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Cerebral water transport using multiple-network poroelastic theory: application to normal pressure hydrocephalus

Published online by Cambridge University Press:  16 November 2010

B. TULLY  and
Y. VENTIKOS
B. TULLY
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX3 7DQ, UK
Y. VENTIKOS*
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX3 7DQ, UK
*
†Email address for correspondence: yiannis.ventikos@eng.ox.ac.uk
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Abstract

The twenty-first century is bearing witness to a drastic change in population demographics and diseases of old age, such as dementia, are placing an unprecedented burden on the global healthcare system. Normal pressure hydrocephalus may be the only curable form of dementia, yet its pathophysiology is paradoxical and a consistent treatment currently remains elusive. A novel application of multiple-network poroelastic theory (MPET) is proposed to investigate water transport in the cerebral environment. Specifically, MPET is modified to allow a detailed investigation of spatio-temporal transport of fluid between the cerebral blood, cerebrospinal fluid (CSF) and brain parenchyma across scales. This framework thus allows an exploration of hypotheses defining the initiation and progression of both acute and chronic hydrocephalus. Results show that a breakdown in the transport mechanisms between the arterial vascular network and interstitial space within the parenchyma may be a cause of accumulation of CSF in the ventricles. Specifically, there must be an increase in the compliance of the arteriole/capillary network, which may combine with a breakdown in the blood–CSF barrier to allow an increased flow from the arteriole/capillary blood to the CSF. The results of this study should prove useful to guide experimental exploration in areas that warrant further investigation and validation.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Convection: Convection in porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 188 - 215
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Agre, P. 2006 The aquaporin water channels. Proc. Am. Thoracic Soc. 3 (1), 5–13.CrossRefGoogle ScholarPubMed
Agre, P., Nielsen, S. & Ottersen, O. P. 2004 Towards a molecular understanding of water homeostasis in the brain. Neuroscience 129 (4), 849–850.CrossRefGoogle ScholarPubMed
Aifantis, E. C. 1979 Continuum basis for diffusion in regions with multiple diffusivity. J. Appl. Phys. 50 (3), 1334–1338.CrossRefGoogle Scholar
Aifantis, E. C. 1980 On the problem of diffusion in solids. Acta Mechanica 37 (3–4), 265–296.CrossRefGoogle Scholar
Aifantis, E. C. & Hill, J. M. 1980 On the theory of diffusion in media with double diffusivity. Part i. Basic mathematical results. Q. J. Mech. Appl. Math. 33 (1), 1–21.CrossRefGoogle Scholar
Amiry-Moghaddam, M. & Ottersen, O. P. 2003 The molecular basis of water transport in the brain. Nature Rev. Neurosci. 4 (12), 991–1001.CrossRefGoogle ScholarPubMed
Anor, T., Grienberg, L., Madsen, J. R. & Karniadakis, G. E. 2009 Large-scale simulation of the human cranial arterial tree: utility in hydrocephalus. Cerebrospinal Fluid Res. 6, Suppl 1, S48.CrossRefGoogle Scholar
Bai, M., Elsworth, D. & Roegiers, J.-C. 1993 Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs. Water Resour. Res. 29 (6), 1621–1633.CrossRefGoogle Scholar
Balédent, O., Gondry-Jouet, C., Meyer, M.-E., De Marco, G., Le Gars, D., Henry-Feugeas, M.-C. & Idy-Peretti, I. 2004 Relationship between cerebrospinal fluid and blood dynamics in healthy volunteers and patients with communicating hydrocephalus. Invest. Radiol. 39 (1), 45–55.CrossRefGoogle ScholarPubMed
