{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T06:23:13Z","timestamp":1791354193622,"version":"4.3.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:00:00Z","timestamp":1784160000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:00:00Z","timestamp":1784160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"European Union Horizon 2020 Research and Innovation Pro- gram SimCardioTest","award":["101016496"],"award-info":[{"award-number":["101016496"]}]},{"name":"French gov- ernment through the National Research Agency","award":["PEPR Digital Health ChroniCar- dio (22-PESN-0015), 3IA C\u00f4te d\u2019Azur, IA Cluster (ANR-19-3IA-0002 and ANR-23-IACL-0001) and RHU Talent (ANR-23-RHUS-0015)"],"award-info":[{"award-number":["PEPR Digital Health ChroniCar- dio (22-PESN-0015), 3IA C\u00f4te d\u2019Azur, IA Cluster (ANR-19-3IA-0002 and ANR-23-IACL-0001) and RHU Talent (ANR-23-RHUS-0015)"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biomech Model Mechanobiol"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s10237-026-02098-y","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T10:12:31Z","timestamp":1784196751000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Global sensitivity analysis through causal discovery for an electromechanical cardiac model"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1864-8190","authenticated-orcid":false,"given":"Safaa","family":"Al-Ali","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jairo","family":"Rodr\u00edguez-Padilla","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxime","family":"Sermesant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irene","family":"Balelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,16]]},"reference":[{"key":"2098_CR1","doi-asserted-by":"publisher","unstructured":"Al-Ali S, Llopis-Lorente J, Mora MT et al (2023) A causal discovery approach to streamline ionic currents selection to improve drug-induced tdp risk assessment. In: 2023 Computing in cardiology (CinC). pp 1\u20134. https:\/\/doi.org\/10.22489\/CinC.2023.009","DOI":"10.22489\/CinC.2023.009"},{"key":"2098_CR2","doi-asserted-by":"crossref","unstructured":"Al-Ali S, MT Mora, M Sermesant, B Tr\u00e9nor, I Balelli (2024) Assessing ionic current blockades and electromechanical biomarkers\u2019 interrelations through a novel multi-channel causal variational autoencoder, in: 2024 Computing in Cardiology Conference, vol. 51.","DOI":"10.22489\/CinC.2024.408"},{"key":"2098_CR3","doi-asserted-by":"crossref","unstructured":"Al-Ali S, Padilla JR, Sermesant M et al (2025) Cardiac electromechanical model sensitivity analysis using causal discovery. In: Chabiniok R, Zou Q, Hussain T et al (eds) Functional imaging and modeling of the heart. Springer Nature Switzerland, Cham, pp 343\u2013355","DOI":"10.1007\/978-3-031-94559-5_31"},{"issue":"2173","key":"2098_CR4","first-page":"20190381","volume":"378","author":"J Campos","year":"2020","unstructured":"Campos J, Sundnes J, Dos Santos R et al (2020) Uncertainty quantification and sensitivity analysis of left ventricular function during the full cardiac cycle. Philosophical Transactions Royal Soc A Math Phys Eng Sci 378(2173):20190381","journal-title":"Philosophical Transactions Royal Soc A Math Phys Eng Sci"},{"issue":"5","key":"2098_CR5","doi-asserted-by":"publisher","first-page":"1415","DOI":"10.1007\/s10237-019-01153-1","volume":"18","author":"JO Campos","year":"2019","unstructured":"Campos JO, Sundnes J, Dos Santos RW et al (2019) Effects of left ventricle wall thickness uncertainties on cardiac mechanics. Biomech Model Mechanobiol 18(5):1415\u20131427","journal-title":"Biomech Model Mechanobiol"},{"key":"2098_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.10.005","volume":"1044","author":"G Camps-Valls","year":"2023","unstructured":"Camps-Valls G, Gerhardus