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.
G. Lenis, N. Pilia, A. Loewe, W. H. W. Schulze, and O. Dössel. Comparison of Baseline Wander Removal Techniques considering the Preservation of ST Changes in the Ischemic ECG: A Simulation Study. In Computational and Mathematical Methods in Medicine, vol. 2017, pp. 9295029, 2017
The most important ECG marker for the diagnosis of ischemia or infarction is a change in the ST segment. Baseline wander is a typical artifact that corrupts the recorded ECG and can hinder the correct diagnosis of such diseases. For the purpose of finding the best suited filter for the removal of baseline wander, the ground truth about the ST change prior to the corrupting artifact and the subsequent filtering process is needed. In order to create the desired reference, we used a large simulation study that allowed us to represent the ischemic heart at a multiscale level from the cardiac myocyte to the surface ECG. We also created a realistic model of baseline wander to evaluate five filtering techniques commonly used in literature. In the simulation study, we included a total of 5.5 million signals coming from 765 electrophysiological setups. We found that the best performing method was the wavelet-based baseline cancellation. However, for medical applications, the Butterworth high-pass filter is the better choice because it is computationally cheap and almost as accurate. Even though all methods modify the ST segment up to some extent, they were all proved to be better than leaving baseline wander unfiltered.
G. Lenis, N. Pilia, T. Oesterlein, A. Luik, C. Schmitt, and O. Dössel. P wave detection and delineation in the ECG based on the phase free stationary wavelet transform and using intracardiac atrial electrograms as reference. In Biomedizinische Technik. Biomedical Engineering, vol. 61(1) , pp. 37-56, 2016
Robust and exact automatic P wave detection and delineation in the electrocardiogram (ECG) is still an interesting but challenging research topic. The early prognosis of cardiac afflictions such as atrial fibrillation and the response of a patient to a given treatment is believed to improve if the P wave is carefully analyzed during sinus rhythm. Manual annotation of the signals is a tedious and subjective task. Its correctness depends on the experience of the annotator, quality of the signal, and ECG lead. In this work, we present a wavelet-based algorithm to detect and delineate P waves in individual ECG leads. We evaluated a large group of commonly used wavelets and frequency bands (wavelet levels) and introduced a special phase free wavelet transformation. The local extrema of the transformed signals are directly related to the delineating points of the P wave. First, the algorithm was studied using synthetic signals. Then, the optimal parameter configuration was found using intracardiac electrograms and surface ECGs measured simultaneously. The reverse biorthogonal wavelet 3.3 was found to be optimal for this application. In the end, the method was validated using the QT database from PhysioNet. We showed that the algorithm works more accurately and more robustly than other methods presented in literature. The validation study delivered an average delineation error of the P wave onset of -0.32+/-12.41 ms when compared to manual annotations. In conclusion, the algorithm is suitable for handling varying P wave shapes and low signal-to-noise ratios.
End-stage chronic kidney disease (CKD) patients are facing a 30% rise for the risk of lethal cardiac events (LCE) compared to non-CKD patients. At the same time, these patients undergoing dialysis experience shifts in the potassium concentrations. The increased risk of LCE paired with the concentration changes suggest a connection between LCE and concentration disbalances. To prove this link, a continuous monitoring device for the ionic concentrations, e.g. the ECG, is needed. In this work, we want to answer if an optimised signal processing chain can improve the result quantify the influence of a disbalanced training dataset on the final estimation result. The study was performed on a dataset consisting of 12-lead ECGs recorded during dialysis sessions of 32 patients. We selected three features to find a mapping from ECG features to [K+]o: T-wave ascending slope, T-wave descending slope and T-wave amplitude. A polynomial model of 3rd order was used to reconstruct the concentrations from these features. We solved a regularised weighted least squares problem with a weighting matrix dependent on the frequency of each concentration in the dataset (frequent concentration weighted less). By doing so, we tried to generate a model being suitable for the whole range of the concentrations.With weighting, errors are increasing for the whole dataset. For the data partition with [K+]o<5 mmol/l, errors are increasing, for [K+]o≥5 mmol/l, errors are decreasing. However, and apart from the exact reconstruction results, we can conclude that a model being valid for all patients and not only the majority, needs to be learned with a more homogeneous dataset. This can be achieved by leaving out data points or by weighting the errors during the model fitting. With increasing weighting, we increase the performance on the part of the [K+]o that are less frequent which was desired in our case.
