{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T06:21:03Z","timestamp":1777357263312,"version":"3.51.4"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T00:00:00Z","timestamp":1633305600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T00:00:00Z","timestamp":1633305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12859-021-04373-4","type":"journal-article","created":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T13:47:56Z","timestamp":1633355276000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis"],"prefix":"10.1186","volume":"22","author":[{"given":"Ronan","family":"Duchesne","sequence":"first","affiliation":[]},{"given":"Anissa","family":"Guillemin","sequence":"additional","affiliation":[]},{"given":"Olivier","family":"Gandrillon","sequence":"additional","affiliation":[]},{"given":"Fabien","family":"Crauste","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"issue":"23","key":"4373_CR1","doi-asserted-by":"publisher","first-page":"3853","DOI":"10.1242\/dev.035139","volume":"136","author":"S Huang","year":"2009","unstructured":"Huang S. Non-genetic heterogeneity of cells in development: more than just noise. Development. 2009;136(23):3853\u201362. https:\/\/doi.org\/10.1242\/dev.035139.","journal-title":"Development"},{"issue":"1","key":"4373_CR2","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1002\/pst.1548","volume":"12","author":"SW Andersen","year":"2013","unstructured":"Andersen SW, Millen BA. On the practical application of mixed effects models for repeated measures to clinical trial data. Pharm Stat. 2013;12(1):7\u201316. https:\/\/doi.org\/10.1002\/pst.1548.","journal-title":"Pharm Stat"},{"issue":"2","key":"4373_CR3","doi-asserted-by":"publisher","first-page":"792","DOI":"10.15252\/msb.20145549","volume":"11","author":"P Ru\u00e9","year":"2015","unstructured":"Ru\u00e9 P, Martinez Arias A. Cell dynamics and gene expression control in tissue homeostasis and development. Mol Syst Biol. 2015;11(2):792. https:\/\/doi.org\/10.15252\/msb.20145549.","journal-title":"Mol Syst Biol"},{"issue":"6119","key":"4373_CR4","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1126\/science.1227670","volume":"339","author":"A Kreso","year":"2013","unstructured":"Kreso A, O'Brien CA, Pv Galen, Gan OI, Notta F, Brown AMK, Ng K, Ma J, Wienholds E, Dunant C, Pollett A, Gallinger S, McPherson J, Mullighan CG, Shibata D, Dick JE. Variable clonal repopulation dynamics influence chemotherapy response in colorectal cancer. Science. 2013;339(6119):543\u20138. https:\/\/doi.org\/10.1126\/science.1227670.","journal-title":"Science"},{"issue":"3","key":"4373_CR5","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1111\/mmi.12575","volume":"92","author":"BB Pradhan","year":"2014","unstructured":"Pradhan BB, Chatterjee S. Reversible non-genetic phenotypic heterogeneity in bacterial quorum sensing. Mol Microbiol. 2014;92(3):557\u201369. https:\/\/doi.org\/10.1111\/mmi.12575.","journal-title":"Mol Microbiol"},{"issue":"15","key":"4373_CR6","doi-asserted-by":"publisher","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","volume":"25","author":"A Raue","year":"2009","unstructured":"Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingm\u00fcller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009;25(15):1923\u20139. https:\/\/doi.org\/10.1093\/bioinformatics\/btp358.","journal-title":"Bioinformatics"},{"issue":"9","key":"4373_CR7","doi-asserted-by":"publisher","first-page":"74335","DOI":"10.1371\/journal.pone.0074335","volume":"8","author":"A Raue","year":"2013","unstructured":"Raue A, Schilling M, Bachmann J, Matteson A, Schelke M, Kaschek D, Hug S, Kreutz C, Harms B, Theis F, Klingm\u00fcller U, Timmer J. Lessons learned from quantitative