Y. Lutz, A. Loewe, S. Meckel, O. Dössel, and G. Cattaneo. Combined local hypothermia and recanalization therapy for acute ischemic stroke: Estimation of brain and systemic temperature using an energetic numerical model.. In Journal of Thermal Biology, vol. 84, pp. 316-322, 2019
Local brain hypothermia is an attractive method for providing cerebral neuroprotection for ischemic stroke patients and at the same time reducing systemic side effects of cooling. In acute ischemic stroke patients with large vessel occlusion, combination with endovascular mechanical recanalization treatment could potentially allow for an alleviation of inflammatory and apoptotic pathways in the critical phase of reperfusion. The direct cooling of arterial blood by means of an intra-carotid heat exchange catheter compatible with recanalization systems is a novel promising approach. Focusing on the concept of "cold reperfusion", we developed an energetic model to calculate the rate of temperature decrease during intra-carotid cooling in case of physiological as well as decreased perfusion. Additionally, we discussed and considered the effect and biological significance of temperature decrease on resulting brain perfusion. Our model predicted a 2 °C brain temperature decrease in 8.3, 11.8 and 26.2 min at perfusion rates of 50, 30 and 10ml100g⋅min, respectively. The systemic temperature decrease - caused by the venous blood return to the main circulation - was limited to 0.5 °C in 60 min. Our results underline the potential of catheter-assisted, intracarotid blood cooling to provide a fast and selective brain temperature decrease in the phase of vessel recanalization. This method can potentially allow for a tissue hypothermia during the restoration of the physiological flow and thus a "cold reperfusion" in the setting of mechanical recanalization.
Each heartbeat is initiated by cyclic spontaneous depolarization of cardiomyocytes in the sinus node forming the primary natural pacemaker. In patients with end-stage renal disease undergoing hemodialysis, it was recently shown that the heart rate drops to very low values before they suffer from sudden cardiac death with an unexplained high incidence. We hypothesize that the electrolyte changes commonly occurring in these patients affect sinus node beating rate and could be responsible for severe bradycardia. To test this hypothesis, we extended the Fabbri et al. computational model of human sinus node cells to account for the dynamic intracellular balance of ion concentrations. Using this model, we systematically tested the effect of altered extracellular potassium, calcium, and sodium concentrations. Although sodium changes had negligible (0.15 bpm/mM) and potassium changes mild effects (8 bpm/mM), calcium changes markedly affected the beating rate (46 bpm/mM ionized calcium without autonomic control). This pronounced bradycardic effect of hypocalcemia was mediated primarily by I attenuation due to reduced driving force, particularly during late depolarization. This, in turn, caused secondary reduction of calcium concentration in the intracellular compartments and subsequent attenuation of inward I and reduction of intracellular sodium. Our in silico findings are complemented and substantiated by an empirical database study comprising 22,501 pairs of blood samples and in vivo heart rate measurements in hemodialysis patients and healthy individuals. A reduction of extracellular calcium was correlated with a decrease of heartrate by 9.9 bpm/mM total serum calcium (p < 0.001) with intact autonomic control in the cross-sectional population. In conclusion, we present mechanistic in silico and empirical in vivo data supporting the so far neglected but experimentally testable and potentially important mechanism of hypocalcemia-induced bradycardia and asystole, potentially responsible for the highly increased and so far unexplained risk of sudden cardiac death in the hemodialysis patient population.
Changes of serum and extracellular ion concentrations occur regularly in patients with chronic kidney disease (CKD). Recently, hypocalcemia, i.e. a decrease of the extra-cellular calcium concentration [Ca2+]o, has been suggested as potential pathomechanism contributing to the unexplained high rate of sudden cardiac death (SCD) in CKD patients. In particular, there is a hypothesis that hypocalcaemia could slow down natural pacemaking in the human sinus node to fatal degrees. Here, we address the question whether there are inter-species differences in the response of cellular sinus node pacemaking to changes of [Ca2+]o. Towards this end, we employ computational models of mouse, rabbit and human sinus node cells. The Fabbri et al. human model was updated to consider changes of intracellular ion concentrations. We identified crucial inter-species differences in the response of cellular pacemaking in the sinus node to changes of [Ca2+]o with little changes of cycle length in mouse and rabbit models (<83 ms) in contrast to a pronounced bradycardic effect in the human model (up to > 1000 ms). Our results suggest that experiments with human sinus node cells are required to investigate the potential mechanism of hypocalcaemia-induced bradycardic SCD in CKD patients and small animal models are not well suited.
Atypical atrial flutter (AFlut) is a reentrant arrhythmia which patients frequently develop after ablation for atrial fibrillation (AF). Indeed, substrate modifications during AF ablation can increase the likelihood to develop AFlut and it is clinically not feasible to reliably and sensitively test if a patient is vulnerable to AFlut. Here, we present a novel method based on personalized computational models to identify pathways along which AFlut can be sustained in an individual patient. We build a personalized model of atrial excitation propagation considering the anatomy as well as the spatial distribution of anisotropic conduction velocity and repolarization characteristics based on a combination of a priori knowledge on the population level and information derived from measurements performed in the individual patient. The fast marching scheme is employed to compute activation times for stimuli from all parts of the atria. Potential flutter pathways are then identified by tracing loops from wave front collision sites and constricting them using a geometric snake approach under consideration of the heterogeneous wavelength condition. In this way, all pathways along which AFlut can be sustained are identified. Flutter pathways can be instantiated by using an eikonal-diffusion phase extrapolation approach and a dynamic multifront fast marching simulation. In these dynamic simulations, the initial pattern eventually turns into the one driven by the dominant pathway, which is the only pathway that can be observed clinically. We assessed the sensitivity of the flutter pathway maps with respect to conduction velocity and its anisotropy. Moreover, we demonstrate the application of tailored models considering disease-specific repolarization properties (healthy, AF-remodeled, potassium channel mutations) as well as applicabiltiy on a clinical dataset. Finally, we tested how AFlut vulnerability of these substrates is modulated by exemplary antiarrhythmic drugs (amiodarone, dronedarone). Our novel method allows to assess the vulnerability of an individual patient to develop AFlut based on the personal anatomical, electrophysiological, and pharmacological characteristics. In contrast to clinical electrophysiological studies, our computational approach provides the means to identify all possible AFlut pathways and not just the currently dominant one. This allows to consider all relevant AFlut pathways when tailoring clinical ablation therapy in order to reduce the development and recurrence of AFlut.
Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. The atrial wall thickness (AWT) can potentially improve our understanding of the mechanism underlying atrial structure that drives AF and provides important clinical information. However, most existing studies for estimating AWT rely on ruler-based measurements performed on only a few selected locations in 2D or 3D using digital calipers. Only a few studies have developed automatic approaches to estimate the AWT in the left atrium, and there are currently no methods to robustly estimate the AWT of both atrial chambers. Therefore, we have developed a computational pipeline to automatically calculate the 3D AWT across bi-atrial chambers and extensively validated our pipeline on both ex vivo and in vivo human atria data. The atrial geometry was first obtained by segmenting the atrial wall from the MRIs using a novel machine learning approach. The epicardial and endocardial surfaces were then separated using a multi-planar convex hull approach to define boundary conditions, from which, a Laplace equation was solved numerically to automatically separate bi-atrial chambers. To robustly estimate the AWT in each atrial chamber, coupled partial differential equations by coupling the Laplace solution with two surface trajectory functions were formulated and solved. Our pipeline enabled the reconstruction and visualization of the 3D AWT for bi-atrial chambers with a relative error of 8% and outperformed existing algorithms by >7%. Our approach can potentially lead to improved clinical diagnosis, patient stratification, and clinical guidance during ablation treatment for patients with AF.
Aims Chronic left atrial enlargement (LAE) increases the risk of atrial fibrillation. Electrocardiogram (ECG) criteria might provide a means to diagnose LAE and identify patients at risk; however, current criteria perform poorly. We seek to characterize the potentially differential effects of atrial dilation vs. hypertrophy on the ECG P-wave. Methods and results We predict effects on the P-wave of (i) left atrial dilation (LAD), i.e. an increase of LA cavity volume without an increase in myocardial volume, (ii) left atrial concentric hypertrophy (LACH), i.e. a thickened myocardial wall, and (iii) a combination of the two. We performed a computational study in a cohort of 72 anatomical variants, derived from four human atrial anatomies. To model LAD, pressure was applied to the LA endocardium increasing cavity volume by up to 100%. For LACH, the LA wall was thickened by up to 3.3 mm. P-waves were derived by simulating atrial excitation propagation and computing the body surface ECG. The sensitivity regarding changes beyond purely anatomical effects was analysed by altering conduction velocity by 25% in 96 additional model variants. Left atrial dilation prolonged P-wave duration (PWd) in two of four subjects; in one subject a shortening, and in the other a variable change were seen. Left atrial concentric hypertrophy, in contrast, consistently increased P-wave terminal force in lead V1 (PTF-V1) in all subjects through an enlarged amplitude while PWd was unaffected. Combined hypertrophy and dilation generally enhanced the effect of hypertrophy on PTF-V1. Conclusion Isolated LAD has moderate effects on the currently used P-wave criteria, explaining the limited utility of PWd and PTF-V1 in detecting LAE in clinical practice. In contrast, PTF-V1 may be a more sensitive indicator of LA myocardial hypertrophy.
Optical mapping is widely used as a tool to investigate cardiac electrophysiology in ex vivo preparations. Digital filtering of fluorescence-optical data is an important requirement for robust subsequent data analysis and still a challenge when processing data acquired from thin mammalian myocardium. Therefore, we propose and investigate the use of an adaptive spatio-temporal Gaussian filter for processing optical mapping signals from these kinds of tissue usually having low signal-to-noise ratio (SNR). We demonstrate how filtering parameters can be chosen automatically without additional user input. For systematic comparison of this filter with standard filtering methods from the literature, we generated synthetic signals representing optical recordings from atrial myocardium of a rat heart with varying SNR. Furthermore, all filter methods were applied to experimental data from an ex vivo setup. Our developed filter outperformed the other filter methods regarding local activation time detection at SNRs smaller than 3 dB which are typical noise ratios expected in these signals. At higher SNRs, the proposed filter performed slightly worse than the methods from literature. In conclusion, the proposed adaptive spatio-temporal Gaussian filter is an appropriate tool for investigating fluorescence-optical data with low SNR. The spatio-temporal filter parameters were automatically adapted in contrast to the other investigated filters.
BACKGROUND: Complementary to clinical and experimental studies, computational cardiac modeling serves to obtain a comprehensive understanding of the cardiovascular system in order to analyze dysfunction, evaluate existing, and develop novel treatment strategies. OBJECTIVES: We describe the basics of multiscale computational modeling of cardiac electrophysiology from the molecular ion channel to the whole body scale. By modeling cardiac ischemia, we illustrate how in silico experiments can contribute to our understanding of how the pathophysiological mechanisms translate into changes observed in diagnostic tools such as the electrocardiogram (ECG). MATERIALS AND METHODS: Quantitative in silico modeling spans a wide range of scales from ion channel biophysics to ECG signals. For each of the scales, a set of mathematical equations describes electrophysiology in relation to the other scales. Integration of ischemia-induced changes is performed on the ion channel, single-cell, and tissue level. This approach allows us to study how effects simulated at molecular scales translate to changes in the ECG. RESULTS: Ischemia induces action potential shortening and conduction slowing. Hence, ischemic myocardium has distinct and significant effects on propagation and repolarization of excitation, depending on the intramural extent of the ischemic region. For transmural and subendocardial ischemic regions, ST segment elevation and depression, respectively, were observed, whereas intermediate ischemic regions were found to be electrically silent (NSTEMI). CONCLUSIONS: In silico modeling contributes quantitative and mechanistic insight into fundamental ischemia-related arrhythmogenic mechanisms. In addition, computational modeling can help to translate experimental findings at the (sub-)cellular level to the organ and body context (e. g., ECG), thereby providing a thorough understanding of this routinely used diagnostic tool that may translate into optimized applications.
