# Analysis of the volumes of the posterior cranial fossa, cerebellum, and herniated tonsils using the stereological methods in patients with Chiari type I malformation.

**ABSTRACT** The aim of this study was to determine the posterior cranial fossa volume, cerebellar volume, and herniated tonsillar volume in patients with chiari type I malformation and control subjects using stereological methods.

These volumes were estimated retrospectively using the Cavalieri principle as a point-counting technique. We used magnetic resonance images taken from 25 control subjects and 30 patients with chiari type I malformation.

The posterior cranial fossa volume in patients with chiari type I malformation was significantly smaller than the volume in the control subjects (P < 0.05). In the chiari type I malformation group, the cerebellar volume was smaller than the control group, but this difference was not statistically significant (P > 0.05). In the chiari type I malformation group, the ratio of cerebellar volume to posterior cranial fossa volume was higher than in the control group. We also found a positive correlation between the posterior cranial fossa volume and cerebellar volume for each of the groups (r = 0.865, P < 0.001). The mean (±SD) herniated tonsillar volume and length were 0.89 ± 0.50 cm(3) and 9.63 ± 3.37 mm in the chiari type I malformation group, respectively. Conclusion. This study has shown that posterior cranial fossa and cerebellum volumes can be measured by stereological methods, and the ratio of these measurements can contribute to the evaluation of chiari type I malformation cases.

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**ABSTRACT:**Chiari malformations are anatomic anomalies that comprise a broad spectrum of neurologic conditions. The most common malformation, a Chiari type I malformation, can present with a variety of signs and symptoms, most frequently an occipital Valsalva-induced headache. Cranial and spinal magnetic resonance (MR) imaging is used to identify the degree of tonsillar descent and document the presence of syringohydromyelia. The advent of cine-MR flow imaging (cine as in "cinema") has provided new insight as to the dynamic process involved in the evolution of this pathophysiology. This article reviews the neuroimaging of this fascinating disorder.Neurologic Clinics 02/2014; 32(1):95-126. · 1.34 Impact Factor

Page 1

The Scientific World Journal

Volume 2012, Article ID 616934, 7 pages

doi:10.1100/2012/616934

The cientificWorldJOURNAL

Research Article

Analysisof theVolumesof the Posterior Cranial Fossa,

Cerebellum,and HerniatedTonsilsUsing theStereological

MethodsinPatients withChiariTypeI Malformation

¨Umit ErkanVurdem,1NiyaziAcer,2Tolga Ertekin,2

Ahmet Savranlar,1and Mehmet Fatih˙Inci3

1Department of Radiology, Kayseri Education and Research Hospital, 38010 Kayseri, Turkey

2Department of Anatomy, Erciyes University School of Medicine, 38039 Kayseri, Turkey

3Department of Radiology, Elazı˘ g Harput State Hospital, 23200 Elazı˘ g, Turkey

Correspondence should be addressed to Niyazi Acer, acerniyazi@yahoo.com

Received 13 December 2011; Accepted 22 January 2012

Academic Editors: J. G. Eriksen and A. Youk

Copyright © 2012¨Umit Erkan Vurdem et al. This is an open access article distributed under the Creative Commons Attribution

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

cited.

Objective. The aim of this study was to determine the posterior cranial fossa volume, cerebellar volume, and herniated tonsillar

volume in patients with chiari type I malformation and control subjects using stereological methods. Material and Methods. These

volumes were estimated retrospectively using the Cavalieri principle as a point-counting technique. We used magnetic resonance

images taken from 25 control subjects and 30 patients with chiari type I malformation. Results. The posterior cranial fossa volume

in patients with chiari type I malformation was significantly smaller than the volume in the control subjects (P < 0.05). In the

chiari type I malformation group, the cerebellar volume was smaller than the control group, but this difference was not statistically

significant (P > 0.05). In the chiari type I malformation group, the ratio of cerebellar volume to posterior cranial fossa volume was

higher than in the control group. We also found a positive correlation between the posterior cranial fossa volume and cerebellar

volume for each of the groups (r = 0.865, P < 0.001). The mean (±SD) herniated tonsillar volume and length were 0.89±0.50cm3

and 9.63 ± 3.37mm in the chiari type I malformation group, respectively. Conclusion. This study has shown that posterior cranial

fossa and cerebellum volumes can be measured by stereological methods, and the ratio of these measurements can contribute to

the evaluation of chiari type I malformation cases.