dynamical modeling in systems biology. PLoS ONE. 2013;8(9):74335. https:\/\/doi.org\/10.1371\/journal.pone.0074335.","journal-title":"PLoS ONE"},{"key":"4373_CR8","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.coisb.2021.03.005","volume":"25","author":"F-G Wieland","year":"2021","unstructured":"Wieland F-G, Hauber AL, Rosenblatt M, T\u00f6nsing C, Timmer J. On structural and practical identifiability. Curr Opin Syst Biol. 2021;25:60\u20139. https:\/\/doi.org\/10.1016\/j.coisb.2021.03.005.","journal-title":"Curr Opin Syst Biol"},{"issue":"6","key":"4373_CR9","doi-asserted-by":"publisher","first-page":"1058","DOI":"10.1152\/ajpendo.1990.258.6.E1058","volume":"258","author":"C Cobelli","year":"1990","unstructured":"Cobelli C, Saccomani MP. Unappreciation of a priori identifiability in software packages causes ambiguities in numerical estimates. Am J Physiol Endocrinol Metab. 1990;258(6):1058\u20139. https:\/\/doi.org\/10.1152\/ajpendo.1990.258.6.E1058.","journal-title":"Am J Physiol Endocrinol Metab"},{"key":"4373_CR10","doi-asserted-by":"publisher","DOI":"10.1201\/b17203","volume-title":"Mixed effects models for the population approach: models, tasks, methods and tools","author":"M Lavielle","year":"2014","unstructured":"Lavielle M, Bleakley K. Mixed effects models for the population approach: models, tasks, methods and tools. London: Chapman & Hall; 2014."},{"key":"4373_CR11","doi-asserted-by":"publisher","DOI":"10.1186\/s12918-015-0203-x","author":"M Karlsson","year":"2015","unstructured":"Karlsson M, Janz\u00e9n D, Durrieu L, Colman-Lerner A, Kjellsson M, Cedersund G. Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it. BMC Syst Biol. 2015. https:\/\/doi.org\/10.1186\/s12918-015-0203-x.","journal-title":"BMC Syst Biol"},{"issue":"3","key":"4373_CR12","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1208\/s12248-009-9133-0","volume":"11","author":"R Savic","year":"2009","unstructured":"Savic R, Karlsson M. Importance of shrinkage in empirical Bayes estimates for diagnostics: problems and solutions. AAPS J. 2009;11(3):558\u201369. https:\/\/doi.org\/10.1208\/s12248-009-9133-0.","journal-title":"AAPS J"},{"issue":"1","key":"4373_CR13","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s10928-015-9459-4","volume":"43","author":"M Lavielle","year":"2016","unstructured":"Lavielle M, Aarons L. What do we mean by identifiability in mixed effects models? J Pharmacokinet Pharmacodyn. 2016;43(1):111\u201322. https:\/\/doi.org\/10.1007\/s10928-015-9459-4.","journal-title":"J Pharmacokinet Pharmacodyn"},{"issue":"6","key":"4373_CR14","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1038\/psp.2013.25","volume":"2","author":"V Shivva","year":"2013","unstructured":"Shivva V, Korell J, Tucker IG, Duffull SB. An approach for identifiability of population pharmacokinetic-pharmacodynamic models. CPT Pharmacomet Syst Pharmacol. 2013;2(6):49. https:\/\/doi.org\/10.1038\/psp.2013.25.","journal-title":"CPT Pharmacomet Syst Pharmacol"},{"key":"4373_CR15","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.cmpb.2016.04.024","volume":"171","author":"DLI Janz\u00e9n","year":"2019","unstructured":"Janz\u00e9n DLI, Jirstrand M, Chappell MJ, Evans ND. Three novel approaches to structural identifiability analysis in mixed-effects models. Comput Methods Programs Biomed. 2019;171:141\u201352. https:\/\/doi.org\/10.1016\/j.cmpb.2016.04.024.","journal-title":"Comput Methods Programs Biomed"},{"key":"4373_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.mbs.2017.10.009","volume":"295","author":"DLI Janz\u00e9n","year":"2018","unstructured":"Janz\u00e9n DLI, Jirstrand M, Chappell MJ, Evans ND. Extending existing structural identifiability analysis methods to mixed-effects models. Math Biosci. 