N. Pilia, M. Hernandez Mesa, O. Dössel, and A. Loewe. ECG-based Estimation of Potassium and Calcium Concentrations: Proof of Concept with Simulated Data. In 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 2610-2613, 2019
In Europe, the prevalence of chronic kidney disease lay at approximately 18.38% in 2016. A common treatment for patients in the end stage of this disease is haemodialysis. However, patients undergoing this therapy suffer from an increased risk of cardiac death. A hypothesis is that the cause is an inbalanced electrolyte concentration. To study the underlying mechanisms of this phenomenon and fight the consequences, a continous non-invasive monitoring technique is desired. In this work, we investigated the possibility to reconstruct the extracellular concentrations of potassium and calcium from ECG signals. Therefore, we extracted 71 ECGs using the simulation results of a modified Himeno et al. ventricular cell model comprising variations of the extracellular ionic concentrations of potassium and calcium. The changes dependent on the different extracellular ionic concentrations were captured with five ECG features. These were used to train an artificial neural network for regression. The study was performed both for noise-free and noisy data. The estimation error for the reconstruction of the potassium concentrations was -0.01±0.14 mmol/l (mean±standard deviation) in the noise- free case, -0.03±0.46mmol/l in the noisy case (30dB SNR). For calcium, the result was 0.01±0.11mmol/l in the noise- free case, 0.02±0.17mmol/l in the noisy case. For both ion types, the result was improved by augmenting the dataset. We therefore conclude that with the calculated features, we are able to reconstruct the extracellular ionic concentrations for both potassium and calcium with an acceptable precision. When analysing noisy signals, the accuracy of the estimation method is still sufficient but can be further improved by an augmentation of the dataset.
A common treatment of focal ventricular tachycardia is the catheter ablation of triggering sites. They have to be found manually by the physician during an intervention in a catheter lab. Thus, a method for determining the position of the focus automatically is desired. The inverse problem of electrocardiography addresses this problem by reconstructing the source of the ectopic beats using the surface ECG. This problem is ill-posed and therefore needs specific methods for solving it. We propose a machine learning approach for localisation of the ectopic foci in the heart to assist cardiologists with their therapy planning.We simulated 600 120-lead ECGs with different known excitation origins in the heart using a cellular automaton followed by a forward calculation. Features from the ECGs were used as input for a support vector regression (SVR). We assumed a functional relation between features from the ECG and the excitation origin. To benchmark SVR, we also used the well-known Tikhonov 0th order regularisation to reconstruct the transmembrane potentials in the heart and detect the location of the ectopic foci. Parameters for SVR and regularisation were chosen using a grid search minimising the error between estimated and true excitation origin. Compared to the Tikhonov regularisation method, SVR achieved a smaller deviation between estimated and real excitation origin evaluated with 6-fold cross validation. Future work could investigate on the behaviour on data from simulations with other torso and electrophysiological models, the influence of other methods for feature extraction and finally the evaluation with clinical data.
