Monitoring of Serum Potassium and Calcium Levels in End-Stage Renal Disease Patients by ECG Depolarization Morphology Analysis.

OBJECTIVE: Non-invasive estimation of serum potassium, [K+], and calcium, [Ca2+], can help to prevent life-threatening ventricular arrhythmias in patients with advanced renal disease, but current methods for estimation of electrolyte levels have limitations. We aimed to develop new markers based on the morphology of the QRS complex of the electrocardiogram (ECG). METHODS: ECG recordings from 29 patients undergoing hemodialysis (HD) were processed. Mean warped QRS complexes were computed in two-minute windows at the start of an HD session, at the end of each HD hour and 48 h after it. We quantified QRS width, amplitude and the proposed QRS morphology-based markers that were computed by warping techniques. Reference [K+] and [Ca2+] were determined from blood samples acquired at the time points where the markers were estimated. Linear regression models were used to estimate electrolyte levels from the QRS markers individually and in combination with T wave morphology markers. Leave-one-out cross-validation was used to assess the performance of the estimators. RESULTS: All markers, except for QRS width, strongly correlated with [K+] (median Pearson correlation coefficients, r, ranging from 0.81 to 0.87) and with [Ca2+] (r ranging from 0.61 to 0.76). QRS morphology markers showed very low sensitivity to heart rate (HR). Actual and estimated serum electrolyte levels differed, on average, by less than 0.035 mM (relative error of 0.018) for [K+] and 0.010 mM (relative error of 0.004) for [Ca2+] when patient-specific multivariable estimators combining QRS and T wave markers were used. CONCLUSION: QRS morphological markers allow non-invasive estimation of [K+] and [Ca2+] with low sensitivity to HR. The estimation performance is improved when multivariable models, including T wave markers, are considered. SIGNIFICANCE: Markers based on the QRS complex of the ECG could contribute to non-invasive monitoring of serum electrolyte levels and arrhythmia risk prediction in patients with renal disease.

Synergistic antiarrhythmic effect of inward rectifier current inhibition and pulmonary vein isolation in a 3D computer model for atrial fibrillation.

AIMS: Recent clinical studies showed that antiarrhythmic drug (AAD) treatment and pulmonary vein isolation (PVI) synergistically reduce atrial fibrillation (AF) recurrences after initially successful ablation. Among newly developed atrial-selective AADs, inhibitors of the G-protein-gated acetylcholine-activated inward rectifier current (IKACh) were shown to effectively suppress AF in an experimental model but have not yet been evaluated clinically. We tested in silico whether inhibition of inward rectifier current or its combination with PVI reduces AF inducibility. METHODS AND RESULTS: We simulated the effect of inward rectifier current blockade (IK blockade), PVI, and their combination on AF inducibility in a detailed three-dimensional model of the human atria with different degrees of fibrosis. IK blockade was simulated with a 30% reduction of its conductivity. Atrial fibrillation was initiated using incremental pacing applied at 20 different locations, in both atria. IK blockade effectively prevented AF induction in simulations without fibrosis as did PVI in simulations without fibrosis and with moderate fibrosis. Both interventions lost their efficacy in severe fibrosis. The combination of IK blockade and PVI prevented AF in simulations without fibrosis, with moderate fibrosis, and even with severe fibrosis. The combined therapy strongly decreased the number of fibrillation waves, due to a synergistic reduction of wavefront generation rate while the wavefront lifespan remained unchanged. CONCLUSION: Newly developed blockers of atrial-specific inward rectifier currents, such as IKAch, might prevent AF occurrences and when combined with PVI effectively supress AF recurrences in human.

Reconstruction of three-dimensional biventricular activation based on the 12-lead electrocardiogram via patient-specific modelling.

