Morphometric analysis of human occipital condyle

Morphometric analysis of human occipital condyle

Clinical Neurology and Neurosurgery 107 (2005) 191–199 Morphometric analysis of human occipital condyle Sait Naderia,∗ , Esin Kormanb , G¨uven C ¸ ıt...

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Clinical Neurology and Neurosurgery 107 (2005) 191–199

Morphometric analysis of human occipital condyle Sait Naderia,∗ , Esin Kormanb , G¨uven C ¸ ıtaka , Mustafa G¨uvenc¸erb , Candan Armanb , Mehmet S¸eno˘glua , S¨uleyman Tetikb , M. Nuri Ardaa a

Department of Neurosurgery, Dokuz Eyl¨ul University School of Medicine, 35340 Izmir, Turkey b Department of Anatomy, Dokuz Eyl¨ ul University School of Medicine, 35340 Izmir, Turkey Received 18 November 2003; received in revised form 28 June 2004; accepted 26 July 2004

Abstract Objective: The human occipital condyle is the unique bony structure connecting the cranium and the vertebral column. The progress in neuroimaging techniques has increased interest for aggressive craniovertebral surgery. Such surgery requires the knowledge regarding anatomical aspects of the craniovertebral junction. The aim of the present study is to analyze the occipital condyle morphometrically. Material and methods: 404 occipital condyles of 202 dry skulls were used for this study. Twenty-seven parameters were measured, including length, width and height of occipital condyle, the distances between the occipital condyle and hypoglossal canal, as well as some important condyle-related angles. Results: The length, width and the height of the occipital condyle were found to be 23.4, 10.6, and 9.2 mm, respectively. The anterior and posterior intercondylar distances are 21.0 and 41.6 mm, respectively. Sagittal intercondylar angle was 59.3◦ . The intracranial orifice of the hypoglossal canal was found in the junction of the second and third quarter on the condyle in more than 55% of specimens. The shape of occipital condyles was classified into eight types as followings—type 1: oval-like condyle; type 2: kidney-like condyle; type 3: S-like condyle; type 4: eight-like condyle; type 5: triangle condyle; type 6: ring-like condyle; type 7: two-portioned condyle and type 8: deformed condyle. The most common type was type 1 (50%), whereas the most unusual type was type 7 (0.8%). Conclusion: It is concluded that the occipital condyle may present various shapes, length, width, and orientation, requiring a careful radiological analysis before craniovertebral junction surgery. © 2004 Elsevier B.V. All rights reserved. Keywords: Occipital condyle; Hypoglossal canal; Surgical anatomy

1. Introduction The occipital condyle is an important part of the craniovertebral junction. It is the only articulation between the occiput and the atlas. It has a ball-pivot relation with lateral mass of C1. This unique anatomical feature results in a unique biomechanical characteristic. Its integrity is of vital importance for the stability of the craniovertebral junction [1]. During the last two decades, craniovertebral junction has been the focus of a variety of anatomical [1–13] and biomechanical studies. Most of these studies focus on morphomet-



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0303-8467/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.clineuro.2004.07.014

ric analysis of some parts of the occipital condyle, and some of them provided information based on the different surgical procedures. The space-occupying lesion ventral to the spinal canal at the level of the foramen magnum can be reached using a ventral or dorsal approach. The difficulties and high rate of morbidity associated with ventral approaches dictates to use a dorsal approach to the ventral processes of the foramen magnum. Such an approach needs a transcondylar approach. Partial resection of the occipital condyle, as made during transcondylar surgical approaches, has been an important step for access to the ventral and ventrolateral foramen magnum [1,12–15]. The interest for transcondylar approach requires information regarding the morphometric aspects of the occipital condyle and structures around it. Whether the shape, size, and angle of the occipital condyle affect our

