Anthropological Science
Online ISSN : 1348-8570
Print ISSN : 0918-7960
ISSN-L : 0918-7960
Original Articles
Cranial vault thickness measurement and distribution: a study with a magnetic calliper
Author information

2019 Volume 127 Issue 1 Pages 47-54


Cranial vault thickness is a widely studied variable in physical anthropology. However, direct physical measurements are difficult to assess in complete skulls, where the endocranial surface is not easily accessible for standard callipers. Computed tomography represents the best alternative, but is expensive and not always available for many field or museum samples. In this study we present a method for the measurement of cranial vault thickness based on magnetism. We measured bone thickness at 71 points of the vault in 30 human skulls with the use of a portable magnetic calliper, which offers a simple, direct, non-invasive, and cost-effective methodology. Magnetic measures were compared with physical measures sampled with a traditional spreading calliper, and error analysis was assessed. Thickness distribution was evaluated and represented in bidimensional maps after spatial interpolation. The two types of callipers provide the same results, suggesting that the magnetic calliper can be used in those situations in which a traditional calliper is not applicable. In accordance with previously published data, the most variable and thickest bones in our sample were the frontal and the occipital bones, and cranial vault thickness distribution follows a pattern of increasing thickness from lateral regions of the vault to the sagittal plane. The magnetic calliper is a reliable and effective tool to measure cranial thickness in those cases in which the endocranial surface is not easily accessible, and where expensive technology cannot be employed for economic or practical reasons.


The skull is the most studied anatomical element of the skeleton because of its complexity and relationship with the brain, as well as with the masticatory and sensory organs (Scheuer and Black, 2000; White et al., 2011). In anthropology and osteoarchaeology, cranial vault thickness (CVT) is a remarkable metric variable, which refers to the distance between the endocranial and ectocranial surfaces of the vault bones (Anzelmo et al., 2015; Eisová et al., 2016), and has been studied by many authors in different species and human groups, and in several biological contexts (e.g. Nawrocki, 1991; Gauld, 1996; Balzeau, 2013; Marsh, 2013). The CVT is thought to be determined by genetic factors and physiological responses to the environment, including hormones and physical activity (Lieberman, 1996), diet, and climate (Endo, 1966; Baab et al., 2010; Menegaz et al., 2010; Gupta, 2016). It has also been related to other biological variables such as sex (Roche, 1953; Ross et al., 1998; Hatipoglu et al., 2008) and age (Roche, 1953; Young, 1957; Koenig et al., 1995; Anzelmo et al., 2015), although ontogenetic studies are still scarce. Finally, other authors have studied CVT in a clinical context in relation to surgical interventions (i.e. cranial bone harvesting) (Koenig et al., 1995; Elahi et al., 1997) and pathological conditions such as craniosynostosis and hydrocephalus (Anderson et al., 1970; Branson and Shroff, 2011).

Traditionally, anthropologists have used spreading callipers or radiographs to measure cranial thickness at specific anatomical landmarks (Todd, 1924; Roche, 1953; Ivanhoe, 1979; Nawrocki, 1991; Koenig et al., 1995; Lynnerup, 2001). Traditional callipers can be easily employed to measure isolated bones and fragmented skulls, but they cannot be used with complete skulls, where the foramen magnum represents the only access to the endocranial cavity. Some authors partially circumvented this problem by modifying callipers or osteometric boards (Munizaga, 1962; Brown, 1987). However, as technologies developed, computed tomography (CT) emerged, and nowadays is one of the most commonly used methodologies when investigating skull thickness. However, CT has a number of disadvantages, namely the high costs and the logistic difficulties, due to the limited possibility of moving samples and specimens to hospitals or radiographic centres. Other techniques use ultrasound, and rely on equipment that is portable and relatively inexpensive (Elahi et al., 1997; Hakim et al., 1997). However, ultrasound devices require much work for sample preparation, and require immersion of the bone in water. Moreover, it has been much more often utilized to measure bone density rather than thickness (Wünsche et al., 2000; Gluër et al., 2004). Here we propose an alternative method based on magnetism that is simpler and quicker to apply than the aforementioned techniques. This methodology is derived from a magnetized instrument called the Hacklinger calliper, which was conceived with the aim of measuring wood thickness in the resonance box of string instruments such as violins, as this is a factor that strongly influences sound quality (Bieber, 2008). Apart from the standard original version, this device can be easily handmade (Bieber, 2008), and digital versions are also available (Figure 1a). The main advantages of this instrument are its low cost compared with other techniques such as CT, its easy transport and use in situ, and the provision of direct and instantaneous measurement in a non-invasive way.