A, Ninad U et al (2023) Discovering causal relations and equations from data. Phys Rep 1044:1\u201368","journal-title":"Phys Rep"},{"issue":"1","key":"2098_CR7","doi-asserted-by":"publisher","DOI":"10.1136\/openhrt-2018-000933","volume":"6","author":"S Cazeau","year":"2019","unstructured":"Cazeau S, Toulemont M, Ritter P et al (2019) Statistical ranking of electromechanical dyssynchrony parameters for crt. Open heart 6(1):e000933","journal-title":"Open heart"},{"issue":"1783","key":"2098_CR8","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1098\/rsta.2001.0828","volume":"359","author":"KD Costa","year":"2001","unstructured":"Costa KD, Holmes JW, McCulloch AD (2001) Modelling cardiac mechanical properties in three dimensions. Philos Trans R Soc London Ser A 359(1783):1233\u20131250","journal-title":"Philos Trans R Soc London Ser A"},{"key":"2098_CR9","doi-asserted-by":"crossref","unstructured":"Desrues G, Feuerstein D, Legay T (2021) Personal-by-design: a 3d electromechanical model of the heart tailored for personalisation. International Conference on Functional Imaging and Modeling of the Heart. Springer, pp 447\u2013457","DOI":"10.1007\/978-3-030-78710-3_43"},{"issue":"9","key":"2098_CR10","doi-asserted-by":"publisher","first-page":"1755","DOI":"10.1016\/j.jcmg.2018.09.021","volume":"12","author":"F D\u2019Ascenzi","year":"2019","unstructured":"D\u2019Ascenzi F, Anselmi F, Piu P et al (2019) Cardiac magnetic resonance normal reference values of biventricular size and function in male athlete\u2019s heart. JACC Cardiovasc Imaging 12(9):1755\u20131765","journal-title":"JACC Cardiovasc Imaging"},{"issue":"1","key":"2098_CR11","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1136\/heart.84.1.106","volume":"84","author":"P Elliott","year":"2000","unstructured":"Elliott P (2000) Diagnosis and management of dilated cardiomyopathy. Heart 84(1):106\u2013106","journal-title":"Heart"},{"key":"2098_CR12","doi-asserted-by":"publisher","unstructured":"Faure F, Duriez C, Delingette H et\u00a0al (2012) SOFA: A Multi-Model Framework for Interactive Physical Simulation. In: Payan Y (ed) Soft tissue biomechanical modeling for computer assisted surgery, studies in mechanobiology, tissue engineering and biomaterials, vol\u00a011. Springer, p 283\u2013321, https:\/\/doi.org\/10.1007\/8415_2012_125, https:\/\/inria.hal.science\/hal-00681539","DOI":"10.1007\/8415_2012_125"},{"issue":"23","key":"2098_CR13","doi-asserted-by":"publisher","first-page":"3095","DOI":"10.1001\/jama.283.23.3095","volume":"283","author":"R Hambrecht","year":"2000","unstructured":"Hambrecht R, Gielen S, Linke A et al (2000) Effects of exercise training on left ventricular function and peripheral resistance in patients with chronic heart failure: a randomized trial. JAMA 283(23):3095\u20133101","journal-title":"JAMA"},{"issue":"1902","key":"2098_CR14","first-page":"3445","volume":"367","author":"GA Holzapfel","year":"2009","unstructured":"Holzapfel GA, Ogden RW (2009) Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philosophical Transactions Royal Soc A Mathematical Phys Eng Sci 367(1902):3445\u20133475","journal-title":"Philosophical Transactions Royal Soc A Mathematical Phys Eng Sci"},{"key":"2098_CR15","unstructured":"Hoyer P, Janzing D, Mooij JM (2008) Nonlinear causal discovery with additive noise models. Adv Neural Inf Process Syst 21:689\u2013696"},{"key":"2098_CR16","unstructured":"Huang B, Zhang K, Gong M (2019) Causal discovery and forecasting in nonstationary environments with state-space models. In: International conference on machine learning, Pmlr. pp 2901\u20132910"},{"issue":"1","key":"2098_CR17","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.stamet.2008.04.001","volume":"6","author":"M Jones","year":"2009","unstructured":"Jones M (2009) Kumaraswamy\u2019s distribution: a