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.
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
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.
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.
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.
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: 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.
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.
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.
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.
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.
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.