Figure 1

Magnetic thickness calliper: (a) MAG-ic probe V5.0 (scale: 3 cm); (b) MAG-ic probe V5.0 calliper in use (scale: 3 cm); (c) detailed picture of MAG-ic probe V5.0 (scale: 3 cm).

Although this methodology had previously only been applied in a musical context by luthiers when making instruments, it can be easily employed in craniometrics, representing a practical, specific solution to the methodological problem of CVT measurement of complete skulls. Here, we present a control study of the application of this magnetic calliper to bone thickness, and visualization maps of the distribution of cranial thickness in a modern human population.

Materials and Methods

A MAG-ic Probe V5.0 (MAG-ic Probe, Dallas) digital magnetic calliper was used in this study. Its functioning is based on the force needed to separate two magnets, which is inversely proportional to the distance between them. The equipment consists of a small and portable device that contains a measurement display screen and a sensor probe topped with a strong neodymium magnet (see Figure 1a). This magnet interacts with the accessory mobile magnet. In this case we made use of the spherical neodymium magnet accessory (measuring range/precision: 0–15.24 mm, instrumental error: 0.1 mm) instead of the smaller cylindrical magnet because of its higher precision and easier mobility across the endocranial surface (see Figure 1b and c). This magnet is positioned on the endocranial surface, and the other on the corresponding ectocranial side, measuring the distance (thickness) between them. The instrument can be connected to a computer with a dedicated software, specifically MAG-ic Probe PRO, which allows the compilation of data directly on an image that can later be used to create contour maps. Here we used the free version of the software, MAG-ic Probe Lite, to record measurements on a sampling points diagram (see Figure 2).

Figure 2

Bidimensional skull diagram in superior view. Sampling points are represented in red and indicated by a number in purple which denotes the order of their measurement as shown in Table 1. Craniometric reference points are represented in red and surrounded by a red circle. Cranial sutures are represented by discontinuous blue lines and green lines reflect the lines traced to get sampling points, apart from those of the sutures. Color figure can be viewed in electronic form.

The study sample consisted of 30 normal adult human skulls, with no taphonomical or pathological alterations. These skeletal remains were selected from an osteological collection referred to as a medieval ossuary excavated in the Santa María de la Soledad church in Almansa (Castilla-La Mancha, Spain). This site was utilized as a cemetery from the 12th to 18th centuries and has been used for several investigations, the results of which have been published elsewhere (Cambra-Moo et al., 2012, 2014; García Gil et al., 2016). Sex and age were not considered in this methodological survey.

Cranial vault thickness was measured at a total of 71 sampling points over the frontal, parietal, temporal, and occipital bones, and the cranial sutures, forming a deformable grid (Figure 2). These points were determined by taking traditional osteometric landmarks (i.e. nasion, bregma, pterion, lambda, asterion, inion, and ophistion) as reference, and their corresponding arcs: nasion–bregma, bregma–lambda, lambda–inion, lambda ophistion, bregma–left pterion, bregma–right pterion, lambda–left asterion, and lambda–right asterion (Buikstra and Ubelaker, 1994; White et al., 2011). In the case of the temporoparietal sutures, we chose to measure the pterion–asterion chords instead. All these cranial lengths were divided into halves, thirds, or quarters (depending on the anatomy and size of each bone), in order to define intermediate equally spaced landmarks able to represent the cranial contours (see Figure 2 and Table 1) (Moreira-Gonzalez et al., 2006).

Table 1 Sampling points
1. N Nasion
2. N-B1, 3. N-B2 Nasion–bregma arc sampling points
4. B Bregma
5. B-L1, 6. B-L2, 7. B-L3 Bregma–lambda arc sampling points
8. L Lambda
9. L-I Lambda–inion arc sampling point
10. L-OP Lambda–ophistion arc sampling point
11. I Inion
12. LPT Left pterion
13. PT-ASl1, 14. PT-ASl2, 15. PT-ASl3 Pterion–asterion left chord sampling points
16. LAS Left asterion
17. B-PTl1, 18. B-PTl2, 19. B-PTl3 Bregma–pterion left arc sampling points
20. F1, 21. F2, 22. F3, 23. F4, 24. F5, 25. F6 Left side frontal sampling points
26. LP1, 27. LP2, 28. LP3, 29. LP4, 30. LP5, 31. LP6, 32. LP7, 33. LP8, 34. LP9 Left parietal sampling points
35. L-ASl1, 36. L-ASl2, 37. L-ASl3 Lambda–asterion left arc sampling points
38. O1, 39. O2, 40. O3, 41. O4 Left side occipital sampling points
42. RPT Right pterion
43. PT-ASr1, 44. PT-ASr2, 45. PT-ASr3 Pterion–asterion right chord sampling points
46. RAS Right asterion
47. B-PTr1, 48. B-PTr2, 49. B-PTr3 Bregma–pterion right arc sampling points
50. F7, 51. F8, 52. F9, 53. F10, 54. F11, 55. F12 Right side frontal sampling points
56. RP1, 57. RP2, 58. RP3, 59. RP4, 60. RP5, 61. RP6, 62. RP7, 63. RP8, 64. RP9 Right parietal sampling points
65. L-ASr1, 66. L-ASr2, 67. L-ASr3 Lambda–asterion right arc sampling points
68. O5, 69. O6, 70. O7, 71. O8 Right side occipital sampling points

