Quantification of cerebellar structures with MRI

PSYCHIATRY RESEARCH NEUROIMAGING

ELSEVIER

Psychiatry Research: Neuroimaging Section 75 (1997) 159-171

Quantification of cerebellar structures with MRI Anjali R. Deshmukh a'b, John E. Desmond c, Edith V. Sullivan b'* , Barton F. Lane b, Barton Lane d, Brian Matsumoto b, Laura Marsh b, Kelvin O. Lim a'b, Adolf Pfefferbaum b'e b

aVA Palo Alto Health Care System, Palo Alto, CA, USA Department of Psychtatry and Behavtoral Sctence, Stanford UniversitySchool of Medicine, Stanford, CA 94305-5721, USA CDep.artmentof Psychology, Stanford UniversitySchool of Medicine, Stanford, CA, USA Department of Radiology, Stanford Universityof Medicine, Stanford, CA, USA eNeuropsychiatryProgram, SRI International, Menlo Park, CA, USA .

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Received 8 May 1997; revised 27 August 1997; accepted 11 September 1997

Abstract Methodological issues have limited neuroimaging studies of cerebeUar structures. In this article we describe a method that addresses some of these limitations and phantom studies that examine the validity of the image manipulations. We compared volumes derived from 3D Spoiled Gradient Recalled Acquisition MR images sliced with respect to three different alignment methods: one based on cerebellar landmarks, another on cerebral landmarks and a third on the plane of acquisition. Examination of coefficients of variation, coefficients of error and convergent validity suggests that although regional cerebellar volumes based on cerebellar landmarks provide the best estimates of the true volumes, observed differences between volume measurements from alignments based on cerebellar or cerebral landmarks were generally not significant and were inconsequential. In this case, the measure was improved with alignment along local, relevant cerebellar landmarks. A set of phantom experiments showed that realignment, reslicing and interpolation in 3-dimensional image processing exerted, at most, trivial distortion on the estimates of actual object volumes. © 1997 Elsevier Science Ireland Ltd.

Keywords: Cerebellum; Magnetic resonance imaging; Measurement; Vermis

* Corresponding author. Tel.: + 1 650 4987328; fax: + 1 650 8595099. 0925-4927/97/$17.00 © 1997 Elsevier Science Ireland Ltd. All rights reserved. PII S 0 9 2 5 - 4 9 2 7 ( 9 7 ) 0 0 0 5 1 - 6

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1.1ntroducfion

Abnormalities of cerebellar structures are implicated in a variety of neuropsychiatric disorders, including alcoholism (Victor et al., 1989; Davila et al., 1994), autism (Courchesne et al., 1988, 1989, 1993, 1994a, 1997) and schizophrenia (Weinberger et al., 1980; Heath et al., 1982; Lippman et al., 1982; Deshmukh et al., 1996, 1997). This complex, morphologically convoluted structure, located in the posterior fossa has been particularly challenging to visualize and measure in vivo. Early studies using computerized tomography (CT) were unable to visualize posterior fossa structures well because of artifacts arising from the surrounding bone. More recent studies with magnetic resonance imaging (MRI) do provide good visualization of posterior fossa structures, including the cerebellum, but some limitations still exist. One of these is that MRI acquisition sequences are often designed to visualize cerebral structures rather than the cerebellum; the other limitation is the use of thick slices, which augment partial voluming artifacts and consequently obscure structural borders and hamper their delineation. Structures that are small or have high spatial frequency, such as the cerebellar vermis, are particularly susceptible to partial voluming. Another pitfall in measuring the vermis is its lack of clear-cut anatomical demarcations from the cerebellar hemispheres. Many clinical MRI acquisition protocols are aligned in the midsagittal plane of the cerebrum according to conventional landmarks, i.e. anterior commissure (AC) and posterior commissure (PC). These acquisition parameters, however, may not be ideal for cerebellar quantification for several reasons. Due to its developmental torque, the cerebellum is aligned differently from the cerebrum (Snyder et al., 1995). Thus slices oriented to cerebral landmarks are not necessarily orthogonal to the plane of cerebellar structures. Courchesne et al. (1994b) have demonstrated in a single case a 30% difference in measuring the midsagittal area of VI and VII of the vermis when aligning on the cerebrum instead of the cerebellum. Realignment can be accomplished either at the time of image acquisition or post-acquisition.

