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 noninvasive 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  (MaxAmp). 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 noise-free 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

Dössel, O.

Loewe, A.

Mesa, M. H.

Pilia, N.

KITopen

Current Directions in Biomedical Engineering 2019;5(1):69–72María Hernández Mesa*, Nicolas Pilia, Olaf Dössel, and Axel LoeweInfluence of ECG Lead Reduction Techniquesfor Extracellular Potassium and CalciumConcentration Estimationhttps://doi.org/10.1515/cdbme-2019-0018Abstract: Chronic kidney disease (CKD) affects 13% of theworldwide population and end stage patients often receivehaemodialysis treatment to control the electrolyte concentra-tions. The cardiovascular death rate increases by 10% - 30%in dialysis patients than in general population. To analyse pos-sible links between electrolyte concentration variation and car-diovascular diseases, a continuous non-invasive monitoringtool enabling the estimation of potassium and calcium con-centration from features of the ECG is desired. Although theECG was shown capable of being used for this purpose, themethod still needs improvement. In this study, we examine theinfluence of lead reduction techniques on the estimation re-sults of serum calcium and potassium concentrations. We usedsimulated 12 lead ECG signals obtained using an adapted Hi-meno et al. model. Aiming at a precise estimation of the elec-trolyte concentrations, we compared the estimation based onstandard ECG leads with the estimation using linearly trans-formed fusion signals. The transformed signals were extractedfrom two lead reduction techniques: principle component anal-ysis (PCA) and maximum amplitude transformation (Max-Amp). Five features describing the electrolyte changes werecalculated from the signals. To reconstruct the ionic concen-trations, we applied a first and a third order polynomial re-gression connecting the calculated features and concentrationvalues. Furthermore, we added 30 dB white Gaussian noise tothe ECGs to imitate clinically measured signals. For the noise-free case, the smallest estimation error was achieved with aspecific single lead from the standard 12 lead ECG. For ex-ample, for a first order polynomial regression, the error was0.0003±0.0767 mmol/l (mean±standard deviation) for potas-sium and -0.0036±0.1710 mmol/l for calcium (Wilson leadV1). For the noisy case, the PCA signal showed the best es-timation performance with an error of -0.003±0.2005 mmol/lfor potassium and -0.0002±0.2040 mmol/l for calcium (bothfirst order fit). Our results show that PCA as ECG lead reduc-*Corresponding author: María Hernández Mesa, Institute ofBiomedical Engineering, Karlsruhe Institute of Technology (KIT),Kaiserstr. 12, 76131 Karlsruhe, Germany, E-mail:publications@ibt.kit.eduNicolas Pilia, Olaf Dössel, Axel Loewe, Institute of BiomedicalEngineering, Karlsruhe Institute of Technology (KIT), Karlsruhe,Germanytion technique is more robust against noise than MaxAmp andstandard ECG leads for ionic concentration reconstruction.Keywords: ECG, PCA, lead reduction techniques, cardiacsignals, ionic concentrations1 IntroductionChronic kidney disease (CKD) patients at end stages oftenundergo haemodialysis treatments to counterbalance the elec-trolyte disbalance. Unexpectedly, the principal mortality causefor CKD patients is sudden cardiac death. The risk of cardiacmortality is 10 to 30 times higher in CKD patients than innon-CKD patients [1]. Recent studies have shown the relation-ship between the extracellular potassium ([K+]o), and calcium([Ca2+]o) concentrations and the pathophysiology of suddencardiac death [2]. Due to this connection, ECG has been pro-posed as a non-invasive method to determine the blood serumelectrolyte concentrations. A reduction of the information ofa 12 lead ECG to a set of most discriminating input data isdesired. In 2011, Corsi et al. [3] used a PCA transform of clin-ical ECG signals for this purpose. Other works in this field [4]used a lead transformation in the direction of the highest am-plitude (MaxAmp) for lead reduction. A comparison betweenthe mentioned lead reduction techniques (PCA and MaxAmp)is still lacking. Furthermore, no studies comparing lead trans-forms and standard leads for the regression are known to theauthors of this work. Additionally, different regression meth-ods, such as neuronal networks or polynomial fit can be ap-plied for the same purpose. The ECG as an electrolyte and acardiac event predictor is a promising tool, which has shownresults with a standard deviation smaller than 0.2 mmol/l for[Ca2+]o and 0.4 mmol/l for [K+]o. However, many parametersand techniques still have to be optimized to obtain a robust andprecise tool for electrolyte estimation. In this study, we com-pare the concentration estimation results based on simulatedsignals from ECG lead reduction techniques (PCA and Max-Amp) and the results from single lead reconstruction from the12 lead ECG. We performed an evaluation for both noisy andnoise-free cases. Moreover, we applied polynomial regressionwith a first and a third order polynomial fit to investigate on theinfluence of the lead reduction techniques on those two regres- Open Access. © 2019 M. Herná  ndez Mesa et al., published by De Gruyter.  