Development of an HPLC–UV method for quantification of posaconazole in low-volume plasma samples: design of experiments and machine learning models

Abstract

Posaconazole (PCZ) is a triazole antifungal agent with a broad-spectrum activity. Our research aims to present a novel approach by combining a 2-level fractional factorial design and machine learning to optimize both chromatography and extraction experiments, allowing for the development of a rapid method with a low limit of quantification (LOQ) in low-volume plasma samples. The PCZ retention time at the optimized condition (organic phase 58%, methanol 6%, mobile pH = 7, column temperature: 39 °C, and flow rate of 1.2 mL/min) was found to be 8.2 ± 0.2 min, and the recovery of the PCZ at the optimized extraction condition (500 µL extraction solvent, NaCl 10% w/v, plasma pH = 11, extraction time = 10 min, and centrifuge time = 1 min) was calculated above 98%. The results of machine learning models were in line with the results of experimental design. Method validation was performed according to ICH guideline. The method was linear in the range of 50–2000 ng/mL and LOQ was found to be 50 ng/mL. Additionally, the validated method was applied to analyze PCZ nanomicelles and conduct pharmacokinetic studies on rats. Half-life (t_1/2), mean residence time (MRT), and the area under the drug concentration–time curve (AUC) were found to be 7.1 ± 0.6 h, 10.5 ± 0.9 h, and 1725.7 ± 44.1 ng × h/mL, respectively.

Graphical Abstract

Introduction

Posaconazole (PCZ) (Fig. 1) is a broad-spectrum triazole having antifungal activity against different pathogens including Candida, Aspergillus, Blastomyces, Coccidioides, Histoplasma species, Cryptococcus neoformans, and Zygomycetes [1]. This agent can be administered to treat fungal infections that are resistant to itraconazole or amphotericin B [2]. PCZ blocks ergosterol synthesis through inhibition of lanosterol 14-α-demethylase changing cell membrane integrity in fungi and consequently causing fungal cell death [1]. The Food and Drug Administration (FDA) first approved this agent as an oral suspension. However, due to the variable bioavailability of the suspension, two other formulations including delayed-release tablets and intravenous solutions have been developed. However, the tablets cannot be administered to individuals having dysphagia and the presence of sulfobutyl ether β-cyclodextrin as an excipient in the intravenous formulation can cause renal toxicity. Furthermore, these injections should not be administered to patients under 18 years [3, 4]. Thus, there is a need for the development of new formulations. To evaluate preclinical pharmacokinetics, PCZ concentrations should be analyzed in low volumes of plasma samples. PCZ is a multi-chiral center drug [1, 5]. Chirality and stereochemistry refer to the three-dimensional arrangement of atoms in a molecule, particularly concerning how this arrangement affects the molecule's biological activity [6]. It is important to note that since a single enantiomer of PCZ is used in pharmaceuticals [1, 5], achiral quantification of PCZ was considered in its pharmacokinetics.

Fig. 1

PCZ chemical structure

To date, various methods have been developed to determine the PCZ plasma concentrations, including high-performance liquid chromatography (HPLC) with either ultraviolet (UV) [7,8,9] or fluorescence detection [10, 11] and liquid chromatography with tandem mass spectrometry (LC–MS/MS) [12, 13], though fluorescence and LC–MS/MS instruments are not available in all labs [7, 11]. Therefore, in this study, UV was used as the detector. The HPLC–UV method has been used previously to quantify PCZ in plasma. However, several points should be considered in these studies (Table 1). Short analysis time is a prerequisite for pharmacokinetic studies due to the large number of samples involved [14, 15]. To analyze many samples within a reasonable timeframe, it is essential to conduct rapid analyses in pharmacokinetic assessments. In this context, a run time of 19 [16] or 36 [17] minutes is considered relatively lengthy for pharmacokinetic samples. Additionally, utilizing low-volume plasma samples is essential in preclinical studies, particularly when working with small animals. This approach enables more efficient sample collection and reduces the impact on the animals involved in the research. Given these considerations, the collection of large plasma volumes in pharmacokinetic studies that necessitate multiple blood samples could potentially pose a risk to the health of the rats [18]. In a study, 500 µL plasma samples were collected in dogs [9]. In other studies, 1000 µL human plasma [19] and 3000 µL koala blood samples [20] were used to develop the HPLC methods. These amounts are considered high in small animals.

Table 1 Summary of studies utilizing the HPLC–UV method to quantify PCZ in plasma and their probable challenges

Another important step in HPLC analysis is the pretreatment of a biological matrix to remove impurities and proteins [21]. In several studies of PCZ analysis, solid-phase extraction [22, 23] and protein precipitation [7, 9, 11, 23] were used for plasma sample preparation. However, these methods may have drawbacks such as being expensive or unclean [24,25,26]. Therefore, liquid–liquid extraction was applied in this study. There was one study that utilized the liquid–liquid extraction method [19], which offers a cleaner chromatogram compared to protein precipitation [24] and a reduced cost compared to solid-phase extraction [25, 26]. However, a limitation of the study was the requirement for a one-mL sample of plasma [19]. Moreover, employing minimal amounts of extraction solvent is essential considering environmental issues [27]. However, 5 mL dichloromethane-hexane-diethyl ether-n-amyl alcohol [19] and 6 mL diethyl ether [28] were utilized in studies on liquid–liquid extraction of PCZ. To provide a comprehensive understanding of the existing manuscript and to shed light on its advancements and challenges of previous studies, a literature review was conducted (Table 1). As evidenced by the studies presented in Table 1, no studies with the liquid-liquid extraction method have employed a low volume of plasma and achieved a limit of quantification (LOQ) of less than 100 ng/mL.

Different variables could affect retention time (RT) and peak resolution in chromatography. Chemometric approaches could determine these variables efficiently via a few experimental trials [21, 34]. In this study, a rapid HPLC–UV detection method was developed using small amounts of plasma, and the effect of five parameters (total organic phase%, methanol% (MeOH%) in organic phase, mobile pH, column temperature, and flow rate) was studied on the RT of PCZ and internal standard (IS) as well as peak resolution using fractional 2-level factorial design. Moreover, the volume of extraction solvent, the addition of salt, pH, extraction time, and centrifuge time might affect the recovery of either drug or IS in the liquid–liquid extraction method [21]. In this experiment, extraction conditions were also optimized with the aid of a chemometric approach. Optimization was further studied using machine learning models. An artificial neural network (ANN) was combined with a genetic algorithm (GA) to optimize both chromatographic and extraction experiments.