Here we describe methods that address issues in the quantification of the left and right cerebellar hemispheres and vermian lobules. Images were acquired with a 3D Spoiled Gradient Recalled Acquisition (SPGR) protocol, which yielded thin slices and small voxels, thereby minimizing partial voluming effects and permitting subsequent realignment and reslicing of image data in user-defined planes. The volumes of structures measured on three different realignment schemes and the measurement error associated with each method were compared. A series of phantom studies was also performed to test the validity and accuracy of the reslicing and realignment procedures. 2. Methods

2.1. Subjects The MR[s of 10 healthy men, chosen to span the adult age range, were selected from a larger sample of MRIs of healthy men recruited from the community to participate in imaging studies [see Pfefferbaum et al. (1994) for detailed description of recruitment procedures]. All selected MRIs were reviewed by a neuroradiologist (B.L.) to screen for clinically determined structural abnormalities. Subjects included in the analysis had a mean + S.D. age of 50.1 + 13.8 years with 16.5 + 1.9 years of education. The estimated IQ was 112.4 + 2.7 as measured by the National Adult Reading Test (Nelson, 1982). Nine men were right-handed and one was left-handed, as determined by a quantitative handedness measure (Crovitz and Zener, 1962). Z2. Image acquisition Subjects were scanned on a GE Signa 1.5 Tesla MR[ scanner (General Electric Signa, Milwaukee, WI) using a 3D SPGR sequence to acquire images of the entire cerebrum and cerebellum in one volumetric data set acquired in the sagittal plane. Sequence parameters were TR = 24 ms; TE = 5 ms; flip angle 40°; 124 slices; 24-cm field of view; 256 x 196 matrix (acquired resolution = 0.9 X 1.2 x 1.5 mm, reconstructed resolution = 0.9 x 0.9 x 1.5 mm).

A.R Deshmukh et al. / PsychiatryResearch: NeuroimagingSection 75 (1997) 159-171 2. 3. Image processing

MRI files were transferred to a laboratory computer for display, reslicing according to user-defined anatomic landmarks, delineation of regions of interest (ROIs), segmentation of ROIs (CSF, gray matter and white matter) and measurement of ROI volumes. Volumes were determined by summation of each ROI on all slices measured. Image analysis tools were developed within the laboratory using Interactive Data Language (IDL) and x-lisp software. Analysis first included a series of transformations (Desmond and Lim, 1997) for aligning the 3-dimensional data set into desired orientations, relating them to standardized coordinates (Talairach and Szikla, 1967) and then slicing 2-dimensional images in that orientation for delineation and measurement of specific ROIs. These transformations are described briefly below and in detail elsewhere (Desmond and Lim, 1997). Once the images had been realigned and sliced in desired orientations, manual point placement and semi-automated edge detection were used for defining ROIs followed by automated segmentation, first into tissue and CSF and then into gray and white matter regions. 2.4. Realignment

The realignment procedure consists of calculating three transformations. The first transformation maps the spatial location of screen pixels

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from computer displayed sagittal, axial, or coronal images into the coordinates of a 2-dimensional 'slice'. To extract user-defined slices from the 3-dimensional volume, it is necessary to next transform the 2-dimensional slice coordinates into a new set of voxel coordinates within the 3-dimensional volume, so that each coordinate on the 2-dimensional slice can be expressed as interpolated pixel intensity from the 3-dimensional volume. This transformation consists of 5 steps: (1) translate the 2-dimensional slice coordinates so that the center of the slice is at the (0,0) coordinate; (2) apply 90° rotations to convert the slice into the appropriate plane (necessary only for coronal or sagittal section; no rotation needed for an axial section); (3) apply rotations about the x-, y- and z-axes that are estimated interactively by the user to compensate for head tilt; (4) scale the slice dimensions according to the field of view and the voxel dimensions of the 3-dimensional data set; and (5) translate the center of the slice to the desired coordinates in the 3-dimensional volume. For step 5, it is desirable to specify a slice using mm units and with respect to a standardized coordinate system. The third transformation converts coordinates of the 3-dimensional volume into a standardized coordinate system in which the origin is defined by the intersection of the AC with the midline plane. The x-axis is orthogonal to the midline plane, the y-axis is defined by the line that runs through the AC and PC in the

