IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 2, FEBRUARY 2007
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Cerebrospinal Fluid Flow in the Normal and
Hydrocephalic Human Brain
Andreas A. Linninger*, Michalis Xenos, David C. Zhu, MahadevaBharath R. Somayaji, Srinivasa Kondapalli, and
Richard D. Penn
Abstract—Advances in magnetic resonance (MR) imaging techniques enable the accurate measurements of cerebrospinal fluid
(CSF) flow in the human brain. In addition, image reconstruction
tools facilitate the collection of patient-specific brain geometry
data such as the exact dimensions of the ventricular and subarachnoidal spaces (SAS) as well as the computer-aided reconstruction
of the CSF-filled spaces. The solution of the conservation of CSF
mass and momentum balances over a finite computational mesh
obtained from the MR images predict the patients’ CSF flow
and pressure field. Advanced image reconstruction tools used in
conjunction with first principles of fluid mechanics allow an accurate verification of the CSF flow patters for individual patients.
This paper presents a detailed analysis of pulsatile CSF flow
and pressure dynamics in a normal and hydrocephalic patient.
Experimental CSF flow measurements and computational results
of flow and pressure fields in the ventricular system, the SAS and
brain parenchyma are presented. The pulsating CSF motion is
explored in normal and pathological conditions of communicating
hydrocephalus. This paper predicts small transmantle pressure
10 Pa).
differences between lateral ventricles and SASs (
The transmantle pressure between ventricles and SAS remains
small even in the hydrocephalic patient ( 30 Pa), but the ICP
pulsatility increases by a factor of four. The computational fluid
dynamics (CFD) results of the predicted CSF flow velocities are
in good agreement with Cine MRI measurements. Differences
between the predicted and observed CSF flow velocities in the
prepontine area point towards complex brain-CSF interactions.
The paper presents the complete computational model to predict
the pulsatile CSF flow in the cranial cavity.
Index Terms—Cerebrospinal fluid, computational fluid dynamics, human brain, hydrocephalus, intracranial pressure,
reconstruction tools.
I. INTRODUCTION
HE central nervous system composed of the brain and
the spinal cord is submerged in cerebrospinal fluid (CSF).
CSF, a colorless liquid with the consistency of blood plasma,
T
Manuscript received January 25, 2006; revised June 24, 2006. This work was
supported in part by the Sussman and Asher Foundation. Asterisk indicates corresponding author.
*A. A. Linninger is with the Laboratory for Product and Process Design
(LPPD), Department of Chemical and Bioengineering, University of Illinois at
Chicago, CEB 216, 851 S. Morgan St, Room 218 SEO, Chicago, IL 60607 USA
(e-mail: linninge@uic.edu).
M. Xenos, M. R. Somayaji, and S. Kondapalli are with the Laboratory for
Product and Process Design (LPPD), Department of Chemical and Bioengineering, University of Illinois at Chicago, Chicago, IL 60607 USA.
D. C. Zhu is with the Cognitive Imaging Research Center, Michigan State
University, East Lansing, MI 48824 USA.
R. D. Penn is with the Departments of Surgery, University of Chicago,
Chicago, IL 60637 USA.
Color versions of Figs. 9 and 10 are available online at http://ieeexplore.ieee.
org.
Digital Object Identifier 10.1109/TBME.2006.886853
is also found in four cavities inside the brain known as the
ventricles, which in turn are connected to the cerebral and the
spinal subarachnoidal spaces (SAS). The CSF surrounding the
brain and the spinal cord is not at rest, but undergoes complex
pulsating fluid motion in synchronization with the heartbeat.
Advances in magnetic resonance imaging (MRI) have made
possible accurate determination of CSF flow patterns in vivo
[1]–[3]. Recently, on-line dynamic in vivo intracranial pressure
(ICP) measurements have become available [4]. Despite of
this progress in observing the CSF flows and pressures, the
CSF flow dynamics in the normal brain and communicating
hydrocephalus have not been accurately accounted for by the
fundamental principles of fluid mechanics [5].
Various causes have been hypothesized to produce hydrocephalus. Early work suggested that large ICP differences between the ventricles and the SAS are responsible for the development of hydrocephalus [6]. More recent studies show in
communicating hydrocephalus large transmantle pressure differences are not present [4], [7]. These clinical observations
were explained by dynamic first principles methods [8]. The difficulty in accounting for intracranial dynamics is partially due
to the structural and geometric complexity of the human brain
which encompasses porous parenchymal brain tissue as well as
fluid filled compartments (ventricles, SAS, and blood vessels).
Several recent CSF flow studies to explain CSF flow patterns
use one-dimensional models [9]–[11]. More realistic flow field
simulations have been limited to small sections in the brain like
the aqueduct of Sylvius [12], [13]. Other CSF flow models only
considered compartmental models [14]. A rigorous quantification of the multidimensional CSF flow field based on basic fluid
physics has not yet been achieved.
