In vitro-in vivo Pharmacokinetic correlation model for quality assurance of antiretroviral drugs.

INTRODUCTION
The in vitro-in vivo pharmacokinetic correlation models (IVIVC) are a fundamental part of the drug discovery and development process. The ability to accurately predict the in vivo pharmacokinetic profile of a drug based on in vitro observations can have several applications during a successful development process.


OBJECTIVE
To develop a comprehensive model to predict the in vivo absorption of antiretroviral drugs based on permeability studies, in vitro and in vivo solubility and demonstrate its correlation with the pharmacokinetic profile in humans.


METHODS
Analytical tools to test the biopharmaceutical properties of stavudine, lamivudine y zidovudine were developed. The kinetics of dissolution, permeability in caco-2 cells and pharmacokinetics of absorption in rabbits and healthy volunteers were evaluated.


RESULTS
The cumulative areas under the curve (AUC) obtained in the permeability study with Caco-2 cells, the dissolution study and the pharmacokinetics in rabbits correlated with the cumulative AUC values in humans. These results demonstrated a direct relation between in vitro data and absorption, both in humans and in the in vivo model.


CONCLUSIONS
The analytical methods and procedures applied to the development of an IVIVC model showed a strong correlation among themselves. These IVIVC models are proposed as alternative and cost/effective methods to evaluate the biopharmaceutical properties that determine the bioavailability of a drug and their application includes the development process, quality assurance, bioequivalence studies and pharmacosurveillance.


Introduction
The in vitro-in vivo pharmacokinetic correlation models (IVIVC) are a fundamental part of the drug discovery and development process. These models can accurately predict the in vivo behavior of drugs based on in vitro observations, and their applications include: pharmacokinetic properties testing, quality assurance, pharmacosurveillance and quality control during the development and scale up of a formulation. Correlation is defined, according to the United States Food and Drug Administration (FDA), as "a predictive mathematical model describing the relationship between an in vitro property of a dosage form and an in vivo response". The property of solid dosage forms most commonly applied for in vitro development and quality control tests is the rate of dissolution of the drug and it is usually correlated with the concentration or amount of drug absorbed that reach the plasma circulation at certain time 1 . Therefore, an IVIVC model based on dissolution tests allows to predict the in vivo behavior of some drugs.
Even though the correlation between in vitro dissolution and in vivo absorption has been recognized, no many comprehensive models that include complementary properties to improve the predictive capacity have been developed. Comprehensive models are required taking into account the physical, chemical and biological factors involve in the dissolution and absorption of drugs. The physicochemical and biopharmaceutical properties of the drug and the physiology of the routes of absorption have to be taken into consideration.
The solubility is determined by factors like the percentage of ionized drug, which determines different properties of the compounds, depending on the pH at the site of dissolution. This is very relevant because the human body displays pH gradients, especially in the gastrointestinal tract (GI), this pH gradient leads to differences in the absorption profile depending on the in vivo pH 2 .
The goal of this study was to develop a comprehensive model to predict the in vivo pharmacokinetic behavior of antiretroviral drugs at the absorption phase, based on in vitro permeability and solubility measurements. The rationale behind this study is set in the current context where advances in the pharmaceutical sciences, the pharmaceutical industry and the government health agencies have consolidated the quality assessment of pharmaceutical products by in vivo bioavailability studies in humans. However, the financial and ethical implications of these studies require the development of alternatives that can substitute the use of humans. These alternatives should consider the physicochemical properties and permeability of the molecules, according to the Biopharmaceutics Classification System (BCS) 3 .

