{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T01:56:22Z","timestamp":1778637382315,"version":"3.51.4"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T00:00:00Z","timestamp":1747785600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T00:00:00Z","timestamp":1747785600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100017212","name":"Sofia University","doi-asserted-by":"publisher","award":["BG-RRP-2.004-0008"],"award-info":[{"award-number":["BG-RRP-2.004-0008"]}],"id":[{"id":"10.13039\/100017212","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Biotheor"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s10441-025-09497-1","type":"journal-article","created":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T12:32:33Z","timestamp":1747830753000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mathematical Modelling of Disability Progression in Patients with Multiple Sclerosis"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-5991-1371","authenticated-orcid":false,"given":"Georgi","family":"Bazlyankov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tihomir","family":"Ivanov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,21]]},"reference":[{"key":"9497_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.mehy.2018.04.004","volume":"115","author":"T Akaishi","year":"2018","unstructured":"Akaishi T, Takahashi T, Nakashima I (2018) Chaos theory for clinical manifestations in multiple sclerosis. Med Hypotheses 115:87\u201393","journal-title":"Med Hypotheses"},{"issue":"5\u20137","key":"9497_CR2","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1002\/sim.4780130509","volume":"13","author":"PS Albert","year":"1994","unstructured":"Albert PS, McFarland HF, Smith ME, Frank JA (1994) Time series for modelling counts from a relapsing-remitting disease: application to modelling disease activity in multiple sclerosis. Statistics in Med 13(5\u20137):453\u2013466","journal-title":"Statistics in Med"},{"issue":"4","key":"9497_CR3","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1002\/ana.21117","volume":"61","author":"A Ascherio","year":"2007","unstructured":"Ascherio A, Munger KL (2007) Environmental risk factors for multiple sclerosis. part i: the role of infection. Ann Neurol 61(4):288\u2013299","journal-title":"Ann Neurol"},{"key":"9497_CR4","unstructured":"Avissar Y, Choi J, DeSaix J, Jurukovski V, Wise R, Rye C et al (2013) Biology (OpenStax). OpenStax"},{"issue":"8","key":"9497_CR5","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1111\/tri.12553","volume":"28","author":"J Bamoulid","year":"2015","unstructured":"Bamoulid J, Staeck O, Halleck F, Khadzhynov D, Brakemeier S, D\u00fcrr M, Budde K (2015) The need for minimization strategies: current problems of immunosuppression. Transplant Int 28(8):891\u2013900","journal-title":"Transplant International"},{"issue":"3","key":"9497_CR6","doi-asserted-by":"publisher","first-page":"57820","DOI":"10.1371\/journal.pone.0057820","volume":"8","author":"L B\u00f6rnsen","year":"2013","unstructured":"B\u00f6rnsen L, Ratzer R, Piehl F, Khademi M, Olsson T, S\u00f8rensen P, Sellebjerg F et al (2013) Systemic inflammation in progressive multiple sclerosis involves follicular t-helper, th17-and activated b-cells and correlates with progression. PloS One 8(3):57820\u201357820","journal-title":"PloS One"},{"key":"9497_CR7","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s00401-009-0601-5","volume":"119","author":"M Bradl","year":"2010","unstructured":"Bradl M, Lassmann H (2010) Oligodendrocytes: biology and pathology. Acta Neuropathol 119:37\u201353","journal-title":"Acta Neuropathol"},{"issue":"7","key":"9497_CR8","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1016\/j.mcm.2007.06.011","volume":"47","author":"V Calvez","year":"2008","unstructured":"Calvez V, Khonsari RH (2008) Mathematical description of concentric demyelination in the human brain: Self-organization models, from liesegang rings to chemotaxis. Math Comput Model 47(7):726\u2013742. https:\/\/doi.org\/10.1016\/j.mcm.2007.06.011","journal-title":"Math Comput Model"},{"issue":"4","key":"9497_CR9","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1093\/brain\/awg081","volume":"126","author":"C Confavreux","year":"2003","unstructured":"Confavreux C, Vukusic S, Adeleine P (2003) Early clinical predictors and progression of irreversible disability in multiple sclerosis: an amnesic process. Brain 126(4):770\u2013782","journal-title":"Brain"},{"issue":"4","key":"9497_CR10","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/j.clinthera.2006.04.005","volume":"28","author":"HJ Crayton","year":"2006","unstructured":"Crayton HJ, Rossman HS (2006) Managing the symptoms of multiple sclerosis: a multimodal approach. Clin Ther 28(4):445\u2013460","journal-title":"Clin Ther"},{"key":"9497_CR11","doi-asserted-by":"publisher","first-page":"115163","DOI":"10.1016\/j.cam.2023.115163","volume":"428","author":"MAM de Paula","year":"2023","unstructured":"de Paula MAM, Melo Quintela B, Lobosco M (2023) On the use of a coupled mathematical model for understanding the dynamics of multiple sclerosis. J Comput Appl Math 428:115163","journal-title":"J Comput Appl Math"},{"issue":"9","key":"9497_CR12","first-page":"2062","volume":"10","author":"MA Dias de Sousa","year":"2022","unstructured":"Dias de Sousa MA, Desid\u00e9rio CS, da Silva Catarino J, Trevisan RO, Alves da Silva DA, Rocha VFR, Bovi WG, Timoteo RP, Bonatti RCF, da Silva AE et al (2022) Role of cytokines, chemokines and ifn-\u03b3+ il-17+ double-positive cd4+ t cells in patients with multiple sclerosis. Biomed 10(9):2062","journal-title":"Biomed"},{"key":"9497_CR13","doi-asserted-by":"publisher","first-page":"109478","DOI":"10.1016\/j.mehy.2019.109478","volume":"135","author":"MF Elettreby","year":"2020","unstructured":"Elettreby MF, Ahmed E (2020) A simple mathematical model for relapsing-remitting multiple sclerosis (rrms). Med Hypotheses 135:109478","journal-title":"Med Hypotheses"},{"issue":"3","key":"9497_CR14","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S1474-4422(05)70023-5","volume":"4","author":"DH Gilden","year":"2005","unstructured":"Gilden DH (2005) Infectious causes of multiple sclerosis. Lancet Neurol 4(3):195\u2013202","journal-title":"&nbsp;Lancet Neurol"},{"issue":"2","key":"9497_CR15","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/s00415-008-0743-8","volume":"255","author":"C Hirst","year":"2008","unstructured":"Hirst C, Ingram G, Pearson O, Pickersgill T, Scolding N, Robertson N (2008) Contribution of relapses to disability in multiple sclerosis. J Neurol 255(2):280\u2013287","journal-title":"J Neurol"},{"issue":"12","key":"9497_CR16","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1177\/1352458510379246","volume":"16","author":"S Inusah","year":"2010","unstructured":"Inusah S, Sormani MP, Cofield SS, Aban IB, Musani SK, Srinivasasainagendra V, Cutter GR (2010) Assessing changes in relapse rates in multiple sclerosis. Mult Scler J 16(12):1414\u20131421","journal-title":"Mult Scler J"},{"issue":"4","key":"9497_CR17","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1089\/thy.2011.0480","volume":"23","author":"A Kawashima","year":"2013","unstructured":"Kawashima A, Yamazaki K, Hara T, Akama T, Yoshihara A, Sue M, Tanigawa K, Wu H, Ishido Y, Takeshita F et al (2013) Demonstration of innate immune responses in the thyroid gland: potential to sense danger and a possible trigger for autoimmune reactions. Thyroid 23(4):477\u2013487","journal-title":"Thyroid"},{"issue":"1","key":"9497_CR18","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1371\/journal.pone.0000150","volume":"2","author":"RH Khonsari","year":"2007","unstructured":"Khonsari RH, Calvez V (2007) The origins of concentric demyelination: self-organization in the human brain. PLoS One 2(1):150","journal-title":"PLoS One"},{"issue":"9","key":"9497_CR19","doi-asserted-by":"publisher","first-page":"028928","DOI":"10.1101\/cshperspect.a028928","volume":"8","author":"S Klineova","year":"2018","unstructured":"Klineova S, Lublin FD (2018) Clinical course of multiple sclerosis. Cold Spring Harb Perspect Med 8(9):028928","journal-title":"Cold Spring Harb Perspect Med"},{"issue":"10","key":"9497_CR20","doi-asserted-by":"publisher","first-page":"1005757","DOI":"10.1371\/journal.pcbi.1005757","volume":"13","author":"E Kotelnikova","year":"2017","unstructured":"Kotelnikova E, Abad NAKE, Martinez-Lapiscina EH, Andorra M, Zubizarreta I, Pulido-Valdeolivas I, Pertsovskaya I, Alexopoulos LG, Olsson T et al (2017) Dynamics and heterogeneity of brain damage in multiple sclerosis. PLoS Comput Biol 13(10):1005757","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"9497_CR21","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1093\/brain\/awh721","volume":"129","author":"M Kremenchutzky","year":"2006","unstructured":"Kremenchutzky M, Rice GPA, Baskerville J, Wingerchuk DM, Ebers GC (2006) The natural history of multiple sclerosis: a geographically based study 9: observations on the progressive phase of the disease. Brain 129(3):584\u2013594","journal-title":"Brain"},{"issue":"11","key":"9497_CR22","doi-asserted-by":"publisher","first-page":"1444","DOI":"10.1212\/WNL.33.11.1444","volume":"33","author":"JF