The lack of quantitative understanding of intracranial dynamics hampers the development of better treatment options
for hydrocephalus. For the last thirty years, treatment relies on
the placement of a shunt system that removes excess CSF from
the cranial vault. Unfortunately, shunting has a high failure
rate and multiple painful and expensive revision operations
are required [15], [16]. Changes to ICP and CSF flow patterns
in the hydrocephalic brain due to shunting are still poorly
understood. The goal of our work is to elucidate the normal
and hydrocephalic CSF flow patterns using rigorous fluid
mechanical principles, and use these findings to improve the
treatment of hydrocephalus.
The computational analysis presented in this paper integrates
Cine MRI phase contrast imaging with accurate reconstruction
of individual patients’ brain geometry of their ventricular and
the SASs. Experimental results include accurate measurements
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of the flow velocities and flow patterns in normal and in hydrocephalic subjects. In a detailed comparison, the CSF dynamics
of one normal subject will be contrasted with the abnormal flow
and pressure dynamics in a patient with communicating hydrocephalus. Rigorous fluid physics principles are used to quantify the flow and pressure fields defined in the computational
grids reconstructed from the MR images for each subject. The
computational approach will be shown to accurately quantify
the changes in the ICP patterns for normal and hydrocephalic
subjects.
Section II introduces the methods for measuring the CSF flow
fields in vivo. It demonstrates the use of image reconstruction
tools for generating accurate computational meshes of the patients’ specific brain geometry and as an accurate framework for
computational analysis of the measured CSF flow patterns. Section III will introduce the computational fluid dynamics (CFD)
analysis for the entire brain and present results of the flow and
pressure patterns of the normal and hydrocephalic case. This
comprehensive model of the entire ventricular system is a first
of its kind.
II. METHODOLOGY
Our aim is to use the physical principles of fluid flow to quantify intracranial CSF dynamics. The rigorous fluid mechanics
approach proceeds in three stages. In step 1, MRI techniques
are used to accurately measure the patients’ individual brain
geometry and the CSF flow velocities in select regions of interest. In step 2, image reconstruction is used to obtain the dimensions of the CSF pathways and the brain. It also converts the
patient-specific MR data into accurate two or three-dimensional
(3-D) surfaces and volumes. Grid generation is then used to partition these spaces into a large number of small finite volumes.
CFD in step 3 solves the equations of fluid motion numerically
over the discretized brain geometry. The agreement of the experimental MRI flow field with the CFD predictions demonstrates
that the detailed mechanistic picture of fluid flows and pressures
that cause intracranial dynamics is correct. Before presenting
the intracranial dynamics in normal and hydrocephalic patients,
the next subsection briefly introduces the experimental method
as well as the mathematical background for this paper.
A. In Vivo CSF Flow Measurement
CSF flow velocity images at different time frames of the
cardiac cycle are collected using two-dimensional (2-D) Cine
phase-contrast techniques [17], [18] from 11 subjects (eight
normal and three with hydrocephalus) on a 3T GE Signa
scanner (GE Medical Systems, Milwaukee, WI). Velocity
images in all three directions in 16 equidistant time frames of
the cardiac cycle are collected at the mid-sagittal slice to view
the major CSF pathways. The velocity images perpendicular to
the slice of interest are collected to measure the CSF flow at 32
equidistant time frames of the cardiac cycle at a mid-coronal
slice of the third ventricle, and then at an axial slice across the
junction between the aqueduct of Sylvius and the fourth ventricle. The CSF pathway is segmented for analysis based on a
-weighted image, in which CSF was enhanced. The velocity
of every pixel in these regions of CSF is calculated. Corrections
are made for spatially dependent offset velocity due to eddy
Fig. 1. Intracranial dynamics of an adult communicating hydrocephalus: The
temporal relationship among the basilar artery, the lateral ventricle area, the CSF
flow at the third ventricle and at the junction of the aqueduct of Sylvius and the
fourth ventricle.
currents or head motion [1], [18], [19]. -weighted volumetric
axial or sagittal images (with CSF signal suppressed) are also
collected to estimate the volumes of the different CSF pathway
sections. Each volume (18 cm 24 cm 24 cm) of images
contains 120 contiguous slices with a 1.5–mm thickness, a
256 reconstructed matrix
24-cm field-of-view and a 256
size. The data acquisition and velocity calculation has been
fully discussed in the paper by Zhu et al. [20]. Fig. 1 displays
the results of MRI experiments: the flow of blood in the basilar
),
artery (ml/min), the lateral ventricle area deformation (
the CSF flow at the third ventricle and at the junction of the
aqueduct of Sylvius and the fourth ventricle (ml/min). Fig. 3
and Table IV summarize the CSF flow measurements of the
patients at six locations of interest obtained with this Cine
phase contrast imaging technique.
