The driving force that causes enlargement of the ventricles remains unclear in case of normal pressure hydrocephalus (NPH). Both healthy and NPH brain conditions are characterized by a low transparenchymal pressure drop, typically 1 mm Hg. The present paper proposes an analytical model for normal and NPH brains using Darcy’s and Biot’s equations and simplifying the brain geometry to a hollow sphere with an internal and external radius. Self-consistent solutions for the large deformation problem that is associated with large ventricle dilation are presented and the notion of equilibrium or stable ventricle position is highlighted for both healthy and NPH conditions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and it is shown that both CSF seepage through the ependyma and parenchymal permeability play a key role. Although very simple, the present model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions.

References

References
1.
Shapiro
,
K.
,
Kohn
,
I. J.
,
Takei
,
F.
, and
Zee
,
C.
, 2009, “
Progressive Ventricular Enlargement in Cats in the Absence of Transmantle Pressure Gradients
,”
J. Neurosurg.
,
67
(
1
), pp.
88
92
.
2.
Stephensen
,
H.
,
Tisell
,
M.
, and
Wikkelsö
,
C.
, 2002, “
There is no Transmantle Pressure Gradient in Communicating or Noncommunicating Hydrocephalus
,”
Neurosurgery
,
50
(
4
), pp.
763
773
.
3.
Linninger
,
A. A.
,
Xenos
,
M.
,
Zhu
,
D. C.
,
Somayaji
,
M. R.
,
Kondapalli
,
S.
, and
Penn
,
R. D.
, 2007, “
Cerebrospinal Fluid Flow in the Normal and Hydrocephalic Human Brain
,”
IEEE Trans. Biomed. Eng.
54
(
2
), pp.
291
302
.
4.
Levine
,
D. N.
, 2008, “
Intracranial Pressure and Ventricular Expansion in Hydrocephalus: Have we Been Asking the Wrong Question?
J. Neurol. Sci.
,
269
(
1-2
), pp.
1
11
.
5.
Linninger
,
A.
,
Sweetman
,
B.
, and
Penn
,
R.
, 2009, “
Normal and Hydrocephalic Brain Dynamics: The Role of Reduced Cerebrospinal Fluid Reabsorption in Ventricular Enlargement
,”
Ann. Biomed. Eng.
,
37
(
7
), pp.
1434
1447
.
6.
Matsumoto
,
T.
,
Nagai
,
H.
,
Kasuga
,
Y.
, and
Kamiya
,
K.
, 1986, “
Changes in Intracranial Pressure (ICP) Pulse Wave Following Hydrocephalus
,”
Acta Neurochir.
,
82
(
1
), pp.
50
56
.
7.
Penn
,
R. D.
,
Lee
,
M. C.
,
Linninger
,
A. A.
,
Miesel
,
K.
,
Lu
,
S. N.
, and
Stylos
,
L.
, 2005, “
Pressure Gradients in the Brain in an Experimental Model of Hydrocephalus
,”
J. Neurosurg.
,
102
(
6
), pp.
1069
1075
.
8.
Penn
,
R. D.
, and
Linninger
,
A.
, 2009, “
The Physics of Hydrocephalus
,”
Pediatr. Neurosurg.
,
45
(
3
), pp.
161
174
.
9.
Børgesen
,
S. E.
, 1984, “
Conductance to Outflow of CSF in Normal Pressure Hydrocephalus
,”
Acta Neurochir.
,
71
(
1
), pp.
1
45
.
10.
Bateman
,
G. A.
, 2000, “
Vascular Compliance in Normal Pressure Hydrocephalus
,”
AJNR Am. J. Neuroradiol.
,
21
(
9
), pp.
1574
1585
.
11.
Tullberg
,
M.
,
Jensen
,
C.
,
Ekholm
,
S.
, and
Wikkelso
,
C.
, 2001, “
Normal Pressure Hydrocephalus: Vascular White Matter Changes on MR Images Must Not Exclude Patients from Shunt Surgery
,”
AJNR Am. J. Neuroradiol.
,
22
(
9
), pp.
1665
1673
.
12.
