ANTROPOLOGIA FORENSE

1. ORIGINAL ARTICLE
Sex estimation using the second cervical vertebra:
a morphometric analysis in a documented Portuguese
skeletal sample
Inês Gama & David Navega & Eugénia Cunha
Received: 30 April 2014 /Accepted: 3 September 2014
# Springer-Verlag Berlin Heidelberg 2014
Abstract Biological sex estimation is one of the main param-
eters required in the construction of a biological profile of an
unknown deceased person. In corpses in an advanced state of
decomposition, skeletonized or severely mutilated, bone anal-
ysis may provide the only way to access biological sex.
Although the hip bones are the most dimorphic and useful
bones for sex estimation, they are often badly preserved and/
or fragmented or may not even be present in some cases. For
that reason, it is necessary to develop sex estimation methods
based on bones less dimorphic. In this study, 13 dimensions of
the second cervical vertebra were measured in order to quan-
tify sex-related variation and to generate a simple predictive
model based on logistic regression analysis. For logistic re-
gression fitting, 190 individuals from the Coimbra Identified
Skeletal Collection were used as a training sample. The
resulting model was also evaluated in an independent test
sample composed of 47 individuals from the Identified
Skeletal Collection of the 21st Century (University of
Coimbra). The developed logistic regression model correctly
estimated known sex in 86.7 to 89.7 % of the cases. The
second cervical vertebra demonstrated to be a useful alterna-
tive for sex estimation when other skeletal elements are not
available or suitable for analysis. This method seems promis-
ing but more reliability studies are required for a more robust
validation.
Keywords Forensic anthropology . Cervical vertebra
(C2) . Sex estimation . Sexual dimorphism . Logistic
regression
Introduction
Sex estimation in human skeletal remains is one of the param-
eters of biological profile and therefore is very important, both
for personal identification in forensic cases and
bioarchaeological studies [1–4].
Due to its reproductive function, the examination of mor-
phological characteristics of the bony pelvis is the most reli-
able technique for estimating sex. The skull and the long
bones are the next most important anatomical regions to
estimate biological sex. The other elements of the skeleton
have a degree of sexual dimorphism generally considered
more tenuous [1, 5, 6].
In several situations, especially when post-mortem interval
increases, the human skeleton suffers taphonomic changes
becoming porous and fragmented [3, 7]. These changes par-
ticularly affect the pelvic bone due to their irregular shape. In
some cases, the bones with greater sexual dimorphism may
even be missing, making necessary to develop techniques that
enable sex estimation based on skeletal regions taken as less
dimorphic [7].
Previous studies have demonstrated that the second cervi-
cal vertebra (C2) presents an amount of sex-specific variation
in its dimensions to allow sex estimation by morphometrical
analysis with a considerable degree of accuracy. The C2 has
several morphological characteristics which allow an easy
identification and quick distinction from the remaining verte-
brae; in addition, studies also indicate that cervical vertebrae
are the best preserved ones [8].
Wescott [9] developed a metric method to estimate sex in
adults based on eight measurements of the C2 and obtained
I. Gama (*) :D. Navega :E. Cunha
Forensic Sciences Centre (CENCIFOR), Largo da Sé Nova, s/n,
3000-213 Coimbra, Portugal
e-mail: ines_gama@hotmail.com
I. Gama :D. Navega :E. Cunha
Department of Life Sciences, Faculty of Sciences and Technology,
University of Coimbra, Calçada Martim de Freitas,
3000-456 Coimbra, Portugal
Int J Legal Med
DOI 10.1007/s00414-014-1083-0

2. accuracy rates ranging from 81.7 to 83.4 %. Marlow and
Pastor [3] tested the method developed by Wescott [9] and
obtained a percentage of correct classification between 70.91
and 78.9 %. Along with the eight measurements described by
Wescott [9], the authors performed an additional measurement
of C2 obtaining a correct classification of 83.3 %. Medina [10]
made 14 measurements to the axis and has reached a percent-
age of correct classification of 84.2 %. Bethard and Seet [11]
tested the method of Wescott [9] in a contemporary American
population sample and correctly classified up to 86.7 % of the
individuals.
The purpose of this study was to evaluate the level of
sexual dimorphism in the second cervical vertebra in
Portuguese sample and determine what measurements were
the most discriminative to create logistic regression model that
allow sex estimation. We also aim to know the performance of
the model when compared with those developed by other
authors for the same vertebra.
