Download Dynamics of lateral ventricle and cerebrospinal fluid in normal and

JOURNAL OF MAGNETIC RESONANCE IMAGING 24:756 –770 (2006)
Original Research
Dynamics of Lateral Ventricle and Cerebrospinal
Fluid in Normal and Hydrocephalic Brains
David C. Zhu, PhD,1 Michalis Xenos, PhD,2 Andreas A. Linninger, PhD,2 and
Richard D. Penn, MD3
DISTURBANCES OF THE CEREBROSPINAL FLUID
(CSF) flow in the brain can lead to hydrocephalus, a
condition affecting thousands of people annually in the
United States. Considerable controversy exists about
fluid and pressure dynamics, and about how the brain
responds to changes in flow patterns and compression
in hydrocephalus. Some information to help understand CSF flow dynamics is currently available from
MRI, including measurements of CSF flow pattern and
velocity at various locations along the CSF pathways
(1–3) and of brain motion (4,5). However, integration of
these measurements to explain CSF flow dynamics is
incomplete. We have used MRI techniques to measure
the lateral ventricle (LV) size change and its temporal
relationship with intracranial blood flow and CSF
movement along the CSF pathways. The ventricular
size changes and CSF flow patterns that we have found
are consistent with the dynamics of intracranial phenomena predicted by a first-principles model introduced by Linninger et al (6). This model, in turn, can be
used to predict intracranial pressure (ICP) dynamics in
normal and hydrocephalic brains. A new quantitative
color-coding technique is introduced to better visualize
the CSF flow patterns.
Purpose: To develop quantitative MRI techniques to measure, model, and visualize cerebrospinal fluid (CSF) hydrodynamics in normal subjects and hydrocephalic patients.
Materials and Methods: Velocity information was obtained
using time-resolved (CINE) phase-contrast imaging of different brain regions. A technique was developed to measure
the change of lateral ventricle (LV) size. The temporal relationships between the LV size change, CSF movement, and
blood flow could then be established. The data were incorporated into a first-principle CSF hydrodynamic model. The
model was then used to generate specific predictions about
CSF pressure relationships. To better-visualize the CSF
flow, a color-coding technique based on linear transformations was developed that represents the magnitude and
direction of the velocity in a single cinematic view.
Results: The LV volume change of the eight normal subjects was 0.901 ⫾ 0.406%. Counterintuitively, the LV decreases as the choroid plexus expands, so that they act
together to produce the CSF oscillatory flow. The amount of
oscillatory flow volume is 21.7 ⫾ 10.6% of the volume
change of the LV from its maximum to its minimum.
Conclusion: The quantification and visualization techniques, together with the mathematical model, provide a
unique approach to understanding CSF flow dynamics.
Key Words: brain ventricle movement; CSF dynamics; visualization; CINE phase-contrast; CSF modeling
J. Magn. Reson. Imaging 2006;24:756 –770.
© 2006 Wiley-Liss, Inc.
BACKGROUND
1
Cognitive Imaging Research Center, Departments of Psychology and
Radiology, Michigan State University, East Lansing, Michigan, USA.
2
Department of Chemical Engineering, University of Illinois at Chicago,
Chicago, Illinois, USA.
3
Department of Neurosurgery, University of Chicago, Chicago, Illinois,
USA.
Contract grant sponsors: Medtronic Inc.; Gilbert Asher; Max Cooper.
Most of the research reported here was conducted while D.C.Z. was
working in the Brain Research Imaging Center at the University of
Chicago.
*Address reprint requests to: D.C.Z., PhD, 358 Giltner Hall, Michigan
State University, East Lansing, MI 48824. E-mail: [email protected]
Received August 22, 2005; Accepted May 24, 2006.
DOI 10.1002/jmri.20679
Published online 6 September 2006 in Wiley InterScience (www.
interscience.wiley.com).
© 2006 Wiley-Liss, Inc.
The LV volumetric change is one of the driving forces
for CSF movement. The magnitude and timing of
these movements needs to be measured to understand quantitatively how much the LV motion contributes to the CSF movement. A periodic 10% to 20%
volume change of the LV was measured by Lee et al (7)
based on the change of MR image signal intensity.
This approach likely contains a serious overestimation. The brain tissue movement within a cardiac
cycle is only a small fraction of a pixel, as found by
Enzmann et al (4) and our own measurements using
the time-resolved (CINE) phase-contrast technique.
Estimating the ventricle size change in the resolution
of pixel size is therefore highly inaccurate. Furthermore, flow artifacts and partial volume effects can
contribute to the change of signal intensity at the
edge of the ventricle. A technique similar to the approach of Oyre et al (8) is instead used in our work.
The edge positions of the ventricle throughout the
756
Dynamics of Lateral Ventricle and CSF
757
Figure 1. The five approximate locations where the twodimensional CINE phase-contrast images were collected. A midsagittal slice is shown. The other four locations are as follows: an axial slice across the middle of
the LV (a), an axial slice across the junction between the
AS and V4 (b), a midcoronal slice at V3 (c), and an axial
slice nearly perpendicular to the basilar artery in the
prepontine region (d).
cardiac cycle are estimated based on the velocity values of the ventricle edge points measured by the CINE
phase-contrast technique. But, unlike Oyre et al (8),
the directions in which the edge positions move are
not assumed in our technique. Along with ventricular
movement, CSF flow rates were measured at the junction of the aqueduct of Sylvius (AS) and the fourth
ventricle (V4) and at the midcoronal section of the
third ventricle (V3), and blood flow rate was measured
in the basilar artery. Since all velocity measurements
could be referenced to the cardiac pulse, their temporal relationship could be established. Because of
the choroid plexus’ complex shape, its motion (which
also drives CSF movement) could not be measured
Figure 2. Demonstration of the color-coding technique. a: The center of the color circle represents zero velocity. The edge of the
color circle represents velocity of 5 mm/second or higher. The 0° or 360° line is indicated. The direction of the color circle is
indicated by the S (superior), I (inferior), A (anterior), and P (posterior), with the positive directions of S–I and A–P. The velocities
at a time frame of the cardiac cycle at two locations (one at the middle of V4 and the other near the entry of the foramen of
Magendie) are equivalently represented by the locations indicated at the color circle. VSI is the velocity in the S–I direction; VAP
is the velocity in the A–P direction; and Vmag is the magnitude of the velocity. b: The velocity view contrast is enhanced by setting
the edge of the color circle to represent 2 mm/second or higher.
