{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T11:04:26Z","timestamp":1790075066643,"version":"4.0.1"},"reference-count":50,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:00:00Z","timestamp":1789776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009620","name":"Science and Technology Program of Gansu Province","doi-asserted-by":"publisher","award":["26CXGE002"],"award-info":[{"award-number":["26CXGE002"]}],"id":[{"id":"10.13039\/501100009620","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Gansu Province College Industry Support Plan Project","award":["26CYZC-58"],"award-info":[{"award-number":["26CYZC-58"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wearable ECG increasingly records fewer than the standard 12 leads, so a model must be accurate, interpretable, and explicit about the information lost under lead reduction. I-GraphECG is a gray-box graph electrophysiology surrogate: an encoder maps a 12-lead median beat to a bounded vector of 47 equivalent electrophysiological descriptors, a constrained eight-node conduction-graph decoder reconstructs the signal, and disease prediction uses the descriptors rather than the waveform. On a clean PTB-XL four-class subset, median beats are reconstructed at median correlation 0.91, and macro-AUROC reaches \u22480.90, near the black-box references (0.920\u20130.924). Myocardial infarction is under-detected (recall \u2248 0.49), consistent with the ST-source\u2019s low observability, so the model must not be used as a stand-alone rule-out for infarction. Observability-based sensor selection makes explicit what each lead set can resolve: lead removal provably cannot lower any Cram\u00e9r\u2013Rao bound; under the data-derived noise models, every optimal three-lead set retains one of the precordial leads V2\u2013V5, and the conventional reduced set is never observability-optimal across seven noise models, though the exact montage is noise-model-dependent. Reconstruction and the observability analysis of the fixed model transfer zero-shot to US and Chinese cohorts; parameter-only disease prediction degrades externally, and infarction, untestable in those cohorts, remains internally demonstrated.<\/jats:p>","DOI":"10.3390\/s26185933","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:21:48Z","timestamp":1790072508000},"page":"5933","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["I-GraphECG: Observability-Based Lead Selection and Interpretable Disease Prediction from the 12-Lead ECG Using a Gray-Box Graph Electrophysiology Surrogate"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0264-6602","authenticated-orcid":false,"given":"Limin","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5449-5427","authenticated-orcid":false,"given":"Hongtao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Pengjian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5420-7985","authenticated-orcid":false,"given":"Weicheng","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-1848-129X","authenticated-orcid":false,"given":"Ningning","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"project-administration","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1038\/s41591-018-0268-3","article-title":"Cardiologist-level arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network","volume":"25","author":"Hannun","year":"2019","journal-title":"Nat. Med."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1038\/s41467-020-15432-4","article-title":"Automatic diagnosis of the 12-lead ECG using a deep neural network","volume":"11","author":"Ribeiro","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1109\/JBHI.2020.3022989","article-title":"Deep learning for ECG analysis: Benchmarks and insights from PTB-XL","volume":"25","author":"Strodthoff","year":"2021","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.pbiomolbio.2010.05.008","article-title":"Models of cardiac tissue electrophysiology: Progress, challenges and open questions","volume":"104","author":"Clayton","year":"2011","journal-title":"Prog. Biophys. Mol. Biol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Colli Franzone, P., Pavarino, L.F., and Scacchi, S. (2014). Mathematical Cardiac Electrophysiology, Springer.","DOI":"10.1007\/978-3-319-04801-7"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1038\/s41569-018-0104-y","article-title":"Computational models in cardiology","volume":"16","author":"Niederer","year":"2019","journal-title":"Nat. Rev. Cardiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102080","DOI":"10.1016\/j.media.2021.102080","article-title":"A framework for the generation of digital twins of cardiac electrophysiology from clinical 12-lead ECGs","volume":"71","author":"Gillette","year":"2021","journal-title":"Med. Image Anal."