Materials and methods
Samples
Two samples of second cervical vertebra (C2) from document-
ed individuals of Portuguese origin were analysed in this
study. The first sample is comprised of 99 males and 91
females from the Coimbra Identified Skeletal Collection
(CISC), hosted at the University of Coimbra (for more details
see [12]). Their age at death ranged from 20 to 69 years old
with a homogenous distribution in both sexes; the death dates
correspond to a time period between 1904 and 1939. This
sample was used as a training set to develop all the sex
prediction models resulting from this study.
The second sample was composed by 24 males and 23
females from the recently created Identified Skeletal
Collection of the 21st Century (ISC-XXI), also hosted at the
University of Coimbra. This sample is composed mostly by
elderly individuals who died between 1996 and 2001. This
sample was used to test the model constructed with sample
mentioned above.
Only part of the ISC-XXI was available for analysis when
data was collected for this study, which limited the number of
individuals included in this sample and did not permitted a
homogenous sampling over age at death. The sample size is
therefore quite small to allow this sample to be used in more
data-intensive statistical procedures such as the logistic regres-
sion equations used in this study to generate sex estimation
models. However, the experimental design employed allowed
to evaluate the possible effect of temporal variation in sex
estimation due to the significant temporal distance between
the samples used in this study. Only vertebrae with normal
morphology (i.e. no pathological or traumatic changes) were
included. Detailed statistical information on the demographic
parameters of the samples used is available on Table 1.
Morphometric data collection and measurement error
assessment
In order to obtain a morphometric characterization of the
second cervical vertebra, 13 measurements were acquired.
All measurements were performed with a sliding calliper
and registered in millimetres with an approximation of
0.5 mm. Eight measurements were adopted from Wescott
[9], one was selected from Medina [10] and another one from
Marlow and Pastor [3]. In addition to the measurements
adopted from previous studies, three new measurements were
included. All measurements are described in Table 2 and
illustrated in Figs. 1, 2 and 3.
In order to analyse the intra- and inter-observer measure-
ment error, a subset of 50 axis (25 females and 25 males) was
randomly drawn from the CISC sample. The first author
performed the 13 measurements on selected subset of individ-
uals in two different sessions (2 weeks apart), and two sets of
measurement results from a different session were compared
in order to assess intra-observer error. A second observer (with
background on physical anthropology) performed the 13 mea-
surements in the same subset (n=50) of individuals in a third
session, the resulting data was compared to the first set of
measurements collected by the first author in order to conduct
an inter-observer error analysis. Absolute and relative techni-
cal errors of measurement (TEM and %TEM) were computed
Table 1 Descriptive statistics of
demographics characteristics of
training and test samples
Sample Sex Variable n Mean sd Min. Max.
CISC (train set) Female Age at death 91 43.25 13.76 21 69
Year of death 91 1926.47 6.55 1910 1934
Male Age at death 99 44.09 13.66 20 69
Year of death 99 1925.57 6.88 1910 1936
ISC-XXI (test set) Female Age at death 23 81.30 9.99 60 92
Year of death 23 1999.61 1.47 1996 2001
Male Age at death 24 70.96 17.15 33 92
Year of death 24 1999.73 1.35 1997 2001
Int J Legal Med

3. following Ulijaszek and Kerr [13] as indicators of the repeat-
ability of each measurement.
Statistical procedures
In order to analyse the differences between males and females,
a t test (two-tailed) was performed. To quantify the amount of
sexual dimorphism (in percentage, SD %), the following
indicator was applied:
SD % ¼
Xm−X f
Xm
 100 ð1Þ
where Xm and Xf are the mean value for males and
females. It was considered that a measurement displayed
strong sexual dimorphism when this indicator had values
higher than 10 %, that is, males are more than 10 % larger
Fig. 1 Measurements of the axis, lateral view: CMA (maximum length of
the axis), AMA (maximum height of the axis), AMD (maximum height of
the odontoid process)
Fig. 2 Measurements of the axis, superior view: LMFV (maximum width
of the vertebral foramen), LMA (maximum width of the axis), DMFS
(maximum distance between the superior facets), CMFS (maximum
length of the superior facet), LMFS (maximum width of the superior
facet), DTD (odontoid process transverse diameter), DSD (odontoid
process sagittal diameter)
Table 2 Measurements taken in this study
Measurements Source
Maximum height of the axis (AMA): length measured
from the lowest point of the edge of the vertebral
body to the uppermost point of the tooth; Fig. 1.