beta-type distribution with some tractability advantages. Statistical methodology 6(1):70\u201381","journal-title":"Statistical methodology"},{"key":"2098_CR18","volume-title":"Physiology of the heart","author":"AM Katz","year":"2010","unstructured":"Katz AM (2010) Physiology of the Heart. Lippincott Williams & Wilkins"},{"key":"2098_CR19","doi-asserted-by":"publisher","unstructured":"Konukoglu E, Relan J, Cilingir U et al (2011) Prog Biophys Mol Biol 107(1):134\u2013146. https:\/\/doi.org\/10.1016\/j.pbiomolbio.2011.07.002. https:\/\/inria.hal.science\/inria-00616198","DOI":"10.1016\/j.pbiomolbio.2011.07.002"},{"key":"2098_CR20","unstructured":"Kosaraju A, Goyal A, Grigorova Y (2017) Left ventricular ejection fraction. StatPearls Publishing, Treasure Island (FL)"},{"issue":"12","key":"2098_CR21","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0243229","volume":"15","author":"J Kotoku","year":"2020","unstructured":"Kotoku J, Oyama A, Kitazumi K et al (2020) Causal relations of health indices inferred statistically using the directlingam algorithm from big data of osaka prefecture health checkups. PLoS ONE 15(12):e0243229","journal-title":"PLoS ONE"},{"issue":"3","key":"2098_CR22","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1007\/s10237-022-01571-8","volume":"21","author":"A Lazarus","year":"2022","unstructured":"Lazarus A, Dalton D, Husmeier D et al (2022) Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics. Biomech Model Mechanobiol 21(3):953\u2013982","journal-title":"Biomech Model Mechanobiol"},{"key":"2098_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112762","volume":"361","author":"F Levrero-Florencio","year":"2020","unstructured":"Levrero-Florencio F, Margara F, Zacur E et al (2020) Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: effect of mechanical parameters on physiologically relevant biomarkers. Comput Methods Appl Mech Eng 361:112762","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2098_CR24","unstructured":"MacQueen J et\u00a0al (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Oakland, CA, USA, pp 281\u2013297"},{"issue":"7","key":"2098_CR25","doi-asserted-by":"publisher","first-page":"2117","DOI":"10.1007\/s11517-024-03048-5","volume":"62","author":"H Majdi","year":"2024","unstructured":"Majdi H, Azarnoosh M, Ghoshuni M et al (2024) Direct lingam and visibility graphs for analyzing brain connectivity in bci. Med Biological Eng Comput 62(7):2117\u20132132","journal-title":"Med Biological Eng Comput"},{"key":"2098_CR26","doi-asserted-by":"publisher","first-page":"1148324","DOI":"10.3389\/fcvm.2023.1148324","volume":"10","author":"K Manabe","year":"2023","unstructured":"Manabe K, D\u2019Souza AW, Washio T et al (2023) Sympathetic and hemodynamic responses to exercise in heart failure with preserved ejection fraction. Front Cardiovascular Med 10:1148324","journal-title":"Front Cardiovascular Med"},{"issue":"7","key":"2098_CR27","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1161\/CIRCRESAHA.117.311059","volume":"121","author":"AJ Marian","year":"2017","unstructured":"Marian AJ, Braunwald E (2017) Hypertrophic cardiomyopathy: genetics, pathogenesis, clinical manifestations, diagnosis, and therapy. Circ Res 121(7):749\u2013770","journal-title":"Circ Res"},{"issue":"2","key":"2098_CR28","doi-asserted-by":"publisher","DOI":"10.1002\/widm.1449","volume":"12","author":"AR Nogueira","year":"2022","unstructured":"Nogueira AR, Pugnana A, Ruggieri S et al (2022) Methods and tools for causal discovery and causal inference. Wiley Interdiscip Rev Data Mining Knowl Discov 12(2):e1449","journal-title":"Wiley Interdiscip Rev Data Mining Knowl Discov"},{"issue":"3","key":"2098_CR29","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1080\/02331888.2015.1060237","volume":"50","author":"C Nowzohour","year":"2016","unstructured":"Nowzohour