{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:41:01Z","timestamp":1777902061727,"version":"3.51.4"},"reference-count":58,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.<\/jats:p>","DOI":"10.3390\/s21134275","type":"journal-article","created":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T22:10:59Z","timestamp":1624399859000},"page":"4275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["ECG Localization Method Based on Volume Conductor Model and Kalman Filtering"],"prefix":"10.3390","volume":"21","author":[{"given":"Yuki","family":"Nakano","sequence":"first","affiliation":[{"name":"Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6571-9807","authenticated-orcid":false,"given":"Essam A.","family":"Rashed","sequence":"additional","affiliation":[{"name":"Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"},{"name":"Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia 41522, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tatsuhito","family":"Nakane","sequence":"additional","affiliation":[{"name":"Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilkka","family":"Laakso","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8336-1140","authenticated-orcid":false,"given":"Akimasa","family":"Hirata","sequence":"additional","affiliation":[{"name":"Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"},{"name":"Center of Biomedical Physics and Information Technology, Nagoya Institute of Technology, Nagoya 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Malmivuo, J., and Plonsey, R. (1995). Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780195058239.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105740","DOI":"10.1016\/j.cmpb.2020.105740","article-title":"Accurate deep neural network model to detect cardiac arrhythmia on more than 10,000 individual subject ECG records","volume":"197","author":"Yildirim","year":"2020","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Le, T.Q., Chandra, V., Afrin, K., Srivatsa, S., and Bukkapatnam, S. (2020). A Dynamic Systems Approach for Detecting and Localizing of Infarct-Related Artery in Acute Myocardial Infarction Using Compressed Paper-Based Electrocardiogram (ECG). Sensors, 20.","DOI":"10.3390\/s20143975"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.cmpb.2015.12.024","article-title":"Arrhythmia recognition and classification using combined linear and nonlinear features of ECG signals","volume":"127","author":"Elhaj","year":"2016","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Fu, L., Lu, B., Nie, B., Peng, Z., Liu, H., and Pi, X. (2020). Hybrid Network with Attention Mechanism for Detection and Location of Myocardial Infarction Based on 12-Lead Electrocardiogram Signals. Sensors, 20.","DOI":"10.3390\/s20041020"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/10.923784","article-title":"Localization of the site of origin of cardiac activation by means of a heart-model-based electrocardiographic imaging approach","volume":"48","author":"Li","year":"2001","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1007\/s10439-009-9873-0","article-title":"Mathematical modeling of electrocardiograms: A numerical study","volume":"38","author":"Boulakia","year":"2010","journal-title":"Ann. Biomed. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1109\/TBME.2003.817637","article-title":"Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model","volume":"50","author":"He","year":"2003","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4063","DOI":"10.1088\/0031-9155\/47\/22\/310","article-title":"Noninvasive three-dimensional activation time imaging of ventricular excitation by means of a heart-excitation model","volume":"47","author":"He","year":"2002","journal-title":"Phys. Med. Biol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/j.jacc.2007.01.024","article-title":"Recommendations for the standardization and interpretation of the electrocardiogram: Part I: The electrocardiogram and its technology. A scientific statement from the American Heart Association Electrocardiography and Arrhythmias Committee, Council on Clinical Cardiology; the American College of Cardiology Foundation; and the Heart Rhythm Society","volume":"49","author":"Kligfield","year":"2007","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0022-0736(80)80040-9","article-title":"The effect of modified limb electrode positions on electrocardiographic wave amplitudes","volume":"13","author":"Rautaharju","year":"1980","journal-title":"J. Electrocardiol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2744","DOI":"10.1002\/cnm.2744","article-title":"Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions","volume":"32","author":"Schenone","year":"2016","journal-title":"Int. J. Numer. Methods Biomed. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1111\/j.1476-5381.2012.02200.x","article-title":"Computational assessment of drug-induced effects on the electrocardiogram: From ion channel to body surface potentials","volume":"168","author":"Zemzemi","year":"2013","journal-title":"Br. J. Pharmacol."