OBJECTIVE: Atrial tachycardia (AT) still pose a major challenge in catheter ablation. Although state-of-the-art electroanatomical mapping systems allow to acquire several thousand intracardiac electrograms (EGMs), algorithms for diagnostic analysis are mainly limited to the amplitude of the signal (voltage map) and the local activation time~(LAT map). We applied spatio-temporal analysis of EGM activity to generate maps indicating reentries and diastolic potentials, thus identifying and localizing the driving mechanism of AT. METHODS: First, the time course of active surface area (ASA) is determined during one basic cycle length (BCL). The global cycle length coverage (gCLC) reflects the relative duration within one BCL for which activity was present in each individual atrium. A local cycle length coverage (lCLC) is computed for circular sub-areas with 20mm diameter. The simultaneous active surface area sASA is determined to indicate the spatial extent of depolarizing tissue. RESULTS: Combined analysis of these spatial scales allowed to correctly identify and localize the driving mechanism: gCLC values of 100% were indicative for atria harbouring a reentrant driver. lCLC could detect micro reentries within an area of 1.651.28cm in simulated data and differentiate them against focal sources. Mid-diastolic potentials, being potential targets for catheter ablation, were identified as the areas showing confined activity based on sASA values. CONCLUSION: The concept of spatio-temporal activity analysis proved successful and correctly indicated the tachycardia mechanism in 20 simulated AT scenarios and three clinical data sets. SIGNIFICANCE: Automatic interpretation of intracardiac mapping data could help to improve the treatment strategy in complex cases of AT.
Catheter ablation is a curative therapeutic approach for atrial fibrillation (AF). Ablation of rotational sources based on basket catheter measurements has been proposed as a promising approach in patients with persistent AF to complement pulmonary vein isolation. However, clinically reported success rates are equivocal calling for a mechanistic investigation under controlled conditions. We present a computational framework to benchmark ablation strategies considering the whole cycle from excitation propagation to electrogram acquisition and processing to virtual therapy. Fibrillation was induced in a patient-specific 3D volumetric model of the left atrium, which was homogeneously remodelled to sustain reentry. The resulting extracellular potential field was sampled using models of grid catheters as well as realistically deformed basket catheters considering the specific atrial anatomy. Virtual electrograms were processed to compute phase singularity density maps to target rotor tips with up to three circular ablations. Stable rotors were successfully induced in different regions of the homogeneously remodelled atrium showing that rotors are not constrained to unique anatomical structures or locations. Phase singularity density maps correctly identified and located the rotors (deviation < 10 mm) based on catheter recordings only for sufficient resolution (inter-electrode distance = 3 mm) and proximity to the wall (< 10 mm). Targeting rotor sites with ablation did not stop reentries in the homogeneously remodelled atria independent from lesion size (1-7 mm radius), from linearly connecting lesions with anatomical obstacles, and from the number of rotors targeted sequentially (up to 3). Our results show that phase maps derived from intracardiac electrograms can be a powerful tool to map atrial activation patterns, yet they can also be misleading due to inaccurate localization of rotor tips depending on electrode resolution and distance to the wall. This should be considered to avoid ablating regions that are in fact free of rotor sources of AF. In our experience, ablation of rotor sites was not successful to stop fibrillation. Our comprehensive simulation framework provides the means to holistically benchmark ablation strategies in silico under consideration of all steps invol
Objectives: This study hypothesized that P-wave morphology and timing under left atrial appendage (LAA) pacing change characteristically immediately upon anterior mitral line (AML) block. Background: Perimitral flutter commonly occurs following ablation of atrial fibrillation and can be cured by an AML. However, confirmation of bidirectional block can be challenging, especially in severely fibrotic atria. Methods: The study analyzed 129 consecutive patients (66 ± 8 years, 64% men) who developed perimitral flutter after atrial fibrillation ablation. We designed electrocardiography criteria in a retrospective cohort (n = 76) and analyzed them in a validation cohort (n = 53). Results: Bidirectional AML block was achieved in 110 (85%) patients. For ablation performed during LAA pacing without flutter (n = 52), we found a characteristic immediate V1 jump (increase in LAA stimulus to P-wave peak interval in lead V1) as a real-time marker of AML block (V1 jump ≥30 ms: sensitivity 95%, specificity 100%, positive predictive value 100%, negative predictive value 88%). As V1 jump is not applicable when block coincides with termination of flutter, absolute V1 delay was used as a criterion applicable in all cases (n = 129) with a delay of 203 ms indicating successful block (sensitivity 92%, specificity 84%, positive predictive value 90%, negative predictive value 87%). Furthermore, an initial negative P-wave portion in the inferior leads was observed, which was attenuated in case of additional cavotricuspid isthmus ablation. Computational P-wave simulations provide mechanistic confirmation of these findings for diverse ablation scenarios (pulmonary vein isolation ± AML ± roof line ± cavotricuspid isthmus ablation). Conclusions: V1 jump and V1 delay are novel real-time electrocardiography criteria allowing fast and straightforward assessment of AML block during ablation for perimitral flutter.
Background: During atrial fibrillation, heterogeneities and anisotropies result in a chaotic propagation of the depolarization wavefront. The electrophysiological parameter called conduction velocity (CV) influences the propagation pattern over the atrium. We present a method that determines the regional CV for deformed catheter shapes, which result due to the catheter movement and changing wall contact.Methods: The algorithm selects stable catheter positions, finds the local activation times (LAT), considers the wall contact and calculates all CV estimates within the area covered by the catheter. The method is evaluated with simulated data and then applied to four clinical data sets. Both sinus rhythm activity as well as depolarization wavefronts initiated by stimulation are analyzed. The regional CV is compared with the fractionation duration (FD) and peak-to-peak (P2P) voltages. A speed of 0.5 m/s was defined to create the simulated LAT.Results: After analyzing the simulated LAT with clinical catheter spatial coordinates, the median CV of 0.5 m/s with an interquartile range of 0.22 and exact CV direction vectors were obtained. For clinical cases, the CV magnitude range of 0.08 m/s to 1.0 m/s was obtained. The P2P amplitude of 0.7 mV to 3.7 mV and the mean FD from 40.79ms to 48.66ms was obtained. The correlation of 0.86 was observed between CV and P2P amplitude, and 0.62 between CV and FD.Conclusion: In this paper, a method is presented and validated which calculates the CV for the deformed catheter and changing wall contact. In an exemplary clinical data set correlation between regional CV with FD and the P2P voltage was observed.
O. Dössel, and A. Loewe. Computerized modeling of the human heart. In Zeitschrift für Medizinische Physik, vol. 27(3) , pp. 167-169, 2017
G. Lenis, N. Pilia, A. Loewe, W. H. W. Schulze, and O. Dössel. Comparison of Baseline Wander Removal Techniques considering the Preservation of ST Changes in the Ischemic ECG: A Simulation Study. In Computational and Mathematical Methods in Medicine, vol. 2017(Article ID 9295029) , pp. 13, 2017
The most important ECG marker for the diagnosis of ischemia or infarction is a change in the ST segment. Baseline wander is a typical artifact that corrupts the recorded ECG and can hinder the correct diagnosis of such diseases. For the purpose of finding the best suited filter for the removal of baseline wander, the ground truth about the ST change prior to the corrupting artifact and the subsequent filtering process is needed. In order to create the desired reference, we used a large simulation study that allowed us to represent the ischemic heart at a multiscale level from the cardiac myocyte to the surface ECG. We also created a realistic model of baseline wander to evaluate five filtering techniques commonly used in literature. In the simulation study, we included a total of 5.5 million signals coming from 765 electrophysiological setups. We found that the best performing method was the wavelet-based baseline cancellation. However, for medical applications, the Butterworth high-pass filter is the better choice because it is computationally cheap and almost as accurate. Even though all methods modify the ST segment up to some extent, they were all proved to be better than leaving baseline wander unfiltered.
A. Loewe, and O. Dössel. Commentary: Virtual In-Silico Modeling Guided Catheter Ablation Predicts Effective Linear Ablation Lesion Set for Longstanding Persistent Atrial Fibrillation: Multicenter Prospective Randomized Study. In Frontiers in Physiology, vol. 8, pp. 1113, 2017
Radiofrequency ablation has become a first-line approach for curative therapy of many cardiac arrhythmias. Various existing catheter designs provide high spatial resolution to identify the best spot for performing ablation and to assess lesion formation. However, creation of transmural and nonconducting ablation lesions requires usage of catheters with larger electrodes and improved thermal conductivity, leading to reduced spatial sensitivity. As trade-off, an ablation catheter with integrated mini electrodes was introduced. The additional diagnostic benefit of this catheter is still not clear. In order to solve this issue, we implemented a computational setup with different ablation scenarios. Our in silico results show that peak-to-peak amplitudes of unipolar electrograms from mini electrodes are more suitable to differentiate ablated and nonablated tissue compared to electrograms from the distal ablation electrode. However, in orthogonal mapping position, no significant difference was observed between distal electrode and mini electrodes electrograms in the ablation scenarios. In conclusion, catheters with mini electrodes bring about additional benefit to distinguish ablated tissue from nonablated tissue in parallel position with high spatial resolution. It is feasible to detect conduction gaps in linear lesions with this catheter by evaluating electrogram data from mini electrodes.
Cardiologists measure electric signals inside the human heart aiming at a better diagnosis and optimized therapy of atrial arrhythmias like atrial flutter and atrial fibrillation. The catheters that are used for this purpose are improving: now they are able to pick up the electric signals at up to 64 positions inside the heart simultaneously. The patterns of electric depolarization are sometimes very simple, comparable to plane waves. But in case of patients with severe atrial arrhythmias they can be quite complex: U-turns around a line of block, ectopic centres, break throughs, reentry circuits, rotors, fractionated signals and chaotic patterns are often observed. Methods of biosignal analysis can support the cardiologists in classifying the signals and extract information of high diagnostic relevance. Computer models of the electrophysiology of the human heart can serve to design better algorithms for data analysis and to test algorithms, because the ground truth is known.
AIMS: P-wave morphology correlates with the risk for atrial fibrillation (AF). Left atrial (LA) enlargement could explain both the higher risk for AF and higher P-wave terminal force (PTF) in lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IAC), which both show tremendous variability. METHODS AND RESULTS: Atrial excitation was triggered from seven different EAS in a cohort of eight anatomically personalized computational models. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed and separated by left and right atrial contributions. Mid-septal EAS yielded the highest PTF-V1. More anterior/superior and more inferior EAS yielded lower absolute PTF-V1 values deviating by a factor of up to 2.0 for adjacent EAS. Earliest right-to-left activation was conducted via Bachmann's Bundle (BB) for anterior/superior EAS and shifted towards posterior IACs for more inferior EAS. Non-conducting posterior IACs increased PTF-V1 by up to 150% compared to intact posterior IACs for inferior EAS. LA contribution to the P-wave integral was 24% on average. CONCLUSION: The electrical contributor's site of earliest activation and intactness of posterior IACs affect PTF-V1 significantly by changing LA breakthrough sites independent from LA size. This should be considered for interpretation of electrocardiographical signs of LA abnormality and LA enlargement.
Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today's high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration.
Whole-chamber mapping using a 64-pole basket catheter (BC) has become a featured approach for the analysis of excitation patterns during atrial fibrillation. A flexible catheter design avoids perforation but may lead to spline bunching and influence coverage. We aim to quantify the catheter deformation and endocardial coverage in clinical situations and study the effect of catheter size and electrode arrangement using an in silico basket model. Atrial coverage and spline separation were evaluated quantitatively in an ensemble of clinical measurements. A computational model of the BC was implemented including an algorithm to adapt its shape to the atrial anatomy. Two clinically relevant mapping positions in each atrium were assessed in both clinical and simulated data. The simulation environment allowed varying both BC size and electrode arrangement. Results showed that interspline distances of more than 20 mm are common, leading to a coverage of less than 50% of the left atrial (LA) surface. In an ideal in silico scenario with variable catheter designs, a maximum coverage of 65% could be reached. As spline bunching and insufficient coverage can hardly be avoided, this has to be taken into account for interpretation of excitation patterns and development of new panoramic mapping techniques.