B. MRI Imaging and Image Reconstruction
- and -weighted images extracted from the MRI are
introduced into image reconstruction tools [21]. Image reconstruction involves the physiologically accurate interpretation
of the different substructures of the brain. Precise dimensions
of the 3-D ventricular spaces, foramina and SAS are collected
from 120 horizontally stacked MR slices of 1.5 mm spacing by
connecting pixels of equal intensity delineating the boundaries
LINNINGER et al.: SCF FLOW IN THE NORMAL AND HYDROCEPHALIC HUMAN BRAIN
of the structures of interest. When connecting the 2-D information of each slice with the adjacent slices, a 3-D patient specific
geometry of the brain or a subsection of it emerges.
After rendering surfaces which represent the boundaries between the parenchyma and the ventricular and SAS, Mimics
image reconstruction software was used to further segment the
3-D volumes into a finite number of small triangular or tetrahedral elements [22]. This triangulation step is performed with a
commercial grid generator tool Gambit. It partitions the patientspecific brain geometry information composed of volumes and
boundary surfaces into a computational mesh with well-defined
mathematical properties. Sagittal brain cuts are reconstructed
for a 2-D analysis of the CSF flow.
C. Computational Analysis of MRI Flow Patterns
In order to interpret the experimental data and to understand
the dynamic forces that cause CSF motion, a computational
model for predicting the CSF fluid motion inside the cranial
vault for each patient was designed. The CSF spaces inside the
brain were extracted from the MR images and discretized versions of the mass and momentum balances were solved with
computational fluid methods. Because the mathematical model
only used these fundamental conservation laws of mass and momentum, it is referred to as a first principles model. Despite
the large data set necessary to accurately represent the patients’
brain geometry, the first principle fluid mechanics approach only
requires a small number of physical parameters. The values
of physical constants including the CSF viscosity ( ), density
( ) as well as porosity ( ) and permeability ( ) of the porous
brain are listed in Table II. In addition, a set of boundary conditions needs to be specified. The results of the CSF analysis
are the flow rate, velocities, and ICP gradients of CSF in the
ventricular system as well as the porous parenchyma. The following discussion of the computational approach will introduce
the mathematical equations, the boundary conditions as well as
a subsection on the numerical solution of the large-scale partial
differential equations.
1) CSF Flow in the Ventricular and Subarachnoid Systems:
CSF motion is described by the equations of mass and momentum conservation for an incompressible Newtonian fluid
[23]. These conservation balances lead to a system of partial
differential equations known as the continuity and the NavierStokes equations. The governing equations for CSF flow are
given in vector form by (1) and (2).
Conservation of mass
(1)
Conservation of momentum
(2)
where is the velocity vector, is the CSF density, and its
viscosity.
CSF Flow Inside the Porous Brain Tissues: CSF is produced
in the choroid plexus from the blood and also from the brain
tissue from which it is believed to seep through the porous extracellular space towards the ventricles. Two thirds of the CSF production enters the ventricles from the choroid arteries [24], [25],
293
one third is believed to be generated diffusely throughout the
brain parenchyma. The CSF flow though the extracellular space
of the brain parenchyma is modeled by a continuity equation and
the momentum equation for flow though porous media. Accordingly, the continuity equation of CSF flow in the parenchyma
has a source term to account for new CSF production as in (3).
The momentum balances of CSF seepage are the Navier-Stokes
equations augmented by an additional term quantifying frictional interaction of CSF with the brain tissue. Here, is the
physical velocity vector flowing through the interstitial medium
which is related to the superficial velocity through the extracellular volume fraction. Fluid flow through porous tissue experiences additional pressure drop proportional to the squared flow
velocity through the porous tissue. Equation (4) is a generalization of the simpler Darcy’s law of flow through porous media
[26], [27]. In this paper, the brain tissue is treated as a homogeneous isotropic porous medium. The material properties, ,
the permeability of the brain tissue, and Forscheimer’s coefficient measuring inertial resistance are listed in Table II. A more
advanced physiologically consistent representation of the brain
tissue would include anisotropy of the white matter leading to
directional dependence of the permeability, porosity and diffusivities. These considerations are beyond the scope of this study.
CSF generation in the parenchyma
(3)
CSF fluid seepage through the porous medium
(4)
Boundary Conditions for Intracranial Dynamics: Fig. 2 illustrates the location of the boundaries within a 2-D sagittal cut
of a normal subject. The boundary conditions for the CSF flow
in the cranium are summarized in Table I. The bulk production
is due to CSF generation in the choroid plexus and parenchyma.
The diffuse production of CSF flow throughout the parenchyma
is accounted for as a source term introduced in (3). The bulk CSF
production is implemented as input flux at the choroid plexus.
