Surg Radiol Anat DOI 10.1007/s00276-015-1434-7

ORIGINAL ARTICLE

The posterior cranial fossa: a comparative MRI-based anatomic study of linear dimensions and volumetry in a homogeneous South Indian population Awalpreet Singh Chadha • Venkatesh S. Madhugiri M. N. Tejus • V. R. Roopesh Kumar

•

Received: 29 May 2014 / Accepted: 19 January 2015 Ó Springer-Verlag France 2015

Abstract Purpose The posterior fossa contains structures that are vital to life. In this study, we aimed at establishing normal linear dimensions and volume data of the posterior fossa in a homogeneous south Indian population. We also evaluated the influence of large tumors on these parameters. We evaluated the accuracy of different techniques of measuring these dimensions and compared them with literature. Materials and methods Control and tumor MRIs were selected from an imaging database. Linear posterior fossa dimensions as well as volumes were measured using Image J and Fiji. The volume data were compared with similar data from literature. The effect of the presence of a tumor on posterior fossa volume was measured. Results The posterior fossa volume was higher in men than in women, irrespective of whether the volume was estimated on axial, sagittal or coronal MR images. Despite the wide variation in the techniques used, there was no significant difference between the volumes reported in literature and the volumes calculated in the current series. The presence of large tumors did not affect linear dimensions or posterior fossa volumes. Among the techniques based on linear measurements that were assessed for concordance with manual segmentation, the technique using the formula for volume of an ellipsoid had the best agreement. A. S. Chadha and V. S. Madhugiri have contributed equally to this work. A. S. Chadha  V. S. Madhugiri (&)  M. N. Tejus  V. R. R. Kumar Department of Neurosurgery, Jawaharlal Institute of Postgraduate Medical Education and Research (JIPMER), Pondicherry 605006, India e-mail: [email protected]

Conclusions Posterior fossa volume is higher in men than in women, Posterior fossa dimensions were not affected by the presence of large tumors. Manual segmentation remains the most accurate method to measure posterior fossa volume. Keywords Posterior fossa  Morphometry  Posterior fossa volume  Image J  Fiji  Supratentorial tumor

Introduction The posterior cranial fossa (PCF) is a compact region that contains many structures that are vital to life. Several developmental disorders affect the shape, dimensions and volume of the PCF including the Chiari malformations, Dandy Walker malformations, spina bifida and craniovertebral junction disorders [6–8, 25, 26, 28–30]. Several studies have compared PCF dimensions in patients with these conditions with those in control individuals [6–8, 26, 28]. Although normative data could indirectly be derived from the control groups of these studies, few studies establish normative values for PCF dimensions [12]. Measuring PCF volume and dimensions becomes important in assessing the response to decompressive surgery or monitoring growth in patients with congenital disorders. The techniques used to measure posterior fossa volume (PCFV) have varied between studies. PCFV has been estimated from dry skulls, using water-fill or resin-fill techniques [12]. In fetuses and neonates, ultrasound scan generated linear measurements have been used to calculate the PCFV [4, 10, 11]. Magnetic resonance imaging (MRI) sequences have been analyzed in several different ways to compute the PCFV in vivo [6, 7, 25, 29]. Manual planimetric segmentation of images is the standard technique

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against which all other radiology-based techniques would need to be compared. Automated image segmentation techniques for computing PCFV have been developed, but remain outside the purview of routine clinical use [2]. In order to generate techniques that would be clinically useful, several simplifying assumptions have been made about posterior fossa geometry so as to estimate PCFV from sets of linear measurements. The PCF has been variously assumed to be a spheroid [7], an inverted cone truncated at the foramen magnum [12], and an ellipsoid [15]. The accuracy of these techniques is dependent on the number of orthogonal planes in which linear measurements are made. The superior delimiting structure of the PCF, the tentorium, is a sheet of dura. It is, thus, theoretically possible for the tentorium to be deformed, either directly by tumors impinging on it or possibly indirectly, as a result of raised pressure in the supratentorial compartment. The mechanisms to compensate for raised intracranial pressure (in the supratentorial space) include displacement of cerebrospinal fluid (CSF) to the lumbar subarachnoid space, deformation of the brain and reduction of blood volume in the venous spaces. Brain ischemia and herniation are terminal events [3, 9, 13, 16–18, 27]. It is possible that there is an anatomic distortion of the tentorium and brain stem as a result of supratentorial space lesions. This would affect PCF dimensions and alter PCFV. The effect of tumors in the supratentorial space (STS) on PCF dimensions and PCFV, if any, has not previously been described in literature. In this study, we aimed at establishing normative data for PCF dimensions and PCFV. Linear PCF dimensions were measured on MRI. PCFV was first estimated by manual segmentation of MRI sequences; images acquired in sagittal, coronal and axial planes were used to estimate the volume. We compared the volumes thus obtained (by segmentation of axial, sagittal and coronal sequence images) to check for concordance with each other. We then compared the PCF volumes estimated by manual segmentation of MR images with the control arm data from studies available in literature. Next, we compared the volumes obtained by manual segmentation with volumes estimated using various linear measurement-based formulae and checked for concordance. Finally, we compared PCFV of patients with STS tumors with the control group of this study, to assess if these dimensions were altered by the presence of a STS tumor.