Fig. 1. Alignmentof 3-dimensionalbrain images in standardizedcoordinate systemin axial (left), coronal (middle) and sagittal (right) planes.

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midline plane and the z-axis is orthogonal to the x- and y-axes. Once this transformation is computed, slices can be specified in standardized coordinates and the inverse of the third transformation can be applied to obtain the coordinates needed in step 5 (Fig. 1). 2.5. Reslieing

We used the realignment capability to derive volumetric measures of the cerebellar hemispheres and vermis as viewed from two different orientations: one defined by cerebellar anatomic landmarks and the other defined by cerebral anatomic landmarks. For each orientation a visually guided 'graphical prescription' tool was used to depict the orientation of slices in a given plane. The third method of slicing ('raw') did not use graphical prescription; instead the slices for the vermis were in the plane of acquisition, and the slices for the hemispheres were in the coronal plane orthogonal to acquisition. 2.5.1. Cerebellar orientation

The cerebellar orientation for measuring cerebellar hemispheres was that of oblique coronal sections oriented parallel to the floor of the fourth ventricle. These derived sections were graphically prescribed from a midline sagittal section (Fig. 2a). This prescription typically yielded 20-25 slices at an interslice interval of 2.5 mm. The alignment procedure for the vermis was first described by

a. Cerebellar Orientation

Courchesne et al. (1994a). Accordingly, the midsagittal plane was determined from axial slices taken through the vermis at three levels: superior, where the cerebral aqueduct becomes continuous with the fourth ventricle; middle, where the vermis first protrudes into the fourth ventricle; and inferior, where the foramen of Luschka opens up in the CSF space. At each level, a midline plane was graphically prescribed in such a way that the section passed through the anterior and posterior convexities of the vermis. The average of these three prescriptions was then calculated and used to reslice the vermis into a midsagittal and four parasagittal slices (two left and two right of the midsagittal slice) with an interval of 1 mm (Fig. 3a). 2.5.2. Cerebral orientation The cerebral orientation for measuring the cerebellar hemispheres was graphically prescribed relative to the A C - P C line (Fig. 2b). This yielded 20-25 coronal slices with a slice interval of 2.5 mm. For the vermis, the midsagittal plane was determined by averaging the graphical prescription obtained at the superior, middle and inferior levels of the vermis, with x-axis parallel to the interhemispheric fissure on the axial plane. This average graphical prescription yielded five slices, one midsagittal and two left and right parasagittal, with a slice interval of 1 mm (Fig. 3b).

b. Cerebral Orientation

Fig. 2. Graphical prescription on sagittal image for cerebellar hemispheres which yields 22 coronal slices at 2.5 mm intervals. (a) Cerebellar orientation is parallel to floor of the fourth ventricle. (b) Cerebral orientation is perpendicular to the AC-PC line.

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a. Cerebellar Orientation

superior

middle

inferior

average

inferior

average

b. Cerebral Orientation

superior

middle

Fig. 3. Graphical prescription on axial images for cerebellar vermis. (a) The cerebellar orientation uses separate intravermian landmarks at superior, middle and inferior levels to compute an average graphical prescription. (b) The cerebral orientation uses the same intravermian landmarks but the graphical prescription is parallel to the interhemispheric fissure at each level and an average is computed. Visual comparison of the average prescription yielded by each method shows that the plane defined in a cerebral orientation indeed falls parallel with the interhemispheric fissure, while that defined in a cerebellar orientation is at an angle.