Dissolution
The kinetics of in vitro dissolution were performed following the specifications of the United States Pharmacopeia, using the dissolution apparatus 2 (Pharma Aliance Group, Model TDT-08L). The rotation was set at 50 rpm, the dissolution media was degassed water at a final volume of 900 mL and a temperature of 37° C ± 0.5. Samples were taken at 10, 20, 30, 45 y 60 min.
Caco-2 cells culture Caco-2 cells (HTB-37) were obtained from the American Type Culture Collection (ATCC). Cells were used between 30 and 50 passes in high glucose (4.5 g/L) DMEM media supplemented with L-Glutamine, 10% fetal bovine serum, 1% nonessential amino acids and 1% penicillin/streptomycin. For the permeability test, 6x10 4 cells/cm 2 were seeded in transwell supports with polycarbonate membrane (0.4 µm, 1.12 cm 2 ; Corning Costar). The integrity of the monolayers was tested by measuring the Transepithelial Electrical Resistance (TEER) before and after every experiment. Only monolayers with TEER higher than 200 Ω/cm 2 were used.
The apparent permeability coefficient (Papp) was determined from the amount of drug transported per unit of time and was calculated using the following equation: Where (ΔQ/Δt) is the accumulated concentration in the recipient compartment (µmol/sec) versus the change in time, A is the surface area of the support (cm 2 ) and C 0 is the initial concentration in the donor compartment (µM). The integrity of the system was evaluated using the permeability coefficient (P). The apparent permeability coefficient (Papp) is associated with the permeability coefficient.
Pharmacokinetics in animals All protocols and procedures were reviewed and approved by CIDEIM Institutional Review Board for research involving animals, in accordance with national and international guidelines for utmost respect and care of animals, recognizing their intrinsic value as living species, as well as deep reflection on the possibilities of replacement, reduction and refinement of techniques and procedures [4][5][6] . In every pharmacokinetic study 10 New Zeeland rabbits were included per group, their weights were between 2.5-3.2 kg. Rabbits were kept at the animal facility under all standard conditions for the handling (20-25° C; 30-70% relative humidity, natural cycle of light/dark), with access to water and food ad libitum up to 2 hours before the study and one hour after the administration of the drug as an oral aqueous suspension. Each group received a single dose of stavudine 8.9 mg/kg, lamivudine 20.8 mg/kg or zidovudine 41.7 mg/kg. Two milliliters blood samples were taken from the marginal ear vein, before the administration

Sample analysis
Human and rabbit plasma samples were analyzed using a UPLC apparatus equipped with UV diode array detector (LaChrome Ultra, Hitachi). Samples were injected onto a Chromolith® Performance RP-18 column (100x4.6 mm, Merck), using a mobile phase containing 10 mM ammonium acetate buffer and acetonitrile (96:4, pH 6.0) at 35º C. The flow rate was 1.2 mL/ min. Plasma proteins were precipitated with methanol and the procedure was validates according to FDA guidelines 7 .
Statistical analysis Pharmacokinetic parameters were calculated using noncompartmental methods, with log transformation of concentration data.

Development and validation of bioanalytical methods
The methods for identification and quantification of stavudine, lamivudine and zidovudine were developed in plasma for the pharmacokinetic studies and in HBSS for permeability tests.
To validate the methods, calibration curves were made by preparing ten different dilutions of the standards (five replicates per concentration) in HBSS or drug free plasma. The linearity was evaluated in the range of 0.25 to 6.0 g/mL for d4T and 3TC, and 0.25 to 8.0 g/mL for AZT. The standards prepared in HBSS and plasma were stable for more than 90 days at -75° +/-5° C. All methods met the criteria: linearity (R² ≥0.8), precision (CV <15%), accuracy (CV <15%) recovery (> 80%), lower limit of detection and quantification (Table 1).

Dissolution profile
The kinetics of dissolution were determined following pharmacopeia parameters at 10, 15, 20, 30, 45, 60 min in 12 independent tests. The mean value at every time point was used to calculate the logarithmic linear regression and the mathematical model of the dissolution profiles, where y is the percentage of dissolved drug and x is time: Stavudine: y = 0.0097ln(x) + 3.6246 Lamivudine:y = 0.0345ln(x) + 5.0272 Zidovudine: y = 0.0975ln(x) + 5.6808 Similar interpolation accumulation periods in Caco-2 monolayers and cells accumulated area under the curve (AUC) pharmacokinetics in humans and rabbits was performed ( Table 2).
Permeability assays in Caco-2 cells The parameters for the permeability assays in cell monolayers were standardized. In addition to test the integrity of the monolayers by TEER, markers for transcellular and paracelullar transport were used, Metoprolol (high permeability) and Mannitol (low permeability), respectively. The Papp of metoprolol was 47.2x10 -6 cm/seg (SD ± 5.5x10 -6 , n= 5). On the other hand, it was not possible to determine the Papp for mannitol since the concentrations in the recipient compartment were below the limit of detection. The determination of the changes in concentration in the receiver compartment at 15, 30, 45, 60, 90 and 120 min in ten independent tests allowed us to evaluate the indicators of diffusion ( These equations were applied to the correlation with dissolution at one hour and the pharmacokinetics in humans and rabbits.

