Estimation of Serum Potassium and Calcium Concentrations from Electrocardiographic Depolarization and Repolarization Waveforms

Chronic kidney disease (CKD), a condition defined by a gradual decline in kidney function over time, has become a global health concern affecting between 11 and 13% of the world population [1]. As renal function declines, CKD patients gradually lose their ability to maintain normal values of potassium concentration ([K+]) in their blood. Elevated serum [K+], known as hyperkalemia, increases the risk for life-threatening arrhythmias and sudden cardiac death [2].An increase in serum [K+] outside the physiological range is commonly silent and is only detected when hyperkalemia is already very severe or when a blood test is performed. Maintenance and monitoring of [K+] in the blood is an important component in the treatment of CKD patients because therapies for hyperkalemia management in CKD patients are designed to prevent arrhythmias and to immediately lower serum [K+] to safe ranges. However, this is currently only possible by taking a blood sample and is associated with a long analysis time. Therefore it is useful to have a simple, noninvasive method to estimate serum [K+], particularly using the electrocardiogram (ECG). Indeed, variations in serum electrolyte levels have been shown to alter the electrical behavior of the heart and to induce changes in the ECG [3¿6]. However, large inter-individual variability existsin the relationship between ion concentrations and ECG features. Previous attempts to estimate serum [K+] from the ECG have therefore shown limitations [7¿9], such as not being applicable to some common types of ECG waveforms or relying on specific ECG characteristics that may present large variations not necessarily associated with hyperkalemia.The aim of this thesis is to develop novel estimates of serum [K+] that are robust enough to detect hypokalemia (reduced [K+]) or hyperkalemia in a timely manner to provide life-saving treatment. Additionally, the effect of changes in other electrolyte levels, like calcium concentration ([Ca2+]), and in heart rate are investigated. These aims are achieved by combining novel ECG signal processing techniques with in silico modeling and simulation of cardiac electrophysiology.The specific objectives are:1. Characterization of hypokalemia or hyperkalemia and hypocalcemia (reduced [Ca2+]) or hypercalcemia (elevated [Ca2+])-induced changes in ventricular repolarization from ECGs (T wave) of CKD patients. This is addressed in chapter 3 and chapter 4. In these chapters, we describe how T waves are extracted from ECGs and how we characterize changes in T waves at varying potassium, calcium and heart rate using analyses based on time warping and Lyapunov exponents. Next, univariable and multivariable regression models including markers of T wave nonlinear dynamics in combination with warping-based markers of T wave morphology are built and their performance for [K+] estimation is assessed.2. Characterization of hypo- or hyperkalemia and hypo- or hypercalcemia-induced changes in ventricular depolarization from the QRS complex of CKD patients. This is reported in chapter 5. In this chapter, we present how QRS complexes from ECGs of CKD patients are processed and how we measure changes at varying [K+], [Ca2+] and heart rate. Univariate and multivariate regression analyses including novel QRS morphological markers in combination with T wave morphological markers are performed to assess the contribution of depolarization and repolarization features for electrolyte monitoring in CKD patients.3. Identification of potential sources underlying inter-individual variability in ECG markers in response to changes in [K+] and [Ca2+]. In silico investigations of cardiac electrophysiology are conducted and ECG features are computed. Simulation results are compared with patient data. This is explained in chapter 3 using one-dimensional (1D) fibers and in chapter 6 using three-dimensional (3D) human heart-torso models. Chapter 6 includes the development of a population of realistic computational models of human ventricular electrophysiology, based on human anatomy and electrophysiology, to better understand how changes in individual characteristics influence the ECG (QRS and T wave) markers that we introduced in previous chapters. ECG waveforms are characterized by their amplitude, duration and morphology. Simulations are performed with the most realistic available techniques to model the electrophysiology of the heart and the resulting ECG. We establish mechanisms that contribute to inter-individual differences in the characterized ECG features.In conclusion, we identify several markers of ECG morphology, including depolarization and repolarization features, that are highly correlated with serum electrolyte (potassium and calcium) concentrations. ECG morphological variability markers vary significantly with [K+] and [Ca2+] in both simulated and measured ECGs, with a wide range of patterns observed for such relationships. The proportions of endocardial, midmyocardial and epicardial cells have a large impact on ECG markers, particularly for serum electrolyte concentrations out of their physiological levels. This suggests that transmural heterogeneities can modulate ECG responses to changes in electrolyte concentrations in CKD patients. Agreement between actual potassium and calcium levels and their estimates derived from the ECG is promising, with lower average errors than previously proposed markers in the literature. These findings can have major relevance for noninvasive monitoring of serum electrolyte levels and prediction of arrhythmic events in these patients.<br /