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Houari, K.E., Kachenoura, A., Albera, L., Bensaid, S., Karfoul, A., Boichon-Grivot, C., Rochette, M., and Hern\u00e1ndez, A. (2017, January 10\u201313). A fast model for solving the ECG forward problem based on an evolutionary algorithm. Proceedings of the IEEE 7th Int\u2019l Workshop Computational Advances in Multi-Sensor Adaptive Processing, Curacao.","DOI":"10.1109\/CAMSAP.2017.8313083"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/10.623049","article-title":"New finite difference formulations for general inhomogeneous anisotropic bioelectric problems","volume":"44","author":"Saleheen","year":"1997","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1012909511833","article-title":"The validation of the finite difference method and reciprocity for solving the inverse problem in EEG dipole source analysis","volume":"14","author":"Vanrumste","year":"2001","journal-title":"Brain Topogr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"123463","DOI":"10.1109\/ACCESS.2019.2938409","article-title":"Forward Electrocardiogram Modeling by Small Dipoles Based on Whole-Body Electric Field Analysis","volume":"7","author":"Nakane","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.cmpb.2004.10.005","article-title":"Lead field computation for the electrocardiographic inverse problem - Finite elements versus boundary elements","volume":"77","author":"Seger","year":"2005","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1109\/TMI.2006.882140","article-title":"Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density","volume":"25","author":"Liu","year":"2006","journal-title":"IEEE Trans. Med. Imaging."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s11517-014-1176-4","article-title":"Binary optimization for source localization in the inverse problem of ECG","volume":"52","author":"Potyagaylo","year":"2014","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/CIC.2005.1588165","article-title":"The use of the simulation results as a priori information to solve the inverse problem of electrocardiography for a patient","volume":"32","author":"Farina","year":"2005","journal-title":"Comput. Cardiol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/10.142641","article-title":"Magnetic Source Images Determined by a Lead-Field Analysis: The Unique Minimum-Norm Least-Squares Estimation","volume":"39","author":"Wang","year":"1992","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF02512477","article-title":"Minimum-norm estimation in a boundary-element torso model","volume":"32","author":"Nenonen","year":"1994","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1118\/1.596568","article-title":"New quantitative and qualitative approaches to the inverse problem of electrocardiology: Their theoretical relationship and experimental consistency","volume":"17","author":"Greensite","year":"1990","journal-title":"Med. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1109\/TBME.2013.2253101","article-title":"Matching Pursuit and Source Deflation for Sparse EEG\/MEG Dipole Moment Estimation","volume":"60","author":"Wu","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1088\/0967-3334\/35\/4\/623","article-title":"Comparison of minimum-norm estimation and beamforming in electrocardiography with acute ischemia","volume":"35","author":"Konttila","year":"2014","journal-title":"Physiol. Meas."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1109\/TBME.2002.803519","article-title":"Noninvasive myocardial activation time imaging: A novel inverse algorithm applied to clinical ECG mapping data","volume":"49","author":"Modre","year":"2002","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1109\/TBME.2014.2358618","article-title":"Noninvasive imaging of 3-dimensional myocardial infarction from the inverse solution of equivalent current density in pathological hearts","volume":"62","author":"Zhou","year":"2015","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1109\/TSP.2005.849172","article-title":"Sparse solutions to linear inverse problems with multiple measurement vectors","volume":"53","author":"Cotter","year":"2005","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/TBME.2006.886640","article-title":"Lp norm iterative sparse solution for EEG source localization","volume":"54","author":"Xu","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1587\/transcom.E96.B.685","article-title":"A User\u2019s Guide to Compressed Sensing for Communications Systems","volume":"E96-B","author":"Hayashi","year":"2013","journal-title":"IEICE Trans. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.jelectrocard.2011.01.001","article-title":"Diagnostic utility of the spatial versus individual planar QRS-T angles in cardiac disease detection","volume":"44","author":"Brown","year":"2011","journal-title":"J. Electrocardio."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0031-9155\/49\/1\/001","article-title":"Development of realistic high-resolution whole-body voxel models of Japanese adult males and females of average height and weight, and application of models to radio-frequency electromagnetic-field dosimetry","volume":"49","author":"Nagaoka","year":"2004","journal-title":"Phys. Med. Biol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1088\/0031-9155\/41\/11\/003","article-title":"The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues","volume":"41","author":"Gabriel","year":"1996","journal-title":"Phys. Med. Biol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1093\/rpd\/ncs064","article-title":"The relationship between anatomically correct electric and magnetic field dosimetry and published electric and magnetic field exposure limits","volume":"152","author":"Kavet","year":"2012","journal-title":"Radiat. Prot. Dosimetry"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1568","DOI":"10.1109\/TBME.2010.2046485","article-title":"Ranking the influence of tissue conductivities on forward-calculated ecgs","volume":"57","author":"Keller","year":"2010","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4479","DOI":"10.1088\/0031-9155\/61\/12\/4479","article-title":"Why intra-epidermal electrical stimulation achieves stimulation of small fibres selectively: A simulation study","volume":"61","author":"Motogi","year":"2016","journal-title":"Phys. Med. Biol."