Abstract
As brain ventricles lose their ability to regulate the cerebrospinal fluid (CSF) pressure, serious brain conditions collectively named hydrocephalus can appear. By modelling ventricular dynamics with the laws of physics, dynamical instabilities are evidenced, caused by either CSF transport dysregulations or abnormal properties of the elasticity of the ependyma. We show that these instabilities would lead, in most cases, to dilation of the ventricles, establishing a close connection to hydrocephalus, or in some other cases to a ventricular contraction as observed in the slit ventricle syndrome. Signs seem to indicate the possibility of phase transitions occurring as a result of these instabilities, which might have important clinical consequences, such as the inability to recover a healthy state. Even so, our dynamical approach could allow the development of a unified view of these complex intracranial conditions along with a classification that might be clinically relevant.
Similar content being viewed by others
References
Greitz, D.: Radiological assessment of hydrocephalus: new theories and implications for therapy. Neurosurg. Rev. 27, 145–165 (2004)
Balédent, O., et al.: Relationship between cerebrospinal fluid and blood dynamics in healthy volunteers and patients with communicating hydrocephalus. Invest. Radiol. 39(1), (2004)
Sweetman, B., Linninger, A.A.: Cerebrospinal fluid flow dynamics in the central nervous system. Ann. Biomed. Eng. 39(1), 484–96 (2011)
Mori, K.: Current concept of hydrocephalus: evolution of new classifications. Child’s Nerv. Syst. 11, 523–532 (1995)
Fin, L., Grebe, R.: Three dimensional modeling of the cerebrospinal fluid dynamics and brain interactions in the aqueduct of Sylvius. Comput. Methods Biomech. Biomed. Eng. 6(3), 163–70 (2003)
Milhorat, T.H.: Experimental hydrocephalus. A technique for producing obstructive hydrocephalus in the monkey. J. Neurosurg. 32, 385–389 (1970)
Hakim, S., Adams, R.D.: The special clinical problem of symptomatic hydrocephalus with normal cerebrospinal fluid pressure. J. Neurol. Sci. 2, 307–327 (1965)
Hakim, C.A., Hakim, R., Hakim, S.: Normal pressure hydrocephalus. Neurosurg. Clin. N. Am. 36(4), 761–772 (2001)
Marmarou, A., Schulman, K., LaMorgese, J.: Compartmental analysis of compliance and outflow resistance of cerebrospinal fluid system. J. Neurosurg. 43, 523–534 (1975)
Ambarki, K., et al.: A new lumped-parameter model of craniospinal hydrodynamics during cardiac cycle in healthy volunteers. IEEE Trans. Biomed. Eng. 54(3), 483–491 (2007)
Wirth, B.: A mathematical model for hydrocephalus. M.Sc. Thesis, University of Oxford (2005)
Nagashima, T., et al.: Biomechanics of hydrocephalus: a new theoretical model. Neurosurgery 21(6), 898–904 (1987)
Drake, J.M., et al.: Realistic simple mathematical model of brain biomechanics for computer simulation of hydrocephalus and other brain abnormalities. Can. J. Neurol. Sci. 23, S5 (1996)
Tenti, G., Sivaloganathan, S., Drake, J.M.: Brain biomechanics: Steady-state consolidation theory of hydrocephalus. Math. Q. 7(1), 111–124 (1999)
Bouzerar, R., et al.: Ventricular dilation as an instability of intracranial dynamics. Phys. Rev. E 72, 51912 (2005)
Takei, F., Hirano, A., Shapiro, K., Kohn, I.J.: New ultrastructural changes of the ependyma in experimental hydrocephalus. Acta Neuropathol. 73, 400–402 (1987)
Milhorat, T.H.: Choroid plexus and CSF production. Science 166, 1514–1516 (1969)
Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch., C 28, 693–703 (1973)
De Gennes, P.G.: Wetting: statics and dynamics. Rev. Mod. Phys. 57, 3 (1985)
Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Courses of Theoretical Physics, vol. 7. Pergamon, Oxford (1970)
David, F.: Geometry and field theory of random surfaces and membranes. In: Nelson, D., Piran, T., Weinberg, S. (eds.) Statistical Mechanics of Membranes and Surfaces. World Scientific, New York (2004)
Willmore, T.J.: Riemannian Geometry. Oxford Science, Oxford (1993)
Bryant, R.: A duality theorem for Willmore surfaces. J. Differ. Geom. 20, 23–53 (1984)
Jost, J.: Riemannian Geometry and Geometric Analysis. Springer, Berlin (2002)
Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Courses of Theoretical Physics, vol. 7. Pergamon, Oxford (1982)
Griffith, M.D., et al.: Pulsatile flow in stenotic geometries: flow behaviour and stability. J. Fluid Mech. 622, 291–320 (2009)
Womersley, J.R.: Method for the calculation of velocity, rate flow, and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127(3), 553–563 (1955)
Balédent, O., et al.: Brain hydrodynamics study by phase-contrast magnetic resonance imaging and transcranial color Doppler. J. Magn. Reson. Imaging 24(5), 995–1004 (2006)
Arfken, G.: Nonhomogeneous equation Green’s functions. In: Arfken, G. (ed.) Mathematical Methods for Physicists, 3rd ed. Academic, Orlando (1985)
Sourisse, A.: Propriétés spectrales de l’opérateur de Dirac avec un champ magnétique intense. Ph.D. Thesis, University of Nantes (2006)
Rekate, H.L.: The slit ventricle syndrome: advances based on technology and understanding. Pediatr. Neurosurg. 40, 259–263 (2004)
Aimedieu, P., Grebe, R.: Tensile strength of cranial pia mater: preliminary results. J. Neurosurg. 100(1), 11–114 (2004)
Sorek, S., Bear, J., Karni, Z.: Resistances and compliances of a compartmental model of the cerebrovascular system. Ann. Biomed. Eng. 17, 1–12 (1989)
Kratochvíl, A., Hrncír, E.: Correlations between the cerebrospinal fluid surface tension value and 1. Concentration of total proteins 2. Number of cell elements. Gen. Physiol. Biophys. 21, 47–53 (2002)
Czosnyka, M., et al.: Cerebrospinal fluid dynamics. Physiol. Meas. 25(5), R51–76 (2004)
Bergsneider, M., et al.: What we don’t (but should) know about hydrocephalus. J. Neurosurg. 104, 157–159 (2006)
Klein, O.: Hydrocéphalie. Mesure du débit de liquide cérébrospinal chez l’adulte hydrocéphale porteur d’une dérivation ventriculaire externe. Ph.D. Thesis, University of Nancy I (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bouzerar, R., Tekaya, I., Bouzerar, R. et al. Dynamics of hydrocephalus: a physical approach. J Biol Phys 38, 251–266 (2012). https://doi.org/10.1007/s10867-011-9239-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10867-011-9239-3