Original Research

Dynamics of Lateral Ventricle and CerebrospinalFluid in Normal and Hydrocephalic Brains

David C. Zhu, PhD,1 Michalis Xenos, PhD,2 Andreas A. Linninger, PhD,2 andRichard D. Penn, MD3

Purpose: To develop quantitative MRI techniques to mea-sure, model, and visualize cerebrospinal fluid (CSF) hydro-dynamics in normal subjects and hydrocephalic patients.

Materials and Methods: Velocity information was obtainedusing time-resolved (CINE) phase-contrast imaging of dif-ferent brain regions. A technique was developed to measurethe change of lateral ventricle (LV) size. The temporal rela-tionships between the LV size change, CSF movement, andblood flow could then be established. The data were incor-porated into a first-principle CSF hydrodynamic model. Themodel was then used to generate specific predictions aboutCSF pressure relationships. To better-visualize the CSFflow, a color-coding technique based on linear transforma-tions was developed that represents the magnitude anddirection of the velocity in a single cinematic view.

Results: The LV volume change of the eight normal sub-jects was 0.901 � 0.406%. Counterintuitively, the LV de-creases as the choroid plexus expands, so that they acttogether to produce the CSF oscillatory flow. The amount ofoscillatory flow volume is 21.7 � 10.6% of the volumechange of the LV from its maximum to its minimum.

Conclusion: The quantification and visualization tech-niques, together with the mathematical model, provide aunique approach to understanding CSF flow dynamics.

Key Words: brain ventricle movement; CSF dynamics; vi-sualization; CINE phase-contrast; CSF modelingJ. Magn. Reson. Imaging 2006;24:756–770.© 2006 Wiley-Liss, Inc.

DISTURBANCES OF THE CEREBROSPINAL FLUID(CSF) flow in the brain can lead to hydrocephalus, acondition affecting thousands of people annually in theUnited States. Considerable controversy exists aboutfluid and pressure dynamics, and about how the brainresponds to changes in flow patterns and compressionin hydrocephalus. Some information to help under-stand CSF flow dynamics is currently available fromMRI, including measurements of CSF flow pattern andvelocity at various locations along the CSF pathways(1–3) and of brain motion (4,5). However, integration ofthese measurements to explain CSF flow dynamics isincomplete. We have used MRI techniques to measurethe lateral ventricle (LV) size change and its temporalrelationship with intracranial blood flow and CSFmovement along the CSF pathways. The ventricularsize changes and CSF flow patterns that we have foundare consistent with the dynamics of intracranial phe-nomena predicted by a first-principles model intro-duced by Linninger et al (6). This model, in turn, can beused to predict intracranial pressure (ICP) dynamics innormal and hydrocephalic brains. A new quantitativecolor-coding technique is introduced to better visualizethe CSF flow patterns.

BACKGROUND

The LV volumetric change is one of the driving forcesfor CSF movement. The magnitude and timing ofthese movements needs to be measured to under-stand quantitatively how much the LV motion con-tributes 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 overestima-tion. The brain tissue movement within a cardiaccycle is only a small fraction of a pixel, as found byEnzmann et al (4) and our own measurements usingthe time-resolved (CINE) phase-contrast technique.Estimating the ventricle size change in the resolutionof pixel size is therefore highly inaccurate. Further-more, flow artifacts and partial volume effects cancontribute to the change of signal intensity at theedge of the ventricle. A technique similar to the ap-proach of Oyre et al (8) is instead used in our work.The edge positions of the ventricle throughout the

1Cognitive Imaging Research Center, Departments of Psychology andRadiology, Michigan State University, East Lansing, Michigan, USA.2Department of Chemical Engineering, University of Illinois at Chicago,Chicago, Illinois, USA.3Department 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. wasworking in the Brain Research Imaging Center at the University ofChicago.*Address reprint requests to: D.C.Z., PhD, 358 Giltner Hall, MichiganState University, East Lansing, MI 48824. E-mail: zhuda@msu.eduReceived August 22, 2005; Accepted May 24, 2006.DOI 10.1002/jmri.20679Published online 6 September 2006 in Wiley InterScience (www.interscience.wiley.com).

JOURNAL OF MAGNETIC RESONANCE IMAGING 24:756–770 (2006)

© 2006 Wiley-Liss, Inc. 756

cardiac cycle are estimated based on the velocity val-ues of the ventricle edge points measured by the CINEphase-contrast technique. But, unlike Oyre et al (8),the directions in which the edge positions move arenot assumed in our technique. Along with ventricularmovement, CSF flow rates were measured at the junc-tion of the aqueduct of Sylvius (AS) and the fourth

ventricle (V4) and at the midcoronal section of thethird ventricle (V3), and blood flow rate was measuredin the basilar artery. Since all velocity measurementscould be referenced to the cardiac pulse, their tem-poral relationship could be established. Because ofthe choroid plexus’ complex shape, its motion (whichalso drives CSF movement) could not be measured

Figure 1. The five approximate locations where the two-dimensional CINE phase-contrast images were col-lected. A midsagittal slice is shown. The other four loca-tions are as follows: an axial slice across the middle ofthe LV (a), an axial slice across the junction between theAS and V4 (b), a midcoronal slice at V3 (c), and an axialslice nearly perpendicular to the basilar artery in theprepontine region (d).