Recently, we have shown that the expansion of the vascular
bed in the systole leads to compression of the lateral ventricle
as well as enlargement of the choroid plexus resulting in CSF
flow out of the ventricles [20]. For this study, the action of the
vascular expansion bed is accounted for via the boundary condition for the choroid plexus as given by (5). Thus, the choroid
boundary condition accounts for the constant CSF production
as well as the pulsatile flow of CSF due to expansion of the
parenchyma as well as choroid plexus in the systole [8], [28].
The frequency of the pulsatile motion is set to 1 Hz approximating the normal cardiac cycle.
Most scientists believe that the majority of reabsorption of the
CSF is into the granulation of the sagittal sinuses. Accordingly,
re-absorption of the fluid takes place at the top of the brain geometry. The re-absorption is assumed to be proportional to the
pressure difference between the ICP in the SAS and the venous
pressure inside the sagittal sinus [29]. This relation is expressed
mathematically by (6).
The expansion of the vascular bed also causes displacement
of CSF from the cranium into the spinal SAS. The fluid displace-
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Fig. 2. Definition of boundaries and meshed geometry of the ventricular system, cerebral SAS and porous structures (cerebrum, cerebellum, brain stem, and
sagittal sinus).
TABLE I
BOUNDARY CONDITIONS (BC)
ment of CSF has been determined in previous work to amount
[2], [30]. With current MR mea1–2
surements, no net flow of CSF into the spinal SAS can be detected. Hence, an oscillatory volumetric flow rate of CSF displacement in the caudal and rostral direction was specified as
the boundary between the cranium and the spinal cord as reported in (7).
CSF generation in the choroid plexus
(5)
CSF reabsorption
(6)
Spinal cord boundary conditions
(7)
III. RESULTS
CSF flow patterns will be illustrated by a detailed discussion
in a normal subject and a patient with communicating hydro-
cephalus. The CSF flow and pressure fields in these two specific individuals are predicted using computational results obtained via the image guided CFD approach. CSF flow fields of
more normal subjects and patients with hydrocephalus are reported elsewhere [20]. The CSF flows were measured in vivo in
six locations depicted by MRI images, Fig. 3(a)-(d). The analysis demonstrates pathological changes to the CSF flow occurring in hydrocephalus. Computational results of the extension
to 3-D motion of the CSF in the ventricular system and SAS of
a normal subject are presented at the end of this section.
A. Two-Dimensional CSF Flow Patterns in Normal and
Hydrocephalic Subjects
We acquired MR data of the brain geometry of a 32-year-old
healthy volunteer and of a 62-year-old patient with communicating hydrocephalus. The ventricles, the SAS and the
parenchyma were reconstructed by using ImageJ [21] as
depicted in Fig. 2. Typical 2-D computational meshes for
simulating this patient’s intracranial dynamics encompassed
37 631 volume elements with 20 337 nodes. Property values for
porosity and permeability of brain parenchyma of both cases
were taken from the literature [31]. The inertia resistance term
, is estimated for the specific values of and
[32]. All
parameter values used in the CFD simulations are summarized
in Table II. The solution of the large-scale transport problems
for these patients generated the 2-D CSF velocity and pressure
fields as a function of the cardiac cycle.
LINNINGER et al.: SCF FLOW IN THE NORMAL AND HYDROCEPHALIC HUMAN BRAIN
Fig. 3. Two-dimensional Pulsatile CSF flow for the normal case during one cardiac cycle.
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TABLE II
PARAMETERS USED FOR CSF FLUID AND FLOW THROUGH POROUS
BRAIN TISSUE
the simulated and measured velocities). In addition, CSF flow
information can be computed consistently in locations that
the MRI technique cannot resolve. As examples consider flow
velocities in the aqueduct of sylvius, the foramina of Luschke
and Magendie, as well as fluid traction at the ventricular walls.
Our first principles approach only required a small number
of physical properties to produce a full description of flow
throughout the cranium and upper spinal canal.
C. Pulsatile Intracranial Pressure Dynamics
B. CSF Flow Patterns in the Normal Brain
We described the MRI-Cine phase contrast technique to measure with accuracy the pulsatile CSF flow field in Section II.
Fig. 3(a)-(d) shows a sequence of the velocity vectors in one
cardiac cycle in select regions of interest. The arrows represent the anterior-posterior (A-P) and superior-inferior (S-I) directions. The right-left (R-L) component of the velocity vectors
were omitted due to the symmetry in the sagittal plane.
Frame-a shows a predominantly rostral flow in the early systole of the cardiac cycle. In the mid-systole, the magnitude of
the CSF flow velocities reaches its peak. This flow pattern continues to the end of the systole shown in frame-c. In the diastole
at 60% of the cardiac cycle, the outflow ends and the CSF flow
reverses its direction. The CSF ascends from the spinal canal
up into the head and also flows back into the ventricles and the
aqueduct of sylvius. This sequence of snapshots shows the complex flow pattern in space and time. A similar graphical account
of the complex CSF flow patterns were presented earlier [2].