758
directly. The timing of its decrease and increase was
assumed to be synchronous with the blood flow at the
basilar artery.
A first-principles model for pulsatile CSF flow, whose
mathematical formulation has been presented by Linninger et al (6), relates three dynamically interacting
systems: the cerebral vascular system, the CSF-filled
ventricular and subarachnoid spaces (SASs), and the
brain parenchyma. With the inputs from MR measurements, the CSF pressure and velocity fields throughout
the brain can be derived, as well as the dynamics of
parenchyma stresses, strains, and displacements using the laws of elastodynamics. The direct MRI measurements and the calculated results from the model
provide not only an understanding of normal CSF flow
dynamics but also important predictions about the
pressure and flow rate changes in hydrocephalus.
To provide a better visualization of CSF movement, a
new color-coding technique for cinematic flow visualization has been developed. Traditional cinematic flow
visualization in CINE phase-contrast MRI has been limited to either the magnitude or one vector component of
the velocity at a time. As a consequence the complex
nature of the flow pattern is not fully represented. The
new color-coding technique combines both the magnitude and direction of the CSF flow velocity in one cinematic view. Using color maps to represent direction is
not new in imaging. For example, color mapping has
often been applied to the directional visualization of
white-matter fiber tracks in diffusion tensor imaging
(DTI) (9). However, the direct translation of the DTI color
mapping technique to flow is not appropriate because
fibers do not require the differentiation of two opposite
directions, as is necessary to depict flow patterns. Our
new color-coding technique represents flow in all directions, and expands color mapping to the time frame,
while maintaining the quantitative nature of the CSF
flow dynamics.
MATERIALS AND METHODS
Data Acquisition and Velocity Calculation
The two-dimensional CINE phase-contrast technique
(10,11) was applied to collect CSF flow data from 11
subjects (eight normal subjects from 23 to 52 years old,
and three with hydrocephalus) on a 3T GE Signa system (GE Medical Systems, Milwaukee, WI, USA)
equipped with a standard quadrature birdcage head
coil. All volunteers signed the consent forms approved
by the Institutional Review Board at the University of
Chicago.
Of the three subjects with hydrocephalus, one subject has mildly enlarged ventricles but was neurologically normal. The second subject has the signs and
symptoms of adult communicating hydrocephalus, and
large ventricles. The third subject has the signs and
symptoms of adult obstructive hydrocephalus, and
moderately enlarged ventricles.
The two-dimensional CINE phase-contrast images
were collected at five different locations (Fig. 1): 1) the
midsagittal slice to view the major CSF pathways; 2) an
axial slice across the middle of the LV to investigate the
Zhu et al.
LV volumetric change; 3) an axial slice across the junction between the AS and V4 to measure the CSF flow
rate; 4) a midcoronal slice at V3 to measure the CSF
flow rate; and 5) an axial slice nearly perpendicular to
the basilar artery in the prepontine region to measure
the blood flow rate. For the first two locations, velocities
in all three directions were measured to investigate the
flow dynamics based on the simple four-point method
(11). Images at 16 equidistant time frames were reconstructed per cardiac cycle. For the latter three locations, only the velocity perpendicular to the slice of
interest was measured so that data could be collected
with a higher temporal resolution. The simple two-point
method was used to calculate the velocity (11). Images
at 32 equidistant time frames were reconstructed per
cardiac cycle. For all studies, flow compensation and
peripheral gating were applied. For CSF flow measurement, a low maximum measurable velocity (VENC) of 5
cm/second was chosen as the limit so that a reasonable
velocity resolution could be achieved. For the blood flow
measurement of the basilar artery, a VENC of 100 cm/
second was chosen. Other acquisition parameters were:
TE ⫽ 8.4 msec, TR ⫽ 18 msec, flip angle ⫽ 20°, field of
view (FOV) ⫽ 24 cm, slice thickness ⫽ 5 mm, matrix
size ⫽ 256 ⫻ 128 for the midsagittal acquisition and
256 ⫻ 192 for the other acquisitions, number of excitations ⫽ 2, and full phase FOV for the midsagittal
acquisition, but 75% phase FOV for the other acquisitions to achieve an effective matrix resolution of 256 ⫻
256.
The CSF pathway was segmented for analysis based
on the T2-weighted fast spin echo (FSE) image (TE ⫽
100 msec, TR ⫽ 4200 msec, echo train length ⫽ 16,
FOV ⫽ 24 cm, slice thickness ⫽ 5 mm, interslice spacing ⫽ 1 mm, number of slices ⫽ 16, matrix size ⫽ 256 ⫻
256) in which CSF was enhanced. The velocity at every
pixel within the regions of CSF was calculated. To reduce the possibility of a spatially-dependent offset velocity due to eddy currents or head motion, the velocity
at each pixel location was corrected by basic subtraction of the time-averaged “velocity” of a nearby solid
brain tissue “background” within a 29 ⫻ 29 mm2 region
having this pixel at its center (4,5,12). In calculating the
velocity of the solid brain tissue, the velocity at each
pixel location was corrected by basic subtraction of the
time-averaged “velocity” of this pixel itself. These approaches are based on the fact that solid brain tissue
does not accumulate net displacement over a complete
cardiac cycle (4,5).
The flow rate at the midcoronal slice across V3, at the
junction of the AS and V4, or in the basilar artery, is
estimated by the multiplication of the average velocity
at the cross-section of the CSF/blood pathway and the
corresponding area. The cross-section of the fluid pathway is segmented based on an image that showed the
best cross-section from the T2-weighted and T1weighted images. The mean oscillatory flow rates of CSF
at the two cross-sections were also calculated based on
the average of the forward and backward flow rate magnitudes through a full cardiac cycle. The mean flow
volume per cycle at the junction of the AS and V4 was
calculated based on the average of the forward and
backward flow volumes through a full cardiac cycle.