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surgical technique, is the main question to be answered in preoperative decision-making process. The aim of this study was to find out such morphometric data regarding the occipital condyle and classify it according to its shape and size. 2. Materials and methods The measurements were performed on 404 occipital condyles of 202 adult human dry skulls of unknown age and sex obtained from Turkish population. Twenty-one parameters, including distances and angles related to the occipital condyles and the structures around them were measured. The measured parameters included length, width and height of occipital condyle, horizontal and sagittal condylar angles, as well as hypoglossal canal-related morphometry (Table 1; Figs. 1 and 2). The distances were measured using a Vernier Calliper accurate to 0.1 mm. In order not to cause interobserver and intraobserver errors, the measurement of each particular parameter was performed by a different researcher and using the predetermined methodology. 2.1. Centre and axes of the occipital condyle The largest AP axis of the occipital condyle was drawn and the midpoint of the axis was detected. The transaction of the midpoint of this line and midpoint of the transverse line dividing condyle was accepted as the cen-

tre or midpoint of the occipital condyle. The height of the occipital condyle was measured on the centre of the condyle. It was realized that the occipital condyles had either mono-axial or bi-axial feature. Therefore, the line joining the centre of the occipital condyle and anterior tip of the occipital condyle was accepted as the occipital condyle axis for anterior angle measurements, i.e., sagittal intercondylar angle, and right and left sagittal condylar angle. In order to locate the hypoglossal canal in an objective and reproductive manner, the largest AP axis of the condyle was measured and divides into four equal portions (Fig. 3; Table 2). And the location of the intracranial orifice of hypoglossal canal was determined with regard to its position in any particular part. The occipital condyles were classified according to their shape and size. Because of destruction of the orifice of the hypoglossal canal, the analysis regarding the location of hypoglossal canal could be performed on 197 from 202 specimens. On the other hand, a possible relationship between the head circumference and the length of the occipital condyle was investigated. Head circumference was measured using a measure traversing from the nasion and the external occipital protuberance. Statistical analysis was used using Mann Whitney U-test. The Pearson correlation test also was performed to find out a possible correlation between the head circumference and length of occipital condyle.

Table 1 The measured parameters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

The length of right occipital condyle The length of left occipital condyle The width of right occipital condyle The width of left occipital condyle The height of right occipital condyle The height of left occipital condyle Anterior intercondylar distance (distance between anterior tips of right and left occipital condyles) Posterior intercondylar distance (distance between posterior tips of right and left occipital condyles) Distance between the anterior tip of right occipital condyle and basion Distance between the anterior tip of left occipital condyle and basion Distance between the anterior tip of right occipital condyle and opisthion Distance between the anterior tip of left occipital condyle and opisthion Distance between the posterior tip of right occipital condyle and basion Distance between the posterior tip of left occipital condyle and basion Distance between the posterior tip of right occipital condyle and opisthion Distance between the posterior tip of left occipital condyle and opisthion Distance between right hypoglossal canal and anterior tip of right occipital condyle Distance between left hypoglossal canal and anterior tip of left occipital condyle Location of intracranial orifice of right hypoglossal canal Location of intracranial orifice of left hypoglossal canal Location of extracranial orifice of right hypoglossal canal Location of extracranial orifice of left hypoglossal canal Sagittal intercondylar angle (the angle between the long axes of right and left occipital condyles) Right sagittal condylar angle (the angle between right occipital condyle axis and midline) Left sagittal condylar angle (the angle between left occipital condyle axis and midline) The distance between basion and opisthion The head circumference

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Fig. 1. The depiction of some important measured parameters: (1) length of occipital condyle, (2) width of occipital condyle, (3) anterior intercondylar distance, (4) posterior intercondylar distance, (5) distance between anterior tip of occipital condyle and basion, (6) distance between anterior tip of occipital condyle and opisthion, (7) distance between posterior tip of occipital condyle and basion, (8) distance between posterior tip of occipital condyle and opisthion.

Fig. 2. The depiction of measured angles: (1) Sagittal intercondylar angle and (2) anterior sagittal condylar angle.

Table 2 Anatomical categorization for hypoglossal canal Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 Location 7

Anterior one-fourth of occipital condyle The junction of first and second one-fourth of occipital condyle Second one-fourth of occipital condyle The junction of second and third one-fourth of occipital condyle Third one-fourth of occipital condyle The junction of third and fourth one-fourth of occipital condyle Fourth one-fourth of occipital condyle

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Fig. 3. The location of intracranial and extracranial orifices of hypoglossal canal.

