Ethanol is a well-known psychoactive depressant drug
consumed worldwide in food and beverages and it is also one
of the most widely used substances of abuse. High doses of
ethanol cause changes in perception and motor incoordination
up to stupor, unconsciousness and coma. Long-term immoderate
consumption of ethanol produces toxic effects leading to abuse up
to physical dependence (chronic alcoholism). Long-term ethanol
misuse is associated with liver and cardiovascular diseases,
cancer and nervous system damage as well as psychiatric
problems such as depression, anxiety and antisocial personality
disorder [1]. Data on ethanol consumption all over the world are
available on the World Health Organization periodic document
“Global status report on alcohol and health 2018” [2].

Many countries have laws regulating the production, sale
and consumption of alcoholic beverages. Moreover, since the
alcohol intake strongly affects the driving capability and the
Blood Alcohol Concentration (henceforth: BAC) is related to the
car crash risk, many countries define threshold values of BAC for
drivers. The Italian regulation identifies three threshold values:
0.5, 0.8 and 1.5 g L^{-1}. Driving having BAC higher than 0.5 g L^{-1} is
forbidden and to have a BAC greater than 0.8 or 1.5 g L^{-1} leads to
harsher penalties.

The analytical measurement of BAC is performed on
venous whole blood by way of i) an enzymatic method based
on the biochemical oxidation with the enzyme ADH (alcohol
dehydrogenase); [3] or ii) a gas-chromatographic (GC) method,
with the headspace (HS) sampling technique (HS-GC) [4]. The
first one is used as screening method, while the second one is
considered as a reference method and provides results having
forensic validity. HS-GC-FID (Flame Ionization Detector) or
-MS (Mass Spectrometry) methods were used for the routine
determination of ethanol concentration on whole blood [4-7],
specifically, for the determination of BAC in suspected drunk
drivers.

Goal of this paper is the evaluation of the measurement
uncertainty of BAC measured by the HS-GC-MS method. The
method was previously in-house validated to ensure a suitable
level of quality in view of a forensic application.

Validation implies the evaluation of the performances of a
measuring system according to a given measurement procedure
[8-10]. Parameters of validation here examined were: sensitivity, range of linearity and uncertainty of the calibration, limit
parameters, carry over, precision (as intra-assay repeatability
and intermediate precision, at two ethanol levels − 0.5 and 0.8 g
L^{-1}), trueness and accuracy. The evaluation of the measurement
uncertainty is important to ensure the selection of a BAC value
suitable to express the judgment of compliance or disconformity
requested by the law [11], and the uncertainty has to be expressed
according to the guidelines of the forensic associations (in Italy:
Group of Italian Forensic Toxicologists) and to a metrological (or
bottom up) approach.

Some papers were found in the literature regarding the
measurement uncertainty of the BAC [7,11-15]. Gullberg
presented the application of the bottom up approach to a
hypothetical example of a forensic blood alcohol analysis
assuming to use a HS-GC method. The refs. 7, 12-15 evaluated
the measurement uncertainty of the BAC on real systems and
an overview on the results obtained in the different works
is shown in Table 1. The most of these works reported data
about measurements conducted by GC-FID and/or in which
water-based ethanol references were used for calibration and/
or quality controls. The estimated relative combined standard
uncertainties are in the range 2 - 3%.

In this work, according to the bottom up approach, the value
of the combined standard uncertainty, at two concentration
levels − 0.5 and 0.8 g L^{-1} − was evaluated for results coming from
a HS-GC-MS method that uses matrix-matched references for
both calibration and quality control procedures. The uncertainty
budget was carried out on the basis of EURACHEM guide lines
[16], and takes into account various contributions of dispersion
of the measurement, derived from the validation procedure
expressly conducted, namely: intra-assay and intermediate
precision, dispensed volumes, calibration straight line and the
recovery uncertainty.

Materials

**Chemicals: **Distilled water was purchased by Broun, ethanol
(purity >99.8%) and 1-propanol (purity >99.5% - GC) were
purchased by Sigma Aldrich (Saint Louis, Missouri, US).

**Reference materials: **Commercial reference materials
bringing the analyte of interest directly in its real matrices were
used to overcome those problems of inaccuracy coming from the
handling of commercial ethanol (very volatile).

