Traumatic brain injury remains a significant global health concern, requiring advanced understanding and mitigation strategies. In current brain concussion research, there is a significant knowledge gap: the critical role of transient cerebrospinal fluid (CSF) flow in the porous subarachnoid space (SAS) has long been overlooked. To address this limitation, we are developing a simplified mathematical model to investigate the CSF pressurization in the porous arachnoid trabeculae and the resulting motion of brain matter when the head is exposed to a translational impact. The model simplifies the head into an inner solid object (brain) and an outer rigid shell (skull) with a thin, porous fluid gap (SAS). The CSF flow in the impact side (coup region) and the opposite side (contrecoup region) is modeled as porous squeezing and expanding flows, respectively. The flow through the side regions, which connect these regions, is governed by Darcy's law. We found that the porous arachnoid trabeculae network significantly dampens brain motion and reduces pressure variations within the SAS compared to a SAS without the porous arachnoid trabeculae (AT). This effect is particularly pronounced under high-frequency, periodic acceleration impacts, thereby lowering the risk of injury. The dampening effect can be attributed to the low permeability of the AT, which increases resistance to fluid movement and stabilizes the fluid and pressure responses within the SAS, thereby reducing extreme pressure fluctuations and brain displacement under impact. This work provides a foundational understanding of CSF flow dynamics, paving the way for innovative approaches to brain injury prevention and management.
REFERENCES
1.
Centers for Disease Control and Prevention
, “
Sports-related recurrent brain injuries—United States
,” Morb. Mortal. Wkly. Rep.
46
, 224
(1997
).2.
D. J.
Thurman
,
C. M.
Branche
, and
J. E.
Sniezek
, “
The epidemiology of sports-related traumatic brain injuries in the United States: Recent developments
,” J. Head Trauma Rehabil.
13
, 1
(1998
).3.
J.
Lang
,
R.
Nathan
, and
Q.
Wu
, “
How to deform an egg yolk? On the study of soft matter deformation in a liquid environment
,” Phys. Fluids
33
, 011903
(2021
).4.
S. H.
Rauchman
,
A.
Zubair
,
B.
Jacob
,
D.
Rauchman
,
A.
Pinkhasov
,
D. G.
Placantonakis
, and
A. B.
Reiss
, “
Traumatic brain injury: Mechanisms, manifestations, and visual sequelae
,” Front. Neurosci.
17
, 1
(2023
).5.
M.
Faul
,
L.
Xu
,
M. M.
Wald
, and
V. G.
Coronado
, “
Traumatic brain injury in the United States; Emergency department visits, hospitalizations, and deaths, 2002–2006
” (
Centers for Disease Control and Prevention National Center for Injury Prevention and Control
, 2010
).6.
M. W.
Collins
,
G. L.
Iverson
,
M. R.
Lovell
,
D. B.
McKeag
,
J.
Norwig
, and
J.
Maroon
, “
On-field predictors of neuropsychological and symptom deficit following sports-related concussion
,” Clin. J. Sport Med.
13
, 222
(2003
).7.
J. A.
Langlois
,
W.
Rutland-Brown
, and
M. M.
Wald
, “
The epidemiology and impact of traumatic brain injury: A brief overview
,” J. Head Trauma Rehabil.
21
, 375
(2006
).8.
M. R.
Schulz
,
S. W.
Marshall
,
F. O.
Mueller
,
J.
Yang
,
N. L.
Weaver
,
W. D.
Kalsbeek
, and
J. M.
Bowling
, “
Incidence and risk factors for concussion in high school athletes, North Carolina, 1996–1999
,” Am. J. Epidemiol.
160
, 937
(2004
).9.
H. S.
Levin
and
R. R.
Diaz-Arrastia
, “
Diagnosis, prognosis, and clinical management of mild traumatic brain injury
,” Lancet Neurol.
14
, 506
(2015
).10.
V.
Pavlov
,
P.
Thompson-Leduc
,
L.
Zimmer
,
J.
Wen
,
J.
Shea
,
H.
Beyhaghi
,
S.
Toback
,
N.
Kirson
, and
M.