1.Introduction

The chiari malformations generally describe increasing

degrees of hindbrain herniation through the foramen mag-

num. Chiari type I malformation (CMI) is defined as a

herniation of the cerebellar tonsils of at least 5mm or more

through the foramen magnum. Syringomyelia is associated

with this condition in 50–75% of cases [1, 2].

The etiology of CMI is unclear and may be mul-

tifactorial. It is believed to be congenital, even though

those who have it do not usually have symptoms until

early childhood or adolescence [3, 4]. Some conditions

under which the herniation of the cerebellar tonsils occurs

include hydrocephalus and intracranial mass. A generally

decreased volume of the posterior cranial fossa is thought

to be one of the predisposing factors in some cases [5,

6].

Several studies have attributed this insufficient posterior

cranial fossa geometry to embryological defects in the

paraxial mesoderm [7–9]. The advent of magnetic resonance

imaging (MRI) in recent years has made it possible to

make an early and accurate noninvasive diagnosis of CMI in

patients whose symptoms might be subtle [10, 11].

There are a few studies which have compared cerebellar

volume(CV)andposteriorcranialfossavolume(PCFV),but

there is no study in the literature that aims to estimate the

herniation of the cerebellar tonsillar volume and explain the

relationship that each of these volumes has with each other.

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(a)

A

B

C

(b)

Figure 1: Brain MR midsagittal T2 demonstrating the posterior cranial fossa boundaries (a), the measurement of herniated tonsils from

sagittal images with A: basion, B: opisthion, and C: degree of tonsillar herniation measured as the length perpendicular from C to AB (b).

The aim of this study was to investigate PCFV, CV,

and herniated tonsillar volume in patients with CMI. We

compared PCFV and CV between the CMI and control

groups using stereological methods with MRI.

2.MaterialandMethods

2.1. Control Subjects. We carried out the present study on

25 subjects consisting of 12 females (mean age, 40.25 ±

12.14 years) and 13 males (mean age, 38.30 ± 11.14 years).

There was no statistically significant difference between sexes

according to age.

The subjects were volunteers, and written informed

consent was obtained. Official permission was also obtained

from the responsible departments of the university and state

hospital administrators. All procedures were fully explained

to the subjects. Those who underwent an MRI complaining

of headaches with the results showing no cranial or intracra-

nial pathology were chosen as the control group.

2.2. Patients. We retrospectively evaluated 70 adult patients

who had been treated in our neurosurgical department

because of CMI between January 2006 and December 2010.

Thirty patients (14 males, mean age 37.0 ± 11.6 years and

16 females mean age 41.9 ± 13.8 years) whose preoperative

radiological studies were available served as subjects in this

study.

The ages of the male and female groups were statistically

matching. To be eligible for the study, each patient was

required to have MRI findings consistent with CMI. The

requirements for enrollment of the latter patients included

having access to all preoperative medical records, radio-

graphic studies, and neurological findings. Patients with

neurological deficits attributable to surgery were excluded.

2.3. Magnetic Resonance Imaging Protocol. We analyzed the

neurologically intact cranial MRIs of all the subjects, and we

obtained T1- and T2-weighted sagittal images using a 1.5

Tesla MRI machine (GE Signa, HDI, France). The following

parameters were used for the imaging process for T1: TR/TE:

425/17.5, FOV: 20, 1.5-mm slice thickness without gap and

matrix 288 × 224. The parameters for T2 were as follows:

TR/TE: 7450/102, FOV: 20, 1.5mm slice thickness without

gap, and matrix 384 × 288. Both T1- and T2-weighted

images were used for examination of the herniated tonsillar

images. We also obtained T2-weighted sagittal images using

the following protocol for the examination of the posterior

cranial fossa and cerebellar sections: TR/TE: 7450/102, FOV:

26, 5mm slice thickness without gap, and matrix 384 ×288.

2.4. The Margins of the Posterior Cranial Fossa. The posterior

cranial fossa was defined as the osseous anatomical area

with a floor formed by the occipital bone (basioccipital

portion of the clivus and supraoccipital portion of the

occipital bone up to the insertion of the tentorium cerebella

forming the superior boundary of this fossa) and the

basisphenoid. The petrous ridges of the temporal bones

formed the anterolateral border of this cavity anteriorly to

their connection (posterior petroclinoid ligament) to the

posterior clinoids [7], (Figure 1(a)).