Figure 2. Demonstration of the color-coding technique. a: The center of the color circle represents zero velocity. The edge of thecolor circle represents velocity of 5 mm/second or higher. The 0° or 360° line is indicated. The direction of the color circle isindicated by the S (superior), I (inferior), A (anterior), and P (posterior), with the positive directions of S–I and A–P. The velocitiesat 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 ofMagendie) 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 settingthe edge of the color circle to represent 2 mm/second or higher.

Dynamics of Lateral Ventricle and CSF 757

directly. The timing of its decrease and increase wasassumed to be synchronous with the blood flow at thebasilar artery.

A first-principles model for pulsatile CSF flow, whosemathematical formulation has been presented by Lin-ninger et al (6), relates three dynamically interactingsystems: the cerebral vascular system, the CSF-filledventricular and subarachnoid spaces (SASs), and thebrain parenchyma. With the inputs from MR measure-ments, the CSF pressure and velocity fields throughoutthe brain can be derived, as well as the dynamics ofparenchyma stresses, strains, and displacements us-ing the laws of elastodynamics. The direct MRI mea-surements and the calculated results from the modelprovide not only an understanding of normal CSF flowdynamics but also important predictions about thepressure and flow rate changes in hydrocephalus.

To provide a better visualization of CSF movement, anew color-coding technique for cinematic flow visual-ization has been developed. Traditional cinematic flowvisualization in CINE phase-contrast MRI has been lim-ited to either the magnitude or one vector component ofthe velocity at a time. As a consequence the complexnature of the flow pattern is not fully represented. Thenew color-coding technique combines both the magni-tude and direction of the CSF flow velocity in one cine-matic view. Using color maps to represent direction isnot new in imaging. For example, color mapping hasoften been applied to the directional visualization ofwhite-matter fiber tracks in diffusion tensor imaging(DTI) (9). However, the direct translation of the DTI colormapping technique to flow is not appropriate becausefibers do not require the differentiation of two oppositedirections, as is necessary to depict flow patterns. Ournew color-coding technique represents flow in all direc-tions, and expands color mapping to the time frame,while maintaining the quantitative nature of the CSFflow 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 11subjects (eight normal subjects from 23 to 52 years old,and three with hydrocephalus) on a 3T GE Signa sys-tem (GE Medical Systems, Milwaukee, WI, USA)equipped with a standard quadrature birdcage headcoil. All volunteers signed the consent forms approvedby the Institutional Review Board at the University ofChicago.

Of the three subjects with hydrocephalus, one sub-ject has mildly enlarged ventricles but was neurologi-cally normal. The second subject has the signs andsymptoms of adult communicating hydrocephalus, andlarge ventricles. The third subject has the signs andsymptoms of adult obstructive hydrocephalus, andmoderately enlarged ventricles.

The two-dimensional CINE phase-contrast imageswere collected at five different locations (Fig. 1): 1) themidsagittal slice to view the major CSF pathways; 2) anaxial slice across the middle of the LV to investigate the

LV volumetric change; 3) an axial slice across the junc-tion between the AS and V4 to measure the CSF flowrate; 4) a midcoronal slice at V3 to measure the CSFflow rate; and 5) an axial slice nearly perpendicular tothe basilar artery in the prepontine region to measurethe blood flow rate. For the first two locations, velocitiesin all three directions were measured to investigate theflow dynamics based on the simple four-point method(11). Images at 16 equidistant time frames were recon-structed per cardiac cycle. For the latter three loca-tions, only the velocity perpendicular to the slice ofinterest was measured so that data could be collectedwith a higher temporal resolution. The simple two-pointmethod was used to calculate the velocity (11). Imagesat 32 equidistant time frames were reconstructed percardiac cycle. For all studies, flow compensation andperipheral gating were applied. For CSF flow measure-ment, a low maximum measurable velocity (VENC) of 5cm/second was chosen as the limit so that a reasonablevelocity resolution could be achieved. For the blood flowmeasurement 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 ofview (FOV) � 24 cm, slice thickness � 5 mm, matrixsize � 256 � 128 for the midsagittal acquisition and256 � 192 for the other acquisitions, number of exci-tations � 2, and full phase FOV for the midsagittalacquisition, but 75% phase FOV for the other acquisi-tions to achieve an effective matrix resolution of 256 �256.

