present in the human torso. A comparative study was conducted to characterize the influence of anisotropic compared to isotropic tissue modeling. Defibrillation shocks with amplitudes of 1000 V and 2000 V were simulated and a set of varying conductivity values and anisotropy ratios was examined. The inclusion of tissue anisotropy produced significantly smaller values for current density compared to isotropic calculations especially in the myocardial tissue.

Abstract:

Simulation of cardiac excitation is often a trade-off between accuracy and speed. A promising minimal, time-efficient cell model with four state variables has recently been presented together with parametrizations for ventricular cell behaviour. In this work, we adapt the model parameters to reproduce atrial excitation properties as given by the Courtemanche model. The action potential shape is considered as well as the restitution of action potential duration and conduction velocity. Simulation times in a single cell and a tissue patch are compared between the two models. We further present the simulation of a sinus beat on the atria in a realistic 3D geometry using the fitted minimal model in a monodomain simulation.

Abstract:

The sinus node (SN), which is the primary pacemaker of the heart, is a heterogeneous structure, i.e. there is a difference between center and periphery regarding morphology, electrophysiology and electrical coupling. The behavior of the whole SN in detail is difficult to investigate experimentally. Therefore, realistic computer models are helpful to understand the electrophysiological mechanisms quantitatively. In this work, different models of the SN including heterogeneity are benchmarked.Several approaches considering SN heterogeneity exist. One possible description of the electrical conduction is the mosaic model, in which the density of two discrete cell types, central and peripheral cells, is varied from the center to the periphery of the SN. The gradient model is another approach for this task. As the name implies, there is a gradual transition in cell morphology and electrophysiology between the center and periphery.The behavior of single nodal cells were described best by the rabbit SN model of Zhang et al. [1], offering explicit formulations for central and peripheral cells. A one-dimensional model of the SN and surrounding atrial tissue and a two-dimensional slice of the SN and adjoining crista terminalis (CT) were applied. Both approaches describing electrical conduction were compared using these different geometric models, in order to find the most exact model in relation to measured data describing activation patterns and action potential durations.

Abstract:

In the course of this project, the effects of the hERG channel mutation N588K on atrial repolar- ization and the predisposition to atrial fibrillation have been analyzed. For this purpose, measured data obtained with whole cell voltage clamp technique of wild-type and mutated hERG channel were implemented in the Courtemanche et al. ionic model. Channel kinetics and density of the model were therefore adjusted using parameter fitting to the measured data. The effects of the mutation in the hERG channel could be analyzed in a single-cell and tissue environment. Hereby, the most relevant factors for cardiac arrhythmias, such as APD, rate dependence, CV, and ERP were determined. The excitation propagation, repolarization and pre- disposition for rotating waves were finally investigated using a schematic anatomical model of the right atrium.The results presented in chapter 5 underline that the proper implementation of measured data in electrophysiological cell models can be affected by the measurement protocol used in the voltage clamp-technique. Since the use of a different pulse duration and return pulse can alter the behavior of the ionic currents, in particular during the recovery from inactivation and deactivation processes, the clamp-protocol used is very important for an accurate analysis of the channel effects on the cell.Further, mutation N588K showed a gain of function effect of IKr caused by the shifted inactivation of the hERG channel towards more positive potentials. In single-cell, this resulted in a significant shortening of the APD to 116 ms. However, the effects of the mutation in tissue were not that strong as in a single-cell. This results from the characteristic behavior of the mutation that shows a dependence on the maximum upstroke reached by depolarization. As a consequence, the effective APD was 220 ms. The ERP was also reduced in the tissue simulations. Combined with the fact that the CV decreases by short BCL, this effect builds a substrate for the initiation and perpetuation of AF. The differences between physiological and mutated case were most visible in the two- dimensional model. Not only the repolarization was shorter, but the mutated model supported the initiation of rotating waves, in contrast to the physiological one. The generated results show that mutation N588K builds, indeed, a substrate that can support the predisposition of AF. For further investigations it is very important to implement measured data which includes the information of the channel processes during recovery from inactivation. This will lead to more accurate analysis about the effects of the mutation, and with it to a better understanding of the electrical behavior underlying cardiac arrhtymia.Finally, a complete three-dimensional anatomical model should be used to further analyze the effect of mutation N588K on the perpetuation of rotating waves. The model used in this work did not include important factors like curvature or sharp edges, which play a very important role for the conduction velocity. In a three-dimensional model the conduction velocity will decrease, resulting in a further shortening of the wavelength. By this way, the model could not only produce one rotating wave, but flutter or fibrillation.