Wescott [9]
Maximum length of the axis (CMA): sagittal length of
the vertebra measured from the most anterior point
of the body to the most posterior point of bifid
spinous process; Fig. 1.
Odontoid process sagittal diameter (DSD): the
maximum sagittal (antero-posterior) diameter of the
dens; Fig 2.
Odontoid process transverse diameter (DTD): The
diameter of the dens measured perpendicular to the
sagittal diameter; Fig. 2.
Maximum distance between the superior facets
(DMFS): maximum distance between the superior
articular facets measured from the most lateral
points of the facets; Fig. 2.
Maximum length of the superior facet (CMFS)a
:
maximum length of the superior articular facet
measured perpendicular to the transverse diameter;
Fig. 2.
Maximum width of the superior facet (LMFS)a
:
maximum width of the superior articular facet
measured perpendicular to the sagittal diameter;
Fig. 2.
Length of the vertebral foramen (CMFV): the internal
length of vertebral foramen, measured at the inferior
edge of the foramen in the median plan; Fig. 3.
Sagittal maximum body diameter (DSMC): maximum
sagittal diameter of the vertebral body measured
from the antero-posterior point of the board to
posterior-inferior point; Fig. 3.
Medina [10]
Maximum width of the vertebral foramen (LMFV):
maximum transverse diameter of the vertebral
foramen measured along the frontal plane; Fig. 2.
Marlow and
Pastor [3]
Maximum height of the odontoid process (AMD):
tooth length measured from the highest point of the
odontoid process to the line passing superiorly to
the superior articular facets; Fig. 1.
Present study
Maximum transverse diameter of the body (DTMC):
maximum transverse diameter of the body
measured between the edges of the body; Fig. 3.
Maximum width of the axis (LMA): maximum width
measured from the more extreme side of the
transverse processes; Fig. 2.
a
The measurements CMFS and LMFS were taken on the left and right
Int J Legal Med

4. than females. For bilateral measurements, a t test (two-tailed)
was also performed to assess symmetry and side differences.
Statistical sex estimation models were constructed using
logistic regression modelling. Logistic regression is a discrim-
inative statistical model analogous discriminant function anal-
ysis (a common technique in forensic anthropology), where
sex estimation is mathematically expressed as:
L ¼ C þ B1X1 þ B2X2 þ ⋯ þ BnXn ð2Þ
where L is the logit or the log-odd, C is a constant value, B
are the regression coefficients and X the measurements used
for sex estimation. In this study, a negative logit value is
associated to a female individual and a positive value associ-
ated to a male individual. C and B are generally estimated
using a maximum likelihood procedure.
Unlike discriminant function analysis, logistic regression is
more robust to outliers, it does not require homogenous
variance-covariance matrices, is generally more tolerant to
co-linear predictors and it also does not require the predictors
to have a Gaussian distribution. The main advantage of logis-
tic regression as a modelling technique is the ability to invert
the log-odds (or logit values) and convert it to posterior
probabilities using the exponential function:
F Lð Þ þ
1
1 þ e−L
ð3Þ
where L is the logit value computed from (2) and e is the
Euler constant, 2.7182. In this study, Eq. (3) computes the
posterior probability of the individual being male. The
probability of the individual being female is simply
given by 1-F(L).
Due the multivariate nature of the prediction task of this
study, logistic regression was executed following a stepwise
variable selection procedure (forward conditional technique)
in order to find the smaller (less variables) and most accurate
model for sex estimation using the second vertebra. All com-
putational analyses were conducted using IBM SPSS (Version
20).
The logistic regression analysis was performed with the
training sample (190 individuals), and the resulting model was
also evaluated in the test sample (47 individuals) in order to
validate the model; in other words, evaluate that whether the
results obtained in the training sample can be generalized to
the Portuguese population.
Results
Tables 3, 4, 5 and 6 summarize simple statistical descriptors of
the measurements performed in both training and test samples.