AIMS: Non-invasive imaging of electrical activation requires high-density body surface potential mapping. The nine electrodes of the 12-lead electrocardiogram (ECG) are insufficient for a reliable reconstruction with standard inverse methods. Patient-specific modelling may offer an alternative route to physiologically constraint the reconstruction. The aim of the study was to assess the feasibility of reconstructing the fully 3D electrical activation map of the ventricles from the 12-lead ECG and cardiovascular magnetic resonance (CMR). METHODS AND RESULTS: Ventricular activation was estimated by iteratively optimizing the parameters (conduction velocity and sites of earliest activation) of a patient-specific model to fit the simulated to the recorded ECG. Chest and cardiac anatomy of 11 patients (QRS duration 126-180 ms, documented scar in two) were segmented from CMR images. Scar presence was assessed by magnetic resonance (MR) contrast enhancement. Activation sequences were modelled with a physiologically based propagation model and ECGs with lead field theory. Validation was performed by comparing reconstructed activation maps with those acquired by invasive electroanatomical mapping of coronary sinus/veins (CS) and right ventricular (RV) and left ventricular (LV) endocardium. The QRS complex was correctly reproduced by the model (Pearson's correlation r = 0.923). Reconstructions accurately located the earliest and latest activated LV regions (median barycentre distance 8.2 mm, IQR 8.8 mm). Correlation of simulated with recorded activation time was very good at LV endocardium (r = 0.83) and good at CS (r = 0.68) and RV endocardium (r = 0.58). CONCLUSION: Non-invasive assessment of biventricular 3D activation using the 12-lead ECG and MR imaging is feasible. Potential applications include patient-specific modelling and pre-/per-procedural evaluation of ventricular activation.

The 'Digital Twin' to enable the vision of precision cardiology.

Providing therapies tailored to each patient is the vision of precision medicine, enabled by the increasing ability to capture extensive data about individual patients. In this position paper, we argue that the second enabling pillar towards this vision is the increasing power of computers and algorithms to learn, reason, and build the 'digital twin' of a patient. Computational models are boosting the capacity to draw diagnosis and prognosis, and future treatments will be tailored not only to current health status and data, but also to an accurate projection of the pathways to restore health by model predictions. The early steps of the digital twin in the area of cardiovascular medicine are reviewed in this article, together with a discussion of the challenges and opportunities ahead. We emphasize the synergies between mechanistic and statistical models in accelerating cardiovascular research and enabling the vision of precision medicine.

Fibrosis and Conduction Abnormalities as Basis for Overlap of Brugada Syndrome and Early Repolarization Syndrome.

Brugada syndrome and early repolarization syndrome are both classified as J-wave syndromes, with a similar mechanism of arrhythmogenesis and with the same basis for genesis of the characteristic electrocardiographic features. The Brugada syndrome is now considered a conduction disorder based on subtle structural abnormalities in the right ventricular outflow tract. Recent evidence suggests structural substrate in patients with the early repolarization syndrome as well. We propose a unifying mechanism based on these structural abnormalities explaining both arrhythmogenesis and the electrocardiographic changes. In addition, we speculate that, with increasing technical advances in imaging techniques and their spatial resolution, these syndromes will be reclassified as structural heart diseases or cardiomyopathies.

Beat-to-beat P-wave morphological variability in patients with paroxysmal atrial fibrillation: an in silico study.

AIMS: P-wave beat-to-beat morphological variability can identify patients prone to paroxysmal atrial fibrillation (AF). To date, no computational study has been carried out to mechanistically explain such finding. The aim of this study was to provide a pathophysiological explanation, by using a computer model of the human atria, of the correlation between P-wave beat-to-beat variability and the risk of AF. METHODS AND RESULTS: A physiological variability in the earliest activation site (EAS), on a beat-to-beat basis, was introduced into a computer model of the human atria by randomizing the EAS location. A methodology for generating multi-scale, spatially-correlated regions of heterogeneous conduction was developed. P-wave variability in the presence of such regions was compared with a control case. Simulations were performed with an eikonal model, for the activation map, and with the lead field approach, for P-wave computation. The methodology was eventually compared with a reference monodomain simulation. A total of 60 P-waves were simulated for each sinus node exit location (12 in total), and for each of the 15 patterns of heterogeneous conduction automatically generated by the model. A P-wave beat-to-beat variability was observed in all cases. Variability was significantly increased in presence of heterogeneous slow conducting regions, up to two-fold the variability in the control case. P-wave variability increased non-linearly with respect to the EAS variability and total area of slow conduction. Distribution of the heterogeneous conduction was more effective in increasing the variability when it surrounded the EAS locations and the fast conducting bundles. P-waves simulated by the eikonal approach compared excellently with the monodomain-based ones. CONCLUSION: P-wave variability in patients with paroxysmal AF could be explained by a variability in sinoatrial node exit location in combination with slow conducting regions.