Methods The imaging database in our department was searched to identify control subjects and patients with STS tumors, who had all been imaged over the past 5 years. Children aged less than 10 years were not included. Only patients

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who belonged to the south Indian state of Tamil Nadu and resided within 100 km of Pondicherry were considered for inclusion in the study. Patients who had been diagnosed with trigeminal neuralgia, pituitary microadenomas, orbital lesions, unruptured aneurysms and those who had undergone a screening cranial MRI along with a cervical spine MRI investigation were included in the control group. Previous studies have established that the PCFV in patients with trigeminal neuralgia is not different from that in normal control individuals [14]. All the selected MRI sequences had been performed as part of a routine clinical diagnostic protocol on a Siemens 1.5T MRI machine. Gd contrast-enhanced T1 sequences (TE = 5.47, TR = 12) in the axial, sagittal and coronal planes were selected for analysis. All patients were positioned supine, with the head in neutral position within the gantry. The interpupillary line was ensured to be parallel to the couch. The vertical laser positioning line was maintained exactly in the midline and the horizontal line at the nasion for all patients. For axial images, the slices were maintained parallel to the AC-PC line. In all selected sequences, the slice thickness was 1 mm and the interslice distance 0.25 mm. The FoV was 256 9 256 mm, with a pixel dimension of 1 9 1 mm. Linear posterior fossa dimensions The image processing software Image J (developed by the National Institutes of Health, Bethesda) was used for all linear image measurements [24]. Selected Gd contrastenhanced T1 sagittal MRI sequences were imported into Image J. The mid-sagittal image was identified for the purposes of this study as that image in which the aqueduct was clearly seen. The junction of the vein of Galen with the straight sinus was identified; this would mark the tentorial apex and the highest point of the PCF roof. Two horizontal lines were drawn, passing through the basion (anterior margin of foramen magnum, AM) and opisthion (posterior margin of foramen magnum, PM) respectively (Fig. 1a, b). The posterior fossa height (PCFH) was measured as the distance between the tentorial apex (junction of the vein of Galen with the straight sinus) and the horizontal lines. Thus, two values of PCFH were measured on each MRI— PCFH-AM and PCFH-PM. The intracranial brainstem length (BSL) was similarly measured as the distance between the roof of the tectal plate and the two horizontal lines to yield two values—BSL-AM and BSL-PM (Fig. 1c). The posterior fossa angle (PCFA) was measured as the angle subtended between two lines—the first joining the basion to the tentorial apex and the second, the tentorial apex to the torcular, parallel to the tentorium (Fig. 1d). These measurements were made on all control as well as tumor MRIs. The mean dimensions of each group were

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Fig. 1 Mid-sagittal image in a Gd contrast-enhanced T1 series. a Shows the landmarks used for posterior fossa morphometry. a apex of the tentorium, b highest point of the brain stem, c basion, d opisthion. b Measuring the posterior fossa height. White arrow— posterior fossa height measured from the opisthion (PCFH-PM), black

arrow—posterior fossa height measured from the basion (PCFHAM). c Measuring the brain stem length. White arrow—brain stem length measured from the opisthion (BSL-PM), black arrow—BSL measured from the basion (BSL-AM). d Posterior fossa angle

compared between males and females using a two-tailed t test; a p value of\0.05 at an a = 95 % was considered to be significant. All statistical analyses were performed on MS Excel 2010 and SPSS (v20, IBM).