Kurtzke","year":"1983","unstructured":"Kurtzke JF (1983) Rating neurologic impairment in multiple sclerosis: an expanded disability status scale (edss). Neurology 33(11):1444\u20131444","journal-title":"Neurol"},{"issue":"11","key":"9497_CR23","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1016\/S0167-5699(98)01320-6","volume":"19","author":"JD Laman","year":"1998","unstructured":"Laman JD, Thompson EJ, Kappos L (1998) Balancing the th1\/th2 concept in multiple sclerosis. Immunol Today 19(11):489\u2013490","journal-title":"Immunol Today"},{"issue":"1","key":"9497_CR24","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1111\/j.1600-065X.1998.tb01207.x","volume":"164","author":"PV Lehmann","year":"1998","unstructured":"Lehmann PV, Targoni OS, Forsthuber TG (1998) Shifting t-cell activation thresholds in autoimmunity and determinant spreading. Immunol Rev 164(1):53\u201361","journal-title":"Immunol Rev"},{"issue":"7","key":"9497_CR25","doi-asserted-by":"publisher","first-page":"1900","DOI":"10.1093\/brain\/awq076","volume":"133","author":"E Leray","year":"2010","unstructured":"Leray E, Yaouanq J, Le Page E, Coustans M, Laplaud D, Oger J, Edan G (2010) Evidence for a two-stage disability progression in multiple sclerosis. Brain 133(7):1900\u20131913","journal-title":"Brain"},{"issue":"2","key":"9497_CR26","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s00285-016-1087-0","volume":"75","author":"MC Lombardo","year":"2017","unstructured":"Lombardo MC, Barresi R, Bilotta E, Gargano F, Pantano P, Sammartino M (2017) Demyelination patterns in a mathematical model of multiple sclerosis. J Math Biol 75(2):373\u2013417","journal-title":"J Math Biol"},{"issue":"4","key":"9497_CR27","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1212\/WNL.46.4.907","volume":"46","author":"FD Lublin","year":"1996","unstructured":"Lublin FD, Reingold SC (1996) Defining the clinical course of multiple sclerosis: results of an international survey. Neurology 46(4):907\u2013911","journal-title":"Neurology"},{"issue":"11","key":"9497_CR28","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1212\/01.WNL.0000096175.39831.21","volume":"61","author":"FD Lublin","year":"2003","unstructured":"Lublin FD, Baier M, Cutter G (2003) Effect of relapses on development of residual deficit in multiple sclerosis. Neurology 61(11):1528\u20131532","journal-title":"Neurol"},{"issue":"3","key":"9497_CR29","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1212\/WNL.0000000000000560","volume":"83","author":"FD Lublin","year":"2014","unstructured":"Lublin FD, Reingold SC, Cohen JA, Cutter GR, S\u00f8rensen PS, Thompson AJ, Wolinsky JS, Balcer LJ, Banwell B, Barkhof F et al (2014) Defining the clinical course of multiple sclerosis: the 2013 revisions. Neurol 83(3):278\u2013286","journal-title":"Neurol"},{"issue":"5","key":"9497_CR30","doi-asserted-by":"publisher","first-page":"3025","DOI":"10.4049\/jimmunol.175.5.3025","volume":"175","author":"MJ McGeachy","year":"2005","unstructured":"McGeachy MJ, Stephens LA, Anderton SM (2005) Natural recovery and protection from autoimmune encephalomyelitis: contribution of cd4+ cd25+ regulatory cells within the central nervous system. J Immunol 175(5):3025\u20133032","journal-title":"J Immunol"},{"key":"9497_CR31","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.neuro.2016.03.020","volume":"61","author":"KA McKay","year":"2017","unstructured":"McKay KA, Jahanfar S, Duggan T, Tkachuk S, Tremlett H (2017) Factors associated with onset, relapses or progression in multiple sclerosis: a systematic review. Neurotoxicology 61:189\u2013212","journal-title":"Neurotoxicology"},{"issue":"2","key":"9497_CR32","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1191\/135248506ms1265oa","volume":"12","author":"DC Mohr","year":"2006","unstructured":"Mohr DC, Hart SL, Fonareva I, Tasch ES (2006) Treatment of depression for patients with multiple sclerosis in neurology clinics. Mult Scler J 12(2):204\u2013208","journal-title":"Mult Scler J"},{"key":"9497_CR33","doi-asserted-by":"publisher","first-page":"103357","DOI":"10.1016\/j.compbiomed.2019.103357","volume":"111","author":"A Montolio","year":"2019","unstructured":"Montolio A, Cegonino J, Orduna E, Sebastian B, Garcia-Martin E, Palomar APD (2019) A mathematical model to predict the evolution of retinal nerve fiber layer thinning in multiple sclerosis patients. Comput Biol Med 111:103357","journal-title":"Comput Biol Med"},{"issue":"6738","key":"9497_CR34","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1038\/399a040","volume":"399","author":"JH Noseworthy","year":"1999","unstructured":"Noseworthy JH (1999) Progress in determining the causes and treatment of multiple sclerosis. Nature 399(6738):40\u201347","journal-title":"Nature"},{"issue":"3","key":"9497_CR35","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.3390\/brainsci3031282","volume":"3","author":"M Podbielska","year":"2013","unstructured":"Podbielska M, Banik NL, Kurowska E, Hogan EL (2013) Myelin recovery in multiple sclerosis: the challenge of remyelination. Brain Sci 3(3):1282\u20131324","journal-title":"Brain Sci"},{"issue":"4","key":"9497_CR36","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/S1474-4422(06)70410-0","volume":"5","author":"M Rovaris","year":"2006","unstructured":"Rovaris M, Confavreux C, Furlan R, Kappos L, Comi G, Filippi M (2006) Secondary progressive multiple sclerosis: current knowledge and future challenges. Lancet Neurol 5(4):343\u2013354","journal-title":"Lancet Neurol"},{"issue":"13","key":"9497_CR37","doi-asserted-by":"publisher","first-page":"1246","DOI":"10.1212\/WNL.0b013e318230a17d","volume":"77","author":"A Scalfari","year":"2011","unstructured":"Scalfari A, Neuhaus A, Daumer M, Ebers GC, Muraro P (2011) Age and disability accumulation in multiple sclerosis. Neurology 77(13):1246\u20131252","journal-title":"Neurol"},{"issue":"1","key":"9497_CR38","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1212\/WNL.0000000000001094","volume":"84","author":"MMP Sold\u00e1n","year":"2015","unstructured":"Sold\u00e1n MMP, Novotna M, Abou Zeid N, Kale N, Tutuncu M, Crusan DJ, Atkinson EJ, Siva A, Keegan BM, Pirko I et al (2015) Relapses and disability accumulation in progressive multiple sclerosis. Neurology 84(1):81\u201388","journal-title":"Neurology"},{"issue":"2","key":"9497_CR39","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1212\/01.wnl.0000194259.90286.fe","volume":"66","author":"H Tremlett","year":"2006","unstructured":"Tremlett H, Paty D, Devonshire V (2006) Disability progression in multiple sclerosis is slower than previously reported. Neurology 66(2):172\u2013177","journal-title":"Neurol"},{"issue":"5271","key":"9497_CR40","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1126\/science.273.5271.104","volume":"273","author":"A Viola","year":"1996","unstructured":"Viola A, Lanzavecchia A (1996) T cell activation determined by t cell receptor number and tunable thresholds. Science 273(5271):104\u2013106","journal-title":"Science"},{"key":"9497_CR41","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.jns.2007.01.065","volume":"256","author":"T Vollmer","year":"2007","unstructured":"Vollmer T (2007) The natural history of relapses in multiple sclerosis. J Neurol Sci 256:5\u201313","journal-title":"J Neurol Sci"},{"issue":"1\u20132","key":"9497_CR42","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/S0165-5728(98)00248-3","volume":"95","author":"R Wei","year":"1999","unstructured":"Wei R, Jonakait GM (1999) Neurotrophins and the anti-inflammatory agents interleukin-4 (IL-4), IL-10, IL-11 and transforming growth factor-\u03b21 (TGF-\u03b21) down-regulate T cell costimulatory molecules B7 and CD40 on cultured rat microglia. J Neuroimmunol 95(1\u20132):8\u201318","journal-title":"J Neuroimmunol"},{"key":"9497_CR43","unstructured":"Wolfram S (2003) The Mathematica Book. Wolfram Research, Inc"},{"issue":"3","key":"9497_CR44","first-page":"65","volume":"10","author":"Wolinsky, J.S., Group, P.T.S.","year":"2004","unstructured":"Wolinsky, J.S., Group, P.T.S. (2004) The pro mise trial: baseline data review and progress report. Mult Scler J 10(3):65\u201372","journal-title":"Mult Scler J"}],"container-title":["Acta Biotheoretica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-025-09497-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10441-025-09497-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-025-09497-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T11:03:05Z","timestamp":1751108585000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10441-025-09497-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,21]]},"references-count":44,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["9497"],"URL":"https:\/\/doi.org\/10.1007\/s10441-025-09497-1","relation":{},"ISSN":["0001-5342","1572-8358"],"issn-type":[{"value":"0001-5342","type":"print"},{"value":"1572-8358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,21]]},"assertion":[{"value":"17 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2025","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 knowledge of any conflicts of interest in connection to the current paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest\u00a0"}}],"article-number":"7"}}