Effect of Na+-channel blockade on the three-dimensional substrate of atrial fibrillation in a model of endo-epicardial dissociation and transmural conduction.

AIMS: Atrial fibrillation (AF) is a progressive arrhythmia characterized by structural alterations that increase its stability. Both clinical and experimental studies showed a concomitant loss of antiarrhythmic drug efficacy in later stages of AF. The mechanisms underlying this loss of efficacy are not well understood. We hypothesized that structural remodelling may explain this reduced efficacy by making the substrate more three-dimensional. To investigate this, we simulated the effect of sodium (Na+)-channel block on AF in a model of progressive transmural uncoupling. METHODS AND RESULTS: In a computer model consisting of two cross-connected atrial layers, with realistic atrial membrane behaviour, structural remodelling was simulated by reducing the number of connections between the layers. 100% of endo-epicardial connectivity represented a healthy atrium. At various degrees of structural remodelling, we assessed the effect of 60% sodium channel block on AF stability, endo-epicardial electrical activity dissociation (EED), and fibrillatory conduction pattern complexity quantified by number of waves, phase singularities (PSs), and transmural conduction ('breakthrough', BT). Sodium channel block terminated AF in non-remodelled but not in remodelled atria. The temporal excitable gap (EG) and AF cycle length increased at all degrees of remodelling when compared with control. Despite an increase of EED and EG, sodium channel block decreased the incidence of BT because of transmural conduction block. Sodium channel block decreased the number of waves and PSs in normal atrium but not in structurally remodelled atrium. CONCLUSION: This simple atrial model explains the loss of efficacy of sodium channel blockers in terminating AF in the presence of severe structural remodelling as has been observed experimentally and clinically. Atrial fibrillation termination in atria with moderate structural remodelling in the presence of sodium channel block is caused by reduction of AF complexity. With more severe structural remodelling, sodium channel block fails to promote synchronization of the two layers of the model.

A left bundle branch block activation sequence and ventricular pacing influence voltage amplitudes: an in vivo and in silico study.

AIMS: The aim of this study was to investigate the influence of the activation sequence on voltage amplitudes by evaluating regional voltage differences during a left bundle branch block (LBBB) activation sequence vs. a normal synchronous activation sequence and by evaluating pacing-induced voltage differences. METHODS AND RESULTS: Twenty-one patients and three computer models without scar were studied. Regional voltage amplitudes were evaluated in nine LBBB patients who underwent endocardial electro-anatomic mapping (EAM). Pacing-induced voltage differences were evaluated in 12 patients who underwent epicardial EAM during intrinsic rhythm and right ventricular (RV) pacing. Three computer models customized for LBBB patients were created. Changes in voltage amplitudes after an LBBB (intrinsic), a normal synchronous, an RV pacing, and a left ventricular pacing activation sequence were assessed in the computer models. Unipolar voltage amplitudes in patients were approximately 4.5 mV (4.4-4.7 mV, ∼33%) lower in the septum when compared with other segments. A normal synchronous activation sequence in the computer models normalized voltage amplitudes in the septum. Pacing-induced differences were larger in electrograms with higher voltage amplitudes during intrinsic rhythm and furthermore larger and more variable at the epicardium [mean absolute difference: 3.6-6.2 mV, 40-53% of intrinsic value; interquartile range (IQR) differences: 53-63% of intrinsic value] compared to the endocardium (mean absolute difference: 3.3-3.8 mV, 28-30% of intrinsic value; IQR differences: 37-40% of intrinsic value). CONCLUSION: In patients and computer models without scar, lower septal unipolar voltage amplitudes are exclusively associated with an LBBB activation sequence. Pacing substantially affects voltage amplitudes, particularly at the epicardium.