A. Loewe, Y. Lutz, M. Wilhelms, D. Sinnecker, P. Barthel, E. P. Scholz, O. Dössel, G. Schmidt, and G. Seemann. In-silico assessment of the dynamic effects of amiodarone and dronedarone on human atrial patho-electrophysiology.. In Europace : European pacing, arrhythmias, and cardiac electrophysiology : journal of the working groups on cardiac pacing, arrhythmias, and cardiac cellular electrophysiology of the European Society of Cardiology, vol. 16(S4) , pp. iv30-iv38, 2014
AIMS: The clinical efficacy in preventing the recurrence of atrial fibrillation (AF) is higher for amiodarone than for dronedarone. Moreover, pharmacotherapy with these drugs is less successful in patients with remodelled substrate induced by chronic AF (cAF) and patients suffering from familial AF. To date, the reasons for these phenomena are only incompletely understood. We analyse the effects of the drugs in a computational model of atrial electrophysiology. METHODS AND RESULTS: The Courtemanche-Ramirez-Nattel model was adapted to represent cAF remodelled tissue and hERG mutations N588K and L532P. The pharmacodynamics of amiodarone and dronedarone were investigated with respect to their dose and heart rate dependence by evaluating 10 descriptors of action potential morphology and conduction properties. An arrhythmia score was computed based on a subset of these biomarkers and analysed regarding circadian variation of drug concentration and heart rate. Action potential alternans at high frequencies was observed over the whole dronedarone concentration range at high frequencies, while amiodarone caused alternans only in a narrow range. The total score of dronedarone reached critical values in most of the investigated dynamic scenarios, while amiodarone caused only minor score oscillations. Compared with the other substrates, cAF showed significantly different characteristics resulting in a lower amiodarone but higher dronedarone concentration yielding the lowest score. CONCLUSION: Significant differences exist in the frequency and concentration-dependent effects between amiodarone and dronedarone and between different atrial substrates. Our results provide possible explanations for the superior efficacy of amiodarone and may aid in the design of substrate-specific pharmacotherapy for AF.
In case of chest pain, immediate diagnosis of myocardial ischemia is required to respond with an appropriate treatment. The diagnostic capability of the electrocardiogram (ECG), however, is strongly limited for ischemic events that do not lead to ST elevation. This computational study investigates the potential of different electrode setups in detecting early ischemia at 10 minutes after onset: standard 3-channel and 12-lead ECG as well as body surface potential maps (BSPMs). Further, it was assessed if an additional ECG electrode with optimized position or the right-sided Wilson leads can improve sensitivity of the standard 12-lead ECG. To this end, a simulation study was performed for 765 different locations and sizes of ischemia in the left ventricle. Improvements by adding a single, subject specifically optimized electrode were similar to those of the BSPM: 211% increased detection rate depending on the desired specificity. Adding right-sided Wilson leads had negligible effect. Absence of ST deviation could not be related to specific locations of the ischemic region or its transmurality. As alternative to the ST time integral as a feature of ST deviation, the K point deviation was introduced: the baseline deviation at the minimum of the ST-segment envelope signal, which increased 12-lead detection rate by 7% for a reasonable threshold.
AIMS: Human ether-a-go-go-related gene (hERG) missense mutations N588K and L532P are both associated with atrial fibrillation (AF). However, the underlying gain-of-function mechanism is different. The aim of this computational study is to assess and understand the arrhythmogenic mechanisms of these genetic disorders on the cellular and tissue level as a basis for the improvement of therapeutic strategies. METHODS AND RESULTS: The IKr formulation of an established model of human atrial myocytes was adapted by using the measurement data of wild-type and mutant hERG channels. Restitution curves of the action potential duration and its slope, effective refractory period (ERP), conduction velocity, reentry wavelength (WL), and the vulnerable window (VW) were determined in a one-dimensional (1D) tissue strand. Moreover, spiral wave inducibility and rotor lifetime in a 2D tissue patch were evaluated. The two mutations caused an increase in IKr regarding both peak amplitude and current integral, whereas the duration during which IKr is active was decreased. The WL was reduced due to a shorter ERP. Spiral waves could be initiated by using mutation models as opposed to the control case. The frequency dependency of the VW was reversed. CONCLUSION: Both mutations showed an increased arrhythmogenicity due to decreased refractory time in combination with a more linear repolarization phase. The effects were more pronounced for mutation L532P than for N588K. Furthermore, spiral waves presented higher stability and a more regular pattern for L532P. These in silico investigations unveiling differences of mutations affecting the same ion channel may help to advance genotype-guided AF prevention and therapy strategies.
The SuLMaSS project  will advance, develop, build, evaluate, and test infrastructure for sustainable lifecycle management of scientific software. The infrastructure is tested and evaluated by an existing cardiac electrophysiology simulation software project, which is currently in the prototype state and will be advanced towards optimal usability and a large and active user community. Thus, SuLMaSS is focused on designing and implementing application-oriented e-research technologies and the impact is three-fold: - Provision of a high quality, user-friendly cardiac electrophysiology simulation software package that accommodates attestable needs of the scientific community. - Delivery of infrastructure components for testing, safe-keeping, referencing, and versioning of all phases of the lifecycle of scientific software. - Serve as a best practice example for sustainable scientific software management. Scientific software development in Germany and beyond shall benefit through both the aforementioned best practice role model and the advanced infrastructure that will, in part, be available for external projects as well. With adding value for the wider scientific cardiac electrophysiology community, the software will be available under an open source license and be provided for a large share of people and research groups that can potentially leverage computational cardiac modeling methods. Institutional infrastructure will be extended to explore, evaluate and establish the basis for research software development regarding testing, usage, maintenance and support. The cardiac electrophysiology simulator will drive and showcase the infrastructure formation, thus serving as a lighthouse project. The developed infrastructure can be used by other scientific software projects in future and aims to support the full research lifecycle from exploration through conclusive analysis and publication, to archival, and sharing of data and source code, thus increasing the quality of research results. Moreover it will foster a community-based collaborative development and improve sustainability of research software.
T. Fritz, E. Kovacheva, G. Seemann, O. Dössel, and A. Loewe. The inverse problem of cardiac mechanics - estimation of cardiac active stress from endocardial motion tracking. In Computational & Mathematical Biomedical Engineering Proceedings, vol. 1, pp. 91-95, 2019
The heart acts as the pump of the cardiovascular system due to the active stress developed in individ- ual cardiac muscle cells. The spatio-temporal distribution of this active stress could contain relevant diagnostic information but can currently not be measured in vivo. We introduce a method to esti- mate dynamic cardiac active stress fields from endocardial surface motion tracking derived from e.g. magnetic resonance imaging data. This ill-posed non-linear problem is solved using Tikhonov regu- larization in space and time in conjunction with a continuum mechanics forward model. We present a proof-of-concept using data from a biophysically detailed multiscale model of cardiac electrome- chanics (7649 tetrahedral elements) in which we could accurately reproduce cardiac motion (surface error <0.4 mm) and identify non-contracting regions due to myocardial infarction scars (active stress error <10 kPa). This inverse method could eventually be used to non-invasively derive personalized diagnostic information in terms of dynamic active stress fields which are not accessible today.
In Western countries, stroke is the third-most cause of death; 35- 55% of the survivors experience permanent disability. Mild therapeutic hypothermia (TH) showed neuroprotective effect in patients returning from cardiac arrest and is therefore assumed to decrease stroke induced cerebral damage. Recently, an intracarotid cooling sheath was developed to induce local TH in the penumbra using the cooling effect of cerebral blood flow via collaterals. Computational modeling provides unique opportunities to predict the resulting cerebral temperature without invasive procedures. In this work, we generated a simplified brain model to establish a cerebral temperature calculation using Pennes’ bio-heat equation and a 1D hemodynamics model of the cranial artery tree. In this context, we performed an extensive literature research to assign the terminal segments of the latter to the corresponding perfused tissue. Using the intracarotid cooling method, we simulated the treatment with TH for different degrees of stenosis in the middle cerebral artery (MCA) and analyzed the resulting temperature spatialtemporal distributions of the brain and the systemic body considering the influence of the collaterals on the effect of cooling.
M. Hernández Mesa, N. Pilia, O. Dössel, and A. Loewe. Influence of ECG Lead Reduction Techniques for Extracellular Potassium and Calcium Concentration Estimation. In Current Directions in Biomedical Engineering, vol. 5(1) , pp. 69-72, 2019
Chronic kidney disease (CKD) affects 13% of the worldwide population and end stage patients often receive haemodialysis treatment to control the electrolyte concentrations. The cardiovascular death rate increases by 10% - 30% in dialysis patients than in general population. To analyse possible links between electrolyte concentration variation and cardiovascular diseases, a continuous non-invasive monitoring tool enabling the estimation of potassium and calcium concentration from features of the ECG is desired. Although the ECG was shown capable of being used for this purpose, the method still needs improvement. In this study, we examine the influence of lead reduction techniques on the estimation results of serum calcium and potassium concentrations.We used simulated 12 lead ECG signals obtained using an adapted Himeno et al. model. Aiming at a precise estimation of the electrolyte concentrations, we compared the estimation based on standard ECG leads with the estimation using linearly transformed fusion signals. The transformed signals were extracted from two lead reduction techniques: principle component analysis (PCA) and maximum amplitude transformation (Max- Amp). Five features describing the electrolyte changes were calculated from the signals. To reconstruct the ionic concentrations, we applied a first and a third order polynomial regression connecting the calculated features and concentration values. Furthermore, we added 30 dB white Gaussian noise to the ECGs to imitate clinically measured signals. For the noisefree case, the smallest estimation error was achieved with a specific single lead from the standard 12 lead ECG. For example, for a first order polynomial regression, the error was 0.0003±0.0767 mmol/l (mean±standard deviation) for potassium and -0.0036±0.1710 mmol/l for calcium (Wilson lead V1). For the noisy case, the PCA signal showed the best estimation performance with an error of -0.003±0.2005 mmol/l for potassium and -0.0002±0.2040 mmol/l for calcium (both first order fit). Our results show that PCA as ECG lead reduction technique is more robust against noise than MaxAmp and standard ECG leads for ionic concentration reconstruction.
Stroke is the third-most cause of death in developed countries. A new promising treatment method in case of an ischemic stroke is selective intracarotid blood cooling combined with mechanical artery recanalization. However, the control of the treatment requires invasive or MRI-assisted measurement of cerebral temperature. An auspicious alternative is the use of computational modeling. In this work, we extended an existing 1D hemodynamics model including the characteristics of the anterior, middle and posterior cerebral artery. Furthermore, seven ipsilateral anastomoses were additionally integrated for each hemisphere. A potential stenosis was placed into the M1 segment of the middle cerebral artery, due to the highest risk of occlusion there. The extended model was evaluated for various degrees of collateralization (“poor”, “partial” and “good”) and degrees of stenosis (0%, 50%, 75% and 99.9%). Moreover, cerebral autoregulation was considered in the model. The higher the degree of collateralization and the degree of stenosis, the higher was the blood flow through the collaterals. Hence, a patient with a good collateralization could compensate a higher degree of occlusion and potentially has a better outcome after an ischemic stroke. For a 99.9% stenosis, an increased summed mean blood flow through the collaterals of +97.7% was predicted in case of good collateralization. Consequently, the blood supply via the terminal branches of the middle cerebral artery could be compensated up to 44.4% to the physiological blood flow. In combination with a temperature model, our model of the cerebral collateral circulation can be used for tailored temperature prediction for patients to be treated with selective therapeutic hypothermia.
A. Loewe, Y. Lutz, A. Fabbri, and S. Severi. Sinus Bradycardia Due to Electrolyte Changes as a Potential Pathomechanism of Sudden Cardiac Death in Hemodialysis Patients. In Biophysical Journal, vol. 116(3 suppl1) , pp. 231A, 2019
A. Loewe, Y. Lutz, N. Nagy, A. Fabbri, C. Schweda, A. Varro, and S. Severi. Inter-Species Differences in the Response of Sinus Node Cellular Pacemaking to Changes of Extracellular Calcium. In 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1875-1878, 2019
Changes of serum and extracellular ion concentrations occur regularly in patients with chronic kidney disease (CKD). Recently, hypocalcaemia, i.e. a decrease of the extracellular calcium concentration [Ca 2+ ] o , has been suggested as potential pathomechanism contributing to the unexplained high rate of sudden cardiac death (SCD) in CKD patients. In particular, there is a hypothesis that hypocalcaemia could slow down natural pacemaking in the human sinus node to fatal degrees. Here, we address the question whether there are inter-species differences in the response of cellular sinus node pacemaking to changes of [Ca 2+ ] o . Towards this end, we employ computational models of mouse, rabbit and human sinus node cells. The Fabbri et al. human model was updated to consider changes of intracellular ion concentrations. We identified crucial inter-species differences in the response of cellular pacemaking in the sinus node to changes of [Ca 2+ ] o with little changes of cycle length in mouse and rabbit models (<83 ms) in contrast to a pronounced bradycardic effect in the human model (up to >1000 ms). Our results suggest that experiments with human sinus node cells are required to investigate the potential mechanism of hypocalcaemia-induced bradycardic SCD in CKD patients and small animal models are not well suited.