The CSF pathway was segmented for analysis basedon 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 spac-ing � 1 mm, number of slices � 16, matrix size � 256 �256) in which CSF was enhanced. The velocity at everypixel within the regions of CSF was calculated. To re-duce the possibility of a spatially-dependent offset ve-locity due to eddy currents or head motion, the velocityat each pixel location was corrected by basic subtrac-tion of the time-averaged “velocity” of a nearby solidbrain tissue “background” within a 29 � 29 mm2 regionhaving this pixel at its center (4,5,12). In calculating thevelocity of the solid brain tissue, the velocity at eachpixel location was corrected by basic subtraction of thetime-averaged “velocity” of this pixel itself. These ap-proaches are based on the fact that solid brain tissuedoes not accumulate net displacement over a completecardiac cycle (4,5).

The flow rate at the midcoronal slice across V3, at thejunction of the AS and V4, or in the basilar artery, isestimated by the multiplication of the average velocityat the cross-section of the CSF/blood pathway and thecorresponding area. The cross-section of the fluid path-way is segmented based on an image that showed thebest cross-section from the T2-weighted and T1-weighted images. The mean oscillatory flow rates of CSFat the two cross-sections were also calculated based onthe average of the forward and backward flow rate mag-nitudes through a full cardiac cycle. The mean flowvolume per cycle at the junction of the AS and V4 wascalculated based on the average of the forward andbackward flow volumes through a full cardiac cycle.

758 Zhu et al.

Inversion-prepared T1-weighted volumetric axial orsagittal images (with CSF signal suppressed) were alsocollected for the purpose of estimating the sizes of dif-ferent regions of the CSF pathway. The acquisition pa-rameters were: TI � 725 msec, flip angle � 6°, receiverbandwidth � �31.25 kHz, FOV � 24 cm, slice thick-ness � 1.5 mm, number of slices � 120, and matrixsize � 256 � 192.

Estimation of LV Volumetric Change

The edge between solid brain tissue and the LV is firstmanually drawn based on an image that shows the bestcross-section from the T2-weighted and T1-weighted im-ages and that has been acquired at exactly the samescan plane (Fig. 1). This drawing marks the initial pixelpositions during a full cardiac cycle. The position shiftof each pixel at the edge of the LV is then estimated foreach time frame of the cardiac cycle by integrating thevelocity over time, including both components of thevelocity. The expected position of each original edgepixel is estimated by adding the initial position with theposition shift. The edge points of the LV at each cardiactime frame, including the initial time frame, are con-nected together by spline interpolation (13). The area ofthe enclosed region at each cardiac time frame is cal-culated. The percent change of the enclosed region fromthe maximum to the minimum within the cardiac cycleis then calculated by comparing it to the time-averagedarea of this enclosed region throughout the cardiaccycle. Assuming the LV increases and decreases uni-formly across the whole ventricle, the percent volumechange of the LV is now estimated based on the follow-ing equation (See Appendix A for derivation):

fV � �1 �fA

4�3

� �1 �fA

4�3

(1)

with

fA �Amax � Amin

Aave

where: fV � the fraction of the LV volume change frommaximum to minimum; fA � the fraction of LV areachange from maximum to minimum; Amax � the maxi-mum LV area; Amin � the minimum LV area; and Aave �the average LV area.

The LV volume is estimated in units of voxel sizebased on the CSF-suppressed T1-weighted volume im-ages, and then is converted to milliliters. The CSF re-gion is isolated from its surrounding solid brain tissuebased on image signal contrast. The change, in millili-ters, from the maximum to the minimum volumes isestimated from the LV volume and fV.

Phantom Study

The above procedure of estimating LV volumetricchange was also applied to data collected from staticsilicone 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

could be evaluated. If the procedure were perfect, the“LV” would not have changed size during the full car-diac cycle. The two-dimensional CINE phase-contrastimages were collected at an axial slice from the phan-tom, with the same scanning parameters as the two-dimensional CINE phase-contrast imaging protocol forhuman subjects at the second of the five slice locations.A photopulse sensor was hooked to the finger of a hu-man volunteer to detect in vivo cardiac pulse, whichserved as the mean for peripheral gating during phan-tom data collection. Six image data sets were collectedand were processed to estimate the LV volumetricchange with the method discussed in the previousparagraphs.

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 body-to-head (inferior-to-superior [I–S]) direction is esti-mated based on the weighted average,

TC_CSF �¥ i�first time frame at a specific flow direction

last time frame at the same flow direction Ti � Fi

¥i�first time frame at a specific flow directionlast time frame at the same flow direction Fi

(2)

where: Ti � time at the ith cardiac time frame in aspecific flow direction, and Fi � flow at the ith cardiactime frame in a specific flow direction.

The CSF flow direction switching point is estimated tobe the midpoint between the centers of gravity of the S–Iand the I–S flow waveforms because the transition timepoint necessarily has a slow flow and is therefore diffi-cult to measure directly with a high level of precision.

The center of gravity of the LV area waveform when itis either above or below the average area is estimated inthe same manner, corresponding to the time point atthe maximum or minimum LV area.