Sobey
,
I.
, and
Wirth
,
B.
, 2006, “
Effect of Non-Linear Permeability in a Spherically Symmetric Model of Hydrocephalus
,”
IMA J. Math Appl. Med. Biol.
,
23
(
4
), pp.
339
361
.
13.
Hamlat
,
A.
,
Adn
,
M.
,
Sid-ahmed
,
S.
,
Askar
,
B.
, and
Pasqualini
,
E.
, 2006, “
Theoretical Considerations on the Pathophysiology of Normal Pressure Hydrocephalus (NPH) and NPH-Related Dementia
,”
Med. Hypotheses
,
67
(
1
), pp.
115
123
.
14.
Nagashima
,
T.
,
Tamaki
,
N.
,
Matsumoto
,
S.
,
Horwitz
,
B.
, and
Seguchi
,
Y.
, 1987, “
Biomechanics of Hydrocephalus: A New Theoretical Model
,”
Neurosurgery
,
21
(
6
), pp.
898
904
.
15.
Levine
,
D.
, 1999, “
The Pathogenesis of Normal Pressure Hydrocephalus: A Theoretical Analysis
,”
Bull. Math. Biol.
,
61
(
5
), pp.
875
916
.
16.
Marmarou
,
A.
,
Shulman
,
K.
, and
LaMorgese
,
J.
, 1975, “
Compartmental Analysis of Compliance and Outflow Resistance of the Cerebrospinal Fluid System
,”
J. Neurosurg.
,
43
(
5
), pp.
523
534
.
17.
Linninger
,
A.
,
Xenos
,
M.
,
Sweetman
,
B.
,
Ponkshe
,
S.
,
Guo
,
X.
, and
Penn
,
R.
, 2009, “
A Mathematical Model of Blood, Cerebrospinal Fluid and Brain Dynamics
,”
J. Math. Biol.
,
59
(
6
), pp.
729
759
.
18.
Levine
,
D. N.
, 2000, “
Ventricular Size in Pseudotumor Cerebri and the Theory of Impaired CSF Absorption
,”
J. Neurol. Sci.
,
177
(
2
), pp.
85
94
.
19.
Franceschini
,
G.
,
Bigoni
,
D.
,
Regitnig
,
P.
, and
Holzapfel
,
G. A.
, 2006, “
Brain Tissue Deforms Similarly to Filled Elastomers and Follows Consolidation Theory
,”
J. Mech. Phys. Solids
,
54
(
12
), pp.
2592
2620
.
20.
Hopkins
,
L. N.
,
Bakay
,
L.
,
Kinkel
,
W. R.
, and
Grand
,
W.
, 1977, “
Demonstration of Transventricular CSF Absorption by Computerized Tomography
,”
Acta Neurochir.
,
39
(
3
), pp.
151
157
.
21.
Smillie
,
A.
,
Sobey
,
I.
, and
Molnar
,
Z.
, 2005, “
A Hydroelastic Model of Hydrocephalus
,”
J. Fluid Mech.
,
539
(
1
), pp.
417
443
.
22.
Momjian
,
S.
, and
Bichsel
,
D.
, 2006, “
Elastic and Poro-Elastic Models of Ventricular Dilatation in Hydrocephalus
,”
COMSOL Users Conference
, Grenoble.
23.
Shahim
,
K.
,
Drezet
,
J.-M.
,
Molinari
,
J.-F.
,
Sinkus
,
R.
, and
Momjian
,
S.
, 2010, “
Finite Element Analysis of Normal Pressure Hydrocephalus: Influence of CSF Content and Anisotropy in Permeability
,”
J. Appl. Biomater. Biomech.
,
7
(
3
), pp.
187
197
.
24.
Kaczmarek
,
M.
,
Subramaniam
,
R.
, and
Neff
,
S.
, 1997, “
The Hydromechanics of Hydrocephalus: Steady-State Solutions for Cylindrical Geometry
,”
Bull. Math. Biol.
,
59
(
2
), pp.
295
323
.
25.
Biot
,
M. A.
, 1941, “
General Theory of Three-Dimensional Consolidation
,”
J. Appl. Phys.
,
12
(
2
), pp.