Miller
, “
Mild traumatic brain injury in the United States: Demographics, brain imaging procedures, health-care utilization and costs
,” Brain Inj.
33
, 1151
(2019
).11.
P.
McMahon
et al, “
Symptomatology and functional outcome in mild traumatic brain injury: Results from the prospective TRACK-TBI study
,” J. Neurotrauma
31
, 26
(2014
).12.
L.
Ganti
,
T.
Stead
,
Y.
Daneshvar
,
A. N.
Bodhit
,
C.
Pulvino
,
S. W.
Ayala
, and
K. R.
Peters
, “
GCS 15: When mild TBI isn't so mild
,” Neurol. Res. Pract.
1
, 6
(2019
).13.
P.
Saboori
and
A.
Sadegh
, “
Material modeling of the head's subarachnoid space
,” Sci. Iran.
18
, 1492
(2011
).14.
M.
Sotudeh Chafi
,
G.
Karami
, and
M.
Ziejewski
, “
Simulation of blast-head interactions to study traumatic brain injury
,” in Volume 2: Biomedical and Biotechnology Engineering
(
ASME
, 2007
), pp. 211
–220
.15.
W. C.
Moss
,
M. J.
King
, and
E. G.
Blackman
, “
Skull flexure from blast waves: A mechanism for brain injury with implications for helmet design
,” Phys. Rev. Lett.
103
, 108702
(2009
).16.
N.
Benko
,
E.
Luke
,
Y.
Alsanea
, and
B.
Coats
, “
Mechanical characterization of the human pia-arachnoid complex
,” J. Mech. Behav. Biomed. Mater.
120
, 104579
(2021
).17.
G.
Fabris
,
Z. M.
Suar
, and
M.
Kurt
, “
Micromechanical heterogeneity of the rat pia-arachnoid complex
,” Acta Biomater.
100
, 29
(2019
).18.
N.
Benko
,
E.
Luke
,
Y.
Alsanea
, and
B.
Coats
, “
Spatial distribution of human arachnoid trabeculae
,” J. Anat.
237
, 275
(2020
).19.
H. E.
Killer
,
H. R.
Laeng
,
J.
Flammer
, and
P.
Groscurth
, “
Architecture of arachnoid trabeculae, pillars, and septa in the subarachnoid space of the human optic nerve: Anatomy and clinical considerations
,” Br. J. Ophthalmol.
87
, 777
(2003
).20.
S.
Gupta
,
M.
Soellinger
,
D. M.
Grzybowski
,
P.
Boesiger
,
J.
Biddiscombe
,
D.
Poulikakos
, and
V.
Kurtcuoglu
, “
Cerebrospinal fluid dynamics in the human cranial subarachnoid space: An overlooked mediator of cerebral disease. I. Computational model
,” J. R Soc. Interface
7
, 1195
(2010
).21.
M.
Olczak
,
ŁA.
Poniatowski
,
A.
Siwińska
, and
M.
Kwiatkowska
, “
Post-mortem detection of neuronal and astroglial biochemical markers in serum and urine for diagnostics of traumatic brain injury
,” Int. J. Legal Med.
137
, 1441
(2023
).22.
M. R.
Grovola
,
C.
von Reyn
,
D. J.
Loane
, and
D. K.
Cullen
, “
Understanding microglial responses in large animal models of traumatic brain injury: An underutilized resource for preclinical and translational research
,” J. Neuroinflammation
20
, 67
(2023
).23.
J.
Lang
,
R.
Nathan
,
D.
Zhou
,
X.
Zhang
,
B.
Li
, and
Q.
Wu
, “
Cavitation causes brain injury
,” Phys. Fluids
33
, 031908
(2021
).24.
A.
Koster
and
A.
Adnan
, “
Dynamic similitude of human head surrogates
,” Multiscale Sci. Eng.
6
, 179
(2024
).25.
Y.
Li
,
P.
Vakiel
,
K.
Adanty
,
S.
Ouellet
,
A. H.
Vette
,
D.
Raboud
, and
C. R.
Dennison
, “
Influence of surrogate scalp material and thickness on head impact responses: Toward a biofidelic head-brain physical model
,” J. Mech. Behav. Biomed. Mater.