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Shamaiah, M., Banerjee, S., and Vikalo, H. (2010, January 15\u201317). Greedy sensor selection: Leveraging submodularity. Proceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA.","DOI":"10.1109\/CDC.2010.5717225"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"ooaf122","DOI":"10.1093\/jamiaopen\/ooaf122","article-title":"ECG-FM: An open electrocardiogram foundation model","volume":"8","author":"McKeen","year":"2025","journal-title":"JAMIA Open"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mansour Atwa, A.E., Atlam, E.S., Ahmed, A., Atwa, M.A., Abdelrahim, E.M., and Siam, A.I. (2025). Interpretable deep learning models for arrhythmia classification based on ECG signals using the PTB-XL dataset. Diagnostics, 15.","DOI":"10.3390\/diagnostics15151950"},{"key":"ref_11","unstructured":"Koh, P.W., Nguyen, T., Tang, Y.S., Mussmann, S., Pierson, E., Kim, B., and Liang, P. (2020, January 13\u201318). Concept bottleneck models. Proceedings of the 37th International Conference on Machine Learning (ICML), Virtual."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1093\/ehjdh\/ztac038","article-title":"Improving explainability of deep neural network-based electrocardiogram interpretation using variational auto-encoders","volume":"3","author":"Bos","year":"2022","journal-title":"Eur. Heart J.\u2014Digit. Health"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105617","DOI":"10.1016\/j.isci.2022.105617","article-title":"A unique cardiac electrocardiographic 3D model. Toward interpretable AI diagnosis","volume":"25","author":"Rueda","year":"2022","journal-title":"iScience"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sahli Costabal, F., Yang, Y., Perdikaris, P., Hurtado, D.E., and Kuhl, E. (2020). Physics-informed neural networks for cardiac activation mapping. Front. Phys., 8.","DOI":"10.3389\/fphy.2020.00042"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Herrero Martin, C., Oved, A., Chowdhury, R.A., Ullmann, E., Peters, N.S., Bharath, A.A., and Varela, M. (2022). EP-PINNs: Cardiac electrophysiology characterisation using physics-informed neural networks. Front. Cardiovasc. Med., 8.","DOI":"10.3389\/fcvm.2021.768419"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sohn, J., Yang, S., Lee, J., Ku, Y., and Kim, H.C. (2020). Reconstruction of 12-lead electrocardiogram from a three-lead patch-type device using a LSTM network. Sensors, 20.","DOI":"10.3390\/s20113278"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Grande-Fidalgo, A., Calpe, J., Red\u00f3n, M., Mill\u00e1n-Navarro, C., and Soria-Olivas, E. (2021). Lead reconstruction using artificial neural networks for ambulatory ECG acquisition. Sensors, 21.","DOI":"10.3390\/s21165542"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1038\/s41746-024-01193-7","article-title":"AI-enhanced reconstruction of the 12-lead electrocardiogram via 3-leads with accurate clinical assessment","volume":"7","author":"Mason","year":"2024","journal-title":"npj Digit. Med."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Nakanishi, R., Hirata, A., and Kubota, Y. (2026). Deep learning-based multi-lead ECG reconstruction from lead I with metadata integration and uncertainty estimation. Sensors, 26.","DOI":"10.3390\/s26010212"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20200258","DOI":"10.1098\/rsta.2020.0258","article-title":"Optimal ECG-lead selection increases generalizability of deep learning on ECG abnormality classification","volume":"379","author":"Lai","year":"2021","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/TBME.1978.326332","article-title":"Limited lead selection for estimation of body surface potential maps in electrocardiography","volume":"BME-25","author":"Lux","year":"1978","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/TITB.2007.896882","article-title":"Optimal electrocardiographic lead systems: Practical scenarios in smart clothing and wearable health systems","volume":"12","author":"Finlay","year":"2008","journal-title":"IEEE Trans. Inf. Technol. Biomed."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109264","DOI":"10.1016\/j.compbiomed.2024.109264","article-title":"Optimal electrode placements for localizing premature ventricular contractions using a single dipole","volume":"183","author":"Ondrusova","year":"2024","journal-title":"Comput. Biol. Med."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.jcp.2017.06.020","article-title":"Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model","volume":"346","author":"Neic","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_25","first-page":"640","article-title":"Reconstruction of three-dimensional biventricular activation based on the 12-lead electrocardiogram via patient-specific modelling","volume":"23","author":"Pezzuto","year":"2021","journal-title":"EP Eur."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"102143","DOI":"10.1016\/j.media.2021.102143","article-title":"Inference of ventricular activation properties from non-invasive electrocardiography","volume":"73","author":"Camps","year":"2021","journal-title":"Med. Image Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103641","DOI":"10.1016\/j.media.2025.103641","article-title":"Accurate and efficient cardiac digital twin from surface ECGs: Insights into identifiability of ventricular conduction system","volume":"105","author":"Grandits","year":"2025","journal-title":"Med. Image Anal."