Chronic kidney disease appears worldwide. In the United States, the number of patients suffering from kid- ney failure doubled from 1998 to 2010. A common treat- ment for these patients is haemodialysis. However, the frequency of deaths caused by cardiovascular diseases is up to 10% to 30% higher in patients undergoing dialysis than in the general population. To analyse the underly- ing effects and for a possible risk prediction, a continuous monitoring of the ionic concentrations that are influenced by dialysis is desired. In this work, a method for the re- construction of the ionic concentrations of calcium and potassium from the ECG is proposed. In a first step, 91 monodomain simulations with the ten Tusscher ventricular cell model were performed for different extracellular ionic concentrations. From there, a standard 12-lead ECG was extracted. Calcium and potassium changes yielded ECGs clearly differing in amplitude and morphology. In a second step, the simulated ECG signals were used for reconstruc- ting the ionic concentrations directly from the ECG. Fea- tures were extracted from the signals designed to describe changes caused by varied ionic concentrations. The in- verse problem, i.e. coming back from the ECG features to the ionic concentrations was solved by regression with an artificial neural network. Results for potassium estimation yield an error of 0.00±0.28 mmol/l (mean±standard de- viation) calculated with 7-fold cross validation. The esti- mation error for calcium was 0.00±0.08 mmol/l. Although these results underline the suitability of the method, the used ECGs differed from the observed in a clinical envi- ronment. However, simulations allow an evaluation un- der controlled conditions of a particular effect that was intended to be investigated. As the application to clinical data is yet missing, this study can be seen as a proof of concept showing that an artificial neural network is capa- ble of exactly estimating potassium and calcium concen- trations from ECG features. 1. Introduction Haemodialysis therapy is a common treatment method for patients suffering from chronic kidney disease (CKD) in the terminal stage. The amount of people in the United States suffering from kidney failure increased from 320,000 in 1998 to 650,000 in 2010. The frequency of deaths caused by cardiovascular events within the dialysis patient group is up to 10% to 30% higher than in gene- ral population . Patients suffering from end-stage CKD experience high variations of blood electrolyte concentra- tions. These can directly influence the functioning of the heart. Thus, research on cardiovascular links could im- prove therapy and risk stratification. One tool which is capable of capturing the electrophysiological properties of the heart in a non-invasive way is the electrocardiogram (ECG). It is known, that electrolyte concentrations of po- tassium (K+) and calcium (Ca2+) affect the ECG . Un- til now, a determination of the concentrations is connec- ted to a blood test. Hence, continuous monitoring of the ionic concentration is impracticable. However, the ECG as a continuous, non-invasive monitoring tool could shed a light on the relation between heart diseases and changes in the ionic concentration particularly after leaving the strictly supervised clinical area where dialysis takes place, i.e allowing a monitoring at home. Articles have been pub- lished showing that the reconstruction of extracellular K+ concentration can be done using just one feature from the ECG with a quadratic regression . In this study, we tried to estimate both K+ and Ca2+ concentrations from the ECG. Therefore, we examined simulated ECGs at dif- ferent concentration levels and designed features descri- bing the observed changes in the ECG. A subset of these was used in connection with a machine learning method to reconstruct the concentrations. 2. Methods 2.1. Simulations A total number of 91 computer simulations of the car- diac electrophysiology were performed at whole heart
Baseline wander removal is one important part of electrocardiogram (ECG) filtering. This can be achieved by many different approaches. This work investigates the influence of three different baseline wander removal techniques on ST changes. The chosen filters were phase-free Butterworth filtering, median filtering and baseline correction with cubic spline interpolation. 289 simulated ECGs containing ischemia were used to determine the influence of these filtering processes on the ST segment. Synthetic baseline wander and offsets were added to the simulated signals. All methods proved to be good approaches by removing most of the baseline wander in all signals. Correlation coefficients between the original signals and the filtered signals were greater than 0.93 for all ECGs. Cubic spline interpolation performed best regarding the preservation of the ST segment amplitude change when compared to the original signal. The approach modified the ST segment by 0.10mV±0.06mV at elevated K points. Median filtering introduced a variation of 0.33mV±0.29mV, Butterworth filtering reached 0.16mV±0.14mV at elevated K points. Thus, all methods manipulate the ST segment.
N. Pilia, G. Lenis, and O. Dössel. Developing a robust method to delineate the P wave using information from intracardiac electrograms. In Biosignalverarbeitung und Magnetische Methoden in der Medizin. Proceedings BBS 2014, pp. 2, 2013
The correct detection of the P wave in the electrocardiogram (ECG) is very important for the evaluation of the atrial activity. The presented algorithm fusions intracardiac measurements and ECG data to detect P waves in the ECG. With this, it is possible to detect P waves simultaneously appearing with T waves and multiple P waves between two ventricular excitations.Die korrekte Erkennung der P-Welle im Elektrokardiogramm (EKG) ist äußerst wichtig zur Erkennung von Krankheiten in den Vorhöfen des Herzens. Hier soll ein Algorithmus vorgestellt werden, der die Informationen aus einer EKG-Messung und einer intrakardialen Messung der elektrischen Aktivität in den Vorhöfen kombiniert. Damit ist es möglich sowohl von T-Wellen überdeckte P-Wellen als auch mehrere P-Wellen zwischen zwei Kammeraktivierungen zu detektieren.
