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.


COMPARISON OF INTER-INDIVIDUAL VARIABILITY IN QRS COMPLEX CHARACTERISTICS AT VARYING [K + ] AND [Ca 2+ ] IN SIMULATIONS AND PATIENTS
Figure S3 shows QRS complexes and the analyzed markers  in the patients, albeit with some quantitative differences.These results were confirmed by computation of Pearson correlation coefficients, as shown in panels c, f and i of the same figure.The ability of our in silico population to reproduce d NL a,Q trends measured in some of the patients was equally valid for other QRS complex markers even if they did not present as remarkable changes as d NL a,Q when varying [K + ] and [Ca 2+ ].
To assess the extent to which our population of models could reproduce the inter-patient variability in QRS complex markers at concomitantly varying electrolyte levels, a correlation analysis was performed.Figure S5 shows the Pearson correlation coefficient r between each QRS complex marker and [K + ], or  [Ca 2+ ], in the simulated and the patients' ECGs.QRS a , d NL w,Q and d NL a,Q were the markers most highly correlated with [K + ] (median r being −0.98, 0.80, 0.71 in simulations, and −0.86, 0.86, 0.87 in patients, respectively) and [Ca 2+ ] (median r being 0.98, −0.82, −0.71 in simulations, and 0.82, −0.71, −0.80 in patients, respectively).Inter-individual variability in the correlation coefficients associated with QRS w and d a,Q was high in both simulations and patients.For all other QRS complex morphology markers, the variability between in silico models only partly reproduced the variability between patients.
Table S2 provides the results for the quantitative comparison between simulated and patients' QRS complex markers, in terms of median and interquartile range of Pearson correlation coefficient r with [K + ] and [Ca 2+ ].As can be seen from the table, all the analyzed morphology-based QRS complex -0.5 0 0.5 1 r 3; 3:2 4; 2:6 5:4; 2 6:2; 1:4 All models All patients Table S2.Median (interquartile range) of Pearson correlation coefficient between QRS complex markers and each of [K + ] and [Ca 2+ ] in the simulated cases and in the patients at varying [K + ], [Ca 2+ ] and their combination.

CONTRIBUTION OF VENTRICULAR WALL COMPOSITION TO INTER-INDIVIDUAL QRS COMPLEX VARIABILITY AT VARYING
The results of the sensitivity analysis performed to investigate how different proportions of endocardial, midmyocardial and epicardial cells contribute to explain individual QRS complex responses when varying both [K + ] and [Ca 2+ ] are presented in Table S3 for all the analyzed simulated QRS markers.The highest Linear and non-linear time warping of QRS complexes for a particular simulated case (C334) are shown in FigureS1at particular [K + ] and [Ca 2+ ].2 EVALUATION OF QRS COMPLEX CHANGES INDUCED BY[K + ] AND [Ca 2+ ] VARIATIONS IN SIMULATIONS QRS complex markers (QRS w , QRS a , d u w,Q , d a,Q , d NL w,Q , d NL a,Q ) computedfrom simulated ECGs at varying [K + ], [Ca 2+ ] and their combinations are shown in Figure S2.All the analyzed markers vary significantly at varying [K + ] and [Ca 2+ ].
FigureS3shows QRS complexes and the analyzed markers QRS w , QRS a , d u w,Q , d a,Q , d NL w,Q and d NL a,Q , computed from the ECGs of a particular model, C514, and a particular patient, P10, when concomitantly varying [K + ] and [Ca 2+ ].More peaked positive QRS complexes can be observed with decreasing [K + ] and increasing[Ca 2+ ] in both the model and the patient.

Figure
FigureS4shows a comparison of the changes in the marker d NL a,Q when varying both [K + ] and [Ca 2+ ] in the simulated cases and the patients.As can be observed by comparing panels a and b, panels d and e and panels g and h, the models in the population reproduced some specific patterns of change of d NL a,Q

Figure S1 :
Figure S1: Linear and non-linear time warping for a particular simulated case (C334) from 3D torso-heart model.Panel (a) shows reference (blue) and investigated (red) QRS complexes obtained from a combination of [K + ] and [Ca 2+ ].Panel (b) shows the warped QRS complexes, which have the same duration while keeping the original amplitude.Panel (c) depicts the warped QRS complexes after normalization by their L2-norms.The area (yellow region) between both QRS complexes in panel (d) represents d uw,Q , which quantifies the total amount of warping.The green solid line is the linear regression function γ * l (t r ) best fitted to γ * (t r ).The marker d NL w,Q quantifies the non-linear warping by computing the area of the dashed magenta region between γ * (t r ) and γ * l (t r ).

Figure S2 :
Figure S2: Panels a-f: Changes in w , QRS a , d u w,Q , d a,Q , d NL w,Q and d NL a,Q for varying [K + ] at fixed [Ca 2+ ]=2.0 mM (black), varying [Ca 2+ ] at fixed [K + ] =5.4mM (red), and the combination of [K + and [Ca 2+ ] (blue), for ECGs simulated from the population of models.Central lines indicate the median, whereas bottom and top edges show the 25th and 75th percentiles, respectively.

Figure S3 :
Figure S3: Panels a-b: QRS complexes at varying [K + ] and [Ca 2+ ], for a simulated case (C514) and for a patient (P10).Panels c-d: Changes in QRS complex markers QRS w , QRS a , d u w,Q , d a,Q , d NL w,Q and d NL a,Q for the same simulated case and patient, respectively.Note the different scales between the plots.

Figure S4 :
Figure S4: Panels a-b, d-e, g-h: Changes in d NL a,Q at varying [K + ] and [Ca 2+ ], in simulated cases and patients.Panel c: Pearson correlation coefficients, r, of d NL a,Q with [K + ] and [Ca 2+ ] for the simulated cases shown in a and the patients shown in b.Panel f: Pearson correlation coefficient r for the simulated cases shown in d and the patients shown in e. Panel i: correlation coefficient r for all the simulated cases and all the patients.h 0 -h 4 are the HD time points corresponding to the onset and end of HD (h 4 with lowest [K + ] and highest [Ca 2+ ] and h 0 with highest [K + ] and lowest [Ca 2+ ].