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Nishikimi, R., Shiraki, Y., Tsukada, S., and Kashino, K. (2026). Cardiac parameter estimation from electrocardiograms based on inversion of physical simulator behavior. PLoS Digit. Health, 5.","DOI":"10.1371\/journal.pdig.0001624"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1109\/TMI.2024.3367409","article-title":"Toward enabling cardiac digital twins of myocardial infarction using deep computational models for inverse inference","volume":"43","author":"Li","year":"2024","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1038\/s41597-020-0495-6","article-title":"PTB-XL, a large publicly available electrocardiography dataset","volume":"7","author":"Wagner","year":"2020","journal-title":"Sci. Data"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"e215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.3758\/s13428-020-01516-y","article-title":"NeuroKit2: A Python toolbox for neurophysiological signal processing","volume":"53","author":"Makowski","year":"2021","journal-title":"Behav. Res. Methods"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0960-0779(95)00089-5","article-title":"A simple two-variable model of cardiac excitation","volume":"7","author":"Aliev","year":"1996","journal-title":"Chaos Solitons Fractals"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0006-3495(61)86902-6","article-title":"Impulses and physiological states in theoretical models of nerve membrane","volume":"1","author":"FitzHugh","year":"1961","journal-title":"Biophys. J."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Macfarlane, P.W., van Oosterom, A., Pahlm, O., Kligfield, P., Janse, M., and Camm, J. (2010). Comprehensive Electrocardiology, Springer. [2nd ed.].","DOI":"10.1007\/978-1-84882-046-3"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1093\/oxfordjournals.eurheartj.a059647","article-title":"Reconstruction of the Frank vectorcardiogram from standard electrocardiographic leads: Diagnostic comparison of different methods","volume":"11","author":"Kors","year":"1990","journal-title":"Eur. Heart J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","article-title":"Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood","volume":"25","author":"Raue","year":"2009","journal-title":"Bioinformatics"},{"key":"ref_40","unstructured":"Roy, O., and Vetterli, M. (2007, January 3\u20137). The effective rank: A measure of effective dimensionality. Proceedings of the 15th European Signal Processing Conference (EUSIPCO), Pozna\u0144, Poland."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1080\/00273171.2020.1743631","article-title":"Effective dimensionality: A tutorial","volume":"56","year":"2021","journal-title":"Multivar. Behav. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1161\/01.CIR.0000145144.56673.59","article-title":"Practice standards for electrocardiographic monitoring in hospital settings: An American Heart Association scientific statement","volume":"110","author":"Drew","year":"2004","journal-title":"Circulation"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"e273","DOI":"10.1161\/CIR.0000000000000527","article-title":"Update to practice standards for electrocardiographic monitoring in hospital settings: A scientific statement from the American Heart Association","volume":"136","author":"Sandau","year":"2017","journal-title":"Circulation"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TSP.2008.2007095","article-title":"Sensor selection via convex optimization","volume":"57","author":"Joshi","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_45","first-page":"235","article-title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","volume":"9","author":"Krause","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01588971","article-title":"An analysis of approximations for maximizing submodular set functions\u2014I","volume":"14","author":"Nemhauser","year":"1978","journal-title":"Math. Program."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/TCNS.2015.2453711","article-title":"On submodularity and controllability in complex dynamical networks","volume":"3","author":"Summers","year":"2016","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"124003","DOI":"10.1088\/1361-6579\/abc960","article-title":"Classification of 12-lead ECGs: The PhysioNet\/Computing in Cardiology Challenge 2020","volume":"41","author":"Gu","year":"2020","journal-title":"Physiol. Meas."},{"key":"ref_49","first-page":"1368","article-title":"An open access database for evaluating the algorithms of electrocardiogram rhythm and morphology abnormality detection","volume":"8","author":"Liu","year":"2018","journal-title":"J. Med. Imaging Health Inform."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1038\/s43856-025-00814-w","article-title":"Evaluating the feasibility of 12-lead electrocardiogram reconstruction from limited leads using deep learning","volume":"5","author":"Presacan","year":"2025","journal-title":"Commun. Med."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5933\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:26:36Z","timestamp":1790072796000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5933"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,19]]},"references-count":50,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26185933"],"URL":"https:\/\/doi.org\/10.3390\/s26185933","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,19]]}}}