How disruption of endo-epicardial electrical connections enhances endo-epicardial conduction during atrial fibrillation.

Aims: Loss of side-to-side electrical connections between atrial muscle bundles is thought to underlie conduction disturbances predisposing to atrial fibrillation (AF). Putatively, disruption of electrical connections occurs not only within the epicardial layer but also between the epicardial layer and the endocardial bundle network, thus impeding transmural conductions ('breakthroughs'). However, both clinical and experimental studies have shown an enhancement of breakthroughs during later stages of AF. We tested the hypothesis that endo-epicardial uncoupling enhances endo-epicardial electrical dyssynchrony, breakthrough rate (BTR), and AF stability. Methods and Results: In a novel dual-layer computer model of the human atria, 100% connectivity between the two layers served as healthy control. Atrial structural remodelling was simulated by reducing the number of connections between the layers from 96 to 6 randomly chosen locations. With progressive elimination of connections, AF stability increased. Reduction in the number of connections from 96 to 24 resulted in an increase in endo-epicardial dyssynchrony from 6.6 ± 1.9 to 24.6 ± 1.3%, with a concomitant increase in BTR. A further reduction to 12 and 6 resulted in more pronounced endo-epicardial dyssynchrony of 34.4 ± 1.15 and 40.2 ± 0.52% but with BTR reduction. This biphasic relationship between endo-epicardial coupling and BTR was found independently from whether AF was maintained by re-entry or by ectopic focal discharges. Conclusion: Loss of endo-epicardial coupling increases AF stability. There is a biphasic relation between endo-epicardial coupling and BTR. While at high degrees of endo-epicardial connectivity, the BTR is limited by the endo-epicardial synchronicity, at low degrees of connectivity, it is limited by the number of endo-epicardial connections.

Segmentation of the left ventricular endocardium from magnetic resonance images by using different statistical shape models.

We evaluate in this paper different strategies for the construction of a statistical shape model (SSM) of the left ventricle (LV) to be used for segmentation in cardiac magnetic resonance (CMR) images. From a large database of LV surfaces obtained throughout the cardiac cycle from 3D echocardiographic (3DE) LV images, different LV shape models were built by varying the considered phase in the cardiac cycle and the registration procedure employed for surface alignment. Principal component analysis was computed to describe the statistical variability of the SSMs, which were then deformed by applying an active shape model (ASM) approach to segment the LV endocardium in CMR images of 45 patients. Segmentation performance was evaluated by comparing LV volumes derived by ASM segmentation with different SSMs and those obtained by manual tracing, considered as a reference. A high correlation (r(2)>0.92) was found in all cases, with better results when using the SSM models comprising more than one frame of the cardiac cycle.

P-wave complexity in normal subjects and computer models.

BACKGROUND: P waves reported in electrocardiology literature uniformly appear smooth. Computer simulation and signal analysis studies have shown much more complex shapes. OBJECTIVE: We systematically investigated P-wave complexity in normal volunteers using high-fidelity electrocardiographic techniques without filtering. METHODS: We recorded 5-min multichannel ECGs in 16 healthy volunteers. Noise and interference were reduced by averaging over 300 beats per recording. In addition, normal P waves were simulated with a realistic model of the human atria. RESULTS: Measured P waves had an average of 4.1 peaks (range 1-10) that were reproducible between recordings. Simulated P waves demonstrated similar complexity, which was related to structural discontinuities in the computer model of the atria. CONCLUSION: The true shape of the P wave is very irregular and is best seen in ECGs averaged over many beats.

An in-silico analysis of the effect of heart position and orientation on the ECG morphology and vectorcardiogram parameters in patients with heart failure and intraventricular conduction defects.

AIM: The aim of this study was to investigate the influence of geometrical factors on the ECG morphology and vectorcardiogram (VCG) parameters. METHODS: Patient-tailored models based on five heart-failure patients with intraventricular conduction defects (IVCDs) were created. The heart was shifted up to 6 cm to the left, right, up, and down and rotated ±30° around the anteroposterior axis. Precordial electrodes were shifted 3 cm down. RESULTS: Geometry modifications strongly altered ECG notching/slurring and intrinsicoid deflection time. Maximum VCG parameter changes were small for QRS duration (-6% to +10%) and QRS-T angle (-6% to +3%), but considerable for QRS amplitude (-36% to +59%), QRS area (-37% to +42%), T-wave amplitude (-41% to +36%), and T-wave area (-42% to +33%). CONCLUSION: The position of the heart with respect to the electrodes is an important factor determining notching/slurring and voltage-dependent parameters and therefore must be considered for accurate diagnosis of IVCDs.

