Use of a semi-physiological pharmacokinetic model to investigate the influence of itraconazole on tacrolimus absorption, distribution and metabolism in mice.

1. The aim of this study was to investigate the influence of itraconazole (ITCZ) on tacrolimus absorption, distribution and metabolism by developing a semi-physiological pharmacokinetic model of tacrolimus in mice. 2. Mice were randomly divided into four groups, namely control group (CG, taking 3 mg kg-1 tacrolimus only), low-dose group (LDG, taking tacrolimus with 12.5 mg kg-1 ITCZ), medium-dose group (MDG, taking tacrolimus with 25 mg kg-1 ITCZ) and high-dose group (HDG, taking tacrolimus with 50 mg kg-1 ITCZ). 3. Liver clearance (CLli) decreased significantly (**p < 0.01) in LDG (35.3%), MDG (45.2%) and HDG (58.7%) mice compared to CG mice. With respect to gut clearance (CLgu), significant (**p < 0.01) decrease was also revealed in LDG (35.9%), MDG (50.2%) and HDG (64.6%) mice. A significant (**p < 0.01) higher tacrolimus brain-to-blood partition coefficient (Kt,br) was found in MDG (25.3%) and HDG (55.9%) mice than in CG mice. Moreover, a significant (*p < 0.05) increase (16.3%) was found in the absorption rate constant (Ka) in HDG mice compared to CG mice. There was a significant (**p < 0.01) association between ITCZ dose and the change in CLgu (ΔCLgu, r= -0.790), the change in CLli (ΔCLli, r= -0.787) and the change in Kt,br (ΔKt,br, r = 0.727), while the association between ITCZ dose and the change in Ka (ΔKa) was not significant (p > 0.05). 4. These findings could be useful in predicting the efficacy and toxicity of tacrolimus, and drug-drug interaction of ITCZ and tarcolimus in human.


Introduction
Fungal infection is one of the most fatal complications in organ transplantation (Brooks et al., 1985;Dummer et al., 1986;Kramer et al., 1991Kramer et al., , 1993. In the setting of intense immune suppression immediately after transplantation, fungi, particularly Aspergillus and Candida, tend to colonise over the new anastomosis that is not yet well vascularised (Dummer et al., 1986;Kramer et al., 1993). The antifungal agent itraconazole (ITCZ) is routinely used as prophylaxis against Aspergillus and Candida infection and often administered to solid organ transplant and haematopoietic stem cell transplantation recipients receiving immunosuppressant (Kramer et al., 2011;Leather et al., 2006;Nara et al., 2013;Togashi et al., 2015). The mechanism of action of ITCZ is the same as the other azole antifungals: it inhibits the fungalmediated synthesis of ergosterol by inhibiting cytochrome P450 3A (CYP3A) in fungi (Grant & Clissold, 1989;Heykants et al., 1989;De Beule & Van Gestel, 2001). In addition to inhibiting CYP3A, ITCZ is also metabolised extensively by CYP3A (Kunze et al., 2006;Peng et al., 2012). The metabolites of ITCZ, keto-ITCZ, hydroxy-ITCZ, and N-desalkyl-ITCZ, also contribute to CYP3A inhibition (Templeton et al., 2010). The persistent inhibition of CYP3A after ITCZ dosing is related to the effects of inhibitory metabolites with long half-life (Templeton et al., 2010). ITCZ and its metabolites have also been shown to be drug transporter P-glycoprotein (P-gp) inhibitors (Isoherranen et al., 2004;Shon et al., 2005;Templeton et al., 2010). Therefore, therapy with other medications metabolised by this route must be monitored for signs of toxicity.
Physiologically based pharmacokinetic (PBPK) modelling, treating the body as anatomical compartments connected by blood flow, uses physiological and chemical-specific parameters, as well as mathematic equations to quantitatively describe the in vivo disposition of xenobiotics (Barrett et al., 2012;Lu et al., 2016). Compared with traditional compartmental modelling and non-compartmental analysis, which usually only focus on analysing concentration-time data in blood, PBPK modelling is a more mechanistic approach for studying xenobiotic absorption, distribution, metabolism and elimination (Nestorov, 2007). PBPK modelling is also capable of extrapolating across dose levels, formulations, routes of administration and species (Barrett et al., 2012;Lu et al., 2016;Rostami-Hodjegan, 2012). Therefore, one application of PBPK models is predicting xenobiotic exposure in humans based on that in experimental animals. In addition, this type of model may allow for the evaluation of the effects of different factors including age, disease, gender, genetics, drug-drug interaction, etc., on xenobiotic disposition (Edginton et al., 2008;Lu et al., 2016;Zhao et al., 2011). Combined with pharmacodynamic data, PBPK modelling also aids the understanding of therapeutic benefits and adverse effects of drugs, leading to optimised dosage regimens (Khalil & Läer, 2011). Because of these advantageous features, the interest in applying PBPK models in pharmaceutical industries and research academies has been rapidly growing in recent years (Rostami-Hodjegan, 2012).
Although antifungal agents have been shown to inhibit tacrolimus metabolism (Furlan et al., 1995), the reported studies concerning drug-drug interactions between ITCZ and tacrolimus in transplant recipients are mostly from case reports or small series (Billaud et al., 1998;Furlan et al., 1998;Outeda Macías et al., 2000). To date, no study systematically evaluated the influence of ITCZ on tacrolimus absorption, distribution and in vivo metabolism, all of which are important in predicting the efficacy and toxicity of tacrolimus. Therefore, we investigated the influence of ITCZ on tacrolimus absorption, distribution, hepatic and intestinal clearance by developing a semi-physiological pharmacokinetic (PK) model of tacrolimus in mice, in order that the findings in the present study could be useful in predicting the efficacy and toxicity of tacrolimus, and drug-drug interaction of itraconazole and tarcolimus in human.