Bateman, G. A. 2000 Vascular compliance in normal pressure hydrocephalus. Am. J. Neuroradiol. 21 (9), 1574–1585.Google ScholarPubMed
Bateman, G. A. 2005 Extending the hydrodynamic hypothesis in chronic hydrocephalus. Neurosurg. Rev. 28 (4), 333–334.CrossRefGoogle ScholarPubMed
Bateman, G. A., Levi, C. R., Schofield, P., Wang, Y. & Lovett, E. C. 2008 The venous manifestations of pulse wave encephalopathy: windkessel dysfunction in normal aging and senile dementia. Neuroradiology 50 (6), 491–497.CrossRefGoogle ScholarPubMed
Bergsneider, M., Egnor, M. R., Johnston, M., Kranz, D., Madsen, J. R., McAllister, J. P., Stewart, C., Walker, M. L. & Williams, M. A. 2006 What we don't (but should) know about hydrocephalus. J. Neurosurg. 104 (3, Suppl.), 157–159.Google ScholarPubMed
Berryman, J. G. 2002 Extension of poroelastic analysis to double-porosity materials: new technique in microgeomechanics. J. Engng Mech. 128 (8), 840.Google Scholar
Biot, M. A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12 (2), 155–165.CrossRefGoogle Scholar
Biot, M. A. & Willis, D. G. 1957 The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601.CrossRefGoogle Scholar
Bradley, W. G. 2000 Normal pressure hydrocephalus: new concepts on etiology and diagnosis. Am. J. Neuroradiol. 21 (9), 1586–1590.Google ScholarPubMed
Bradley, W. G. 2008 Idiopathic normal pressure hydrocephalus: new findings and thoughts on etiology. Am. J. Neuroradiol. 29 (1), 1–3.CrossRefGoogle ScholarPubMed
Bradley, W. G., Bahl, G. & Alksne, J. F. 2006 Idiopathic normal pressure hydrocephalus may be a two hit disease: benign external hydrocephalus in infancy followed by deep white matter ischemia in late adulthood. J. Magn. Reson. Imaging 24 (4), 747–755.CrossRefGoogle ScholarPubMed
Bradley, W. G., Safar, F. G., Furtado, C., Hurtado, C., Ord, J. & Alksne, J. F. 2004 Increased intracranial volume: a clue to the etiology of idiopathic normal-pressure hydrocephalus? Am. J. Neuroradiol. 25 (9), 1479–1484.Google Scholar
Brodal, P. 2004 The Central Nervous System: Structure and Function, 3rd edn. Oxford University Press.Google Scholar
Byrd, C. 2006 Normal pressure hydrocephalus: dementia's hidden cause. Nurse Pract. 31 (7), 28–29, 31–35; quiz 36–37.
Carpenter, M. 1991 Core Text of Neuroanatomy. William and Wilkins.Google Scholar
Castejón, O. J. 2009 Blood–brain barrier ultrastructural alterations in human congenital hydrocephalus and Arnold–Chiari malformation. Folia Neuropathol./Assoc. Polish Neuropathol. Med. Res. Centre Polish Acad. Sci. 47 (1), 11–19.Google ScholarPubMed
Cheng, S. 2006 The role of brain tissue mechanical properties and cerebrospinal fluid flow in the biomechanics of the normal and hydrocephalic brain. PhD thesis, University of New South Wales, Sydney, Australia.Google Scholar
Clarke, M. J. & Meyer, F. B. 2007 The history of mathematical modeling in hydrocephalus. Neurosurg. Focus 22 (4), E3, 1–5.CrossRefGoogle ScholarPubMed
Clatz, O., Litrico, S., Delingette, H., Paquis, P. & Ayache, N. 2007 Dynamic model of communicating hydrocephalus for surgery simulation. IEEE Trans. Bio-Med. Engng 54 (4), 755–758.CrossRefGoogle ScholarPubMed
Corkill, R. G., Garnett, M. R., Blamire, A. M., Rajagopalan, B., Cadoux-Hudson, T. A. D. & Styles, P. 2003 Multi-modal MRI in normal pressure hydrocephalus identifies pre-operative haemodynamic and diffusion coefficient changes in normal appearing white matter correlating with surgical outcome. Clin. Neurol. Neurosurg. 105 (3), 193–202.CrossRefGoogle ScholarPubMed