Each sampling point was measured three times and the mean value was used as the final figure. Statistics were computed with SPSS Statistics version 24.0 (IBM Corporation, Armonk). Error analysis was divided in two parts. On one hand, a cluster analysis based on Euclidean distances and paired average (UPGMA) was performed to evaluate the replicability of the method. For the UPGMA analysis, each thickness variable and individual were included and, additionally, four individuals were randomly selected to replicate their measurements. Among these, individuals AL-CR8, AL-CR10, and AL-14307 were measured twice, while the individual AL-CR14191 was measured twice a day for three days, i.e. a total of six measurements. UPGMA was computed with PAST 2.17c (Hammer et al., 2001). On the other hand, uncertainty was evaluated with a single thickness mean value for all the points and all the replicas in the UPGMA analysis and its standard deviation.

Ten fragmented adult skulls were selected from the same collection and five landmarks were chosen to compare the measurements taken with the magnetic calliper with measurements acquired with a traditional calliper: bregma, Pl3, Pl6, Pl9, and lambda. Bone thickness was measured twice on each point using the MAG-ic probe V5.0 and a standardized spreading calliper, respectively. Values were compared using an intraclass correlation test (two-way mixed, absolute agreement), a paired-samples t-test, and Wilcoxon’s test (P = 0.01). The intraclass correlation test was used in order to see the concordance between measurements of both methods, whereas the paired-samples t-test and the Wilcoxon test were used to check if measurements were equal or not. The values of the cranial vault thickness obtained by using the magnetic calliper were compared with those in previous studies focused on the normal and non-deformed/non-pathological cranium in order to show the normality of measurements.

CVT distribution maps for thickness mean and standard deviation were computed on the skull bidimensional diagram through Kriging interpolation (Olea, 1974). Maps were created with Surfer®13 (Golden Software LLC, Golden, CO).


Table 2 shows the comparison between traditional and magnetic callipers. The paired-samples t-test and the Wilcoxon test results show no significant differences between the magnetic and the standard calliper mean values, and the correlation between the two values is very high (ICC ≥ 0.97). UPGMA after repeated measures shows that replicated individuals cluster together, suggesting sufficient reliability on the replicability of the method (Figure 3). As for the uncertainty measure, we obtained a thickness mean value of 6.51 (SD = 0.85). Descriptive results of all variables are included in Table 3. Table 4 shows descriptive results per bone; variation is represented by the standard deviation (SD), median and P25 and P75 quartiles, and the coefficient of variation (SD/mean). The occipital bone has the highest mean thickness value, followed by the frontal, parietal, and temporal bones, respectively. The occipital and frontal bones also display a larger degree of variation, while the temporal bones are the least variable.

Table 2 Comparison of physical calliper and magnetic calliper measurements
Statistics Method Bregma LP3 LP6 LP9 Lambda
Mean Physical 7.0 6.5 7.7 7.6 7.2
Magnetic 7.0 6.5 7.6 7.5 7.3
Standard deviation Physical 1.2 0.9 1.2 1.2 1.9
Magnetic 1.1 0.9 1.2 1.1 1.7
Median Physical 7.3 6.5 7.5 7.5 7.3
Magnetic 7.2 6.3 7.5 7.5 7.4
Minimum Physical 4.5 5.5 6.0 5.5 4.5
Magnetic 4.6 5.2 5.5 5.8 4.6
Maximum Physical 8.5 8.0 10.0 9.5 10.2
Magnetic 8.2 8.0 9.8 9.6 10.2
Intraclass correlation test ICC = 0.98 ICC = 0.97 ICC = 0.99 ICC = 0.98 ICC = 0.99
95% CI: 95% CI: 95% CI: 95% CI: 95% CI:
0.926–0.995 0.885–0.993 0.951–0.997 0.925–0.995 0.960–0.997
F = 49.32 F = 31.87 F = 76.01 F = 48.38 F = 90.66
p = 0.0001 p = 0.0001 p = 0.0001 p = 0.0001 p = 0.0001
Student’s t-test t = –0.325 t = 0.020 t = 0.903 t = 0.313 t = −0.646
df = 9 df = 9 df = 9 df = 9 df = 9
p = 0.753 p = 0.984 p = 0.390 p = 0.761 p = 0.534
Wilcoxon test z = −0.306 z = −0.357 z = −0.918 z = −0.255 z = −0.770
p = 0.760 p = 0.721 p = 0.359 p = 0.799 p = 0.441
Figure 3