Accelerating stabilization of whole-heart models after changes in cycle length

International audienceParameter changes can cause long-term drift in membrane models. To reduce the cost of whole-heart simulations with such changes the stabilization can be performed in isolated-cell models, but it can then still take many beats to stabilize the full model. We hypothesized that differences in activation time leading to cycle length (CL) variability before the first beat contribute to this. To remove this variability we froze most state variables of the model until the sodium current activated. Simulations were performed with CL 400, 500, 600 and 1000 ms and modified Ten Tusscher-Panfilov 2006 dynamics. Isolated endocardial, mid-myocardial, and epicardial cells were simulated for 1000 beats. Their final states were then copied to a model of the whole human ventricles, which was run for 5 beats, with and without freezing. Stabilization of the full model took three to four beats. Freezing of the membrane state accelerated stabilization in some cell types but caused opposite drifts in others. Drifts were largest in the epicardial and mid-myocardial layers, and not in particular at their interfaces. Freezing of membrane state may help to accelerate stabilization but in our scenarios other types of drift dominate and may be aggravated by freezing, as it inhibits electrotonic interactions

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 diseas

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

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 (¿t, ¿wt) and a divergence-related index (¿). 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 ¿ 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.ariability allow noninvasive monitoring of [K+] in ESRD patients. Significance: ECG markers have the potential to be used for hypo- and hyperkalemia screening in ESRD patient

QRS Slopes for Potassium and Calcium Monitoring in End-Stage Renal Disease Patients

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Inter-individual differences in cell composition across the ventricular wall may explain variability in ECG response to serum potassium and calcium variations

International audienceNon-invasive monitoring of serum potassium ([K + ]) and calcium ([Ca 2+ ]) concentration can help to prevent arrhythmia in kidney patients. Current electrocardiogram (ECG) markers, including the T wave width (T w) and its time-warped temporal morphological variability (d U w), correlate significantly with [K + ] and [Ca 2+ ] but these relations vary strongly between patients. We hypothesized that inter-individual differences in cell type distribution across the ventricular wall can explain this variability. We computed T w and d U w in simulated ECGs from a human heart-torso model at different proportions of endo-, mid-, and epicardial cells, while varying [K + ] (3 to 6.2 mM) and [Ca 2+ ] (1.4 to 3.2 mM). Electrical activity was simulated with a reaction-diffusion model with modified Ten Tusscher-Panfilov dynamics. Results were compared to data from 29 patients. T w and d U w correlated strongly with [K + ] (absolute median Pearson coefficient r = 0.70 to 0.93) and [Ca 2+ ] (r = 0.69 to 0.86) in simulations and in patients. Different cell type distributions reproduced inter-patient variability, with the same sign and magnitude of r. In conclusion, the inter-patient variability in the relation between serum electrolytes and their ECG markers can indeed be explained by inter-individual differences in cell type distribution across the ventricular wall

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

International audienceObjective: Non-invasive estimation of serum potassium, [K + ], and calcium, [Ca 2+ ], 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 [Ca 2+ ] 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 [Ca 2+ ] (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 [Ca 2+ ] when patient-specific multivariable estimators combining QRS and T wave markers were used. Conclusion: QRS morphological markers allow non-invasive estimation of [K + ] and [Ca 2+ ] 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

Estimación del nivel de potasio en sangre mediante las pendientes del QRS del electrocardiograma en pacientes renales crónicos

Noninvasive estimation of serum potassium concentration can help prevent ventricular arrhythmias and sudden cardiac death in patients with chronic renal failure (CKD), but current outpatient estimation methods are limited. In this study, we estimated serum potassium concentration by evaluating the slopes of the “QRS complex” of the electrocardiogram in 29 patients with CRF during and after hemodialysis

Estimación del nivel de potasio en sangre mediante las pendientes del QRS del electrocardiograma en pacientes renales crónicos

Noninvasive estimation of serum potassium concentration can help prevent ventricular arrhythmias and sudden cardiac death in patients with chronic renal failure (CKD), but current outpatient estimation methods are limited. In this study, we estimated serum potassium concentration by evaluating the slopes of the “QRS complex” of the electrocardiogram in 29 patients with CRF during and after hemodialysis

Characterization of t wave amplitude, duration and morphology changes during hemodialysis: Relationship with serum electrolyte levels and heart rate

Objective: Chronic kidney disease affects more than 10% of the world population. Changes in serum ion concentrations increase the risk for ventricular arrhythmias and sudden cardiac death, particularly in end stage renal disease (ESRD) patients. We characterized how T wave amplitude, duration and morphology descriptors change with variations in serum levels of potassium and calcium and in heart rate, both in ESRD patients and in simulated ventricular fibers. Methods: Electrocardiogram (ECG) recordings from twenty ESRD patients undergoing hemodialysis (HD) and pseudo-ECGs (pECGs) calculated from twenty-two simulated ventricular fibers at varying transmural heterogeneity levels were processed to quantify T wave width (Tw), T wave slope-to-amplitude ratio (TS/A) and four indices of T wave morphological variability based on time warping (dw, dNLw, da and dNLa). Serum potassium and calcium levels and heart rate were measured along HD. Results: dNL with serum potassium, dw with calcium and da with heart rate, after correction for covariates. Median values of partial correlation coefficients were 0.75,−0.74 and −0.90, respectively. For all analyzed T wave descriptors, high inter-patient variability was observed in the pattern of such relationships. This variability, accentuated during the first HD time points, was reproduced in the simulations and shown to be influenced by differences in transmural heterogeneity. Conclusion: Changes in serum potassium and calcium levels and in heart rate strongly affect T wave descriptors, particularly those quantifying morphological variability. Significance: ECG markers have the potential to be used for monitoring serum ion concentrations in ESRD patients