Y. Lutz, R. Daschner, L. Krames, A. Loewe, O. Dössel, and G. Cattaneo. Estimating Local Therapeutic Hypothermia in Case of Ischemic Stroke Using a 1D Hemodynamics Model and an Energetic Temperature Model. In 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 3983-3986, 2019
In Western countries, stroke is the third-most widespread cause of death. 80% of all strokes are ischemic and show a mortality rate of about 25%. Furthermore, 35-55% of affected patients retain a permanent disability. Therapeutic hypothermia (TH) could decrease inflammatory processes and the stroke-induced cerebral damage. Currently, the standard technique to induce TH is cooling of the whole body, which can cause several side effects. A novel cooling sheath uses intra-carotid blood cooling to induce local TH. Unfortunately, the control of the temporal and spatial cerebral temperature course requires invasive temperature measurements. Computational modeling could be used to predict the resulting temperature courses instead. In this work, a detailed 1D hemodynamics model of the cerebral arterial system was coupled with an energetic temperature model. For physiological conditions, 50% and 100% M1-stenoses, the temperatures in the supply area of the middle cerebral artery (MCA) and of the systemic body was analyzed. A 2K temperature decrease was reached within 10min of cooling for physiological conditions and 50% stenosis. For 100% stenosis, a significant lower cooling effect was observed, resulting in a maximum cerebral temperature decrease of 0.7K after 30min of cooling. A significant influence of collateral flow rates on the cooling effect was observed. However, regardless of the stenosis degree, the temperature decrease was strongest within the first 20min of cooling, which demonstrates the fast and effective impact of intra-carotid blood cooling.
N. Pilia, M. H. Mesa, O. Dössel, and A. Loewe. ECG-based Estimation of Potassium and Calcium Concentrations: Proof of Concept with Simulated Data. In 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 2610-2613, 2019
In Europe, the prevalence of chronic kidney disease lay at approximately 18.38% in 2016. A common treatment for patients in the end stage of this disease is haemodialysis. However, patients undergoing this therapy suffer from an increased risk of cardiac death. A hypothesis is that the cause is an inbalanced electrolyte concentration. To study the underlying mechanisms of this phenomenon and fight the consequences, a continous non-invasive monitoring technique is desired. In this work, we investigated the possibility to reconstruct the extracellular concentrations of potassium and calcium from ECG signals. Therefore, we extracted 71 ECGs using the simulation results of a modified Himeno et al. ventricular cell model comprising variations of the extracellular ionic concentrations of potassium and calcium. The changes dependent on the different extracellular ionic concentrations were captured with five ECG features. These were used to train an artificial neural network for regression. The study was performed both for noise-free and noisy data. The estimation error for the reconstruction of the potassium concentrations was -0.01±0.14 mmol/l (mean±standard deviation) in the noise- free case, -0.03±0.46mmol/l in the noisy case (30dB SNR). For calcium, the result was 0.01±0.11mmol/l in the noise- free case, 0.02±0.17mmol/l in the noisy case. For both ion types, the result was improved by augmenting the dataset. We therefore conclude that with the calculated features, we are able to reconstruct the extracellular ionic concentrations for both potassium and calcium with an acceptable precision. When analysing noisy signals, the accuracy of the estimation method is still sufficient but can be further improved by an augmentation of the dataset.
S. Schuler, A. Loewe, and O. Dössel. Forcing Transmembrane Voltages to Decrease Slowly: A Temporal Regularization for ECG Imaging. In Computing in Cardiology, vol. 45, 2018
ECG imaging aims to reconstruct the cardiac electrical activity from non-invasive measurements of body surface potentials (BSP) by finding unique and physiologically meaningful solutions to the inverse problem of electrocardiography. This can be accomplished using regularization, which reduces the space of admissible solutions by demanding solution properties that are already known beforehand. Messnarz et. al. proposed a regularization scheme that requires transmembrane voltages (TMV) to not decrease over time. We suggest a generalization of this method that forces TMVs to decrease only slowly and as a result can also be applied to irregular cardiac activity. We first develop the method using a simplified spherical geometry and then show its benefit for imaging fibrillatory activity on a realistic geometry of the atria.
O. Dössel, T. Oesterlein, L. Unger, A. Loewe, C. Schmitt, and A. Luik. Spatio-temporal Analysis of Multichannel Atrial Electrograms Based on a Concept of Active Areas. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, vol. 2018, pp. 490-493, 2018
Atrial tachycardia and atrial flutter are frequent arrhythmia that occur spontaneously and after ablation of atrial fibrillation. Depolarization waves that differ significantly from sinus rhythm propagate across the atria with high frequency (typically 140 to 220 beats per minute). A detailed and personalized analysis of the spread of depolarization is imperative for a successful ablation therapy. Thus, catheters with several electrodes are employed to measure multichannel electrograms inside the atria. Here we propose a new concept for spatio-temporal analysis of multichannel electrograms during atrial tachycardia and atrial flutter. It is based on the calculation of simultaneously active areas. The method allows to identify atrial tachycardia and to automatically distinguish between subtypes of focal activity, micro-reentry and macro-reentry.
Patients suffering from end stage of chronic kid- ney disease (CKD) often undergo haemodialysis to normalize the electrolyte concentrations. Moreover, cardiovascular disease (CVD) is the main cause of death in CKD patients. To study the connection between CKD and CVD, we investi- gated the effects of an electrolyte variation on cardiac signals (action potential and ECG) using a computational model. In a first step, simulations with the Himeno et al. ventricular cell model were performed on cellular level with different extra- cellular sodium ([Na+]o), calcium ([Ca2+]o) and potassium ([K+]o) concentrations as occurs in CKD patients. [Ca2+]o and [K+]o changes caused variations in different features describ- ing the morphology of the AP. Changes due to a [Na+]o varia- tion were not as prominent. Simulations with [Ca2+]o varia- tions were also carried out on ventricular ECG level and a 12-lead ECG was computed. Thus, a multiscale simulator from ion channel to ECG reproducing the calcium-dependent inactivation of ICaL was achieved. The results on cellular and ventricular level agree with results from literature. Moreover, we suggest novel features representing electrolyte changes that have not been described in literature. These results could be helpful for further studies aiming at the estimation of ionic concentrations based on ECG recordings.
The contraction of the heart is a complex process involving the interaction of the passive properties of the tissue and the active tension development, which is elicited by the electrical activation of the cells. In this study, the electro-mechanical delay (EMD) was investigated as well as its dependence on the length of the sarcomeres, which are the contractile units within the cell. EMD was defined as the time offset between the electrical activation of the cell and the time of maximal tension. On a simple bar geometry with unidirectional fibre orientation and a linear local activation time distribution, the EMD proved to be inhomogeneous. The contraction of the early activated regions caused an elongation of the sarcomere (stretch) in the neighbouring regions, which ware electrically activated at a later time. The tension in the stretched region reached twice the value of the cells in the not-stretched, early activated region . Furthermore, the EMD in the early electrically activated region was more than 0.2 s, which was about twice the EMD of the stretched regions. In conclusion, the stretched region developed higher tension within a shorter time interval compared to the early activated region. Future studies will investigate how the inhomogeneous EMD affects cardiac output.
Background: Perimitral flutter commonly occurs following ablation of atrial fibrillation (AF) and can be cured by an anterior mitral line (AML). However, confirmation of bidirectional block can be challenging. Objective: We hypothesized that P-wave morphology and timing under left atrial appendage (LAA) pacing changes upon AML- block. Methods: We analyzed 129 consecutive patients (66±8 y, 64%male) who developed perimitral flutter after AF ablation. We designed ECG-criteria in a retrospective cohort (n=76) and analyzed them in a validation cohort (n=53). Results: Bidirectional AML-block was achieved in 110 patients (85%). For ablation performed during LAA-pacing without flutter (n=52), we found an immediate V1-jump (increase in LAA- stimulus to P-wave peak in lead V1) as a real-time marker of AML-block (V1-jump ≥30ms: sensitivity 95%, specificity 100%, PPV 100%, NPV 88%). Since V1-jump is not applicable when block coincides with termination of flutter, absolute V1-delay was used as a criterion applicable in all cases (n=129) with a delay of 203ms indicating block (sensitivity 92%, specificity 84%, PPV 90%, NPV 87%). Furthermore, an initial negative P-wave portion in the inferior leads was observed, which was attenuated in case of additional cavotricuspid isthmus (CTI) ablation. Computational P-wave simulations provide mechanistic confirmation of these findings for diverse ablation scenarios (pulmonary vein isolation±AML±roof-line±CTI ablation). Conclusion: V1-jump and V1-delay are novel real-time ECG- criteria allowing fast and straightforward assessment of AML- block during ablation for perimitral flutter.
A. Loewe, Y. Lutz, A. Fabbri, and S. Severi. Severe sinus bradycardia due to electrolyte changes as a pathomechanism of sudden cardiac death in chronic kidney disease patients undergoing hemodialysis. In Heart Rhythm, vol. 15(5S) , pp. S354-S355, 2018
Background: For chronic kidney disease patients undergoing maintenance hemodialysis (HD), the risk to die from sudden cardiac death (SCD) is 14x higher compared to patients with a history of cardiovascular disease and normal kidney function. Traditional SCD risk factors cannot explain this high rate. Two recent human studies using implantable loop recorders surprisingly point towards bradycardia and asystole as the prevailing arrhythmias causing SCD in HD patients. This suggests a decisive role of the sinus node. Objective: To identify the effect of altered electrolyte levels (as systematically occurring in HD patients) on pacemaking in a computational model of human sinus node cells. Methods: We enhanced the Fabbri et al. model of human sinus node cells to account for the dynamic intracellular balance of all considered electrolytes. The model was exposed to clinically relevant extracellular electrolyte concentrations of potassium, sodium, and calcium to study their effect on spontaneous beating rate and underlying pacemaking mechanisms. The level of sympathetic stimulation was kept constant. Results: The beating rate showed a monotonic relationship with altered electrolyte concentrations starting from a baseline value of 72.5bpm. It increased with sodium (70.8-73.8bpm for [Na+]o from 120-150mM), with potassium (70.7-81.9bpm for [K+]o from 3-9mM), and most pronouncedly with calcium (33.5- 133.8bpm for [Ca2+]o from 0.8-3mM). The severe bradycardia under hypocalcemic conditions was due to hyperpolarized maximum diastolic potential and slower diastolic depolarization driven by attenuation of ICaT and INCX, the latter due to depletion of intracellular calcium. Conclusion: Our human computational study suggests that hypocalcemia causes a pronounced decrease of cellular sinus node pacing rate, which may be a relevant mechanism in HD patients. While increased sympathetic tone will likely compensate the lower basal beating rate, patients developing severe hypocalcaemia are at high risk to experience severe bradycardia and die from SCD during a sudden loss of sympathetic tone.
A. Daub, A. Loewe, and B. Frohnapfel. Haemodynamics in an elasto-mechanic model of the human heart. In Annual Scientific Conference of the International Association of Applied Mathematics and Mechanics, 2018
Numerical modelling enables a quantitative evaluation of physiological and patho-physiological relationships within the human heart and the circulatory system. Surgical planning and optimisation of medical equipment using a virtual heart become possible by merging of empirical studies with physical and mathematical knowl- edge. These goals motivate a multi-physical coupling between electro-physiology, elasto-mechanics, blood flow and the circulatory system. In a first step a one-way coupling of all four relevant physical domains is considered. Simulation of electro- physiological excitation spread in conjunction with excitation contraction coupling yields the spatio-temporal distribution of cardiac active tension. This, as well as a closed loop model of the circulatory system, drive the continuum mechanics simulation of cardiac deformation and pressure, which in turn serve as a boundary condition for blood flow simulation. Physiological blood flow dynamics are dominated by the formation of a ring vortex that washes out the ven- tricles and thereby reduces the risk of thrombogenesis and flow stasis. This process is strongly affected by the heart valves. However, including the three dimensional leaflets and their interaction with the blood flow is computationally expensive. Further, the effort for construction is not negligible. Therefore, a simpler model is implemented as a first step. It comprises of three layers of porous cells that move with the valve plane and time dependently block or open the plane respectively. First results illustrate a high potential of the model to reliably reproduce the physiological vortex formation in the ventricles.