CSF Hydrodynamic Model

The mathematic equations and assumptions applied tobuild a CSF hydrodynamic model have been fully dis-cussed by Linninger et al (6). Building a subject-specificmodel requires a set of fixed variables and a set of inputboundary conditions that are assumed to be the sameacross subjects, as well as a set of subject-specific brainvariables. The set of fixed variables are the CSF andtissue properties as listed in Table 1. The input bound-ary conditions for the system are the CSF productionrate, the choroid plexus expansion, and the venousblood pressure derived from the literature (6). The sub-ject-specific variables, including ventricular areas, di-mensions of the foramina and SAS, are extracted fromCSF-suppressed T1-weighted volumetric images usingthe graphical image reconstruction tool, Mimics (17).The application of the model will be demonstrated withtwo case studies (one normal brain and one communi-cating hydrocephalic brain).

Velocity Color-Coding Technique

Two (red and green) of the three colors in the red-green-blue (RGB) color model were selected to represent the

Dynamics of Lateral Ventricle and CSF 759

two velocity components. A color circle can be builtbased on the mixture of these two colors (Fig. 2a), withthe color intensity representing the magnitude of thevelocity and the hue of color representing the directionof the velocity. The velocity magnitude is directly pro-portional to the color intensity, which in turn is basedon the total amount of color. The center of the circle haszero color intensity, corresponding to zero velocity. Theedge of the circle has the maximum color intensity,corresponding to the maximum velocity magnitude tobe represented. The angle of the velocity is representedby the linear combination of the two colors. One purecolor, green in this example, represents the 0° velocitydirection. The other nearly pure color, red in this exam-ple, represents the velocity direction just below 360°.Therefore, the velocity-color map transformation canfollow these equations:

fred �Vmag

Vmax�

�

360(3)

fgreen �Vmag

Vmax� �1 �

�

360�fblue � 0

where, fred, fgreen, fblue � fraction of red, green, or blue inan RGB color space, � � the angle of velocity in degrees,Vmax � the maximum velocity to represent, Vmag � mag-nitude of velocity, and Vmag � Vmax for Vmag � Vmax. Thus,the total fraction of color

ftotal � fred � fgreen � fblue �Vmag

Vmax(4)

ftotal, is linearly related to Vmag up to Vmax and is inde-pendent of the velocity angle. The velocity magnitudeview contrast can be adjusted by changing Vmax, anal-ogous to the window level in image viewing. With Vmax

reduced, the velocity magnitude view contrast is en-hanced, and thus the flow directions are emphasized(Fig. 2b).

At any pixel location, if the velocity is smaller thanVmax, the color map can easily converted back to nu-meric velocity based on the following equations:

� �360

fgreen

fred� 1

(5)

Vmag � �fredVmax�360

�

VAP � Vmagcos���

VSI � Vmagsin���

In some cases, abrupt changes of flow color (calleddiscontinuity artifacts in this article, as in DTI (9)) willnecessarily be seen when the CSF flow contains veloc-ities at the red–green transition region. This occursbecause color-coding starts with pure green at 0° andends with nearly pure red at just below 360°. Theseartifacts disappear after rotating the color circle, forexample, by 90° (Fig. 3). An appropriate orientation ofthe color circle is one way to remove the discontinuityartifacts. As an alternative approach, the simultaneousutilization of these two color circles can be applied forthe visualization of complex flow patterns. Because ofhigh sensitivity to the red–green abrupt transition, thediscontinuity artifacts can even be applied to advantagefor identifying the flow directions with a high level ofprecision.

The above color-coding technique was implementedin Matlab, and was applied to all pixels along the CSFpathway at all cardiac time frames collected. The color-coded velocity map was then overlaid on a high-resolu-tion T2-weighted FSE image.

RESULTS

MRI Measurements of Normal Subjects

The temporal relationship between the blood flow ratethrough the basilar artery, the LV volumetric change,the flow rate at the midcoronal section of V3, and theflow rate at the junction of the AS and V4 in normalsubjects is shown in Figs. 4 and 5. All data were nor-malized to percent of the cardiac cycle to remove thedifference in heart rate. The normal subjects showedthe following temporal characteristics (Table 2): 1) TheLVs begin to decrease between the minimum and max-imum flow time points in the basilar artery, specifically,8.24 � 8.64% after the minimum flow time point and

Table 1Tissue and Fluid Properties

Property Value Source

The measured young modulus of the tissue 2100 N/m2 Miga et al (14)3500 N/m2 Derived from Aimedieu and Grabe (15)

Fluid density, �f 1004-1007 kg/m3 Bruni (16)Fluid viscosity, � 10–3 Pa second Assumed as for waterSpring elasticity, ke 8 N/m (normal) Derived from the Young ModulusBrain dampening, kd 0.35 � 10-3 (N second)/m Assumed; low dampening effectEpendyma density, �w 1000 kg/m3 Equal to waterReabsorption constant, 1.067 � 10–11 m3/(Pa second) Estimated from medical data for hydrocephalic humans

760 Zhu et al.

7.39 � 10.04% before the maximum flow time points. 2)The LV expands ahead of the switch of CSF flow direc-tion 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

the switch of flow direction from the direction of I–S tothat of S–I by 11.27 � 9.95% of the cardiac cycle. As-suming the change of LV size is one of the driving forcesof CSF flow, there is a delayed flow response. The LVs

Figure 3. The potential abrupt change of flow color (called discontinuity artifacts in this work) when the CSF flow containsvelocities at the red–green transition region. The discontinuity artifacts in (a) are not seen after a 90° rotation of the color circleto the one in (b). The same is true for (b), with a –90° rotation of the color circle to the one in (a).