These clinical measurements can be compared to the CFD
simulations based on the model introduced in Section II.
Fig. 3(e)-(h) depicts the results obtained through CFD. The 2-D
image of the patient specific brain geometry was produced by
the image reconstruction step. After solving the first principles
CFD model with equations and boundary conditions (1)–(7),
we obtain the flow and pressure field inside the cranial vault.
We observe additional details such as an upward flow through
the SAS in the location of the sagittal sinus. This flow pattern
is indicative of CSF reabsorption in the arachnoid villi. The
orientation, magnitude, and timing of the transient velocity
fields are in good agreement with the clinically observed data.
Fig. 4 plots the measured and predicted CSF velocity at the
inlet of the fourth ventricle. We do observe discrepancy in
the velocity maxima in the prepontine area. These differences
are most likely attributable to distension of the vasculature
occurring at the prepontine area. The basilar artery traverses
this narrow area in front of the brain stem and thus might
increase CSF pulsatility in this region. The current simulations
cannot account for this effect because the dilating vascular
system is not considered. These discrepancies could also occur
due to complex phenomena such as rostral/caudal brain motion
with each pulse [1], [2], [30]. The proposed CFD simulation
accurately predicts the CSF flow pattern in the ventricular
system in all phases of the cardiac cycle as shown in Table IV
(e.g., less than 5% error in the hydrocephalic case between
Fig. 5 displays the ICP field of a normal subject at 86%
of the cardiac cycle (early systole). The ICP is highest in the
parenchyma and lowest in the SAS at systole. This prediction is
an expected consequence of the assumption of CSF generation
in the choroid plexuses and the parenchyma. The pressure
gradients between parenchyma and ventricles never exceed 160
Hg); these gradients drive CSF seepage flows
Pa (
from deep tissues inside the brain towards the ventricles and
the SAS, the remainder draining to other porous structures. In
of the CSF production drained into the
our simulation,
ventricles,
into SAS. The pressure difference between
lateral ventricle and porous parenchyma is approximately 1.13
mm Hg (151 Pa). In contrast, the pressure drop in the clear fluid
pathways of the ventricular system is small compared to the
pressure drop inside the parenchyma. The transmantle pressure
gradient defined as the difference between the ICP in the SAS
and the lateral ventricle remains below 10 Pa. With open CSF
pathways the oscillatory fluid motion requires only very small
pressure gradients. The high and low ICP locations for the
normal and hydrocephalic case are listed in Table IV. The ICP
pressure amplitude was found to be about 27 Pa.
D. Pathological CSF Dynamics in the Hydrocephalic Brain
The predicted CSF flow field in a hydrocephalic patient is
shown in Fig. 6. It also shows a sequence of the velocity vectors
obtained during one cardiac cycle. The calculations also provide information about pressure gradients not measurable with
MRI. The pulsating motion of the CSF peaks at the systole (i.e.,
of the cardiac cycle). Highest velocities were observed
in the foramina and in the aqueduct of Sylvius. In comparison
to the normal subject, the CSF velocities of the hydrocephalic
patient are 2.7 times higher. The increase in pulsatile flow also
augments the volumetric flow rate by a factor of 10.4. In all ventricles, an irregular flow pattern with recirculation of the CSF
occurs. This effect is particularly pronounced in the lateral and
the third ventricles as well as the prepontine SAS where several
eddies formed as shown in Fig. 7. The significance of CSF flow
stagnation warrants further investigation.
Fig. 8 depicts the ICP field computed for the hydrocephalic
patient at 86% of the cardiac cycle (early systole). Pressure is
highest in the parenchyma and lowest in the SAS. The most
striking change in the hydrocephalic case is in the increase in
the ICP amplitude. It is about 4.6 times higher than normal.
The transmantle pressure between the SAS and the lateral ventricle is also elevated compared to normal, but it does not exceed 30 Pa. It is important to point out that the pressure difference between lateral ventricle and porous parenchyma is only
162 Pa. The hydrocephalic pressure difference is also small and
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Fig. 4. Validation of the simulations with MRI data for normal (left) and hydrocephalic case (right) down the aqueduct of sylvius and fourth ventricle.
only marginally larger than value of 151 Pa in the normal subject. This result confirms again the absence of large transmantle
pressure differences as pointed out in our earlier work [4]. The
total ICP of the hydrocephalus patient is elevated. In the real
brain, it is expected that biomechanical properties like elastances, porosity and permeability change with increasing ICP.
These effects were accounted for in the simulations as shown in
Table II. Even when using much smaller tissue permeability for
hydrocephalus simulations, the transmantle pressure gradients
stayed small as stated above.