Multi-scale computational modeling of cardiac electrophysiology has fostered our understanding of the genesis of the ECG. While current models capture the relevant processes under physiological and many disease conditions with high fidelity, proper representation of the conditions in the extracellular milieu remains challenging. The recent human ventricular myocyte model by Himeno et al. is one of the first biophysical models which faithfully represents the dependence of the action potential (AP) duration on the extracellular calcium concentration ([Ca2+]o). Here, we present a heterogeneous formulation of the Himeno et al. cellular model and integrate it into a multi-scale framework to compute body surface ECGs. We propose three variants of the Himeno et al. model to account for transmural heterogeneity. The ionic current level parameter sets representing subendocardial, M, and subepicardial cell types were informed by the experimental data presented with the O’Hara-Rudy model and tuned to match AP level features such as repolarization stability. As shown in a previous work by Keller et al., an apico-basal gradient of IKs conductance is a likely mechanism causing concordant T-waves. Therefore, we increased the IKs conductance in the Himeno et al. model at the apex by a factor of 3.5 compared to the base to obtain an APD shortening of 12.5%. The model setup comprising transmural and apico-basal heterogeneity yielded a physiological ventricular ECG comparable to previous setups building on the ten Tusscher et al. cellular model. Our novel setup allows to study, for the first time, how realistic changes of the AP under hypo- and hypercalcaemic conditions translate to changes in the ECG. Resulting QT prolongation under hypocalcaemic conditions quantitatively matched human experimental data. In conclusion, the setup presented here provides a tool to study the effect of altered calcium levels in the extracellular milieu of the heart, as e. g. occurring during renal failure, across multiple spatial scales mechanistically.
The sinoatrial node (SAN) is the normal pacemaker of the mammalian heart. Over several decades, a large amount of data on the ionic mechanisms underlying the spontaneous electrical activity of SAN pacemaker cells has been obtained, mostly in experiments on single cells isolated from rabbit SAN. This wealth of data has allowed the development of mathematical models of the electrical activity of rabbit SAN pacemaker cells. However, the translation of animal data/models to humans is not straightforward. Even less so for SAN pacemaker cells than working myocar- dial cells given the big di↵erence in their main output (i.e. pacing rate) between human and laboratory animals. The development of a comprehensive model of the electrical activity of a human SAN pacemaker cell strictly based on and constrained by the available electrophysiological data will be presented. We started from the Severi-DiFrancesco rabbit SAN model, which integrates the two principal mecha- nisms that determine the beating rate: the ”membrane clock” and ”calcium clock”. Several current formulations were updated based on available measurements. A set of parameters, for which no specific data were available, were automatically opti- mized to reproduce the measured AP and calcium transient data. The model was then validated by assessing the e↵ects of several mutations a↵ecting heart rate and rate modulation. Moreover, two recent applications of the model will be presented: i) We used our SAN AP computational model to assess the e↵ects of the inclu- sion of the small conductance K+ current (ISK) on the biomarkers that describe the AP waveform and calcium transient; ii) We analysed the e↵ect of altered elec- trolyte levels (as systematically occurring in hemodialysis patients) on pacemaking to investigate the possible mechanisms of the bradycardic sudden cardiac deaths pointed out by two recent human studies using implantable loop recorders.
L. Baron, A. Loewe, and O. Dössel. From clinics to the virtual beating heart a general modeling workflow for patient-specific electromechanical heart simulations. In BMTMedPhys 2017, vol. 62(S1) , pp. S70, 2017
Generating meshes of complex structures in the human body like the heart organ is a prerequisite for computational simulations of of organ function. The quality of the conclusions derived from these simulations greatly depends on the quality and accuracy of the mesh they are based on. Volumetric computation domain can be represented by an equally-spaced voxel grid, or – in case of more sophisticated partial differential equation discretization methods (finite elements, finite volumes) – first, second or even higher order tetrahedral meshes. Here, we present a workflow that is capable of creating high quality meshes for such simulations. The workflow contains segmentation, surface mesh generation, volume mesh generation, and patient-specific parameter fitting to produce the desired results. While segmentation itself is a more or less unique mapping from a grayscale DICOM data set to a labeled, three-dimensional voxel mesh, different approaches exist for their transformation to a surface mesh. Our process involves a two-level approach for obtaining triangular or mixed rectangular surface meshes of desired quality and resolution. Both are crucial for the next step: obtaining a volumetric tetrahedral grid with the desired degrees of freedom. In the last step, a derivative-free parameter estimation approach is used to calibrate the dynamic behavior and tailor the model patient-specifically. All software used in the workflow is published under open source licenses and freely available. Its capability is demonstrated by means of an elastomechanical simulation of a human heart and yields measurable validation quantities in physiological ranges. We want to stress that the presented approach is generic and can easily be used for the model generation of other organs like liver, lungs or the aortic arch as well. The resulting meshes can be used for various types of simulations (electrical excitation propagation, blood flow) and use cases (clinical diagnostics, therapy planning etc.).
Today, patients suffering from atrial arrhythmias like atrial flutter (AFlut) or atrial fibrillation (AFib) are examined in the EP-lab (electrophysiology lab) in order to understand and treat the disease. Multichannel catheters are advanced into the atria in order to measureelectric signals at manyintracardiacpositions simultaneously. Complementary to clinical learning,comprehension of the disease and therapeutic strategies can be improved with computer modeling of the heart. This way, hypotheses about initiation and perpetuation of the arrhythmia can be tested and ablation strategies can be assessed in-silico. Modeling and biosignal analysis can benefit from mutual fertilization. On the one hand, modeling can be improved and personalization can be achieved via high density mapping of the atria. On the other hand, new algorithms for the interpretation of multichannel electrograms can be developed and evaluated with synthetic signals from computer models of the atria. This article illustrates the synergetic potential by examples and highlights challenges to be addressed in the future.
The Purkinje system is part of the fast-conducting ventricular excitation system. The anatomy of the Purkinje system varies from person to person and imposes a unique excitation pattern on the ventricular myocardium, which defines the morphology of the QRS complex of the ECG to a large degree. While it cannot be imaged in-vivo, it plays an important role for personalizing computer simulations of cardiac electrophysiology. Here, we present a new method to automatically model and customize the Purkinje system based on the measured electrocardiogram (ECG) of a patient. A graphbased algorithm was developed to generate Purkinje systems based on the parameters fibre density, minimal distance from the atrium, conduction velocity, and position and timing of excitation sources mimicking the bundle branches. Based on the resulting stimulation profile, the activation times of the ventricles were calculated using the fast marching approach. Predescribed action potentials and a finite element lead field matrix were employed to obtain surface ECG signals. The root mean square error (RMSE) between the simulated and measured QRS complexes of the ECGs was used as cost function to perform optimization of the Purkinje parameters. One complete evaluation from Purkinje tree generation to the simulated ECG could be computed in about 10 seconds on a standard desktop computer. The measured ECG of the patient used to build the anatomical model was matched via parallel simplex optimization with a remaining RMSE of 4.05 mV in about 16 hours. The approach presented here allows to tailor the structure of the Purkinje system through the measured ECG in a patient-specific way. The computationally efficient implementation facilitates global optimization.
Atrial arrhythmias such as atrial flutter and atrial fibrillation are a burden for patients and a major challenge for modern healthcare systems. Identification of patients at risk to develop atrial arrhythmias at an early stage carries the potential to reduce the incidence by implementing appropriate strategies to mitigate the risks. Diagnostic methods based on the ECG are ideal risk markers due to their noninvasiveness and omnipresence. The left atrium (LA) plays a major role in the intiation and perpetuation of atrial reentry arrhythmias. However, the LA is not well represented in the P-wave derived through standard ECG leads. Here, we optimize ECG lead positions to maximize LA information content. Towards this end, we used a cohort of eight personalized computational models providing the unique opportunity to separate LA and right atrial (RA) contributions to the P-wave, which is not feasible in vivo. The location of maximum P-wave signal energy was located on the center of the chest for all subjects with marked overlap between regions of maximum LA and RA P-wave amplitude. The regions of highest ratio between LA and RA signal energy differed between patients. However, a region with LA signal energy being higher than that of the RA and providing a sufficiently large absolute P-wave amplitude was identified at the center of the back consistently across five models of the cohort. Optimized linear combinations of standard 12-lead signals yielded comparably good results. Our newly proposed electrode positions on the back as well as selected linear combinations of standard 12-lead signals improve the LA information content considerably. By using these, more relevant diagnostic information regarding the anatomical and electrophysiological properties of the LA can be derived in future.
Chronic kidney disease (CKD) affects more than 30 million patients in the European Union. CKD causes alterations in the extracellular plasma electrolyte concentrations, which affect cardiac electrophysiology. A total of 25% of all deaths of CKD patients are due to sudden cardiac death (SCD). Until recently, ventricular fibrillation was assumed to be the main reason. In a 2015 study, Wong et al. observed bradycardia and asystole as the predominant mechanisms of SCD in patients with CKD. This shows that the influence of electrolyte changes on the underlying mechanisms of pacemaking in the sinoatrial node (SAN) needs to be better understood. In this work, we have updated the computational model of the human SAN given by Fabbri et al. and investigated the CKD-induced change of [Ca2+]o (0.6-3mM), [K+]o (3-9mM) and [Na+]o (120-150mM) on pacemaking. [Ca2+]o had the most dominant effects on SAN function. Low [Ca2+]o caused severe bradycardia in the model (down to 17 bpm) for 0.6 mM. A critical concentration range of calcium in the subspace [Ca2+]sub was identified as the possible underlying mechanism for pacemaking. For increasing [Ca2+]o, the heart rate (HR) increased, resulting in 142 bpm for the highest calcium concentration. The effect of [K+]o variation was similar to the one for [Ca2+]o, but caused less pronounced change. The resultant changes due to variation of [Na+]o were relatively small. In this work, several potential mechanisms for SCD in CKD patients could be identified. The low HR for low [Ca2+]o is seen as a possible link to the observed bradycardia in CKD patients. The findings in this work could lead to a better surveillance of [Ca2+]o in hemodialysis patients, and therefore to a decrease in the SCD rate.
Cardiac excitation during atrial fibrillation (AFib) is changing dynamically, compromising the ability to identify underlying mechanisms by intracardiac catheter mapping. Statistical analysis of dominant excitation patterns may help to identify and subsequently eliminate the drivers of this tachycardia. As the morphology of local bipolar intracardiac electrograms (EGMs) depends on the orientation of the propagating excitation wave, its evaluation for a fixed multichannel catheter position can provide information about the stability of the depolarization pattern. Up to date, analysis of morphology is most often done by computing a similarity index or the recurrence rate of individual EGMs, reflecting how often similar excitations appear. We sougth to extend this approach to a classification based analysis technique. In each multichannel EGM, local activation waves (LAWs) were automatically detected by assessing instantaneous signal energy. A greedy algorithm was implemented to cluster LAWs based on their similiarity. New clusteres were formed when similarity fell below a predefined threshold. The concept was tested using simulated EGM data (quadratic patch of cardiac tissue, bidomain simulation, both planar and focal excitations, various catheter types). Results demonstrated that the algorithm correctly identified and classified the simulated excitation patterns. Subsequent quantitative analysis allowed to both discard singular classes of excitation and identify dominant excitations. The presented method forms the basis for statistical assessment of prevailing depolarization patterns, and for computation of additional features like conduction velocity, presence of focal sources, or dissociation when applied on multichannel data.