2.6. Cerebellar ROIs: anatomical definitions Criteria for each R O I were based on anatomical landmarks and defined with reference to a brain atlas and consultation with a neuroanatomist and a neuropathologist. Each R O I was manually outlined by two separate raters (A.R.D. and B.F.L.), with one rater (A.R.D.) repeating the outlining after an interval of 4 weeks. The ROIs were defined as follows. 2.6.1. Cerebellar hemispheres The left and right cerebellar hemispheres are outlined separately on the coronal slices (Fig. 4a).

The hemispheres are arbitrarily labeled A or B, where A and B are equally likely to represent the left or right side of the brain. The most anterior point of the measured images is the first appearance of the floor of the fourth ventricle, and the most posterior slice measured is the last slice on which the hemispheres are seen bilaterally. Structural guides for outlining the cerebeUar hemispheres include the tentorium cerebelli as it stretches over the hemispheres superiorly, and the posterior, inferior and lateral surfaces of the meninges overlying the occipital bone. The vermis separates the two hemispheres. The detailed anatomy of the vermis is not well-defined on the

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coronal plane, which is the preferred plane for measuring the hemispheres. The crescent-shaped lobules of the cerebellum have varying radii of curvature; consequently, all are not present in every coronal slice. The bulk of the anterior lobules is seen in most anterior slices, whereas several posterior lobules are seen in the more posterior slices. The tonsils are smaller, ovoid lobules that protrude from the anterior and inferior medial surfaces of the hemispheres and which abut each other inferiorly in the midline. On the slices that are posterior to the tonsils, the biventer or gracile lobule forms the inferomedial margin of the cerebellar hemispheres. For visual reference to these descriptions, it is useful to refer to Press et al. (1990) for MRI-based atlases of the

cerebellar hemispheres presented in the coronal plane. 2.6.2. Vermis The vermis is divided into four regions which we have designated as V1-V4 (Fig. 4b) and measured on sagittal slices. V1 (anterior superior vermis) includes lobules I - V (lingula, centralis and culmen) and is bound by the superior medullary velum and the primary fissure. V2 includes lobules VI and VII (declive, folium and tuber) and is bounded by the primary and the prepyramidal fissures. V3 includes lobule VIII (pyramis) and is demarcated by the prepyramidal and secondary fissures. V4 includes lobules IX and X (uvula and nodulus), which lie between the

a. Cerebellar Hemisphere

nisphere

b. Vermis

3 (lobule VIII) (lobules IX-X) Fig. 4. Illustration of ROI boundaries of cerebellar hemispheres and vermian lobules V1-V4 at four different levels in (a) the coronal and (b) sagittal planes. The ROIs were segmented with a fully automated procedure into three compartments: gray matter shown in dark gray, white matter shown in light gray and CSF shown in black.

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secondary fissure and the inferior medullary velum. The junction of all vermian ROIs is the apex of the fourth ventricle. The tonsil is identified with relative ease due to its characteristic ellipsoid shape, orientation of its axis, which is parallel to the posterior surface of the medulla, and its sharply convex shape with a prominent caudal extent. V1 and V2 are measured on five slices. V3 and V4 are measured on the three middle slices (the midsagittal and two parasagittal slices). For visual reference to these descriptions, it is useful to refer to Courchesne et al. (1989) for MRI-based atlases of the vermis presented in the sagittal plane. 2. 7. A u t o m a t e d three-compartment segmentation

The 3D SPGR sequence employed in this study gives adequate contrast and signal-to-noise ratio to segment each ROI into three compartments: gray matter, white matter and CSF. After the ROIs are manually outlined, a fully automated process is applied to segment each image (Lim and Pfefferbaum, 1989). This technique is based on a non-parametric operator, which does not assume any a priori distribution of signal intensities (Otsu, 1979). Two steps are required to obtain the three compartments. First, CSF and tissue are separated; then, the resulting tissue compartment is separated into gray and white matter compartments. The two tissue types in each step of the process are separated by a discriminant function analysis of the pixel intensity histogram, which divides it into two classes of pixel intensity. The point of separation is the intensity value that maximizes the between-class variance of the resuiting two classes (CSF and tissue, then gray matter and white matter). We did not analyze the