the ROI manager tool and then multiplied by the slice thickness (plus interslice distance) to obtain the PCFV. This estimation of PCFV by manual delineation of the PCF boundaries was carried out on axial, sagittal as well as coronal images. This planimetric volume was designated VolSeg. The PCFV was compared between males and females and a two-tailed t test applied to check for any significant differences. An analysis of variance (ANOVA) was carried out to check if the volumes estimated using images acquired in the three orthogonal planes (axial, sagittal and coronal) were significantly different. In order to assess the degree of concordance of the PCFV volumes estimated on axial, sagittal and coronal

Posterior fossa volume by manual image segmentation (VolSeg) The PCFV was calculated using Fiji, a version of Image J with several preloaded plugins [23]. The posterior fossa was delimited by drawing the boundaries manually on each image of the selected MRI sequences (Fig. 2). The total surface area of the segmented areas was measured using

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Fig. 2 Measuring the posterior fossa volume using Fiji Region of interest (ROI) manager. a Drawing out the posterior fossa on a sagittal image. b All the ROIs superimposed in the ROI manager

images, the mean agreement index was calculated for each pair of measurements—sag-axial, sag-coronal and axialcoronal. The AI was calculated as follows—   P ij AImean ¼ 1n ni¼1 1  jVViiv , where Vi = VolSeg for each i ð þv 2 Þ MRI and vi = volume calculated by the technique being compared with VolSeg. A perfect concordance would mean that AI = 1ðVi  vi ¼ 0Þ. Comparison with literature We compared the PCFV estimated by manual image segmentation in this series with the normative data obtained from the control arms of papers published over the past 5 years. Only studies that had used radiologic images to estimate the PCFV were included. A PubMed search was performed using the advanced search builder and the search strings ‘‘posterior fossa volume’’ and ‘‘posterior fossa morphometry’’. All papers were screened to check if a control arm of normal MRI or CT data was included. Those that had such control arm data were included for comparison of PCFV data. PCFV data for males and females were separated where possible. Several studies had normalized the PCFV with respect to the intracranial volume; such data were not considered and only raw PCFV data were included for analysis. Where more than one technique was applied in a study to compute PCFV, the results of each technique were included separately. Oneway ANOVA was applied to check for significant differences in PCFV reported by these studies. The PCFV estimations obtained on axial, sagittal and coronal images

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in this study were included as separate measurements for this analysis. PCFV estimation using linear measurement-based formulae PCFV was also estimated using two linear measurementbased formulae that made simplifying assumptions regarding posterior fossa geometry. The first was to assume that the posterior fossa was an inverted cone truncated at the foramen magnum [12]. Here, the base of the cone was a line joining the dorsum sellae to the inion (Fig. 3). This distance was halved to obtain R1, the radius of the base of the cone. The height of the truncated cone, H, was measured between this line forming the base and another line joining the basion and opisthion, in a mid-sagittal image. The radius of the foramen magnum was measured as R2. Using Thales’ theorem, the height of the truncated part H0 2 was calculated as H 0 ¼ RHR . The PCFV was calculated 1 R2 from these parameters as described by Habibi et al. [12]: PFV ¼

H þ H0 3 H0 3 pR1  pR2 3 3

This volume was designated VolCone. The other technique that was employed was to assume that the PCF is an ellipsoid and to calculate the PCFV using the formula v ¼ abc 2 [15]. Here, a was the PCFH-AM and b was the distance between the tentorial apex and the inion/torcular. Figure 1c, the transverse diameter of the PCF, was calculated by counting the number of sagittal slices on which the posterior fossa was visualized and multiplying this by the

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found to be suitable for inclusion in the tumor group; this group had 8 men. The gender distribution was not significantly different between the two groups. The mean age of the control group was 43.6 years and that of the tumor group was 43.06 years (2 tailed p = 0.9). Thus, the control and tumor groups were well matched with respect to age and gender distribution. Normative linear posterior fossa dimensions

Fig. 3 Measuring the posterior fossa volume assuming it to be an inverted cone. 1 R1, radius of the base, 2 R2, radius of the foramen magnum where the cone is truncated, 3 H, height of the PCF, 4 H0 , height of the truncated portion. The extension of the posterior fossa above the base of the cone is evident

slice thickness plus interslice distance. The volume obtained thus was designated VolEll. The volumes calculated by these formula-based techniques were compared with the PCFV estimated using manual segmentation (VolSeg). Volumes obtained using each of the sequences (axial, sagittal and coronal) were compared separately in two ways with the formula estimates to look for concordance. First, means vs differences (Bland–Altman, BA) plots were generated for VolCone Vs VolSeg and VolEll Vs VolSeg [5]. Concordance was checked for by looking at the number of measurements lying outside the mean difference ±1.96 SD lines. Second, the mean agreement index (AI) for each technique with VolSeg was calculated as already described. Control vs tumor MRIs All the posterior fossa dimensions and the PCFV were measured on the MRIs of patients with STS tumors. A twotailed t test was applied to look for any significant difference in the mean values between these two groups. Only the volumes estimated by manual image segmentation were used for this analysis.