Chemicals, reagents and animals
Tacrolimus (purity >98%) and ascomycin (purity >98%) reference standards were purchased from the National Institutes for Food and Drug Control (Beijing, China). Tacrolimus raw materials (purity >98%) used for preparing the solutions for gavage were provided by Struchem Co., Ltd. (Jiangsu, China), while ITCZ raw materials (purity >98%) used for preparing the solutions for gavage were provided by Hubei Jusheng Technology Co., Ltd. (Tianmen, China). Methanol of HPLC grade was purchased from Fisher Scientific (Fair Lawn, NJ). Distilled water was prepared from demineralised water throughout the study. Other chemicals were of analytical grade.
Male Kunming strain mice (22 ± 2 g) were kindly provided by the Experimental Animal Centre of Shenyang Pharmaceutical University (Shenyang, China) and fed with unlimited access to food and water in an air-conditioned animal centre at a temperature of 22 ± 2 C and a relative humidity of 50 ± 10%, with a natural light-dark cycle for a week and then fasted with only access to water for 12 h prior to the experiment. The animal study was carried out in accordance with the Guideline for Animal Experimentation of Shenyang Pharmaceutical University, and the protocol was approved by the Animal Ethics Committee of the institution.

Preparation of tacrolimus and ITCZ solutions
The preparation procedure of tacrolimus solution used for gavage administration was as follows: the drug was supplied as 25 mg of tacrolimus in 1 mL of polysorbate 80. Before administration, the drug was diluted in distilled water maintaining a concentration of drug of about 0.165 mg mL À1 .
The preparation procedure of ITCZ solutions used for gavage administration was as follows: The drug was supplied as 100 mg of ITCZ in 2 mL of polysorbate 80. Before administration, the drug was diluted in distilled water maintaining a concentration of drug of about 0.685, 1.37 and 2.74 mg mL À1 , respectively.