To evaluate the application of the developed method in the preclinical study, a novel nanosystem of PCZ (micelles) was prepared and the formulation was characterized regarding the percentage of entrapment efficiency (%EE) and particle size. This formulation was administered to rats intravenously. Blood samples were collected and PCZ concentration was quantified using the optimized sample preparation procedure and the HPLC conditions. Finally, the pharmacokinetic parameters were reported. To the best of our knowledge, PCZ micelles composed of DSPE-PEG have not been prepared previously.

This study introduces a novel approach in the field of HPLC analysis and method development by combining factorial design with ANN. A review of the literature has revealed limited research on the application of machine learning and the design of experiments in optimizing HPLC–UV methods. To the best of our knowledge, this study represents one of the pioneering instances where a combined approach of factorial design and ANN has been employed to optimize both chromatography and extraction conditions. The primary aim was to develop a rapid HPLC–UV method with a low LOQ to accurately quantify low amounts of PCZ in low-volume plasma samples. This is of particular importance due to the limited bioavailability of PCZ. Furthermore, the use of low-volume plasma samples is crucial in preclinical pharmacokinetic studies, particularly when working with small animals.

Materials and methods

Reagents and instruments

PCZ was obtained from BrightGene Co., Ltd. (China). Diazepam (as an IS) was supplied by Chemidarou Pharmaceutical Company (Tehran, Iran). 1,2-Distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy (polyethylene glycol)-2000] (DSPE-PEG) was purchased from Lipoid GmbH (Switzerland). Deionized water was prepared freshly, using a Millipore Direct-Q water purifying system. Acetonitrile (ACN; HPLC grade), MeOH (HPLC grade), n-hexane, tertiary butyl methyl ether (TBME), chloroform, ethyl acetate, dichloromethane, sodium chloride, sodium hydroxide, hydrochloric acid, and orthophosphoric acid were provided from Merck/Sigma-Aldrich (Germany).

Chromatographic experiments were performed using a Knauer HPLC system (Germany) equipped with a WellChrom K-1001 solvent delivery pump and an online degasser, a WellChrom K-2600 UV detector (λ = 262 nm; Knauer MZ, Germany), a column oven, and a 100 μL injection loop. PCZ was separated on a PerfectSil Target C8 column (250 × 4.6 mm i.d, 5 μm particle size, MZ-Analysentechnik GmbH, Germany).

Application of fractional 2-level factorial design for chromatographic experiment

Factors affecting the chromatography procedure were determined based on the preliminary studies. Effect of five independent variables, including the percentage of total organic phase (A) and MeOH (B) in the mobile phase, mobile pH (C), column temperature (D), and flow rate (E)) on the RT of PCZ and IS as well as the peak resolution was studied (Table 2). A combination of ACN and MeOH was used as an organic phase in the mobile phase. Orthophosphoric acid was used to adjust the pH. Parameters were evaluated and optimized using fractional 2-level factorial design (Design-Expert^® Statistical Software version 7, USA), constituted by 16 experimental runs and 4 center points. High and low levels were selected based on the preliminary studies. Experiments were carried out in random order. Significant factors were evaluated by analysis of variance (ANOVA) with a p-value < 0.05.

Table 2 Variables and their levels in the fractional factorial design of chromatographic and extraction experiments

Application of fractional 2-level factorial design for sample preparation

To evaluate the recovery of PCZ and IS in liquid–liquid extraction, preliminary studies were performed using various common extraction solvents, including TBME, n-hexane, ethyl acetate, chloroform, and dichloromethane. To 100 μL aliquots of spiked plasma, 25 μL IS (2 μg/mL) and 1500 μL extraction solvent were added. Samples were vortexed (10 min) and centrifuged (10 min at 12,000 rpm). The organic phase was then separated and evaporated under the nitrogen flow at room temperature. Following the addition of 140 μL of mobile phase, samples were vortexed (2 min), centrifuged (2 min at 12,000 rpm), and finally injected into the HPLC system. The selection of the extraction solvent for further investigation was based on the highest recovery of both PCZ and IS as well as obtaining a clean plasma. After performing preliminary studies, a 2^5–1 fractional factorial design generated by Design-Expert^® Statistical Software (version 7, USA) was employed to investigate the effect of the volume of extraction solvent (A´), plasma pH (B´), NaCl% (C´), extraction time (D´), and centrifuge time (E´) on the recovery of PCZ and IS (Table 2). Levels of each variable were selected based on the preliminary studies. Experimental runs were conducted in random order in triplicate. Statistical analysis of the variables' effects on the extraction procedure was performed using ANOVA with a p-value < 0.05.

Optimization of chromatographic and extraction experiments using fractional factorial design and desirability function

To optimize the chromatography and extraction experiments, a desirability function was used. The desirability function takes into account multiple factors simultaneously and provides a comprehensive evaluation of the solutions. The optimization process involved considering the ranges of the independent and dependent variables and selecting the suggested solution that is provided by the software with the highest desirability function [35].

Optimization of chromatographic and extraction experiments using machine learning model; ANN-GA hybrid modeling

To train the model a feed-forward with a back-propagation algorithm was used. The first step for designing an ANN is to select the number of hidden layers and neurons. To reach this objective, several architectures such as 2, 3, and 4 hidden layers were investigated. Mean squared error (MSE) was calculated. The architecture with the lowest MSE was chosen for further optimization. After the collection of data from factorial design experiments, normalization of data was done using the adjusted min–max method [36] as mentioned in the Supplementary data. The datasets obtained from the experiments were divided into 70% for training and 30% for validation and testing.

To validate the ANN model, statistical characteristics such as mean absolute error (MAE), MSE, and R-squared (R²) were calculated as described in the Supplementary data. To optimize the experiments, non-linear multi-response optimization (MRO) and ANN-GA hybrid models were used. Finally, the desirability function was used to predict optimal values for chromatographic and extraction experiments. For the development of the model, Python programming language was employed.

HPLC method validation

After optimizing chromatographic and extraction experiments, the best conditions were validated based on the International Council for Harmonization (ICH) guideline [37], regarding linearity, selectivity, accuracy, precision, LOQ, carry-over, and stability of quality control (QC) samples.

