{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T03:13:50Z","timestamp":1790392430555,"version":"4.1.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T00:00:00Z","timestamp":1774569600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T00:00:00Z","timestamp":1774915200000},"content-version":"vor","delay-in-days":4,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"Ministry of University and Research","award":["CUP B13C23005640006"],"award-info":[{"award-number":["CUP B13C23005640006"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-026-46006-x","type":"journal-article","created":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:05:40Z","timestamp":1774591540000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Towards a more reliable assessment of aortic diameters using a Bayesian Z-score"],"prefix":"10.1038","volume":"16","author":[{"given":"Luca","family":"Bindini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laurence","family":"Campens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jesse","family":"Davis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Mui\u00f1o-Mosquera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon","family":"D\u2019hulst","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julie","family":"De Backer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Nistri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paolo","family":"Frasconi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,27]]},"reference":[{"key":"46006_CR1","doi-asserted-by":"publisher","first-page":"1209","DOI":"10.1016\/j.jacc.2016.06.025","volume":"68","author":"JB Kim","year":"2016","unstructured":"Kim, J. B. et al. Risk of aortic dissection in the moderately dilated ascending aorta. Journal of the American College of Cardiology 68, 1209\u20131219 (2016).","journal-title":"Journal of the American College of Cardiology"},{"key":"46006_CR2","doi-asserted-by":"publisher","first-page":"220","DOI":"10.3390\/diagnostics11020220","volume":"11","author":"P Frasconi","year":"2021","unstructured":"Frasconi, P. et al. Two-Dimensional Aortic Size Normalcy: A Novelty Detection Approach. Diagnostics 11, 220. https:\/\/doi.org\/10.3390\/diagnostics11020220 (2021).","journal-title":"Diagnostics"},{"key":"46006_CR3","doi-asserted-by":"publisher","first-page":"914","DOI":"10.1016\/j.amjcard.2014.06.024","volume":"114","author":"L Campens","year":"2014","unstructured":"Campens, L. et al. Reference values for echocardiographic assessment of the diameter of the aortic root and ascending aorta spanning all age categories. The American Journal of Cardiology 114, 914\u2013920. https:\/\/doi.org\/10.1016\/j.amjcard.2014.06.024 (2014).","journal-title":"The American Journal of Cardiology"},{"key":"46006_CR4","unstructured":"Bindini, L., Perini, L., Nistri, S., Davis, J. & Frasconi, P. Dealing with uncertainty in contextual anomaly detection. Transactions on Machine Learning Research (2026)."},{"key":"46006_CR5","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.strusafe.2008.06.020","volume":"31","author":"AD Kiureghian","year":"2009","unstructured":"Kiureghian, A. D. & Ditlevsen, O. Aleatory or epistemic? Does it matter?. Structural Safety 31, 105\u2013112. https:\/\/doi.org\/10.1016\/j.strusafe.2008.06.020 (2009).","journal-title":"Structural Safety"},{"key":"46006_CR6","unstructured":"Kendall, A. & Gal, Y. What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? In Advances in Neural Information Processing Systems, vol.\u00a030 (2017)."},{"key":"46006_CR7","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/s10994-021-05946-3","volume":"110","author":"E H\u00fcllermeier","year":"2021","unstructured":"H\u00fcllermeier, E. & Waegeman, W. Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods. Machine Learning 110, 457\u2013506. https:\/\/doi.org\/10.1007\/s10994-021-05946-3 (2021) (1910.09457.).","journal-title":"Machine Learning"},{"key":"46006_CR8","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1016\/j.neucom.2021.10.119","volume":"489","author":"X Zhou","year":"2022","unstructured":"Zhou, X., Liu, H., Pourpanah, F., Zeng, T. & Wang, X. A survey on epistemic (model) uncertainty in supervised learning: Recent advances and applications. Neurocomputing 489, 449\u2013465. https:\/\/doi.org\/10.1016\/j.neucom.2021.10.119 (2022).","journal-title":"Neurocomputing"},{"issue":"507\u2013512","key":"46006_CR9","first-page":"00846","volume":"64","author":"MJ Roman","year":"1989","unstructured":"Roman, M. J., Devereux, R. B., Kramer-Fox, R. & O\u2019Loughlin, J. Two-dimensional echocardiographic aortic root dimensions in normal children and adults. The American journal of cardiology 64(507\u2013512), 00846 (1989).","journal-title":"The American journal of cardiology"},{"key":"46006_CR10","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1016\/j.amjcard.2012.05.063","volume":"110","author":"RB Devereux","year":"2012","unstructured":"Devereux, R. B. et al. Normal limits in relation to age, body size and gender of two-dimensional echocardiographic aortic root dimensions in persons $$\\ge$$15 years of age. The American Journal of Cardiology 110, 1189\u20131194. https:\/\/doi.org\/10.1016\/j.amjcard.2012.05.063 (2012).","journal-title":"The American Journal of Cardiology"},{"key":"46006_CR11","doi-asserted-by":"publisher","DOI":"10.1161\/CIRCIMAGING.117.006979","volume":"10","author":"L Lopez","year":"2017","unstructured":"Lopez, L. et al. Relationship of echocardiographic z scores adjusted for body surface area to age, sex, race, and ethnicity. Circulation: Cardiovascular Imaging 10, e006979. https:\/\/doi.org\/10.1161\/CIRCIMAGING.117.006979 (2017).","journal-title":"Circulation: Cardiovascular Imaging"},{"key":"46006_CR12","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jjcc.2016.03.010","volume":"69","author":"M Cantinotti","year":"2017","unstructured":"Cantinotti, M. et al. Nomograms for two-dimensional echocardiography derived valvular and arterial dimensions in caucasian children. J. Cardiol. 69, 208\u2013215. https:\/\/doi.org\/10.1016\/j.jjcc.2016.03.010 (2017).","journal-title":"J. Cardiol."},{"key":"46006_CR13","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0208362","volume":"13","author":"A Martinez-Millana","year":"2018","unstructured":"Martinez-Millana, A. et al. Optimisation of children z-score calculation based on new statistical techniques. PLoS One 13, e0208362. https:\/\/doi.org\/10.1371\/journal.pone.0208362 (2018).","journal-title":"PLoS One"},{"key":"46006_CR14","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.echo.2021.09.011","volume":"35","author":"HN Patel","year":"2022","unstructured":"Patel, H. N. et al. Normal values of aortic root size according to age, sex, and race: Results of the World Alliance of Societies of Echocardiography study. J. Am. Soc. Echocardiogr. 35, 267\u2013274. https:\/\/doi.org\/10.1016\/j.echo.2021.09.011 (2022).","journal-title":"J. Am. Soc. Echocardiogr."},{"key":"46006_CR15","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.echo.2012.09.021","volume":"26","author":"W Mawad","year":"2013","unstructured":"Mawad, W., Drolet, C., Dahdah, N. & Dallaire, F. A review and critique of the statistical methods used to generate reference values in pediatric echocardiography. J. Am. Soc. Echocardiogr. 26, 29\u201337. https:\/\/doi.org\/10.1016\/j.echo.2012.09.021 (2013).","journal-title":"J. Am. Soc. Echocardiogr."},{"key":"46006_CR16","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.echo.2012.11.005","volume":"26","author":"SD Colan","year":"2013","unstructured":"Colan, S. D. The why and how of z scores. J. Am. Soc. Echocardiogr. 26, 38\u201340. https:\/\/doi.org\/10.1016\/j.echo.2012.11.005 (2013).","journal-title":"J. Am. Soc. Echocardiogr."