CSF compartment for the hemispheres of the vermis because we were unable to determine the outer border of these structures. Thus, we tested reliability for the gray matter, white matter and total tissue measures for the hemispheres and vermis. Fig. 4 presents examples of raw and automatically segmented coronal images of the cerebellar hemispheres and sagittal images of the vermian ROIs. 2.8. Statistical analysis

Interrater reliability was established on the graphical prescription, vermis alignment and reslicing, and the outlining of the ROIs. Interand intra-rater reliability was assessed with intraclass correlations, that is, generalizability coefficients, which assumed random raters (Cronbach et al., 1972). Within-subject differences between pairs of measures were examined with paired t-tests and confirmed with non-parametric Wilcoxon tests; only the parametric test results are summarized in the text. Relationships between measures were tested with Pearson and Spearman correlations. 3. Results 3.1. Interrater and intrarater measurement reliability

Reliability for ROI volume measures using the graphical prescription method was established between two raters. Intrarater reliability was also established for the same rater, who measured the structures again 4 weeks later. Reliability estimates of gray matter, white matter and total tissue of each hemisphere and of the four vermian ROIs were calculated as intraclass correlations,

Table 1 Measurement reliabilitybetween two scores expressed as G-coefficients

Gray matter White matter Total tissue

Cerebellar hemispheres Left Right

Vermis V1

V2

V3

V4

0.960 0.797 0.895

0.960 0.891 0.916

0.837 0.968 0.987

0.785 0.845 0.930

0.820 0.726 0.768

0.977 0.882 0.941

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G-coefficients (Table 1). Reliability was high for most ROIs, especially the two hemispheres and V1 and V2; it was lowest for V3 and V4, which are the two smallest ROIs measured, and thus they have the smallest true variances, consequently reducing the opportunity of obtaining high reliabilities.

3.2. Comparison of volumes derived from three different alignment methods We assessed difference in ROI volumes derived from three alignment methods: images aligned with respect to cerebellar landmarks ('cerebellar'), images aligned with respect to cerebral landmarks ('cerebral') and images resliced orthogonally to the plane of acquisition ('raw'). For cerebellar and cerebral orientations, slices were created with graphical prescription. The cerebral-oriented volumes differed significantly from the cerebellar-oriented volumes for only 5 of the 18 comparisons; the volumes from the cerebellar method were in four out of five cases larger than those from the cerebral method (Table 2). Parametric and non-parametric paired comparisons yielded the same results.

3.3. Validity of the three measurement methods The coefficient of variation (CV) served as an index of average measurement error for each alignment method. The CV is calculated as the standard deviation divided by the mean, expressed as a percent. In general, the CVs were largest for the raw measures and were about the same for the volumes based on the cerebellar and cerebral alignments (Table 2). In a summary analysis, we compared the average CVs for gray matter and white matter volumes for the hemispheres across the three alignment methods. The mean CVs for the two graphically prescribed alignments were nearly the same (cerebellar---19.3%; cerebral = 19.2%) and each was significantly smaller than the mean CV for the raw alignment (23.6%; P < 0.022 for each comparison). The CV was also used to examine differences in measurement error when the vermis size was determined by a multislice volume vs. a single

slice area. On average across the four vermian regions and two tissue types, the CV was slightly but not significantly larger for the area than for the volume measures (mean differences between area and volume CVs for each alignment method = 1.5% for cerebellar, 0.2% for cerebral and 5.1% for raw). The coefficient of error of the volume (CE[V]), coupled with concepts derived from the quadratic approximation formula developed by Matheron (1975) and adapted by Gundersen and Jensen (Gundersen and Jensen, 1987; Gundersen et al., 1988), provided an index of the adequacy to which each measure estimated the actual volume of a given ROI. The accuracy of the estimate is likely to improve when more slices are used to calculate a volume. This point is relevant to the hemisphere measurements, which were based on a different number of slices depending upon the alignment method employed. The average number of slices used to estimate the volume of the hemispheres was 19.3 for the cerebellar method, 21.5 for the cerebral method and 25.2 for the raw method. Despite this variability, the CE[V] for these methods was low and ranged from 1.2% to 1.7%. The CE[V] for vermian volumes ranged from 7 to 8% for V1 and V2, which were derived from five slices, and from 12 to 13% for V3 and V4, which were derived from three slices and were larger than the CE[V]s observed for V1 and V2, as would be expected with decreasing number of slices.

