{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T03:21:49Z","timestamp":1772767309794,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T00:00:00Z","timestamp":1676505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2023R59"],"award-info":[{"award-number":["PNURSP2023R59"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The watery cerebrospinal fluid that flows in the subarachnoid space (SAS) surrounds the entire central nervous system via symmetrical thermo-solute flow. The significance of this study was to present a flexible simulation based on theoretical vivo inputs onto a mathematical framework to describe the interaction of cerebrospinal fluid circulation restricted to a pathological disorder. The pathophysiology disorder hydrocephalus is caused by an enormous excess of asymmetric fluid flow in the ventricular region. This fluid imposition increases the void space of its boundary wall (Pia mater). As a result, the dumping effect affects an inertial force in brain tissues. A mathematical model was developed to impose the thermal dynamics of hydrocephalus, in which solute transport constitutes the excess watery CSF fluid caused by hydrocephalus, in order to demonstrate perspective changes in ventricular spaces. This paper investigated brain porous spaces in order to strengthen the acceleration and thermal requirements in the CNS mechanism. To characterize neurological activities, a unique mathematical model that includes hydrodynamics and nutrient transport diffusivity was used. We present the analytical results based on physical experiments that use the novel Laplace method to determine the nutrients transported through permeable pia (brain) parenchyma with suitable pulsatile boundary conditions. This causes high CSF pressure and brain damage due to heat flux over the SAS boundary wall. As a result of the increased Schmidt number, the analysis of the hydrocephalus problem revealed an increase in permeability and drop in solute transport. A high-velocity profile caused a rise in thermal buoyancy (Grashof number). When the CSF velocity reached an extreme level, it indicated a higher Womersley number. Additionally, the present study compared a number of clinical studies for CSF amplitude and pressure. We validated the results by providing a decent justification with the clinical studies by appropriate field references.<\/jats:p>","DOI":"10.3390\/sym15020534","type":"journal-article","created":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T05:11:29Z","timestamp":1676524289000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Computational Modeling of Thermodynamical Pulsatile Flow with Uncertain Pressure in Hydrocephalus"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7451-693X","authenticated-orcid":false,"given":"Hemalatha","family":"Balasundaram","sequence":"first","affiliation":[{"name":"Vels Institute of Science, Technology and Advance Studies, Chennai 600117, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3283-4870","authenticated-orcid":false,"given":"Nazek","family":"Alessa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6435-2916","authenticated-orcid":false,"given":"Karuppusamy","family":"Loganathan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Vijayalakshmi","sequence":"additional","affiliation":[{"name":"Department of Science and Humanities, Karpagam Academy of Higher Education, Coimbatore 641021, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nayani Uday Ranjan","family":"Goud","sequence":"additional","affiliation":[{"name":"Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad 500043, Telangana, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1136\/jnnp.64.6.792","article-title":"Intracerebral temperature in patients with hydrocephalus of varying aetiology","volume":"64","author":"Hirashima","year":"1998","journal-title":"J. Neurol. Neurosurg. Psychiatry"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sathish, R., Qu, H., and Zakalik, K. (2015, January 1\u20134). Thermal measurement of cerebrospinal fluid flow rate in hydro-cephalus shunt. Proceedings of the 2015 IEEE SENSORS, Busan, Republic of Korea.","DOI":"10.1109\/ICSENS.2015.7370415"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1227\/NEU.0b013e3181fe2db6","article-title":"Anwar. Evaluation of the Shunt Check noninvasive thermal technique for shunt flow detection in hydro-cephalic patients","volume":"68","author":"Balasundaram","year":"2011","journal-title":"Neurosurgery"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"366","DOI":"10.3171\/ped.2005.103.4.0366","article-title":"Measurement of flow of cerebrospinal fluid in shunts by transcutaneous thermal convection","volume":"103","author":"Neff","year":"2005","journal-title":"J. Neurosurg. Pediatr."},{"key":"ref_5","first-page":"215","article-title":"Thermodynamic Approach to Cerebrospinal Fluid Circulation","volume":"1","author":"Herbowski","year":"2011","journal-title":"J. Neurol. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1007\/s11571-020-09637-y","article-title":"The thermodynamic brain and the evolution of intellect: The role of mental energy","volume":"14","year":"2020","journal-title":"Cogn. Neurodynamics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1186\/s13054-014-0693-8","article-title":"The thermodynamic brain","volume":"18","author":"Donnelly","year":"2014","journal-title":"Crit. Care"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1134\/S0021894417030026","article-title":"Numerical simulation of cerebrospinal fluid hydrodynamics in the healing process of hydrocephalus patients","volume":"58","author":"Gholampour","year":"2017","journal-title":"J. Appl. Mech. Tech. Phys."},{"key":"ref_9","unstructured":"Zakharov, M., and Sadovsky, M. (2013). The role of blood circulatory system in thermal regulation of animals explained by entropy production analysis. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Keong, N.C., Pena, A., Price, S.J., Czosnyka, M., Czosnyka, Z., De Vito, E.E., Housden, C.R., Sahakian, B.J., and Pickard, J.D. (2017). Diffusion tensor imaging profiles reveal specific neural tract distortion in normal pressure hydro-cephalus. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0181624"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.3171\/2014.12.JNS132352","article-title":"An update on research priorities in hydrocephalus: Overview of the third National Institutes of Health-sponsored symposium \u201cOpportunities for Hydrocephalus Research: Pathways to Better Outcomes\u201d","volume":"123","author":"McAllister","year":"2015","journal-title":"J. Neurosurg."