S. Schuler, L. Baron, A. Loewe, and O. Dössel. Developing and coupling a lumped element model of the closed loop human vascular system to a model of cardiac mechanics. In BMTMedPhys 2017, vol. 62(S1) , pp. S69, 2017
Modelling the interaction of the heart and the vascular system allows to study the pumping efficiency of the heart in a controlled environment under various cardiac and vascular conditions such as arrhythmias, dyssynchronies, regions of stiffened myocardium, valvular stenoses or decreased vascular compliances. To pose realistic hemodynamic boundary conditions to a four-chambered elastomechanical heart model, we developed a lumped element model of the closed loop human vascular system. Systemic and pulmonary circulations were each represented by a three-element Windkessel model emptying into a venous compliance. Both circulations were coupled by connecting the venous compliances to the corresponding atrium via venous resistances. Cardiac valves were represented by ideal diodes and resistances. Strong coupling between the heart and the vascular system model was accomplished by estimating the cardiac pressures that lead to continuous flows across the model interfaces. Active regulatory mechanisms were not considered. Pressures, flows and volumes throughout the circulatory system were simulated until a steady state was reached and the effects of model parameters on these hemodynamic parameters were evaluated in a sensitivity analysis. Increasing the systemic peripheral resistance by 50% caused an 8% decrease in stroke volume (SV) and a 33% increase in mean arterial pressure. Increased venous resistance descreased the E/A wave ratio of the atrioventricular flow and led to a reduced SV by impeding passive cardiac filling. Increasing the arterial compliance decreased mean cardiac pressures, while only slightly reducing the SV. Larger arterial resistances mainly caused higher peak systolic pressures. Furthermore, we show that embedding the heart model into surrounding elastic tissue by forcing permanent contact at the pericardial surface leads to more realistic time courses of atrial volumes and atrial pressure-volume curves composed of an A and a V loop as found in measurements. In conclusion, this work enables simulations of diseases that involve significant cardiovascular interaction.
Acquiring adequate mapping data in patients with atrial fibrillation is still one of the main obstacles in the treatment of this atrial arrhythmia. Due to the lack of catheters with both a panoramic field of view and sufficient electrode density for simultaneous mapping, electrophysiologists are forced to fall back on sequential mapping techniques. But, because activation patterns change rapidly during atrial fibrillation, they cannot be mapped sequentially. We propose that mapping tissue properties which are time independent, in contrast, allows a sequential approach. Here, we use the shortest measured electrogram cycle length to estimate the effective refractory period of the underlying tissue in a simulation study. Atrial fibrillation was simulated in a spherical model of the left atrium comprised of regions with varied refractory period. We found that the minimal measured electrogram cycle length correlates with the effective refractory period of the underlying tissue if the regions with distinct refractory properties are large enough and if the absolute difference in effective refractory periods is sufficient. This approach is capable of identifying regions of lowered effective refractory period without the need for cardioversion. Those regions are likely to harbor drivers of atrial fibrillation, which emphasizes the necessity of their localization.
Atrial fibrillation (AF) ablation guided by basket catheter mapping has shown to be beneficial. Yet, the initial excitement is mitigated by a growing skepticism due to the difficulty in verifying the protocol in multicenter studies. Overall, the underlying assumptions of rotor ablation require further verification. The aim of this study was therefore to test such hypotheses by using computational modeling. The 3D left atrial geometry of an AF patient was segmented from a pre-operative MR scan. Atrial activation was simulated on the 3D anatomy using the monodomain approach and a variant of the Courtemanche action potential model. Ablated tissue was assigned zero conductivity. Reentry was successfully initialized by applying a single suitably delayed extra stimulus. Unipolar electrograms were computed at the simulated electrode positions. The final dataset was generated by varying location of reentry and catheter position within the LA. The effect of inter-electrode distance and distance to the atrial wall was studied in relation to the ability to recover rotor trajectory, as computed by a novel algorithm described here. The effect of rotor ablation was also assessed.
O. Dössel, and A. Loewe. V 10 Computer Modelling pharmakologischer Effekte. In Frühjahrstagung der Deutschen Gesellschaft für Kardiologie, 2017
A. Fabbri, A. Loewe, R. Wilders, and S. Severi. Propagation of the primary pacemaker activity in the human heart: a computational approach. In European Medical and Biological Engineering Conference (EMBEC), vol. 65, pp. 201, 2017
The sinoatrial node (SAN) is the natural pacemaker of our heart. How this small tissue is able to drive a remarkably larger number of intrinsically quiescent atrial cells is still debated; a computational investigation of the underlying mechanisms can help to better understand the SAN’s ability to pace-and-drive the surrounding atrium. Aim of this work is to elucidate how the human SAN action potential can successfully be captured by and propagate into the surrounding atrial tissue. The Fabbri et al. and the Courtemanche et al. models were used to describe the human SAN and atrial cells, respectively. The behaviour of two coupled regions was investigated varying the interregional conductivity (σ) and relative size. Simulations showed that it requires at least an isopotential SAN region 2.85 times wider than the atrial one. A 1D strand of homogeneously coupled SAN and atrial elements was used to identify an interval for σ showing pace-and-drive behaviour (100 SAN vs 100 atrial elements) and to investigate the source-sink interplay (10, 50 or 100 SAN elements vs 100 atrial elements). The 1D strand showed pace-and-drive behaviour for 𝜎 = 0.08 − 36 S/m; a stronger source, with a higher number of SAN elements, led to a wider 𝜎 range that allowed pace-and-drive behaviour, whereas a stronger sink did not affect the behaviour of the tissue. This preliminary work shows the ability of a small human SAN region to pace-and-drive the surrounding atrial tissue. Further investigations are needed to explore different conductivity configurations, including spatial gradients.
A. Loewe, Y. Lutz, A. Fabbri, S. Severi, G. Seemann, and D. Dössel. Influence of Electrolyte Concentration Changes on Sinus Node Function - A new Player Regarding Sudden Cardiac Death in Patients with Chronic Kidney Disease?. In Gordon Research Conference on Cardiac Arrhythmia Mechanisms, 2017
Atrial fibrillation and atrial flutter are the most common atrial arrhythmias placing a heavy burden on patients and posing a challenge on healthcare systems. If patients at risk to develop atrial arrhythmias can be identified at an early stage, the arrhythmia incidence can be lowered by implementing appropriate strategies to mitigate the risks. Diagnostic methods based on the ECG are ideal risk markers due to their noninvasiveness and omnipresence. The left atrium (LA) plays a major role in the initiation and perpetuation of atrial reentry arrhythmias. However, the LA is not well represented in the P-wave derived through standard ECG leads. Here, we optimize ECG leads to maximize LA information content. Towards this end, we used a cohort of eight personalized computational models providing the unique opportunity to separate LA and right atrial (RA) contributions to the P-wave, which is not feasible in vivo. The location of maximum P-wave signal energy was located on the center of the chest for all subjects with marked overlap between regions of maximum LA and RA P-wave amplitude. The regions of highest ratio between LA and RA signal energy differed between patients. However, a region with LA signal energy being higher than that of the RA and providing a sufficiently large absolute P-wave signal energy was identified at the lower left quadrant of the back consistently across most subjects of the cohort. Optimized linear combinations of standard 12-lead signals (considering the eight independent leads) yielded comparably good results amplifying LA information by more than one order of magnitude. Our newly proposed electrode positions on the back as well as selected combinations of standard ECG signals improve the LA information content considerably. By using these, more relevant diagnostic information regarding anatomical and electrophysiological properties of the LA can be derived in future.
Atrial arrhythmias like atrial fibrillation and atrial flutter are a major health challenge in developed countries. Radiofrequency ablation performed via intracardiac catheters is a curative therapy for these reentrant arrhythmias. However, the optimal location of ablation lesions is not straightforward to determine, particularly for complex activation patterns. Thus, a clinical need for tools to intuitively visualize complex activation patterns and to provide a platform to evaluate different ablation strategies in dry runs is apparent. Here, we present a virtual reality system that allows to interactively simulate atrial excitation propagation and place ablation lesions. Our software builds on the IMHOTEP framework for the Unity3D engine and implements a multithreaded model-view-controller design pattern. Excitation propagation is computed using a fast marching approach considering refractoriness. Interactive rewind and playback is supported through a combination of the flyweight pattern for simulation data with complete snapshots for key frames. The system was evaluated in a user study using the HTC ViveTM headset including two controllers. For high fidelity virtual reality interaction, a minimum frame rate of 60 per second is required. In a biatrial anatomical model comprising 36,059 nodes (Figure 1), even complex activation patterns with multiple wavefronts could be simulated and rendered down to 2x slow motion (1 sec activation sequence displayed during 2 sec wall time) on a desktop machine. Results of the user study suggest added value regarding the comprehension of arrhythmias and ablation options and very good intuitiveness of the user interface requiring almost no teach-in. The virtual reality tool is ready to be used for educational purposes and prepared to import personalized models supporting diagnosis and therapy planning for atrial arrhythmias in the future.
Chronic kidney disease appears worldwide. In the United States, the number of patients suffering from kid- ney failure doubled from 1998 to 2010. A common treat- ment for these patients is haemodialysis. However, the frequency of deaths caused by cardiovascular diseases is up to 10% to 30% higher in patients undergoing dialysis than in the general population. To analyse the underly- ing effects and for a possible risk prediction, a continuous monitoring of the ionic concentrations that are influenced by dialysis is desired. In this work, a method for the re- construction of the ionic concentrations of calcium and potassium from the ECG is proposed. In a first step, 91 monodomain simulations with the ten Tusscher ventricular cell model were performed for different extracellular ionic concentrations. From there, a standard 12-lead ECG was extracted. Calcium and potassium changes yielded ECGs clearly differing in amplitude and morphology. In a second step, the simulated ECG signals were used for reconstruc- ting the ionic concentrations directly from the ECG. Fea- tures were extracted from the signals designed to describe changes caused by varied ionic concentrations. The in- verse problem, i.e. coming back from the ECG features to the ionic concentrations was solved by regression with an artificial neural network. Results for potassium estimation yield an error of 0.00±0.28 mmol/l (mean±standard de- viation) calculated with 7-fold cross validation. The esti- mation error for calcium was 0.00±0.08 mmol/l. Although these results underline the suitability of the method, the used ECGs differed from the observed in a clinical envi- ronment. However, simulations allow an evaluation un- der controlled conditions of a particular effect that was intended to be investigated. As the application to clinical data is yet missing, this study can be seen as a proof of concept showing that an artificial neural network is capa- ble of exactly estimating potassium and calcium concen- trations from ECG features. 1. Introduction Haemodialysis therapy is a common treatment method for patients suffering from chronic kidney disease (CKD) in the terminal stage. The amount of people in the United States suffering from kidney failure increased from 320,000 in 1998 to 650,000 in 2010. The frequency of deaths caused by cardiovascular events within the dialysis patient group is up to 10% to 30% higher than in gene- ral population . Patients suffering from end-stage CKD experience high variations of blood electrolyte concentra- tions. These can directly influence the functioning of the heart. Thus, research on cardiovascular links could im- prove therapy and risk stratification. One tool which is capable of capturing the electrophysiological properties of the heart in a non-invasive way is the electrocardiogram (ECG). It is known, that electrolyte concentrations of po- tassium (K+) and calcium (Ca2+) affect the ECG . Un- til now, a determination of the concentrations is connec- ted to a blood test. Hence, continuous monitoring of the ionic concentration is impracticable. However, the ECG as a continuous, non-invasive monitoring tool could shed a light on the relation between heart diseases and changes in the ionic concentration particularly after leaving the strictly supervised clinical area where dialysis takes place, i.e allowing a monitoring at home. Articles have been pub- lished showing that the reconstruction of extracellular K+ concentration can be done using just one feature from the ECG with a quadratic regression . In this study, we tried to estimate both K+ and Ca2+ concentrations from the ECG. Therefore, we examined simulated ECGs at dif- ferent concentration levels and designed features descri- bing the observed changes in the ECG. A subset of these was used in connection with a machine learning method to reconstruct the concentrations. 2. Methods 2.1. Simulations A total number of 91 computer simulations of the car- diac electrophysiology were performed at whole heart
G. Seemann, A. Loewe, and E. M. Wülfers. Effects of Fibroblasts Coupling on the Electrophysiology of Cardiomyocytes from Different Regions of the Human Atrium: A Simulation Study. In Computing in Cardiology, vol. 44, 2017
Atrial fibrillation is a common cardiac arrhythmia. The disturbance of the normal repolarization process due to heterogeneous myocyte-fibroblast coupling might play a role for this disease. We investigate this interaction in the heterogeneous atrium using a computational approach. Human atrial myocyte computational models represent- ing 10 different regions of the atrium were each coupled to a human atrial fibroblast model and the impact of the myocyte-fibroblast coupling on action potential measures was investigated. Myocytes from the pulmonary vein are affected most by the coupling to fibroblasts. Action potential amplitude is reduced from 105 mV to 94 mV and the upstroke velocity changes from 192 V/s to 152 V/s, potentially reducing the conduction velocity. In general, the action potential dura- tion of myocytes with short action potentials is prolonged and that of those with long is shortened. The large effect on pulmonary vein action potentials is mainly due to reduced IK1 in these cells compared to other regions of the atrium. The strong effects of fibroblast cou- pling to pulmonary vein myocytes are likely to be an addi- tional reason for the crucial role of the pulmonary veins in atrial fibrillation.
G. Seemann, A. Loewe, and E. M. Wülfers. Computational Study on Regional Differences in Pro-Arrhythmic Effects of Fibroblasts Coupling to Human Atrial Myocytes. In TRM Forum, 2017
Atrial fibrillation (AF) is the most common type of arrhythmia encountered in clinical practice but its maintaining mechanisms remain elusive. Over the last years, various theories have been proposed to target AF mechanisms. Recently, there has been an increasing interest in understanding how spiral waves and rotors sustain AF and how they might be therapeutic targets for catheter-based ablation. Phase mapping has recently been used as a robust method to characterize the spatiotemporal variability of electrical activities. In this study, we propose an independent approach for basket catheter electrogram (EGM) processing to detect rotors in AF. An improved version of the sinusoidal recomposition method for the local activation timings (LATs) has been developed and 3D phase maps have been reconstructed. An algorithm able to detect stable and meandering rotors on the left atrium (LA) surface was then developed. This workflow has been validated on synthetic EGMs and in silico showing excellent results. On in vivo data, we found 4.0±3.4 and 4.6±5.0 localized and meandering rotors with a persistence in time: 303.2 ±58.2ms and 302.3±52.0ms respectively.
E. M. Wülfers, A. Loewe, and G. Seemann. A Computational Study on the Electrophysiological Effects of Fibroblasts Coupling to Human Atrial Myocytes from Different Regions. In Cardiac Physiome Project, 2017
P-wave assessment is frequently used in clinical practice to recognize atrial abnormalities. However, the use of P-wave criteria to diagnose specific atrial abnormalities such as left atrial enlargement has shown to be of limited use since these abnormalities can be difficult to distinguish using P-wave criteria to date. Hence, a mechanistic understanding how specific atrial abnormalities affect the P-wave is desirable. In this study, we investigated the effect of left atrial hypertrophy on P-wave morphology using an in silico approach. In a cohort of four realistic patient models, we homogeneously increased left atrial wall thickness in up to seven degrees of left atrial hypertrophy. Excitation conduction was simulated using a monodomain finite element approach. Then, the resulting transmembrane voltage distribution was used to calculate the corresponding extracellular potential distribution on the torso by solving the forward problem of electrocardiography. In our simulation setup, left atrial wall thickening strongly correlated with an increased absolute value of the P-wave terminal force (PTF) in Wilson lead V1 due to an increased negative amplitude while P-wave duration was unaffected. Remarkably, an increased PTF-V1 has often been associated with left atrial enlargement which is defined as a rather increased left atrial volume than a solely thickened left atrium. Hence, the observed contribution of left atrial wall thickness changes to PTF-V1 might explain the poor empirical correlation of left atrial enlargement with PTF-V1.
P-wave morphology correlates with the risk for atrial fibrillation (AF). Left atrial (LA) enlargement could ex- plain both the higher risk for AF and higher P-wave ter- minal force (PTF) in ECG lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypoth- esize that LA hypertrophy, i.e. a thickening of the myocar- dial wall, also contributes to increased PTF-V1 and is part of the reason for the rather low specificity of increased PTF-V1 regarding LA enlargement. To show this, atrial excitation propagation was simulated in a cohort of four anatomically individualized models in- cluding rule-based myocyte orientation and spatial elec- trophysiological heterogeneity using the monodomain ap- proach. The LA wall was thickened symmetrically in steps of 0.66 mm by up to 3.96 mm. Interatrial conduction was possible via discrete connections at the coronary sinus, Bachmann’s bundle and posteriorly. Body surface ECGs were computed using realistic, heterogeneous torso mod- els. During the early P-wave stemming from sources in the RA, no changes were observed. Once the LA got activated, the voltage in V1 tended to lower values for higher degrees of hypertrophy. Thus, the amplitude of the late positive P- wave decreased while the amplitude of the subsequent neg- ative terminal phase increased. PTF-V1 and LA wall thick- ening showed a correlation of 0.95. The P-wave duration was almost unaffected by LA wall thickening (∆ ≤2 ms). Our results show that PTF-V1 is a sensitive marker for LA wall thickening and elucidate why it is superior to P-wave area. The interplay of LA hypertrophy and dilation might cause the poor empirical correlation of LA size and PTF- V1.
P-wave morphology correlates with the risk for AF. Left atrial (LA) enlargement could explain both the higher risk for AF and higher P-wave terminal force (PTF) in lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IAC), which both show tremendous variability. Atrial excitation was triggered from seven different EAS on the epicardial surface around the sinus node region in eight anatomically personalized computational models including rule-based myocyte orientation and spatial electrophysiological heterogeneity. EAS1 was located midway between the tip of the right atrial appendage (RAA) and its junction with the superior vena cava (SVC), EAS2 at the superior part of the anterior wall, and EAS3 at the junction of the RAA and the SVC. EAS4 to EAS7 were uniformly distributed along the crista terminalis between EAS3 and orifice of the inferior vena cava (EAS7). IACs connected the atria at Bachmann’s bundle, coronary sinus and posteriorly. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed using realistic, heterogeneous torso models. Mid-septal EAS yielded the highest PTF-V1 measured as the product of the duration and the maximal amplitude of the negative phase of the P-wave in V1. More anterior/superior and more inferior EAS yielded lower absolute values deviating by a factor of up to 2.0 for adjacent EAS. Earliest right-to-left activation was conducted via BB for EAS1-3 and shifted towards posterior IACs for EAS 4-7. Non-conducting posterior IACs increased PTF-V1 by up to 150%. The electrical contributors EAS and intactness of posterior IACs affect PTF-V1 significantly by changing LA breakthrough sites. This should be considered when assessing LA anatomy based on the ECG.
Aim: P-wave morphology correlates with the risk for AF. Left atrial enlargement could explain both the higher risk for AF and higher P-wave terminal force in lead V1 (PTF-V1). However, PTF-V1 has been shown to correlate poorly with left atrial size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IACs), which both show tremendous variability. Methods: Atrial excitation was triggered from seven different EASs (Fig 1A,B) in eight anatomically personalized computational models including rule-based fiber orientation and spatial electrophysiological heterogeneity. IACs connected the atria at Bachmann’s bundle, coronary sinus, and posteriorly. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed using realistic, heterogeneous torso models of the same subjects. Results: Mid-septal EASs yielded the highest PTF-V1 measured as the product of the duration and the maximal amplitude of the negative phase of the P-wave in V1. More anterior/superior and more inferior EASs yielded lower absolute values deviating by a factor of up to 2.0 for adjacent EAS (Fig 1C). Earliest right-to-left activation was conducted via BB for EAS1-EAS3 and shifted towards posterior IACs for EAS4-EAS7. Non- conducting posterior IACs increased PTF-V1 by up to 150% (Fig 1D). Conclusions: Location of EAS in the right atrium and its proximity to functioning IACs affect PTF-V1 independently of the left atrial size and further support the caution that needs to be exercised when interpreting electrocardiographically signs of left atrial abnormality, which include PTF-V1.
Atrial arrhythmia is the most common cardiac arrhythmia. Parameters such as conduction velocity (CV), CV restitution etc. are under analysis in order to understand the cardiac arrhythmias. A number of methods have been proposed for CV calculation in simulation as well as clinical environments. Regional CV gives the information about the magnitude and direction of the propagating depolarization wavefronts on the atrium with homogeneous and heterogeneous tissue. The CV in different regions can provide important quantitative electrophysiological information about the underlying tissue. In this work the regional CV has been calculated using simulated local activation times (LAT) on clinical atrial geometries. Regions with homogeneous and heterogeneous propagation were manually selected for LAT simulation and later the regional CV has been calculated. The calculated CV for both the homogeneous and heterogeneous cases for all the clinical cases have been visualized on the atrial geometries. The visualization of the CV on the atrium represents insight into the regional behavior of the atrial substrate. The benefit of the region-specific study in clinical context is that it could enable the localization of critical sites in the patient specific atrial anatomies. Thus, this could aid physicians in cardiac therapies.
One promising application of electrocardiographic (ECG) imaging is noninvasive reconstruction of atrial activities. However, despite numerous clinical studies, which are mostly concerned with complex irregular excitation patterns, there are relatively few in silico investigations on the imaging of ectopic activation. In the present work, we explore the localization accuracy of ECG imaging regarding atrial focal sites. For the forward calculations, we used four realistic geometrical models with complex anatomical structure and a rule-based fiber orientation embedded into the atrial model. Excitation propagation was simulated with the monodomain model. For each geometrical model, 20 activation sequences originating from the posterior wall of the left atrium were simulated. Based on the bidomain theory, the body surface potential maps resulting from these focal events were computed. For the inverse reconstructions, we employed a full-search procedure based on the fastest route algorithm assuming uniform excitation propagation. Localization errors were revealed to be dependent on the model-specific atrial geometry. We also performed similarity analysis for the first halves of the P wave duration, which improved the results in three models.
ECG markers derived from the P-wave are used frequently to assess atrial function and anatomy, e.g. left atrial enlargement. While having the advantage of being routinely acquired, the processes under- lying the genesis of the P-wave are not understood in their entirety. Particularly the distinct contributions of the two atria have not been analyzed mechanistically. We used an in silico approach to simulate P-waves originating from the left atrium (LA) and the right atrium (RA) separately in two realistic models. LA contribution to the P-wave integral was limited to 30% or less. Around 20 % could be attributed to the first third of the P-wave which reflected almost only RA depolarization. Both atria contributed to the second and last third with RA contribution being about twice as large as LA contribution. Our results foster the comprehension of the difficulties related to ECG-based LA assessment.
The clinical efficacy in preventing the recurrence of atrial fibrillation (AF) is higher for amiodarone than for dronedarone. Moreover, pharmacotherapy with these drugs is less successful in patients with remodeled substrate induced by chronic AF (cAF) and patients suffering from familial AF. To date, the reasons for these phenomena are only incompletely understood. We analyzed the effects of these two drugs in a computational model of atrial electrophysiology. The Courtemanche-Ramirez-Nattel model was adapted to represent cAF remodeled tissue and hERG mutations N588K and L532P. The pharmacodynamics of amiodarone and dronedarone were investigated with respect to their dose and heart rate dependence by evaluating 10 descriptors of action potential morphology and conduction properties. An arrhythmia score was computed based on a subset of these biomarkers and analyzed regarding circadian variation of drug concentration and heart rate. Action potential alternans at high frequencies was observed over the whole dronedarone concentration range at high frequencies, while amiodarone caused alternans only in a narrow range. The total score of dronedarone reached critical values in most of the investigated dynamic scenarios, while amiodarone caused only minor score oscillations. Compared with the other substrates, cAF showed significantly different characteristics resulting in a lower amiodarone but higher dronedarone concentration yielding the lowest score. Significant differences exist in the frequency and concentration-dependent effects between amiodarone and dronedarone and between different atrial substrates. Our results provide possible explanations for the superior efficacy of amiodarone and may aid in the design of substrate-specific pharmacotherapy for AF.