Czosnyka, M., Czosnyka, Z., Momjian, S. & Pickard, J. D. 2004 Cerebrospinal fluid dynamics. Physiol. Meas. 25 (5), R51–R76.CrossRefGoogle ScholarPubMed
Del Bigio, Marc R. 2004 Cellular damage and prevention in childhood hydrocephalus. Brain Pathol. 14 (3), 317–24.CrossRefGoogle ScholarPubMed
Dombrowski, S., Crutchfield, K., Ligon, K., Becker, J. & Luciano, M. 2009 Evidence for CSF–vascular compliance coupling in normal pressure hydrocephalus. Cerebrospinal Fluid Res. 6, Suppl 1, S36.CrossRefGoogle Scholar
Drake, J. M., Kulkarni, A. V. & Kestle, J. 2009 Endoscopic third ventriculostomy versus ventriculoperitoneal shunt in pediatric patients: a decision analysis. Child's Nerv. Syst. 25 (4), 467–472.CrossRefGoogle ScholarPubMed
Drapaca, C. S., Tenti, G., Rohlf, K. & Sivaloganathan, S. 2006 A Quasi-linear viscoelastic constitutive equation for the Brain: application to hydrocephalus. J. Elast. 85 (1), 65–83.CrossRefGoogle Scholar
Egnor, M. R., Rosiello, A. & Zheng, L. 2001 A model of intracranial pulsations. Pediatr. Neurosurg. 35 (6), 284–298.CrossRefGoogle Scholar
Fard, P. J. M., Tajvidi, M. R. & Gharibzadeh, S. 2007 High-pressure hydrocephalus: a novel analytical modeling approach. J. Theor. Biol. 248 (3), 401–410.CrossRefGoogle ScholarPubMed
Gallia, G. L., Rigamonti, D. & Williams, M. A. 2006 The diagnosis and treatment of idiopathic normal pressure hydrocephalus. Nature Clin. Pract. Neurol. 2 (7), 375–381.CrossRefGoogle ScholarPubMed
Gevertz, J. L. & Torquato, S. 2008 A novel three-phase model of brain tissue microstructure. PLoS Comput. Biol. 4 (8), e1000152.CrossRefGoogle ScholarPubMed
Greitz, D. 2004 Radiological assessment of hydrocephalus: new theories and implications for therapy. Neurosurg. Rev. 27 (3), 145–165; discussion 166–167.CrossRefGoogle ScholarPubMed
Greitz, D. 2007 a Paradigm shift in hydrocephalus research in legacy of Dandy's pioneering work: rationale for third ventriculostomy in communicating hydrocephalus. Child's Nerv. Syst. 23 (5), 487–489.CrossRefGoogle ScholarPubMed
Greitz, D. 2007 b The bulk flow model cannot explain communicating hydrocephalus and must be replaced by a new concept. Child's Nerv. Syst. 23 (11), 1229–1231.CrossRefGoogle Scholar
Greitz, D., Wirestam, R., Franck, A., Nordell, B., Thomsen, C. & Ståhlberg, F. 1992 Pulsatile brain movement and associated hydrodynamics studied by magnetic resonance phase imaging. The Monro–Kellie doctrine revisited. Neuroradiology 34 (5), 370–380.CrossRefGoogle ScholarPubMed
Grinberg, L., Anor, T., Madsen, J. R., Yakhot, A. & Karniadakis, G. E. 2009 Large-scale simulation of the human arterial tree. Clin. Exp. Pharmacol. Physiol. 36 (2), 194–205.CrossRefGoogle ScholarPubMed
Hakim, S. 1971 Biomechanics of hydrocephalus. Acta Neurol. Latinoam. 1, Suppl. 1, 169–194.Google ScholarPubMed
Hakim, S. & Adams, R. D. 1965 The special clinical problem of symptomatic hydrocephalus with normal cerebrospinal fluid pressure. Observations on cerebrospinal fluid hydrodynamics. J. Neurol. Sci. 2 (4), 307–327.CrossRefGoogle ScholarPubMed
Hakim, S., Venegas, J. G. & Burton, J. D. 1976 The physics of the cranial cavity, hydrocephalus and normal pressure hydrocephalus: mechanical interpretation and mathematical model. Surg. Neurol. 5 (3), 187–210.Google ScholarPubMed
Hamlat, A., Abderrahmane, H., Sid-Ahmed, S., Seddik, S.-A., Adn, M., Mahmoudreza, A., Askar, B., Brahim, A., Pasqualini, E. & Edouardo, P. 2006 Idiopathic normal pressure hydrocephalus: theoretical concept of a spinal etiology. Med. Hypotheses 67 (1), 110–114.CrossRefGoogle ScholarPubMed