2.5. Measurement of the Herniated Tonsillar Length. The

extent of cerebellar herniation was measured from the tips

of the cerebellar tonsils to a line drawn between the basion

and opisthion (Figure 1(b)).

2.6. Cavalieri Estimator. The MRIs of a section series with

5mm thickness were used for CV and PCFV estimation. A

section series with 1.5mm thickness was used for tonsillar

herniation volume estimation. The images were saved in

the computer and the transparent square grid test system

with d = 0.8cm between test points was superimposed for

the posterior cranial fossa and cerebellum. For herniated

tonsillar sections, d = 0.25cm between test points was

superimposed randomly covering the entire image frame.

The points hitting the cerebellum, posterior cranial fossa,

and tonsillar herniation-sectioned surface area were counted

for each area (Figures 2(a) and 2(b)). These volumes

were estimated using the modified formula for volume

estimations of radiological images as shown below [12–14]

?SU ×d

SL

V = T ×

?2

×

?P.

(1)

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(a) (b)

Figure 2: Representative midsagittal MRI for the cranial fossa and cerebellum (a) and herniated tonsils (b) with a grid overlaid for the

calculation of volumes using the Cavalieri method.

In the formula, “T” is the section thickness, “SU” the scale

unit of the printed film, “d” the distance between the test

points of the grid, “SL” the measured length of the scale

printed on the film, and “?P” the total number of points

hitting the cut, sectioned surface areas of the cerebellum,

posterior cranial fossa, and herniated tonsils.

According to this volumetric technique, a square grid of

test points was positioned on each MRI, and all points that

hit were counted.

2.7.VolumeFractionEstimation. Thevolumefractionisused

toexpresstheproportionofaphaseorcomponentwithinthe

whole structure. The volume fraction of an X phase within a

Y reference volume is simply expressed as follows:

VV(X,Y) =Volume of X phase in Y reference space

Volume of Y reference space

.

(2)

Volume fraction ranges from 0 to 1 and is often expressed as

a percentage [15–17].

The volume fraction formula with the combination of a

point-counting grid can be written as

VV(X,Y) =

?PX

?PY.

(3)

In this formula, “?PX” indicates the number of points

the reference space Y.

Weestimatedthevolumefractionoftheherniatedtonsils

within the whole cerebellum by means of the following

formula:

hitting the X phase and “?PY” the number of points hitting

VV(Herniation, Cerebellum) =

?PHerniation

?PCerebellum.

(4)

In this formula,?Pherniationis the total number of points hit-

is the total number of points hitting sectioned surface of the

cerebellum, including all its parts.

ting the components of the herniated tonsil, and?Pcerebellum

Table 1: An example of the application of volume and the volume

fraction method described in the present study. P(Y) = number of

points hitting the cross section of the cerebellum. P(X) = number

of points hitting the cross section of the herniated tonsil.

Section

number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

Total

P(Y)

P(X)

P(Y) ×P(X)

0

42

117

380

336

360

420

464

377

276

231

270

286

198

120

60

17

10

0

0

0

3964

?P(Y)2

4

36

169

400

441

576

900

841

841

529

441

729

676

484

400

400

289

100

49

36

4

8345

?P(X)2

0

49

81

361

256

225

196

256

169

144

121

100

121

81

36

9

1

1

0

0

0

2207

2

6

0

7

9

19

16

15

14

16

13

12

11

10

11

9

6

3

1

1

0

0

0

173

13

20

21

24

30

29

29

23

21

27

26

22

20

20

17

10

7

6

2

375

The application of the described approaches for the

estimation of volume and volume fraction is presented

(Table 1):

?SU ×d

SL

?2 ×0.8

1.95

V(Cerebellum) = T ×

?2

?

×

?P

= 0.5 ×

×375 = 124.55cm3,

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V(Herniation) = T ×

?SU ×d

SL

?0.2 ×0.25

0.25

?2

×

?P

?

= 0.15 ×

×173 = 1.04cm3,

(5)

CE =

?

k

k −1

? ?u2

?u?u+

?

?u2

?v?v−2

?uv

?u?u

3964

(375 ×173)

??1/2

,

CE =

?

21

21 −1

8345

(375)2+2207

(173)2−2

??1/2

= 0.10 = 10%.