Blood and tissue sample collection
A total of 144 mice were randomly divided into four groups, namely control group (CG), low-dose group (LDG), mediumdose group (MDG) and high-dose group (HDG). Animal numbers in each group was calculated based on the power analysis with a power of larger than 80% (effect size results see Table S1 and S2). Dose selection was based on the clinical dosages for both tacrolimus (0.3 mg kg À1 day À1 ) and ITCZ (100, 200 and 400 mg day À1 ), and scaled to mice using the body surface area (BSA) method.
An oral dose of 12.5 (LDG), 25 (MDG) and 50 mg kg À1 (HDG) ITCZ were first given to the mice and tacrolimus solution were given orally at a dose of 3 mg kg À1 an hour later. Blood samples of about 0.6 mL were collected from each animal by cardiac puncture and placed into heparinised centrifuge tubes, at 0.083, 0.5, 2, 8, 12 and 24 h after dosing. These samples were stored at À80 C until analysis.
The tissue distribution study was also carried out on 144 mice, with the dosing regimen same as that mentioned in the blood sample collection procedure. After administration, the mice were sacrificed at 0.083, 0.5, 2, 8, 12 and 24 h, and tissues (brain, fat, gut, heart, kidneys, liver, lungs, muscle and spleen) were collected at the same time. The tissue samples were rinsed in ice-cold normal saline, blotted dry with filter paper, and then stored at À80 C until analysis.

Tacrolimus assay
The quantitative analytical method of tacrolimus in mouse blood/tissues is established based on the liquid chromatography-mass spectrometry (LC-MS, Waters Co., Milford, MA) method. Briefly, chromatographic separation was performed using a Hypersil BDS C 18 (50 mm Â 2.1 mm, 3.0 mm particle size) (Elite Analytical Instruments Co., Ltd., Dalian, China) column kept at 25 C with a constant flow rate of 0.2 mL min À1 . The mobile phase consisted of methanol-2 mmol L À1 ammonium acetate (95:5, v/v). Tandem mass spectrometry detection was performed in the positive ion, multiple reaction monitoring (MRM) mode following the transition m/z 821.7 ! 768.9 for tacrolimus, and the transition m/z 809.8 ! 757.0 for internal standard (IS, ascomycin). The IS stock solution was prepared at a concentration of 0.1 mg mL À1 and further diluted with methanol to achieve a final concentration of 1 mg mL À1 for blood samples, and 5 mg mL À1 for tissue samples. A volume of 50 mL methanol and 50 mL IS solution were added into 500 mL blood samples. Tissue samples were accurately weighed and homogenised with methanol (w/v, 1:2). A volume of 20 mL methanol and 20 mL IS solution were added into 300 mL of the tissue homogenates. These bio-samples were deposited down the protein using 600 mL of 0.2 M ZnSO 4 :acetonitrile (50:50, v/v) aliquot, and then extracted with a volume of 3 mL ethyl acetate, vortex-mixed for 5 min and centrifuged at 4000 Âg for 10 min. The upper extract was then evaporated to dryness at 35 C under nitrogen stream. The residue of blood/tissue samples was reconstituted with 100 mL mobile phase, and a 10 mL aliquot was injected onto the LC-MS system.
The retention times for tacrolimus and IS were approximately 1.8 and 1.4 min, respectively. No interference from any metabolites and endogenous substances was observed. The method was linear over the concentration range of 0.5-200 ng mL À1 for mouse blood (2.5-5000 ng g À 1 for mouse tissues) (Table S3), with the lower limit of qualification (LLOQ) of 0.5 ng mL À1 for mouse blood and 2.5 ng g À 1 for mouse tissues, respectively. The method showed good intraassay precision and accuracy with relative standard deviation (%, RSD) values from 5.5 to 10.3% and mean relative error (%, MRE) from À2.5 to 3.2%, as well as good inter-assay precision and accuracy with RSD from 4.1 to 6.7%. The recoveries for all the bio-samples were over 66.7% (66.7-74.3%). There was no significant matrix effect for all the ratios within the range 102-110% for all the bio-samples. The MREs of short-term stability (À0.5 to 7.5%), freeze-thaw stability (À7.3 to 5.3%), auto-sampler stability (À1.5 to 5.7%), and long-term stability (À3.4 to 9.3%) of tacrolimus in all the bio-samples were found to be within the range ±15% (Table S4 and S5).