Patient-specific modelling of cardiac electrophysiology in heart-failure patients.

AIMS: Left-ventricular (LV) conduction disturbances are common in heart-failure patients and a left bundle-branch block (LBBB) electrocardiogram (ECG) type is often seen. The precise cause of this pattern is uncertain and is probably variable between patients, ranging from proximal interruption of the left bundle branch to diffuse distal conduction disease in the working myocardium. Using realistic numerical simulation methods and patient-tailored model anatomies, we investigated different hypotheses to explain the observed activation order on the LV endocardium, electrogram morphologies, and ECG features in two patients with heart failure and LBBB ECG. METHODS AND RESULTS: Ventricular electrical activity was simulated using reaction-diffusion models with patient-specific anatomies. From the simulated action potentials, ECGs and cardiac electrograms were computed by solving the bidomain equation. Model parameters such as earliest activation sites, tissue conductivity, and densities of ionic currents were tuned to reproduce the measured signals. Electrocardiogram morphology and activation order could be matched simultaneously. Local electrograms matched well at some sites, but overall the measured waveforms had deeper S-waves than the simulated waveforms. CONCLUSION: Tuning a reaction-diffusion model of the human heart to reproduce measured ECGs and electrograms is feasible and may provide insights in individual disease characteristics that cannot be obtained by other means.

A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography.

OBJECTIVE: Noninvasive electrocardiographic imaging (ECGI) reconstructs cardiac electrical activity from body surface potential measurements. However, current methods have demonstrated inaccuracies in reconstructing sinus rhythm, and in particular breakthrough sites. This study aims to combine existing inverse algorithms, making the most of their advantages while minimizing their limitations. METHOD: The "patchwork method" (PM) combines two classical numerical methods for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials, computed using the boundary element method (BEM), provides the most accurate solution. The PM selects for each heart node and time step the method whose estimated reconstruction error is smallest. The performance of the PM was evaluated using simulated ectopic and normal ventricular beats. RESULTS: Cardiac potentials and activation maps obtained with the PM (CC = 0.63 ± 0.01 and 0.61 ± 0.05 respectively) were more accurate than MFS (CC = 0.61 ± 0.01 and 0.48 ± 0.05 respectively), FEM (CC = 0.58 ± 0.01 and 0.51 ± 0.02 respectively) or BEM (CC = 0.57 ± 0.02 and 0.49 ± 0.02 respectively). The PM also located all epicardial breakthrough sites, whereas the traditional numerical methods usually missed one. Furthermore, the PM showed its robustness and stability in the presence of Gaussian noise added to the torso potentials. CONCLUSION: The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats. SIGNIFICANCE: This novel method for optimizing ECGI solutions opens a new avenue for improving not only ECGI but also other inverse problems.

Differences in ventricular wall composition may explain inter-patient variability in the ECG response to variations in serum potassium and calcium.