(6)

The volume fraction of the phase Y was estimated as:

VV(Herniation, Cerebellum)

?PHerniation

=

?PCerebellum

=

1.04cm3

124.55cm3= 0.01 = 1%.

(7)

2.8. Error Prediction for Point Counting Technique with

Volume Fraction. Accordingly, the efficiency of sampling and

the density of grid points were performed as documented

in the literature [17, 18]. The coefficient of error (CE) was

calculated following the formula:

CE =

?

k

k −1

? ?u2

?u?u+

?u2

?v?v−2

?uv

?u?u

??1/2

.

(8)

In this formula, there are k images, and each summation is

over 1 to k. An example of the application of this type of

calculation is given in Table 1. The coefficient of error (CE)

of this estimate was approximated using (8).

2.9. Statistical Analyses. The statistical analyses were per-

formed using statistical package for the Social Sciences for

Windows (SPSS, Inc., Chicago, IL) 7.5 version software.

Meanvaluesarepresentedwiththeirstandarddeviations.We

assessedthemeandifferencesintheCVfor30patientsand25

control subjects using independent sample Student’s t-tests.

Significancewasindicatedbyatwo-tailedP valueoflessthan

0.05.

3.Results

Therewere13malesand12femalesinthecontrolgroupwith

a mean age of 39.24 ± 11.43. The mean (±SD) PCFV, CV,

and CV to PCFV ratios were 165.57 ± 19.37cm3, 125.74 ±

16.25cm3,and76.06±6.54%incontrolsubjects,respectively

(Table 2). In males, the mean (±SD) PCFV, CV, and CV to

PCFV ratios were 172.98 ± 20.36cm3, 133.10 ± 15.29cm3,

and 77.35±8.42%, respectively. In females, the mean (±SD)

PCFV, CV, and CV to PCFV ratios were 157.54 ± 15.25cm3,

117.77 ± 13.70cm3, and 74.68 ± 3.47%, respectively. While

there were no significant differences for age and CV to PCFV

ratio (P < 0.05), a significant difference was found for PCFV

and CV between genders (P > 0.05; Table 2).

There were 14 males and 16 females in the CMI group

with a mean age of 39.63 ± 12.88. The mean (±SD) PCFV,

CV, herniated tonsillar volume, herniated tonsillar length,

CV to PCFV ratio, and herniated tonsillar volume to CV

ratio were 146.01 ± 19.07cm3, 117.49 ± 18.28cm3, 0.89 ±

0.50cm3,9.63 ± 3.37mm,80.39 ± 6.68%, and0.77 ± 0.38%

in the CMI group, respectively (Table 3).

In males, the mean (±SD) PCFV, CV, herniated tonsillar

volume, herniated tonsillar length, CV to PCFV ratio, and

herniated tonsillar volume to CV ratio were 152.53 ±

24.79cm3, 122.58 ± 21.50cm3, 1.01 ± 0.61cm3, 10.35 ±

3.93mm, 80.39 ± 5.65%, and 0.83 ± 0.42%, respectively.

In females, the mean (±SD) PCFV, CV, herniated tonsillar

volume, herniated tonsillar length, CV to PCFV ratio, and

herniated tonsillar volume to CV ratio were 140.24 ±

9.81cm3, 113.03 ± 14.14cm3, 0.79 ± 0.37cm3, 9.00 ±

2.78mm, 80.40 ± 7.65%, and 0.71 ± 0.35%, respectively.

There were no significant differences between genders for all

parameters (P > 0.05) (Table 3).

The PCFV in the CMI patients was significantly smaller

thaninthecontrolsubjects(P < 0.05).IntheCMIgroup,the

CV was smaller than in the control group, but this difference

was not statistically significant (P > 0.05). In the CMI group,

the CV to PCFV ratio was higher than in the control group.

Our results revealed that chiari subjects had less PCFV and

CV than the control group (Table 4).

There was a correlation between the PCFV and CV (r =

0.799, P < 0.001) in the control subjects and CMI group

(r = 0.865, P < 0.001). There was also a correlation between

herniated tonsillar volume and length (r = 0.703, P < 0.001)

in the CMI group (Figure 3) (Table 5).

The mean time (±SD) needed to estimate the CV and

herniated tonsillar volume using the point-counting tech-

nique was 5 ± 2.1min with a range of 2–8min. The mean

of the CE for the estimation of herniated tonsillar volume to

CV ratio was under 10%.