Inter- and intra-observer error analysis demonstrated that
the majority of measurements employed in this study can be
acquired with measurement error close to 0.5 %; exceptions
are the LMFSE (maximum width of the facet upper right) and
DSMC (maximum sagittal body diameter) which presented
error rates exceeding 1 % (1.03 and 1.35 %).
In t test analysis for differences among sexes, the CMFV
was the only measurement not showing significant statistical
differences between males and females (p value<0.05). The
LMA showed a level of sexual dimorphism of 11.18 % and
DSMC a sexual dimorphism index of 10.6 %, representing the
most dimorphic dimensions of the second vertebra. The
Fig. 3 Measurements of the axis, inferior view: CMFV (length of the
vertebral foramen l), DTMC (maximum transverse diameter of the body),,
DSMC (sagittal maximum body diameter)
Table 3 Descriptive statistics of male individuals, CISC sample
Measurement n Min. Max. Mean sd
AMD 99 13 19 16.20 1.31
CMA 92 44 55 49.49 2.46
AMA 99 28.5 45 38.43 2.73
DSD 99 10 13.5 11.68 0.73
DTD 99 8 12 10.38 0.91
LMA 84 49 67.5 55.89 3.55
DMFS 99 40 52.5 46.44 2.41
LMFSE 99 13 29 16.94 1.81
LMFSD 99 14 21 17.16 1.46
CMFSE 99 14 21 18.22 1.48
CMFSD 99 14 22 18.06 1.60
CMFV 99 12 21 16.25 1.73
LMFV 99 19.5 27.5 23.32 1.67
DSMC 99 13 19 15.29 1.30
DTMC 99 16 24 19.12 1.72
Int J Legal Med

5. CMFV is less dimorphic measurement, with males being only
2.7 % larger than females.
The t test analysis (two-tailed) of bilateral measurements,
LMFS and CMFS, identified significant statistical differences
between measurements taken on the left and the right side (p
value <0.05).
Logistic regression analysis with stepwise variable selec-
tion resulted in a multivariate model with four variables. The
most predictive variables included in the model (in decreasing
order of importance) were LMA, DSMC, CMA and LMFS
(right side). Detailed information on the model fitting is avail-
able in Table 7. The resulting model correctly identified the
sex of individual of the training set in 89.7 % of the cases
(Table 8). In the test sample, the sex was correctly estimated in
86.7 % of the cases. The fitted logistic regression model is
described according to the following equation:
L ¼ −62; 170 þ 0:561 Â CMAð Þ þ 0:677 Â LMAð Þ
þ −0:818 Â LMFSDð Þ þ 0:977 Â DSMCð Þ ð4Þ
Table 4 Descriptive statistics of female individuals, CISC sample
Measurement n Min. Max. Mean sd
AMD 91 11 19 15.11 1.37
CMA 72 30 50.5 45.09 2.96
AMA 91 29 41 35.49 2.41
DSD 91 8.5 13 11.02 0.88
DTD 91 8 11.5 9.75 0.77
LMA 65 41 57 49.64 3.48
DMFS 91 37 54 43.34 2.95
LMFSE 91 11.5 20 15.77 1.70
LMFSD 91 12 21 16.19 1.69
CMFSE 91 12.5 20 17.16 1.41
CMFSD 91 13 21 16.90 1.44
CMFV 91 12.5 20 15.82 1.53
LMFV 91 18 25.5 22.09 1.41
DSMC 91 11 17 13.67 1.16
DTMC 91 14 24 18.14 1.88
Table 5 Descriptive statistics of male individuals, ISC-XXI sample
Measurement n Min. Max. Mean sd
AMD 23 12.5 20 16.72 2.01
CMA 16 39.5 56 50.81 4.13
AMA 22 32.5 45 39.55 3.10
DSD 24 10 13 11.23 0.87
DTD 24 9.5 12 10.75 0.59
LMA 13 50.5 63.5 57.58 4.07
DMFS 24 42 54 46.63 2.81
LMFSE 24 14.5 20 16.92 1.30
LMFSD 24 15 21 17.25 1.55
CMFSE 24 16 21 18.29 1.67
CMFSD 24 15 21 18.27 1.67
CMFV 23 12 21 15.83 1.94
LMFV 23 14.5 27 22.67 2.50
DSMC 22 14 18 16.07 1.22
DTMC 22 16 25 20.05 2.37
Table 6 Descriptive statistics of female individuals, ISC-XXI sample
Measurement n Min. Max. Mean sd
AMD 21 13.5 19 16.05 1.30
CMA 15 41 50 46.33 2.67
AMA 21 16 41 35.21 4.78
DSD 23 10 12 10.98 0.65
DTD 23 9 11.5 10.15 0.71
LMA 8 48.5 59.5 53.13 3.18
DMFS 22 39 48 44.11 2.33
LMFSE 22 13 18 15.80 1.39
LMFSD 22 15 19 16.61 1.09
CMFSE 23 13.5 20 17.26 1.42
CMFSD 21 15 20 17.48 1.20
CMFV 22 12 17.5 14.68 1.30
LMFV 22 19 27 21.98 1.84