Dynamics of Lateral Ventricle and CSF
759
Inversion-prepared T1-weighted volumetric axial or
sagittal images (with CSF signal suppressed) were also
collected for the purpose of estimating the sizes of different regions of the CSF pathway. The acquisition parameters were: TI ⫽ 725 msec, flip angle ⫽ 6°, receiver
bandwidth ⫽ ⫾31.25 kHz, FOV ⫽ 24 cm, slice thickness ⫽ 1.5 mm, number of slices ⫽ 120, and matrix
size ⫽ 256 ⫻ 192.
Estimation of LV Volumetric Change
The edge between solid brain tissue and the LV is first
manually drawn based on an image that shows the best
cross-section from the T2-weighted and T1-weighted images and that has been acquired at exactly the same
scan plane (Fig. 1). This drawing marks the initial pixel
positions during a full cardiac cycle. The position shift
of each pixel at the edge of the LV is then estimated for
each time frame of the cardiac cycle by integrating the
velocity over time, including both components of the
velocity. The expected position of each original edge
pixel is estimated by adding the initial position with the
position shift. The edge points of the LV at each cardiac
time frame, including the initial time frame, are connected together by spline interpolation (13). The area of
the enclosed region at each cardiac time frame is calculated. The percent change of the enclosed region from
the maximum to the minimum within the cardiac cycle
is then calculated by comparing it to the time-averaged
area of this enclosed region throughout the cardiac
cycle. Assuming the LV increases and decreases uniformly across the whole ventricle, the percent volume
change of the LV is now estimated based on the following equation (See Appendix A for derivation):
冉
fV ⫽ 1 ⫹
fA
4
冊 冉
3
⫺ 1⫺
fA
4
冊
3
(1)
with
could be evaluated. If the procedure were perfect, the
“LV” would not have changed size during the full cardiac cycle. The two-dimensional CINE phase-contrast
images were collected at an axial slice from the phantom, with the same scanning parameters as the twodimensional CINE phase-contrast imaging protocol for
human subjects at the second of the five slice locations.
A photopulse sensor was hooked to the finger of a human volunteer to detect in vivo cardiac pulse, which
served as the mean for peripheral gating during phantom data collection. Six image data sets were collected
and were processed to estimate the LV volumetric
change with the method discussed in the previous
paragraphs.
Interpretation of Temporal Relationship
The center of gravity of the CSF flow waveform (TC_CSF)
in the head-to-body (superior-to-inferior [S–I]) or bodyto-head (inferior-to-superior [I–S]) direction is estimated based on the weighted average,
T C_CSF ⫽
¥
last time frame at the same flow direction
i⫽first time frame at a specific flow direction
last time frame at the same flow direction
i⫽first time frame at a specific flow direction
¥
Ti 䡠 Fi
Fi
(2)
where: Ti ⫽ time at the ith cardiac time frame in a
specific flow direction, and Fi ⫽ flow at the ith cardiac
time frame in a specific flow direction.
The CSF flow direction switching point is estimated to
be the midpoint between the centers of gravity of the S–I
and the I–S flow waveforms because the transition time
point necessarily has a slow flow and is therefore difficult to measure directly with a high level of precision.
The center of gravity of the LV area waveform when it
is either above or below the average area is estimated in
the same manner, corresponding to the time point at
the maximum or minimum LV area.
CSF Hydrodynamic Model
fA ⫽
A max ⫺ Amin
Aave
where: fV ⫽ the fraction of the LV volume change from
maximum to minimum; fA ⫽ the fraction of LV area
change from maximum to minimum; Amax ⫽ the maximum LV area; Amin ⫽ the minimum LV area; and Aave ⫽
the average LV area.
The LV volume is estimated in units of voxel size
based on the CSF-suppressed T1-weighted volume images, and then is converted to milliliters. The CSF region is isolated from its surrounding solid brain tissue
based on image signal contrast. The change, in milliliters, from the maximum to the minimum volumes is
estimated from the LV volume and fV.
Phantom Study
The above procedure of estimating LV volumetric
change was also applied to data collected from static
silicone gel phantoms, using a region of interest (ROI)
for analysis similar in size to the LV of the human brain,
so that the potential underestimation or overestimation
The mathematic equations and assumptions applied to
build a CSF hydrodynamic model have been fully discussed by Linninger et al (6). Building a subject-specific
model requires a set of fixed variables and a set of input
boundary conditions that are assumed to be the same
across subjects, as well as a set of subject-specific brain
variables. The set of fixed variables are the CSF and
tissue properties as listed in Table 1. The input boundary conditions for the system are the CSF production
rate, the choroid plexus expansion, and the venous
blood pressure derived from the literature (6). The subject-specific variables, including ventricular areas, dimensions of the foramina and SAS, are extracted from
CSF-suppressed T1-weighted volumetric images using
the graphical image reconstruction tool, Mimics (17).
The application of the model will be demonstrated with
two case studies (one normal brain and one communicating hydrocephalic brain).
Velocity Color-Coding Technique
Two (red and green) of the three colors in the red-greenblue (RGB) color model were selected to represent the
760
Zhu et al.
Table 1
Tissue and Fluid Properties
Property
Value
Source
2100 N/m
3500 N/m2
1004-1007 kg/m3
10–3 Pa second
8 N/m (normal)
0.35 ⫻ 10-3 (N second)/m
1000 kg/m3
1.067 ⫻ 10–11 m3/(Pa second)
Miga et al (14)
Derived from Aimedieu and Grabe (15)
Bruni (16)
Assumed as for water
Derived from the Young Modulus
Assumed; low dampening effect
Equal to water
Estimated from medical data for hydrocephalic humans
2
The measured young modulus of the tissue
Fluid density, ␳f
Fluid viscosity, ␮
Spring elasticity, ke
Brain dampening, kd
Ependyma density, ␳w
Reabsorption constant, ␬
two velocity components. A color circle can be built
based on the mixture of these two colors (Fig. 2a), with
the color intensity representing the magnitude of the
velocity and the hue of color representing the direction
of the velocity. The velocity magnitude is directly proportional to the color intensity, which in turn is based
on the total amount of color. The center of the circle has
zero color intensity, corresponding to zero velocity. The
edge of the circle has the maximum color intensity,
corresponding to the maximum velocity magnitude to
be represented. The angle of the velocity is represented
by the linear combination of the two colors. One pure
color, green in this example, represents the 0° velocity
direction. The other nearly pure color, red in this example, represents the velocity direction just below 360°.
