Population Pharmacokinetic of the Diterpenes ent-Polyalthic Acid and Dihydro-ent-Agathic Acid from Copaifera Duckei Oil Resin in Rats

Abstract

Copaifera duckei oleoresin is a plant product extensively used by the Brazilian population for multiple purposes, such as medicinal and cosmetic. Despite its ethnopharmacological relevance, there is no pharmacokinetic data on this important medicinal plant. Due to this, we determined the pharmacokinetic profile of the major nonvolatile compounds of C. duckei oleoresin. The diterpenes ent-polyalthic acid and dihydro-ent-agathic acid correspond to approximately 40% of the total oleoresin. Quantification was performed using LC-MS/MS, and the validated analytical method showed to be precise, accurate, robust, reliable, and linear between 0.57 and 114.74 µg/mL plasma and 0.09 to 18.85 µg/mL plasma, respectively, for ent-polyalthic acid and dihydro-ent-agathic acid, making it suitable for application in preclinical pharmacokinetic studies. Wistar rats received a single 200 mg/kg oral dose (gavage) of C. duckei oleoresin, and blood was collected from their caudal vein through 48 h. Population pharmacokinetics analysis of ent-polyalthic and dihydro-ent-agathic acids in rats was evaluated using nonlinear mixed-effects modeling conducted in NONMEN software. The pharmacokinetic parameters of ent-polyalthic acid were absorption constant rate = 0.47 h⁻¹, central and peripheral apparent volume of distribution = 0.04 L and 2.48 L, respectively, apparent clearance = 0.15 L/h, and elimination half-life = 11.60 h. For dihydro-ent-agathic acid, absorption constant rate = 0.28 h⁻¹, central and peripheral apparent volume of distribution = 0.01 L and 0.18 L, respectively, apparent clearance = 0.04 L/h, and elimination half-life = 3.49 h. The apparent clearance, central apparent volume of distribution, and peripheral apparent volume of distribution of ent-polyalthic acid were approximately 3.75, 4.00-, and 13.78-folds higher than those of dihydro-ent-agathic.

Keywords

Copaifera duckei - dihydro-ent-agathic acid - ent-polyalthic acid - Leguminosae - pharmacokinetic

Introduction

The Copaifera genus (Leguminosae), commonly known as “Copaíbas”, “Copaibeiras”, or “Copaívas”, encompasses approximately 70 species of large trees that are widely distributed in Brazil, primarily in the northern region, with a particular emphasis on the states of Amazonas, Pará, and Roraima [1], [2], [3]. The oleoresins extracted from the trunk of these plants have long been utilized in traditional Brazilian medicine, demonstrating various beneficial properties such as anti-inflammatory, antimicrobial, analgesic, wound healing, antitumor, purgative, and antiparasitic activities [1], [2], [3]. Moreover, these oleoresins hold significant pharmacological value and are commercially sold as crude oil to serve as raw material for producing cosmetics [1], [3], [4].

These oleoresins exhibit variable viscosity and color and comprise volatile sesquiterpenes and nonvolatile acid diterpenes [1], [5]. Despite notable variations in the chemical composition among Brazilian Copaifera species, sesquiterpene compounds such as δ-cadinene, α-cadinol, α-cubebene, β-elemene, α-copaene, α-humulene, β-caryophyllene, and caryophyllene oxide, as well as kaurane, clerodane, and labdane diterpenes, have been identified in all examined species [1], [6], [7].

Among the various Copaifera oleoresins found in Brazil, the oleoresin from Copaifera duckei Dwyer is the most prominent representative of Amazonian “Copaíbas”. This oleoresin comprises approximately 72% nonvolatile components, including the diterpenes ent-polyalthic acid and dihydro-ent-agathic acid [6], [7] ([Fig. 1]).

Fig. 1 Chemical structures of the major nonvolatile constituents of Copaifera duckei oil resin: ent-polyalthic acid (1) and dihydro-ent-agathic acid (2).