Linear posterior fossa dimensions were only measured on sagittal images. The linear PCF dimensions are displayed in Table 1. The BSL-AM was significantly higher in men than in women (p = 0.006). The PCFH-PM was also different between men and women (p = 0.054). On performing Pearson’s bivariate correlation analysis, the BSLAM was the only linear measure that correlated with the final PCFV measured on sagittal sequences (p = 0.048). Linear regression was used to model the relationship between BSL-AM and the PCFV, however, the model poorly predicted the PCFV (R2 = 0.13). Posterior fossa volume by manual image segmentation (VolSeg) The mean PCFVs in the control group calculated by manual planimetry using images acquired in the 3 planes were as follows: sagittal PCFV, 152.07 ± 24.32 cc; axial PCFV, 160.29 ± 29.57; and coronal PCFV, 154.33 ± 25.51. ANOVA revealed that there was no statistically significant difference in the volumes estimated on sagittal, axial and coronal sequences (p = 0.48). The agreement indices for PCFV estimated on each sequence with the others are displayed in Table 2; there was no significant difference in the agreement indices between the groups. Thus, PCFV could be estimated by manual image segmentation using images acquired in any of the 3 orthogonal planes. The PCFV was significantly higher in men than in women (Table 3). This difference remained significant irrespective of whether sagittal, coronal or axial images were used for the volume estimation. Since the two gender groups were not significantly different with respect to mean age (males—45.4 ± 16.75 years, females—41.94 ± 14.49, p = 0.54), the difference in PCFV between genders was not a result of varying age distribution in the two groups. Posterior fossa volume: comparison with literature

Results A total of 31 MRIs were included in the control arm, 15 of these were males. MRI sequences from 16 patients were

Eight papers published within the past 5 years were found suitable for inclusion to compare the mean PCFV [2, 7, 12, 14, 15, 20, 28, 31]. The control group data from these studies were compared with the control group data from the

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Surg Radiol Anat Table 1 Linear posterior fossa dimensions in the control group All values in mm

Males

Females

Overall Mean

SD

Two-tailed t test for difference between men and women, p

Mean

SD

Mean

SD

BSL-PM

59.36

6.28

55.63

6.64

57.37

6.641

0.127

BSL-AM

57.07

2.70

52.56

5.13

54.67

4.700

0.006

PFH-PM

68.36

6.20

64.25

4.97

66.17

5.861

0.054

PFH-AM

65.93

7.29

61.06

8.46

63.33

8.185

0.105

PFA-AM

66.00

8.02

67.31

9.97

66.70

8.983

0.697

The bold italicized p value was the only parameter that differed significantly between men and women SD standard deviation, BSL brain stem length, PFH posterior fossa height, PFA posterior fossa angle, AM anterior margin of the foramen magnum, PM posterior margin of the foramen magnum

Table 2 Agreement of posterior fossa volumes estimated on sagittal, coronal and axial images with each other Agreement index

PFV sagittal–PFV axial images (mean ± SD)

PFV sagittal–PFV coronal images (mean ± SD)

PFV axial–PFV coronal images (mean ± SD)

AI

0.83 ± 0.12

0.88 ± 0.12

0.86 ± 0.1

ANOVA for difference in AIs

F = 2.144, p = 0.12

PFV posterior fossa volume, AI agreement index, SD standard deviation, ANOVA analysis of variance

Table 3 Gender differences in the posterior fossa volume estimated by manual image segmentation Gender

Sagittal images PFV (mean ± SD, in cc)

Axial images PFV (mean ± SD, in cc)

Coronal images PFV (mean ± SD, in cc)