3. Results The results obtained from the linear and angular measurements are presented in Table 3. The mean length, width and height of occipital condyle were found to be 23.6 ± 2.5 (right), 23.2 ± 2.4 (left), 10.6 ± 1.4 (right), 10.6 ± 1.4 (left), 9.2 ± 1.4 (right), 9.2 ±1.3 mm (left), respectively. The mean anterior intercondylar distance and posterior intercondylar distance were measured as 21.0 ± 2.8 and 41.6 ± 2.9 mm, respectively. The distance between the anterior tip of occipital condyle and basion was found to be 10.5 ± 1.5 and 11.1 ± 1.5 mm in the right and left, respectively. The distance between the anterior tip of occipital condyle and opisthion was found to be 38.9 ± 2.9 and 39.1 ± 3.0 mm in the right and left, respectively. The distance between the posterior tip of occipital condyle and basion was found to be 27.5 ± 2.0 and 28.1 ± 2.0 mm in the right and left, respectively. The distance between the posterior tip of occipital condyle and opisthion was found to be 26.7 ± 2.4 and 26.2 ± 2.2 mm in the right and left, respectively. The distance between hypoglossal canal and anterior tip of ipsilateral occipital condyle was found to be 10.6 ± 1.9 and 9.6 ± 2.0 mm in right and left, respectively. The sagittal intercondylar angle was found to be 59.3 ± 13.6◦ . The sagittal condylar angle was found to be 30.0 ± 7.5◦ and 29.2 ± 7.9◦ in right and left, respectively. There were significant differences between the results of right and left sides, in OCAT-B, OCPT-B and HGC-OCAT (P < 0.05), but there were not significant differences between the results of right and left sides, in other parameters (Table 3). The distance between the basion and opisthion was found to be 34.7 ± 2.3 mm. The head circumference was found to be

490.0 ± 1.5 mm. The intracranial orifice of the hypoglossal canal was found to be in the location 4 in 56.8 and 55.8% of specimens in the right and left sides, respectively (Table 4). The intracranial orifice of the hypoglossal canal was not observed in location 1 in any specimen. Extracranial orifice in 77.1 and 50.7% of condyles was found in location 1 in right and left sides, respectively (Table 4). The shape of occipital condyles was classified into eight types as follows—type 1: oval-like condyle, type 2: kidneylike condyle, type 3: S-like condyle, type 4: eight-like condyle, type 5: triangle condyle, type 6: ring-like condyle, type 7: two-portioned condyle and type 8: deformed condyle. The most common type was type 1 (50.0%), whereas the most unusual type was type 7 (0.8%). Other types were seen in the following frequency—type 2: 3.5%, type 3: 23.2%, type 4: 4.2%, type 5: 9.0%, type 6: 4.0% and type 8: 5.5% (Fig. 4; Table 5). When right and left occipital condyles of the same skull compared a symmetrical shape was found in 103 skulls (51.0%) and an asymmetrical shape was found in 99 skulls (49.0%). Occipital condyle was classified according to its length. The condyle of 23 ± 3 mm (i.e., mean length ± standard deviation) (20–26 mm) was called as a type 2 (moderate), the condyle shorter than 20 mm was called as type 1 (short) and condyle longer than 26 mm was called as a type 3 (long) occipital condyle. Occipital condyle was found to be short in 35 condyles (8.6%), moderate in 312 (77.2%) and long 57 condyles (14.1%) (Fig. 5). There was a weak correlation between the length of occipital condyle and AP diameters of foramen magnum in both right (r: 0.399, P: 0.00) and left sides (r: 0.367, P: 0.00).

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Table 3 The results of measured linear and angular parameters Parameter

Mean (mm)

Length of occipital condyle (R) Length of occipital condyle (L) Length of occipital condyle (total) Width of occipital condyle (R) Width of occipital condyle (L) Width of occipital condyle (total) Height of occipital condyle (R) Height of occipital condyle (L) Height of occipital condyle (total) Anterior intercondylar distance Posterior intercondylar distance OCAT-B (R) OCAT-B (L) OCAT-B (total) OCAT-O (R) OCAT-O (L) OCAT-O (total) OCPT-B (R) OCPT-B (L) OCPT-B (total) OCPT-O (R) OCPT-O (L) OCPT-O (total) HGC-OCAT (R) HGC-OCAT (L) HGC-OCAT (total) BOD Head circumference

23.6 23.2 23.4 10.6 10.6 10.6 9.2 9.2 9.2 21.0 41.6 10.5 11.1 10.8 38.9 39.1 39.0 27.5 28.1 27.8 26.7 26.2 26.4 10.6 9.6 10.1 34.7 490.0

The sagittal intercondylar angle (◦ ) The sagittal condylar angle (R) (◦ ) The sagittal condylar angle (L) (◦ )

59.3 30.0 29.2

S.D.