In Brazilian folk medicine, the recommended oral dosage is 3 – 5 drops dispersed in warm water or honey, taken up to three times daily to treat internal ailments [8], [9]. Despite the oral administration of these oleoresins, there is a lack of information regarding their pharmacokinetic studies. Consequently, we have developed and validated an analytical method to determine the pharmacokinetic profiles of ent-polyalthic and dihydro-ent-agathic acids in rat plasma samples following a single oral dose of C. duckei oleoresin administration.

Results and Discussion

The mass spectra in the mobile phase and the chromatograms of plasma samples of the ent-polyalthic and dihydro-ent-agathic acids and the internal standard (IS) warfarin are depicted in [Figs. 2] and [3]. The matrix effect, linearity, precision, accuracy, and stability are shown in [Table 1]. The carryover tests of the ent-polyalthic and dihydro-ent-agathic acids and the IS warfarin are shown in [Fig. 3]. Chromatographic peak areas of the blank plasma samples were lower than 20% of the lower limit quality control (LLQC) areas, as shown in [Fig. 3].

Fig. 2 Full scan mass spectrum of Copaifera duckei oil resin, dihydro-ent-agathic, ent-polyalthic acids, and warfarin sodium (internal standard) diluted in the mobile phase.

Fig. 3 Chromatograms of the lower limit quality control (LLQC), low-quality control (LQC), and high-quality control (HQC) samples and of blank plasma samples immediately following HQC sample analysis of ent-polyalthic and dihydro-ent-agathic acids.

Table 1 Validation parameters of the method of analysis of ent-polyalthic and dihydro-ent-agathic acids in rat plasma samples.

NMF = normalised matrix factor, CV = coefficient of variation, RSE = relative standard error, LLQC = lower limit of quantification, LQC = low-quality control, MQC = medium quality control, HQC = high-quality control
Parameter	ent-Polyalthic acid		Dihydro-ent-agathic acid
Matrix effect Mean NMF (CV%) LQC HQC	0.40 (8.61%) 0.39 (4.74%)		0.94 (5.83%) 0.51 (6.06%)
Linearity range (µg/mL) Regression equation Correlation coefficient (r)	0.57 – 114.74 y = 0.422 126 × x − 0.226 519 0.993 176		0.09 – 18.85 y = 3.16 888 × x − 0.146 839 0.996 044
Stability	CV%	RSE%	CV%	RSE%
Shor-term (25 °C, 6 h)
LQC	(n = 3) 4.03	−  6.26	(n = 4) 3.51	− 3.71
HQC	(n = 4) 3.78	− 10.14	(n = 4) 2.60	− 7.58
Post-processing (12 °C, 10 h)
LQC	(n = 3) 3.00	− 12.65	(n = 3) 5.73	− 5.77
HQC	(n = 4) 6.81	5.84	(n = 5) 2.03	2.36
Freeze/thaw cycles (25 °C, 6 h)
LQC	(n = 5) 1.52	4.59	(n = 5) 4.09	− 5.30
HQC	(n = 5) 3.03	10.82	(n = 5) 4.37	− 6.26
Precision and accuracy	CV%	RSE%	CV%	RSE%
Intra-assay
LLQC	(n = 7) 2.61	− 0.20	(n = 7) 5.02	3.34
LQC	(n = 7) 3.53	8.57	(n = 7) 5.17	− 5.60
MQC	(n = 7) 6.30	4.81	(n = 7) 3.29	− 4.89
HCQ	(n = 7) 4.05	− 4.24	(n = 7) 2.27	− 2.53
Inter-assays (3 assays)
LLQC	(n = 22) 8.57	0.10	(n = 22) 5.98	8.80
LQC	(n = 17) 9.61	− 1.46	(n = 20) 6.45	− 1.06
MQC	(n = 22) 6.48	0.47	(n = 22) 7.07	− 2.24
HCQ	(n = 19) 7.30	3.69	(n = 21) 3.20	− 5.01

Both ent-polyalthic and dihydro-ent-agathic acid pharmacokinetics were characterized as a bicompartmental structural model with first-order absorption and elimination. Plasma concentrations versus time curves of ent-polyalthic and dihydro-ent-agathic acids are presented in [Fig. 4]. The typical values of the parameters and interindividual variability (IIV) are presented in [Table 2] (θ _{i =} θ _TV × e^η , where θ _i is the parameter value of an individual animal, θ _TV is the population parameter typical value, and η is a random variable with mean zero and variance ω ²).