Selectivity

The selectivity was evaluated by analyzing the blank plasma samples of six individual rats. The influence of the existing interfering components on the RT of PCZ and IS was evaluated.

Linearity

Stock solutions were prepared (both PCZ and IS at the concentration of 1000 μg/mL) in MeOH. They were stored at −20 °C for further analysis. Working methanolic solutions (10 and 100 μg/mL) of PCZ and IS were also prepared freshly from the stock solutions. Appropriate amounts of PCZ were spiked to the blank plasma to prepare samples of calibration (0.05–2.00 μg/mL). The calibration curve was obtained by plotting PCZ concentration as a function of PCZ/IS peak area ratios. After linear regression, R² was calculated. This parameter shows how the data points fit the regression line and is known as a coefficient of determination.

Determination of LOQ

The LOQ was estimated at 10 times the baseline noise [38].

Precision and accuracy

The intra- and inter-day accuracy and precision were calculated by analyzing QC samples. Blank plasma samples were spiked with PCZ to prepare QC samples. PCZ concentrations of 0.05, 0.10, 0.75, and 1.50 μg/mL were chosen as QC samples. Each sample was analyzed in five replications for three days. The percentage of relative error (%RE) and coefficient of variation (%CV) were calculated as follows and considered as the accuracy and precision, respectively [39].

$$RE \left( \% \right) = \frac{Measured\, concentration - nominal\, concentration}{{Nominal\, concentration}} \times { }100$$

(1)

$$CV \left( \% \right) = \frac{Standard\, deviation\, at\, each\, concentration}{{Mean\, of\, the\, concentration}} \times { }100$$

(2)

Carry-over

Carry-over exhibits the residual of an analyte that remains in the instrument. Carry-over was evaluated by analyzing the blank plasma after the injection of the highest concentration of the calibration samples (2 μg/mL) into the HPLC system [37]. The areas of the peaks in the blank plasma were compared to the response of both the PCZ (at LOQ) and IS.

Stability of QC samples

The stability of QC samples was assessed in triplicate following the storage at room temperature (4 h) and at −20 °C (14 days). The stability after freeze–thaw cycles (three cycles at −20 °C and room temperature) was also evaluated. The area under the peaks of the freshly prepared and stored samples was calculated.

Robustness

The robustness of an analytical method refers to its ability to remain unaffected by variations in specific parameters that are intentionally changed within the defined limits [21]. In the case of the robustness assessment, the effect of the organic phase portion (58 ± 0.5% v/v), MeOH portion (6 ± 0.5% v/v), pH (7 ± 0.2), and column temperature (39 ± 0.5 °C) were studied on the PCZ RT, IS RT, and peak resolution.

Preparation and characterization of PCZ micelles

PCZ nanoformulations were obtained by a dry film method, as previously reported by Haeri et al. for sirolimus micelles [40]. Briefly, a methanolic solution of PCZ (1.5 mg/mL) was added to a chloroform solution containing DSPE-PEG (5 mM). A rotary evaporator was used to remove the organic solvents and consequently, a thin film layer was formed. Micelles were formed after adding normal saline to the prepared film followed by bath sonication. The free drug was then separated using a 0.22 μm syringe filter.

HPLC was employed for the assay of the drug loaded in the micelles. After the separation of the free drug, the nanoformulation was diluted 20 times with MeOH. Afterward, the sample was sonicated for 10 min to digest micelles and centrifuged. 100 μL of the diluted solution was injected into the HPLC system. %EE was calculated using Eq. 3 [40]:

$$EE \left( \% \right) = \frac{Amount\, of\, PCZ\, loaded\, into\, micelles}{{Initial\, amount\, of\, PCZ }} \times 100$$

(3)

Micelles were diluted 20 times with deionized water before measuring their particle size. The size distribution, average diameter, and polydispersity index (PDI) of micelles were measured by a Malvern Zetasizer Nano ZS (UK).

Application to preclinical pharmacokinetics of PCZ nanomicelles

Male Wistar rats weighing 220–250 g (obtained from the Pasteur Institute, Tehran, Iran) were housed under standard conditions. The quantity of nanoformulation given to the rats corresponds to the PCZ loaded in the nanomicelles and the dosage was based on the weight of each animal. A nanomicelle formulation was intravenously administered (1.5 mg PCZ/kg) via a tail vein. Blood samples were obtained from the tail vein and collected in heparinized tubes at specific time intervals (0, 0.25, 0.5, 0.75, 1, 2, 4, 6, 8, and 10 h) after the injection. Blood samples were immediately centrifuged for 10 min at 12,000 rpm, and 100 μL of the obtained plasma was stored at −20 °C until the HPLC assay. The drug was extracted from frozen plasma using the optimized preparation conditions. A non-compartmental method was used to calculate pharmacokinetic parameters, including half-life (t_1/2), mean residence time (MRT), and the area under the drug concentration–time curve (AUC). After pharmacokinetics studies, animals were euthanized by carbon dioxide inhalation. Death was confirmed by continuous exposure to CO₂ for at least 10 min after the animals’ apparent death. Animal studies were performed according to the protocol approved by the local Animal Ethics Committee of Shahid Beheshti University of Medical Sciences (approval No: IR.SBMU.PHARMACY.REC.1401.013).

Statistical analysis

The data were represented as mean ± standard error of the mean (SEM). T-test and ANOVA were used for comparisons and a p-value < 0.05 was considered statistically significant.

Results and discussion

In recent studies, the concept of chemometric strategies to optimize a chromatographic method has attracted much attention. The design of the experiment is considered a part of chemometric approaches which could screen and optimize various parameters [21, 41]. Traditional optimization of analytical methods (changing one factor at a time) requires a lot of experiments and is time-consuming [34, 42,43,44]. Moreover, the advantage of the design experiment approach is understanding the negative or positive effect of each factor on the desired response and the interactions between them [21, 45, 46]. Additionally, this approach ensures efficiency and consistency in method performance across various settings and facilitates a direct transfer of the method without requiring re-validation [47]. In the present research, a 2-level fractional factorial design (2^5–1) with a V resolution was employed to screen and optimize (along with the desirability function) the chromatography and sample preparation experiments. In fractional factorial designs with a resolution V, all main effects and two-factor interactions can be estimated if higher-order interactions are assumed to be unimportant [48,49,50]. Thus, in the present study, we investigated the effect of the main parameters and the two-factor interactions. Investigating the impact of each main parameter and two-factor interactions was studied in other research utilizing the 2-level factorial design [48, 51,52,53]. As an example, Nageeb et al. employed a 2^5–1 fractional factorial design with resolution V to optimize the factors affecting the characteristics of liposomes. The effect of preparation technique, hydration volume, sonication type, and cholesterol as well as the amount and molar ratio of phosphatidylcholine were studied on EE, zeta potential, and particle size. Additionally, the effect of two-factor interactions was investigated [48].