Figure 4. Eight normal sub-ject study. The temporal rela-tionship between the LV areaand the CSF flow rate at thejunction of the AS and V4.Each data point is shown asmean � SD.

Dynamics of Lateral Ventricle and CSF 761

have an average volume of 16.4 � 4.7 mL. The amountof volume change from the LV’s maximum to its mini-mum was estimated to be 0.147 � 0.084 mL. Theamount of CSF oscillatory flow volume (the average ofS–I and I–S flow volumes) in one cycle was 0.0289 �0.0161 mL. This amount of CSF oscillatory flow volumeis 21.7 � 10.6% of the volume change of the LV from itsmaximum to its minimum. As shown in Table 2 (alsosee Movie 1 in the Supplementary Material (Movies 1-5)to visualize the LV movement; available online at:http://www.interscience.wiley.com/jpages/1053-1807/suppmat/) for the eight normal subjects studied,the maximum displacement of all the pixels at the edgeof the LV was 0.128 � 0.042 mm on the same scanningplane, and was 0.165 � 0.042 mm in all three spatialdirections. The range of pixel displacement was only asmall 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 inMaterials and Methods) at the center of V3 (based onseven subjects) was 3.91 � 1.46 mL/minute, and at thejunction of the AS and V4 it was 3.97 � 1.62 mL/minute.

The MRI measurements for the following case studiesare also included in Table 2. The color-coding techniqueshown in Fig. 2 was used to generate the movies for themidsagittal CSF visualization with the Vmax set at 5 mm/second for almost all case studies. To visualize a highervelocity range in the communicating hydrocephalus casestudy, a Vmax of 10 mm/second was applied instead.

Case Studies

Case 1. Normal Subject (see Table 2; Fig. 6; and Movie2 in the Supplementary Material)

This case study is a representative of the eight normalsubjects. The flow rate measurements are within theranges of the corresponding measurements of the nor-mal subjects. The temporal relationship between mea-surements is similar to other normal subjects and isshown in Fig. 6. Figure 6 and Movie 2 both show a clearforward–reverse oscillatory CSF movement in the path-way. The application of the flow visualization techniqueis demonstrated by watching Movie 2: a higher flowvelocity is seen at the prepontine SAS and at the fora-men of Magendie. The flow pattern at V4 is more com-

Figure 5. The temporal relationship(based on five normal subjects) be-tween 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 measure-ments were normalized within thetime scale of each cardiac cycle andas a percent of the absolute maxi-mum before being combined. Eachdata point is shown as mean � SD.

762 Zhu et al.

plicated than that at the narrow sections of the path-way. The I–S flow from the foramen of Magendie losessome momentum in the I–S direction in V4 and divertsto the anterior direction. A flow void is also seen in V4.There is an overall strong presence of flow in the pos-terior–anterior direction. These observations are ingood agreement with Quencer et al (18).

In this normal subject case study, the following subject-specific variables have been used in building the model:volume of LV � 9.81 mL, volume of V3 � 2.5 mL, volumeof V4 � 3.32 mL, volume of SAS � 103.0 mL, radius offoramina of Monro (FM) � 1.5 mm, length of FM � 3 mm,radius of AS � 1.0 mm, length of AS � 11 mm, radius offoramina of Luschke (FL) �1.25 mm and length of FL � 15mm. The accuracy of this model was validated by itsrelatively close match with the MRI flow rate measure-ment at the region between the AS and V4 (Fig. 7), giventhat our simulations were performed with a standard si-nusoidal function (6). The mean pulsatile flow estimatedfrom the model for this region was 2.84 mL/minute. Thepredicted ICP along the CSF pathways, from the LVs to V4and cranial SAS are depicted in Fig. 8. The pressure dif-ference driving the CSF flow in the ventricles is approxi-mately 7 Pa. This low pressure difference agrees with themeasurements in animal studies by Penn et al. (19).

