A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus

Justin Kauffman, Corina Stefania Drapaca

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

Hydrocephalus is a serious neurological disorder characterized by abnormalities in the cerebrospinal fluid (CSF) circulation, resulting in an excessive accumulation of CSF in the ventricles of the brain, brain compression and sometimes an increase in the intracranial pressure. It is believed that hydrocephalus may be caused by increased CSF production, or by obstruction of CSF circulation or of the venous outflow system. Therefore, the treatment is based on CSF flow diversion. Given that the response of patients who have been treated continues to be poor, there is an urgent need to design better therapy protocols for hydrocephalus. An important step in this direction is the development of predictive mathematical models that better explain the fundamental science behind this clinical condition. One of the first mathematical models of CSF pressure-volume compensation introduced by Marmarou in the 1970s provides a theoretical basis for studying hydrocephalus. However, the model fails to fully capture the complex CSF dynamics. In this paper we propose a generalization of Marmarou's model using fractional calculus. We use a modified Adomian decomposition method to solve analytically the proposed fractional order nonlinear differential equation. Our results show temporal multi-scaling behavior of the CSF dynamics.

Original languageEnglish (US)
Title of host publicationMechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics
Pages179-184
Number of pages6
DOIs
StatePublished - Jan 1 2014
Event2013 Annual Conference on Experimental and Applied Mechanics - Lombard, IL, United States
Duration: Jun 3 2013Jun 5 2013

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
Volume4
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Other

Other2013 Annual Conference on Experimental and Applied Mechanics
CountryUnited States
CityLombard, IL
Period6/3/136/5/13

Fingerprint

Cerebrospinal fluid
Fluid dynamics
Brain
Mathematical models
Flow of fluids
Differential equations
Decomposition

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Computational Mechanics
  • Mechanical Engineering

Cite this

Kauffman, J., & Drapaca, C. S. (2014). A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus. In Mechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics (pp. 179-184). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 4). https://doi.org/10.1007/978-3-319-00777-9_26
Kauffman, Justin ; Drapaca, Corina Stefania. / A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus. Mechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics. 2014. pp. 179-184 (Conference Proceedings of the Society for Experimental Mechanics Series).
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Kauffman, J & Drapaca, CS 2014, A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus. in Mechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics. Conference Proceedings of the Society for Experimental Mechanics Series, vol. 4, pp. 179-184, 2013 Annual Conference on Experimental and Applied Mechanics, Lombard, IL, United States, 6/3/13. https://doi.org/10.1007/978-3-319-00777-9_26

A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus. / Kauffman, Justin; Drapaca, Corina Stefania.

Mechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics. 2014. p. 179-184 (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 4).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Kauffman J, Drapaca CS. A fractional pressure-volume model of cerebrospinal fluid dynamics in hydrocephalus. In Mechanics of Biological Systems and Materials - Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics. 2014. p. 179-184. (Conference Proceedings of the Society for Experimental Mechanics Series). https://doi.org/10.1007/978-3-319-00777-9_26