Nowadays, artificial intelligence along with chemometric approaches, has got much interest. ANN is a learning algorithm in the field of artificial intelligence with high accuracy [54, 55]. Considering this issue, we aimed to develop and optimize both chromatography and plasma preparation conditions using the combined approach of factorial design and ANN.

Chirality may play a significant role in the pharmacological properties and therapeutic effects of pharmaceutical compounds [56]. PCZ with four chiral centers (Fig. 1) has 16 potential stereoisomers. However, the pharmaceutical industry utilizes only the enantiomerically pure RRSS isomer of PCZ in pharmaceutical products [1, 5]. Accordingly, the present study aims to optimize chromatography conditions for the achiral quantification of PCZ in low-volume plasma samples.

Application of fractional 2-level factorial design for chromatographic experiment

Effect of five independent factors, including the total organic phase% (A), MeOH% (B), pH of the mobile phase (C), column temperature (D), and flow rate (E) on the RT of PCZ and IS as well as the resolution was investigated using a 2^5–1 fractional factorial design. Table 3 shows the suggested matrix of the chromatographic conditions and the corresponding responses. Based on the results, the RT of PCZ and IS ranged from a minimum of 7.9 min to a maximum of 31.8 min, and 8.3 min to 20.8 min, respectively. Moreover, the resolution ranged from 0.0 (PCZ and IS not separated) to 10.1. According to the ANOVA results (Table S1‒S3, Supplementary data), the models were significant for all responses with the F-value of 148, 221, and 481 for the RT of PCZ and IS and peak resolution, respectively (p < 0.001). The lack of fit was not statistically significant (p > 0.05), indicating that the model fits the actual response behavior. There was an agreement between the adjusted and predicted R² values, showing that the predicted responses may be close to the experimentally obtained responses (Table S4, Supplementary data). It should be noted that the model was simplified by removing non-significant factors (p > 0.05). To describe the variations of the dependent factors concerning independent factors, polynomial equations were exhibited in terms of coded factors as follows:

$$PCZ \, RT \, \left( {min} \right) \, = \, 15.9 \, - \, 4.2 \, A \, + \, 2.0 \, B \, + \, 1.3 \, C \, - \, 3.9 \, E \, - \, 1.1 \, AB \, - \, 0.8 \, AC \, + \, 0.9 \, AE \, + \, 0.7 \, BC$$

(4)

$$IS \, RT \, \left( {min} \right) \, = \, 13.4 \, - \, 1.9 \, A \, + \, 0.8 \, B \, - \, 0.3 \, D \, - \, 3.2 \, E \, - \, 0.4 \, AB \, - \, 0.2 \, AC \, + \, 0.3 \, AE \, - \, 0.3 \, BE$$

(5)

$$Resolution \, = \, 3.2 \, - \, 2.1 \, A \, + \, 1.4 \, B \, + \, 1.3 \, C \, + \, 0.2 \, D \, - \, 1.0 \, AB \, - \, 1.0 \, AC \, - \, 0.3 \, AD \, + \, 0.4 \, BC \, - \, 0.1 \, BD \, + \, 0.3 \, BE \, + \, 0.3 \, DE$$

(6)

Table 3 Matrix of the chromatographic and extraction conditions suggested by software and responses obtained experimentally for each run (mean ± SEM, n = 3)

Each equation showed both the influence of factors individually and their two-factor interactions on the mentioned responses.

Factors affecting PCZ RT

Figure 2a indicates a Pareto chart (reflecting the influence of each factor and interaction with other factors) with the Bonferroni and t-value limits. Factors above the Bonferroni limit are considered highly significant, whereas those between the two limits and under the t-value limit are considered significant and insignificant, respectively. Orange and blue colors are considered parameters with positive and negative effects on the response, respectively. According to Eq. 4 and the Pareto chart, it was observed that an increase in (A) and (E) variables and a decrease in (B) and (C) factors decreased the PCZ RT. To evaluate the combined effect of the interactions between the variables on the PCZ RT, three-dimensional surface response plots were constructed. Three-dimensional plots offer a more comprehensive visualization of the relationships compared to the equations and Pareto charts. This can make it easier for the audience to understand the complex relationships between variables. Some other studies also used three-dimensional surface response plots as part of a 2-level factorial design [57, 58].

Fig. 2

a Pareto chart and three-dimensional surface response plots of b total organic phase and methanol, c organic phase and mobile pH, d organic phase and flow rate, and e methanol and mobile pH on the PCZ RT, f Pareto chart and three-dimensional surface response plots of g total organic phase and methanol, h organic phase and mobile pH, i organic phase and flow rate, and j methanol and flow rate on the IS RT. A total organic phase, B methanol, C mobile pH, D column temperature, E flow rate, IS internal standard, PCZ posaconazole, RT retention time

These plots were obtained by changing two factors in the experimental range and keeping other factors constant at the center point (medium levels). When the MeOH-free mobile phase was used and the amount of the total organic phase increased to its highest level (60% v/v), the minimum RT of PCZ was achieved (Fig. 2b). By keeping the total organic phase constant at a high level (60% v/v), the minimum RT of PCZ was obtained at a low level of pH (Fig. 2c) and a high level of flow rate (Fig. 2d). Moreover, low levels of both MeOH and pH led to a minimum RT of PCZ (Fig. 2e).

It has been reported that a change in the pH of the mobile phase could alter the RT of components. Compounds in their unionized form exhibited longer RTs. Thus, by modifying the ionization of components using a different pH of the mobile phase, shorter RT could be achieved [59]. Santana et al. studied the influence of the pH of the mobile phase on the PCZ RT. They demonstrated that among the three pH values of 2.5, 3.5, and 4.5, the lowest RT was achieved at a pH of 3.5 [8]. In this article, the influence of a wider range of pH was studied on the PCZ RT. Based on Eq. 4, increasing pH from 3 to 7 led to an increment in the PCZ RT.