Therefore, the velocity-color map transformation can
follow these equations:
f red ⫽
f green ⫽
Vmag
␪
⫻
Vmax 360
冉
(3)
冊
Vmag
␪
⫻ 1⫺
Vmax
360
f blue ⫽ 0
where, fred, fgreen, fblue ⫽ fraction of red, green, or blue in
an RGB color space, ␪ ⫽ the angle of velocity in degrees,
Vmax ⫽ the maximum velocity to represent, Vmag ⫽ magnitude of velocity, and Vmag ⫽ Vmax for Vmag ⱖ Vmax. Thus,
the total fraction of color
f total ⫽ fred ⫹ fgreen ⫹ fblue ⫽
Vmag
Vmax
␪⫽
360
f green
⫹1
fred
(5)
360
␪
V mag ⫽ 共fredVmax兲
V AP ⫽ Vmagcos共␪兲
V SI ⫽ Vmagsin共␪兲
In some cases, abrupt changes of flow color (called
discontinuity artifacts in this article, as in DTI (9)) will
necessarily be seen when the CSF flow contains velocities at the red– green transition region. This occurs
because color-coding starts with pure green at 0° and
ends with nearly pure red at just below 360°. These
artifacts disappear after rotating the color circle, for
example, by 90° (Fig. 3). An appropriate orientation of
the color circle is one way to remove the discontinuity
artifacts. As an alternative approach, the simultaneous
utilization of these two color circles can be applied for
the visualization of complex flow patterns. Because of
high sensitivity to the red– green abrupt transition, the
discontinuity artifacts can even be applied to advantage
for identifying the flow directions with a high level of
precision.
The above color-coding technique was implemented
in Matlab, and was applied to all pixels along the CSF
pathway at all cardiac time frames collected. The colorcoded velocity map was then overlaid on a high-resolution T2-weighted FSE image.
RESULTS
(4)
ftotal, is linearly related to Vmag up to Vmax and is independent of the velocity angle. The velocity magnitude
view contrast can be adjusted by changing Vmax, analogous to the window level in image viewing. With Vmax
reduced, the velocity magnitude view contrast is enhanced, and thus the flow directions are emphasized
(Fig. 2b).
At any pixel location, if the velocity is smaller than
Vmax, the color map can easily converted back to numeric velocity based on the following equations:
MRI Measurements of Normal Subjects
The temporal relationship between the blood flow rate
through the basilar artery, the LV volumetric change,
the flow rate at the midcoronal section of V3, and the
flow rate at the junction of the AS and V4 in normal
subjects is shown in Figs. 4 and 5. All data were normalized to percent of the cardiac cycle to remove the
difference in heart rate. The normal subjects showed
the following temporal characteristics (Table 2): 1) The
LVs begin to decrease between the minimum and maximum flow time points in the basilar artery, specifically,
8.24 ⫾ 8.64% after the minimum flow time point and
Dynamics of Lateral Ventricle and CSF
761
Figure 3. The potential abrupt change of flow color (called discontinuity artifacts in this work) when the CSF flow contains
velocities at the red– green transition region. The discontinuity artifacts in (a) are not seen after a 90° rotation of the color circle
to the one in (b). The same is true for (b), with a –90° rotation of the color circle to the one in (a).
7.39 ⫾ 10.04% before the maximum flow time points. 2)
The LV expands ahead of the switch of CSF flow direction from the direction of S–I to that of I–S by 15.16 ⫾
8.44% of the cardiac cycle, and then decreases ahead of
Figure 4. Eight normal subject study. The temporal relationship between the LV area
and the CSF flow rate at the
junction of the AS and V4.
Each data point is shown as
mean ⫾ SD.
the switch of flow direction from the direction of I–S to
that of S–I by 11.27 ⫾ 9.95% of the cardiac cycle. Assuming the change of LV size is one of the driving forces
of CSF flow, there is a delayed flow response. The LVs
762
Zhu et al.
Figure 5. The temporal relationship
(based on five normal subjects) between the basilar arterial flow rate,
the LV area, the CSF flow rates at V3,
and at the junction of the AS and V4.
All the flow rate and area measurements were normalized within the
time scale of each cardiac cycle and
as a percent of the absolute maximum before being combined. Each
data point is shown as mean ⫾ SD.
have an average volume of 16.4 ⫾ 4.7 mL. The amount
of volume change from the LV’s maximum to its minimum was estimated to be 0.147 ⫾ 0.084 mL. The
amount of CSF oscillatory flow volume (the average of
S–I and I–S flow volumes) in one cycle was 0.0289 ⫾
0.0161 mL. This amount of CSF oscillatory flow volume
is 21.7 ⫾ 10.6% of the volume change of the LV from its
maximum to its minimum. As shown in Table 2 (also
see Movie 1 in the Supplementary Material (Movies 1-5)
to visualize the LV movement; available online at:
http://www.interscience.wiley.com/jpages/10531807/suppmat/) for the eight normal subjects studied,
the maximum displacement of all the pixels at the edge
of the LV was 0.128 ⫾ 0.042 mm on the same scanning
plane, and was 0.165 ⫾ 0.042 mm in all three spatial
directions. The range of pixel displacement was only a
small fraction of the pixel size of 0.938 ⫻ 0.938 mm2.
The LV volume change was estimated to be 0.901 ⫾
0.406%. The mean oscillatory flow rate (as described in
Materials and Methods) at the center of V3 (based on
seven subjects) was 3.91 ⫾ 1.46 mL/minute, and at the
junction of the AS and V4 it was 3.97 ⫾ 1.62 mL/
minute.
The MRI measurements for the following case studies
are also included in Table 2. The color-coding technique
shown in Fig. 2 was used to generate the movies for the
midsagittal CSF visualization with the Vmax set at 5 mm/
second for almost all case studies. To visualize a higher
velocity range in the communicating hydrocephalus case
study, a Vmax of 10 mm/second was applied instead.