This work is licensed under the Creative Commons Attribution 4.0 License. Bereitgestellt von | Karlsruher Institut für Technologie KIT-BibliothekAngemeldetHeruntergeladen am | 09.10.19 11:297 M.H. Mesa et al., Influence of ECG Lead Reduction Techniques for Ionic Concentration Estimation0 100 200 300 400 500 600Time in ms-1.5-1-0.500.511.5Amplitude in mV[Ca2+]o = 0.6mmol/l[Ca ]  = 3.0mmol/l2+oFig. 1: Two exemplary simulated ventricular ECG signals at differ-ent [Ca2+]o levels corrupted by 30dB white Gaussian noise (leadEinthoven 1).sion methods. This allowed us to appraise which combinationis adequate for our objective of estimating [Ca2+]o and [K+]o.2 Methods2.1 Simulations80 computer simulations of the cardiac electrophysiology atventricular level were performed. The heterogeneous formula-tion from the Himeno et al. [5] model proposed by Loewe etal. [6] was used. In the original formulation [K+]o was set to4.5 mmol/l and [Ca2+]o to 1.8 mmol/l. In this study, we variedthe ionic concentrations in equally distributed steps as in a for-mer study [4]. Further settings were applied as described there.Since a ventricular cell model was used, no P wave was con-tained in the extracted ECG signals. For a realistic simulationof the pathophysiological cases, we added noise to the sim-ulated signals. We added white Gaussian noise to the signalsachieving an SNR of 30 dB. As in clinically measured ECGsignals, we low-pass filtered the noise signals with a cut-offfrequency of 80 Hz using a butterworth 6th order phase freefilter. The low-pass filtered noise signals were added to eachsetup of the ECG simulated signals. The generation of noisesignals was repeated 30 times per setup to augment the datasetas described in [7]. This allowed us to augment the data set.The addition of noise to the ECG signals and the influence of[Ca2+]o on the ECG can be observed in Figure 1.2.2 Lead reductionFor the ionic concentration estimation, features from ECG sig-nals were extracted as described in [7]. The following featureswere used for further steps: center of the T wave, amplitudeof the T wave, upslope of the T wave, ratio of energy of thesecond half of the T wave to the energy of the whole T wave,and R amplitude. Feature estimation was applied to signalsfrom three different combinations. The first combination wasa standard 12 lead ECG. Thus, the features from all 12 signalswere calculated. The second combination used MaxAmp asECG lead reduction technique. MaxAmp lead reduction wasapplied in the direction of the QRS complex and in the direc-tion of the T wave; i.e., 2 signals were calculated with this re-duction method. Features related to changes in the QRS com-plex were extracted from the MaxAmp signal that maximizedR peak amplitude and features regarding changes of the shapeand amplitude of the T wave were extracted from the MaxAmpsignal that maximized T wave amplitude. The third combina-tion used the PCA as lead reduction technique. PCA was ap-plied to the 8 linearly independent ECG leads. The QRS com-plex generally has a higher amplitude than the T wave, thusthe first component of the PCA (PCA 1st) is higher influencedby this part of the signal. Therefore, we also calculated thesecond component of the PCA (PCA 2nd) and additionally thePCA of the signal part containing the T wave (PCA T). There-fore, the impact of both parts of the signal could be observed,especially considering that changes of [Ca2+]o and [K+]o havea dominant influence on the T wave [8]. Summarizing, featureswere calculated for the 17 signals extracted from all combina-tions (12 leads, 2 signals from MaxAmp and 3 signals fromthe PCA technique).2.3 RegressionPolynomial regression was chosen for reconstructing ionicconcentrations of [K+]o and [Ca2+]o from the feature values.For the validation of the methods, 20-fold cross validation wasused. The grouping of the setups was the same for all inputsetups and for all regression techniques. The estimation errorwas determined and minimized for each partition data using aTikhonov regularization.3 ResultsFigure 2 and 3 show the results of applying different lead re-ductions techniques to a standard 12 lead ECG and MaxAmprespectively. For both analyzed ionic concentrations ([K+]oand [Ca2+]o), estimation performance was evaluated by ana-lyzing the mean error and the standard deviation of the errors.Results are summarized in Tables 1 and 2. Table 1 shows theestimation errors using a polynomial fit of first order as re-0Bereitgestellt von | Karlsruher Institut für Technologie KIT-BibliothekAngemeldetHeruntergeladen am | 09.10.19 11:29M.H. Mesa et al., Influence of ECG Lead Reduction Techniques for Ionic Concentration Estimation0 100 200 300 400 500 600Time in ms-8-6-4-20246Amplitude in mVPCA 1stPCA 2ndPCA TFig. 2: Signals resulting from an information reduction of a stan-dard ECG using PCA.0 100 200 300 400 500 600Time in ms-20-100102030405060Amplitude in mVMaxAmp in the direction of the QRS complexMaxAmp in the direction of the T waveFig. 