The standard solutions for the calibration procedure were
prepared by dilution of certified reference materials (CRMs),
made of ethanol in human whole blood, with an aqueous solution
of 1-propanol (1.0 g L^{-1}), where 1-propanol was used as internal
standard (IS). Medidrug Ethanol VB 080, 200 and 300 (Medichem,
Steinenbronn Germany) were used. The nominal concentration
of ethanol (g L^{-1} ± forensic confidence interval) in these solutions
were 0.808 ± 0.062, 1.995 ± 0.100 and 2.972 ± 0.149, respectively.

The CRMs (ACQ Science GmbH, Germany) with 0.5 and 0.8 g
L^{-1} of ethanol in whole blood, were used for the quality control
during the measurement and 44 BAC values obtained on CRMs in a period of about 1 year, with one measure per week, were
employed for the trueness evaluation. The stabilized CRMs are
stored at 4°C.

**Sample collection and preparation: **Whole blood from
driving persons suspected to drive at high levels of BAC was
collected into specific tubes (Vacutainers, total volume 10 mL)
containing 100 mg of sodium fluoride as preservative. The same
protocol was applied to the whole blood levied for a non-drinker
patient − a healthy abstaining subjects, woman − and used
as blank. 80 μL of sample were then mixed with 200 μL of the
aqueous solution of IS (1-propanol 1.0 g L^{-1}) in 20 mL capacity
Supelco vials (dimension of 75.5 × 22.5 mm) and brought to the analysis.

**Apparatuses: **The gas-chromatograph Autosystem XL GC,
equipped with Turbo Mass mass spectrometer and a Turbo Matrix
headspace autosampler, was from Perkin Elmer (Waltham, MA,
USA). A capillary column Perkin Elmer Elite Volatiles 60 m × 0.25
mm ID (internal diameter) and film thickness 1.4 μm was used.

Pipettes 10-100 μL (model Eppendorf 100) and 20-200 μL
(model Eppendorf 200) capacities were used.

Methods

**Analytical methods: **The automated headspace system of the
HS-GC-MS system worked at 80°C and the equilibration time was
of 16 minutes. Helium carrier gas was settled at 18 psi (pounds
per square inch). Oven temperature was maintained at 120°C;
elution program was isothermal. The GC cycle, thermo-stating,
pressurization, injection and withdrawal times were 7.7, 16, 0.3
and 0.5 min, respectively. As to mass analysis, monitored ions
were 45 m/z (CH_{3}CH_{2}O+) and 46 m/z (CH_{3}CH_{2}OH·+, the quantifier
ion) for ethanol and 59 m/z for 1-propanol (CH_{3}CH_{2}CH_{2}O+). The
signals were collected in SIM mode (Selected Ion Monitoring)
because more suitable for quantitative determinations. The
ratio between the signals of ions 45 m/z and 46 m/z was used to
identify the analyte. The results, expressed in grams of ethanol
per liter (g L^{-1}), were calculated by the calibration straightline.
Calibration straight-line was built using the ratio between
ethanol area and IS area plotted vs ethanol concentration (g L^{-1}).
Internal standard (IS) used to quantify was 1-propanol because it
is the alcohol that shows the most similar chemical behavior with
respect the analyte and, therefore, assures a high quality response.
1-propanol could be observed at low concentration in severely
decomposed corpses in case of post-mortem determination,
consequently, only in these cases, it is not the ideal IS [17].

Kristoffersen et al. [18], reported the risk of ethanol oxidation
to acetaldehyde during the sample heating in the range 50 – 70°C
in the headspace sampling system, but the concentration of
acetaldehyde detected by Kristoffersen et al. [18], is so low to be
negligible in the concentration range of ethanol here considered
(g L^{-1}). Monitoring the ions with m/z 44, 43 and 29 (CH_{3}CHO^{·+},
CH_{3}CO^{+} and HCO^{+}, respectively) we can exclude the presence
of such a criticism in our procedure. Finally, in case of a little
amount of ethanol oxidized to acetaldehyde, the same loss of
analyte would manifest itself in both the sample and standards and the interference would be thus removed (according to the
principles of comparative methods of quantification).

**Software: **All data obtained were presented using the
software Origin 6.1. (by OriginLab) and analyzed using XlStat
2013.2.04 software package and SPSS Statistics 17.0 (by SPSS).

**Statistical evaluation: **Cochran test to verify the
homoscedasticity (variance homogeneity) among set of data
at different concentration was used (P = 0.95). Consequently,
weighted or not weighted linear regression model to fit
data of calibration was used. In addition, the formula used
to estimate the calibration uncertainty was chosen on the
basic of homoscedasticity (homogeneity of variances) or
heteroscedasticity of data.