Case Studies
Case 1. Normal Subject (see Table 2; Fig. 6; and Movie
2 in the Supplementary Material)
This case study is a representative of the eight normal
subjects. The flow rate measurements are within the
ranges of the corresponding measurements of the normal subjects. The temporal relationship between measurements is similar to other normal subjects and is
shown in Fig. 6. Figure 6 and Movie 2 both show a clear
forward–reverse oscillatory CSF movement in the pathway. The application of the flow visualization technique
is demonstrated by watching Movie 2: a higher flow
velocity is seen at the prepontine SAS and at the foramen of Magendie. The flow pattern at V4 is more com-
763
*Temporal relationships were based on percent of cardiac cycle.
ASV4 ⫽ junction between the aqueduct of Sylvius and V4, V4 ⫽ fourth ventricle, V3 ⫽ third ventricle, LV ⫽ lateral ventricle, Max ⫽ maximum, Min ⫽ minimum, Max-Min LV ⫽ difference between
the maximum and minimum lateral ventricle volume.
Subject studies
Overall: normal
3.97 ⫾ 1.62 3.91 ⫾ 1.46 0.901 ⫾ 0.406 16.4 ⫾ 4.7 0.147 ⫾ 0.084 0.0289 ⫾ 0.0161 21.7 ⫾ 10.6 0.128 ⫾ 0.042 0.165 ⫾ 0.042 15.16 ⫾ 8.44 11.27 ⫾ 9.95 8.24 ⫾ 8.64 7.39 ⫾ 10.04
CSF
Case 1: normal
3.44
4.51
1.550
9.8
0.152
0.0236
15.5
0.105
0.128
22.0
20.0
0.71
11.79
CSF
Case 2:
9.12
9.00
1.161
30.9
0.358
0.0609
17.0
0.140
0.182
–4.2
–9.1
34.34
–18.71
abnormal CSF
flow but
normal brain
function
Case 3:
29.11
27.91
0.312
250.3
0.782
0.2274
29.1
0.154
0.198
27.8
26.2
–11.50
24.00
communication
hydrocephalus
Case 4:
2.36
3.32
0.822
35.5
0.291
0.0157
5.39
0.165
0.195
29.7
24.9
–14.11
39.11
obstructive
hydrocephalus
Volume of
LV (mL)
Max-Min LV
change (mL)
Mean flow
volume per cycle
at ASV4 (mL)
Max-Min LV
% volume
change
Mean flow
at V3 (mL/
minute)
Mean flow
at ASV4
(mL/minute)
Table 2
LV Volumetric Change, CSF Flow, Basilar Artery Blood Flow, and Temporal Relationships*
Mean flow
volume
over MaxMin LV
change (%)
Average edge
pixel in-plane
position shift
(mm)
Average edge
pixel position
shift all three
directions
(mm)
LV
expansion
precedes
change of
S-I to I-S (%
cycle)
LV size
decrease
precedes
change of
I-S to S-I (%
cycle)
Min basilar
artery blood
flow
precedes
LV size
decrease
(% cycle)
LV size
decrease
precedes
max basilar
artery blood
flow (%
cycle)
Dynamics of Lateral Ventricle and CSF
plicated than that at the narrow sections of the pathway. The I–S flow from the foramen of Magendie loses
some momentum in the I–S direction in V4 and diverts
to the anterior direction. A flow void is also seen in V4.
There is an overall strong presence of flow in the posterior–anterior direction. These observations are in
good agreement with Quencer et al (18).
In this normal subject case study, the following subjectspecific variables have been used in building the model:
volume of LV ⫽ 9.81 mL, volume of V3 ⫽ 2.5 mL, volume
of V4 ⫽ 3.32 mL, volume of SAS ⫽ 103.0 mL, radius of
foramina of Monro (FM) ⫽ 1.5 mm, length of FM ⫽ 3 mm,
radius of AS ⫽ 1.0 mm, length of AS ⫽ 11 mm, radius of
foramina of Luschke (FL) ⫽1.25 mm and length of FL ⫽ 15
mm. The accuracy of this model was validated by its
relatively close match with the MRI flow rate measurement at the region between the AS and V4 (Fig. 7), given
that our simulations were performed with a standard sinusoidal function (6). The mean pulsatile flow estimated
from the model for this region was 2.84 mL/minute. The
predicted ICP along the CSF pathways, from the LVs to V4
and cranial SAS are depicted in Fig. 8. The pressure difference driving the CSF flow in the ventricles is approximately 7 Pa. This low pressure difference agrees with the
measurements in animal studies by Penn et al. (19).
2. Neurologically Normal Subject But Abnormal
Ventricle Size and CSF Flow (see Table 2; Fig. 9; and
Movie 3 in the Supplementary Material)
Anatomic images show brain atrophy and a larger than
expected SAS inferior to the cerebrum. Both the volume
of the LV and the pulsatile flow rate were approximately
two times that of the normal subjects (Table 2). Table 2
and Fig. 9 also show that the LV starts to decrease later
than normal. Instead of decreasing before the change
from S–I to I–S, as in normal subjects, the LV starts to
decrease 9.1% of a cardiac cycle later. Except at the
SAS at the inferior region of the cerebrum, Movie 3
demonstrates a similar flow pattern as in normal cases,
but of a larger magnitude.
3. Patient With Adult Communicating Hydrocephalus
(see Table 2; Fig. 10; and Movie 4 in the
Supplementary Material)
The LV volume is approximately 15 times that of normal
subjects, and the pulsatile flow rate (approximately 29
mL/minute) is approximately 7.3 times normal. The
anatomic images also show generalized atrophy. Although the pixels at the ventricle wall move more than
in the normal subjects, this does not translate into a
larger LV volume percent change because different regions of the ventricle decrease and increase in a highly
asynchronous manner. The percent change is only onethird of the normal subjects. However, because the LV
is highly enlarged, the change of LV volume is approximately 5.3 times that of normal subjects. As shown in
Fig. 10, the temporal relationship of basilar artery blood
flow, the LV volumetric change and the CSF flow is
similar to that of the normal cases. However, Fig. 10
does not convey the complete flow pattern, which is
better depicted by Movie 4. Unlike the normal cases,
764
Zhu et al.