Factors affecting IS RT

Regarding Eq. 5 and the Pareto chart (Fig. 2f), increasing flow rate (E), total organic phase (A), and column temperature (D) decreased the IS RT, while increasing MeOH (B) increased the IS RT. As shown in Fig. 2g, the minimum IS RT was obtained at high and low levels of the total organic phase and MeOH, respectively. Figure 2h demonstrated that at neutral mobile pH, low levels of total organic phase (52%) contribute to an RT of 15.6 min for IS. At high levels of both total organic phase and flow rate, the minimum IS RT was achieved (Fig. 2i). By maintaining MeOH at high levels and decreasing the flow rate to the lowest level, the IS RT was increased to 16.6 min (Fig. 2j).

Factors affecting peak resolution

Based on Eq. 6 and the Pareto chart (Fig. 3a), total organic phase (A) was the most significant factor that affected the resolution negatively, while MeOH (B), mobile pH (C), and column temperature (D) had positive influences on the resolution. High levels of the total organic phase with low levels of MeOH (Fig. 3b) and pH = 3 (Fig. 3c) led to a low resolution. At a high level of the total organic phase, changing column temperature from high level to low level did not affect resolution (Fig. 3d). According to Figs. 3e-g, keeping MeOH at a low level, mobile pH at 3, column at room temperature, and a flow rate of 0.7 mL/min resulted in a low resolution. At the flow rate of 1.0 mL/min, by increasing the column temperature from 25 to 40 °C, an increment in resolution was observed (Fig. 3h). According to the results, variations in the column temperature affected the resolution, probably due to the changes in peak shapes. Since increasing temperature did not affect the PCZ RT, the high resolution might be a result of narrowing the width of peaks. It has been reported that the elevated column temperature could result in narrower and more symmetrical peaks in proteins [60]. On the contrary, it was reported that by increasing column temperature, the resolution between colistimethate sodium forms was reduced probably due to a reduction in the viscosity of the mobile phase [61]. Our data supported an increased resolution at a higher temperature.

Fig. 3

a Pareto chart and three-dimensional surface response plots of b total organic phase and methanol, c organic phase and mobile pH, d organic phase and column temperature, e methanol and mobile pH, f methanol and column temperature, g methanol and flow rate, and h column temperature and flow rate on resolution. A total organic phase, B methanol, C mobile pH, D column temperature, E flow rate

A mixture of ACN-MeOH (49:8, % v/v) was previously used as an organic phase to quantify PCZ in human plasma. The mobile phase consisted of an organic phase-phosphate buffer (pH 6.7) (57:43, % v/v). However, the effect of the total organic phase and MeOH proportion in the mobile phase on PCZ responses was not studied [22]. In this study, based on the data depicted in Fig. 3, adding MeOH into the mobile phase enhanced chromatographic resolution between PCZ and IS peaks. Thus, a combination of ACN and MeOH was chosen as the organic phase leading to a reasonable resolution. Gikas and coworkers developed and optimized an HPLC method to quantify colistimethate sodium in the injectable products. They reported that using ACN alone contributed to a low resolution between the chromatographic peaks and a combination of ACN and MeOH as the organic modifiers of the mobile phase resulted in both accepted resolution and shape (considering asymmetry) due to the affinity of the analyte for the organic solvent [61].

Optimization of chromatographic conditions

To optimize chromatographic conditions, ranges of the independent and dependent variables were set according to Table S5 (supplementary data). Based on Eqs. 4–6, the optimized condition (58% v/v total organic phase, 6% v/v MeOH, neutral pH, column temperature of 39 °C, and flow rate of 1.2 mL/min) was suggested by the software according to the higher desirability function (0.926). By a similar approach, Abd-AlGhafar et al. employed a 2-level full factorial design, along with the desirability function, to optimize the tailing factor and the peak resolution between azelastine and cetirizine. The design considered the flow rate, mobile pH, and ACN percentage in the mobile phase as independent variables [62].

After investigating the proposed optimized condition, statistical analysis using a t-test showed there was no difference between predicted and observed responses at this chromatographic condition (P > 0.05) indicating that the model had great potential to predict data (Table S5, supplementary data).

Figure 4a exhibited the PCZ RT (1 μg/mL) and IS (0.5 μg/mL) following optimized chromatography conditions. As illustrated, PCZ and IS were efficiently separated and no significant interfering peak was seen at the RT of both PCZ and IS.

Fig. 4

a Chromatograms of IS (0.5 μg/mL) and PCZ (1 μg/mL) in methanol, determination of the LOQ of PCZ in plasma, and 6 individual blank plasma samples, b Stability study results obtained for PCZ samples (mean ± SEM, n = 3), c The mean plasma concentration–time profile of PCZ-loaded nanomicelles in rats (mean ± SEM, n = 3). IS internal standard, LOQ limit of quantification, PCZ posaconazole

Application of fractional 2-level factorial design for sample preparation

In most studies, protein precipitation has been used as a method of plasma sample preparation [7, 9, 20, 30, 33]. In this method, the plasma matrix may remain dirty and malfunction of the chromatographic column is probable due to the presence of some proteins and endogens [24, 63]. However, the liquid–liquid extraction method is simple and leads to a cleaner plasma. As a result, liquid–liquid extraction was used for sample preparation in this study. Different extraction solvents were investigated in preliminary studies. Based on a preliminary study, TBME was chosen as the extraction solvent (Table S6, supplementary data). This solvent resulted in obtaining a cleaner plasma matrix compared to other solvents. Also, the recovery of PCZ was higher in this solvent. As mentioned earlier, a 2^5–1 fractional factorial design was implemented to evaluate the influence of five variables (Table 2) on the PCZ and IS recovery. Data demonstrated that PCZ and IS recovery ranged from 30.3% to 101.1% and 44.9% to 80.9%, respectively (Table 3). Statistical analysis with ANOVA indicated that the model was significant (p < 0.0001) for both PCZ and IS recovery (with F-values of 57 and 16, respectively) and a lack of fit was not significant (p > 0.05) for both responses. The difference between adjusted and predicted R² indicated a great agreement between the predicted and experimentally obtained results (Table S7-S9, supplementary data).

