## Correlation between the cross sectional area of skull base with existing formulae to determine skull volume

#### Author(s): Manjunath K.Y.

#### Vol. 54, No. 2 (2005-07 - 2005-12)

**Manjunath K.Y.**

St.John's Medical College, Bangalore.

**Abstract:** Estimation of cranial volume is an important investigation used for reconstruction of brain or skull in
forensic or anthropological studies. In the present study an attempt was made to find out if any correlation existed
between the endocranial volume and the cross sectional surface area of the skull base. 54 cadaver heads (37 males and
17 females) were evaluated. Cranial volume was calculated by applying formulae using linear dimensions. The heads
were then sectioned horizontally along a plane passing through the frontal eminences and the inion and the linear
dimension of the skull base were noted and the cross sectional area was computed. On applying statistical evaluation
using correlation coefficient and regression equation it was seen that the area of skull base show significant correlation
with calculated endocranial volume in male cadavers. However, in female cadaver head there was only a weak correlation
of area of skull base and endocranial volume.

**Key words:** Cranial volume, cross sectional area, skull, cadavers head.

### Introduction:

Estimation of cranial volume is important is anthropological forensic and medical studies. Various investigations have described various methods to calculate cranial volumes by making use of part or the entire skull in different species.

Stewart (1934) used the volume of mustard seeds that could be packed in dried skulls as cranial volume. Radinsky (1967), Routal et al (1984) and Rao GS (1973) used the surface area of foramen magnum as a parameter to calculate cranial volume in various species. Mackinnon et al (1955) used radiological cranial length as a parameter for clculation of cranial volume while Venkatesan and Cooper (1975) calculated cranial volume by standard calvarial displacement volume method.

The present study was then performed to establish a correlation between the cross sectional area of skull base and cranial volume if any.

### Materials and Methods:

Fifty – four dissecting room cadaver heads were studied of which 37 cadavers were male while 17 were females. The following measurements were taken using a steel measuring tape, spreading caliper and a Todd's head spanner to the nearest millimeter.

- Occiptio frontal circumference
- Maximum head length (L) – Measured from glabella to inion with calliper.
- Maximum head breadth (B) – Measured between the two parietal eminences with the calliper.
- Head height (H) – Measured from the flow of external acoustic meatus to hightest point of vertex with Todd's head spanner. Each measurement was recorded three times and the mean was considered for computation.

The cranial volume was computed using following two formulae

- Williams, Warwick, Bannister and Dyson, (1980)

Males: 0.000337 (L – 11) × (H –11) + 406.01

Females: 0.0004 (L –11) × (B –11) × (H – 11) + 206.60 - Spheroid formula (Dekaban et al, 1964).

For this the cadaveric heads were first horizontally sectioned along a plane passing through the frontal eminences and the inion. The calvaria and the brain were then removed. The soft tissue and skull thickness was measured using the sliding caliper at different points namely anterior, posterior lateral on each side, region of parietal eminences and a mean of thickness was taken in each cadaver head (t).

The cranial volume was computed as 0.523 (L-2t) × (B –2t) × (h-t)

Finally, the following measurements of base of skull were taken using the sliding caliper.

- Maximum anteroposterior length ; h
- Maximum width ; w

Surface area of base of skull was computed as follows:

¼ × Ö × w × h

the correlation coefficient between the surface area of base of skull and the cranial volume, computed by the two methods, was calculated and a regression equation was derived in males and females.

### Results:

Table 1 and table 2 depict the surface area of skull base of the cadaver heads and the cranial volume in male and females respectively. The mean cranial volumes calculated in male cadaver heads was 1211.54 ± 100 (range: 1017.0 -1425.45) and 1202.406 ±150.68 (range: 902.32-1517.17) by the two formulae. The mean surface area of male cadavers was 150.894 ± 15.205. A regression equation could be derived in each formula given below as :

- 506.363 + 4.673 A
- 116.594 + 7.196 A

A : surface area of skull base

In female cadaver heads the mean cranial volume calculated by the two methods was 1117.82 ± 99.09 (range 975.14-1298.64) and 1081.00 ± 111.6 (range: 1008.82-1303.04). The mean surface area of skull base calculated was 140.612 ± 10.77. Regression equation obtained in the two cases was:

- 731.05 + 2.764 A
- 611.766 + 3.337 A

A: surface area of skull base

### Discussion:

According to Hooton (1926), the cranial capacity constitutes one of the most important characters for determining the racial differences since the racial characters are best defined in the skull. Lee and Pearson (1901) used external measurements of the skulls to calculate the cranial capacity which had an added advantage as it can be sued in case of living persons, as well as in the dead where skulls have been slightly broken or damaged. Some attempt appears to have been made to estimate the cranial capacity of Indian cadavers by Venkatesan and Cooper (1975). These authors used the calvarial displacement volume as a guide to cranial capacity; heads of fresh cadavers were immersed up to giabella -inion level in a specially constructed apparatus and the volume of water displaced was noted. The procedure was repeated after removal of the scalp and the scalp volume was estimated. Further the calvarium and brain volume were estimated by the same method after removal. The data was correlated with Lee-Pearson and the spheroidal formulae. No details of this study could be traced in the form of published report for comparison.