Fig. 4 Observed plasma concentrations over time of ent-polyalthic acid and dihydro-ent-agathic acids in 44 Wistar rats following a 200-mg/kg Copaifera duckei oil resin dose administrated by gavage (91.79 mg/kg of ent-polyalthic acid and 18.08 mg/kg of dihydro-ent-agathic acid).

Table 2 Estimates of the population pharmacokinetic model of ent-polyalthic acid and dihydro-ent-agathic acid in rats following oral administration (gavage) of a 200-mg/kg dose of Copaifera duckei oleoresin (91.79 mg/kg of ent-polyalthic acid and 18.08 mg/kg of dihydro-ent-agathic acid).

Parameter	ent-Polyalthic acid				Dihydro-ent-agathic acid
	Estimates		Bootstrap (n = 1000)		Estimates		Bootstrap (n = 1000)
	Typical value (θ) RSE	IIV (ω 2) RSE	Typical value median PI (2.5 – 97.5%)	IIV median PI (2.5 – 97.5%)	Typical value (θ) RSE	IIV (ω 2) RSE	Typical value median PI (2.5 – 97.5%)	IIV median PI (2.5 – 97.5%)
CL/F: apparent clearance. Vc/F: apparent central volume of distribution; Q: intercompartmental clearance; Vp/F: apparent peripheral volume of distribution; IIV: interindividual variability. RSE%: residual standard error; PI: percentile interval range; SD: standard deviation. Cmax: maximum concentration. Tmax: time to achieve Cmax. t 1/2: half-life. Relative F: relative bioavailability between ent-polyalthic/dihydro-ent-agathic acids
Ka (h−1)	0.47 12.16%	–	0.47 (0.37 – 0.90)	–	0.28 12.9%	–	0.28 (0.22 – 0.67)	–
CL/F (L/h)	0.15 13.91%	0.25 44.68%	0.15 (0.099 – 0.19)	0.26 (0.05 – 0.75)	0.04  9.3%	0.329 26.1%	0.04 (0.03 – 0.05)	0.31 (0.16 – 0.54)
Vc/F (L)	0.04 20.17%	–	0.04 (0.03 – 0.09)	–	0.01 27.6%		0.01 (0.01 – 0.04)
Q/F (L/h)	0.13 11.91%	–	0.14 (0.10 – 0.21)	–	0.02 30.1%		0.02 (0.01 – 0.05)
Vp/F (L)	2.48 30.36%	0.98 37.09%	2.50 (1.33 – 4.66)	0.98 (0.26 – 2.05)	0.18 14.0%	–	0.19 (0.14 – 0.31)	–
σ 2	0.15 21.26%	–	0.14 (0.09 – 0.20)	–	0.17 15.6%	–	0.16 (0.11 – 0.22)	–
	Median PI (25 – 75%)	Mean (SD)			Median PI (25 – 75%)	Mean (SD)
Tmax (h)	0.50 (0.45 – 0.75)	0.64 (0.36)			0.75 (0.50 – 1.50)	1.26 (0.87)
Cmax (µg/mL)	41.63 (33.25 – 50.91)	42.75 (13.22)			22.65 (16.97 – 29.36)	22.03 (9.80)
t 1/2 (h)	11.60 (7.85 – 15.15)	11.60 (7.14)			3.49 (2.52 – 4.78)	3.49 (2.17)
AUC0–48 (μg · h/mL)	130.74 (96.43 – 176.64)	144.89 (131.16)			103.00 (69.84 – 150.67)	118.76 (68.62)
Relative F			0.245

The residual variability of both acids was described by a proportional residual error model. Therefore, the concentration estimates of each time (j) and animal (i) was

Y_{ij =} F _ij + F _ij × ε_ij

where Y_ij is the observed concentration, F_ij is the concentration estimate, and ε _ij is a random variable with mean zero and variance σ ² ([Table 2]).