155
164
.
26.
Hakim
,
S.
,
Venegas
,
J. G.
, and
Burton
,
J. D.
, 1976, “
The Physics of the Cranial Cavity, Hydrocephalus and Normal Pressure Hydrocephalus: Mechanical Interpretation and Mathematical Model
,”
Surg. Neurol.
,
5
(
3
), pp.
187
210
.
27.
Wirth
,
B.
, 2005, “
A Mathematical Model for Hydrocephalus
,” M.S. thesis, University of Oxford, St. Anne’s College, University of Oxford.
28.
Green
,
M. A.
,
Bilston
,
L. E.
, and
Sinkus
,
R.
, 2008, “
In vivo Brain Viscoelastic Properties Measured by Magnetic Resonance Elastography
,”
NMR Biomed.
,
21
(
7
), pp.
755
764
.
29.
Gideon
,
P.
,
Ståhlberg
,
F.
,
Thomsen
,
C.
,
Gjerris
,
F.
,
Sørensen
,
P. S.
, and
Henriksen
,
O.
, 1994, “
Cerebrospinal Fluid Flow and Production in Patients with Normal Pressure Hydrocephalus Studied by MRI
,”
Neuroradiology
,
36
(
3
), pp.
210
215
.
30.
Momjian
,
S.
,
Owler
,
B. K.
,
Czosnyka
,
Z.
,
Czosnyka
,
M.
,
Pena
,
A.
, and
Pickard
,
J. D.
, 2004, “
Pattern of White Matter Regional Cerebral Blood Flow and Autoregulation in Normal Pressure Hydrocephalus
,”
Brain
,
127
(
5
), pp.
965
972
.
31.
Silverberg
,
G. D.
,
Huhn
,
S.
,
Jaffe
,
R. A.
,
Chang
,
S. D.
,
Saul
,
T.
,
Heit
,
G.
,
Von Essen
,
A.
, and
Rubenstein
,
E.
, 2002, “
Downregulation of Cerebrospinal Fluid Production in Patients with Chronic Hydrocephalus
,”
J. Neurosurg.
,
97
(
6
), pp.
1271
1275
.
32.
Czosnyka
,
M.
,
Whitehouse
,
H.
,
Smielewski
,
P.
,
Simac
,
S.
, and
Pickard
,
J. D.
, 1996, “
Testing of Cerebrospinal Compensatory Reserve in Shunted and Non-Shunted Patients: A Guide to Interpretation Based on an Observational Study
,”
J. Neurol., Neurosurg. Psychiatry
,
60
, pp.
549
558
.
33.
May
,
C.
,
Kaye
,
J. A.
,
Atack
,
J. R.
,
Schapiro
,
M. B.
,
Friedland
,
R. P.
, and
Rapoport
,
S. I.
, 1990, “
Cerebrospinal Fluid Production is Reduced in Healthy Aging
,”
Neurology
,
40
(
1
), pp.
500
503
.
34.
Marlin
,
A. E.
,
Wald
,
A.
,
Hochwald
,
G. M.
, and
Malhan
,
C.
, 1978, “
Kaolin-Induced Hydrocephalus Impairs CSF Secretion by the Choroid Plexus
,”
Neurology
,
28
(
9
), pp.
945
949
.
35.
Dombrowski
,
S. M.
,
Schenk
,
S.
,
Leichliter
,
A.
,
Leibson
,
Z.
,
Fukamachi
,
K.
, and
Luciano
,
M. G.
, 2006, “
Chronic Hydrocephalus-Induced Changes in Cerebral Blood Flow: Mediation Through Cardiac Effects
,”
J. Cereb. Blood Flow Metab.
,
26
(
10
), pp.
1298
1310
.
36.
Klinge
,
P. M.
,
Samii
,
A.
,
Muhlendyck
,
A.
,
Visnyei
,
K.
,
Meyer
,
G.-J.
,
Walter
,
G. F.
,
Silverberg
,
G. D.
, and
Brinker
,
T.