Figure 6. Case study of a normal brain. The temporal
relationship between the basilar arterial flow rate, the
LV area, the CSF flow rates at V3, and at the junction of
the AS and V4.
Movie 4 shows the simultaneous coexistence of CSF
flow in opposite directions at various locations, such as
in V3 and the AS. Other complex flow patterns are also
seen at various locations of the CSF pathway.
In this hydrocephalic case study, the following subject-specific variables have been used in building the
model: volume of LV ⫽ 250.2 mL, volume of V3 ⫽ 11.3
mL, volume of V4 ⫽ 4.57 mL, and volume of SAS ⫽
105.0 mL; the dimensions of the foramina were the
same as in the normal subject case study except that a
radius of 2 mm instead of 1 mm was estimated for the
AS. A condition of CSF malabsorption at the arachnoid
granulations was applied in the model, based on clinical evidence (6). The accuracy of this model is validated
by comparing the predicted CSF volumetric flow cardiac time course with MRI measurement at the region
between the AS and V4 (Fig. 11). The estimated mean
oscillatory flow rate across the cardiac cycle at the junction of the AS and V4 was 29.6 mL/minute. The maximum flow rate at the same region was 48.6 mL/minute.
Figure 7. Comparison of CSF flow rates measured with
CINE phase-contrast MRI and model simulation results
at the junction between the AS and V4 for the normal
brain study.
Dynamics of Lateral Ventricle and CSF
765
Figure 8. Results from model simulation. The ICP profile along the ventricular pathways for the normal brain
study. Reference pressure: 1 atm or 1.01325 ⫻ 105 Pa.
Despite a predicted ICP rise of 1200 Pa within the entire
ventricular system, the pressure difference between the
LV and the SAS (transmural pressure) does not exceed
50 Pa in each cycle (Fig. 12). This low pressure difference corresponds with the recent animal studies by
Penn et al (19). In that study the pressure gradients
between ventricles, brain tissue, and SAS in the kaolininduced hydrocephalic dog brains were below 66.7 Pa.
Case 4: Patient With Obstructive Hydrocephalus Due
To Aqueductal Stenosis (see Table 2; Fig. 13; and
Movie 5 in the Supplementary Material)
The LV volume is moderately enlarged, approximately
two times that of the normal subjects, and the pulsatile
flow rate (approximately 2.36 mL/minute at the junction of the AS and V4) is below that of the normal
Figure 9. Case study of an abnormal CSF flow. The temporal relationship between the basilar arterial flow rate, the LV area, the
CSF flow rates at V3, and at the junction of the AS and V4.
766
Zhu et al.
Figure 10. Case study of an adult communicating hydrocephalus. The temporal relationship between the
basilar arterial flow rate, the LV area, the CSF flow rates
at V3, and at the junction of the AS and V4.
subjects. The LV percent volume change is within the
range of the normal subjects. However, because the LV
is enlarged, the change of LV volume from its maximum
to its minimum is approximately two times that of normal subjects. Because of the aqueductal obstruction,
the pulsatile flow volume at the junction of the AS and
V4 is only 5.39% of the LV volume change. As shown in
Fig. 13, the temporal relationship of basilar artery blood
flow rate, the LV volumetric change, and the CSF flow
rate at the junction of the AS and V4 is similar to that of
the normal cases. The CSF flow pattern in V3 is different from normal with a relatively shorter duration of
flow in the anterior–posterior direction but a relatively
longer duration of flow in the posterior–anterior direction. The unusually stagnant flow pattern in V3 of this
patient is also depicted in Movie 5.
Figure 11. Comparison of CSF flow rates measured
with CINE phase-contrast MRI and model simulation
results at the junction between the AS and V4 for the
communicating hydrocephalus case study.
Dynamics of Lateral Ventricle and CSF
767
Figure 12. Results from model simulation. The ICP profile along the ventricular pathways in the communicating hydrocephalus case study. Reference pressure: 1
atm or 1.01325 ⫻ 105 Pa.
Phantom Study
DISCUSSION
Analysis of the six data sets collected from the gel phantom images showed a 0.169 ⫾ 0.071% LV volume
change during a full “cardiac cycle.” The ROI used as
the “LV” had the area range from 762 to 1322 mm2
(1052 ⫾ 334 mm2). The LV volumetric change for the
phantom should have been zero if the procedure were
perfect.
An understanding of the magnitude and timing of LV
volumetric change are needed to evaluate how much
the LV motion contributes to CSF movement in normal
subjects and hydrocephalic patients. Our new quantification technique for LV motion relies on the accurate
velocity information measured by the CINE phase-contrast technique. We applied the general velocity estima-
Figure 13. Case study of an adult obstructive hydrocephalus: The temporal relationship between the basilar
arterial flow rate, the LV area, the CSF flow rates at V3,
and at the junction of the AS and V4.
768
tion technique that has been used by other groups for
CSF and solid brain tissue measurements (4,5). Our
technique of estimating the ventricle size change labels
the solid brain tissue immediately adjacent to the true
LV edge as the “edge.” This approach allows the velocity
at each pixel location to be corrected by the time-average “velocity” of this pixel itself, taking advantage of the
fact that there is no net displacement of solid brain
tissue over a complete cardiac cycle. The underlying
assumption of our technique is that the labeled “edge”
pixel within the solid brain tissue moves simultaneously with the same magnitude and direction at all
points of the cardiac cycle with the corresponding and
adjacent pixel at the true edge of the ventricle. If this
assumption does not hold, the LV size change may be
under- or overestimated. On the other hand, the maximum and minimum ventricle sizes are compared to
find the ventricle size change. This type of comparison
likely leads to some systematic overestimation, due to
system imperfection and noise, as suggested by the
phantom data of nonzero volumetric change per cardiac
cycle. To utilize the velocity measurement at a single
slice location within a time-limited scan session, the
estimation of the LV size change has been based on a
model that the LV is a sphere and it increases and
decreases uniformly. To improve the estimation of LV
size change, velocity will need to be measured at multiple slice locations, and this method is being actively
investigated.