E. Three-Dimensional Subject Specific Analysis
We also acquired 3-D MR data of the brain geometry of a
32-year-old healthy volunteer. One-hundred-twenty MRI slices
were imported into Mimics and the complex pathways of the
ventricles (Fig. 9, yellow) and the cerebral SAS (Fig. 9, red)
were reconstructed in three dimensions. Fig. 10 displays the reconstructed 3-D geometry of the patient with hydrocephalus.
The ventricular system is enlarged and shown in yellow and the
CSF filled cranial SAS is depicted in red. For the healthy volunteer, the lateral ventricles were found to contain 9.2
of CSF;
the third ventricle 2.48
, fourth ventricle 3.31
while the
. In the hydrocephalic pacerebral SAS measured
tient, the lateral ventricles were found to contain total 250.2
of CSF; the third ventricle 11.3
, fourth ventricle 4.57
.
The geometrical data are summarized in Table III. The lateral
ventricular size in the hydrocephalic case was 27.2 times larger
than normal. There were no significant size differences in the
SAS of the hydrocephalic patient.
The solution of the 3-D transport problems for the normal
subject generated the complete CSF flow and pressure fields
as a function of time. To the best of our knowledge, the computational results for the 3-D intracranial dynamics have not
been reported before in the literature. Maximum CSF velocity
of 23 mm/s in the aqueduct was reported [12], [13]. Finally, the
pressure difference between lateral ventricle and SAS does not
exceed 10 Pa, consistent with the 2-D results.
IV. DISCUSSION
A. CSF Fluid Flow Pattern
The results of our CFD simulations for the normal subject as
well as for the hydrocephalic patient are in good agreement with
MRI measurements as shown in Figs. 3 and 7. Maximum velocities in the normal condition occur in the aqueduct of Sylvius
TABLE III
DIMENSIONS OF THE BRAIN SUBSTRUCTURES
(0.012 m/s) which is the narrowest structure of the ventricular
system. These values are in the same range as previously published results [12], [13], [28]. In the hydrocephalic case, the amplitude of the CSF flow pulsations is about 2.7 times higher than
in the normal; the maximum velocity in the aqueduct of a communicating hydrocephalic patient was found to be 0.035 m/s.
This increment of the CSF pulsations also affects the shape of
the velocity field leading to several areas of stagnation. In the
normal subject only small areas of recirculation were observed
in the third and fourth ventricle. Recirculation in the hydrocephalus case occurred throughout the ventricular system with
the formation of eddies in every ventricle. The largest eddies
appear in the lateral and third ventricles and in the prepontine
SAS.
B. Noninvasive Prediction of Intracranial Pressures and MR
Current image-based analysis of intracranial dynamics is
incomplete, because the absolute ICP cannot be measured with
MRI directly. Knowledge of the absolute ICP is important for
assessing the patients’ status. Chronic ICP can be monitored in
vivo with invasive techniques by implanting intraparenchymal
or subdural sensors for direct ICP measurements at a specific
location [4]. The CFD analysis quantifies the increment of
CSF pulsatility due to changing flow pattern in hydrocephalus.
Specifically, an increment in ICP amplitude of 27 Pa was
predicted. The inference of absolute ICP by computational fluid
mechanics is not possible, because the absolute pressure, ,
does not occur in the equations of motion of an incompressible
. Accordingly, the predicfluid, only the pressure gradient
tions of pressure gradients and pressure wave amplitudes are
proper, but not absolute ICPs.
Two approaches to infer absolute ICP that might be successful
in the future come to mind. The first one hinges upon the correlation between ICP pulsatilty and the pressure volume relationships. However, because of the variability of brain compliance,
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TABLE IV
COMPARISON OF CSF FLOW VELOCITIES AND INTRACRANIAL PRESSURES OBTAINED FROM CFD AND MRI
Fig. 5. Two-dimensional static pressure for the normal case at 86% of the cardiac cycle (early systole).
Fig. 6. Two-dimensional pulsatile CSF flow for the hydrocephalic case during one cardiac cycle [(a)–(d) CSF velocities].
pulse pressure or its wave form cannot be used to reliably predict absolute pressure [29], [33]. Differences in patient-specific
elastances of the parenchyma as well as alterations during the
course of hydrocephalus diminish the predictive capability of
this method.
The second avenue of inferring ICP from image data is the
attempt to correlate brain tissue deformations to the ICP. In
theory, the ICP is directly related to the total volumetric tissue
strain. Hence, the ICP could accurately be predicted if the tissue
strain and biomechanical properties of the brain were known
[26]. Recently, we have presented data to demonstrate the feasibility of measuring the lateral ventricle deformation with gated
phase contrast MRI [20]. The use of such information to infer
ICP noninvasively will be the subject of further investigation.