3. 4. Convergent validity for selection of alignment method Comparison of the three measurement approaches does not indicate which method better reflects the true volume. In such cases, convergent validity can be used toward making this decision (cf. Mathalon et al., 1993). Previous studies have shown that cortical gray matter but not white matter volume declines with normal aging (Jernigan et al., 1991; Lim et al., 1992; Pfefferbaum et al., 1994); further, the volume of the cerebellar hemispheres and the total area of the vermis also decreases with age (Raz et al., 1997). We calculated correlations between age and re-

Table 2 ROI volumes (cm 3) based on three alignment methods ROI

Hemispheres Left Gray White Total Right Gray White Total Vermis V1 Gray White Total V2 Gray White Total V3 Gray White Total V4 Gray White Total

Cerebellum

Cerebrum

Mean

S.D.

29.13 22.14 51.27 28.83 22.49 51.32

t-test P-values for differences between means a

Raw (CV %)

Cerebellum vs. Cerebrum

4.57 3.17 6.78

16.4 14.9 13.8

4.25 3.66 7.14

0.159 0.250 0.409

20.5 27.6 22.3

0.020 0.014 0.028 0.017 0.026 0.031

ICV (%)

Mean

S.D.

4.40 3.03 6.16

15.1 13.7 12.0

29.36 21.06 50.42

4.33 2.72 6.36

15.0 12.1 12.4

29.25 21.31 50.56

0.162 0.268 0.430

0.023 0.043 0.048

14.0 18.4 10.9

0.111 0.177 0.288

0.023 0.042 0.050

0.047 0.089 0.136 0.076 0.113 0.180

Cerebellum vs. Raw

Cerebrum vs. Raw

n.s 0.0173 n.s.

0.0001 0.0001 0.0001

0.0001 0.0001 0.0001

15.3 16.8 14.4

n.s. 0.0007 n.s.

0.0001 0.0001 0.0001

0.0001 0.0001 0.0001

0.029 0.038 0.043

18.1 15.4 10.7

n.s. n.s. n.s.

0.016 0.008 0.0002

0.0317 0.0521 0.0002

0.137 0.182 0.319

0.037 0.046 0.080

34.1 29.4 20.5

0.312 n.s. 0.0051

0.0024 n.s. 0.0087

0.0003 n.s. 0.0044

33.1 16.3 15.7

0.053 0.071 0.124

0.012 0.029 0.028

30.9 27.6 16.5

0.0436 n.s. n.s.

n.s. n.s. n.s.

n.s. n.s. n.s.

26.0 38.0 24.6

0.064 0.068 0.133

0.033 0.039 0.056

26.0 38.0 24.6

n.s. n.s. n.s.

n.s. n.s. n.s.

n.s. n.s. n.s.

CV (%)

Mean

S.D.

4.35 2.91 6.37

14.8 13.8 12.6

27.95 21.25 49.20

4.23 2.85 6.48

14.5 13.4 12.8

27.85 21.77 49.61

0.162 0.261 0.423

0.024 0.044 0.054

15.0 16.9 11.9

17.1 25.4 17.0

0.102 0.174 0.275

0.023 0.037 0.049

0.019 0.024 0.031

30.1 20.8 20.3

0.054 0.084 0.138

0.016 0.028 0.032

24.1 25.8 21.0

0.083 0.103 0.186

~-

5.

o~ ~'

~; /

Same results obtained with Wilcoxon Tests.