The motion of the choroid plexus has not been assessed directly because of its complex shape. The expansion of the choroid plexus is assumed to be synchronous with each pulse of blood through the basilar
artery. The middle and anterior of cerebral arteries,
which feed the vascular bed, could be better choices.
However, the basilar artery is easier to identify for flow
measurement within a limited total scan time and thus
was used in this study. The blood flows in the basilar
artery and the cerebral arteries are assumed to share
the same temporal characteristics based on their anatomic proximity.
Based on the temporal relationship found in the eight
normal subjects between the basilar artery blood flow
rate, the LV volumetric change, and the CSF movement,
the LV appears to decreases as the choroid plexus also
expands. These two forces act together to produce the
CSF oscillatory flow. They are in turn driven by the
pulsation in blood flow. The temporal relationship between the LV volumetric change and the basilar artery
blood flow rate (Fig. 5) measured by us shows a good
agreement with the temporal relationship between the
intracranial volumetric change and the transcranial arterial inflow rate measured by Alperin et al (3). The LV
volumetric change is expected to be a fraction of the
intracranial volumetric change. Thus the LV volumetric
change of 0.147 ⫾ 0.084 mL we measured in normal
subjects is consistent with the intracranial volumetric
change of 0.34 –1.3 mL measured by Alperin et al (3).
The temporal relationship between the CSF oscillatory
flow directions at the AS or V3, and the LV volumetric
change, indicates that the LV motion plays an important role in the CSF flow. However, the oscillatory flow
volume only accounts for about 21.7 ⫾ 10.6% of the LV
Zhu et al.
volume change. This suggests that some ventricular
CSF moves into the brain parenchyma during its decrease in size and is released from the brain parenchyma during expansion. The spinal and cisternal CSF
volumetric changes very likely contribute to CSF pulsation, but their contributions will require further investigation.
The mean oscillatory flow rate at the junction of the
AS and V4 was measured to be 3.97 ⫾ 1.62 mL/minute,
which is higher than the measurement of 1.72 ⫾ 0.34
mL/minute at the AS made by Enzmann et al (4). This
discrepancy could have been caused by differences in
ROI drawing and in the location of the two measurements. A lower flow rate measurement would not alter
the general observation that only a fraction of the LV
volume change is needed to drive the CSF oscillatory
flow.
The simulations were performed with a standard sinusoidal function (6). In reality the pulsatile CSF waveform is more complicated. As a result there are unavoidable variations between the measured and
simulated CSF waveforms. However, given the intersubject variations that have been seen in MRI flow measurements, it appears acceptable to say that the measurements agree with the simulations of the flow
dynamics (6). The quantitative agreement between the
MRI measured flow rate and that predicted by the
model in both the normal subject case study (Fig. 7) and
in the communicating hydrocephalic subject case
study (Fig. 11) further validates our hydrodynamic
model. This also means that the pressure differences
needed to create such flow can be estimated. As Fig. 8
illustrates, these pressure differences are low. The
maximum difference between the LV and the SAS is less
than 7 Pa in either direction of flow. This is as one might
expect from a fluid system connected by relatively low
resistance pathways and small amounts of fluid movement. Note that the flow rate would be the same regardless of absolute pressures within normal ranges. This is
true until the blood flow, the driving force of the CSF
flow in the intracranial space, is significantly reduced
by elevated ICP. Until cerebral perfusion is compromised, the dynamic CSF flow is independent of ICP. A
subject standing up will have the same flow as when
lying down even though the ICP varies due to the position by up to 15 torr (1999 Pa) (20).
Importantly, even if the ICP is elevated as in communicating hydrocephalus, the pressure gradients needed
to produce CSF flow remain low. As Fig. 12 shows for
our example of communicating hydrocephalus, the
model predicts a difference of less than 50 Pa. This is
true even with the increased flow rates measured by
CINE phase-contrast MRI in this patient.
The relatively low pressure gradient and the reversal
of the gradients that create the oscillatory flow pattern
demonstrated in CINE phase-contrast MRI means that
large pressure gradients cannot exist between the outside of the brain and the ventricles. Hydrocephalus
cannot be produced by such forces as hypothesized by
Hakim et al (21). Moreover, to produce oscillatory CSF
motion the huge pressure gradients suggested by
Hakim et al (21) would have to invert in each cardiac
cycle for CSF to reverse its flow direction in the ventric-
Dynamics of Lateral Ventricle and CSF
ular system and the prepontine SAS. Recent measurements published using ICP monitors in a dog model of
hydrocephalus confirm this (19). In spite of massive ICP
increases with acute or chronic hydrocephalus, pressure gradients between the ventricles, brain tissue, or
SAS could not be found. Hakim et al’s (21) hypothesis of
pressure gradients creating hydrocephalus will have to
be reconsidered, as well as any other theories that hypothesize large pressure gradients in the brain and
fluid spaces.
The color-coded technique presented in this work
brings together the information of both the magnitude
and direction of the CSF flow in a single cinematic view.
Since this technique is based on linear transformations
of the velocity within the magnitude range to view selected by the user, its quantitative nature has been
maintained. This visualization method is expected to
provide assistance in diagnosis and surgical planning.
The technique discussed here is for two-dimensional
flow visualization. By adding another RGB color (blue),
the same concept can be expanded to three-dimensional flow visualization. However, the visualization becomes more complex for three-dimensional expansion
and less straightforward than its two-dimensional
counterpart. A visualization technique using streamlines, arrows, and particle paths developed by Buonocore (22) for cardiac imaging might also be promising to
visualize the CSF flow patterns.
In conclusion, the quantification and visualization
techniques, together with the mathematical model, provide a unique approach to understanding CSF flow dynamics. The results provide information on temporal
and pressure relationships in normal subjects and
demonstrate the abnormal CSF dynamics in hydrocephalic patients.
ACKNOWLEDGMENTS
We thank Dr. Michael Buonocore for suggestions on
data acquisition and velocity calculation, Dr. David
Levin for suggestions on velocity calculation, Dr. WenMing Luh for suggestions on volumetric imaging, Mr.
Robert Lyons on scanning assistance, Dr. David Wright
for carefully proofreading this manuscript, and Materialise Inc. for providing a trial version of the Mimics
reconstruction software.