Male

171.77 ± 19.57

179.17 ± 28.70

169.07 ± 22.52

Female T test, PCFV male vs female

135.00 ± 11.84 p \ 0.0001

144.95 ± 20.34 p = 0.002

141.57 ± 21.08 p = 0.003

PFV posterior fossa volume, cc cubic centimeters

present study (Table 4). For the purpose of analysis, each of the PCF volumes estimated in the present study by manual image segmentation (PCFV-sagittal, axial and coronal) was included as a separate volume. PCFV estimates for male and female subjects were compared separately; studies with mixed gender groups were not included since it is clear from the preceding analysis that the PCFV differs significantly between men and women. One-way ANOVA revealed that there was no significant difference in the mean PCFVs reported by these studies for either men (p = 0.08) or women (p = 0.07). The techniques used to compute PCFV were classified as manual segmentation, linear measurement-based formulae and semi-automated or automated image segmentation. When studies were grouped by technique used, the difference in PCFV values between studies was still insignificant.

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PCFV estimation using linear measurement-based formulae PCFV obtained by two linear measurement formulae (VolEll and VolCone) was compared with the volumes estimated by manual image segmentation (VolSeg) for concordance (Fig. 4). BA plots were generated to look for concordance of the VolCone with the PCFV estimates by manual segmentation (sagittal, axial and coronal). The plots are displayed in the left side panel of Fig. 4. The BA plots for VolCone show a significant degree of scatter. Only the plot for VolCone vs VolSeg-sagittal does not show any points lying outside the mean ± 1.96 SD lines. The BA plots for VolEll versus the manual segmentation volumes are displayed in Fig. 4d–f. The plots for VolEll vs VolSeg show that there are outliers beyond the

Surg Radiol Anat Table 4 Studies that reported posterior fossa volume of control subjects. Blank cells indicate that data are not available References

Year

Country/ population

Material used

Technique used

Sample size

Sex

Mean age (years)

Mean PFV (in cc)

±SD

Female

36

195.15

0.6364

181.6

15.9

Female control data Bagci [1]

2013

USA

MRI

Manual segmentation

Horinek [2] Kanodia [3]

2009

Prague

MRI

Automated segmentation

2012

North India

CT

Formula for ellipsoid

36

Female

51.3

148.99

26.51

Kanodia [3]

2012

North India

CT

Automated segmentation

36

Female

51.3

148.73

18.86

Vurdem [4] Present study

2012

Turkey

MRI

12

Female

40.25

157.54

15.23

2014

South India

MRI

Automated segmentation, sagittal images Manual segmentation, axial images

16

Female

41.94

135

11.84

Present study

2014

South India

MRI

Manual segmentation, coronal images

16

Female

41.94

144.95

20.34

Present study Present study

2014

South India

MRI

Manual segmentation

16

Female

41.94

141.57

21.1

2014

South India

MRI

Formula for ellipsoid

16

Female

41.94

125.24

20.67

2014

South India

MRI

Formula for cone

16

Female

41.94

137.36

27.16

Male

32.5

196.575

11.71306

207.3

11.8

Present study

2

Female

Male control data Bagci [1]

2013

USA

MRI

Manual segmentation

Horinek [2]

2009

Prague

MRI

Automated segmentation

4

Kanodia [3]

2012

North India

CT

Formula for ellipsoid

64

Male

51.3

162.88

27.68

Kanodia [3]

2012

North India

CT

Automated segmentation

64

Male

51.3

165.68

27.16

Vurdem [4]

2012

Turkey

MRI

Automated segmentation

13

Male

38.3

172.98

20.36

Present study

2014

South India

MRI

Manual segmentation,

15

Male

45.4

171.77

19.57

Present study

2014

South India

MRI

Manual segmentation,

15

Male

45.4

179.17

28.7

Present study

2014

South India

MRI

Manual segmentation,

15

Male

45.4

169.072

22.52

Present study

2014

South India

MRI

Formula for ellipsoid

15

Male

45.4

160.55

22.84

Present study

2014

South India

MRI

Formula for cone

15

Male

45.4

176.53

29.38

Furtado [5]

2009

India

MRI

Volume of a sphere

21

Mixed

252.8

Milhorat [6]

2010

USA

MRI, CT

Automated segmentation

80

Mixed

151.8

Trigyldas [7]

2008

Canada

MRI

Semi-automated segmentation

7

Mixed

Male

sagittal images axial images coronal images

Mixed groups

14

3.14

145.14

PFV posterior fossa volume

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Fig. 4 Bland–Altman plots. a–c BA plots for VolCone and VolSeg values measured on a sagittal, b axial and c coronal MRI images. d–f BA plots for VolEll and VolSeg values measured on d sagittal, e axial and f coronal MRI images