C, B\u00fchlmann P (2016) Score-based causal learning in additive noise models. Statistics 50(3):471\u2013485","journal-title":"Statistics"},{"key":"2098_CR30","doi-asserted-by":"crossref","unstructured":"Oomen PJ, Phung T, Weinberg SH (2022) A rapid electromechanical model to predict reverse remodeling following cardiac resynchronization therapy. Biomech Model Mechanobiol 21(1):231\u2013247","DOI":"10.1007\/s10237-021-01532-7"},{"key":"2098_CR31","doi-asserted-by":"publisher","first-page":"721","DOI":"10.3389\/fphys.2019.00721","volume":"10","author":"P Pathmanathan","year":"2019","unstructured":"Pathmanathan P, Cordeiro JM, Gray RA (2019) Comprehensive uncertainty quantification and sensitivity analysis for cardiac action potential models. Front Physiol 10:721","journal-title":"Front Physiol"},{"key":"2098_CR32","doi-asserted-by":"crossref","unstructured":"Pearl J (2009) Causality. Cambridge University Press","DOI":"10.1017\/CBO9780511803161"},{"key":"2098_CR33","unstructured":"Pearl J, Mackenzie D (2018) The book of why: the new science of cause and effect. Basic books"},{"issue":"1","key":"2098_CR34","first-page":"2009","volume":"15","author":"J Peters","year":"2014","unstructured":"Peters J, Mooij JM, Janzing D et al (2014) Causal discovery with continuous additive noise models. J Mach Learning Res 15(1):2009\u20132053","journal-title":"J Mach Learning Res"},{"issue":"1","key":"2098_CR35","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1186\/s12968-017-0327-9","volume":"19","author":"SE Petersen","year":"2016","unstructured":"Petersen SE, Aung N, Sanghvi MM et al (2016) Reference ranges for cardiac structure and function using cardiovascular magnetic resonance (cmr) in caucasians from the uk biobank population cohort. J Cardiovasc Magn Reson 19(1):18","journal-title":"J Cardiovasc Magn Reson"},{"key":"2098_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2023.106696","volume":"156","author":"A Petras","year":"2023","unstructured":"Petras A, Gsell MA, Augustin CM et al (2023) Mechanoelectric effects in healthy cardiac function and under left bundle branch block pathology. Comput Biol Med 156:106696","journal-title":"Comput Biol Med"},{"key":"2098_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.envsoft.2015.01.004","volume":"67","author":"F Pianosi","year":"2015","unstructured":"Pianosi F, Wagener T (2015) A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. Environ Modelling Softw 67:1\u201311","journal-title":"Environ Modelling Softw"},{"issue":"6","key":"2098_CR38","doi-asserted-by":"publisher","first-page":"H936","DOI":"10.1152\/ajpheart.00050.2022","volume":"322","author":"J Rodr\u00edguez-Padilla","year":"2022","unstructured":"Rodr\u00edguez-Padilla J, Petras A, Magat J et al (2022) Impact of intraventricular septal fiber orientation on cardiac electromechanical function. Am J Physiol-Heart Circulatory Physiol 322(6):H936\u2013H952","journal-title":"Am J Physiol-Heart Circulatory Physiol"},{"key":"2098_CR39","unstructured":"Sadeghi Z, Matwin S (2024) A review of global sensitivity analysis methods and a comparative case study on digit classification. arXiv preprint arXiv:2406.16975"},{"issue":"3","key":"2098_CR40","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1111\/0272-4332.00040","volume":"22","author":"A Saltelli","year":"2002","unstructured":"Saltelli A (2002) Sensitivity analysis for importance assessment. Risk Anal 22(3):579\u2013590","journal-title":"Risk Anal"},{"key":"2098_CR41","unstructured":"Saltelli A, Tarantola S, Campolongo F (2004) Sensitivity analysis in practice: a guide to assessing scientific models, vol 1. Wiley Online Library"},{"key":"2098_CR42","doi-asserted-by":"publisher","unstructured":"Saltelli A, Annoni P, Azzini I et\u00a0al (2010) Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index. Computer