APPENDIX A
LV Volumetric Change Fraction Calculation
The following derivation is based on the assumption
that the LV expands uniformly. Since the change of the
ventricle size is small, we can also assume that the
radius increase when the ventricle increases to its maximum size is the same as the radius decrease when it
decreases to its minimum size.
Let Aave ⫽ the mean area at the cross-section of the
LV ⫽ ␲ R2, where R ⫽ radius, Amax ⫽ maximum area
after ventricle expansion, and Amin ⫽ minimum area
after the ventricle decreasing its size. The fractional
area change of the LV between the Amax and Amin can be
estimated as:
769
fA ⫽
A max ⫺ Amin ␲共R ⫹ ⌬R兲2 ⫺ ␲共R ⫺ ⌬R兲2 4⌬R
⬇
⫽
Aave
␲R2
R
Then,
⌬R ⫽
fA
R
4
Assuming the LV is equivalent to a sphere, the average
4
volume of the LV is Vave ⫽ ␲R3, and the LV will have a
3
4
maximum value of Vmax ⫽ ␲共R ⫹ ⌬R兲3 and a mini3
4
mum value of Vmin ⫽ ␲共R ⫺ ⌬R兲3. The fractional
3
volume change of the LV between the maximum and
minimum can be estimated as
4
4
␲共R ⫹ ⌬R兲3 ⫺ ␲共R ⫺ ⌬R兲3
3
V max ⫺ Vmin 3
fV ⬇
⫽
Vave
4 3
␲R
3
共R ⫹ ⌬R兲 ⫺ 共R ⫺ ⌬R兲
⫽
R3
3
⫽
3
冉
冊 冉
fA
R⫹ R
4
3
fA
⫺ R⫺ R
4
R3
冉 冊 冉 冊
⫽ 1⫹
fA
4
3
⫺ 1⫺
fA
4
冊
3
3
(A1)
REFERENCES
1. Quencer RM, Post MJ, Hinks RS. Cine MR in the evaluation of
normal and abnormal CSF flow: intracranial and intraspinal studies. Neuroradiology 1990;32:371–391.
2. Naidich TP, Altman NR, Gonzalez-Arias SM. Phase contrast cine
magnetic resonance imaging: normal cerebrospinal fluid oscillation
and applications to hydrocephalus. [Review.] Neurosurg Clin N Am
1993;4:677–705.
3. Alperin NJ, Lee SH, Loth F, Raksin PB, Lichtor T. MR-Intracranial
pressure (ICP): a method to measure intracranial elastance and
pressure noninvasively by means of MR imaging: baboon and human study. Radiology 2000;217:877– 885.
4. Enzmann DR, Pelc NJ. Brain motion: measurement with phasecontrast MR imaging. Radiology 1992;185:653– 660.
5. Poncelet BP, Wedeen VJ, Weisskoff RM, Cohen MS. Brain parenchyma motion: measurement with cine echo-planar MR imaging.
Radiology 1992;185:645– 651.
6. Linninger AA, Tsakiris C, Zhu DC, et al. Pulsatile cerebrospinal
fluid dynamics in the human brain. IEEE Trans Biomed Eng 2005;
52:557–565.
7. Lee E, Wang JZ, Mezrich R. Variation of lateral ventricular volume
during the cardiac cycle observed by MR imaging. AJNR Am J
Neuroradiol 1989;10:1145–1149.
8. Oyre S, Ringgaard S, Kozerke S, et al. Quantitation of circumferential subpixel vessel wall position and wall shear stress by multiple sectored three-dimensional paraboloid modeling of velocity encoded cine MR. Magn Reson Med 1998;40:645– 655.
9. Pajevic S, Pierpaoli C. Color schemes to represent the orientation of
anisotropic tissues from diffusion tensor data: application to white
matter fiber tract mapping in the human brain. Magn Reson Med
1999;42:526 –540.
10. Dumoulin CL, Souza SP, Walker MF, Yoshitome E. Time-resolved
magnetic resonance angiography. Magn Reson Med 1988;6:275–
286.
11. Pelc NJ, Bernstein MA, Shimakawa A, Glover GH. Encoding strategies for three-direction phase-contrast MR imaging of flow. J Magn
Reson Imaging 1991;1:405– 413.
770
12. Buonocore MH, Bogren H. Factors influencing the accuracy and
precision of velocity-encoded phase imaging. Magn Reson Med
1992;26:141–154.
13. de Boor C. A practical guide to splines. Springer-Verlag, 1978.
14. Miga MI, Paulsen KD, Hoopes PJ, Kennedy FE, Hartov A, Roberts
DW. In vivo modeling of interstitial pressure in the brain under
surgical load using finite elements. J Biomech Eng 2000;122:354 –
363.
15. Aimedieu P, Grabe R. Tensile strength of cranial pia mater: preliminary results. J Neurosurg 2004;100:111–114.
16. Bruni JE. Cerebral ventricular system and cerebrospinal fluid. In:
Encyclopedia of human biology, 2nd edition. Academic Press;
1997. p 635– 643.
17. Materialise, Inc.. Mimics. Available at: http://www.materialise.be/
mimics/main_ENG.html. Last accessed: 30 May 2005.
Zhu et al.
18. Quencer RM, Post MJ, Hinks RS. Cine MR in the evaluation of
normal and abnormal CSF flow: intracranial and intraspinal studies. Neuroradiology 1990;32:371–391.
19. Penn RD, Lee MC, Linninger AA, Miesel K, Lu SN, Stylos L. Pressure
gradients in the brain in an experimental model of hydrocephalus.
J Neurosurg 2005;102:1069 –1075.
20. Frim DM, Lathrop D. Telemetric assessment of intracranial pressure changes consequent to manipulations of the Codman-Medos
programmable shunt valve. Pediatr Neurosurg 2000;33:237–242.
21. Hakim S, Venegas JG, Burton JD. The physics of the cranial cavity,
hydrocephalus and normal pressure hydrocephalus: mechanical
interpretation and mathematical model. Surg Neurol 1976;5:187–
210.
22. Buonocore MH. Visualizing blood flow patterns using streamlines,
arrows, and particle paths. Magn Reson Med 1998;40:210 –226.