Minimum

Maximum

2.5 2.4 2.5 1.4 1.4 1.4 1.4 1.3 1.4 2.8 2.9 1.5 1.5 1.5 2.9 3.0 2.9 2.0 2.0 2.9 2.4 2.2 2.3 1.9 2.0 2.0 2.3 1.5

16.7 16.2 16.2 6.5 7.0 6.5 5.8 6.5 5.8 13.8 35.1 6.4 7.1 6.4 26.5 27.2 26.5 21.8 22.0 21.8 21.2 18.9 18.9 5.4 4.2 4.2 29.5 450.0

30.6 30.6 30.6 15.8 15.7 15.8 18.2 18.1 18.2 32.5 48.3 15.8 18.0 18.0 47.1 47.1 47.1 32.6 34.2 34.2 34.5 34.2 34.5 15.8 14.9 15.8 43.5 540.0

13.6 7.5 7.9

22.0 10.0 11.0

103.0 54.0 54.0

P 0.710

0.967

0.574

0.000

0.333

0.007

0.035

0.000

0.252

S.D.: standard deviation; OCAT: occipital condyle anterior tip; OCPT: occipital condyle posterior tip; B: basion; O: opisthion; HGC: hypoglossal canal; BOD: basion–opisthion distance; R: right; L: left.

The mean head circumference was found to be 485.3, 486.2 and 500.9 mm, in type 1, type 2, and type 3 occipital condyles, respectively. There was a weak correlation between the head circumference and the length of right (r: 0.145, P: 0.072) and left (r: 0.10, P: 0.214) occipital condyle. 4. Discussion Craniovertebral junction lesions are currently approached by lateral approaches. Many varieties of lateral approaches to this region have been reported, including transfacetal apTable 4 The location of intracranial and extracranial orifices of hypoglossal canal

Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 Location 7

Intracranial orifice

Extracranial orifice

Right

Left

Right

Left

– 8 (4.1%) 24 (12.8%) 112 (56.8%) 51 (25.8%) 2 (1.1%) –

– 18 (9.1%) 38 (19.2%) 110 (55.8%) 31(15.7%) – –

152 (77.1%) 40 (20.3%) 5 (2.5%) – – – –

100 (50.7%) 79 (40.1%) 17 (8.5%) 1 (0.5%) – – –

proach, the partial transcondylar approach, the complete transcondylar approach, the extreme-lateral transjugular approach and the transtubercular approach with or without division of the sigmoid sinus [1,11–15]. Most of these approaches necessitate resection of the occipital condyle partially or completely, and morphometrical analysis of the occipital condyle. The occipital condyles form the lateral limits of the craniovertebral junction. The configuration and orientation of the occipital condyle, as well as the location of the intracranial and extracranial orifices of the hypoglossal canal may affect the lateral approaches to the craniovertebral junction. Table 5 The rates of occipital condyles of different types Type

Right

Left

Total

1 2 3 4 5 6 7 8

96 (23.8%) 8 (2.0%) 47 (11.6%) 12 (3.0%) 22 (5.5%) 6 (1.5%) 1 (0.3%) 10 (2.5%)

106 (26.2%) 6 (1.5%) 47 (11.6%) 5 (1.2%) 14 (3.5%) 10 (2.5%) 2 (0.5%) 12 (3.0%)

202 (50.0%) 14 (3.5%) 94 (23.2%) 17 (4.2%) 36 (9.0%) 16 (4.0%) 3 (0.8%) 22 (5.5%)

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Fig. 4. Types of occipital condyles—type 1: oval-like condyle; type 2: kidney-like condyle; type 3: S-like condyle; type 4: eight-like condyle; type 5: triangle condyle; type 6: ring-like condyle; type 7: two-portioned condyle and type 8: deformed condyle.

The results of this study are in line with the results of other studies focusing on craniovertebral junction anatomy and particularly on occipital condyle anatomy [4,7–9]. These results confirm the variability in almost all measured occipital condyle parameters, including length, width, height and a variety of angles. This variability seems to be due to the use of occipital condyles of each age and gender as material.