The goodness of fit plot (GOF) and visual predictive check (VPC) of ent-polyaltic and dihydro-ent-agatic acids ([Figs. 5] and [6]) indicated a good fit of the predicted plasma concentrations to the observed data, and the bootstraps ([Table 2]) indicate acceptable bias and good accuracy of the fixed and random effects estimates. In addition, the bootstrap had only 11.1% minimization failures.

Fig. 5 Goodness of fit plot of ent-polyaltic and dihydro-ent-agatic acids. Observed concentrations over population and individual predictions (left). Conditional weighted residuals (CWRES) over population predictions and time (right). Red line: trend line; dashed lines: identity line and two and half times the identity (left plots); 2, 0, and − 2 CWRES (right plots).

Fig. 6 Visual predictive check (VPC) of ent-polyaltic and dihydro-ent-agatic acids in rat plasma over time. Dots: observed plasma concentrations. Lines: 5th, 50th, and 95th percentiles of observed concentrations. Shaded areas: 5th, 50th, and 95th percentiles of the simulated concentrations (n = 1000).

The influence of animal weight and age on the pharmacokinetic parameters of ent-polyaltic and dihydro-ent-agatic acids were explored however due to the uniformity of weight and age values among the animals no effect was identified.

To our knowledge, this is the first method for analyzing ent-polyaltic and dihydro-ent-agatic acids in the plasma of rats by LC-MS/MS. The method presented a wide linearity range and low lower limit of quantification (LLOQ) (0.57 – 114.74 and 0.09 – 18.85 µg/mL plasma, respectively), which makes it suitable to be applied to preclinical pharmacokinetic studies.

We could not analyze the ent-polyalthic and dihydro-ent-agathic acids by multiple reactions monitoring (MRM). Despite several fragmentation tests with different ionization energies and argon flux, their ionized molecules did not generate fragment ions appreciably. A similar difficulty was also described by Gasparetto et al. [10] in the analysis of kaurenoic acid, a diterpene contained in Guaco.

The sample preparation method did not present a significant matrix effect for standard or lipemic plasma samples ([Table 1]). However, the matrix effect for hemolyzed plasma was higher than 15%, and the hemolyzed plasma samples should be disregarded.

The method is selective for ent-polyalthic and dihydro-ent-agathic acids at concentrations ≥ the LLQC. The chromatogramsʼ peak areas of interferents were lower than 20% compared to the chromatogramsʼ peak analytes at LLQC concentrations ([Fig. 3]).

The analytical method showed good intra- and inter-assay precision and accuracy, with the coefficient of variation (CV) and relative standard error (RSE) of quality controls lower than 15%. Similarly, the stability of the freeze/thaw cycles, post-processing in an auto-injector, and short-term on a bench had a CV and RSE lower than 15%.

The C. duckei oleoresin sample was prepared at 20 mg/mL in saline with Cremophor 10% to furnish a homogeneous suspension able to provide the dose of 200 mg of oleoresin per kilogram of rat in a volume not exceeding 10 mL/kg of rat, as described by the Good Practices for the Administration of Substances and Blood Collection [11]. Blood samples in volumes lower than 400 µL were collected from the caudal vein, not exceeding three samples per animal. The volume collected was less than 10% of the animalʼs total blood volume, making volume replacement unnecessary, according to the Good Practice Guide for the Administration of Blood Substances and Collections, which would cause changes in pharmacokinetic parameters [11].