142
, 105859
(2023
).26.
S. O.
Linge
,
V.
Haughton
,
A. E.
Løvgren
,
K. A.
Mardal
, and
H. P.
Langtangen
, “
CSF flow dynamics at the craniovertebral junction studied with an idealized model of the subarachnoid space and computational flow analysis
,” Am. J. Neuroradiol.
31
, 185
(2010
).27.
U.
Kertzscher
,
T.
Schneider
,
L.
Goubergrits
,
K.
Affeld
,
D.
Hänggi
, and
A.
Spuler
, “
In vitro study of cerebrospinal fluid dynamics in a shaken basal cistern after experimental subarachnoid hemorrhage
,” PLoS One
7
, e41677
(2012
).28.
P. L. H.
Chong
,
D.
Garic
,
M. D.
Shen
,
I.
Lundgaard
, and
A. J.
Schwichtenberg
, “
Sleep, cerebrospinal fluid, and the glymphatic system: A systematic review, sleep
” Med. Rev.
61
, 101572
(2022
).29.
J.
Lang
,
S.
Santhanam
, and
Q.
Wu
, “
Exact and approximate solutions for transient squeezing flow
,” Phys. Fluids
29
, 103606
(2017
).30.
J.
Lang
,
L.
Wang
, and
Q.
Wu
, “
Theoretical study of oscillating squeezing flow through a porous medium
,” Tribol. Int.
162
, 107110
(2021
).31.
J.
Lang
,
R.
Nathan
, and
Q.
Wu
, “
Theoretical and experimental study of transient squeezing flow in a highly porous film
,” Tribol. Int.
135
, 259
(2019
).32.
J.
Stefan
, “
Versuche über die scheinbare adhäsion
,” Ann. Phys.
230
, 316
(1875
).33.
P. J.
Leider
and
R. B.
Bird
, “
Squeezing flow between parallel disks. I. Theoretical analysis
,” Ind. Eng. Chem. Fundam.
13
, 336
(1974
).34.
H. M.
Laun
,
M.
Rady
, and
O.
Hassager
, “
Analytical Solutions for Squeeze Flow with Partial Wall Slip
,” J. Nonnewton. Fluid Mech.
81
, 1
(1999
).35.
R.
Scheidl
and
C.
Gradl
, “
An approximate computational method for the fluid stiction problem of two separating parallel plates with cavitation
,” J. Fluids Eng.
138
, 61301
(2016
).36.
D. B.
Roemer
,
P.
Johansen
,
H. C.
Pedersen
, and
T. O.
Andersen
, “
Fluid stiction modeling for quickly separating plates considering the liquid tensile strength
,” J. Fluids Eng.
137
, 61205
(2015
).37.
J. L.
Livesey
, “
Inertia effects in viscous flows
,” Int. J. Mech. Sci.
1
, 84
(1960
).38.
J. D.
Jackson
, “
A study of squeezing flow
,” Appl. Sci. Res. Sect. A
11
, 148
(1963
).39.
C. J.
Lawrence
,
Y.
Kuang
, and
S.
Weinbaum
, “
The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solutions
,” J. Fluid Mech.
156
, 479
(1985
).40.
S.
Weinbaum
,
C. J.
Lawrence
, and
Y.
Kuang
, “
The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytic solutions; inviscid and small-but finite-Reynolds-number limits
,” J. Fluid Mech.
156
, 463
(1985
).41.
J.
Lang
,
R.
Nathan
, and
Q.
Wu
, “
Experimental study of transient squeezing film flow
,” J. Fluids Eng.
141
, 081110
(2019
).42.
C.-Y.
Wang
, “
The squeezing of a fluid between two plates
,” J. Appl. Mech.
43
, 579
(1976
).43.
E. A.
Moss
,
A.
Krassnokutski
,
B. W.
Skews
, and
R. T.
Paton
, “
Highly transient squeeze-film flows
,” J. Fluid Mech.
671
, 384
(2011
).44.
T.
Hayat
,
A.
Qayyum
, and
A.