C. ICP Trajectory in Normal and Hydrocephalic Brain
The ICP in normal subjects is of the order of 500 Pa (4 mm
Hg above the venous pressure); elevations up to 1630 Pa (12 mm
Hg) are still considered normal [13]. In abnormal conditions the
Hg above the
ICP can increase as high as 3000 Pa (
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Fig. 7. The complex flow pattern in Hydrocephalus: left-CFD simulations and right-MRI measurements of CSF flow during Systole.
Fig. 8. Two-dimensional static pressure for the hydrocephalic case at 86% of the cardiac cycle (early systole).
venous pressure) or even higher [34]. In this study, we assumed
a baseline ICP of 500 Pa for the normal case and 2700 Pa for
the hydrocephalic case. The range of the ICP amplitude for the
normal 2-D case is of the order of 27 Pa (Fig. 5). The pressure
Hg higher than in
in the normal brain parenchyma is
the ventricular system, which is consistent with physiological
measurements [25]. The transmantle pressure—the pressure between lateral ventricles and SAS—does not exceed 10 Pa. This
is in agreement with previously published results of a very small
in the aqueduct of Sylvius
pressure drop of the order of
[12], [13] or in the whole ventricular system [20], [28].
In the hydrocephalic brain, the pressure field is significantly
affected by the high velocities of the pulsating CSF and the increase of the total ventricular volume. The pressure difference
during each cardiac cycle is of the order of 68 Pa, which is
about twice more than in the normal brain. However, the transmantle pressure between the lateral ventricle and the SAS was
found not to exceed 30 Pa. This result is in accordance with
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times higher than the normal) and an increase at the pressure
amplitude (68 Pa) and total pressure of the brain (above 20 mm
Hg) support the notion of a less compliant hydrocephalic brain.
The computation with wide parameter variations indicates that
the transmantle pressure is a weak function of the tissue properties and does not produce a large enough force to enlarge the
ventricles as had been suggested.
D. Three-Dimensional Analysis of Intracranial Dynamics
Fig. 9. Three-dimensional reconstruction of the CSF pathways for a normal
subject: ventricular system (yellow), cerebral SAS (red).
Fig. 10. Three-dimensional reconstruction of the CSF pathways for a hydrocephalic patient: ventricular system (yellow), cerebral SAS (red).
recently published experimental data in hydrocephalic dogs [4]
and challenges the notion that hydrocephalus occurs due to large
transmantle pressures [5], [35], [36]. Finally, the ICP in the hydrocephalic patient is highest peaking at 3051 Pa. This value is
based on typical absolute ICP occurring in hydrocephalus [37].
This is 4.6 times higher than the normal ICP at the same cycle
time. The pressure between parenchyma and lateral ventricle remains small and is close to the values in normal subjects. This
small pressure drop was seen even though for the simulation we
lowered the hydrocephalic tissue permeability by one order of
magnitude.
The ICP increments are most likely due to increases in brain
elastance occurring in hydrocephalus. It is known that the ICP
is related to the volume of the ventricular space and to the elastance of the brain tissue [3]. When the brain parenchyma is compressed during a pathological enlargement of ventricles, stiffer
brain tissue will lead to more pulsatility in response to pressure
waves produced from the arterial blood. Our clinical and computational results of rapid increase of the pulsating velocity (2.7
In the 3-D case, the velocities at each foramen and in the aqueduct are almost identical to those in the 2-D case. The presented
experimental data and the CFD simulations show that velocity
and pressure amplitudes are increased drastically in the hydrocephalic case. Small differences in the flow velocities are expected since the 2-D representation alters the ratio of ventricular
to subarachnoidal CSF volume content.
Knowledge of the changes in flow patterns and pressure gradients that occur with the development of hydrocephalus should
help in the design of more effective shunting systems used for
treatment. Currently, the valves that control CSF diversion respond to absolute pressure changes or attempt to control flow
rates. As pointed out by the Cambridge group, these systems
have different flow characteristics when subjected to pulsatile
CSF flow [38]. Our computational and MRI-based observations
provide the information necessary to match a valve to a specific
patient that reflects that patient’s CSF dynamics. The fact that
in controlled studies, the various current shunting systems perform equally poorly suggests that much more design work using
new physiological observations needs to be done. It may be that
control systems just based on static flow and pressure considerations are not enough to deal with the dramatically changing
state of hydrocephalus patients. Our techniques should provide
quantitative insight into what might work at each state of hydrocephalus. The detailed investigation of the 3-D intracranial
dynamics is beyond the scope of the present analysis and will
be presented in a follow-up paper.
V. CONCLUSION
This paper introduces a computational fluid mechanics model
of the CSF flow inside the cranium. The equations of motion
for CSF flow in the ventricular and subarachnoidal pathways as
well as CSF seepage inside the porous brain parenchyma were
solved. The boundary conditions for the complex brain geometry were formulated. The computations used patient-specific
computational meshes obtained by image reconstruction tools.