Abstract:

Die vorliegende Arbeit befasst sich mit der optischen Erfassung von elektrischen Signalen im Herzen, welche eine kontaktlose Messung der elektrischen Signale von der Herzoberfläche ermöglicht. Hieraus lassen sich elektrophysiologische und mechanische Parameter bestimmen, welche für die Erstellung von virtuellen Computermodellen des menschlichen Herzens essentiell sind. Mit rechnergestützten Simulationen können z.B. Erkrankungen im Herzen nachgestellt und deren Auswirkungen beobachtet werden.

Abstract:

Since the Dutch physiologist William Einthoven had established the electrocardiographin 1903 there has been a huge interest in ECG signals. ECG signalsare biosignals and give information on the healthy state of the patient's heart.Therefore it is used in the field of medicine and health science in cardiology.To investigate on heart diseases the QT-interval and its change is in special interest.Abnormalities like QT prolongation can cause the development of ventriculartachyarrhythmias such as Torsades de Points and ventricular fibrillationoften leading to sudden cardiac death. Drug induced QT prolongation of antiarrhythmicahas been known for many years, but in the last two decades even somenon cardiac drugs have been recognized to have an inuence on the QT-interval.As in the early 1990's an antihistamine drug was associated with Torsades dePoints and sudden cardiac death, the medical community, regulatory agenciesand pharmaceutical companies became more sensitive for drug induced QT prolongation.Since then lists of cardiac and even non cardiac drugs which seem tocause QT prolongation and increase the risk of sudden cardiac death have beenexposed. [Zar07] QT-intervals mainly change with the heart rate. To documentthe effect on QT-interval caused by a drug, QT-interval changes depending onheart rate changes have to be removed. There are many correction formulas publishedbut still the formula of Bazett is quasi-standard. But QT does not onlyreact instantaneously on changes of RR. A "memory" effect is actually observed.Four models are presented in this thesis, motivated by analysis of measured andsimulated data of action potential duration (APD) in heart cells at different basiccycle length (BCL).

Abstract:

This thesis explores image post-processing methods to reduce motion in images acquired with a microscope showing contracting muscles. The registration methods used include Thin-Plate Splines (TPS), Gaussian Elastic Body Splines (GEBS), and Fluid Flow.TPS are based on point correspondences between images and are widely used in image registra- tion. While GEBS are also based on landmarks they propose a better model for the displacements in body tissue. The registration algorithms spatially align two images without user interaction. Point correspondences are established using regional cross-correlation. The large amount of landmarks is filtered based on minimal normalized correlation-coefficients, identical displacements from dif- ferent template sizes (used in regional cross-correlation), and clustering of adjacent and identical displacements. The filtering parameters are optimized based on minimization of the sum of squared intensity difference (SSD) by testing 15 parameter variations. GEBS parameters are optimized se- quentially by using a golden-section search algorithm. Fluid Flow registration serves for compari- son of a voxel intensity based registration.The advantages of GEBS are: displacements in one direction affect other directions, landmarks have a locally restricted influence, and elasticity from physical model corresponds to tissue prop- erties. Compared to TPS these benefits lead to a better registration of images showing a contract- ing heart muscle. TPS cause amplification of landmark displacements at the image borders, while GEBS restrict landmark influence to a local region. Over a set of 87 images GEBS are shown to register images more robust than TPS, which in some cases cannot reduce movements. In all cases GEBS perform equally well or better than TPS. Compared to Fluid Flow registration GEBS work comparably well.Registration of an image sequence showing a contracting muscle is realized by spatially aligning the image with largest contraction with an image at rest and then interpolating the movement of the muscle for the other images. This interpolation is done by an analytical description of the contraction of heart muscle, fitted to the voxel similarity measurement SSD, which is assumed to be proportional to muscle movement.Validation through visualization of action potentials on contracting muscle reveals that GEBS and Fluid Flow registration best match the reference image without movement. Motion artifacts remain in regions with low contrast. Image post-processing cannot correctly align images in low-contrast regions due to lack of infomation. In image regions with prominent structures GEBS registration successfully removes motion artifacts in action potentials.

