Evaluating the Detection Performance of a Drug Screening Device

In this case, the specific antibody (Ab) is present in a limited amount. Its binding sites are competed for by the labeled antigen (Ag*), which is in excess, and the same but unlabeled antigen (Ag), which is present in the sample and being measured. Both antigens occupy the antibody binding sites.

Ag+Ag*+Ab→Ag−Ab+Ag*−Ab+Ag+Ag* {\rm{Ag}} + {\rm{A}}{{\rm{g}}^*} + {\rm{Ab}} \to {\rm{Ag}} - {\rm{Ab}} + {\rm{A}}{{\rm{g}}^*} - {\rm{Ab}} + {\rm{Ag}} + {\rm{A}}{{\rm{g}}^*}

In this method, the specific antibody is present in excess. The measured antigen reacts with it, and for quantification, a labeled suitable specific antibody (Ab*) is used. The amount of analyte is directly proportional to the amount of complex [Ag–Ab*].

Benzodiazepines can be extracted with methanol from various preparations and analyzed by gas chromatography with flame-ionization detection, which, however, may cause thermal degradation [10]. The GC-MS method is highly effective, combining the separation capability of chromatography with the precise identification of compounds by mass spectrometry. In combination with suitable standards, it provides very accurate results [10]. HPLC is less suitable due to the complicated separation of diverse benzodiazepines, though separation efficiency can be improved by the choice of column and solvent.

The identification of drugs in blood, urine, and saliva is more complex than the analysis of such substances in pharmaceuticals or illicit preparations. Cocaine and its metabolites can be determined by GC-MS, but immunological tests targeting benzoylecgonine show low reactivity to cocaine, which may lead to false negatives [11]. A case of death from overdose demonstrated significant differences in concentrations between blood and urine, leading to a negative immunoassay result. The elimination half-life of cocaine and its metabolites varies.

THC can also be determined by mass spectrometry; however, GC-MS/MS is used in this case due to its low concentrations in body fluids [12]. Metabolite extraction is performed by solid-phase extraction or the MEPS method, which is effective for small sample volumes [13]. However, sample preparation is time-consuming and includes protein precipitation with cold acetonitrile, centrifugation, buffering, and homogenization.

Amphetamine and methamphetamine are usually determined from urine, where about 43 % of methamphetamine and 5 % of amphetamine (from methamphetamine conversion) are present after 24 hours [14]. The analysis involves GC-MS and solid-phase extraction; the sample is alkalized, extracted with methanol, and derivatized with trifluoroacetic acid.

Drug content can also be determined from hair, which is easily accessible and stores well. Cocaine, opiates, MDMA, and amphetamines can be detected and are divided into two groups with different extraction procedures. Cocaine and opiates are extracted with methanol and purified on a solid phase, whereas amphetamines undergo hydrolysis, extraction with ethyl acetate, derivatization, and GC-MS analysis. Despite the absence of solid-phase extraction, this remains a complex process.

The first step was the preparation of the reference solution. Reference materials were prepared using the gravimetric method. As a matrix, a test solution intended to simulate human saliva was used. The same composition of synthetic saliva was applied in research on the influence of saliva on dental alloys [15]. This approach was beneficial for achieving more realistic conditions. Nevertheless, the stability of these reference materials was insufficient. Therefore, the reference solutions of drugs were prepared in distilled water to avoid potential interactions between the matrix and the drugs themselves. Each substance was prepared separately at a concentration equal to the detection limit. Certified reference materials with known concentrations were chosen as the starting point for preparation. Measurements were performed on the DDT 5000 with standard saliva collectors. Collectors for six substances were used, except for methadone and ketamine, for which collectors for eight substances were necessary.

Reference solutions were prepared by diluting purchased reference materials, which had a concentration of 1 mg of the given substance per 1 ml of solvent. To achieve very low concentrations, multiple dilutions were necessary, as in the case of THC. Sample dilutions were carried out exclusively in water, since organic solvents cannot be applied to the collectors.

The first measurement for all drugs was performed at the concentration corresponding to the detection limit defined by the manufacturer. There is only one detection limit for all substances except THC. Multiple detection limits are available for THC depending on the device settings (see Table 3).

The required amount of a given addictive substance is calculated based on the desired concentration and the required volume of the prepared solution, as shown in (1). (1) mi=c⊙⋅V⊙ {m_i} = {c_ \odot } \cdot {V_ \odot } where:

• m_i – mass of the substance i,

• c_⊙ – concentration of the desired solution,

• V_⊙ – volume of the desired solution.