,z,

A.I~ Deshmukh et al. / Psychiatry Research: Neuroimaging Section 75 (1997) 159-171

168

gional cerebellar gray matter based upon volumes derived from the three alignment methods, with the assumption that the correlations would be highest for the approach that had the least measurement error. Although the age correlations based on cerebellar alignment were generally larger than either of the other two alignment methods (Table 3), the only a g e / g r a y matter volume correlation to reach significance was for V2. However, the differences between correlations were not significant. This lack of significant difference between correlations for the various alignment methods held even for V2 [t(9) = 1.806, n.s.]. Thus, this analysis provides little statistical support for use of one alignment method over another in estimating regional volumes of the cerebellum and vermis.

3.5. Phantom studies of realignment, reslicing and interpolation Image manipulation involving realignment, reslicing and interpolation increases the ease of structural quantification, but each maneuver can also be a source of measurement error. To examine these effects on volume measurements, we performed the following simulations. A volume of 186 × 240 x 240 mm was defined by a set of 124 sagittal images, each of 256 x 256 pixel dimensions; these parameters were identical to those of our 3D SPGR sequence. A cube of dimensions Table

3

Pearson

correlations

Region

between

Alignment

gray matter

volumes

and age

method

Cerebellar

Cerebral

Raw

Left

- 0.28

- 0.23

- 0.20

Right

- 0.28

- 0.22

- 0.26

Total

- 0.28

- 0.23

- 0.23

V1

- 0.57

- 0.59

- 0.46

V2

- 0.76*

- 0.45

- 0.46

V3

- 0.37

- 0.26

- 0.23

V4

- 0.33

- 0.10

- 0.29

Total

- 0.67*

- 0.58

- 0.52

Hemispheres

Vermis

* P < 0.5.

40 x 32 X 48 pixels was defined at the center of this volume as follows: the innermost cube of dimensions 20 x 16 x 32 pixels was assigned an arbitrary 'white matter' value of 150, and the remaining pixels were assigned a 'gray matter' value of 100. All other pixels surrounding the 40 x 32 x 48 cube were assigned a value of 0. Given that the simulated voxel dimensions are 1.5 x 0.9375 x 0.9375 mm, the white matter cube had a volume of 30 x 15 X 30 mm = 13 500 mm 3. The gray matter volume was equal to the total volume of the white + gray matter cube, i.e. 60 x 30 × 45 mm = 81000 mm 3, minus the white matter volume; thus, the gray matter volume was 81000 - 13 500 = 67 500 mm 3. Having defined the volume of interest, it was arbitrarily realigned with rotations along the x-, y- and z-axes, thereby simulating realignment of a brain, for example, with respect to the interhemispheric fissure and A C - P C line. A set of 24 oblique sections spaced at 2.2 mm intervals were graphically prescribed from a sagittal image. The volume of the gray and white tissue was measured from these sections using an automated threshold-based pixel counting algorithm. The threshold assigned was the midpoint value between the tissue types, i.e. pixels > 125 were assigned to white matter, pixels > 50 and < 125 were assigned to gray matter, and pixels < 50 were neither gray nor white. The volume measured for the resliced cube was 67474 mm 3 for gray matter, 13 461 mm 3 for white matter and 80 936 mm 3 total, a result that was 99.92% of the expected volume measurement. Identical results were obtained for different arbitrary realignments of the cube and for differently oriented graphical prescriptions. Using our automated segmentation program, in which threshold values between tissue types are computed from the data, we obtained nearly identical results: The volume measured for the resliced cube was 67 383 mm 3 for gray matter, 13 666 mm 3 for white matter and 81050 mm 3 total, a result that was 99.94% of the expected volume measurement. We conclude from these simulations that the distortion in the volume measurements that occurs as a result of realignment, reslicing and interpolation is minimal.

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Finally, we performed five phantom studies to validate the assumption that volumes measured on MRI adequately represented actual volumes of scanned objects (Table 4). The objects measured had a known volume against which to compare the MRI-derived volume. In the last two studies, we measured the same object twice but graphically prescribed the orientation of measurement to be non-orthogonal to the plane of acquisition. A comparison of the actual and MRI-derived volumes revealed that the maximum percentage error in any condition was under 3%. The MRI volume of an orange, which most resembled the brain in terms of its different tissue types and varied signal intensities, overestimated the true volume by less than 0.5%. 4. Discussion

This study indicates that there can be significant, albeit small, differences in the volumes of cerebellar structures derived from reslicing the images relative to local anatomical landmarks. Alignment using the standardized coordinates reduces measurement error due to asymmetry and probably enhances measurement reliability. The differences between measures based on cerebellar and cerebral alignment were small and in most cases insignificant. A test of convergent validity, however, suggested that the cerebellar alignment provides a better estimate of gray matter volume in V2, which comprises lobules VI and VII. Furthermore, reorientation may be indicated when a structure is undersampled, as can occur with measurements based on areas rather than volumes.