The systematic procedure for conducting a detailed CFD flow
analysis for individual patients based on MRI data is reported for
the first time. The simulations proposed in this paper accounts
for individual differences in geometric features as well as flow
and pressure patterns in each patient. State-of-the-art Cine phase
contrast MRI techniques provided accurate CSF flow velocity
measurements in three dimensions. The clinical in vivo flow
measurement was used to validate the proposed computational
model. It may be possible in the future to determine CSF production and reabsorption rates by a combination of Cine-MRI
CSF measurement with the computational model. There is also
the possibility of inferring biomechanical properties of the brain
such as compliance or permeability using such methods.
LINNINGER et al.: SCF FLOW IN THE NORMAL AND HYDROCEPHALIC HUMAN BRAIN
Our CSF measurements and simulations presented a complete picture of the pulsatile CSF dynamics during the cardiac
cycle. Cine MRI measurements and CFD simulations demonstrated CSF flow reversal in the ventricular system as well as in
the prepontine SAS. The exchange of CSF with the spinal SAS
and the influence of spinal SAS compliance on intracranial dynamics appears to be insufficiently recognized in the existing
models of the brain as a closed cavity (Monroe-Kelly doctrine).
The paper also demonstrated drastic differences in the CSF flow
patters in hydrocephalic patients compared to normal subjects.
The peak CSF flow velocity increased by 2.7 times in a hydrocephalic patient compared to normal. The total volume of the
hydrocephalic lateral ventricles was found to be enlarged by
more than an order of magnitude. The increase in CSF pulsatility
in addition to the expansion of the dimensions of the ventricular
pathways including the aqueduct of Sylvius results in more than
a tenfold increase in CSF volumetric flow rate. We also observed
more complex flow patterns causing eddies and areas of stagnation in the ventricles of the hydrocephalus patient.
In addition to predicting the flow field, our first principles
approach accurately quantifies the ICP dynamics in all locations of the brain. This knowledge could be important for assessing the specific clinical state of a patient based only on a
handful of known physical and biomechanical properties. The
ICP flow patterns cannot be measured by MRI, yet may be important in determining the development of normal pressure hydrocephalus. Our CFD simulations revealed small transmantle
pressure difference in the normal patient and hydrocephalic patient. We found a four to fivefold increase of the ICP amplitude
in the hydrocephalic brain.
The successful integration of the MRI-CFD approach for
studying intracranial dynamics presented in this paper holds
promise for considering patient-specific observations in the
design of treatment options in the future.
VI. FUTURE DIRECTIONS
Complex brain motion patterns causing CSF displacement
and brain deformation were observed previously [1], [39]. These
phenomena are due to the interaction of the expanding vascular
bed, gravity and the buoyancy of the brain tissue inside the cranium. Recently, the size change in the lateral ventricles has been
measured by our group [20]. The CFD approach presented in
this paper does not directly account for brain motion and the
spinal cord or deformations of the parenchyma. We are currently
working on quantifying the vascular expansion and its dynamic
interaction with the parenchyma and the CSF. When this additional work is completed with the methods of moving boundary
fluid-structure interaction models, it is expected to allow the predictions of intracranial dynamics using only the arterial and venous pressure waves as well as the patient’s brain geometry as
input.
ACKNOWLEDGMENT
The authors would like to thank Materialise Inc. for providing
free research trial license of the Mimics image reconstruction
software. The Fluent Inc. is acknowledged for supporting this
research with trial Fluent and Gambit licenses.
301
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Michalis Xenos received the M.S. and Ph.D. degrees
from the University of Patras, Patras, Greece.
He is a Postdoctoral Research Associate at the
Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois
at Chicago, Chicago. His research interests are in
CFD and transport phenomena.
David C. Zhu received the Ph.D. degree from the
University of California at Davis, Davis. He is an
Assistant Professor, Cognitive Imaging Research
Center at Michigan State University. His main
research interests concerns magnetic resonance
imaging and biomedical engineering.
MahadevaBharath R. Somayaji received the
M.Tech degree in Chemical Engineering from A.C.
College of Technology, Anna University, Chennai,
India. He is currently working towards the Ph.D.
degree in the Laboratory for Product and Process
Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago. His research
interests are in CFD and transport phenomena.
Srinivasa Kondapalli, photograph and biography not available at the time of
publication.
Andreas A. Linninger received the Ph.D. degree
from the Vienna University of Technology, Vienna,
Austria, in 1992.
He is an Associate Professor in the Departments
of Chemical Engineering and Bioengineering at
the University of Illinois at Chicago, Chicago. His
research interests include hydrocephalus, computational models for intracranial dynamics and drug
delivery to the human brain.
Richard D. Penn received the M.D. degree from
Columbia University, College of Physicians and
Surgeons, New York, in 1966.
He is a Professor in the Department of Neurosurgery at the University of Chicago, Chicago, IL.
His main research interests are hydrocephalus and
drug delivery to the brain.