The mass of the available standard of the given substance is calculated using (2). (2) mstd=micstd⋅ρstd {m_{{\rm{std}}}} = {{{m_i}} \over {{c_{{\rm{std}}}}}} \cdot {\rho _{{\rm{std}}}} where:

• m_std – mass of the starting standard,

• m_i – mass of the addictive substance,

• c_std – concentration of the starting standard,

• ρ_std – density of the starting standard.

The amount of solvent needed to prepare the desired volume of the solution can be calculated as the remainder of the total volume, as shown in (3). (3) Vroz=V⊙−Vstd {V_{{\rm{roz}}}} = {V_ \odot } - {V_{{\rm{std}}}} where:

• V_roz – volume of added solvent,

• V_⊙ – volume of the prepared solution,

• V_std – volume of the added starting standard.

A similar procedure is followed when preparing a multi-component solution containing several addictive substances. According to (1), the mass of each substance being tested is calculated. Based on this data, the mass of the standard for each substance is determined using (2). The amount of solvent required to achieve the desired final volume of the prepared solution is determined from (4). (4) Vroz=V⊙−∑i=1kVstdi {V_{{\rm{roz}}}} = {V_ \odot } - \sum\limits_{i = 1}^k {{V_{{\rm{st}}{{\rm{d}}_i}}}} where:

• V_roz – volume of added solvent,

• V_⊙ – volume of the prepared solution,

• V_stdi– volume of the added starting standard of substance i.

Water is always used as the added solvent. It is necessary to account for changes in its density depending on temperature. This can be calculated using (5) [16]. (5) ρwater=a51−(t+a1)2t+a2a3t+a4 {\rho _{{\rm{water}}}} = {a_5}\left[ {1 - {{{{(t + {a_1})}^2}\left( {t + {a_2}} \right)} \over {{a_3}\left( {t + {a_4}} \right)}}} \right]

Given the amount of solvent (water) and the original standard added, the effect of volume contraction is neglected. The final concentration of the prepared solution is calculated using (6). (6) ci=mi⋅ρwmsol {c_i} = {{{m_i} \cdot {\rho _{\rm{w}}}} \over {{m_{{\rm{sol}}}}}} where:

• c_i – concentration of substance i in the prepared solution,

• ρ_w – density of the added solvent (water),

• m_i – mass of added substance i,

• m_sol – mass of the prepared solution.

The uncertainty of the final concentration of the prepared solution is expressed as the expanded uncertainty U, with an expansion factor of 2, which ensures a 95 % probability that the value lies within this interval, assuming a normal distribution. Sources of uncertainty include the repeatability of weighing, the uncertainty of the input standard, characteristics of the balance, uncertainty in the molecular weight of the substances used, and uncertainty in the density of the solvents used.

The sample standard deviation represents the repeatability of the measurements and can be presented as a Type A uncertainty. The sample standard deviation is calculated using (7). (7) uA=s=1n⋅n−1∑xi−x¯2 {u_{\rm A}} = s = \sqrt {{1 \over {n \cdot \left( {n - 1} \right)}}\sum {{{\left( {{x_i} - \bar x} \right)}^2}} } where:

• s – sample standard deviation,

• u_A – Type A uncertainty,

• n – number of measurements,

• x_i – value of the measured quantity,

• x̄ – mean of the measured values.

Type B uncertainty includes the other described contributions.

The uncertainty of the balance is taken from the calibration certificate for the given balance. The calibration already accounts for eccentricity. Additionally, the drift of the balance, specified by the manufacturer as 0.2 mg, and the uncertainty due to the resolution of the balance are also included. The uncertainty arising from weighing is given by (8). (8) um=ucal2+udrift2+ures2 {u_m} = \sqrt {u_{{\rm{cal}}}^2 + u_{{\rm{drift}}}^2 + u_{{\rm{res}}}^2} where:

• u_cal – the uncertainty from the calibration sheet,

• u_drift – the uncertainty caused by drift,

• u_res – uncertainty caused by the resolution of the display.

The uncertainty stated in the calibration certificate is 0.13 mg for a mass of 1 g. The uncertainty arising from reading the balance display is given by (9). (9) ures=d3 {u_{{\rm{res}}}} = {d \over {\sqrt 3 }} where:

• d – the smallest value displayed.

The next contribution to Type B uncertainty comes from the uncertainty in the calculation of the water volume. The amount of added starting standard is negligible compared to the amount of added solvent. Therefore, the uncertainty associated with the density of water is considered. When using the given equation to calculate the density of water as a function of temperature, this contribution is equal to 9 × 10⁻⁷ g/ml [17].