2. Neurologically Normal Subject But AbnormalVentricle Size and CSF Flow (see Table 2; Fig. 9; andMovie 3 in the Supplementary Material)

Anatomic images show brain atrophy and a larger thanexpected SAS inferior to the cerebrum. Both the volumeof the LV and the pulsatile flow rate were approximatelytwo times that of the normal subjects (Table 2). Table 2and Fig. 9 also show that the LV starts to decrease laterthan normal. Instead of decreasing before the changefrom S–I to I–S, as in normal subjects, the LV starts todecrease 9.1% of a cardiac cycle later. Except at theSAS at the inferior region of the cerebrum, Movie 3demonstrates 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 theSupplementary Material)

The LV volume is approximately 15 times that of normalsubjects, and the pulsatile flow rate (approximately 29mL/minute) is approximately 7.3 times normal. Theanatomic images also show generalized atrophy. Al-though the pixels at the ventricle wall move more thanin the normal subjects, this does not translate into alarger LV volume percent change because different re-gions of the ventricle decrease and increase in a highlyasynchronous manner. The percent change is only one-third of the normal subjects. However, because the LVis highly enlarged, the change of LV volume is approx-imately 5.3 times that of normal subjects. As shown inFig. 10, the temporal relationship of basilar artery bloodflow, the LV volumetric change and the CSF flow issimilar to that of the normal cases. However, Fig. 10does not convey the complete flow pattern, which isbetter depicted by Movie 4. Unlike the normal cases,

Tab

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(mL/

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(mL/

min

ute)

Max

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LV%

volu

me

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ge

Vol

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(mL)

Max

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(mL)

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3.44

4.51

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152

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Dynamics of Lateral Ventricle and CSF 763

Movie 4 shows the simultaneous coexistence of CSFflow in opposite directions at various locations, such asin V3 and the AS. Other complex flow patterns are alsoseen at various locations of the CSF pathway.

In this hydrocephalic case study, the following sub-ject-specific variables have been used in building themodel: volume of LV � 250.2 mL, volume of V3 � 11.3mL, volume of V4 � 4.57 mL, and volume of SAS �105.0 mL; the dimensions of the foramina were thesame as in the normal subject case study except that a

radius of 2 mm instead of 1 mm was estimated for theAS. A condition of CSF malabsorption at the arachnoidgranulations was applied in the model, based on clini-cal evidence (6). The accuracy of this model is validatedby comparing the predicted CSF volumetric flow car-diac time course with MRI measurement at the regionbetween the AS and V4 (Fig. 11). The estimated meanoscillatory flow rate across the cardiac cycle at the junc-tion of the AS and V4 was 29.6 mL/minute. The maxi-mum flow rate at the same region was 48.6 mL/minute.

Figure 6. Case study of a normal brain. The temporalrelationship between the basilar arterial flow rate, theLV area, the CSF flow rates at V3, and at the junction ofthe AS and V4.

Figure 7. Comparison of CSF flow rates measured withCINE phase-contrast MRI and model simulation resultsat the junction between the AS and V4 for the normalbrain study.

764 Zhu et al.

Despite a predicted ICP rise of 1200 Pa within the entireventricular system, the pressure difference between theLV and the SAS (transmural pressure) does not exceed50 Pa in each cycle (Fig. 12). This low pressure differ-ence corresponds with the recent animal studies byPenn et al (19). In that study the pressure gradientsbetween ventricles, brain tissue, and SAS in the kaolin-induced hydrocephalic dog brains were below 66.7 Pa.

Case 4: Patient With Obstructive Hydrocephalus DueTo Aqueductal Stenosis (see Table 2; Fig. 13; andMovie 5 in the Supplementary Material)

The LV volume is moderately enlarged, approximatelytwo times that of the normal subjects, and the pulsatileflow rate (approximately 2.36 mL/minute at the junc-tion of the AS and V4) is below that of the normal

Figure 8. Results from model simulation. The ICP pro-file along the ventricular pathways for the normal brainstudy. Reference pressure: 1 atm or 1.01325 � 105 Pa.

Figure 9. Case study of an abnormal CSF flow. The temporal relationship between the basilar arterial flow rate, the LV area, theCSF flow rates at V3, and at the junction of the AS and V4.

Dynamics of Lateral Ventricle and CSF 765

subjects. The LV percent volume change is within therange of the normal subjects. However, because the LVis enlarged, the change of LV volume from its maximumto its minimum is approximately two times that of nor-mal subjects. Because of the aqueductal obstruction,the pulsatile flow volume at the junction of the AS andV4 is only 5.39% of the LV volume change. As shown inFig. 13, the temporal relationship of basilar artery blood

flow rate, the LV volumetric change, and the CSF flowrate at the junction of the AS and V4 is similar to that ofthe normal cases. The CSF flow pattern in V3 is differ-ent from normal with a relatively shorter duration offlow in the anterior–posterior direction but a relativelylonger duration of flow in the posterior–anterior direc-tion. The unusually stagnant flow pattern in V3 of thispatient is also depicted in Movie 5.

Figure 10. Case study of an adult communicating hy-drocephalus. The temporal relationship between thebasilar arterial flow rate, the LV area, the CSF flow ratesat V3, and at the junction of the AS and V4.

Figure 11. Comparison of CSF flow rates measuredwith CINE phase-contrast MRI and model simulationresults at the junction between the AS and V4 for thecommunicating hydrocephalus case study.