Hebb, A. O. & Cusimano, M. D. 2001 Idiopathic normal pressure hydrocephalus: a systematic review of diagnosis and outcome. Neurosurgery 49 (5), 1166–1184; discussion 1184–1186.Google ScholarPubMed
Jellinger, K. 1976 Neuropathological aspects of dementias resulting from abnormal blood and cerebrospinal fluid dynamics. Acta Neurol. Belgica 76 (2), 83–102.Google ScholarPubMed
Johanson, C., McMillan, P., Tavares, R., Spangenberger, A., Duncan, J., Silverberg, G. & Stopa, E. 2004 Homeostatic capabilities of the choroid plexus epithelium in Alzheimer's disease. Cerebrospinal Fluid Res. 1 (1), 3.CrossRefGoogle ScholarPubMed
Kaczmarek, M., Subramaniam, R. P. & Neff, S. R. 1997 The hydromechanics of hydrocephalus: steady-state solutions for cylindrical geometry. Bull. Math. Biol. 59 (2), 295–323.CrossRefGoogle ScholarPubMed
Kestle, J., Drake, J., Milner, R., Sainte-Rose, C., Cinalli, G., Boop, F., Piatt, J., Haines, S., Schiff, S., Cochrane, D., Steinbok, P. & MacNeil, N. 2000 Long-term follow-up data from the shunt design trial. Pediatr. Neurosurg. 33 (5), 230–236.CrossRefGoogle ScholarPubMed
Kruse, S. A., Rose, G. H., Glaser, K. J., Manduca, A., Felmlee, J. P., Jack, C. R. & Ehman, R. L. 2008 Magnetic resonance elastography of the brain. NeuroImage 39 (1), 231–237.CrossRefGoogle ScholarPubMed
Kurtcuoglu, V., Poulikakos, D. & Ventikos, Y. 2005 Computational modeling of the mechanical behavior of the cerebrospinal fluid system. J. Biomech. Engng 127 (2), 264–269.CrossRefGoogle Scholar
Lee, E., Wang, J. Z. & Mezrich, R. 1989 Variation of lateral ventricular volume during the cardiac cycle observed by MR imaging. Am. J. Neuroradiol. 10 (6), 1145–1149.Google ScholarPubMed
Levine, D. N. 1999 The pathogenesis of normal pressure hydrocephalus: a theoretical analysis. Bull. Math. Biol. 61 (5), 875–916.CrossRefGoogle ScholarPubMed
Levine, D. N. 2000 Ventricular size in pseudotumor cerebri and the theory of impaired CSF absorption. J. Neurol. Sci. 177 (2), 85–94.CrossRefGoogle ScholarPubMed
Levine, D. N. 2008 Intracranial pressure and ventricular expansion in hydrocephalus: have we been asking the wrong question? J. Neurol. Sci. 269 (1–2), 1–11.CrossRefGoogle ScholarPubMed
Linninger, A. A., Sweetman, B. & Penn, R. 2009 Normal and hydrocephalic brain dynamics: the role of reduced cerebrospinal fluid reabsorption in ventricular enlargement. Ann. Biomed. Engng 37 (7), 1434–1447.CrossRefGoogle ScholarPubMed
Linninger, A. A., Xenos, M., Zhu, D. C., Somayaji, M. R., Kondapalli, S. & Penn, R. D. 2007 Cerebrospinal fluid flow in the normal and hydrocephalic human brain. IEEE Trans. Bio-Med. Engng 54 (2), 291–302.CrossRefGoogle ScholarPubMed
Malm, J. & Eklund, A. 2006 Idiopathic normal pressure hydrocephalus. Pract. Neurol. 6 (1), 14–27.CrossRefGoogle Scholar
McAllister, J. P. & Chovan, P. 1998 Neonatal hydrocephalus. Mechanisms and consequences. Neurosurg. Clinics North Am. 9 (1), 73–93.CrossRefGoogle ScholarPubMed
McComb, J. G., Bradley, W. G., Safar, F. G., Furtado, C., Hurtado, C., Ord, J. & Alksne, J. F. 2004 Is a large hat size hazardous to your health? Am. J. Neuroradiol. 25 (9), 1454–1455; author reply 1455.Google ScholarPubMed
Miller, K., Taylor, Z. & Wittek, A. 2006 Mathematical models of brain deformation behaviour for computer-integrated neurosurgery.Google Scholar
Monro, A., Creech, W., Donaldson, T., Cameron, G., Elmsley, P., Fyfe, A., Longman, T. & Murray, J. 1783 Observations on the Structure and Functions of the Nervous System: Illustrated with Tables. William Creech; and Joseph Johnson.Google Scholar
Oakes, W. J. 2005 Shunts in Africa. J. Neurosurg. 102 (4), Suppl, 357; discussion 357.Google ScholarPubMed