2018;295:1\u201310. https:\/\/doi.org\/10.1016\/j.mbs.2017.10.009.","journal-title":"Math Biosci"},{"issue":"1","key":"4373_CR17","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0025-5564(85)90098-7","volume":"77","author":"JA Jacquez","year":"1985","unstructured":"Jacquez JA, Greif P. Numerical parameter identifiability and estimability: integrating identifiability, estimability, and optimal sampling design. Math Biosci. 1985;77(1):201\u201327. https:\/\/doi.org\/10.1016\/0025-5564(85)90098-7.","journal-title":"Math Biosci"},{"issue":"1","key":"4373_CR18","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1080\/00986448908940662","volume":"83","author":"S Vajda","year":"1989","unstructured":"Vajda S, Rabitz H, Walter E, Lecourtier Y. Qualitative and quantitative identifiability analysis of nonlinear chemical kinetic models. Chem Eng Commun. 1989;83(1):191\u2013219. https:\/\/doi.org\/10.1080\/00986448908940662.","journal-title":"Chem Eng Commun"},{"issue":"2","key":"4373_CR19","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10928-005-0062-y","volume":"32","author":"GC Pillai","year":"2005","unstructured":"Pillai GC, Mentr\u00e9 F, Steimer JL. Non-linear mixed effects modeling\u2014from methodology and software development to driving implementation in drug development science. J Pharmacokinet Pharmacodyn. 2005;32(2):161\u201383. https:\/\/doi.org\/10.1007\/s10928-005-0062-y.","journal-title":"J Pharmacokinet Pharmacodyn"},{"key":"4373_CR20","first-page":"61","volume-title":"CMSB","author":"F Fr\u00f6hlich","year":"2014","unstructured":"Fr\u00f6hlich F, Theis F, Hasenauer J. Uncertainty analysis for non-identifiable dynamical systems: profile likelihoods, bootstrapping and more. In: Mendes P, Dada J, Smallbone K, editors. CMSB. Cham: Springer; 2014. p. 61\u201372."},{"key":"4373_CR21","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1214\/13-EJS770","volume":"7","author":"W Wang","year":"2013","unstructured":"Wang W. Identifiability of linear mixed effects models. Electron J Stat. 2013;7:244\u201363. https:\/\/doi.org\/10.1214\/13-EJS770.","journal-title":"Electron J Stat"},{"issue":"2","key":"4373_CR22","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1093\/biomet\/84.2.429","volume":"84","author":"F Mentr\u00e9","year":"1997","unstructured":"Mentr\u00e9 F, Mallet A, Baccar D. Optimal design in random-effects regression models. Biometrika. 1997;84(2):429\u201342. https:\/\/doi.org\/10.1093\/biomet\/84.2.429.","journal-title":"Biometrika"},{"issue":"2","key":"4373_CR23","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1081\/BIP-120019267","volume":"13","author":"S Retout","year":"2003","unstructured":"Retout S, Mentr\u00e9 F. Further developments of the fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics. J Biopharm Stat. 2003;13(2):209\u201327. https:\/\/doi.org\/10.1081\/BIP-120019267.","journal-title":"J Biopharm Stat"},{"issue":"12","key":"4373_CR24","doi-asserted-by":"publisher","first-page":"1005227","DOI":"10.1371\/journal.pcbi.1005227","volume":"12","author":"A White","year":"2016","unstructured":"White A, Tolman M, Thames H, Withers H, Mason K, Transtrum M. The limitations of model-based experimental design and parameter estimation in sloppy systems. PLoS Comput Biol. 2016;12(12):1005227. https:\/\/doi.org\/10.1371\/journal.pcbi.1005227.","journal-title":"PLoS Comput Biol"},{"issue":"8","key":"4373_CR25","doi-asserted-by":"publisher","first-page":"2522","DOI":"10.1039\/C1MB05046J","volume":"7","author":"R Chachra","year":"2011","unstructured":"Chachra R, Transtrum MK, Sethna JP. Comment on \u201cSloppy models, parameter uncertainty, and the role of experimental design\u201d. Mol BioSyst. 