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Possible limitations of the graphical prescription approach include the fact that images were resliced in planes non-orthogonal to the plane of acquisition, and thus would have less independent spatial resolution than those sliced orthogonaUy (anisotropy). The metrics of a volumetric data set compared with a typical multislice spin echo 2-dimensional data set minimize potential anisotropy. As an example, we calculated anisotropy indices for a typical multislice spin echo 2-dimensional data set (slice thickness of 3-5 mm, 16-24 cm FOV, 256 x 256) and the 3-dimensional protocol used in this study. The anisotropy index was defined as the maximum diagonal h/(x*x+y*y + z'z), where x, y and z are the dimensions of the voxel in each axis] divided by the minimum dimension of the voxel. The maximum diagonal represents the maximum spacing between the center of any two voxels. The 2-dimensional image matrix results in voxel sizes of 1.95-4.75 mm 3, and the 3-dimensional protocol has an effective voxel size of 1.62 mm 3. For slices 3-5 mm thick and FOVs of 16-24 cm, the range of the maximum diagonal is 3.13-5.17 mm, and the anisotropy index range is 3.50-8.12. For the 3-dimensional sequence, the maximum diagonal is 2.14 mm and the anisotropy index is 2.28. If the slice is oriented orthogonal to the direction of the maximal diagonal, the length of the maximal diagonal is also the minimum independent interslice distance because the maximum diagonal represents the maximum distance that two voxels could be separated. In this study, reconstructed slice interval ranged from 1.5 mm to 2.5 mm. In summary, post-acquisition realignment of

Table 4 P h a n t o m studies Object

Orange Water in Water in W a t e r in W a t e r in

MRI-measured

shot glass tall box, slanted angle small box, parallel angle small box, slanted angle

a Volumes are expressed in m m 3.

Known volume a

Volume

Percent error

198 144 10 000 331462 72557 72 557

199001 10 291 332 240 71 270 73 840

+0.43 + 2.91 + 0.23 - 1.77 + 1.77

170

A.aK Deshmukh et al. / Psychiatry Research: Neuroimaging Section 75 (1997) 159-171

images can reduce measurement error and improve the capability to estimate regional cerebellar volumes. Although volumes based on the cerebellar orientation method for V2 tended to be superior to those based on the cerebral orientation method, the differences between orientation methods were for the remaining measures inconsequential. Thus, we conclude that either alignment method is acceptable in most cases with the critical proviso that the original data are sufficiently sampled. This conclusion is supported by the small and minimally different CE[V] across slice orientations in spite of different numbers of slices available with the different orientations. The indefinite borders inherent in cerebellar anatomy, particularly for the vermis, will continue, however, to pose significant measurement limitations with existing technology. Despite these limitations, the volumetric approach outlined here provides justification for its use in quantifying regional brain volumes in normal as well as pathological conditions involving the cerebellum, such as chronic alcoholism (Sullivan et al., 1996) and schizophrenia (Deshmukh et al., 1996, 1997).

Acknowledgements We would like to thank Lysia Forno, M.D. and Greer Murphy, Ph.D., M.D. for their helpful guidance on the neuroanatomy of the cerebellum, Daniel H. Mathalon, Ph.D., M.D. for his invaluable direction in statistical analysis and Margaret J. Rosenbloom for her assistance with the manuscript. This work was supported by the Department of Veterans Affairs and grants from N I H (AA10723, AA05965, A G l 1 4 2 7 and MH30854), NINDS (1F32NS09628) and the Norris Foundation.

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