Abstract:

This work contributes to the development of a new tool for the simulation of cardiac electro- physiology. A few years ago, the simulation of such a large scale problem was not possible. Due to recent developments in hardware and software the problem is no longer insolvable. High performance computers and clusters are able to work on the problem by using paral- lelization. Several powerful libraries have been developed to enable parallel programming for the normal user.The new tool was implemented in parallel by using the PETSc library [90]. To achieve extensibility of the program a modular structure was chosen. The bidomain equations constitute the mathematical basis of the implementation. Solving the bidomain equations numerically yields to a linear system of equations (LSE) which approximates the discretized problem.The first part of this work encloses the parallel implementation of the matrix generation for the LSE. Fundamentally, a Laplaces equation is to be solved approximately. Though, the weighting factor σ, a tensor described in section 4.4, complicates the structure of the sparse matrix in a way that a maximum number of 19 nonzero entries exist in each row of the matrix for the finite difference method.The solving of the LSE is the most expensive part of the numerical solution of the bidomain equations. On account of the size of problems in cardiac electrophysiology, a direct method can not be used. Alternatively, iterative methods such as Krylov subspace methods (KSP) enable the efficient solution of the sparse linear system. Preconditioning techniques improve the performance of the iterative solver. Therefore, the second part of this work deals with the investigation of several KSP solvers and preconditioners provided by PETSc. A pro- gram was implemented to optimize the iterative solution by using PETSc runtime options. Selected preconditioning parameters were adjusted to improve the time and memory per- formance of the solvers. In particular, the ASM and SOR preconditioner were investigated. Using ASM preconditioning turned out to be a bad choice which is surprising. The ASM domain decomposition method is known to be a capable preconditioning technique. One possible reason for the unsatisfactory results escpecially in time performance might be the way of how it is implemented in PETSc. Furthermore, because the PETSc library does not provide a relaxation factor for weigthing, no damping of the preconditioner is possible. After the disappointing results of ASM, the SOR method was investigated as precondi- tioning method. Adjusting two parameters of SOR, the preconditioned iterative method yielded to an execution time reduction of more than 50 % compared to the untuned ver- sion. Concerning the memory requirements, the SOR preconditioner was among the best methods. Although the SOR preconditioner achieved better and more stable results in time and memory performance, a general adjustment of the preconditioning parameters was not possible. Thus to conclude, the optimal parameter choice is highly problem dependent. The disparsities in the runtime analysis achieved within the computation on the three different geometries are a possible indication that the modeling contains inconsistencies. A different ratio between tissue and bath yielded to different optimal KSP solvers and different pa- rameters, respectively. Here, caution is advised, especially when the percentage of bath in the simulation block is relatively high.The third part of the results contains the validation of the program. By means of a publica- tion of Henriquez et al. [1] the simulation results computed by the new tool were validated. In addition, the results were compared to those of the former tool. Qualitatively as well as quantitatively the achieved simulation results were very similar. Disparities in excitation conduction velocity can be explained by the choice of different cell models. To investigate the scalability of the implementation, the exemplary simulation of the validation was also performed on a high performance computer: the Blue Gene/L of IBM, New York. As a re- sult the runtimes, speedups and efficiencies for different numbers of processors up to 2048 CPUs were computed. It was shown that the program is scalable and that the imlementa- tion was efficiently parallelized.Finally, a simulation in both ventricles of a human heart was computed to show the facili- ties of the new program.It is to be summarized that the new tool enables large scale simulations of cardiac electro- physiology within moderate time and memory requirements. Optimization of solvers and preconditioning parameters lead to efficient improvement of the performance. The exten- sibility of the program provides the possibilities to achieve even more realistic simulation results. Compared to the former program, time and memory requirements are reduced by a high factor. The simulation results are validable and very satisfying by comparison within the former tool and results in literature. New records in size and complexity of the simulation problems can be set within the implementation.