3: Signals resulting from an information reduction of a stan-dard ECG using a MaxAmp transformation.gression method, Table 2 using a third order polynomial fit.The upper part of the table shows the results for the noise-freecase and the lower part for the noisy case. For the regressionusing a standard 12 lead ECG without reduction techniquesthe estimation error was calculated for each lead. The resultsdepict the lead with the smallest estimation error (best lead).For noise-free signals and a first order polynomial regres-sion, Wilson lead V1 showed the smallest standard deviationand MaxAmp the highest standard deviation of the estima-tion . When applying noise, the second component of the PCAyielded the smallest standard deviation of errors. There are dis-crepancies between the results using a first order and a third or-der polynomial regression model. For a third order polynomialregression, Wilson lead V1 and PCA T showed the smalleststandard deviation of errors for [K+]o and [Ca2+]o respectivelyfor the noise-free case; PCA T and PCA 2nd for the noisy case.The highest standard deviation for the [K+]o estimation errorwas obtained when using a PCA 1st as lead reduction tech-nique for both the noisy and noise-free case for a third orderpolynomial fit. For [Ca2+]o, the highest standard deviation oferrors ocurred when using MaxAmp for noise-free signals andTab. 1: Influence of different lead reduction techniques on a firstorder regression. Estimation errors represent mean error ± stan-dard deviation. The smallest and highest standard deviation oferrors per regression method are highlighted in green and red,respectively.noise-free [K+]o in mmol/l [Ca2+]o in mmol/lPCA 1st -0.0072±0.2778 0.0034±0.2148PCA 2nd -0.0054±0.1857 0.0038±0.2055PCA T -0.0049±0.2152 0.0021±0.1938MaxAmp -0.0004±0.3159 -0.0057±0.5379V1/V1 (best lead) 0.0003±0.0767 -0.0036±0.1710noisy [K+]o in mmol/l [Ca2+]o in mmol/lPCA 1st -0.0001±0.9830 0.0001±0.7394PCA 2nd -0.003±0.2005 -0.0002±0.2040PCA T -0.0036±0.2376 -0.001±0.2128MaxAmp -0.0019±0.3412 0.0099±0.6556V2/V2 (best lead) -0.0003±0.8321 -0.0011±0.7482Wilson lead V2 for noisy signals. Additionally we observedthat the standard deviation of error for a 12 lead standard ECGincreased more than for MaxAmp and PCA.4 DiscussionSimilar to the studies by Corsi et al. [2] and Pilia et al. [3]the ionic concentration estimation errors showed an accept-able range. The results underline that the estimation errorshighly depend on the regression method, the prevalence ofnoise and the lead or lead reduction technique used. In bothregression methods, the estimation error of ECG lead regres-sion with single leads of the ECG in noise-free signals showedsmaller standard deviation of the errors. Due to the results pre-sented in the previous section, we consider that for noise-freesignals using a standard 12 lead ECG achieves better resultsthan using lead reduction techniques. We believe it is worthto mention that except for [K+]o estimation with a first orderpolynomial fit, MaxAmp showed the highest standard devia-tion of errors for all combinations. When considering noisysignals, the lowest standard deviation of error was achievedfor PCA 2nd or PCA T. The biggest standard deviation of er-rors were obtained by either the first component of the PCAor the single ECG lead estimation in both regression models.Lead reduction techniques are apparently more robust againstnoise than a standard 12 lead ECG as visible in Table 1 and2. Thus, when working with noisy signals, a lead reductiontechnique should be used. In this study, applying PCA 2nd ora PCA T showed the best results. As electrolyte variation hasa higher impact on the T wave than on the QRS complex forthe evaluated features, we have shown with this study how im-71Bereitgestellt von | Karlsruher Institut für Technologie KIT-BibliothekAngemeldetHeruntergeladen am | 09.10.19 11:29M.H. Mesa et al., Influence of ECG Lead Reduction Techniques for Ionic Concentration EstimationTab. 