The equations relating the responses to the investigated variables were proposed as follows:

$$PCZ \, recovery \, \left( \% \right) \, = \, 70.3 \, + \, 2.3 \, A + \, 17.2 \, B - \, 6.1 \, C - \, 6.4 \, AB - \, 4.5 \, AC + \, 3.8 \, AD + \, 4.4 \, AE + \, 5.8 \, BC + \, 2.5 \, CD - \, 3.6 \, DE$$

(7)

$$IS \, recovery \, \left( \% \right) \, = \, 60.9 \, + \, 2.5 \, A + \, 2.1 \, B + \, 2.5 \, C + \, 2.0 \, D - \, 3.8 \, AC + \, 2.8 \, AE + \, 4.6 \, CD - \, 1.7 \, DE$$

(8)

Factors affecting PCZ recovery

Regarding the Pareto graph (Fig. 5a) and Eq. 7, the plasma pH (B´) and the volume of extraction solvent (A´) positively influenced the PCZ recovery and there was a negative correlation between the amount of salt (C´) and the mentioned response. Based on a three-dimensional plot (Fig. 5b), by keeping pH at 11, changing the volume of extraction solvent from 500 to 1500 μL had little effect on PCZ recovery. Setting salt concentration to the lowest level and volume of extraction solvent to the highest level led to an increment in PCZ recovery (Fig. 5c). Maintaining both the volume of extraction solvent and the extraction time at high levels contributed to a higher response (Fig. 5d). At the low level of centrifuge time, changing the volume of extraction solvent slightly altered the recovery (Fig. 5e). Figure 5f illustrated that at plasma pH 11, increasing salt concentration from 0 to 10% w/v did not affect the mentioned response. Keeping both salt concentration and extraction time at low levels resulted in high PCZ recovery (Fig. 5g). According to Fig. 5h, at the constant level of centrifuge time (1 min), increasing extraction time from 1 to 10 min resulted in a slight increment in the response.

Fig. 5

a Pareto chart and three-dimensional surface response plots of b volume of extraction solvent and plasma pH, c volume of extraction solvent and NaCl, d volume of extraction solvent and extraction time, e volume of extraction solvent and centrifuge time, f plasma pH and NaCl, g NaCl and extraction time, and (h) extraction and centrifuge time on PCZ recovery. i Pareto chart and three-dimensional surface response plots of j volume of extraction solvent and NaCl, k volume of extraction solvent and centrifuge time, l NaCl and extraction time, and m extraction and centrifuge time on IS recovery A: volume of extraction solvent; B: plasma pH; C: NaCl; D: extraction time; E: centrifuge time; IS internal standard, PCZ posaconazole

It has been reported that components in their unionized forms are better extracted from the plasma than their ionized forms [64]. In a study, to extract PCZ from plasma, sodium hydroxide (0.1 M) was added [65]. On the other hand, in another study, sodium carbonate (1.0 M) was added to the serum sample [19]. However, the effect of adding either acid or base to the plasma on PCZ recovery was not investigated in these studies [19, 65]. In the present work, the effect of plasma pH on the drug recovery was investigated and the extraction condition was optimized. Based on the results, a pH of 11 resulted in a high recovery of PCZ. Studies using the liquid–liquid extraction method either used a mixture of extraction solvents or high plasma volumes. Mistretta and coworkers, analyzed seven azole antifungals using a mixture of diethyl ether-hexane-n-amyl alcohol-dichloromethane as an extraction solvent [19]. In another study 3 mL of methylene chloride-hexane (3:7, v/v) was used as an extraction solvent [66]. Kahle et. al prepared plasma samples using 500 μL plasma and diethyl ether as an extraction solvent. Albeit, to reach a high and reasonable PCZ recovery, extraction was performed in two steps [65]. In the present study, a single-step, single-solvent (TBME) extraction, and a smaller amount of plasma was used.

Factors affecting IS recovery

Equation 8 and the Pareto chart (Fig. 5i) indicated that all independent variables had a positive correlation with IS recovery. The influence of salt concentration on IS recovery was probably due to the salting-out effect and a mass transfer of components toward the organic phase. Therefore, increasing salt concentration could increase the recovery of the components from plasma samples [67]. The combined effects of variables on IS recovery are illustrated in Figs. 5j-m. Increasing the volume of extraction solvent from 500 to 1500 μL in the absence of salt resulted in an increment in the response (Fig. 5j). Based on Fig. 5k, by increasing the volume of extraction solvent at the low level of centrifuge time, recovery did not change. High IS recovery was obtained at both high levels of salt concentration and extraction time (Fig. 5l). It was observed that increasing extraction time at the lowest level of centrifuge time had little influence on the response (Fig. 5m).

Optimization of sample preparation

Considering Eqs. 7 and 8 as well as the ranges of the independent and dependent variables (Table S10, supplementary data), run 15´ was suggested by the software as the optimized extraction condition (Table 3). To evaluate the model, blank plasma samples were spiked with appropriate amounts of PCZ (to obtain concentrations of 0.5, 1, and 1.5 μg/mL) and IS (final concentration of 0.5 μg/mL). Observed responses were compared to the predicted ones for each concentration and no significant difference was found between the two values (p > 0.05) (Table S10, supplementary data).

Optimization of chromatographic and extraction experiments using artificial intelligence model; ANN-GA hybrid modeling

ANN is comprised of neurons that are connected by weights that form a stochastic-weighted relationship between inputs and outputs. ANNs are multilayered systems consisting of input, hidden, and output layers. A stochastic weight causes the cease of the algorithm in local extrema and reduces the training process [55, 68]. In advanced calculus and optimization, removing the local extrema from ANNs needs heuristic techniques. The GA is a stochastic optimization and a population-based search algorithm that works using a string coding of variables [69].

Several hidden layers and neurons were investigated and two hidden layer architectures with seven neurons were adopted because of the lower MSE than others. The summary of ANN model specification is presented in Fig. 6a. The schematics of ANNs for chromatographic and extraction experiments are illustrated in Fig. 6b and c, respectively. The performance of ANN was evaluated by MSE, MAE, and R² for both chromatographic and extraction experiments (Tables S11 and S12). Figure 6b and c demonstrated R² plots for comparison between actual and predicted values.