},{"key":"ref_38","unstructured":"Klabunde, R.E. (2012). Cardiovascular Physiology Concepts, Lippincott Williams & Wilkins\/Wolters Kluwer. [2nd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/MCOM.2012.6122530","article-title":"A wireless wearable ECG sensor for long-term applications","volume":"50","author":"Nemati","year":"2012","journal-title":"IEEE Commun. Mag."},{"key":"ref_40","first-page":"72","article-title":"Analytic validation of a three-dimensional scalar-potential finite-difference code for low-frequency magnetic induction","volume":"11","author":"Dawson","year":"1996","journal-title":"J. Appl. Comput. Electromagn. Soc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1088\/0031-9155\/43\/2\/001","article-title":"Induced current densities from low-frequency magnetic fields in a 2 mm resolution, anatomically realistic model of the body","volume":"43","author":"Dimbylow","year":"1998","journal-title":"Phys. Med. Biol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"N241","DOI":"10.1088\/0031-9155\/58\/17\/N241","article-title":"Confirmation of quasi-static approximation in SAR evaluation for a wireless power transfer system","volume":"58","author":"Hirata","year":"2013","journal-title":"Phys. Med. Biol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"7753","DOI":"10.1088\/0031-9155\/57\/23\/7753","article-title":"Fast multigrid-based computation of the induced electric field for transcranial magnetic stimulation","volume":"57","author":"Laakso","year":"2012","journal-title":"Phys. Med. Biol."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ghimire, S., Sapp, J.L., Horacek, M., and Wang, L. (2017, January 11\u201313). A variational approach to sparse model error estimation in cardiac electrophysiological imaging. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Quebec City, QC, Canada.","DOI":"10.1007\/978-3-319-66185-8_84"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/TMI.2018.2866951","article-title":"Noninvasive activation imaging of ventricular arrhythmias by spatial gradient sparse in frequency domain\u2014application to mapping reentrant ventricular tachycardia","volume":"38","author":"Yang","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1109\/TMI.2015.2429134","article-title":"Temporal sparse promoting three dimensional imaging of cardiac activation","volume":"34","author":"Yu","year":"2015","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Harville, D.A. (1997). Linear Spaces: Row and Column Spaces. Matrix Algebra From a Statistician\u2019s Perspective, Springer.","DOI":"10.1007\/b98818"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"H243","DOI":"10.1152\/ajpheart.01125.2003","article-title":"Total heart volume variation throughout the cardiac cycle in humans","volume":"287","author":"Carlsson","year":"2004","journal-title":"Am. J. Physiol. Circ. Physiol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s11265-009-0447-z","article-title":"Gaussian noise filtering from ECG by Wiener filter and ensemble empirical mode decomposition","volume":"64","author":"Chang","year":"2011","journal-title":"J. Signal. Process. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"4902","DOI":"10.1118\/1.3480985","article-title":"4D XCAT phantom for multimodality imaging research","volume":"37","author":"Segar","year":"2010","journal-title":"Med. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1109\/TMI.2017.2707413","article-title":"Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality","volume":"37","author":"Rodrigo","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1109\/TMI.2002.804426","article-title":"Automatic construction of multiple-object three-dimensional statistical shape models: Application to cardiac modeling","volume":"21","author":"Frangi","year":"2002","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.jelectrocard.2018.02.013","article-title":"Geometrical constraint of sources in noninvasive localization of premature ventricular contractions","volume":"51","author":"Svehlikova","year":"2018","journal-title":"J. Electrocardiol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2576","DOI":"10.1109\/TBME.2016.2561973","article-title":"Influence of Modeling Errors on the Initial Estimate for Nonlinear Myocardial Activation Times Imaging Calculated with Fastest Route Algorithm","volume":"63","author":"Potyagaylo","year":"2016","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.jneumeth.2015.08.015","article-title":"EEG source localization: Sensor density and head surface coverage","volume":"256","author":"Song","year":"2015","journal-title":"J. Neurosci. Methods"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"789","DOI":"10.3389\/fnins.2021.695668","article-title":"High-resolution EEG source localization in segmentation-free head models based on finite-difference method and matching pursuit algorithm","volume":"15","author":"Moridera","year":"2021","journal-title":"Front. Neurosci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1080\/00405000.2018.1548079","article-title":"Customized 3D digital human model rebuilding by orthographic images-based modelling method through open-source software","volume":"110","author":"Gu","year":"2019","journal-title":"J. Text. Inst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1778765.1778863","article-title":"Parametric Reshaping of Human Bodies in Images","volume":"29","author":"Zhou","year":"2010","journal-title":"ACM. Trans."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4275\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:21:10Z","timestamp":1760163670000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,22]]},"references-count":58,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21134275"],"URL":"https:\/\/doi.org\/10.3390\/s21134275","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,22]]}}}