, 2003, “
Cerebral Hypoperfusion and Delayed Hippocampal Response After Induction of Adult Kaolin Hydrocephalus
,”
Stroke
,
34
(
1
), pp.
193
199
.
37.
Boon
,
A. J. W.
,
Tans
,
J. T. J.
,
Delwel
,
E. J.
,
Egeler-Peerdeman
,
S. M.
,
Hanlo
,
P. W.
,
Wurzer
,
H. A. L.
, and
Hermans
,
J.
, 1999, “
Dutch Normal-Pressure Hydrocephalus Study: The Role of Cerebrovascular Disease
,”
J. Neurosurg.
,
90
(
2
), pp.
221
226
.
38.
Bradley
,
W.
, Jr.
,
Whittemore
,
A.
,
Watanabe
,
A.
,
Davis
,
S.
,
Teresi
,
L.
, and
Homyak
,
M.
, 1991, “
Association of Deep White Matter Infarction with Chronic Communicating Hydrocephalus: Implications Regarding the Possible Origin of Normal-Pressure Hydrocephalus
,”
AJNR Am. J. Neuroradiol.
,
12
(
1
), pp.
31
39
.
39.
Boon
,
A. J. W.
,
Tans
,
J. T. J.
,
Delwel
,
E. J.
,
Egeler-Peerdeman
,
S. M.
,
Hanlo
,
P. W.
,
Wurzer
,
H. A. L.
,
Avezaat
,
C. J. J.
,
de Jong
,
D. A.
,
Gooskens
,
R. H. J. M.
, and
Hermans
,
J.
, 1998, “
Dutch Normal-Pressure Hydrocephalus Study: Randomized Comparison of Low- and Medium-Pressure Shunts
,”
J. Neurosurg.
,
88
(
3
), pp.
490
495
.
40.
Silverberg
,
G. D.
, 2004, “
Normal Pressure Hydrocephalus (NPH): Ischaemia, CSF Stagnation or Both
,”
Brain
,
127
(
5
), pp.
947
948
.
41.
Naidich
,
T. P.
,
Epstein
,
F.
,
Lin
,
J. P.
,
Kricheff
,
I. I.
, and
Hochwald
,
G. M.
, 1976, “
Evaluation of Pediatric Hydrocephalus by Computed Tomography
,”
Radiology
,
119
(
2
), pp.
337
345
.
42.
Milhorat
,
T. H.
,
Clark
,
R. G.
,
Hammock
,
M. K.
, and
McGrath
,
P. P.
, 1970, “
Structural, Ultrastructural, and Permeability Changes in the Ependyma and Surrounding Brain Favoring Equilibration in Progressive Hydrocephalus
,”
Arch. Neurol.
,
22
(
5
), pp.
397
407
.
43.
Shulyakov
,
A. V.
,
Cenkowski
,
S. S.
,
Buist
,
R. J.
, and
Del Bigio
,
M. R.
, 2011, “
Age-Dependence of Intracranial Viscoelastic Properties in Living Rats
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
3
), pp.
484
497
.
44.
Welch
,
K.
, 1963, “
Secretion of Cerebrospinal Fluid by Choroid Plexus of the Rabbit
,”
Am. J. Physiol.
,
205
(
3
), pp.
617
624
.
45.
Del Bigio
,
M. R.
, 1995, “
The Ependyma: A Protective Barrier Between Brain and Cerebrospinal Fluid
,”
Glia
,
14
(
1
), pp.
1
13
.
46.
Dutta-Roy
,
T.
,
Wittek
,
A.
, and
Miller
,
K.
, 2008, “
Biomechanical Modelling of Normal Pressure Hydrocephalus
,”
J. Biomech.
,
41
(
10
), pp.
2263
2271
.
47.
Peña
,
A.
,
Harris
,
N.
,
Bolton
,
M.
,
Czosnyka
,
M.
, and
Pickard
,
J.
, 2002, “
Communicating Hydrocephalus: The Biomechanics of Progressive Ventricular Enlargement Revisited
,”
Acta Neurochir. Suppl. (Wien)
81
, pp.
59
63
.
You do not currently have access to this content.