Objective: Chronic kidney disease patients have a decreased ability to maintain normal electrolyte concentrations in their blood, which increases the risk for ventricular arrhythmias and sudden cardiac death. Non-invasive monitoring of serum potassium and calcium concentration, [K+] and [Ca2+], can help to prevent arrhythmias in these patients. Electrocardiogram (ECG) markers that significantly correlate with [K+] and [Ca2+] have been proposed, but these relations are highly variable between patients. We hypothesized that inter-individual differences in cell type distribution across the ventricular wall can help to explain this variability. Methods: A population of human heart-torso models were built with different proportions of endocardial, midmyocardial and epicardial cells. Propagation of ventricular electrical activity was described by a reaction-diffusion model, with modified Ten Tusscher-Panfilov dynamics. [K+] and [Ca2+] were varied individually and in combination. Twelve-lead ECGs were simulated and the width, amplitude and morphological variability of T waves and QRS complexes were quantified. Results were compared to measurements from 29 end-stage renal disease (ESRD) patients undergoing hemodialysis (HD). Results: Both simulations and patients data showed that most of the analyzed T wave and QRS complex markers correlated strongly with [K+] (absolute median Pearson correlation coefficients, r, ranging from 0.68 to 0.98) and [Ca2+] (ranging from 0.70 to 0.98). The same sign and similar magnitude of median r was observed in the simulations and the patients. Different cell type distributions in the ventricular wall led to variability in ECG markers that was accentuated at high [K+] and low [Ca2+], in agreement with the larger variability between patients measured at the onset of HD. The simulated ECG variability explained part of the measured inter-patient variability. Conclusion: Changes in ECG markers were similarly related to [K+] and [Ca2+] variations in our models and in the ESRD patients. The high inter-patient ECG variability may be explained by variations in cell type distribution across the ventricular wall, with high sensitivity to variations in the proportion of epicardial cells. Significance: Differences in ventricular wall composition help to explain inter-patient variability in ECG response to [K+] and [Ca2+]. This finding can be used to improve serum electrolyte monitoring in ESRD patients.

A computer model of endo-epicardial electrical dissociation and transmural conduction during atrial fibrillation.

AIMS: Structural alterations during atrial fibrillation (AF) not only lead to electrical dissociation within the epicardial layer, but also between the epicardial layer and the endocardial bundle network. The aim of the study was to investigate the role of transmural conduction in the stability of AF episodes using a dual-layer computer model. METHODS AND RESULTS: A proof-of-principle dual-layer model was developed in which connections between the layers can be introduced or removed at any time during the simulation. Using an S1-S2 protocol, a spiral wave was initiated in one of the layers, which degenerated into a complex AF pattern after connection with the other layer at six randomly chosen sites. After 6 s, connections were either retained (dual-layer simulations) or removed (single-layer simulations). Dual-layer simulations were more complex, as indicated by the higher number of waves and phase singularities. Tracking waves through both layers revealed that the number of waves in dual-layer simulations was significantly higher than in the single-layer simulations, reflecting more opportunities for reentry and a concomitant increase in AF stability. In the dual-layer model, only 12% of the AF episodes died out within 6 s, while 59% died out in the single-layer model. CONCLUSION: Atrial fibrillation patterns are more complex and AF episodes are more stable in a dual-layer model. This study indicates an important role for endo-epicardial conduction for the stabilization of AF.

Similarities and differences between electrocardiogram signs of left bundle-branch block and left-ventricular uncoupling.

AIMS: A left bundle-branch block (LBBB) electrocardiogram (ECG) type may be caused by either a block in the left branch of the ventricular conduction system or by uncoupling in the working myocardium. We used a realistic large-scale computer model to evaluate the effects of uncoupling with and without left-sided block and in combination with biventricular pacing. METHODS AND RESULTS: Action potential propagation was simulated using a reaction-diffusion model of the human ventricles. Electrocardiograms and cardiac electrograms were computed from the simulated action potentials by solving the bidomain equations. In all situations, diffuse uncoupling reduced QRS amplitude, prolonged QRS duration, and rotated the QRS axis leftward. Uncoupling by 50% increased QRS duration from 90 to 120 ms with a normal conduction system and from 140 to 190 ms when the left bundle branch was blocked. Biventricular pacing did not change QRS duration but reduced total ventricular activation time. CONCLUSION: Uncoupling in the working myocardium can mimic left-sided block in the ventricular conduction system and can explain an LBBB ECG pattern with relatively low amplitude. Biventricular pacing improves ventricular activation in true LBBB with or without uncoupling but not in case of 50% uncoupling alone.

Computer simulation of ECG manifestations of left ventricular electrical remodeling.