Otahal, J., Stepanik, Z., Kaczmarska, A., Marsik, F., Broz, Z. & Otahal, S. 2007 Simulation of cerebrospinal fluid transport. Adv. Engng Softw. 38 (11–12), 802–809.CrossRefGoogle Scholar
Owler, B. K. & Pickard, J. D. 2001 Normal pressure hydrocephalus and cerebral blood flow: a review. Acta Neurol. Scand. 104 (6), 325–342.CrossRefGoogle ScholarPubMed
Patwardhan, R. V. & Nanda, A. 2005 Implanted ventricular shunts in the United States: the billion-dollar-a-year cost of hydrocephalus treatment. Neurosurgery 56 (1), 139–144; discussion 144–145.CrossRefGoogle ScholarPubMed
Penn, R. D., Lee, M. C., Linninger, A. A., Miesel, K., Lu, S. N. & Stylos, L. 2005 Pressure gradients in the brain in an experimental model of hydrocephalus. J. Neurosurg. 102 (6), 1069–1075.CrossRefGoogle Scholar
Raleigh, V. S. 1999 World population and health in transition. BMJ 319 (7215), 981–984.CrossRefGoogle ScholarPubMed
Rekate, H. L. 2008 The definition and classification of hydrocephalus: a personal recommendation to stimulate debate. Cerebrospinal Fluid Res. 5, 2.CrossRefGoogle ScholarPubMed
Rubenstein, E. 1998 Relationship of senescence of cerebrospinal fluid circulatory system to dementias of the aged. Lancet 351 (9098), 283–285.CrossRefGoogle ScholarPubMed
Sack, I., Beierbach, B., Hamhaber, U., Klatt, D. & Braun, J. 2008 Non-invasive measurement of brain viscoelasticity using magnetic resonance elastography. NMR Biomed. 21 (3), 265–271.CrossRefGoogle ScholarPubMed
Sack, I., Beierbach, B., Wuerfel, J., Klatt, D., Hamhaber, U., Papazoglou, S., Martus, P. & Braun, J. 2009 The impact of aging and gender on brain viscoelasticity. NeuroImage 46 (3), 652–657.CrossRefGoogle ScholarPubMed
Sada, Y., Moriki, T., Kuwahara, S., Yamane, T. & Hara, H. 1994 Immunohistochemical study on blood–brain barrier in congenitally hydrocephalic HTX rat brain. Zentralbl. Pathol. 140 (4–5), 289–298.Google Scholar
Sato, O. 1994 Consensus: nosographic identification. Child's Nerv. Syst. 10 (3), 167–171.CrossRefGoogle ScholarPubMed
Seyfert, S., Becher, A., Ohring, R. & Faulstich, A. 2004 The permeability of the blood–CSF barrier in hydrocephalus, polyradiculitis, and meningitis. J. Neurol. 251 (3), 355–356.CrossRefGoogle ScholarPubMed
Seyfert, S. & Faulstich, A. 2003 Is the blood–CSF barrier altered in disease? Acta Neurol. Scand. 108 (4), 252–256.CrossRefGoogle ScholarPubMed
da Silva, M. C., Michowicz, S., Drake, J. M., Chumas, P. D. & Tuor, U. I. 1995 Reduced local cerebral blood flow in periventricular white matter in experimental neonatal hydrocephalus-restoration with CSF shunting. J. Cereb. Blood Flow Metab. 15 (6), 1057–1065.CrossRefGoogle ScholarPubMed
Silverberg, G. D., Heit, G., Huhn, S., Jaffe, R. A., Chang, S. D., Bronte-Stewart, H., Rubenstein, E., Possin, K. & Saul, T. A. 2001 The cerebrospinal fluid production rate is reduced in dementia of the Alzheimer's type. Neurology 57 (10), 1763–1766.CrossRefGoogle ScholarPubMed
Silverberg, G. D., Mayo, M., Saul, T., Rubenstein, E. & McGuire, D. 2003 Alzheimer's disease, normal-pressure hydrocephalus, and senescent changes in CSF circulatory physiology: a hypothesis. Lancet Neurol. 2 (8), 506–511.CrossRefGoogle ScholarPubMed
Sivaloganathan, S. 2005 Biomechanics of the brain: a theoretical and numerical study of Biot's equations of consolidation theory with deformation-dependent permeability. Intl J. Non-Linear Mech. 40 (9), 1149–1159.CrossRefGoogle Scholar
Sivaloganathan, S., Stastna, M., Tenti, G. & Drake, J. 2005 A viscoelastic approach to the modelling of hydrocephalus. Appl. Math. Comput. 163 (3), 1097–1107.Google Scholar