The occipital condyle is an oval mass articulating with C1 lateral mass. Its length ranges between 16.7 and 30.6 mm (mean 23.6 mm). This measured length is comparable to measured occipital condyle length reported by Guidotti (23.7 mm) [7], Lang and Hornung (22.9 mm) [9], Oliver (23.7 mm) [8] and Bozbu˘ga et al. (23.1 mm) [4]. Occipital condyle width ranges between 6.5 to 15.8 mm (mean

Fig. 5. A long (a) and short (b) occipital condyle.

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Table 6 Comparison of our results and results reported in literature regarding occipital condyle and paracondylar structures

OC length OC width OC height OCPT-Op OCMB-Op PICD SCA SCA-R SCA-L

Naderi

Dowd

Wen

de Oliviera

Bozbu˘ga

Oliver

Guidotti

Lang

23.6 10.5 9.2 26.0 – 41.6 59.2 30.2◦ 29.1◦

30.0

21.0



23.1 11.3 – 24.3 – 30.2 57.8 28.2 29.7

23.7 11.5 8.8

23.7

22.9

40.0 29.4

41.4

OC: occipital condyle, OCPT: occipital condyle posterior tip, Op: opisthion, OCMB: occipital condyle medial border, PICD: posterior intercondylar distance, SCA: sagittal condylar angle, R: right, L: left.

10.5 mm). The height of occipital condyle ranges between 5.8 and 18.2 mm (mean 9.2 mm). This is smaller than the results reported by Bozbu˘ga and Oliver [4,8] (Table 6). Occipital condyles converge ventrally. The anterior and posterior intercondylar distances are 21.0 and 41.6 mm, respectively. This leads occipital condyle to have different anterior and posterior angles. Sagittal intercondylar angle ranges between 22.0 and 103.0◦ (mean 59.3◦ ). This wide range reflects the asymmetry in the orientation, length and shape of occipital condyles and may affect the lateral approach. According to recent studies [2] condylectomy provides the wider angle of exposure. The presence of already wider sagittal condylar angle seems to be more advantageous for reaching the ventral foramen magnum. The distances between anterior tip and posterior tip of occipital condyle and basion were measured as 10.8 mm (right: 10.5 mm, left: 11.1 mm) and 28 mm (right: 27.5 mm, left: 28.1 mm), respectively. The distances between anterior tip and posterior tip of the occipital condyle and opisthion were measured as 39.0 mm (right: 38.9 mm, left: 39.1 mm) and 26.4 mm (right: 26.7mm, left: 26.2mm), respectively. The distance between the posterior tip of occipital condyle and opisthion is also an important anatomical factor. The larger the distance, the free the corridor for posterolateral approaches. Intracranial orifice of hypoglossal canal is located medial to occipital condyle and extracranial orifice is located lateral to occipital condyle. The distance between the hypoglossal canal and anterior tip of occipital condyle is about 10.1 mm (right: 10.6 mm, left: 9.6 mm). The detection of the location of the intracranial and extracranial orifices of the hypoglossal canal is an important step of lateral approaches. Wen reported that the intracranial orifice of the hypoglossal canal is located in the middle one-third of occipital condyle [12]. The canal is directed ventrally and laterally at a 45◦ angle with the sagittal plane and the extracranial orifice of the hypoglossal canal is located above the junction of the anterior and middle one-third of hypoglossal canal. This study revealed that the location of extracranial and intracranial orifices of the hypoglossal canal might vary (Figs. 6 and 7). The intracranial orifice was found in location 4 in more than 55% of specimens, i.e., in the junction of second and

third quarter of the hypoglossal canal. The extracranial orifice of hypoglossal canal was found in more than 90% of specimens in locations 1 and 2, i.e., in the first one-fourth or in the junction of the first and second quarter of the hypoglossal canal. The location of intracranial and extracranial orifices of the hypoglossal canal is important during condylectomy. Too dorsally located intracranial orifice of the hypoglossal canal may complicate and limit the condylectomy procedure. To avoid hypoglossal nerve injury the location of the hypoglossal canal should be determined in preoperative imaging stage. Furthermore, the direction and the location of the extracranial orifice of the hypoglossal canal should be also detected. Some authors addressed the shape of occipital condyle. Guidotti classified the occipital condyle as (1) flat, (2) partitioned without interruption of the articular surface and (3) partitioned with a clear angle but without separation of the surfaces or doubling of the condyles [7]. Guidotti reported

Fig. 6. Variations in the extracranial orifice of hypoglossal canal: (a) location 1, (b) location 2, (c) location 3 and (d) location 4.