Type B uncertainty u_B is calculated using (10). (10) uB=∂c∂mi2umi2+∂c∂msol2umsol2+∂c∂ρw2uρw2 {u_{\rm{B}}} = \sqrt {{{\left( {{{\partial c} \over {\partial {m_i}}}} \right)}^2}u_{{m_i}}^2 + {{\left( {{{\partial c} \over {\partial {m_{{\rm{sol}}}}}}} \right)}^2}u_{{m_{{\rm{sol}}}}}^2 + {{\left( {{{\partial c} \over {\partial {\rho _{\rm{w}}}}}} \right)}^2}u_{{\rho _{\rm{w}}}}^2}

The standard uncertainty u of the prepared solution is calculated using (11). (11) u=uA2+uB2 u = \sqrt {u_{\rm{A}}^2 + u_{\rm{B}}^2}

The expanded uncertainty U of the prepared solution is obtained by multiplying the standard uncertainty by the expansion factor corresponding to a 95 % probability for a normal distribution, as shown in (12). (12) U=2⋅u U = 2 \cdot u

The uncertainty is calculated for an amphetamine solution with a concentration of 97.6 ng/ml. First, the relative standard deviation is calculated based on the weighing of the primary standard and the solvent. The standard deviation is determined from repeated weighings using Excel software. This value represents a Type A uncertainty. The weighing is performed ten times. The Type A uncertainty values for the solvent (water), u_Amw and the primary standard, u_Ami, are as follows: uAmw=2.18⋅10−4 g uAmi=9.17⋅10−5 g \matrix{ {{u_{{\rm{A}}{m_{\rm{w}}}}} = 2.18 \cdot {{10}^{ - 4}}\;\;\;\left( {\rm{g}} \right)} \hfill \cr {\;{u_{{\rm{A}}{m_i}}} = 9.17 \cdot {{10}^{ - 5}}\;\;\;\left( {\rm{g}} \right)} \hfill \cr }

Type A uncertainty can also be expressed relatively, in percent, for later use. uArmw=4.35⋅10−5 % uArmi=2.36⋅10−1 % \matrix{ {{u_{{\rm{Ar}}{m_w}}} = 4.35 \cdot {{10}^{ - 5}}\;\;\;\left( \% \right)} \hfill \cr {\;{u_{{\rm{Ar}}{m_i}}} = 2.36 \cdot {{10}^{ - 1}}\;\;\;\left( \% \right)} \hfill \cr }

The first component of Type B uncertainty originates from the calibration and characteristics of the balance. The individual components are summarized in Table 4 for the starting standard and in Table 5 for the solvent (water).

In the following step, the derivations described (10) are carried out, resulting in (13). The calculated values of uncertainties and the corresponding sensitivity coefficients are presented in Table 6.

(13) uB=ρwmsol2umi2+miρwmsol22umsol2+mimsol2uρw2 {u_{\rm{B}}} = \sqrt {{{\left( {{{{\rho _{\rm{w}}}} \over {{m_{{\rm{sol}}}}}}} \right)}^2}u_{{m_i}}^2 + {{\left( {{{{m_i}{\rho _{\rm{w}}}} \over {m_{{\rm{sol}}}^2}}} \right)}^2}u_{{m_{{\rm{sol}}}}}^2 + {{\left( {{{{m_i}} \over {{m_{{\rm{sol}}}}}}} \right)}^2}u_{{\rho _{\rm{w}}}}^2}

The nearly identical values of u_B and u_Br are due to the prepared concentration of the reference material being close to 100 ng/ml.

Based on the above, the relative uncertainty u_rci can be calculated as shown in (14). The main contribution to the overall uncertainty is from Type A uncertainty, which results from the very small sample weights of the addictive substance. (14) urci=uArmi2+uBr2=0.24 % {u_{{\rm{r}}{c_i}}} = \sqrt {u_{Ar{m_i}}^2 + u_{{\rm{Br}}}^2} = 0.24\;\;\;\left( \% \right)

The standard uncertainty expressed in absolute terms and the corresponding expanded uncertainty with a coverage factor of k = 2 for a 95 % confidence level are as follows: uci=97.6⋅0.0024=0.24ng/mlUci=0.24⋅2=0.48ng/ml \matrix{ {{u_{{c_i}}} = 97.6 \cdot 0.0024 = 0.24} \hfill & {\left( {{\rm{ng}}/{\rm{ml}}} \right)} \hfill \cr {{U_{{c_i}}} = 0.24 \cdot 2 = 0.48} \hfill & {\left( {{\rm{ng}}/{\rm{ml}}} \right)} \hfill \cr }