766 Zhu et al.

Phantom Study

Analysis of the six data sets collected from the gel phan-tom images showed a 0.169 � 0.071% LV volumechange during a full “cardiac cycle.” The ROI used asthe “LV” had the area range from 762 to 1322 mm2

(1052 � 334 mm2). The LV volumetric change for thephantom should have been zero if the procedure wereperfect.

DISCUSSION

An understanding of the magnitude and timing of LVvolumetric change are needed to evaluate how muchthe LV motion contributes to CSF movement in normalsubjects and hydrocephalic patients. Our new quanti-fication technique for LV motion relies on the accuratevelocity information measured by the CINE phase-con-trast technique. We applied the general velocity estima-

Figure 12. Results from model simulation. The ICP pro-file along the ventricular pathways in the communicat-ing hydrocephalus case study. Reference pressure: 1atm or 1.01325 � 105 Pa.

Figure 13. Case study of an adult obstructive hydro-cephalus: The temporal relationship between the basilararterial flow rate, the LV area, the CSF flow rates at V3,and at the junction of the AS and V4.

Dynamics of Lateral Ventricle and CSF 767

tion technique that has been used by other groups forCSF and solid brain tissue measurements (4,5). Ourtechnique of estimating the ventricle size change labelsthe solid brain tissue immediately adjacent to the trueLV edge as the “edge.” This approach allows the velocityat each pixel location to be corrected by the time-aver-age “velocity” of this pixel itself, taking advantage of thefact that there is no net displacement of solid braintissue over a complete cardiac cycle. The underlyingassumption of our technique is that the labeled “edge”pixel within the solid brain tissue moves simulta-neously with the same magnitude and direction at allpoints of the cardiac cycle with the corresponding andadjacent pixel at the true edge of the ventricle. If thisassumption does not hold, the LV size change may beunder- or overestimated. On the other hand, the max-imum and minimum ventricle sizes are compared tofind the ventricle size change. This type of comparisonlikely leads to some systematic overestimation, due tosystem imperfection and noise, as suggested by thephantom data of nonzero volumetric change per cardiaccycle. To utilize the velocity measurement at a singleslice location within a time-limited scan session, theestimation of the LV size change has been based on amodel that the LV is a sphere and it increases anddecreases uniformly. To improve the estimation of LVsize change, velocity will need to be measured at mul-tiple slice locations, and this method is being activelyinvestigated.

The motion of the choroid plexus has not been as-sessed directly because of its complex shape. The ex-pansion of the choroid plexus is assumed to be syn-chronous with each pulse of blood through the basilarartery. 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 flowmeasurement within a limited total scan time and thuswas used in this study. The blood flows in the basilarartery and the cerebral arteries are assumed to sharethe same temporal characteristics based on their ana-tomic proximity.

Based on the temporal relationship found in the eightnormal subjects between the basilar artery blood flowrate, the LV volumetric change, and the CSF movement,the LV appears to decreases as the choroid plexus alsoexpands. These two forces act together to produce theCSF oscillatory flow. They are in turn driven by thepulsation in blood flow. The temporal relationship be-tween the LV volumetric change and the basilar arteryblood flow rate (Fig. 5) measured by us shows a goodagreement with the temporal relationship between theintracranial volumetric change and the transcranial ar-terial inflow rate measured by Alperin et al (3). The LVvolumetric change is expected to be a fraction of theintracranial volumetric change. Thus the LV volumetricchange of 0.147 � 0.084 mL we measured in normalsubjects is consistent with the intracranial volumetricchange of 0.34–1.3 mL measured by Alperin et al (3).The temporal relationship between the CSF oscillatoryflow directions at the AS or V3, and the LV volumetricchange, indicates that the LV motion plays an impor-tant role in the CSF flow. However, the oscillatory flowvolume only accounts for about 21.7 � 10.6% of the LV

volume change. This suggests that some ventricularCSF moves into the brain parenchyma during its de-crease in size and is released from the brain paren-chyma during expansion. The spinal and cisternal CSFvolumetric changes very likely contribute to CSF pul-sation, but their contributions will require further in-vestigation.

The mean oscillatory flow rate at the junction of theAS and V4 was measured to be 3.97 � 1.62 mL/minute,which is higher than the measurement of 1.72 � 0.34mL/minute at the AS made by Enzmann et al (4). Thisdiscrepancy could have been caused by differences inROI drawing and in the location of the two measure-ments. A lower flow rate measurement would not alterthe general observation that only a fraction of the LVvolume change is needed to drive the CSF oscillatoryflow.