Development of the semi-physiological PK model
The whole physiological model contains 12 single-organ models (Figure 1), which were selected and optimised based on a significantly drop of residual errors and biological plausibility of the PK parameters. All the single-organ compartments were connected by blood flow. As tacrolimus is extensively eliminated by metabolism in liver and gut (Iwasaki, 2007;Jeong & Chiou, 2006;Marchetti et al., 2007), both hepatic (CL li ) and intestinal (CL gu ) elimination pathways, which were assumed to be involved in the clearance of tacrolimus, were included in the model structure. The following differential equations were used to describe the model structure for tacrolimus disposition: Lung (lu): Artery (ar): Brain (br): V br, e Â dC br, e dt Heart (he), spleen (sp), kidney (ki), muscle (mu) and remainder (re): Dosing compartment: Gut (gu): Liver (li): Fat (fa): Vein (ve): where C ar represents the tacrolimus concentration in artery blood; C tissue represents the drug concentration in tissues; C ve represents the tacrolimus concentration in venous blood; CL tissue represents tissue clearance; K a is the absorption rate constant; K in, fa is the first-order association coefficient for fat; K out, fa is the first-order dissociation coefficient for fat; K p, br is the permeability-limited distribution coefficient for brain; K t,tissue is the tissue-to-blood partition coefficient; Q co represents cardiac output; Q tissue represents tissue blood flow; V ar represents the volume of the artery blood pool, V tissue represents tissue volume and V ve represents the volume of the venous blood pool. The initial conditions for Equations (1)-(5) and (7)- (11) were all set to 0, and dosing compartment was regarded as the dosing site.
Physiological parameters, such as tissue volumes, blood flow rates to different organs and fractions of vascular space in tissues were fixed to literature values reported in Table 1 (Brown et al., 1997;Davies & Morris, 1993). All tissues that were not sampled were lumped into a remainder compartment. A density of 1 g cm À3 was assumed for all tissues.

Data analysis
The semi-physiological PK model was constructed using MATLAB R2012b (The MathWorks, Natick, MA). All parameters were estimated using maximum likelihood, and the variance model was defined as: where C obs (t i ) is the observed concentration of the ith data point, C pred (, t i ) is the ith model-fitted concentrations and " i, obs represents a normally distributed random variable with a mean of 0.
The areas under the concentration-time curve (AUCs) of tacrolimus were calculated by non-compartmental analysis of blood and tissue concentration versus time data using WinNonlin version 6.0 (Pharsight Corporation, Mountain View, CA). All statistical analyses were conducted using Matlab R2012b (MathWorks Corporation, Natick, MA). Normality test of the PK parameters were performed using the Lilliefors test. The comparison of PK parameters between CG and the other three groups was possessed using independent samples t-test (data normally distributed) or the Mann-Whitney U-test (data non-normally distributed). Hepatic venous blood flow. c Calculated as body weight subtract sum of weight of lungs, brain, heart, spleen, liver, gut, kidneys, muscle and fat. d Calculated as 100 subtract sum of blood flow of brain, heart, liver, kidneys, muscle and fat. All statistical tests were two sided with *p50.05 as the probability required to declare a difference.