Abstract:

In the course of this diploma thesis the Particle Swarm Algorithm was successfully implemented into the previously existing Script Optimizer environment. Multiple parameters that control its behavior have been thoroughly tested and optimized to guarantee a high rate of successful opti- mizations while keeping the average number of iteration loops at a minimum. Benchmark functions provided a relatively fast way to obtain statistically significant information concerning the effec- tiveness of various parameter setups and the comparison to the existing Powell algorithm. The influence of the swarm size and the allowed maximum number of iteration loops on the optimiza- tions performance were further subjects of investigations.The enhanced Particle Swarm Optimization setup proved to be very robust in terms of a high rate of successful minimizations even for multi-dimensional functions that contain numerous local minima. In direct comparison with an existing optimization algorithm, however, the PSO needed by far more iteration loops for a successful optimization. The results of these experiments showed that it is important to accurately adjust the algorithm to the specific problem at hand.While using the PSO, an individual fitness value needs to be calculated for each particle during one iteration. Those repeated calculations account for the high robustness especially in multiple di- mensions but unfortunately also imply an immense computational work. To reduce the calculation time to an acceptable duration advantage was taken of the independence of the single processes. A technology that is integrated in the Apples Mac OS X operating system called Xgrid offers the possibility to distribute the workload on a cluster of network computers. Thus the optimization framework was altered so that it allowed simultaneous calculations of independent particles. Additionally, the performance of Xgrid was experimentally investigated leading to the conclusion that the jobs that are submitted to the grid need to meet certain requirements to be efficiently split into parallel executable tasks.Based on the experimental findings both the PSO algorithm and the Xgrid architecture were ad- justed to attain optimal performance. The optimization framework was then used to address a practical parameter fitting scenario. The in-vivo measured characteristics of a mutated ion channel should be reproduced by a well-established mathematical cell model. Therefore multiple param- eters that determine the cell models electrophysiological behavior had to be varied according to the used optimization strategy.It could be shown that it is possible to fit an individual ion current in the mathematical cell model of ten Tusscher et al. to the measured data of reggae mutated zERG channels of zebrafish. The parameter fit using the Zhang et al. model of rabbit sinoatrial node cells failed due to the inability of the cell model to adapt its ion current IKr to the measured values.Finally, changes to the optimization framework allowed to approximate the behavior of a relatively new and simplified cell model that allows large scale calculations at relatively low computational costs to the characteristics shown by the well-established and -accepted complex mathematical cell models. An optimization of this simplified Fenton 4 State model to fit the ten Tusscher et al. cell models action potential showed even better results than the adaption published by the inventors of the Fenton 4 State model. The possibilities of the presented optimization framework was concludingly demonstrated by fitting the Fenton 4 State model to the Courtemanche et al. model for human atrial myocytes. A close match of the AP morphology could be achieved allowing the time-saving simulation of atrial arrhythmias in future research projects.

Abstract:

Atrial fibrillation (AF) is the most common arrhythmia in the human heart. Its prevalence increases with rising age, with about 8 % of people over 80 having AF. AF is usually characterized by symptoms of rapid and irregular heart rate. The human heart normally contracts at a rate of 60 to 80 BPM in nomal sinus rhythm. During AF, the atrial rate could rise to between 400 and 600 BPM. AF is normally not as fatal as ventricular fibrillation, but it can cause not only palpitation, fainting, chest pain or congestive heart failure, but also a higher chance of stroke (about 2 to 7 times of the regular population) [1]. AF is a self perpetuating disease, because AF can lead to electrophysiological and anatomical changes in the atria, prolonging the AF episodes or initiate new AF. Thats why paroxysmal AF often progresses to chronic AF. About 18 % of patients with lone paroxysmal atrial fibrillation also developed sustained fibrillation [2]. The success rate of electrical atrial defibrillation is related to the duration of the AF. Terminating AF using cardioversion by patients with chronic AF is often not successful. A better understanding of fundamental mechanism underlying AF is of great benefit to the therapeutic approaches [3]. The ionic channel properties of the atrial myocytes play an important role in the heart rhythm. As revealed by recent researches, AF can occur on a familial basis, pointing to a genetic cause of arrhythmia in some individuals [4]. Study on the influences of genetic defects to the ionic channels could help understanding the mechanisms of AF better and contribute to the prevention and treatment of AF. Three different genetic mutations are incorporated in this work with a mathematical model which describes the cellular mechanisms. To realize an accurate simulation of exciation in atria it is necessary to consider different anatomy structures . Because of the different electrophysiological properties of these structures they must be incorporated properly. In this work, new anatomical structures such as the fossa ovalis (FO) and the cardiac opening areas (ostia) are incorporated