},{"key":"46006_CR17","doi-asserted-by":"publisher","first-page":"124","DOI":"10.12945\/j.aorta.2016.16.014","volume":"04","author":"A Curtis","year":"2016","unstructured":"Curtis, A., Smith, T., Ziganshin, B. & Elefteriades, J. The mystery of the z-score. AORTA 04, 124\u2013130. https:\/\/doi.org\/10.12945\/j.aorta.2016.16.014 (2016).","journal-title":"AORTA"},{"key":"46006_CR18","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1017\/S1047951100005217","volume":"9","author":"PEF Daubeney","year":"1999","unstructured":"Daubeney, P. E. F. et al. Relationship of the dimension of cardiac structures to body size: An echocardiographic study in normal infants and children. Cardiol. Young 9, 402\u2013410. https:\/\/doi.org\/10.1017\/S1047951100005217 (1999).","journal-title":"Cardiol. Young"},{"issue":"2","key":"46006_CR19","doi-asserted-by":"publisher","first-page":"179","DOI":"10.4103\/0974-2069.99622","volume":"5","author":"H Chubb","year":"2012","unstructured":"Chubb, H. & Simpson, J. M. The use of z-scores in paediatric cardiology. Ann. Pediatr. Cardiol. 5179. https:\/\/doi.org\/10.4103\/0974-2069.99622 (2012).","journal-title":"Ann. Pediatr. Cardiol."},{"key":"46006_CR20","doi-asserted-by":"publisher","unstructured":"Sluysmans, T. & Colan, S. D. Structural measurements and adjustments for growth. In Echocardiography in Pediatric and Congenital Heart Disease, chap. 5, 61\u201372. https:\/\/doi.org\/10.1002\/9781118742440.ch5 (John Wiley & Sons Ltd (2016).","DOI":"10.1002\/9781118742440.ch5"},{"key":"46006_CR21","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1016\/j.amjcard.2009.11.040","volume":"105","author":"M Gautier","year":"2010","unstructured":"Gautier, M. et al. Nomograms for aortic root diameters in children using two-dimensional echocardiography. Am. J. Cardiol. 105, 888\u2013894. https:\/\/doi.org\/10.1016\/j.amjcard.2009.11.040 (2010).","journal-title":"Am. J. Cardiol."},{"key":"46006_CR22","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1111\/j.2517-6161.1964.tb00553.x","volume":"26","author":"GEP Box","year":"1964","unstructured":"Box, G. E. P. & Cox, D. R. An analysis of transformations. J. R. Stat. Soc. Ser. B Stat. Methodol. 26, 211\u2013243. https:\/\/doi.org\/10.1111\/j.2517-6161.1964.tb00553.x (1964).","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"46006_CR23","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1001\/archinte.1916.00080130010002","volume":"XVII","author":"D Du Bois","year":"1916","unstructured":"Du Bois, D. & Du Bois, E. F. A Formula to Estimate the Approximate Surface Area If Height and Weight Be Known. Archives of Internal Medicine XVII, 863\u2013871. https:\/\/doi.org\/10.1001\/archinte.1916.00080130010002 (1916).","journal-title":"Archives of Internal Medicine"},{"key":"46006_CR24","first-page":"255","volume":"44","author":"H Goldstein","year":"1972","unstructured":"Goldstein, H. The construction of standards for measurements subject to growth. Hum. Biol. 44, 255\u2013261 (1972).","journal-title":"Hum. Biol."},{"key":"46006_CR25","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1002\/sim.4780121003","volume":"12","author":"DG Altman","year":"1993","unstructured":"Altman, D. G. Construction of age-related reference centiles using absolute residuals. Stat. Med. 12, 917\u2013924. https:\/\/doi.org\/10.1002\/sim.4780121003 (1993).","journal-title":"Stat. Med."},{"key":"46006_CR26","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.1136\/heartjnl-2012-301773","volume":"98","author":"S Fernandes","year":"2012","unstructured":"Fernandes, S. et al. Bicuspid aortic valve and associated aortic dilation in the young. Heart 98, 1014\u20131019. https:\/\/doi.org\/10.1136\/heartjnl-2012-301773 (2012).","journal-title":"Heart"},{"key":"46006_CR27","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.ins.2013.07.030","volume":"255","author":"R Senge","year":"2014","unstructured":"Senge, R. et al. Reliable classification: Learning classifiers that distinguish aleatoric and epistemic uncertainty. Inf. Sci. 255, 16\u201329. https:\/\/doi.org\/10.1016\/j.ins.2013.07.030 (2014).","journal-title":"Inf. Sci."},{"key":"46006_CR28","doi-asserted-by":"publisher","DOI":"10.1186\/s12968-020-00688-y","volume":"23","author":"F Ricci","year":"2021","unstructured":"Ricci, F. et al. Cardiovascular magnetic resonance reference values of mitral and tricuspid annular dimensions: The uk biobank cohort. Journal of Cardiovascular Magnetic Resonance 23, 5. https:\/\/doi.org\/10.1186\/s12968-020-00688-y (2021).","journal-title":"Journal of Cardiovascular Magnetic Resonance"},{"key":"46006_CR29","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.echo.2018.10.006","volume":"32","author":"FM Asch","year":"2019","unstructured":"Asch, F. M. et al. Need for a global definition of normative echo values\u2013rationale and design of the World Alliance of Societies of Echocardiography normal values study (wase). J. Am. Soc. Echocardiogr. 