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Fig. 7. Variations in the intracranial orifice of hypoglossal canal: (a) location 2, (b) location 3, (c) location 4, (d) location 5 and (e) location 6.

that the flat condyle was seen more commonly in the left side [7]. Oliver classified the occipital condyle as (1) normal constricted and (2) subdivided [8]. This classification is not useful in the preoperative decision-making process. This is so, because they did not address the size and angles of the occipital condyle, which is of importance suring transcondylar approaches. Bozbu˘ga classified occipital condyles as two semicircles type, oval type, rhombus type, bean-shaped, prismatic types, flattened types, convex types, flattened convex types, flat types, short and broad types, flat and long types, small and convex types [4]. The classification offered by Bozbu˘ga, is not clinically relevant. It is so complex. In summary, although the studies reported by Oliver [8], Bozbu˘ga [4] and Guidotti [7] addressed the types of occipital condyles; these studies did not mention the rate of each particular type. On the other hand, first two classifications are inadequate and too simple and the third study is too complex and not applicable to clinical practice. Our study is the first study, which made a systematic and detailed classification of human occipital condyle, based on its shape, and revealed the percentage of each particular type. The current study found out that the occipital condyle is most commonly (more than 50%) oval-shaped. However, occipital condyle may be in different types, including kidney-like, S-like, eight-like, triangle-like, ring-like, two-portioned, and deformed. The shape of occipital condyle may affect the amount of condylectomy. Among the different types of occipital condyle, the triangle type, the deformed type and kidney-like type occipital condyle may require a more extensive condylectomy to reach to the ventral lesions. Guidotti addressed the relationship between the occipital condyle and the load applied. Guidotti compared the cranial

volume and the surface of the occipital condyle [7]. However, he found no correlation between the occipital condyle surface and the volume of the skull. On the basis of the lack of correlation, Guidotti concluded that there was no relationship between the surface area of the occipital condyle and the load applied to it [7]. The current study found a weak correlation between the length of occipital condyle and head circumference. On the other hand, there is no relation between the circumference of the head and length of the occipital condyle. The lack of correlation between head circumference and occipital condyle supports the results reported by Guidotti [7]. We also found no correlation between occipital condyle length and basion–opisthion distance. The lack of relationship between length of occipital condyle and head circumference, also the lack of correlation between anteroposterior diameter of foramen magnum and head circumference suggests that the occipital condyle and foramen magnum may be in different sizes. A surgeon cannot decide on the easiness of condylectomy based on the head size. A condylectomy procedure requires a radiological investigation. It seems that length of the occipital condyle is not dependent on the diameter of neither foramen magnum nor head circumference. Therefore, we classified occipital condyles according to their lengths. The length of occipital condyle is an important surgical issue. The anatomical and biomechanical results of partial condylectomy in a short type are different from the results obtained in a long type occipital condyle (Fig. 5). The same amount of partial condylectomy may cause greater occipitocervical instability in short occipital condyle, whereas a long condyle may require a more extensive resection for optimum visualization. Similar surgical considerations may be correct for the occipital condyle

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Fig. 8. A wide (a) and narrow (b) occipital condyle.

width. Surgery in a wider condyle may be more demanding (Fig. 8). In summary, the occipital condyle is an important part of the craniovertebral junction, connecting the cranium to the upper cervical spine. Several anatomical parameters such as shape, size, orientation of occipital condyle and the location of hypoglossal canal should be taken into consideration during posterior and lateral approaches to the craniovertebral junction. The determined variabilities reported in this study require a careful radiological analysis of occipital condyle before craniovertebral junction surgery. The major limitation of this study is the lack of knowledge regarding the age and gender of the subjects whose condyles were studied.

Acknowledgements ˙ The authors thank Dr. U˘gur T¨ure, Dr. Ibrahim Ziyal for reviewing the manuscript, and also thank Ms. Ena Margaret Larkın for editorial assistance of the manuscript.

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