Alsaedi
, “
MHD Unsteady Squeezing Flow over a Porous Stretching Plate
,” Eur. Phys. J. Plus
128
, 157
(2013
).45.
S.
Ishizawa
, “
The unsteady laminar flow between two parallel discs with arbitrarily varying gap width
,” Bull. JSME
9
, 533
(1966
).46.
S.-M.
Yang
and
L. G.
Leal
, “
Thin fluid film squeezed with inertia between two parallel plane surfaces
,” J. Tribol.
115
, 632
(1993
).47.
J.
Lang
and
Q.
Wu
, “
Modeling of the transient cerebrospinal fluid flow under external impacts
,” Eur. J. Mech. - B/Fluids
87
, 171
(2021
).48.
A. I.
King
,
J. S.
Ruan
,
C.
Zhou
,
W. N.
Hardy
, and
T. B.
Khalil
, “
Recent advances in biomechanics of brain injury research: A review
,” J. Neurotrauma
12
, 651
(1995
).49.
W. N.
Hardy
,
C. D.
Foster
,
A. I.
King
, and
S.
Tashman
, “
Investigation of brain injury kinematics: Introduction of a new technique
,” ASME Appl. Mech. Div.
225
, 241
(1997
).50.
P.
Saboori
,
C.
Germanier
, and
A.
Sadegh
, “
Mechanics of CSF Flow through trabecular architecture in the brain
,” in 26th Southern Biomedical Engineering Conference SBEC 2010, April 30-May 2, 2010
,
College Park, Maryland
(
Springer
, 2010
), pp. 440
–443
.51.
G. A.
Ateshian
, “
The role of interstitial fluid pressurization in articular cartilage lubrication
,” J. Biomech.
42
, 1163
(2009
).52.
Q.
Wu
,
Y.
Andreopoulos
,
S.
Xanthos
, and
S.
Weinbaum
, “
Dynamic compression of highly compressible porous media with application to snow compaction
,” J. Fluid Mech.
542
, 281
(2005
).53.
Q.
Wu
,
S.
Santhanam
,
R.
Nathan
, and
Q.
Wang
, “
A biphasic approach for the study of lift generation in soft porous media
,” Phys. Fluids
29
, 043602
(2017
).54.
Q.
Wu
,
Y.
Igci
,
Y.
Andreopoulos
, and
S.
Weinbaum
, “
Lift mechanics of downhill skiing and snowboarding
,” Med. Sci. Sports Exerc.
38
, 1132
(2006
).55.
T.
Gacka
,
Z.
Zhu
,
R.
Crawford
,
R.
Nathan
, and
Q.
Wu
, “
From red cells to soft lubrication, an experimental study of lift generation inside a compressible porous layer
,” J. Fluid Mech.
818
, 5
(2017
).56.
Z.
Zhu
,
R.
Nathan
, and
Q.
Wu
, “
An experimental study of the lubrication theory for highly compressible porous media, with and without lateral leakage
,” Tribol. Int.
127
, 324
(2018
).57.
J.
Feng
and
S.
Weinbaum
, “
Lubrication theory in highly compressible porous media: The mechanics of skiing, from red cells to humans
,” J. Fluid Mech.
422
, 281
(2000
).58.
Q.
Wu
,
Y.
Andreopoulos
, and
S.
Weinbaum
, “
From red cells to snowboarding: A new concept for a train track
,” Phys. Rev. Lett.
93
, 194501
(2004
).59.
Q.
Wu
,
Y.
Andreopoulos
, and
S.
Weinbaum
, “
Lessons learned from the exquisite design of the endothelial surface glycocalyx and their amazing applications
,” WIT Trans. Ecol. Environ.
73
, 1
(2004
).60.
R.
Crawford
,
R.
Nathan
,
L.
Wang
, and
Q.
Wu
, “
Experimental study on the lift generation inside a random synthetic porous layer under rapid compaction
,” Exp. Therm. Fluid Sci.
36
, 205
(2012
).61.
Q.
Wu
and
Q.
Sun
, “
A comprehensive skiing mechanics theory with implications to snowboard optimization
,” Med. Sci. Sports Exerc.