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1017\/S0022112005005707","article-title":"A hydroelastic model of hydrocephalus","volume":"539","author":"Smillie","year":"2005","journal-title":"J. Fluid Mech."},{"key":"ref_13","first-page":"756","article-title":"Dynamics of lateral ventricle and cerebrospinal fluid in normal and hydrocephalic brains","volume":"24","author":"Zhu","year":"2006","journal-title":"J. Magn. Reson. Imaging Off. J. Int. Soc. Magn. Reson. Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2144","DOI":"10.1016\/j.jbiomech.2015.02.018","article-title":"CNS wide simulation of flow resistance and drug transport due to spinal microanatomy","volume":"48","author":"Tangen","year":"2015","journal-title":"J. Biomech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s42003-021-01920-w","article-title":"Boundary conditions investigation to improve computer simulation of cere-brospinal fluid dynamics in hydrocephalus patients","volume":"4","author":"Gholampour","year":"2021","journal-title":"Commun. Biol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Gholampour, S. (2018). FSI simulation of CSF hydrodynamic changes in a large population of non-communicating hydro-cephalus patients during treatment process with regard to their clinical symptoms. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0196216"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Balasundaram, H., Sathiamoorthy, S., Santra, S.S., Ali, R., Govindan, V., Dreglea, A., and Noeiaghdam, S. (2021). Effect of Ventricular Elasticity Due to Congenital Hydrocephalus. Symmetry, 13.","DOI":"10.3390\/sym13112087"},{"key":"ref_18","first-page":"399","article-title":"On inverting the Laplace transforms connected with the error function","volume":"7","author":"Hetnarski","year":"1964","journal-title":"Appl. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jocn.2016.09.012","article-title":"Evaluating the effect of hydrocephalus cause on the manner of changes in the effective parameters and clinical symptoms of the disease","volume":"35","author":"Gholampour","year":"2017","journal-title":"J. Clin. Neurosci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106049","DOI":"10.1016\/j.cmpb.2021.106049","article-title":"Hydrodynamic comparison of shunt and endoscopic third ventricu-lostomy in adult hydrocephalus using in vitro models and fluid-structure interaction simulation","volume":"204","author":"Seifollah","year":"2021","journal-title":"Comput. Methods Pro-Grams Biomed."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1146\/annurev-fluid-122414-034321","article-title":"Cerebrospinal Fluid Mechanics and Its Coupling to Cerebrovascular Dynamics","volume":"48","author":"Linninger","year":"2016","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1007\/s10439-010-0141-0","article-title":"Cerebrospinal Fluid Flow Dynamics in the Central Nervous System","volume":"39","author":"Sweetman","year":"2011","journal-title":"Ann. Biomed. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1097\/00004424-200103000-00003","article-title":"Cerebrospinal fluid flow waveforms: MR analysis in chronic adult hydrocephalus","volume":"36","author":"Baledent","year":"2001","journal-title":"Investig. Radiol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/j.jbiomech.2003.11.027","article-title":"Reassessment of brain elasticity for analysis of biomechanisms of hydrocephalus","volume":"37","author":"Taylor","year":"2004","journal-title":"J. Biomech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"054501","DOI":"10.1115\/1.4001025","article-title":"Computational Model of the Cerebral Ventricles in Hydrocephalus","volume":"132","author":"Cheng","year":"2010","journal-title":"J. Biomech. Eng."},{"key":"ref_26","first-page":"e137646","article-title":"TRPV4 antagonists ameliorate ventriculomegaly in a rat model of hydrocephalus","volume":"5","author":"Hochstetler","year":"2020","journal-title":"J. Clin. Investig."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1186\/1743-8454-7-5","article-title":"Cerebrospinal fluid pulse pressure amplitude during lumbar infusion in idiopathic normal pressure hydrocephalus can predict response to shunting","volume":"7","author":"Eide","year":"2010","journal-title":"Fluids Barriers CNS"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"105938","DOI":"10.1016\/j.cmpb.2021.105938","article-title":"Computerized biomechanical simulation of cerebrospinal fluid hydrodynamics: Challenges and opportunities","volume":"200","author":"Gholampour","year":"2021","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1016\/j.jbiomech.2013.03.008","article-title":"A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation","volume":"46","author":"Lefever","year":"2013","journal-title":"J. Biomech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e358","DOI":"10.1016\/j.wneu.2019.11.171","article-title":"Effect of Ambient Temperature Changes on Blood Flow in Anterior Cerebral Artery of Patients with Skull Prosthesis","volume":"135","author":"Taher","year":"2020","journal-title":"World Neurosurg."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1080\/10407782.2014.916101","article-title":"Investigation of Heat Transfer Enhancement in a Forward-Facing Contracting Channel Using FMWCNT Nanofluids","volume":"66","author":"Safaei","year":"2014","journal-title":"Numer. Heat Transf. Part A Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1093\/imammb\/dqr001","article-title":"Aging impact on brain biomechanics with applications to hydrocepha-lus","volume":"29","author":"Wilkie","year":"2012","journal-title":"Math. Med. Biol. A J. IMA"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2558","DOI":"10.1016\/j.jbiomech.2013.07.040","article-title":"Computational modelling of hydrocephalus","volume":"46","author":"Miller","year":"2013","journal-title":"J. Biomech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2250071","DOI":"10.1142\/S0219519422500713","article-title":"Mathematical modeling of thermo-solutal transport in pulsating flow in the hydrocephalus","volume":"22","author":"Balasundaram","year":"2022","journal-title":"J. Mech. Med. Biol."},{"key":"ref_35","first-page":"107209","article-title":"A mathematical framework for the dynamic interaction of pulsatile blood, brain, and cerebro-spinal fluid","volume":"2022","author":"Gholampour","year":"2022","journal-title":"Comput. Methods Programs Biomed."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:38:10Z","timestamp":1760121490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,16]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020534"],"URL":"https:\/\/doi.org\/10.3390\/sym15020534","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,16]]}}}