DSMC 23 12 18.5 14.33 1.40
DTMC 22 14.5 22 17.23 1.78
Table 7 Logistic regression model fitting steps (stepwise variable selec-
tion via forward conditional method)
Step Variable B S.E. Wald Sig. Exp (B)
Step 1a
LMA 0.612 0.104 34.348 0.000 1.843
Constant −31.758 5.453 33.924 0.000 0.000
Step 2b
LMA 0.600 0.177 26.068 0.000 1.821
DSMC 0.862 0.253 11.630 0.001 2.367
Constant −43.490 7.518 33.460 0.000 0.000
Step 3c
CMA 0.353 0.138 6.508 0.011 1.423
LMA 0.539 0.124 18.836 0.000 1.715
DSMC 0.660 0.272 5.903 0.015 1.935
Constant −54.183 9.766 30.783 0.000 0.000
Step 4d
CMA 0.561 0.188 8.867 0.003 1.752
LMA 0.677 0.150 20.461 0.000 1.967
LMFSD −0.818 0.269 7.611 0.006 0.441
DSMC 0.977 0.350 7.796 0.005 2.657
Constant −62.170 11.790 27.808 0.000 0.000
a
Variable introduced in step1: LMA (maximum width of the axis)
b
Variable introduced in step 2: DSMC (sagittal maximum body diameter)
c
Variable introduced no step 3: CMA (maximum length of the axis)
d
Variable introduced in step 4: LMFSD (maximum width of the right
superior facet)
Int J Legal Med

6. Negative values are associated to a female individual,
whereas positive values correspond to a male. The value of
L, logit, can be converted in a probability of an individual
being male using Eq. (3).
Discussion
The intra-and inter-observer errors were very low and compa-
rable to previous studies [3, 9–11]. This demonstrates that the
measurements are replicable, an essential factor for the reli-
ability of any metric method.
In this study, the measurements with the highest discrimi-
nate power were maximum width of the axis (LMA), sagittal
maximum body diameter (DSMC), maximum length of the
axis (CMA) and the maximum width of the right superior
facet (LMFSD). In Wescott [9] study, the most discriminating
measures were, in decreasing order, maximum length of the
axis, maximum length of the superior facet, maximum width
of the superior facet, length of the vertebral foramen and
maximum height of the axis. In Marlow and Pastor [3], the
most discriminative measurements were maximum distance
between the superior facets, maximum length of the axis,
maximum width of the vertebral foramen and odontoid pro-
cess sagittal diameter. Medina [10] identified the sagittal
maximum body diameter, the maximum length of the superior
facet, the length of the vertebral foramen, the maximum width
of the superior facet and the maximum distance between the
superior facets as the most important measurements for sex
estimation. In the present analysis, the CMFV was the only
variable that did not show any significant differences between
both sexes; furthermore, it presented the lowest rate of sexual
dimorphism. This result is not in agreement with Wescott [9],
in where CMFV was the variable with the fourth largest
discriminant value or either with the study of Medina [10],
in which the same variable was the third more discriminating
one.
We observed that the more discriminate measurements are
not common to all studies, which can be explained by the
inter-population variability. However, the CMA demonstrated
not only to be relevant in this research but also in the studies of
Wescott [9] and Marlow and Pastor [3]. The measured DSMC
performed by us and also by Medina [10], showed strong
discriminate value in both studies.
The measurement LMA, exclusive to this research, has
demonstrated a quite strong sexual dimorphism (11.18 %)
and also to be the one measurement with greater discrimina-
tive value according to the logistic regression model.
Measurements AMD and DTMC, also analysed for the first
time, showed a sexual dimorphism of 6.7 and 5.1 % respec-
tively, and they were not considered relevant by the statistical
sex estimation model.