Fig. 6

a Summary of ANN model specification, b Schematic of ANN architecture for chromatographic conditions where ${x}_{1}$, ${x}_{2}$, ${x}_{3}$,${x}_{4}$, and ${x}_{5}$ variables are respectively $A$, $B$, $C$, $D$, and $E$ factors (input variables) and ${y}_{1}$, ${y}_{2}$, and ${y}_{3}$ variables are respectively RT of PCZ and IS and resolution (response variables), and R² plots for comparison between actual and predicted values of PCZ RT, IS RT, and peak resolution, c Schematic of ANN architecture for extraction conditions where ${x}_{1}$, ${x}_{2}$, ${x}_{3}$,${x}_{4}$, and ${x}_{5}$ variables are respectively $A$´, $B$´, $C$´, $D$´, and $E$´ factors (input variables) and ${y}_{1}$ and ${y}_{2}$ variables are respectively PCZ and IS recovery (response variables), and R² plots for comparison between actual and predicted values of PCZ and IS recovery. ANN artificial neural network, IS internal standard, PCZ posaconazole, RT retention time

The conflict among the responses could be resolved using MRO when there are non-linear relationships. Dimension reduction is an effective approach in MRO [70]. The desirability function as a dimension reduction approach has been used to optimize multiple-response problems. The desirability function comprises various preference parameters that reflect the decision maker's preferences [70]. As a novelty in the optimization technique, the generalized desirability function was used. This function was manipulated for more compatibility with ANN prediction results.

The general form of the desirability function is formulated as follows [70]:

$$D = (d_{1} \left( {\hat{y}_{1} \left( x \right)} \right) \times d_{2} \left( {\hat{y}_{2} \left( x \right)} \right) \times ... \times d_{k} \left( {\hat{y}_{k} \left( x \right)} \right))^{\frac{1}{k}}$$

(9)

Based on the nature of the responses to be optimized, the desirability function can be classified into one-sided and two-sided transformations. One-sided transformations include the larger-the-better (LTB) type, used for maximizing objectives, and the smaller-the-better (STB) type, used for minimizing objectives. Nominal-the-best (NTB) represents a two-sided transformation [70, 71]. These transformations were calculated as follows:

LTB type response:

$$d_{i} (\hat{y}_{i} (x)) = \left\{ \begin{gathered} 0,\mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{\mathop {\mathop {}\nolimits_{{}} }\nolimits_{{}} }} \mathop {}\nolimits_{{}} \hat{y}_{i} (x) \le y_{i}^{\min } \hfill \\ \left( {\frac{{\hat{y}_{i} (x) - y_{i}^{\min } }}{{y_{i}^{\max } - y_{i}^{\min } }}} \right)^{{r_{i} }} ,y_{i}^{\min } \le \hat{y}_{i} (x) \le y_{i}^{\max } ,r_{i} \ge 0\mathop {}\nolimits_{{}} i = 1,2,...,k \hfill \\ \hfill \\ 1,\mathop {}\nolimits_{{\mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} }} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{\mathop {}\nolimits_{{}} }} \mathop {}\nolimits_{{}} \hat{y}_{i} (x) \ge y_{i}^{\max } \hfill \\ \end{gathered} \right\}$$

(10)

STB type response:

$$d_{i} (\hat{y}_{i} (x)) = \left\{ \begin{gathered} 1,\mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{\mathop {\mathop {}\nolimits_{{}} }\nolimits_{{}} }} \hat{y}_{i} (x) \le y_{i}^{\min } \hfill \\ \left( {\frac{{\hat{y}_{i} (x) - y_{i}^{\max } }}{{y_{i}^{\min } - y_{i}^{\max } }}} \right)^{{r_{i} }} ,y_{i}^{\min } \le \hat{y}_{i} (x) \le y_{i}^{\max } ,r_{i} \ge 0\mathop {}\nolimits_{{}} i = 1,2,...,k \hfill \\ \hfill \\ 0,\mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{\mathop {}\nolimits_{{}} }} \hat{y}_{i} (x) \ge y_{i}^{\max } \hfill \\ \end{gathered} \right\}$$

(11)

NTB type response:

$$d_{i} (\hat{y}_{i} (x)) = \left\{ \begin{gathered} \left( {\frac{{\hat{y}_{i} (x) - y_{i}^{\min } }}{{T_{i} - y_{i}^{\min } }}} \right)^{{s_{i} }} ,y_{i}^{\min } \le \hat{y}_{i} (x) \le T_{i} ,s_{i} \ge 0\mathop {}\nolimits_{{\phantom{a}}} i = 1,2,...,k \hfill \\ \left( {\frac{{\hat{y}_{i} (x) - y_{i}^{\max } }}{{T_{i} - y_{i}^{\max } }}} \right)^{{t_{i} }} ,T_{i} \le \hat{y}_{i} (x) \le y_{\max } ,t_{i} \ge 0\mathop {}\nolimits_{{\phantom{a}}} i = 1,2,...,k \hfill \\ \hfill \\ 0,\mathop {}\nolimits_{{\mathop {}\nolimits_{{}} }} \mathop {}\nolimits_{{\mathop {\mathop {}\nolimits_{{\mathop {}\nolimits_{{}} }} }\nolimits_{{}} \mathop {}\nolimits_{{}} \mathop {}\nolimits_{{}} }} \mathop {}\nolimits_{{}} \hat{y}_{i} \le y_{i}^{\min } \mathop {\phantom{a}}\limits_{{\phantom{a}}} or\mathop {\phantom{a}}\limits_{{\phantom{a}}} \hat{y}_{i} \ge y_{i}^{\max } \hfill \\ \end{gathered} \right\}$$

(12)

where ${y}_{i}^{min}$ and ${y}_{i}^{max}$ are the minimum and maximum feasible values for ${\widehat{y}}_{i}(x)$, respectively and the parameter ${T}_{i}$ is the target value. In this paper, ${T}_{i}$ was imported from the predicted values by the ANN-GA model and finally, the set $\left\{{r}_{i},{s}_{i},{t}_{i}\right\}$ shows the shape of the desirability function.