Pharmacokinetics in rabbits
The doses administered to the animals (d4T 0.60 mg/Kg, 3TC 2.13 mg/Kg y AZT 4.14 mg/Kg) were normalized with respect to the doses for human volunteers, to calculate the proportionality between them (rabbit/human). These factors were: d4T 14, The simulated data obtained using these equations, adjusted by the factor corresponding to human doses, were used in the noncompartmental pharmacokinetic analysis to test the partial and accumulative areas under the curve (AUC 0-t , AUC Acum ) according to the Wagner-Nelson (Fig. 1), and calculated by: Expressed as: The main pharmacokinetic parameters are described in Table  4. The plasma concentration of the three antiretrovirals reached a maximum value rapidly and later decreased to reach baseline values 6 h after treatment. These results showed the rapid absorption and high permeability of the three APIs. AZT reached the highest bioavailability of the three antiretrovirals.

Pharmacokinetics in humans
The pharmacokinetic profiles were the main reference parameter for the in vitro-in vivo correlation ( Table 4). The plasma profile of concentration versus time after the administration of a single oral dose of stavudine (40 mg) or lamivudina (150 mg)/zidovudine (300 mg) is shown in Figure 2.
The linear regression of the logarithm of the plasma concentration versus time, provided the mathematical models for the elimination phase (R² >0.97). The three antiretroviral tested were rapidly absorbed after oral administration (Tabla 4).

In vitro-in vitro correlations
Dissolution versus permeability. The percentages of concentration changes between zero and one hour (maximum time of dissolution) and the changes in concentration in the recipient compartment in the permeability test were compared ( Table 2). The linear regression mathematical models showed that the dissolution data are optimal to predict permeability by diffusion (R² >0.80).  Table 2. Dissolutions profiles and accumulation percent in Caco-2, rabbits and humans. Where y is the AUC accumulative percentages in Caco-2 cells and x is the percentage of dissolution. These functions can be implemented to predict the quality of drugs in terms of permeability and the quality of excipients from different sources during the manufacturing process.

In vivo-in vivo correlations
Rabbit vs. humans. The cumulative areas under the curve were correlated and a statistical analysis by least squares was applied (Fig. 3). A high correlation between the pharmacokinetic profiles in humans and in the animal model was observed (stavudine R 2 = 0.987, lamivudine R 2 = 0.885 and zidovudine R 2 = 0.989). The AUC 0-t for zidovudine in both species was proportional to the dose. However, for lamivudine even though the ratio rabbit/human was ten, the AUC 0-t only exceeded the value in humans by a factor of two. For stavudine, the dose ratio was 15 times higher for rabbits than humans, but the AUC 0-t in rabbits was only two and a half times the AUC 0-t in humans.
The C max values presented the largest interspecies differences regarding the fraction of drug absorbed, therefore the use of this parameter to predict the behavior of these drugs is not recommended. The time to reach the maximum concentration (T max ) of zidovudine was two times higher in humans than in rabbits (0.75 h and 0.33 h, respectively), while for lamivudine and stavudine the values were similar (Table 4). Consequently, for these drugs T max in rabbits was directly related to the expected results in humans. The comparison of the in vivo results, in rabbits and humans for AUC 0-t , was based on the plasma profiles and patterns of elimination in the curve of the logarithm of concentration versus time for simulated changes in the same periods (Wagner Nelson Method).

Correlation of the accumulative percentages of AUC in humans versus rabbits
The mathematical models of the linear correlation and the corresponding factors (R 2 ) to the least squares regression were:   Table 4. Pharmacokinetics parameters in the animal model and humans  X values represent cumulative AUC in rabbits interpolated for cumulative AUC in humans at the same period for equivalent doses. The correlation factors demonstrated the ability of the rabbit species to predict bioavailability in humans due to the amount of absorbed and accumulated drug over time, with a probability close to or greater than 90%. These mathematical models exceed the biological variability analysis and inter-species differences because each subject responded comprehensively combining the physiological properties of the animal and the human subject under test conditions.

In vitro-in vivo correlations
Dissolution versus AUC 0-t in Humans. The dissolution profiles and pharmacokinetics in animals and humans were compared ( Table 2). Direct, exponential correlation between the percentage of the drug dissolved in vitro and cumulative AUC in humans was found (R 2 > 0.99).
Stavudine: y = 1.4842 e0.5376x Lamivudine: y = 0.0902 e0.6906x Zidovudine: y = 1.7444 e0.5619x In these equations x represents dissolution percentage values and y represents in vivo projected AUC for the same period. The Pharmacokinetic data in the animal model also showed satisfactory results with exponential models and correlation factors greater than 0.98. A direct exponential relationship between the percent of dissolution and the amount of drug available in the blood plasma was used to predict the effectiveness of the absorption processes based on the data of in vitro dissolution percentages.
Permeability versus AUC in humans. Cumulative AUC values in the Caco-2 system were correlated with AUC values in vivo in the first two hours since the permeability test was performed for two hours. A directly proportional relation for lamivudine was found, while for stavudine and zidovudine the relation was logarithmic (Fig. 4). Similar results with correlations greater than 0.97 were obtained from the multiple regressions, considering the same variables in the animal model.