C. Nagel, N. Pilia, A. Loewe, and O. Dössel. Quantification of Interpatient 12-lead ECG Variabilities within a Healthy Cohort. In Current Directions in Biomedical Engineering, vol. 6(3) , pp. 493-496, 2020
The morphology of the electrocardiogram (ECG) varies among different healthy subjects due to anatomical and structural reasons, such as for example the shape of the heart geometry or the position and size of surrounding organs in the torso. Knowledge about these ECG morphology changes could be used to parameterize electrophysiological simula- tions of the human heart. In this work, we detected the boundaries of ECG waveforms, i.e. the P-wave, the QRS-complex and the T-wave, in 12- lead ECGs from 918 healthy subjects in the Physionet Com- puting in Cardiology Challenge 2020 Database with the IBT openECG toolbox. Subsequently, we obtained the onset, the peak and the offset of each P-wave, QRS-complex and T-wave in the signal. In this way, the duration of the P-wave, the QRS- complex and the T-wave, the PQ-, RR- and the QT-interval as well as the amplitudes of the P-wave, the Q-, R- and S- peak and the T-wave in each lead were extracted from the 918 healthy ECGs. Their statistical distributions and correlation between each other were assessed. The highest variabilities among the 918 healthy subject were found for the RR interval and the amplitudes of the QRS- complex. The highest correlation was observed for feature pairs that represent the same feature in different leads. Es- pecially the R-peak amplitudes showed a strong correlation across different leads. The calculated feature distributions can be used to optimize the parameters of populations of cardiac electrophysiological models. In this way, realistic in-silico generated surface ECGs can be simulated in large scale and could be used as input data for machine learning algorithms for a classification of cardio- vascular diseases.
M. Hernández Mesa, N. Pilia, O. Dössel, and A. Loewe. Influence of ECG Lead Reduction Techniques for Extracellular Potassium and Calcium Concentration Estimation. In Current Directions in Biomedical Engineering, vol. 5(1) , pp. 69-72, 2019
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 non-invasive 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 (Max- Amp). 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 noisefree 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.
C. Nagel, N. Pilia, L. Unger, and O. Dössel. Performance of Different Atrial Conduction Velocity Estimation Algorithms Improves with Knowledge about the Depolarization Pattern. In Current Directions in Biomedical Engineering, vol. 5(1) , pp. 101-104, 2019
Quantifying the atrial conduction velocity (CV) reveals important information for targeting critical arrhythmia sites that initiate and sustain abnormal electrical pathways, e.g. during atrial flutter. The knowledge about the local CV distribution on the atrial surface thus enhances clinical catheter ablation procedures by localizing pathological propagation paths to be eliminated during the intervention. Several algorithms have been proposed for estimating the CV. All of them are solely based on the local activation times calculated from electroanatomical mapping data. They deliver false values for the CV if applied to regions near scars or wave collisions. We propose an extension to all approaches by including a distinct preprocessing step. Thereby, we first identify scars and wave front collisions and provide this information for the CV estimation algorithm. In addition, we provide reliable CV values even in the presence of noise. We compared the performance of the Triangulation, the Polynomial Fit and the Radial Basis Functions approach with and without the inclusion of the aforementioned preprocessing step. The evaluation was based on different activation patterns simulated on a 2D synthetic triangular mesh with different levels of noise added. The results of this study demonstrate that the accuracy of the estimated CV does improve when knowledge about the depolarization pattern is included. Over all investigated test cases, the reduction of the mean velocity error quantified to at least 25 mm/s for the Radial Basis Functions, 14 mm/s for the Polynomial Fit and 14 mm/s for the Triangulation approach compared to their respective implementations without the preprocessing step. Given the present results, this novel approach can contribute to a more accurate and reliable CV estimation in a clinical setting and thus improve the success of radio-frequency ablation to treat cardiac arrhythmias.
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.
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.