This is the first report on the population pharmacokinetics of ent-polyalthic and dihydro-ent-agathic acids. With few reports on the bioavailability of natural products and limited population pharmacokinetic studies on natural products, finding similar data for comparison is difficult.

ent-Polyalthic and dihydro-ent-agathic acids have similar lipophilicity (logP = 4.9 and 4.7, respectively) and polar surface area (50.4 and 74.6 Ų, respectively) [12]. However, the apparent clearance (CL/F), central apparent volume of distribution (Vc/F), and peripheral apparent volume of distribution (Vp/F) of ent-polyalthic acid are approximately 3.75-, 4.00-, and 13.78-folds higher than the dihydro-ent-agathic ones, and the relative bioavailability between ent-polyalthic and dihydro-ent-agathic acids is 0.245 ([Table 2]).

Due to the Brazilian populationʼs extensive use of copaibaʼs oleoresin, further studies are needed to establish safe and effective doses for humans. Furtado et al. [13] reported no genotoxic activity at doses up to 2000 mg of oleoresin/kg of animal for six different Copaifera species (C. duckei, Copaifera multijuga, Copaifera paupera, Copaifera pubiflora, Copaifera reticulata, and Copaifera trapezifolia). However, they observed cytotoxic activity of C. duckei oleoresin on Chinese hamster fibroblast cells at a concentration of 9.8 µg/mL. Castro-e-Silva et al. [14] reported the oral treatment of rats with 600 mg oleoresin/kg/day for 7 days and after partial hepatectomy. They also observed a decrease in hepatocellular proliferation and mitochondrial breathing in the liver. Noteworthy is that in the present study, the C. duckei oleoresin sample was prepared at 20 mg/mL in saline with Cremophor 10% to furnish a homogeneous suspension able to provide the dose of 200 mg of oleoresin per kilogram of rat in a volume not exceeding 10 mL/kg of rat, as described by the Good Practices for the Administration of Substances and Blood Collection.

Finally, it is possible to conclude that the developed LC-MS/MS analytical method is reliable for the pharmacokinetic studies of Copaifera oleoresin ent-polyalthic and dihydro-ent-agathic acid diterpenes. The CL/F, Vc/F, and Vp/F of ent-polyalthic acid are higher than that of dihydro-ent-agathic. It is also essential to observe that the literature reports that diterpenes with an oxidized furan ring, such as teucrin A, are known liver toxic compounds [15]. All these facts indicate the need for further toxicological and clinical studies to better understand the safety aspects of using Copaifera oleoresin.

Material and Methods

Plant materials and chemicals

C. duckei Dwyer oleoresin was collected in Belém (Pará State, Brazil) at coordinates S01°06.933′, O48°19.781′. A voucher specimen (NID:96/2012) was obtained and deposited in the Herbarium of the Brazilian Agricultural Research Corporation (Embrapa Eastern Amazon). The Botanist Silvane Tavares Rodrigues identified the specimen (voucher number 175 206). ent-Polyalthic acid and dihydro-ent-agathic acid ([Fig. 1]) were isolated and identified through nuclear magnetic resonance analysis by our research group from the same oleoresin used in this study [6], [16]. Their purity was also evaluated by integrating the area under the signals corresponding to the compounds of interest in the ¹H NMR spectrum.

The IS was warfarin sodium, purchased from FURP. The following HPLC grade reagents were used: Milli Q Plus purified water (Millipore), methanol (Merck), acetonitrile (Sigma-Aldrich), methyl tert-butyl ether (Fischer Scientific), and isopropanol (J. T. Baker). Formic acid and glacial acetic acid (J. T. Baker), both of analytical grade, were employed as mobile phase modifiers.