4.Discussion

Magnetic resonance imaging has become a useful diagnostic

and investigative tool in brain research. Therefore, it is essen-

tial for the quantitative analysis of volumetric estimation.

This quantitative information allows researchers to study

the potential relationship between subtle neuroanatomic

changes along with some neurological and neuropsychiatric

diseases.

Several studies have found associations between cere-

bellar atrophy and neuropsychiatric symptomatology. The

cerebellum is known to be involved in such diseases as

alcoholism and ataxia [19, 20].

Stereological methods provide quantitative data on

three-dimensional structures using two-dimensional images,

although several studies have considered estimating the

PCFV and cerebellar volume [7, 12, 17, 21]. According to

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Table 2: Mean (±SD) age, CV, PCFV, and CV to PCFV ratio for both sexes in the control group.

AgeCV (cm3)PCFV (cm3)

CV to PCFV

ratio (%)

77.35 ±8.42

74.68 ±3.47

76.06 ±6.54

0.319

Men (n: 13)

Women (n: 12)

Total (n: 25)

P

38.30 ±11.14

40.25 ±12.14

39.24 ±11.43

0.681

133.10 ±15.29

117.77 ±13.70

125.74 ±16.25

0.015

172.98 ±20.36

157.54 ±15.23

165.57 ±19.37

0.440

CV: cerebellar volume, PCVF: posterior cranial fossa volume.

Table 3: Mean (±SD) values for age, CV, PCFV, and CV to PCFV ratio, herniated tonsillar length, herniated tonsillar volume, and herniated

tonsillar volume to CV ratio for both sexes in the CMI group.

AgeCV (cm3)PCFV (cm3)

CV to PCFV

ratio (%)

Herniated tonsil

lenght (mm)

10.35 ± 3.93

9.0 ±2.78

9.63 ±3.37

0.280

Herniated tonsil

volume (cm3)

1.01 ±0.61

0.79 ±0.37

0.89 ±0.50

0.239

Herniated tonsil volume

to CV ratio (%)

0.83 ±0.42

0.71 ±0.35

0.77 ±0.38

0.424

Men (n: 14)

Women (n: 16) 41.9 ±13.8

Total (n: 30)

P

37.0 ±11.6122.58±21.50 152.53±29.79 80.39 ±5.65

113.03±14.14 140.24 ±9.81

39.63 ±12.88 117.49±18.28 146.01±19.07 80.39 ±6.68

0.330 0.157

80.40 ±7.65

0.7900.997

CV: cerebellar volume, PCVF: posterior cranial fossa volume.

Table 4: Comparison of CV, PCFV, and CV to PCFV ratio between

the two groups.

Control (n = 25)

Mean ± SD

125.74 ±16.25

165.57 ±19.37

76.06 ±6.54

CMI (n = 30)

Mean ± SD

117.49±18.28

146.01±19.07

80.39 ±6.68

P

CV (cm3)

PCFV (cm3)

CV to PCFV ratio (%)

0.085

0.001

0.019

CV: cerebellar volume, PCVF: posterior cranial fossa volume.

our knowledge, there is no study on both cerebellar and

herniated tonsillar volumes or CV to PCFV fraction that

applies the unbiased techniques of stereological methods

using MRI.

The etiology of chiari type I malformation remains

unclear. One theory to describe this form of hindbrain

herniation suggests that a smaller than normal posterior

cranial fossa predisposes a normal-sized cerebellum to

traverse the foramen magnum during development [9].

Ekincietal.[17]usedtheMRIsobtainedfrom24normal

volunteers ranging from 20 to 25 years of age and measured

the total brain, cerebral, and cerebellar volume. They found

that the mean cerebellar volume was 117.75 ± 10.7cm3and

111.83 ± 8.0cm3in males and females, respectively. Acer

et al. [12] used MRI for CV estimates using two different

methods in both sexes. They found that the mean results of

thestereologicalmethodwere116.69±10.1cm3and114.41±

9.3cm3in males and females, respectively. Their results

demonstrated that female subjects had smaller cerebellar

volumes than males. However, the difference between the

genders was not statistically significant (P > 0.05). We

found that the mean (±SD) CV was 133.10 ± 15.29cm3and

117.77 ± 13.70cm3in the male and female control subjects,

respectively. Our research yielded similar results to other

previous research.