2: Influence of different lead reduction techniques on a thirdorder regression. Estimation errors represent mean error ± stan-dard deviation. The smallest and highest standard deviation oferrors per regression method are highlighted in green and red,respectively.noise-free [K+]o in mmol/l [Ca2+]o in mmol/lPCA 1st -0.0416±0.3591 0.0158±0.1465PCA 2nd -0.0288±0.2733 0.0126±0.1251PCA T -0.0112±0.1076 0.0025±0.0714MaxAmp -0.0072±0.1579 0.0256±0.4659V1/II (best lead) 0.0026±0.0663 0.0012±0.0747noisy [K+]o in mmol/l [Ca2+]o in mmol/lPCA 1st 0.0007±0.9863 0.0008±0.7445PCA 2nd -0.01±0.1736 0.0011±0.0810PCA T -0.0037±0.1579 -0.0005±0.1094MaxAmp 0.0016±0.2734 -0.0084±0.6084V2/V2 (best lead) 0.001±0.8339 -0.0012±0.7518portant a lead reduction in the correct direction is. This can beobserved by comparing the results of PCA 1st with the resultsof PCA 2nd and PCA T. We consider relevant to mention thatMaxAmp showed higher standard deviation of errors than theerrors obtained from using PCA 2nd and PCA T. Additionally,we observed the smallest standard deviation of errors using athird order polynomial fit instead of a first order polynomial fit.Therefore, third order polynomial fit is a better suited regres-sion method when aiming at a serum blood estimation of [K+]oand [Ca2+]o using the ECG because non-linear behaviour be-tween features and ionic concentrations can be better captured.The following limitations should be taken into account regard-ing this study. On the one hand, the evaluation of the influ-ence of ECG lead reduction techniques has been carried outfor simulated signals. Although we added noise to the signalsto reproduce a more realistic scenario, the results using clinicaldata may differ from the results presented here. We observedthat the estimation errors depend on the regression methodused. In this study, we have analyzed a first order and a thirdorder polynomial fit. However, when utilizing other regressionmodels like for example neuronal networks, the results mayvary. We evaluated the results of lead reduction as we suspectthat too many features can decrease the accuracy of the esti-mation. However, we did not prove if the full information ofthe 12-lead ECG would deliver better results.5 ConclusionsIn this work, we used simulated signals with the adapted Hi-meno et al. model to study the influence of ECG lead reductiontechniques on ionic concentration estimation. Therefore, weused 2 different regression methods and were able to show, thatthe third order polynomial regression yielded smaller standarddeviation of estimation errors than a first order polynomial fit.We showed that for the noise-free case, using single leads ofthe ECG reached generally better results than using signalsobtained by lead reduction techniques like PCA or MaxAmp.However, when adding noise to the signals, a lead reductionusing principal component analysis showed generally the bestresults. This supports the promising idea of using ECG as anon invasive method for [K+]o and [Ca2+]o estimation and thesubsequent prediction of cardiac events in CKD patients.Author StatementResearch funding: María Hernández’ work was supported byFresenius Medical Care. Conflict of interest: Authors state noconflict of interest. Informed consent: Informed consent is notapplicable. Ethical approval: The conducted research is not re-lated to either human or animals use.References[1] M. J. Sarnak, A. S. Levey, et al., "Kidney disease as a riskfactor for development of cardiovascular disease," Circula-tion, 2003;108:2154-2169.[2] A. Loewe, Y. Lutz, et al., Severe sinus bradycardia due toelectrolyte changes as a pathomechanism of sudden car-diac death in chronic kidney disease patients undergoinghemodialysis, Heart Rhythm Scientific Sessions 2018.[3] C. Corsi, M. Cortesi, et al., "Noninvasive quanti- fication ofblood potassium concentration from ECG in he- modialysispatients," Scientific Reports, 2017;7:4249.[4] N. Pilia, O. Dössel, et al., “ECG as a tool to estimate potas-sium and calcium concentrations in the extracellular space.”,Computing in Cardiology, 2017;44.[5] Y. Himeno, K. Asakura, et al., ”A human ventricular myocytemodel with a refined representation of excitation-contractioncoupling”, Biophysical Journal, 2015, 109.2: 415-427.[6] A. Loewe, M. Hernández Mesa, et al., “A heterogeneousformulation of the Himeno et al. human ventricular myocytemodel for simulation of body surface ECGs.” Computing inCardiology, 2018;45.[7] N. Pilia, M. Hernández Mesa, et al., ”ECG-based Estimationof Potassium and Calcium Concentrations: Proof of Conceptwith Simulated Data”, Engineering in Medicine and BiologySociety, 2019, accepted.[8] M. Hernández Mesa, N. Pilia, et al., ”Effects of Serum Cal-cium Changes on the Cardiac Action Potential and the ECGin a Computational Model”, Current Directions in BiomedicalEngineering, 2018, 4(1): 251-254.72Bereitgestellt von | Karlsruher Institut für Technologie KIT-BibliothekAngemeldetHeruntergeladen am | 09.10.19 11:29

Influence of ECG Lead reduction techniques for extracellular potassium and calcium concentration estimation

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Influence of ECG Lead reduction techniques for extracellular potassium and calcium concentration estimation

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