Atrial arrhythmias like atrial fibrillation and atrial flutter are a major health challenge in developed countries. Radiofrequency ablation performed via intracardiac catheters is a curative therapy for these reentrant arrhythmias. However, the optimal location of ablation lesions is not straightforward to determine, particularly for complex activation patterns. Thus, a clinical need for tools to intuitively visualize complex activation patterns and to provide a platform to evaluate different ablation strategies in dry runs is apparent. Here, we present a virtual reality system that allows to interactively simulate atrial excitation propagation and place ablation lesions. Our software builds on the IMHOTEP framework for the Unity3D engine and implements a multithreaded model-view-controller design pattern. Excitation propagation is computed using a fast marching approach considering refractoriness. Interactive rewind and playback is supported through a combination of the flyweight pattern for simulation data with complete snapshots for key frames. The system was evaluated in a user study using the HTC ViveTM headset including two controllers. For high fidelity virtual reality interaction, a minimum frame rate of 60 per second is required. In a biatrial anatomical model comprising 36,059 nodes (Figure 1), even complex activation patterns with multiple wavefronts could be simulated and rendered down to 2x slow motion (1 sec activation sequence displayed during 2 sec wall time) on a desktop machine. Results of the user study suggest added value regarding the comprehension of arrhythmias and ablation options and very good intuitiveness of the user interface requiring almost no teach-in. The virtual reality tool is ready to be used for educational purposes and prepared to import personalized models supporting diagnosis and therapy planning for atrial arrhythmias in the future.
A computer system for determining Ventricular Far Field contribution in atrial electrograms of a patient. The system includes an interface module configured to receive a plurality of electrical signals generated by a plurality of sensors wherein the plurality of electrical signals relate to a plurality of locations in an atrium of the patient; a reference module configured to determine a reference signal reflecting electrical excitation of the patient's ventricles; and a data processing module. The data processing module is configured to select from the plurality of the received electrical signals such electrical signals which are recorded a number of conditions. The data processing module is further configured to determine a spatio-temporal distribution of the Ventricular Far Field inside the atrium by approximating the spatio-temporal distribution (VFFc) based on signal data of the selected signals by using an approximation model.
Student Theses (2)
N. Pilia. Characterization and reconstruction of ionic concentrations in the human ventricles analyzing the action potential and the surface ECG. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Bachelorarbeit. 2016
In the United States of America, 13.1% of the population suffer from chronic kidney dis- ease (CKD) . Patients suffering from end-stage CKD are often treated by haemodialysis where ionic concentrations of calcium, potassium and sodium get corrected. However, the frequency of deaths caused by cardiovascular diseases is up to 10% to 30% higher in patients undergoing dialysis than in the general population . The electrocardiogram (ECG) as a continuous, non-invasive monitoring tool could permit new insights into pos- sible links between heart diseases and changed ionic concentrations. In this work, methods for reconstruction of the ionic concentrations from the ECG are evaluated. In a first step, monodomain simulations with the ten Tusscher ventricular cell model  were performed on single cell, strand and whole heart level for different extracellular concentrations. The latter simulations were forward calculated and a standard 12-lead ECG was extracted. Extracellular sodium was varied between 120mmol/l and 150mmol/l, extracellular cal- cium between 0.6mmol/l and 3mmol/l, and extracellular potassium between 3mmol/l and 9 mmol/l as done in . These ranges are comparable to clinically observed ionic con- centrations. Sodium concentration changes showed minimal variations on all three simula- tion levels and were excluded from further investigations. Calcium and potassium changes yielded action potentials and ECGs clearly differing in amplitudes and morphologies. In a second step, 91 simulated ECG signals at different potassium and calcium concentrations - each including one beat - were used for reconstructing the ionic concentrations directly from the ECG. Features were extracted from the signals designed to describe changes caused by varied ionic concentrations. The inverse problem, i.e. coming back from the ECG features to the ionic concentrations was solved by regression. Two methods from literature  , linear regression, linear regression with regularisation (both with a linear and third order polynomial model), random forest regression and regression by artificial neural networks were implemented. Best results for potassium estimation were achieved by neural network regression yielding an estimation error of 0.007 mmol/l±0.2402 mmol/l (mean±standard deviation). Calcium estimation was best performed by third order poly- nomial regression achieving an estimation error of -0.0010 mmol/l±0.0511 mmol/l. Errors were calculated by 13-fold cross validation. Further investigations on the behaviour of the methods could be performed using simulated signals, which are generated with other models, and real measurements. Nevertheless, these first results seem to be very promis- ing: an adequate estimation of potassium and calcium concentrations could be shown to be possible.
N. A. Pilia. A robust method to detect and characterise the P wave in the electrocardiogram. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Bachelorarbeit. 2013