Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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.