2011;7(8):2522\u20132522. https:\/\/doi.org\/10.1039\/C1MB05046J.","journal-title":"Mol BioSyst"},{"key":"4373_CR26","doi-asserted-by":"publisher","DOI":"10.1201\/9781315120003","volume-title":"Parameter redundancy and identifiability","author":"D Cole","year":"2020","unstructured":"Cole D. Parameter redundancy and identifiability. London: Chapman and Hall; 2020. https:\/\/doi.org\/10.1201\/9781315120003."},{"issue":"1","key":"4373_CR27","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.cmpb.2009.09.012","volume":"98","author":"C Bazzoli","year":"2010","unstructured":"Bazzoli C, Retout S, Mentr\u00e9 F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0. Comput Methods Programs Biomed. 2010;98(1):55\u201365. https:\/\/doi.org\/10.1016\/j.cmpb.2009.09.012.","journal-title":"Comput Methods Programs Biomed"},{"key":"4373_CR28","doi-asserted-by":"crossref","unstructured":"Vanrolleghem PA, Dochain D. Bioprocess model identification. In: Advanced instrumentation, data interpretation, and control of biotechnological processes. Springer; 1998. p. 251\u2013318.","DOI":"10.1007\/978-94-015-9111-9_10"},{"issue":"1\u20132","key":"4373_CR29","doi-asserted-by":"publisher","first-page":"55","DOI":"10.3233\/ISB-190471","volume":"13","author":"R Duchesne","year":"2019","unstructured":"Duchesne R, Guillemin A, Crauste F, Gandrillon O. Calibration, selection and identifiability analysis of a mathematical model of the in vitro erythropoiesis in normal and perturbed contexts. ISB. 2019;13(1\u20132):55\u201369. https:\/\/doi.org\/10.3233\/ISB-190471.","journal-title":"ISB"},{"key":"4373_CR30","unstructured":"Monolix version 2018R1. http:\/\/lixoft.com\/products\/monolix\/. Antony: Lixoft SAS; 2018."},{"issue":"12","key":"4373_CR31","doi-asserted-by":"publisher","first-page":"1002585","DOI":"10.1371\/journal.pbio.1002585","volume":"14","author":"A Richard","year":"2016","unstructured":"Richard A, Boullu L, Herbach U, Bonnafoux A, Morin V, Vallin E, Guillemin A, Papili Gao N, Gunawan R, Cosette J, Arnaud O, Kupiec J, Espinasse T, Gonin-Giraud S, Gandrillon O. Single-cell-based analysis highlights a surge in cell-to-cell molecular variability preceding irreversible commitment in a differentiation process. PLoS Biol. 2016;14(12):1002585. https:\/\/doi.org\/10.1371\/journal.pbio.1002585.","journal-title":"PLoS Biol"},{"issue":"11","key":"4373_CR32","doi-asserted-by":"publisher","first-page":"0225166","DOI":"10.1371\/journal.pone.0225166","volume":"14","author":"A Guillemin","year":"2019","unstructured":"Guillemin A, Duchesne R, Crauste F, Gonin-Giraud S, Gandrillon O. Drugs modulating stochastic gene expression affect the erythroid differentiation process. PLoS ONE. 2019;14(11):0225166. https:\/\/doi.org\/10.1371\/journal.pone.0225166.","journal-title":"PLoS ONE"},{"issue":"10","key":"4373_CR33","doi-asserted-by":"publisher","first-page":"2764","DOI":"10.1093\/emboj\/18.10.2764","volume":"18","author":"O Gandrillon","year":"1999","unstructured":"Gandrillon O, Schmidt U, Beug H, Samarut J. TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism. EMBO J. 1999;18(10):2764\u201381. https:\/\/doi.org\/10.1093\/emboj\/18.10.2764.","journal-title":"EMBO J"},{"issue":"4","key":"4373_CR34","doi-asserted-by":"publisher","first-page":"1020","DOI":"10.1016\/j.csda.2004.07.002","volume":"49","author":"E Kuhn","year":"2005","unstructured":"Kuhn E, Lavielle M. Maximum likelihood estimation in nonlinear mixed effects models. Comput Stat Data Anal. 2005;49(4):1020\u201338. https:\/\/doi.org\/10.1016\/j.csda.2004.07.002.","journal-title":"Comput Stat Data Anal"},{"key":"4373_CR35","unstructured":"Burnham K, Anderson D. Model selection and multimodel inference: a practical information-theoretic approach. New York: Springer; 2010. OCLC: 934366523."