Development and validation of an analytical method for ent-polyalthic acid and dihydro-ent-agathic acid in rat plasma

LC-MS/MS analysis

Chromatographic analysis was conducted using an Alliance e2695 Waters system (Waters Corp.). A LiChrospher 100 CN (5 µm) column with a LiChroCART 125 – 4 mm (Merck) pre-column was utilized and maintained at a temperature of 27 °C. The mobile phase consisted of a mixture of water, acetonitrile, isopropanol, and formic acid (64.8 : 20 : 15 : 0.2 v/v/v/v) with a 0.7 mL/min flow rate. Mass spectrometry detection was performed using a Quattro Micro Liquid Chromatograph triple quadrupole (Micromass) equipped with an electrospray ionization (ESI) source. The ent-polyalthic acid and dihydro-ent-agathic acid were detected in the single ion recording (SIR) mode, while warfarin (IS) was detected in the MRM mode. The ESI source was set to the negative mode. The parameters were configured as follows: capillary voltage − 3.00 kV, source and desolvation temperatures of 125 and 400 °C, respectively, cone and desolvation gas flow (N₂) were set at 50 and 800 L/h, respectively, and argon was employed as the collision gas at a rate of 0.15 mL/min. The cone voltage, collision energies, and ion transitions for each analyte were optimized according to [Table 3]. Data acquisition and sample quantifications were performed using MassLynx 4.1 version (Waters).

Table 3 Precusor/product ion pairs and parameters for multiple reactions monitoring of ent-polyalthic acid, dihydro-ent-agathic acid, and the internal standard (IS) warfarin.

Compound	Retention time (min)	MS mode	Transitions (precursor > product)	Cone voltage (V)	Collision energy (eV)
ent-Polyalthic acid	11.18	SIR	315	50	2
Dihydro-ent-agathic acid	5.72	SIR	335	50	2
IS	5.06	MRM	307.1 > 161.5	30	20

Preparation of standard solutions

Stock solutions of ent-polyalthic (5 mg/mL) acid, dihydro-ent-agathic acid (1 mg/mL), and warfarin sodium (IS, 5 mg/mL) were prepared separately in methanol and kept at − 20 °C. The calibration standards were prepared by successive dilutions in methanol to obtain concentrations of 1.15, 2.29, 3.44, 4.59, 6.88, 9.18, 22.95, 45.90, 91.79, 114.74, 137.69, 183.58, and 229.48 µg of ent-polyalthic acid/mL methanol and 0.19, 0.38, 0.57, 0.75, 1.13, 1.51, 3.77, 7.54, 15.08, 18.85, 22.62, 30.16 e 37.70 µg of dihydro-ent-agathic acid/mL methanol. Warfarin sodium (IS) solution was further diluted in methanol to obtain a 5 µg/mL concentration.

Sample preparation

Fifty microliters of plasma sample (or blank plasma for calibration curves) were added to 2000 µL microtubes (Axygen Scientific) to begin the sample preparation. Subsequently, 25 µL of IS solution (5 µg/mL), 50 µL of 0.75 M acetic acid, and 25 µL of methanol (or 25 µL of each standard solution for calibration curves) were added. The microtubes were then vortexed for 30 s using a vortex mixer (Phoenix Luferco, model AP56). After mixing, 500 µL of the extraction solution (methyl tert-butyl ether : isopropanol, 4 : 1 v/v) were added to the microtubes. Another 30-s vortex mixing was performed, followed by centrifugation for 10 min at 21 500 g, 4 °C (Himac CF8DL). The resulting supernatants were carefully transferred to other clean microtubes and subjected to evaporation until dryness using a vacuum concentrator. The dried residues were then reconstituted in 100 µL of the mobile phase and mixed for 30 s. The processed samples were stored in the automatic injector at 12 °C, and 60 µL of each sample were injected into the LC-MS/MS system. For the construction of calibration curves, peak area ratios (analyte/IS) were plotted against plasma concentrations. The concentration ranges were 0.57 to 114.74 µg/mL and 0.09 to 18.85 µg/mL for ent-polyalthic acid and dihydro-ent-agathic acid, respectively.

Method validation

The analytical method was validated according to FDA and EMA guidelines [17]. The quality control samples were prepared at the plasma concentrations shown in [Table 4].

Table 4 Quality control concentrations of ent-polyalthic and dihydro-ent-agathic acids in rat plasma.