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mean ± 1.96 SD lines on every plot, indicating a poor concordance with the manually estimated volumes (VolSeg). The mean agreement indices for each of these formula-based techniques with the volumes estimated by manual image segmentation in three planes are displayed in Table 5. The posterior fossa volumes estimated by linear measurement formulae agree best with the manual volumes estimated using sagittal images. However, the agreement was modest and not accurate. Controls vs Tumor MRI images 16 patients were included in the tumor group (8 men). The mean age of the tumor group was 43.06 (±15.4) years. All patients were conscious and alert at the time of performing MRI; thus, herniation was not a confounding factor. 12 patients had histologically proven glioblastoma (WHO grade IV) and the others, meningiomas in various supratentorial locations. Only the glioma group was included for the estimation of PCFV. The mean tumor volume was 78.27 ± 53.1 cc. There was no difference in any of the linear parameters between the control and tumor groups. The PCFV calculated on tumor MRIs was not significantly from the control group values, irrespective of which orthogonal plane images were acquired in. Thus, neither the PCF dimensions nor the PCFV was altered by the presence of a large tumor; the posterior fossa space remains unaltered even in the presence of large STS lesions.

Discussion Posterior fossa morphometry is performed as part of the evaluation of patients with a variety of developmental disorders. There is no uniformity in the material used to estimate PCFV. Authors have reported the use of dry skulls [15], MR images [2, 7, 12, 14, 15, 29, 31] and CT images [15, 20] to estimate PCFV. There also exists a discrepancy between the actual volume of the PCF and the volume of its contents. Some authors have estimated both and found significant differences between these values [20]. On sagittal MRI images, the superior boundary of the posterior

fossa would be the tentorium; the anterior boundary, the clivus and the inferior boundary, the line joining the opisthion and basion (Fig. 2). The area thus measured would include the brain stem, cerebellum and vermis, posterior fossa vasculature and CSF spaces including the IV ventricle. This is the clinically relevant PCFV or the volume of the posterior fossa contents as against the dry bone volume. The boundaries of the posterior fossa are easiest to visualize on sagittal images. However, in this study, we estimated PCFV by manual image segmentation on sagittal, axial as well as coronal images. There was no statistically significant difference in the volumes estimated using these sequences. Thus, the PCFV could be estimated from images acquired in any of the three orthogonal planes. The sequences used in this study had 1 mm slices with a 0.25 mm interslice distance. MRI images are subject to distortion and loss of accuracy of spatial resolution as the slice thickness reduces, interslice distance reduces or acquisition parameters vary [1, 21, 32, 34]. The volumes calculated on MR images are only an estimation of the true PCFV. However, most clinically relevant measurements will be made on CT or MR images. Therefore, measurement techniques on MR and CT images, including parameters such as slice thickness and interslice distance, need to be validated and standardized. Although different techniques have been used to estimate posterior fossa volumes, there was no statistically significant difference in the PCFV values reported in various studies (Table 4). Intuitively, however, the most accurate method to estimate PCFV in vivo would appear to be manual delineation of the boundaries of the posterior fossa on thin images of an MRI sequence. However, this is a labor intensive technique that entails drawing out the boundaries of the PCF on every slice of an MRI sequence. Evidently, thinner slices on the MRI sequence would mean more accurate results and thus, this technique could also be time-consuming. One way around this problem is to randomly select slices and apply the Cavalieri principle [19]. This would reduce the number of slices that need to be manually segmented, while preserving accuracy. Even if uniformity were to be achieved with respect to technique, geographic variations are likely to exist due to differing body morphology in various parts of the world; these

Table 5 Agreement indices of the linear measurement-based formulae with the posterior fossa volumes estimated by manual image segmentation in various planes Formula used