An increased QRS voltage is considered to be specific for the electrocardiogram (ECG) diagnosis of left ventricular hypertrophy (LVH). However, the QRS-complex patterns in patients with LVH cover a broader spectrum: increased QRS voltage, prolonged QRS duration, left axis deviation, and left anterior fascicular block- and left bundle branch block-like patterns, as well as pseudo-normal QRS patterns. The classical interpretation of the QRS patterns in LVH relates these changes to increased left ventricular mass (LVM) per se, while tending to neglect the modified active and passive electrical properties of the myocardium. However, it has been well documented that both active and passive electrical properties in LVH are altered. Using computer simulations, we have shown that an increased LVM is not the only determinant of QRS complex changes in LVH, as these changes could also be produced without changing the left ventricular mass, implying that these QRS patterns can be present in patients before their LVM exceeds the arbitrary upper normal limits. Our results link the experimental evidence on electrical remodeling with clinical interpretation of ECG changes in patients with LVH and stress the necessity of a complex interpretation of the QRS patterns considering both spatial and nonspatial determinants in terms of the spatial angle theory. We assume that hypertrophic electrical remodeling in combination with changes in left ventricular size and shape explains the variety of ECG patterns as well as the discrepancies between ECG and left ventricular mass.

Estimation of potassium levels in hemodialysis patients by T wave nonlinear dynamics and morphology markers.

OBJECTIVE: Noninvasive screening of hypo- and hyperkalemia can prevent fatal arrhythmia in end-stage renal disease (ESRD) patients, but current methods for monitoring of serum potassium (K+) have important limitations. We investigated changes in nonlinear dynamics and morphology of the T wave in the electrocardiogram (ECG) of ESRD patients during hemodialysis (HD), assessing their relationship with K+ and designing a K+ estimator. METHODS: ECG recordings from twenty-nine ESRD patients undergoing HD were processed. T waves in 2-min windows were extracted at each hour during an HD session as well as at 48 h after HD start. T wave nonlinear dynamics were characterized by two indices related to the maximum Lyapunov exponent (λt, λwt) and a divergence-related index (η). Morphological variability in the T wave was evaluated by three time warping-based indices (dw, reflecting morphological variability in the time domain, and da and daNL, in the amplitude domain). K+was measured from blood samples extracted during and after HD. Stage-specific and patient-specific K+ estimators were built based on the quantified indices and leave-one-out cross-validation was performed separately for each of the estimators. RESULTS: The analyzed indices showed high inter-individual variability in their relationship with K+. Nevertheless, all of them had higher values at the HD start and 48 h after it, corresponding to the highest K+. The indices η and dw were the most strongly correlated with K+ (median Pearson correlation coefficient of 0.78 and 0.83, respectively) and were used in univariable and multivariable linear K+ estimators. Agreement between actual and estimated K+ was confirmed, with averaged errors over patients and time points being 0.000 ± 0.875 mM and 0.046 ± 0.690 mM for stage-specific and patient-specific multivariable K+ estimators, respectively. CONCLUSION: ECG descriptors of T wave nonlinear dynamics and morphological variability allow noninvasive monitoring of K+ in ESRD patients. SIGNIFICANCE: ECG markers have the potential to be used for hypo- and hyperkalemia screening in ESRD patients.

The effect of reduced intercellular coupling on electrocardiographic signs of left ventricular hypertrophy.

BACKGROUND: The electrocardiographic (ECG) diagnosis of left ventricular hypertrophy (LVH) is based on the assumption that QRS voltage increases with left ventricular mass. However, most of patients with echocardiographically detected LVH do not have increased QRS voltage. Reduced intercellular coupling has been observed in LVH patients and animal models. The purpose of this study was to show that this uncoupling can explain relatively low QRS voltage in LVH patients. METHODS: Electrocardiograms and vectorcardiograms (VCG) were simulated with a realistic large-scale computer model of the human heart and torso that reliably represented the effects of reduced coupling on both propagation and ECG voltage. RESULTS: Uncoupling reduced QRS voltage in all leads except aVL, reflecting a decrease in vector amplitude as well as a leftward axis deviation that suggested left anterior fascicular block. CONCLUSIONS: Low QRS voltage does not necessarily contradict a diagnosis of LVH but may be an indication for electrical uncoupling. The diagnostic value of this "relative voltage deficit" needs to be demonstrated in clinical studies.