A. Loewe, Y. Xu, E. P. Scholz, O. Dössel, and G. Seemann. Understanding the cellular mode of action of vernakalant using a computational model: answers and new questions. In Current Directions in Biomedical Engineering, vol. 1(1) , pp. 418-422, 2015
Vernakalant is a new antiarrhythmic agent for the treatment of atrial fibrillation. While it has proven to be effective in a large share of patients in clinical studies, its underlying mode of action is not fully understood. In this work, we aim to link experimental data from the subcellular, tissue, and system level using an in-silico approach. A Hills equation-based drug model was extended to cover the frequency dependence of sodium channel block. Two model variants were investigated: M1 based on subcellular data and M2 based on tissue level data. 6 action potential (AP) markers were evaluated regarding their dose, frequency and substrate dependence. M1 comprising potassium, sodium, and calcium channel block reproduced the reported prolongation of the refractory period. M2 not including the effects on potassium channels reproduced reported AP morphology changes on the other hand. The experimentally observed increase of ERP accompanied by a shortening of APD90 was not reproduced. Thus, explanations for the drug-induced changes are provided while none of the models can explain the effects in their entirety. These results foster the understanding of vernakalants cellular mode of action and point out relevant gaps in our current knowledge to be addressed in future in-silico and experimental research on this aspiring antiarrhythmic agent.
Baseline wander removal is one important part of electrocardiogram (ECG) filtering. This can be achieved by many different approaches. This work investigates the influence of three different baseline wander removal techniques on ST changes. The chosen filters were phase-free Butterworth filtering, median filtering and baseline correction with cubic spline interpolation. 289 simulated ECGs containing ischemia were used to determine the influence of these filtering processes on the ST segment. Synthetic baseline wander and offsets were added to the simulated signals. All methods proved to be good approaches by removing most of the baseline wander in all signals. Correlation coefficients between the original signals and the filtered signals were greater than 0.93 for all ECGs. Cubic spline interpolation performed best regarding the preservation of the ST segment amplitude change when compared to the original signal. The approach modified the ST segment by 0.10mV±0.06mV at elevated K points. Median filtering introduced a variation of 0.33mV±0.29mV, Butterworth filtering reached 0.16mV±0.14mV at elevated K points. Thus, all methods manipulate the ST segment.
Atrial fibrillation is a common irregular heart rhythm. Until today there is still a need for research to quantify typical signal characteristics of rotors, which can induce atrial fibrillation. In this work, signal characteristics of a stable and a more unstable rotor in a realistic heart model including fiber orientation were analyzed with the following methods: peak-to-peak amplitude, Hilbert phase, approximate entropy and RS-difference. In this simulation model the stable rotor rotated with a cycle length of 145 ms and stayed in an area of 1.5 mm x 3 mm. Another more unstable rotor with a cycle length of 190 ms moved in an area of 10 mm × 4 mm. In a distance of 2 mm to the rotor tip, the peak-to-peak amplitude decreased significantly, whereas the RS-difference and the approximate entropy were maximal. The rotor center trajectories were detected by phase singularity points determined by the Hilbert transform. We showed that more unstable rotors resulted in more amplitude changes over time and also the cycle length differed more. Furthermore, we presented typical activation time patterns of the Lasso catheter centered at the rotor tip and in different distances to the rotor tip. We suggest that cardiologists use a combination of the described methods to determine a rotor tip position in a more robust manner.
Diagnosis of atrial flutter caused by ablation of atrial fibrillation is complex due to ablation scars. This paper presents an approach to replicate the clinically measured flutter circuit in a dynamic computer model. In a first step, important anatomical features of the flutter circuit are extracted manually based on the clinical measurement. With the help of this information, the electrical excitation propagation is simulated on the atrial geometry using the fast marching method. The simulated flutter circuit is used to estimate the global and local conduction velocity by approximating it iteratively. The parameterized flutter simulation is supposed to support the physician during diagnosis and treatment of atrial flutter.
The fiber orientation in the atria has a significant contribution to the electrophysiologic behavior of the heart and to the genesis of arrhythmia. Atrial fiber orientation has a direct effect on excitation propagation, activation patterns and the P-wave. We present a rule-based algorithm that works robustly on different volumetric meshes composed of either isotropic hexahedra or arbitrary tetrahedra as well as on 3-dimensional triangular surface meshes in patient-specific geometric models. This method fosters the understanding of general pro-arrhythmic mechanisms and enhances patient-specific modeling approaches.
Pharmacological therapy of atrial fibrillation (AF) is still a major clinical challenge. Particularly AF of early onset has a significant familiar component and was asso- ciated with various gene mutations. In this study, we de- signed and optimized antiarrhythmic agents for atrial sub- strates affected by human ether-a`-go-go-related gene mu- tations L532P and N588K. A virtual multichannel blocker was designed aiming at a restoration of the wild-type (WT) action potential (AP) on the single cell and tissue level. Furthermore, the amiodarone and dronedarone concen- trations yielding the smallest difference between WT and mutated APs were identified. The WT AP at a basic cy- cle length (BCL) of 1000 ms could be restored by signifi- cant block of IK r and IK ur (\039%) and less pronounced block of IKs, ICa,L, Ib,Na, and Ib,Ca (17%) for both mutations. Effective dronedarone concentrations of 88 nM for L532P and 40 nM for N588K yielded matches almost as good while amiodarone could not sufficiently restore the WT AP. APD90 restitution was effectively restored by the tuned N588K agent whereas differences of up to 34 ms were observed for low BCLs using the tuned L532P agent. Our results provide insight into the pharmacodynamic re- sponse of mutated myocytes and may aid in the optimiza- tion of patient group-specific therapeutic approaches.
A. Loewe, M. Wilhelms, O. Dössel, and G. Seemann. Influence of chronic atrial fibrillation induced remodeling in a computational electrophysiological model. In Biomedizinische Technik / Biomedical Engineering, vol. 59(S1) , pp. S929-S932, 2014
Atrial fibrillation (AF) is a common arrhythmia with progressive nature. This progression is partly caused by AF itself by modifying amongst others the electrophysiological properties of the myocytes. These changes are referred to as electrical remodeling and were integrated in a computational model of human atrial myocytes in this work.In particular, the maximum conductivities of Ito, IK1, IKs, IKur, ICa,L, INa,Ca, and the Ca2+ leak current from the sarcoplasmic reticulum, as well as the cell capacitance were altered. In an additional setup, the influence of potential gap junction remodeling was investigated.Wavelength was reduced from 225 mm to 110 mm, respectively 92 mm when considering gap junction remodeling at a basic cycle length of 400 ms. Action potential morphology was changed from spike-and-dome to a more triangular repolarization phase. However, our results show that including IKur remodeling prevents the plateau phase from disappearing completely.
Y. Lutz, A. Loewe, O. Dössel, and G. Seemann. Specific antiarrhythmic therapy for familial atrial fibrillation in a numerical model of human atrial electrophysiology. In Biomedizinische Technik / Biomedical Engineering, vol. 59(s1) , pp. s933-s936, 2014
Atrial fibrillation (AF) is still a major health problem in the western society. Especially for familial AF, the pharmacological therapy is still not sufficiently successful. In this work, channel blocker properties were in-silico adapted to optimize drug therapy for patients suffering from familial AF. The Courtemanche-Ramirez-Nattel (CRN) cell model was the basis for the simulations. Adaptations in the model due to familial AF were implemented using an existing description of the L532P mutation. A fitting algorithm was designed which adapted all conductivities of the ion channels described in the CRN model to restore the healthy action potential (AP). To find the minimal deviation of the healthy AP and the AP of the L532P mutation, the trust-region-reflective algorithm was used. The best matched APs were achieved by a significant blockade of the IKr and the IKur current. 1D tissue strand simulations were performed using different basic cycle lengths (BCL) to evaluate the results of the optimization. It was shown that for the found adaptation of the conductivities, the AP duration, and the progressions of the conduction velocity, effective refractory period, and wavelength (WL) could be restored. The WL was increased by 53.37% compared to the mutation and had a value of 233.48 mm (BCL = 1 s).
While human ether-à-go-go-related gene (hERG) mutations N588K and K897T are associated with atrial fib- rillation (AF), the underlying arrhythmogenic mechanisms are understood only incompletely. In this work, an ap- proach integrating IKr measurement data from transgenic Xenopus oocytes into established computational models of cardiac electrophysiology is presented. Parameters are es- timated using a minimization formulation, which is handled by a hybrid particle swarm optimization (PSO) and trust- region-reflective (TRR) algorithm. Cell models adapted to the mutation measurements show a significantly shorter ac- tion potential (AP) with less pronounced spike-and-dome morphology. Results of single cell simulations compare with myocytes in chronic AF.
ECG imaging is a non-invasive technique of characterizing the electrical activity and the corresponding excitation conduction of the heart using body surface ECG. The method may provide great opportunities in the planning of cardiac interventions and in the diagnosis of cardiac diseases. This work introduces an algorithm for the imaging of transmembrane voltages that is based on a Kalman filter with an augmented measurement model. In the latter, a regularization term is integrated as additional measurement. The filter is trained using a-priori-knowledge from a simulation model. Two effects are investigated: the influence of the training data on the reconstruction quality and the representation of a-priori knowledge in the trained covariance matrices. The proposed algorithm shows a promising quality of reconstruction and may be used in the future to introduce generic physiological knowledge in solutions of cardiac source imaging.
The early detection of myocardial ischemia is an essential lever for its successful treatment. We investigated an ECG monitoring system with 3 electrodes. Optimal electrode positions are determined using a cellular automaton. The spatially heterogeneous effects of myocardial ischemia were modeled by altering 4 electrophysiological parameters: action potential amplitude and duration, conduction velocity as well as resting membrane voltage. Both, transmural heterogeneity and the influence of the border zone were considered in the simulations on three patient models. The detection of myocardial ischemia is based on ST segment deviation from the physiological case. The signals used to find the best electrode positions comprise ischemic regions with different transmural extents in all 17 AHA segments. We show which ischemic ECGs can be detected given a realistic signal-to-noise ratio, false positive rate and maximum response time of the system.
A computer system for determining Ventricular Far Field contribution in atrial electrograms of a patient. The system includes an interface module configured to receive a plurality of electrical signals generated by a plurality of sensors wherein the plurality of electrical signals relate to a plurality of locations in an atrium of the patient; a reference module configured to determine a reference signal reflecting electrical excitation of the patient's ventricles; and a data processing module. The data processing module is configured to select from the plurality of the received electrical signals such electrical signals which are recorded a number of conditions. The data processing module is further configured to determine a spatio-temporal distribution of the Ventricular Far Field inside the atrium by approximating the spatio-temporal distribution (VFFc) based on signal data of the selected signals by using an approximation model.
A computer-implemented method for calculating a multi-dimensional wavelet transform in an image processing system comprising a plurality of computation units includes receiving multi-dimensional image data. An overlap value corresponding to a number of non-zero filter coefficients associated with the multi-dimensional wavelet transform is identified. Then the multi-dimensional image data is divided into a plurality of multi-dimensional arrays, wherein the multi-dimensional arrays overlap in each dimension by a number of pixels equal to the overlap value. A multi-dimensional wavelet transform is calculated for each multi-dimensional array, in parallel, across the plurality of computation units
A computer-implemented method for reconstruction of a magnetic resonance image includes acquiring a first incomplete k-space data set comprising a plurality of first k-space lines spaced according to an acceleration factor and one or more calibration lines. A parallel imaging reconstruction technique is applied to the first incomplete k-space data to determine a plurality of second k-space lines not included in the first incomplete k-space data set, thereby yielding a second incomplete k-space data set. Then, the parallel imaging reconstruction technique is applied to the second incomplete k-space data to determine a plurality of third k-space lines not included in the second incomplete k-space data, thereby yielding a complete k-space data set.
A. Loewe. Modeling human atrial patho-electrophysiology from ion channels to ECG : substrates, pharmacology, vulnerability, and P-waves. KIT Scientific Publishing. Dissertation. 2016
Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This thesis presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF.
Student Theses (2)
A. Loewe. Arrhythmic potency of human electrophysiological models adapted to chronic and familial atrial fibrillation. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Masterarbeit. 2013
A. Loewe. Comparison of cardiac simulation tools regarding the modeling of acute ischemia. Institut für Biomedizinische Technik, Karlsruher Institut für Technologie (KIT). Bachelorarbeit. 2010