{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T15:22:18Z","timestamp":1787757738683,"version":"build-2784847793"},"reference-count":48,"publisher":"Ovid Technologies (Wolters Kluwer Health)","issue":"Suppl 2","content-domain":{"domain":["lww.com","ovid.com"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background:<\/jats:title>\n                    <jats:p>Various studies highlight the significance of alterations in cerebrospinal fluid (CSF) and cerebral blood flow (CBF) dynamics in the pathogenesis of hydrocephalus and suggest the role of mathematical modeling in studying these complex interactions.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Objective:<\/jats:title>\n                    <jats:p>This narrative review discusses mathematical models of CSF and CBF dynamics, including Marmarou's compartmental model of CSF spaces and a model of cardiac changes in cerebral arterial blood volume. The diagnostic utility of CSF compensatory parameters is described along with current information on secondary model-based indices of cerebral hemodynamics in hydrocephalus.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions:<\/jats:title>\n                    <jats:p>Compensatory parameters derived from the model of CSF circulation have long been used in the diagnosis and management of hydrocephalus patients. However, recent studies using mathematical models of cerebral circulation also show alterations in CBF dynamics, and model-based indices of cerebral hemodynamics, which can be calculated non-invasively using transracranial Doppler ultrasonography, can be used as a complementary source of information about the state of the cerebrospinal space.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.4103\/0028-3886.332259","type":"journal-article","created":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T01:37:09Z","timestamp":1640655429000},"page":"S275-S282","update-policy":"https:\/\/doi.org\/10.1097\/lww.0000000000001000","source":"Crossref","is-referenced-by-count":3,"title":["Mathematical Modelling in Hydrocephalus"],"prefix":"10.4103","volume":"69","author":[{"given":"Agnieszka","family":"Kazimierska","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arkadiusz","family":"Zi\u00f3\u0142kowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Magdalena","family":"Kasprowicz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Afroditi","family":"Lalou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zofia","family":"Czosnyka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marek","family":"Czosnyka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"276","reference":[{"key":"R1-5-20240907","doi-asserted-by":"crossref","first-page":"E3","DOI":"10.3171\/foc.2007.22.4.4","article-title":"The history of mathematical modeling in hydrocephalus","volume":"22","author":"Clarke","year":"2007","journal-title":"Neurosurg Focus"},{"key":"R2-5-20240907","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/01616412.2000.11741033","article-title":"Brain biomechanics: Mathematical modeling of hydrocephalus","volume":"22","author":"Tenti","year":"2000","journal-title":"Neurol Res"},{"key":"R3-5-20240907","first-page":"169","article-title":"Biomechanics of hydrocephalus","volume":"1","author":"Hakim","year":"1971","journal-title":"Acta Neurol Latinoam"},{"key":"R4-5-20240907","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1227\/00006123-198712000-00019","article-title":"Biomechanics of hydrocephalus: A new theoretical model","volume":"21","author":"Nagashima","year":"1987","journal-title":"Neurosurgery"},{"key":"R5-5-20240907","doi-asserted-by":"crossref","first-page":"332","DOI":"10.3171\/jns.1978.48.3.0332","article-title":"A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics","volume":"48","author":"Marmarou","year":"1978","journal-title":"J Neurosurg"},{"key":"R6-5-20240907","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF00313579","article-title":"The usefulness of mathematical modeling in hydrocephalus research","volume":"10","author":"Rekate","year":"1994","journal-title":"Child's Nerv Syst"},{"key":"R7-5-20240907","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12987-019-0131-z","article-title":"Enhanced in vitro model of the CSF dynamics","volume":"16","author":"Benninghaus","year":"2019","journal-title":"Fluids Barriers CNS"},{"key":"R9-5-20240907","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF02441352","article-title":"Instrumentation for cerebrospinal fluid hydrodynamic studies in man","volume":"20","author":"Friden","year":"1982","journal-title":"Med Biol Eng Comput"},{"key":"R11-5-20240907","doi-asserted-by":"crossref","first-page":"R51","DOI":"10.1088\/0967-3334\/25\/5\/R01","article-title":"Cerebrospinal fluid dynamics","volume":"25","author":"Czosnyka","year":"2004","journal-title":"Physiol Meas"},{"key":"R12-5-20240907","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1212\/WNL.20.6.534","article-title":"A simple constant-infusion manometric test for measurement of CSF absorption. 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