It is important to note that due to fragmentation of the
vertebrae, CMA and LMAwere not always measurable, since
both the spinous process and the transverse processes are the
anatomical portions of the vertebra where we observed greater
levels of fragmentation.
Regarding the accuracy of the sex estimation model, results
obtained are consistent with previous studies on sex estima-
tion through metrical analysis of the second vertebra. The
Table 8 Logistic regression model classification accuracy
Observed Training sampleª Accuracy (%) Test sampleb
Accuracy (%)
Sex Sex
Female Male Female Male
Step 1 Sex Female 42 14 75.0 2 4 33.3
Male 10 70 87.5 0 9 100.0
Total (%) 82.4 73.3
Step 2 Sex Female 47 9 83.9 3 3 50.0
Male 8 72 90.0 0 9 100.0
Total (%) 87.5 80.0
Step 3 Sex Female 45 11 80.4 3 3 50.0
Male 8 72 90.0 0 9 100.0
Total (%) 86.0 80.0
Step 4 Sex Female 48 8 85.7 4 2 66.7
Male 6 74 92.5 0 9 100.0
Total (%) 89.7 86.7
a
CISC
b
ISC-XXI
Int J Legal Med

7. dimorphism of this bone allows correct sex estimation in more
the 80 % of the cases. On the training sample, sex was
correctly estimated in 89.7 % of the cases. The model is
slightly biased towards correct sex estimation in males (92.5
vs. 85.7 % in females). The results obtained are slightly more
accurate than previous studies, but one should take in consid-
eration that the results on training sample were obtained by re-
substitution and can overestimate the true performance of the
method. More robust cross-validation schemes such as k-fold
or leave-one-out methods are not implemented for logistic
regression in the version of the software used. For this reason,
only re-substitution error rates are reported.
To account for the limitation previously mentioned, the
method was also tested in independent sample composed of
the remains of contemporaneous Portuguese individuals. The
accuracy of the fitted model in this sample was more consis-
tent with the previous studies with 86.7 % of the individual
correctly classified according to known sex. As in training
sample, the model was once more biased towards male correct
sex estimation (100 vs. 66 % in females, Table 8). Without
considering sex-specific accuracy, the difference in accuracy
between training and test sample can be considered negligible.
However, the pattern of sex-specific accuracy in the test
sample is suggestive of possible degree of secular change.
As described in Case and Ross [14], a positive secular
change in bone dimensions is usually associated to a higher
misclassification of contemporaneous females and higher
probability of correct sex estimation of male individuals,
when applying a method fitted in sample representative of
the population in older time period, as occurred in this study.
We should not discard the simple effect of sampling variation
and error given that the number of test individuals to whom
the model was applied is very low, due to the degree of
preservation of the material in analysis (Table 8). It was only
possible to measure 47 C2 and test the method in 15, due to
absence or fragmentation. In addition, the sample is formed
mainly by individuals with an age at death over 70 years. In
the future, in order to test this method with more reliability, a
more representative test sample that could also provide greater
age diversity should be analysed.
The results of this study are consistent with those observed
in previous studies indicating that the second cervical vertebra
is useful in sex estimation with accuracy similar to other
elements of the skeleton [15–18].
Conclusion
The results observed in this study allow to affirm that there is
considerable sexual dimorphism in the second cervical verte-
bra, which is in accordance with previous studies [3, 9–11].
The accuracy of the logistic regression model fitted in this
study ranged from 86.7–89.7 %, which is similar with other
methods using other skeletal anatomical regions. The mea-
sures with the highest significance in decreasing order were
the maximum width of the axis (LMA), the maximum body
sagittal diameter (DSMC), the maximum length of the axis
(CMA) and the maximum width of the right superior facet
(LMFSD). Since the LMA was analysed for the first time,
which showed to be quite dimorphic, we thought that it is
important that this should be added in future studies.
The regression model fitted in this study should be more
extensively tested in the Portuguese contemporaneous skeletal
material in order to confirm its reliability in forensic contexts.
In the future, the model should be re-fitted with a more robust
sample of Portuguese contemporaneous skeletal remains. At
the moment, the model is an important addition to the forensic
expert’s toolbox, although it should be applied with cautions
due to the limitations exposed.
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