Tonsillar length (cm)

201816141210 864

3

2.5

2

1.5

1

0.5

0

Tonsillar volume (cm3)

Figure 3: The figure shows the correlation between the herniated

tonsillar length and volume.

Milhorat et al. [9] found that the total volume of the

posterior cranial fossa was decreased by an average of more

than 10cm3in some patients with CMI compared with a

control population. Tubbs et al. [7] found that the mean

PCFV was 208.5cm3in chiari patients. They did not find

any statistically significant difference between controls and

patients with CMI.

Furtado et al. [22] found that the PCFV in childhood

patients with chiari malformation was significantly lower

than in the control group (P = 0.002). They found that

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Table 5: Correlation values among the three parameters.

Parameters

Pearson correlation test

Correlation

0.799

0.865

Significance

P < 0.001

P < 0.001

PCFV-CV(Control)

PCFV-CV (CMI)

Herniated tonsillar

length-herniated tonsillar volume

0.703

P < 0.001

CV: cerebellar volume, PCVF: posterior cranial fossa volume.

the mean PCFV was 204.1cm3in patients with CMI and

252.8cm3in the age- and sex-matched control group. Also,

they found that the PCFV in adult patients with chiari

malformation was 245.4cm3. Nishikawa et al. [23] found

that the PCFV in adult chiari patients and the PCFV in

the control group were 186cm3and 193cm3, respectively.

They noted a smaller PCFV in the CMI patients. Our results

revealed that chiari subjects had less PCFV and CV than the

control group.

Schady et al. [24] found an inverse relationship between

the size of the posterior cranial fossa and the degree of

cerebellar herniation, whereas Stovner et al. [25] showed

a strong positive correlation. We found that there was a

correlation between the PCFV and CV in the control and

chiari groups in our study.

The chiari type I malformation is traditionally char-

acterized by the downward herniation of the cerebellar

tonsils with a descent of 5mm or more below the foramen

magnum [26]. In literature, in patients with chiari type I

malformations,herniationofthecerebellartonsilsiswithina

range of 3 to 29mm below the foramen magnum [3, 22, 26].

Our results are similiar to the values obtained by other

authors, and we showed a correlation between herniated

tonsillar volume and length in the chiari group.

5.Conclusion

This study has shown that there are statically significant

differences in the posterior cranial fossa volumes between

CMI patients and control subjects. On the other hand,

smaller CV is seen in CMI patients, but this difference is

not statistically significant. We have highlighted several new

features, such as herniated tonsillar volume of the CMI

malformationthatprovideforabetterunderstandingofhow

touseitasaradiologicalassessment.Wealsofoundapositive

correlation between the PCFV and CV for each group. There

was also a correlation between herniated tonsillar volume

and length in the CMI group.

We believe that these correlations and measurements will

facilitate the diagnosis of chiari malformations by radiolo-

gists and neurosurgeons. The clinicians and radiologists can

consider the size of the herniated tonsils of the cerebellum

if they know the herniated tonsillar length. The findings of

the current study using stereological methods provide useful

data for the evaluation of normal and pathologic volumes of

the cerebellar and posterior cranial fossa.

Authors’Contribution

Theauthorsofthispaper,whoareindicatedinthetitle,made

substantial contributions to the following tasks of research:

initial conception and design (¨U. E. Vurdem, T. Ertekin, N.

Acer A. Savranlar, M. F.˙Inci); administrative, technical, or

material support (¨U. E. Vurdem, A. Savranlar, M. F.˙Inci);

acquisition of data (¨U. E. Vurdem, N. Acer, T. Ertekin, A.

Savranlar, M. F.˙Inci); laboratory analysis and interpretation

of data (¨U.E. Vurdem, N. Acer,T. Ertekin, A.Savranlar,M. F.

˙Inci); drafting of the paper (N. Acer, T. Ertekin); and critical

revision of the paper for important intellectual content (¨U.

E. Vurdem, N. Acer, A. Savranlar, T. Ertekin, M. F.˙Inci).

The views expressed herein are those of the authors and not

necessarily of their institutions or sources of support.

Acknowledgments

The authors wish to thank Professor Dr. Erdo˘ gan Unur,

Professor Dr. Kenan Aycan, Prof. Dr Harun Ulger, Halil

˙Ibrahim C ¸elik and Sibel Erciyes for their skillful technical

assistance.

References

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