Smillie, A., Sobey, I. & Molnar, Z. 2005 A hydroelastic model of hydrocephalus. J. Fluid Mech. 539, 417–443.CrossRefGoogle Scholar
Sobey, I. & Wirth, B. 2006 Effect of non-linear permeability in a spherically symmetric model of hydrocephalus. Math. Med. Biol. 23 (4), 339–361.CrossRefGoogle Scholar
Stein, S. C., Burnett, M. G. & Sonnad, S. S. 2006 Shunts in normal-pressure hydrocephalus: do we place too many or too few? J. Neurosurg. 105 (6), 815–822.CrossRefGoogle ScholarPubMed
Stephensen, H., Tisell, M. & Wikkelsö, C. 2002 There is no transmantle pressure gradient in communicating or noncommunicating hydrocephalus. Neurosurgery 50 (4), 763–771; discussion 771–773.CrossRefGoogle ScholarPubMed
Stoquart-ElSankari, S., Balédent, O., Gondry-Jouet, C., Makki, M., Godefroy, O. & Meyer, M.-E. 2007 Aging effects on cerebral blood and cerebrospinal fluid flows. J. Cerebr. Blood Flow Metab. 27 (9), 1563–1572.CrossRefGoogle ScholarPubMed
Stoquart-Elsankari, S., Lehmann, P., Villette, A., Czosnyka, M., Meyer, M.-E., Deramond, H. & Balédent, O. 2009 A phase-contrast MRI study of physiologic cerebral venous flow. J. Cerebr. Blood Flow Metab. 29 (6), 1208–1215.CrossRefGoogle ScholarPubMed
Terzaghi, K. 1943 Theoretical Soil Mechanics. John Wiley and Sons.CrossRefGoogle Scholar
Tisell, M., Tullberg, M., Månsson, J.-E., Fredman, P., Blennow, K. & Wikkelsø, C. 2004 Differences in cerebrospinal fluid dynamics do not affect the levels of biochemical markers in ventricular CSF from patients with aqueductal stenosis and idiopathic normal pressure hydrocephalus. Eur. J. Neurol. 11 (1), 17–23.CrossRefGoogle Scholar
Tuli, S., Alshail, E. & Drake, J. 1999 Third ventriculostomy versus cerebrospinal fluid shunt as a first procedure in pediatric hydrocephalus. Pediatr. Neurosurg. 30 (1), 11–15.CrossRefGoogle ScholarPubMed
Tully, B. & Ventikos, Y. 2009 Coupling poroelasticity and CFD for cerebrospinal fluid hydrodynamics. IEEE Trans. Bio-Med. Engng 56 (6), 1644–1651.CrossRefGoogle ScholarPubMed
Williams, H. 2008 The venous hypothesis of hydrocephalus. Med. Hypotheses 70 (4), 743–747.CrossRefGoogle ScholarPubMed
Winkler, F., Gschwendtner, A., Theisen, D., Peraud, A. & Straube, A. 2007 Reversible dementia and corresponding CSF alterations due to intraspinal lumbosacral metastasis of a prostate carcinoma. Eur. J. Neurol. 14 (12), 1400–1402.CrossRefGoogle ScholarPubMed
Wirth, B. & Sobey, I. 2006 An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus. Math. Med. Biol. 23 (4), 363–388.CrossRefGoogle ScholarPubMed
Wirth, B. & Sobey, I. 2009 Analytic solution during an infusion test of the linear unsteady poroelastic equations in a spherically symmetric model of the brain. Math. Med. Biol. 26 (1), 25–61.CrossRefGoogle Scholar
Woodworth, G. F., McGirt, M. J., Williams, M. A. & Rigamonti, D. 2009 Cerebrospinal fluid drainage and dynamics in the diagnosis of normal pressure hydrocephalus. Neurosurgery 64 (5), 919–925; discussion 925–926.CrossRefGoogle ScholarPubMed
Zienkiewicz, O. C. 1982 Basic formulation of static and dynamic behaviours of soil and other porous media. Appl. Math. Mech. 3 (4), 457–468.CrossRefGoogle Scholar
Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Paul, D. K. & Shiomi, T. 1990 Static and dynamic behaviour of soils: a rational approach to quantitative solutions. Part I. Fully saturated problems. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. (1934–1990) 429 (1877), 285–309.Google Scholar
Zienkiewicz, O. C. & Shiomi, T. 1984 Dynamic behaviour of saturated porous media; the generalized Biot formulation and its numerical solution. Intl J. Numer. Anal. Methods Geomech. 8 (1), 71–96.CrossRefGoogle Scholar