Physics Communications 181(2):259\u2013270. https:\/\/doi.org\/10.1016\/j.cpc.2009.09.018, https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0010465509003087","DOI":"10.1016\/j.cpc.2009.09.018"},{"key":"2098_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2021.104674","volume":"136","author":"M Salvador","year":"2021","unstructured":"Salvador M, Fedele M, Africa PC et al (2021) Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia. Comput Biol Med 136:104674","journal-title":"Comput Biol Med"},{"issue":"8","key":"2098_CR44","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.220638","volume":"9","author":"P Sanchez","year":"2022","unstructured":"Sanchez P, Voisey JP, Xia T et al (2022) Causal machine learning for healthcare and precision medicine. Royal Soc Open Sci 9(8):220638","journal-title":"Royal Soc Open Sci"},{"issue":"1","key":"2098_CR45","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.media.2011.07.003","volume":"16","author":"M Sermesant","year":"2012","unstructured":"Sermesant M, Chabiniok R, Chinchapatnam P et al (2012) Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in crt: a preliminary clinical validation. Med Image Anal 16(1):201\u2013215","journal-title":"Med Image Anal"},{"key":"2098_CR46","unstructured":"Shimizu S, Hoyer PO, Hyv\u00e4rinen A (2006) A linear non-gaussian acyclic model for causal discovery. J Mach Learn Res 7(10):2003\u20132030"},{"key":"2098_CR47","first-page":"1225","volume":"12","author":"S Shimizu","year":"2011","unstructured":"Shimizu S, Inazumi T, Sogawa Y (2011) Directlingam: a direct method for learning a linear non-gaussian structural equation model. Journal of Machine Learning Research-JMLR 12:1225\u20131248","journal-title":"Journal of Machine Learning Research-JMLR"},{"key":"2098_CR48","doi-asserted-by":"publisher","unstructured":"Sobol\u2019 I (2001) Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Math Comput Simul 55(1):271\u2013280. https:\/\/doi.org\/10.1016\/S0378-4754(00)00270-6. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0378475400002706, the Second IMACS Seminar on Monte Carlo Methods","DOI":"10.1016\/S0378-4754(00)00270-6"},{"issue":"1","key":"2098_CR49","doi-asserted-by":"publisher","first-page":"672","DOI":"10.5114\/pjr.2021.112310","volume":"86","author":"M Stachera","year":"2021","unstructured":"Stachera M, Przyby\u0142o P, Sznajder K et al (2021) Cardiac magnetic resonance in the assessment of hypertrophic cardiomyopathy phenotypes and stages-pictorial review. Pol J Radiol 86(1):672\u2013684","journal-title":"Pol J Radiol"},{"key":"2098_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.artmed.2022.102310","volume":"128","author":"T Uchida","year":"2022","unstructured":"Uchida T, Fujiwara K, Nishioji K et al (2022) Medical checkup data analysis method based on lingam and its application to nonalcoholic fatty liver disease. Artif Intell Med 128:102310","journal-title":"Artif Intell Med"}],"container-title":["Biomechanics and Modeling in Mechanobiology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-026-02098-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10237-026-02098-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-026-02098-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T16:30:42Z","timestamp":1788193842000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10237-026-02098-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,16]]},"references-count":50,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["2098"],"URL":"https:\/\/doi.org\/10.1007\/s10237-026-02098-y","relation":{},"ISSN":["1617-7959","1617-7940"],"issn-type":[{"value":"1617-7959","type":"print"},{"value":"1617-7940","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,16]]},"assertion":[{"value":"30 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"83"}}