A positive significant correlation between endocrinal volume and surface area of the foramen magnum has been demonstrated by Routal et al. (1984) in their study of Gujarati crania.

Post-mortem estimation of cranial capacity has acquired some significance because of its potential applications in estimating brain atrophy. Variations of brain weights and volumes often indicate pathological states. However, these parameters are more meaningful when related to intra cranial volume. The most useful derived parameter is the difference between intra cranial volume and brain volume expressed as a percentage (potential intra cranial space).

In the present study a significant correlation of surface area of base of skull with cranial volume was observe in the male cadaver heads with each formula (p =0.001). The regression equation was also computed. In the case of female cadaver heads the correlation between surface area of skull base and the estimated cranial volume was less significant (p<0.5) by either formula. However all regression equation could be obtained in them also.

In the present study a significant correlation of surface area of base of skull with cranial volume was observe in the male cadaver heads with each formula (p =0.001). The regression equation was also computed. In the case of female cadaver heads the correlation between surface area of skull base and the estimated cranial volume was less significant (p<0.5) by either formula. However all regression equation could be obtained in them also.

#### Table 1 unavailable

#### Table-2:Cranial Volume Of Male Cadavers

S.No. | Surface area of cross section of the skull base(Sq.cms) | CRANIAL VOLUME(Cm3 )* | |
---|---|---|---|

Lee-Pearsons'Formula (See text for the details) | Spheroid formula (See text for the details) | ||

1 | 139.89 | 1142.00 | 1114.32 |

2 | 138.95 | 1299.00 | 1303.04 |

3 | 131.88 | 0975.14 | 0908.82 |

4 | 137.38 | 1116.00 | 1081.51 |

5 | 141.3 | 1169.00 | 1140.39 |

6 | 140.8 | 1128.14 | 1097.24 |

7 | 141.3 | 1165.41 | 1141.59 |

8 | 125.73 | 1037.00 | 0982.4 |

9 | 135.18 | 1040.00 | 0986.91 |

10 | 153.08 | 1095.00 | 1051.09 |

11 | 138.16 | 1012.00 | 0952.74 |

12 | 145.07 | 1189.00 | 1166.69 |

13 | 143.54 | 1086.40 | 0983.66 |

14 | 151.54 | 1204.11 | 1187.7 |

15 | 163.28 | 1055.00 | 1009.34 |

16 | 147.96 | 1270.24 | 1270.43 |

17 | 115.4 | 1052.00 | 0999.84 |

Mean±SD: | 140.612 ± 10.77 | 1117.82 ± 99.09 | 1081.00± 111 |

Corr.coef (r)/p: | 0.333/ 0.5 | 0.322/ < 0.5 | |

Regression Equation : | 731.105 + 2.764 A | 611.766 +3. 337 A |

### Conclusion:

In the present study there was a significant correlation seen between the random cross sectional area of skull base and the estimated cranial volume in case of cadaver heads. It was better in male than in female cadaver heads.

### Acknowledgements:

The author is grateful to the following individuals for their help in preparing this manuscript : Dr. A.S. Dekaban of National Institute of Health, Bethesda, Maryland, USA for a copy of his paper on the cranial volume of Caucasians. To Rev. Fr. Harry Byovet and Rev. Fr. Salafia for their translation of some articles in German and Italian respectively. Mr. K.N. Kittur, librarian, St. John's Medical College, Bangalore for procuring some reprints on the subject.

- Dekaban, A. and Lieberman, J.E. : Calculation of cranial capacity by linear dimensions. Anatomical Record. 1964; 115: 215-219.
- Dekaban, A: Tables of cranial and orbital measurements, cranial volume and derived indexed in males and females from 7 days to 20 years of age. Annais of Neurology. 1977; 2(6): 485- 491.
- Lee, A. and Pearson, K.: Data for the problem of evolution in man – a first study of the correlation of the human skull. Philosophical Transactions of Royal Society, London. 1901; 196a : 225-264.
- Mackinnon, I.L.: The relation of the capacity of the human skull to its Roentgenological length American Journal of Roentgenology, Radium therapy and Nuclear Medicine. 1955; 14:06:1026- 1029.
- Pearson, K: Correlation of the intellectual ability with size and shape of head. Proceedings of the Royal society. 1902; 69:333.
- Radinsky, L: Relative brain size: A new measure. Sciences. 1967; 155: 836-838.
- Rao, G.S.: Area of formen magnum as an index to endocranial volume. Journal of Anatomical Society of India. 1973; 22:13.
- Routal, R.V., Pal, G.P., and Bhagawat, S.S. : Relationship between endocranial volume and the area of the foramen magnum. Journal of Anatomical Society of India. 1984;33(3) : 145-149.
- Venkatesan, B. and Cooper, M.M: Calvarial displacement volume as a guide to cranial capacity. (abstract)23rd annual conference of Anatomical Society of India, Institute of medical Sciences, Banaras Hindu University, Banaras. Journal of Anatomical Society of India . 1975;l 24(1) : 40.
- Williams, P.L. Warwick, R. Dyson. M. Bannister, L.H.: Gray's Anatomy, 36th edition. London: Churchill Livingston 1980; 349.