32, 157-162.e2. https:\/\/doi.org\/10.1016\/j.echo.2018.10.006 (2019).","journal-title":"J. Am. Soc. Echocardiogr."},{"key":"46006_CR30","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1093\/ehjci\/jet008","volume":"14","author":"P Lancellotti","year":"2013","unstructured":"Lancellotti, P. et al. Normal reference ranges for echocardiography: Rationale, study design, and methodology (norre study). European Heart Journal - Cardiovascular Imaging 14, 303\u2013308. https:\/\/doi.org\/10.1093\/ehjci\/jet008 (2013).","journal-title":"European Heart Journal - Cardiovascular Imaging"},{"key":"46006_CR31","volume-title":"Doing Bayesian Data Analysis","author":"JK Kruschke","year":"2015","unstructured":"Kruschke, J. K. Doing Bayesian Data Analysis 2nd edn. (Academic Press, 2015).","edition":"2nd edn."},{"key":"46006_CR32","unstructured":"Goldberg, P., Williams, C. & Bishop, C. Regression with input-dependent noise: A gaussian process treatment. In Advances in Neural Information Processing Systems, vol.\u00a010, 493\u2013499 (MIT Press, 1997)."},{"key":"46006_CR33","doi-asserted-by":"publisher","DOI":"10.1145\/1541880.1541882","volume":"41","author":"V Chandola","year":"2009","unstructured":"Chandola, V., Banerjee, A. & Kumar, V. Anomaly detection: A survey. ACM Computing Surveys 41, 15:1\u201315:58. https:\/\/doi.org\/10.1145\/1541880.1541882 (2009).","journal-title":"ACM Computing Surveys"},{"key":"46006_CR34","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1109\/TKDE.2007.1009","volume":"19","author":"X Song","year":"2007","unstructured":"Song, X., Wu, M., Jermaine, C. & Ranka, S. Conditional anomaly detection. IEEE Trans. Knowl. Data Eng. 19, 631\u2013645. https:\/\/doi.org\/10.1109\/TKDE.2007.1009 (2007).","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"46006_CR35","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1007\/s10618-023-00967-z","volume":"37","author":"Z Li","year":"2023","unstructured":"Li, Z. & van Leeuwen, M. Explainable contextual anomaly detection using quantile regression forests. Data Min. Knowl. Discov. 37, 2517\u20132563. https:\/\/doi.org\/10.1007\/s10618-023-00967-z (2023).","journal-title":"Data Min. Knowl. Discov."},{"key":"46006_CR36","volume-title":"Gaussian Processes for Machine Learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen, C. E. & Williams, C. K. I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning (MIT Press, Cambridge, 2006)."},{"key":"46006_CR37","unstructured":"Titsias, M. Variational learning of inducing variables in sparse Gaussian processes. In Artificial intelligence and statistics, 567\u2013574 (2009)."},{"key":"46006_CR38","unstructured":"Matthews, A. G. d.\u00a0G. et al. Gpflow: A gaussian process library using tensorflow. Journal of Machine Learning Research 18, 1\u20136 (2017)."},{"key":"46006_CR39","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1080\/01621459.2015.1044091","volume":"111","author":"A Datta","year":"2016","unstructured":"Datta, A., Banerjee, S., Finley, A. O. & Gelfand, A. E. Hierarchical nearest-neighbor gaussian process models for large geostatistical datasets. J. Am. Stat. Assoc. 111, 800\u2013812 (2016).","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46006-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46006-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46006-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T13:43:13Z","timestamp":1776346993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46006-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,27]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["46006"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-46006-x","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,27]]},"assertion":[{"value":"17 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"10848"}}