The simulations were performed with a standard si-nusoidal function (6). In reality the pulsatile CSF wave-form is more complicated. As a result there are un-avoidable variations between the measured andsimulated CSF waveforms. However, given the inter-subject variations that have been seen in MRI flow mea-surements, it appears acceptable to say that the mea-surements agree with the simulations of the flowdynamics (6). The quantitative agreement between theMRI measured flow rate and that predicted by themodel in both the normal subject case study (Fig. 7) andin the communicating hydrocephalic subject casestudy (Fig. 11) further validates our hydrodynamicmodel. This also means that the pressure differencesneeded to create such flow can be estimated. As Fig. 8illustrates, these pressure differences are low. Themaximum difference between the LV and the SAS is lessthan 7 Pa in either direction of flow. This is as one mightexpect from a fluid system connected by relatively lowresistance pathways and small amounts of fluid move-ment. Note that the flow rate would be the same regard-less of absolute pressures within normal ranges. This istrue until the blood flow, the driving force of the CSFflow in the intracranial space, is significantly reducedby elevated ICP. Until cerebral perfusion is compro-mised, the dynamic CSF flow is independent of ICP. Asubject standing up will have the same flow as whenlying down even though the ICP varies due to the posi-tion by up to 15 torr (1999 Pa) (20).

Importantly, even if the ICP is elevated as in commu-nicating hydrocephalus, the pressure gradients neededto produce CSF flow remain low. As Fig. 12 shows forour example of communicating hydrocephalus, themodel predicts a difference of less than 50 Pa. This istrue even with the increased flow rates measured byCINE phase-contrast MRI in this patient.

The relatively low pressure gradient and the reversalof the gradients that create the oscillatory flow patterndemonstrated in CINE phase-contrast MRI means thatlarge pressure gradients cannot exist between the out-side of the brain and the ventricles. Hydrocephaluscannot be produced by such forces as hypothesized byHakim et al (21). Moreover, to produce oscillatory CSFmotion the huge pressure gradients suggested byHakim et al (21) would have to invert in each cardiaccycle for CSF to reverse its flow direction in the ventric-

768 Zhu et al.

ular system and the prepontine SAS. Recent measure-ments published using ICP monitors in a dog model ofhydrocephalus confirm this (19). In spite of massive ICPincreases with acute or chronic hydrocephalus, pres-sure gradients between the ventricles, brain tissue, orSAS could not be found. Hakim et al’s (21) hypothesis ofpressure gradients creating hydrocephalus will have tobe reconsidered, as well as any other theories that hy-pothesize large pressure gradients in the brain andfluid spaces.

The color-coded technique presented in this workbrings together the information of both the magnitudeand direction of the CSF flow in a single cinematic view.Since this technique is based on linear transformationsof the velocity within the magnitude range to view se-lected by the user, its quantitative nature has beenmaintained. This visualization method is expected toprovide assistance in diagnosis and surgical planning.The technique discussed here is for two-dimensionalflow visualization. By adding another RGB color (blue),the same concept can be expanded to three-dimen-sional flow visualization. However, the visualization be-comes more complex for three-dimensional expansionand less straightforward than its two-dimensionalcounterpart. A visualization technique using stream-lines, arrows, and particle paths developed by Buono-core (22) for cardiac imaging might also be promising tovisualize the CSF flow patterns.

In conclusion, the quantification and visualizationtechniques, together with the mathematical model, pro-vide a unique approach to understanding CSF flow dy-namics. The results provide information on temporaland pressure relationships in normal subjects anddemonstrate the abnormal CSF dynamics in hydroce-phalic patients.

ACKNOWLEDGMENTS

We thank Dr. Michael Buonocore for suggestions ondata acquisition and velocity calculation, Dr. DavidLevin for suggestions on velocity calculation, Dr. Wen-Ming Luh for suggestions on volumetric imaging, Mr.Robert Lyons on scanning assistance, Dr. David Wrightfor carefully proofreading this manuscript, and Materi-alise Inc. for providing a trial version of the Mimicsreconstruction software.

APPENDIX A

LV Volumetric Change Fraction Calculation

The following derivation is based on the assumptionthat the LV expands uniformly. Since the change of theventricle size is small, we can also assume that theradius increase when the ventricle increases to its max-imum size is the same as the radius decrease when itdecreases to its minimum size.

Let Aave � the mean area at the cross-section of theLV � R2, where R � radius, Amax � maximum areaafter ventricle expansion, and Amin � minimum areaafter the ventricle decreasing its size. The fractionalarea change of the LV between the Amax and Amin can beestimated as:

fA �Amax � Amin

Aave�

�R � �R�2 � �R � �R�2

R2 �4�R

R

Then,

�R �fA

4R

Assuming the LV is equivalent to a sphere, the average

volume of the LV is Vave �43

R3, and the LV will have a

maximum value of Vmax �43

�R � �R�3 and a mini-

mum value of Vmin �43

�R � �R�3. The fractional

volume change of the LV between the maximum andminimum can be estimated as

fV �Vmax � Vmin

Vave�

43

�R � �R�3 �43

�R � �R�3

43

R3

��R � �R�3 � �R � �R�3

R3 �

�R �fA

4R�3

� �R �fA

4R�3

R3

� �1 �fA

4�3

� �1 �fA

4�3

(A1)

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