Quality control sample	ent-Polyalthic acid (µg/mL)	Dihydro-ent-agathic acid (µg/mL)
LLQC: lower limit concentrations quality control, LQC: lower concentration quality control, MQC: medium concentration quality control, HQC: higher quality control concentrations, DQC: dilution quality control
LLQC	0.57	0.09
LQC	1.72	0.28
MQC	57.37	9.42
HQC	91.79	15.08
DQC	114.74	18.85

The matrix effect was assessed using eight 50 µL aliquots of blank plasma obtained from different rats, including two lipemic samples, two hemolyzed samples, and four standard samples. The blank plasma extracts were then spiked with standard solutions at concentrations corresponding to the high-quality control (HQC) and low-quality control (LQC), along with the addition of the IS solution. Additionally, exact standard solutions in methanol spiked with the IS solution were analyzed. The matrix factor normalized with the IS (NMF) was calculated by dividing the peak area ratios of analyte/IS from the post-extracted plasma samples by the peak area ratios of analyte/IS from the neat solutions. The matrix effect was determined by calculating the CV of all obtained MFs.

Selectivity was evaluated using blank plasma from eight different sources, including four standard samples, two lipemic samples, and two hemolyzed samples. The resulting chromatograms were compared to LLQC concentration samples.

Linearity was assessed through triplicate calibration curves, including a blank and zero samples. The carryover effect was evaluated by consecutively injecting three blank samples, followed by injecting the sample at the HQC concentration.

Precision and accuracy (intraday and inter-day) were evaluated by performing seven replicates of LLQC, LQC, medium quality control (MQC), and HQC of ent-polyalthic and dihydro-ent-agathic acids in a single analytical run (intra-assay) and in three different analytical runs (inter-assay). The precision and accuracy results are expressed as the CV and RSE.

Stability tests in rat plasma were conducted using four replicates of LQC and HQC samples. For the freeze/thaw stability evaluation, the LQC and HQC replicates were subjected to three cycles of freezing at − 70 °C for 24 h, followed by thawing at room temperature and freezing again at − 70 °C for 24 h. The samples were then analyzed at the end of the three cycles. Short-term stability was assessed by keeping the LQC and HQC samples at room temperature for 1 h before preparation and analysis. Post-processing stability was evaluated by storing the processed LQC and HQC samples in the automatic injector at 12 °C for 24 h before analysis. The stability results are expressed as the CV and RSE.

Population pharmacokinetics of ent-polyalthic acid and dihydro-ent-agathic acid in rats

Animal experiments

Male Wistar rats (260 ± 30 g, n = 44) were housed in metabolic cages under controlled temperature (25 ± 1 °C), relative humidity (40 – 70%), a 12-h light-dark cycle, and with free access to food and water. On December 9, 2015, the Ethics Committee of Universidade de Franca (CEUA) approved the experimental protocol on the Use of Animals under protocol number 057/15.

After 12 h fasting, 20 mg/mL C. duckei oleoresin, dissolved in physiological saline solution with 1.0% Cremophor, were orally administered by gavage at a dose of 200 mg/kg (91.79 mg/kg of ent-polyalthic acid and 18.08 mg/kg of dihydro-ent-agathic acid) to a total of 44 rats. Serial blood samples of 200 µL (3 to 4 samples per animal) were collected from tail vein at 5, 15, 30, 45 min, and 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 18, 20, 24, 30, 36, and 48 h (n = 8 for each sampling time) after oleoresin administration and transferred to tubes containing heparin as an anticoagulant (Liquemine 5000 IU; Roche). After centrifugation (10 min, 9560 g, 4 °C), the plasma samples were stored at − 70 °C until analysis.

Population pharmacokinetic models

Population pharmacokinetics models of ent-polyalthic and dihydro-ent-agathic acids in rats were evaluated by nonlinear mixed-effects modelling conducted in NONMEN software, version 7.4.3 (ICON Development Solutions), with compiler GNU Fortran 4.6 (Free Software Foundation, Inc.) and interface PsN, version 4.9.0 (Perlspeaks-NONMEM) [18]. R version 3.6.1 (R Foundation for Statistical Computing) was used to reorganize the dataset, statistical summaries, and graphics.

