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A mathematical model of blood, cerebrospinal fluid and brain dynamics

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Abstract

Using first principles of fluid and solid mechanics a comprehensive model of human intracranial dynamics is proposed. Blood, cerebrospinal fluid (CSF) and brain parenchyma as well as the spinal canal are included. The compartmental model predicts intracranial pressure gradients, blood and CSF flows and displacements in normal and pathological conditions like communicating hydrocephalus. The system of differential equations of first principles conservation balances is discretized and solved numerically. Fluid–solid interactions of the brain parenchyma with cerebral blood and CSF are calculated. The model provides the transitions from normal dynamics to the diseased state during the onset of communicating hydrocephalus. Predicted results were compared with physiological data from Cine phase-contrast magnetic resonance imaging to verify the dynamic model. Bolus injections into the CSF are simulated in the model and found to agree with clinical measurements.

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Abbreviations

cAr:

Carotid artery

Ar:

Arteries

Al:

Arterioles

Cp:

Capillaries

Vl:

Veinules

V:

Veins

vSinus:

Venous sinus

Lv:

Lateral ventricle

3V:

Third ventricle

4V:

Fourth ventricle

SAS:

Cranial subarachnoid space

sp.canal:

Spinal subarachnoid space

br:

Brain

exf:

Extracellular fluid

xxL,R :

Signifying two equations, one for the left brain hemisphere and one for the right brain hemisphere

xxR :

Right compartment

xxL :

Left compartment

\({{f}_{xx_{\rm in}}}\) :

Flow into the compartment

\({{f}_{xx_{\rm out}}}\) :

Flow out of the compartment

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Authors and Affiliations

  1. Laboratory for Product and Process Design (LPPD), Department of Bioengineering and Chemical Engineering, University of Illinois at Chicago, Chicago, USA

    Andreas A. Linninger, Michalis Xenos, Brian Sweetman & Sukruti Ponkshe

  2. Department of Bioengineering and Chemical Engineering, University of Illinois at Chicago, Science and Engineering Offices (SEO), Room 218 (M/C 063), 851 S Morgan St, Chicago, IL, 60607-7052, USA

    Andreas A. Linninger

  3. Department of Neurosurgery, University of Chicago, Chicago, USA

    Xiaodong Guo & Richard Penn

Authors
  1. Andreas A. Linninger
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  2. Michalis Xenos
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  3. Brian Sweetman
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  4. Sukruti Ponkshe
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  5. Xiaodong Guo
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  6. Richard Penn
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Correspondence to Andreas A. Linninger.

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Linninger, A.A., Xenos, M., Sweetman, B. et al. A mathematical model of blood, cerebrospinal fluid and brain dynamics. J. Math. Biol. 59, 729–759 (2009). https://doi.org/10.1007/s00285-009-0250-2

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  • DOI: https://doi.org/10.1007/s00285-009-0250-2

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