UPGMA cluster analysis. Resulting replicas are grouped in boxes.

Table 3 Descriptive results
N N-B1 N-B2 B B-L1 B-L2 B-L3 L L-I L-OP I LPT PT-ASl1 PT-ASl2 PT-ASl3 LAS B-PTl1 B-PTl2 B-PTl3 F1 F2 F3 F4 F5
N 30 30 30 30 30 30 30 30 30 30 30 29 30 30 30 30 30 30 30 30 30 29 30 30
Min. 8.5 5.4 3.3 5.2 4.6 4.1 4.0 4.5 4.9 3.9 6.7 2.5 1.3 1.1 4.0 2.9 3.3 4.5 5.3 4.8 2.2 3.3 3.2 3.9
Max. 15.2 12.5 10.7 9.6 9.3 11.1 10.1 10.4 12.0 15.2 15.2 5.9 6.9 4.7 8.0 8.1 8.7 11.3 9.8 15.2 8.4 7.8 11.7 11.0
Mean 13.5 8.3 7.2 7.1 6.7 7.4 6.8 6.7 8.1 8.4 12.0 4.0 4.2 2.4 6.1 5.9 5.5 6.8 6.9 9.5 4.8 5.7 6.8 6.2
SD 2.0 1.7 1.5 1.1 1.3 1.6 1.6 1.5 1.9 2.8 2.7 0.8 1.4 0.8 1.0 1.2 1.4 1.6 1.0 2.5 1.4 1.4 2.1 1.7
F6 LP1 LP2 LP3 LP4 LP5 LP6 LP7 LP8 LP9 L-ASl1 L-ASl2 L-ASl3 O1 O2 O3 O4 RPT PT-ASr1 PT-ASr2 PT-ASr3 RAS B-PTr1 B-PTr2
N 30 29 30 30 29 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
Min. 4.3 2.8 3.8 4.5 3.2 3.6 4.8 3.0 4.4 4.7 3.4 4.6 4.5 3.1 3.3 3.9 2.7 2.3 1.9 1.5 4.5 3.8 3.6 4.8
Max. 9.9 7.8 8.3 10.1 6.1 9.6 12.0 7.8 9.9 11.3 8.8 9.2 10.0 7.8 11.4 8.3 10.1 5.9 5.2 4.3 9.3 9.1 7.8 10.0
Mean 7.0 4.6 6.2 6.5 4.6 6.4 7.8 4.6 6.5 7.2 5.1 6.4 6.7 5.5 7.2 5.6 6.5 4.1 3.2 2.5 6.7 5.8 5.2 6.7
SD 1.6 1.1 1.2 1.4 0.9 1.4 1.7 1.1 1.4 1.5 1.3 1.1 1.5 1.0 1.8 1.2 1.7 0.8 0.9 0.7 1.2 1.3 1.2 1.4
B-PTr3 F7 F8 F9 F10 F11 F12 RP1 RP2 RP3 RP4 RP5 RP6 RP7 RP8 RP9 L-ASr1 L-ASr2 L-ASr3 O5 O6 O7 O8
N 30 29 30 30 30 30 30 29 30 30 29 29 30 29 30 30 30 30 30 30 30 30 30
Min. 4.7 4.9 1.3 3.5 3.6 3.7 4.0 3.3 4.3 5.0 2.7 3.8 5.2 3.2 4.5 4.4 3.2 4.5 4.2 3.9 4.3 4.0 3.8
Max. 10.0 13.4 6.9 8.9 11.3 9.5 9.9 6.9 8.5 9.9 7.4 9.5 10.4 5.8 9.6 10.7 8.3 8.7 9.0 9.3 10.8 8.1 10.0
Mean 7.1 9.5 4.4 5.6 6.6 5.9 7.1 4.5 6.4 6.7 4.2 6.1 7.6 4.4 6.1 7.1 5.1 6.5 6.5 6.0 8.0 5.5 7.3
SD 1.2 2.0 1.4 1.3 1.8 1.6 1.6 1.0 1.2 1.3 1.0 1.4 1.5 0.7 1.2 1.6 1.2 1.1 1.4 1.3 1.8 1.1 1.7
Table 4 Mean, standard deviation (SD), coefficient of variation (CV) and quartiles per bone (mm)
Mean SD CV (%) P25 quartile Median P75 quartile
Frontal 7.2 2.7 37.7 5.4 6.7 8.4
Left parietal 6.0 1.7 28.3 4.8 5.9 7.0
Right parietal 5.9 1.7 28.6 4.7 5.7 6.8
Left temporal 3.3 1.4 43.3 2.3 2.8 4.6
Right temporal 2.8 0.9 29.8 2.2 2.8 3.4
Occipital 7.3 2.6 35.2 5.4 6.7 8.4