The estimations were conducted based on the first-order conditional estimation with the interaction method (FOCE-I). The model-building criteria included (1) successful minimization, (2) reduced relative standard error and shrinkage values of estimates, (3) number of significant digits, (4) successful covariance step, (5) correlation between model parameters, and (6) acceptable gradients at the last iteration [19], [20].

All fixed and random effects were introduced into the model according to a stepwise procedure exploring mono- or bicompartmental pharmacokinetics with first order and elimination and different absorption models (first-order, lag-time, or transit compartment models). The residual variability was explored by additive, proportional, or proportional combined with additive error models. The IIV was explored in all parameters assuming a log-normal distribution.

Comparison between hierarchical models was based on graphic and statistical methods that included (1) reduction of the objective function value (OFV) and AIC (Akaike information criteria), (2) values of relative standard error and shrinkage, (3) GOF that included plots of the predicted population (PRED) and individual (IPRED) concentrations versus the observed concentrations and the conditional weighted residuals (CWRES) versus population predicted concentrations and time [20], [21].

A stepwise forward inclusion/backward elimination procedure was used for covariate selection, according to the concept that the difference in − 2 log likelihood between two models is approximately χ² distributed, with degrees of freedom equal to the difference in the number of parameters between the hierarchical models [22]. The covariates were introduced one by one and retained if a decrease in OFV of at least 3.84 units (p < 0.05) was observed. During the backward elimination procedure, an increase in OFV of at least 7.8 units (p < 0.005) was used as a criterion for a significant effect.

The predictive performance of ent-polyalthic and dihydro-ent-agathic acid pharmacokinetic models was assessed via graphical and statistical methods, including VPCs [20], [21], [23] and bootstrapping [24], in addition to graphical evaluation of the GOF. VPCs were obtained from 1000 simulations per animal of the ent-polyalthic and dihydro-ent-agathic acid plasma concentrations from 0 to 48 h. Bootstrap analysis identified bias, stability, and precision of the estimates obtained with the model and was performed with 1000 new datasets generated by resampling individuals (with replacement) from the original dataset.

The area under the plasma concentration from 0 to 48 h (AUC_0 – 48) of ent- polyalthic and dihydro-ent-agathic acids was calculated by the trapezoidal rule in R version 3.6.1 from the modelʼs individual predicted concentrations over time. Then, the relative bioavailability between ent-polyalthic/dihydro-ent-agathic acids of each animal was accessed through the equation:

F = AUC_0 – 48 of ent-polyalthic acid × dose of dihydro-ent-agathic acid

AUC_0 – 48 of dihydro-ent-agathic acid × dose of ent-polyalthic acid

Contributorsʼ Statement

Data collection: F. A. Aguila, Nardotto G. H. B., Oliveira, L. C.; design of the study: F. A. Aguila, Bastos, J. K., Veneziani R. C. S., Nardotto G. H. B., Oliveira, L. C., Rocha, A., Lanchote, V. L., Ambrosio S.R; statistical analysis: F. A. Aguila, Nardotto G. H. B., Oliveira, L. C., Rocha, A., Lanchote, V. L., Ambrosio S.R; analysis and interpretation of the data: F. A. Aguila, Bastos, J. K., Veneziani R. C. S., Nardotto G. H. B., Oliveira, L. C., Rocha, A., Lanchote, V. L., Ambrosio S.R; drafting the manuscript: Bastos, J. K., Veneziani R. C. S., Rocha, A., Lanchote, V. L., Ambrosio S.R; critical revision of the manuscript: Bastos, J. K., Veneziani R. C. S., Lanchote, V. L., Ambrosio S.R, Ambrosio S. R.

Conflict of Interest

The authors declare that they have no conflict of interest.

Acknowledgements

The authors thank the State of São Paulo Research Foundation (FAPESP) for financial support (grant number 2011/13 630 – 7) and CAPES and CNPq for fellowships.

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