Discussion
Drugs that require metabolism by the same CYP enzymes or transport by the same influx/efflux transporters compete for metabolism by the CYPs or binding to the transporters. Therefore, in theory, any two drugs that are metabolised by identical CYP isoenzymes or transported by identical transporters have a potential for interaction. However, the clinical significance of this interaction will rely on the drug's relative affinities for binding to these enzymes/transporters, dependence on CYP/transporter for elimination, concentrations achieved in the target tissue/organ after therapeutic doses, and therapeutic ratios (Slaughter & Edwards, 1995;Venkatakrishnan et al., 2000).
Tacrolimus is primarily metabolised by CYP3A isoenzymes, which are the most abundant isoforms of CYP, accounting for nearly 30% of the total CYP content in liver and as much as 70% in the gut wall (Hoensch et al., 1976;Iwasaki, 2007;Lin et al., 1999Lin et al., , 2002Michalets, 1998;Obach et al., 2001;Shimada et al., 1994). Therefore, there is a potential for major drug interactions between itraconazole, a potent inhibitor of CYP3A, and tacrolimus. Our findings in the present study supported this speculation. The physiological PK analysis results showed that the liver and gut clearance of tacrolimus decrease significantly (**p50.01) in mice co-administrated ITCZ, with the increase of tacrolimus AUCs in almost all tissues (*p50.05).
A strong gut clearance (CL gu ) was revealed based on the physiological PK analysis (Table 3), and there are two possible reasons that can explain this phenomenon. One of the explanations is that CYP3A was in a continuous saturation state at the beginning of drug absorption. In this stage, tacrolimus highly concentrated in the gut wall and cannot be metabolised timely. As CL gu is the average of the gut clearance rate, the final estimate may be high due to the zeroorder elimination at the beginning of drug absorption. The other explanation is the existence of P-gp in the gut wall. Tacrolimus is also a substrate of P-gp (Hooks, 1994; Table 2. AUC 0-24 h values in mouse blood/tissues after an oral dose of 3 mg kg À 1 tacrolimus with or without ITCZ (Median ± SD, n = 6).  Scott et al., 2003;Venkataramanan et al., 1995), which is a membrane efflux transporter that is normally expressed in mammalian tissues, such as the small intestine, brain capillary endothelial cells and renal proximal tubules (Thiebaut et al., 1987). The high concentration of tacrolimus in the gut wall at the beginning of drug absorption may also make P-gp continuously in its maximum transport capacity (zero-order elimination). Although tacrolimus AUC rose significantly in almost every tissue as ITCZ dose increased, the magnitude of increase in AUCs (DAUC) was not proportional to ITCZ dose elevation. ITCZ dose adjusted DAUC (DAUC/Dose) was higher (*p50.05) in lung, brain, liver, gut, kidney, muscle, fat and blood in HDG mice than MDG and LDG mice, which indicated that the increase of AUC accelerated when ITCZ dose reached 50 mg kg À1 . On the other hand, CL gu and CL li accelerated to decrease when ITCZ dose reached 50 mg kg À1 . Notably, K a was also found to rise significantly (*p50.05) in HDG mice, which indicated that high dose of ITCZ may accelerate tacrolimus absorption. Moreover, as high dose of Figure 4. Correlation between ITCZ doses with the changes of PK parameters (Dparameter, %). CL gu : gut clearance; CL li : liver clearance; K a : absorption rate constant; K t, br : brain-to-blood partition coefficient. Grey lines: median Dparameters versus ITCZ doses; Black lines: linear regression of Dparameters versus ITCZ doses. Table 3. Pharmacokinetic parameters of tacrolimus in mice after an oral dose of 3 mg kg À1 with or without ITCZ (Median ± SD, n = 6). 3.02e-03 ± 5.03e-04 2.91e-03 ± 4.12e-04 2.86e-03 ± 5.66e-04 3.33e-03 ± 7.23e-04 CL gu : intestinal clearance; CL li : hepatic clearance; K a : absorption rate constant; K in, fa : first-order association coefficient for fat; K out, fa : first-order dissociation coefficient for fat; K p, br : permeability-limited distribution coefficient for brain; K t, br : partition coefficient for brain; K t, fa : partition coefficient for fat; K t, gu : partition coefficient for gut; K t, he : partition coefficient for heart; K t, ki : partition coefficient for kidney; K t, li : partition coefficient for liver; K t, lu : partition coefficient for lung; K t, mu : partition coefficient for muscle; K t, re : partition coefficient for the remainder compartment; K t, sp : partition coefficient for spleen. *p: the null hypothesis at the 5% significance level; **p: the null hypothesis at the 1% significance level.