The value of the correlation coefficient calculated for a linear
regression model is considered inadequate to estimate carefully
the linearity of a dataset [19], therefore, the Mandel test to verify
the linearity of the calibration points, at both working and low
concentration ranges, was applied. Shapiro and Wilk test to
verify the normality of a set of repeated data was used.

Significance of the intercept of a straight line was verified with
a t-test with a specific discriminating function to choose a linear
regression model of interpolation forced (y = ax, one parameter)
or not (y = a + bx, two parameters) through zero.

To evaluate the precision (both intra-assay and intermediate
one), outliers were tested by means of the Huber test. Outliers
on calibration data were also identified examining visually the
values of the residuals.

**Data elaboration: **Calibration uncertainty was estimated at
two levels of concentration, 0.5 and 0.8 g L^{-1}, to be responder as
to forensic requirements of reliability, applying the equation (1):

˗ whvar( y_{ob s} ) is the variance of the observed response

˗ n is the number of data points in the calibration,

˗ b is the calculated best fit gradient,

˗ w_{i} is the weight assigned to y_{i},

standard deviation of the signals of the i^{th} point [14]

The data collected for the estimation of intermediate-precision
were elaborated with multi-factor Analysis of Variance (ANOVA)
to detect the significant factors of variability (significance level = 0.05).

The uncertainty budget was built based on the relationship
(2) that combines relative standard uncertainties - u_{r}(x_{i}) - of the
variables x_{i}. This reckoning is used according to an empirical
approach [14]:

Calibration parameters at working concentrations

Monitoring BAC in a routine clinical/forensic laboratory
implies to be ready for daily measurements in a wide
concentration range. Specific measurements of BAC were
conducted in the working range of concentration − 0.1 - 3.0
g L^{-1} − with five experimental points and three replicates per
point, to estimate sensitivity, linearity range and uncertainty
of calibration for routine application of the method. Tests to
verify homoscedasticity and linearity returned the necessity to
adopt a weighted linear fitting to model the experimental data of
calibration. Parameters calculated for the five calibration curves
in the working concentration range (75 experimental points
in all) are collected in Table 2. For each level of concentration
considered − 0.5, 0.8 g L^{-1} − the value of uncertainty associated to
the calibration was estimated (for details see the *Data elaboration*
paragraph in the *Material and Methods* section). As averaged
result, we have the following values of relative uncertainties (u_{r})
of calibration: u_{r} (0.5) = 0.0278, u_{r} (0.8) = 0.0196; these values
will be considered as input contributes to the uncertainty budget
estimation.

Calibration at low concentration: limit parameters

Specific measurements were conducted at low concentration
− in the range 0.005 - 0.1 g L^{-1}, four experimental points − to
estimate the limit of detection (LoD) and the limit of quantification
(LoQ). A test to ensure the applicability of a linear model to
the experimental data of calibration at low concentration was
applied. Five replicates, one per day, of the calibration procedure
were done and the blank signals were measured ‒ ten replicates
per day − on venous whole blood levied for a non-drinker patient
(woman). The standard deviation of the blank signals and the
calibration parameters were used to determine LoD and LoQ
values applying the formula proposed by Long and Winefordner
[20]. The results obtained with the five replicates enable us to
estimate a reliable LoD value of 5.8 ∙ 10^{-4} g L^{-1} as mean of the five
experimental values obtained, comprised between 1.3 ∙ 10^{-4} and
1.1 ∙ 10^{-3} g L^{-1} of ethanol. The correspondent LoQ value is 1.8 ∙
10^{-3} g L^{-1}.

The limit values were also evaluated using the signal-to-noise
ratio (henceforth: S/N), a typical method used in chromatographic
analysis. The formula used is LoD = C[F(N/S)] [21], where C is the concentration of the analyte, F is a coverage factor often
assumed equal to 3, S is the magnitude of the instrumental signal
(as the height of the analyte peak) and N is the magnitude of the
instrumental signal when the analyte is not eluted. In order to
estimate the S/N values, the instrumental signals of solutions
with 5 ∙ 10^{-3} and 1 ∙ 10^{-2} g L^{-1} of ethanol were recorded. The values
obtained – LoD = 2.5 ∙ 10^{-4} g L^{-1} and LoQ = 7.6 ∙ 10^{-4} g L^{-1} – are lower
than the mean value estimated using the Long and Winefordner
[20] formula, but are included in the variability range reported above.