There are some approaches for formulating the desirability function. For the composite function, Harrington aggregated the individual desirability functions ${d}_{i}({\widehat{y}}_{i}(x))$ into a geometric mean while Derringer and Suich aggregated ${d}_{i}({\widehat{y}}_{i}(x))$ into a weighted geometric mean [71]. Both of these aggregated approaches are formulated as below:

$${\text{Geometric mean approach}}:{ }D\left( y \right) = \left[ {\mathop \prod \limits_{i = 1}^{k} d_{i} \left( {\hat{y}_{i} } \right)} \right]^{{\frac{1}{{k }}}}$$

(13)

$${\text{Weighted geometric mean approach}}:{ }D\left( y \right) = \left[ {\mathop \prod \limits_{i = 1}^{k} d_{i} \left( {\hat{y}_{i} } \right)^{w_{i}}} \right]^{{\frac{1}{{\mathop \sum \nolimits_{i = 1} w_{i} }}}}$$

(14)

Derringer and Suich suggested that the weighted geometric mean approach should be used when at least one response has greater importance than the others [71]. Since in this study, all of the responses have equal values, Harrington’s approach was used for the optimization. The optimization process using the desirability function approach for response variables based on ANN-GA predicted values was calculated in Excel Solver. Finally, the optimal values for the input variables were obtained as follows:

Optimal values for the optimization of chromatographic conditions:

$${x}_{1}^{*}=58\%\, v/v,{x}_{2}^{*}=6\%\, v/v,{x}_{3}^{*}=7,{x}_{4}^{*}=39^\circ C,\text{and }{x}_{5}^{*}=1.2 mL/min$$

where x₁, x₂, x₃, x₄, and x₅ are the total organic phase%, MeOH%, mobile pH, column temperature, and flow rate, respectively.

Optimal values for the optimization of extraction conditions:

$${x}_{1}^{*}=500\, \mu L,{x}_{2}^{*}=11,{x}_{3}^{*}=10\%\, w/v,{x}_{4}^{*}=10 min,\text{and }{x}_{5}^{*}=1\, min$$

where x₁, x₂, x₃, x₄, and x₅ are the volume of the extraction solvent, plasma pH, NaCl%, extraction time, and centrifuge time, respectively.

Results obtained from ANN-GA models for both chromatographic and extraction conditions are in line with the results obtained from fractional factorial designs.

HPLC method validation

The calibration curve was linear in the range of 0.05–2.00 μg/mL with R² = 0.992, a y-intercept of 0.050, and a slope of 3.12. %RE and %CV were less than 20% at LOQ and ≤ 15% in other calibration concentrations. LOQ was found to be 0.050 μg/mL (Fig. 4a). Method validation requires the preparation of at least four different concentrations for QC samples. Each concentration level should have an overall precision and accuracy within ± 15% of the nominal concentration. However, the criteria for the LOQ is ± 20% [37]. Intra- and inter-day precision and accuracy are summarized in Table S13. The intra- and inter-day %RE were found to be in the range of −8.9% to 7.1% and −6.5% to −2.0%, respectively. %CV ranged from 1.5% to 10.4% and 1.5% to 14.0% for intra- and inter-day analysis, respectively. The obtained results were in line with the criteria. In accordance with the ICH guideline, the assessment of selectivity was conducted to determine if any noteworthy interferences were present at the RT of PCZ and IS in the blank rat plasma samples. To meet the guideline's criteria, responses from interfering components should not exceed 20% and 5% of the analyte and IS responses, respectively, in the LOQ sample [37]. Based on the obtained data, no significant interferences were observed at the PCZ RT in the blank rat plasma samples (Fig. 4a) and data met the specified criteria. Carry-over was 0.0 and 3.8 at the RT of PCZ and IS, respectively. The criteria for carry-over are similar to the criteria for selectivity. The results met the ICH criteria [37]. QC samples were stable following storage at 25 and -20 °C for 4 h and 14 days, respectively, and no degradation was seen after three freeze–thaw cycles (Fig. 4b). The robustness of the optimized chromatographic condition was assessed using Eqs. 4–6. The evaluation was conducted by making intentional modifications to the method parameters to assess their influence on the results. These parameters included organic phase (58 ± 0.5% v/v), MeOH (6 ± 0.5% v/v), mobile pH (7 ± 0.2), and column temperature (39 ± 0.5 °C). The observed variations in the HPLC approach (as shown in Table S14) did not have a significant impact on its performance, thereby indicating its robustness.

Characterization of PCZ micelles

After developing and optimizing an HPLC method, PCZ-loaded nanomicelles were prepared. Micelles are nanoformulations consisting of core–shell structures with almost a size range of 10–200 nm that could entrap hydrophobic drugs. The improved drug exposure, controlled drug release profile, and improved activity of antifungal agents are some of the advantages of micelles. These nanoformulations could be administered for antifungal purposes in various routes such as buccal, dermal, ocular, and intravenous [72]. PCZ micelles exhibited an EE of 52% with a z-average of 40.1 ± 3.1 nm and a PDI of 0.18 ± 0.02 that suggested nearly all particles were relatively uniform in size.

Application to pharmacokinetics in rats

In the present study, nanoformulation was administered to rats, blood samples were collected at specific time intervals and plasma samples were prepared. PCZ was extracted from plasma and the obtained sample was injected into the HPLC system. In this study, rapid analysis of low-volume plasma samples was highlighted and the pharmacokinetics of PCZ-loaded micelles were evaluated. The concentration–time curve obtained for plasma samples of PCZ after intravenous administration of micelles is given in Fig. 4c. Based on the results, t_1/2, AUC, and MRT were found to be 7.1 ± 0.6 h, 1726 ± 44 ng × h/mL, and 10.5 ± 0.9 h, respectively.

Conclusion

In the current study, an HPLC method using a UV detector was developed and optimized to quantify PCZ plasma concentrations. Optimization was studied in two phases of chromatography and plasma preparation conditions. In each phase, the effect of five parameters on the desired responses was studied using the design of the experiment approach (a fractional 2-level factorial design). The optimized model exhibited great potential in the prediction of HPLC data. ANN was also employed for further optimization. Results obtained from ANN were in agreement with the experimental data. Based on the data, the total organic phase%, flow rate, and MeOH% in the mobile phase were the three main factors affecting PCZ RT. Moreover, PCZ recovery was influenced mainly by the plasma pH, the addition of salt, and the volume of extraction solvent. The present method can be considered a rapid method using low volumes of plasma samples in preclinical studies. Further improvements should be made in terms of reducing the amount of mobile phase used, employing bio-based organic solutions, minimizing waste [73, 74], miniaturization of the method, and replacement of toxic chemicals with greener alternatives [75]. These aspects should be considered in future studies to address the concern of method greenness.