Discussion
Regulations require assessing the quality of drugs through in vivo bioavailability and bioequivalence tests in healthy adult humans. This study proved the validity of applying surrogate in vitro tests to reduce the costs and ethical risks associated to the inclusion of humans in research, as long as solid scientific evidence support the substitution. These tests are based on the solubility and permeability properties of the active pharmaceutical ingredients, according to the biopharmaceutics classification system (BCS) 3 . Stavudine, lamivudine and zidovudine are Type I compounds, highly soluble and highly permeable 8 . Type I drugs in immediate release oral products, can be waived from human studies, however, currently their quality is demonstrated by in vivo bioavailability and bioequivalence tests.
Physicochemical assessment and dissolution test The analyzed products meet the quality specifications for drug content, dose uniformity and dissolution profile according to the United States pharmacopeia (USP34, NF29, 2011) and related documents [9][10][11][12][13] . In less than 20 min 99.0% of lamivudine, 91.2% of zidovudine and 93.5% of stavudine were dissolved. The solubility test supported the recommendation of exemption from in vivo bioequivalence studies for dosage forms of immediate release like stavudine, lamivudine and zidovudine 14,15 . The dissolution profile confirmed that 81.8% of zidovudine was released from the tablets in the first 10 minutes and 93.4% of lamivudine. The capsules of stavudine released more than 90.0% of the API in the first 15 min.
Permeability tests in Caco-2 cells Metoprolol and mannitol were used as high and low permeability standards respectively and the results were concordant with other studies and FDA guidelines 16,17 . This support the suitability of our in vitro system to discriminate between high and low permeability compounds. The results obtained when testing stavudine and lamivudine were very similar and fit the definition of highly permeable drugs. The permeability of zidovudine was three times higher than the permeability of stavudine and lamivudine which is related to its physicochemical properties of lipophilicity. This methodology is in compliance with the requirements of the guidelines for in vitro test for the evaluation of solubility and permeability properties established in the BCS and other publication in the field [18][19][20][21] . The functionality of the Caco-2 system was confirmed by calculating the apparent permeability coefficient (Papp), permeability coefficient (P) and flux coefficient (J).
Pharmacokinetic studies The rabbit animal model proved to be an efficient way to evaluate absorption process according to biological and biochemical properties that are similar to humans, therefore supporting its use in pre-clinical research [22][23] . The guidelines for good laboratory practices and use of animals in bioavailability and bioequivalence studies were followed 24-29 . The three drugs reached the maximum plasma concentration in an hour or less, being around 20 min for stavudine. The half-life time in rabbits for lamivudine was 0.95 h, shorter than the experimental value in humans (2.68 h), it was slightly longer for zidovudine 1.12 h (0.72 h) and shorter for stavudine 1.0h (1.37 h).
The human studies were taken as references for quality in terms of plasma concentration and AUC for a period of 12 h 30-33 . The evaluated parameters were: maximum concentration (C max ), area under the curve in time (AUC 0-t ) and time required to reach the maximal concentration (T max ).
This study demonstrated the bioavailability of the dosage forms zidovudine 300 mg/lamivudine 150 mg tablets and stavudine 40 mg capsules manufactured by Humax Pharmaceutical S.A, and the compliance with quality standards according to the dissolution properties, drug content and other physicochemical properties described for these dosage forms. The diffusion and permeability capacity of the compounds was confirm using the cell monolayer model and a direct correlation with the pharmacokinetic of absorption in the animal model and humans was found. The analytical methods and validated procedures applied to in vitro tests demonstrated the direct correlation with the results obtained in the pharmacokinetic studies, with correlation coefficients greater than 0.85.

Conclusions
This study achieve the goal to implement analytical methodologies, that are commonly applied in the discovery and development of new drugs, to measure the physical and biological properties of the compounds that correlate with the bioavailability studies in humans, according to the principles of IVIVC. In all the comparisons the linear regression by the least square method provided correlation factors close or greater than 0.9, the tested comparisons were: The results of this study support the proposal to revise the regulatory requirements in force in Colombia, related to in vivo tests like bioequivalence studies for immediate release products with APIs classified as BCS-I, specifically antiretroviral nucleoside reverse transcriptase inhibitors.
It is proposed to improve the capacity of the pharmaceutical industry to standardize in vitro and in vivo (rabbits) methods, complementary to the dissolution tests, in order to validate the results between them and to give strength and power, which is essential for quality assurance for in vivo behavior.