The spatial distribution of the bone thickness is represented as interpolated contour maps in Figure 4. The areas with the highest mean thickness values (colored in red) are the nasion and inion and adjacent areas in the frontal and occipital bones, respectively. The lower values (colored in violet) are located within the squama of the temporal bones. Thickness of the lateral regions of the vault is generally lower than the thickness of the sagittal plane, displaying an organizational pattern. The distribution of the SD values shows regions of high and low variation, with the occipital and frontal bones again being the most variable regions, along with the region surrounding the centre of the sagittal suture; and the temporal bones the least variable ones, as reflected in Table 4.

Figure 4

Mean and standard deviation (SD) thickness distributions represented on contour maps. The color scale represents thickness values in mm. Color figure can be viewed in electronic form.


CVT has been approached in many different ways because it has always posed a challenge in anthropological research. Hence, the principal aim of this paper was to introduce a new thickness measuring methodology that allows researchers to study dry complete skulls without the necessity of imaging methods. The electronic version of the Hacklinger magnetic calliper, originally created for string instruments, represents a very useful tool specifically when applied to craniology. The equipment is portable and the method is non-invasive and cheap, and applicable in many different circumstances. The results of the magnetic calliper are similar to the results obtained with the traditional device, and the error analysis proves the replicability of the method and an acceptable uncertainty value when using the MAG-ic probe V5.0; however, it should be emphasized that measurement errors are based on mean data of three times repeated measuring. Anatomical expertise and experience is, anyway, necessary to properly handle the position of the magnets through the corresponding ectocranial and endocranial surfaces.

In general, studies on cranial thickness report similar results, including when using different methodologies (Marsh, 2013; Anzelmo et al., 2015) or working on different geographic populations (e.g. Smith et al., 1985). The occipital bone is the thickest and most variable bone followed by the frontal, as demonstrated by previous analyses (Marsh, 2013). Moreira-Gonzalez et al. (2006) found an average thickness for the frontal bone of 6.65–7.24 mm and about 5.5 mm for the occipital bone (measured at two locations). These results are similar to those presented in this study, although in our case ranges were wider and values were considerably higher for the occipital bone. The large variation in frontal and occipital bones is due to the heterogeneous anatomy of these regions, which include flat squamas, sinuses, and muscular insertions (White et al., 2011). Parietal bones, as reflected in other studies, are more uniform (Anzelmo et al., 2015). Moreira-Gonzalez et al. (2006) report the mean thickness values of the parietals as between 5.3 and 7.0 mm, which is a very similar range to the one found in the present study, though ours is wider and considers both parietals. Temporal bones turned out to be the least variable bones, although only two points were measured on each temporal, and these bones are not usually considered in CVT studies. The analysis of CVT distribution shows an organizational pattern in which thickness increases from the lateral regions of the vault to the sagittal plane. This tendency has also been found in other modern studies (Marsh, 2013; Anzelmo et al., 2015). In light of these results, more exhaustive studies on the organization and distribution of CVT, taking into account factors such as asymmetry, should be included in our future work.

In conclusion, the methodology based on magnetism presented in this study has proven to be accurate and appropriate for measuring the CVT of skeletal remains. The Hacklinger calliper is an appropriate and useful device to measure cranial thickness in complete dry skulls, and should be considered for use in future anthropometrical studies.


This research was supported by the Spanish Government (CGL2015-65387-C3-3-P, MAT2013-48426-C2-1-R, CGL2015-68363-P, HAR2016-78036-P, HAR2016-74846-P, HAR2017-82755-P, HAR2017-83004-P).

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