43
, 1955
(2011
).62.
B.
Barabadi
,
R.
Nathan
,
K.
Jen
, and
Q.
Wu
, “
On the characterization of lifting forces during the rapid compaction of deformable porous media
,” J. Heat Transfer
131
, 101006
(2021
).63.
H.
Wu
, “
Squeeze-film behavior for porous annular disks
,” j. Lubr. Technol.
92
, 593
(1970
).64.
N. B.
Naduvinamani
,
P. S.
Hiremath
, and
G.
Gurubasavaraj
, “
Squeeze film lubrication of a short porous journal bearing with couple stress fluids
,” Tribol. Int.
34
, 739
(2001
).65.
T.
Karmakar
and
G. P.
Raja Sekhar
, “
Squeeze-film flow between a flat impermeable bearing and an anisotropic porous bed
,” Phys. Fluids
30
, 043604
(2018
).66.
H. C.
Brinkman
, “
A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, flow
,” Turbul. Combust.
1
, 27
(1949
).67.
S.
Whitaker
, “
Flow in porous media I: A theoretical derivation of Darcy's law
,” Transp. Porous Media
1
, 3
(1986
).68.
Q.
Wu
,
S.
Weinbaum
, and
Y.
Andreopoulos
, “
Stagnation-point flows in a porous medium
,” Chem. Eng. Sci.
60
, 123
(2005
).69.
Z.
Zhu
,
Q.
Wang
, and
Q.
Wu
, “
On the examination of the darcy permeability of soft fibrous porous media; new correlations
,” Chem. Eng. Sci.
173
, 525
(2017
).70.
R.
Crawford
,
G. F.
Jones
,
L.
You
, and
Q.
Wu
, “
Compression-dependent permeability measurement for random soft porous media and its implications to lift generation
,” Chem. Eng. Sci.
66
, 294
(2011
).71.
M. H.
Hamdan
, “
Single-phase flow through porous channels a review of flow models and channel entry conditions
,” Appl. Math. Comput.
62
, 203
(1994
).72.
T. W.
Barber
,
J. A.
Brockway
, and
L. S.
Higgins
, “
The density of tissues in and about the head
,” Acta Neurol. Scand.
46
, 85
(1970
).73.
A. F.
Frydrychowski
,
A.
Szarmach
,
B.
Czaplewski
, and
P. J.
Winklewski
, “
Subarachnoid space: New tricks by an old dog
,” PLoS One
7
, e37529
(2012
).74.
Y.
Watanabe
,
S.
Abe
,
K.
Takagi
,
T.
Yamamoto
, and
T.
Kato
, “
Evolution of subarachnoid space in normal fetuses using magnetic resonance imaging
,” Prenat. Diagn.
25
, 1217
(2005
).75.
M. M.
Mortazavi
et al, “
Subarachnoid trabeculae: A comprehensive review of their embryology, histology, morphology, and surgical significance
,” World Neurosurg.
111
, 279
(2018
).76.
E.
Mori
,
N.
Hirono
,
H.
Yamashita
,
T.
Imamura
,
Y.
Ikejiri
,
M.
Ikeda
,
H.
Kitagaki
,
T.
Shimomura
, and
Y.
Yoneda
, “
Premorbid brain size as a determinant of reserve capacity against intellectual decline in Alzheimer's disease
,” Am. J. Psychiatry
154
, 18
(1997
).77.
C.
Decarli
,
P.
Maillard
,
M. P.
Pase
,
A. S.
Beiser
,
D.
Kojis
,
C. L.
Satizabal
,
J. J.
Himali
,
H. J.
Aparicio
,
E.
Fletcher
, and
S.
Seshadri
, “
Trends in intracranial and cerebral volumes of Framingham heart study participants born 1930 to 1970
,” JAMA Neurol.
95817
, 471
(2024
).78.
Y.
Chen
,
Y.
Wang
,
Z.
Song
,
Y.
Fan
,
T.
Gao
, and
X.
Tang
, “
Abnormal white matter changes in Alzheimer's disease based on diffusion tensor imaging: A systematic review
,” Ageing Res. Rev.
87
, 101911
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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