Mean AI with PFV sagittal

Mean AI with PFV axial

Mean AI with PFV coronal

Volume of a truncated cone

0.82 ± 0.14

0.76 ± 0.14

0.76 ± 0.16

Volume of an ellipse

0.85 ± 0.085

0.79 ± 0.14

0.83 ± 0.12

AI agreement index, PFV posterior fossa volume

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differences would predicate the establishment of regional standards for such data. Linear measurements form an important aspect of PCF morphometry. Various morphometric lines have been described (for e.g., Twining’s line, McRae’s line, the clival-canal line, etc.) and large series have reported the normal values of lengths of these lines. In this study, we opted to use two simple linear measurements—the maximum posterior fossa height and the intracranial brain stem length. The BSL-AM values differed significantly between men and women (p = 0.006). This was also the only line that correlated with PCFV (p = 0.048). Thus, not all these morphometric lines necessarily correlate with PCFV; this lack of correlation has also been noted previously [2]. Every study published in literature has described different linear dimensions in an attempt to describe the posterior fossa shape. However, the lack of correlation of these linear measurements with the PCFV casts a doubt on their utility. In the current study as well, only the BSL-AM correlated with the PCFV. The posterior fossa angle or tentorial angle is another measurement that reflects the shape of the PCF. Sade et al. [22] found the PFA to be 50.9 ± 11.5° in a North American population. The mean PFA determined in the current study was 67.85 ± 7.12°. A t test showed that this difference was significant (p \ 0.001), although the measurement technique was the same in both studies. It is important to standardize measurements of the PFA since this may have several clinical implications. The PFA has been found to correlate with the operating distance to the trigeminal nerve and the VII-VIII complex while operating on the cerebellopontine angle via the retrosigmoid approach [22]. The PFA has also been found to correlate with sleep cycle disturbances in patients with traumatic brain injury [33]. Various linear measurement-based formulae have therefore been evolved to simplify the estimation of PCFV for routine clinical applications. One of these methods is to consider the PCF to be an inverted cone (VolCone). There are two problems with this assumption—first, the suboccipital bone is not as angulated to the vertical plane as the clivus is. Second, the base of the inverted cone is either a line drawn from the dorsum sellae to the inion or Twining’s line (tuberculum sellae to inion) (Fig. 3). However, since the tentorium arches superiorly towards the mid-sagittal plane, a significant volume of the posterior fossa would lie above this line [2, 12]. The other linear measurement-based formula is that for volume of an ellipsoid, assuming the PCF to be an ellipsoid. The formula for volume of an ellipsoid could be simplified to read v = abc/2. The VolEll calculation is the only linear measurement-based formula that considers measurements in three orthogonal planes. Therefore, when VolCone and VolEll were compared with the manual segmentation volume in this study, the ellipsoid

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formula had a much higher agreement index that the other (Table 5). Thus, it is evident that although linear measurement-based formulae make it possible to easily estimate the PCFV, these estimates are neither accurate nor reliable. Neither the linear PCF dimensions nor the PCFV varied between patients with a supratentorial tumor and the control group. All patients with tumors included in this study were completely conscious and alert, thereby implying that tonsillar herniation had not occurred. This was also confirmed on MR images. The lack of variation in PCF dimensions and PCFV implies that the posterior fossa is a relatively rigidly confined space. Thus, sudden increases in pressure in the supratentorial space would be transmitted to the neural contents, blood vessels and CSF in the posterior fossa, since the delimiting structures are rigid and unyielding. In the absence of accommodative distortion of the PCF walls, a sudden increase in supratentorial pressure would lead to herniation of the tonsils through the foramen magnum. Thus, there is probably no accommodative distortion of the posterior fossa shape or volume in response to an increase in supratentorial pressure due to any cause.

Conclusions The BSL-AM differed between men and women and correlated with the PCFV. In general, linear PCF measurements did not correlate with PCFV. Linear measurementbased formulae for PCFV did not have good concordance with the volume estimated by manual image segmentation; the best agreement index was for the formula abc/2 (AI = 0.85). The mean PCFV in a south Indian population was estimated using MR images. The volumes estimated on sagittal, coronal and axial images were not significantly different. However, the PCFV was significantly higher in men than in women. Neither linear PCF dimensions nor PCFV was affected by the presence of supratentorial lesions. The values of PCFV reported in literature were not significantly different from the volumes reported in this series, despite the various methods used for estimation. However, in the interests of exactitude, standardization is required and normative data need to be generated for each technique and region. Acknowledgements The authors would like to acknowledge the contribution of Dr. Gopalakrishnan M S, Department of Neurosurgery, Jawaharlal Institute of Postgraduate Medical Education and Research, who is responsible for generating and maintaining the departmental imaging database, without which this study would not have been possible. Ethical standards We declare that this manuscript does not contain any clinical studies or identifiable patient data.

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