},{"issue":"2","key":"4373_CR36","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1093\/biomet\/92.2.351","volume":"92","author":"F Vaida","year":"2005","unstructured":"Vaida F, Blanchard S. Conditional Akaike information for mixed-effects models. Biometrika. 2005;92(2):351\u201370. https:\/\/doi.org\/10.1093\/biomet\/92.2.351.","journal-title":"Biometrika"},{"issue":"1","key":"4373_CR37","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1214\/14-EJS890","volume":"8","author":"M Delattre","year":"2014","unstructured":"Delattre M, Lavielle M, Poursat M. A note on BIC in mixed-effects models. Electron J Stat. 2014;8(1):456\u201375. https:\/\/doi.org\/10.1214\/14-EJS890.","journal-title":"Electron J Stat"},{"key":"4373_CR38","unstructured":"Delattre M, Poursat M. BIC strategies for model choice in a population approach. arXiv:1612.02405 [stat]; 2016. Accessed 17 May 2017."},{"issue":"3","key":"4373_CR39","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1080\/07350015.2013.773905","volume":"31","author":"G Koop","year":"2013","unstructured":"Koop G, Pesaran MH, Smith RP. On identification of Bayesian DSGE models. J Bus Econ Stat. 2013;31(3):300\u201314. https:\/\/doi.org\/10.1080\/07350015.2013.773905.","journal-title":"J Bus Econ Stat"},{"issue":"1","key":"4373_CR40","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1038\/sj.clpt.6100241","volume":"82","author":"M Karlsson","year":"2007","unstructured":"Karlsson M, Savic R. Diagnosing model diagnostics. Clin Pharmacol Ther. 2007;82(1):17\u201320. https:\/\/doi.org\/10.1038\/sj.clpt.6100241.","journal-title":"Clin Pharmacol Ther"},{"key":"4373_CR41","unstructured":"Allison PD. Multiple regression: a primer. Thousand Oaks: Pine Forge Press; 1999. Open Library ID: OL378019M."},{"issue":"5","key":"4373_CR42","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.stem.2018.04.003","volume":"22","author":"S Haas","year":"2018","unstructured":"Haas S, Trumpp A, Milsom MD. Causes and consequences of hematopoietic stem cell heterogeneity. Cell Stem Cell. 2018;22(5):627\u201338. https:\/\/doi.org\/10.1016\/j.stem.2018.04.003.","journal-title":"Cell Stem Cell"},{"issue":"1","key":"4373_CR43","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1186\/s12867-015-0048-2","volume":"16","author":"O Arnaud","year":"2015","unstructured":"Arnaud O, Meyer S, Vallin E, Beslon G, Gandrillon O. Temperature-induced variation in gene expression burst size in metazoan cells. BMC Mol Biol. 2015;16(1):20. https:\/\/doi.org\/10.1186\/s12867-015-0048-2.","journal-title":"BMC Mol Biol"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-021-04373-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-021-04373-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-021-04373-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T13:48:01Z","timestamp":1633355281000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/s12859-021-04373-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,4]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["4373"],"URL":"https:\/\/doi.org\/10.1186\/s12859-021-04373-4","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.03.01.433388","asserted-by":"object"}]},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,4]]},"assertion":[{"value":"1 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All methods were carried out in accordance with relevant guidelines and regulations, notably the DIRECTIVE 2010\/63\/EU OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 22 September 2010 regarding - the killing of animals solely for the use of their organs or tissues.-(\n                      \n                      )","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"478"}}