In both cases, the LoQ value is quite lower than the lower
limit of the calibration range, therefore the operational LoQ value
of the method results to be 0.1 g L^{-1}.

Carry-over

The carry-over, or memory effects or effect of dragging, is
characteristic of a separation-based analytical method and it is
a typical problem coming from repeated injections, or injection
of dirty samples, that overload the injection port. The carryover
was tested by injecting a blank after the injection of the
highest concentration of ethanol employed (the CRM with 3
g L^{-1} of ethanol). The experimental procedure was repeated
in triplicate. The calculation was performed according to the
approach proposed by Haeckel [22,23]. The carry-over (C.O.)
was expressed as percentage, or as ethanol concentration value,
starting from the ratio:

where y_{b1} = signal of the blank injected after the standard, y_{b2} =
signal of the blank (injected in sharply favourable conditions), y_{std}
= signal of highest concentration of ethanol employed. The mean
*C.O.* resulted 0.021% of the concentration of the standard used. It
corresponds to a concentration of 6.3 ∙ 10^{-4} g L^{-1} of ethanol. This
value is lower than the LoQ and this indicates that the memory
effect does not affect the measurement outcome.

Precision

**Intra-assay precision: **Precision was evaluated (P = 0.95)
as intra-assay repeatability in the same day (intra-day), with the
same operator and apparatus at two concentration levels, 0.45
and 0.70 g L^{-1} ethanol (average values). For each level, eleven
replicates were carried out. Two aliquots of a pool of human
whole blood were spiked with different volumes of 99.8% ethanol
up to reach values of ethanol concentration near to the nominal
one (namely, 0.5 and 0.8 g L^{-1}) selected in this paper according
to Italian regulation prescriptions. The real concentrations
are lower than the nominal ones because of the volatility of
the ethanol that strongly affects the handling. For each level of
concentration considered, the value of uncertainty associated
to the repeatability was estimated. Table 3 reports the results
obtained. For the intra-day repeatability it was possible to work
with a not stabilised pooled.

**Intermediate precision: **According to International
Standard ISO 5725-3:1994 [24], precision was estimated by studying the repeatability under different experimental
conditions. Experiments were planned in order to evaluate
the effect related to the variation of three factors: i) the time,
ii) the operator and iii) the volume of liquids dispensed by
the pipettes used for the sample preparation. Two operators
analysed four samples per day, each of one using two different
pipettes, with a total of 8 replicates per day (n). Replicates of the
measurements were done along 5 days (40 experimental points
in all) on solutions with 0.5 and 0.8 g L^{-1} (nominal concentration)
of ethanol, prepared by dilution of CRMs, in order to mimic the
routine sample preparation. In this case, employing stabilised
CRMs it was necessary to avoid coagulation processes often
caused by the variation of the thermal conditions between
measuring and storage step.

The data were elaborated with multi-factor Analysis of
Variance (ANOVA) to detect the significant factors of variability.
The outcome of the test shows that the changing of both the
operator and the pipettes does not affect significantly the
precision of the measurements, while the time is a significant
factor. Therefore, the within-day repeatability (S_{r}) was estimated
using the equation reported below (4):

where *d* is the number of days; S_{rj}^{2} is the variance of each group
of data. The degrees of freedom (*d* = 5, n = 8) for S_{r}^{2} are ν = *d* (n− 1) = 35.

The intermediate precision SI was calculated as reported in
ref. 25 and results to be 0.034 and 0.039 g L^{-1} at 0.5 and 0.8 g L^{-1},
respectively.

Trueness and accuracy

The trueness of the measures was evaluated at the two
concentration levels (0.5 and 0.8 g L^{-1}) by the comparison of
the results of 44 replicated measurements on CRMs and the
corresponding reference values. The mean values obtained are
0.5005 ± 0.0047 g L^{-1} and 0.7968 ± 0.0048 g L^{-1} (P = 95%, ν =
43) on CRMs with 0.500 ± 0.020 g L^{-1} and 0.793 ± 0.035 g L^{-1} of
ethanol (statistic uncertainty reported, P = 95%), respectively.
The method provides unbiased results.

In order to compare method performance including both
distortion (trueness) and dispersion (precision) contributions
the accuracy can be calculated [8,24], as Mean Squared Error
(MSE), therefore as the sum of the squared bias and the observed
variance at each level of concentration. MSE (0.5) = 6.3·10^{-5} (g L^{-1})^{2} and MSE (0.8) = 2.5·10^{-4} (g L^{-1})^{2}, using the intra-assay
repeatability, and MSE (0.5) = 1.2·10^{-3} (g L^{-1})^{2} and MSE (0.8) =
1.5·10^{-3} (g L^{-1})^{2}, considering the intermediate precision.