ITCZ may significantly inhibit the activity of CYP3A and P-gp in the gut wall, it may also raise the bioavailability of tacrolimus, leading to a higher amount of tacrolimus absorption. Collectively, a single 50 mg kg À1 dose of ITCZ in mice is assumed to approximate the maximum CYP3A and/or P-gp inhibition in vivo. As the metabolism of ITCZ was very slow (Grant & Clissold, 1989;Heykants et al., 1989), the existence of additional ITCZ may raise the exposure of tacrolimus in vivo and further raise the risk of its toxicity. Tissue-to-blood partition coefficients (K t, tissue ) are chemical-specific parameters that are mainly determined by the lipid solubility of the drug, the lipid and transporter content in tissues, and the transport capacity of transporters, etc. In the present study, all the K t, tissue s remained unchanged (p > 0.05), except that K t,br increased significantly (**p50.01) in MDG and HDG mice. This increase may be due to the transporterrich structure of blood-brain barrier (BBB). These transporters (especially P-gp) play an important role in efflux of xenobiotic and keeping the homeostasis in the brain. However, the efflux of tacrolimus may be weakened by coadministration with ITCZ, which may competitively bind to P-gp. This may further cause an increase of tacrolimus concentrations in the brain and an increasing risk of neurotoxicity.
Compared with a significant increase of tacrolimus AUC in almost every tissue, changes in the physiological pharmacokinetics mainly focussed on several PK parameters, such as CL li , CL gu , K t,br and K a . However, this did not cause any over-or underestimation of the observed concentrations. In fact, the model-fitted concentration-time profiles fit the observations very well. The reason of this phenomenon is that, although the single-organ models were integrated into a uniform physiological model, they were connected in a complex way (parallel, serial, circular and attenuate). In other words, a single PK parameter can influence the drug concentration in every single-organ model in a complex exponential manner. This is beneficial to improve the description ability of the PK model, especially when the observations are sparse, which is not the case when using the non-compartmental analysis. This means the physiological PK model is suitable for investigating the mechanisms of drug interaction. In addition, compared with the PK parameters in the classical compartmental models, the physiological PK parameters are characterised by more physiological significance and relatively stable in different species. These parameters can be further used for interspecies scaling, mainly for predicting the disposition procedure of a drug in human (Bradshaw-Pierce et al., 2007;Hu et al., 2014;Kagan et al., 2011;Lu et al., 2016).
However, we did not developed an advanced compartmental absorption and transit (ACAT) model (Sinha et al., 2012) for mouse or human in the present study because of the lack of P-gp content information in tissues. An alternative extrapolation (from mouse to human) method is to use the species-specific parameters (such as tissue clearance and permeability-limited distribution coefficient), which are scaled with body weight using empirical allometric exponents. This manner of extrapolation for species-specific parameters is routinely used in PBPK modelling (Anderton et al., 2004;Bradshaw-Pierce et al., 2007;Meno-Tetang et al., 2006), but may not always be accurate or valid because there are considerable differences in abundance and function of drug-metabolising enzymes, drug transporters and other molecules across species (Hu & Hayton, 2001;Sharma & McNeill, 2009). All these confounding factors can contribute to the discrepancies between the simulated and observed data. Collectively, the discrepancies between simulations and the observations imply that once available, more species-specific and/or chemical-specific parameters should be incorporated to achieve better model prediction. Therefore, the current semi-physiological PK model could be refined when more species-specific data and mechanisms regarding tacrolimus disposition become available.

Conclusion
A semi-physiological pharmacokinetic model was applied to investigate the influence of itraconazole on tacrolimus absorption, distribution and metabolism. The results in the current study indicated that itraconazole at a dose of 50 mg kg À1 in mice may raise the absorption rate, raise the brain-to-tissue partition coefficient, and reduce the hepatic and intestinal clearance of tacrolimus. These findings could be useful in predicting the efficacy and toxicity of tacrolimus, and drug-drug interaction of itraconazole and tarcolimus in human. The developed physiological pharmacokinetic model could be further refined by combining more chemical-and/or species-specific data for predicting tacrolimus disposition in human.

Declaration of interest
The authors declare no conflict of interest.