Uncertainty budget

− Sources of uncertainty identified wprecision of the
measurement: the uncertainty contribution derived from the
precision of the measurement, *u(s)*, was estimated using both
intra-assay and intermediate precision data;

− dispensed liquids: the uncertainty derived from the
use of calibrated pipettes, *u*(V), was estimated from the random
error declared by the supplier and considering a triangular
distribution. We also considered that the variability of the
dispensed whole blood volumes is higher than that declared for
non-viscous samples, however its contribution to the uncertainty
is included in the calibration process;

− calibration straight line: uncertainty *u*(y) on the
instrumental signal;

− CRM concentration: the uncertainty *u*(CRM) associated
to the concentration of the reference materials used for the
calibrating solutions and declared by the supplier. The statistic
confidence interval, expressed with a confidence level of 95%,
was used;

− Recovery uncertainty: although our method is
unbiased, the uncertainty associated to the determination of the
bias, *u*(rec), may be expressed as the uncertainty of the analytical
recovery (value observed divided by value expected) [16].

All these sources of variability were considered in the
uncertainty budget assessment and the corresponding
uncertainties were combined as reported in the paragraph *Data
Elaboration* in the *Material and Methods* section. The various
contributions to the uncertainty of the ethanol concentration are
reported in Table 4, with the combined uncertainty, expressed as
relative and absolute values, and with the expanded uncertainty
evaluated with a coverage factor k = 2. The results are reported
for each concentration level taken into account, using the
contribution of the intra-assay repeatability and intermediate
precision. The values of absolute combined standard uncertainty
are *u*^{c}(0.5) = 0.017 g L^{-1}, *u*^{c}(0.8) = 0.025 g L^{-1}, using the intraassay
repeatability, and *u*^{c}(0.5) = 0.036 g L^{-1}, *u*^{c}(0.8) = 0.048 g
L^{-1}, considering the intermediate precision. Relative combined
standard uncertainty, for the two concentration levels (in
bracket), are: intra-assay repeatability (0.5) =3.4% and (0.8) =
3.1%, intermediate precision (0.5) = 7.3% and (0.8) = 6.0%.

The statistical variability of the analytical results and the
variability of the signals of the reference solutions are the
main contributions to the measurement uncertainty (Figure 1) considering both the intra-assay repeatability and the
intermediate precision.

The uncertainty values could be used to express the result
of the forensic analysis, in view of a decision of compliance/
non-compliance to a lawful limit, starting from the data of
ethanol concentration calculated from the calibration curve. If
the analytical result exceeds the limit value plus the expanded
uncertainty of the measure, non-compliance is considered clearly
demonstrated [16]. The choice of the factor k used to obtain
the expanded uncertainty is based on the level of confidence
desired and, for an approximate level of confidence of 95%, k is
equal to 2. By the use of the expanded uncertainty it is possible
to express to calculate the decision limits, i.e. the concentration
beyond which the BAC value can be considered, with a certain
probability, higher than the threshold values defined by the law
[7,11]. Table 4 reports the decision limits calculated with the
expanded uncertainty values estimated in this work.

The HS-GC-MS analytical method for ethanolemia
measurement in venous whole blood was validated − according
to a specific experimental procedure (in-house modality) and
statistical approach − to verify those metrological performances
useful to establish a reliable medico-legal applicability. The
analytical procedure adopted employs matrix-matched
references in order to take into account the matrix effect on the
analytical result. The use of specific CRMs during both calibration
and quality control procedures accounts for the conditions of
real samples, and this improves the traceability of the analytical
response. Nevertheless, the procedure is easy, practical, safe
to use, suitable for routine application of a clinical/forensic
laboratory and it ensures a very good level of quality in term of
both precision and trueness.

The estimation of the measurement uncertainty was carried
out strictly following the guidelines provided by EURACHEM
[16], and in accordance with the Gullberg approach [11]. The
results show that the variability of replicated measurements and
the calibration procedure are the main sources of uncertainty;
therefore, in order to increase the quality of the measurement, it
is rational to act on these two analytical steps. Moreover, the value of the expanded uncertainty can be used to express a prudential
value of BAC suitable to give forensic judgement concerning the
exceeding of threshold values.