FormalPara Key Points

The physiologically based pharmacokinetic (PBPK) framework proposed in this work was capable of simulating the interplay between the inhibition and induction of cytochrome P450 (CYP) 3A4 in the gut and liver as well as hepatic active transporters (uptake and efflux) for the prediction of the DDI between ritonavir-boosted atazanavir (ATV/r) and rifampicin.

A twice-daily dose of ATV/r seems to provide the most clinically sustainable opportunity to overcome the DDI, rather than opting for a higher once-daily dose, considering the associated hepatotoxicity risk.

1 Introduction

According to the World Health Organization (WHO), the risk of people living with HIV (PLWH) developing tuberculosis is 16–27 times greater than that of HIV-negative individuals [1]. In 2018, more than 37.9 million people were living with HIV, with one-third of AIDS-related deaths globally (251,000 of the overall 770,000 global HIV deaths in 2018) being linked to tuberculosis [1, 2]. The WHO recommends that all PLWH co-infected with tuberculosis should receive antiretroviral therapy (ART), regardless of their CD4 count, within 8 weeks of initiating antituberculosis treatment [3]. However, antiretroviral (ARV) drugs have a high potential for drug–drug interactions (DDIs), both as victims and perpetrators, and their coadministration with numerous drugs is contraindicated [4, 5]. Although global ART roll-out has been highly successful, with 23.3 million individuals estimated to be receiving ART [6], increasing numbers are failing first-line regimens and require second-line therapy [7]. WHO-recommended second-line regimens when failing first-line regimens with dolutegravir (DTG) are based on protease inhibitors (PI), with the ‘preferred’ choice being ritonavir-boosted atazanavir (ATV) because of its once-daily dosing regimen and improved clinical tolerability compared with older PIs such as lopinavir [7]. With increasing uptake of DTG, individuals failing non-nucleoside reverse transcriptase inhibitor (NNRTI)-based first-line therapy are recommended to switch to DTG-based second-line regimens [8]. However, as DTG is increasingly used as first-line throughout the world, future treatment failures that emerge will still require boosted PI-based second-line regimens.

PIs are known to be substrates of cytochrome P450 (CYP) 3A enzymes, efflux, and uptake transporters. Atazanavir is a P-glycoprotein (P-gp), organic anion transporting polypeptide (OATP), and CYP3A4 substrate extensively metabolized by the liver [9]. Although ATV can be used alone in the treatment of naive patients with HIV, the coadministration with a low dose of ritonavir (RTV) is recommended given the potent inhibition by RTV of CYP3A4 [10]. RTV ‘boosting’ of ATV (ATV/r) improves the pharmacokinetic and virologic activity of ATV [11]. The relationship between the ATV trough concentration (Ctrough) and effective ART response has been previously described, and a Ctrough of 150 ng/mL correlated with a plasma HIV RNA load < 50 copies/mL following 24 weeks of treatment with ATV 300 mg plus RTV 100 mg [10, 12].

Ritonavir is metabolized by CYP3A4 and CYP2D6 and is both a P-gp substrate and inhibitor [13,14,15,16]. It is also a weak inducer of CYP3A4 [17] and an inhibitor of OATPB1. The inhibition of this class of transporters can decrease the hepatic uptake and metabolism of many drugs [18]. Rifampicin (RIF), which is the mainstay of first-line tuberculosis treatment, is a strong inducer of many CYPs (CYP2A, CYP2B, CYP2C, and CYP3A) and transporters [19, 20] and an inhibitor of OATP1B1 [21]. The coadministration of ATV and RIF results in a substantial decrease in ATV plasma concentration [22, 23].

The investigation of clinically relevant DDIs can be limited by numerous ethical and logistical barriers. In vitro methodologies can provide a quantitative description of the induction and inhibition effect of drugs on metabolic enzymes and transporters; however, these approaches may have limitations depending on their experimental design. For example, the experiments may not reflect the concentrations used therapeutically, or they may not reproduce concurrent inhibition and inducing effects. Furthermore, the cell system used may not represent physiologically relevant enzyme or transporter expression and activity, hindering in vivo extrapolation. In silico techniques can be utilized to overcome some of the limitations mentioned above, specifically the prediction of multiple concurrent DDI mechanisms [24].

Physiologically based pharmacokinetic (PBPK) modelling is a ‘bottom-up’ approach in which the in vitro data of a drug (intrinsic clearance, blood-to-plasma ratio, protein binding, Caco-2 cell permeability, etc.), physicochemical properties (logP, pKa, polar surface area, hydrogen bond donors [HBDs]), anatomical, physiological, and demographic characteristics of a population are integrated into mathematical equations to describe absorption, distribution, metabolism, and excretion (ADME) [25]. PBPK modelling can be applied to simulate different clinical scenarios concerning DDIs and to identify potential dose adjustments [26].

The aim of this study was to develop and verify a PBPK framework to simulate the interplay between the inhibition and induction of CYP3A4 in the gut and liver as well as hepatic active transporters (uptake and efflux) for the prediction of the DDI between ATV/r and RIF. Alternative ATV/r dosing strategies were simulated to overcome the magnitude of RIF DDIs, suggesting potential ATV/r regimens achieving the clinical Ctrough cut-off of ATV required for the successful treatment of PLWH co-infected with tuberculosis.

2 Methods

2.1 Physiologically Based Pharmacokinetic (PBPK) Model

The model was designed using Simbiology® v.5.8.2, a product of MATLAB® v.R2019a (MathWorks, Natick, MA, USA; 2019). Some of the key assumptions considered in the simulations were first-order kinetics, blood flow-limited distribution, no drug reabsorption from the colon, and instant distribution of the drug in tissues and organs (well-stirred model), except in the liver where the distribution of ATV was refined by a mechanistic transport-based model that included active efflux (P-gp) and uptake mediated transport of the drug. For ATV and RTV, a full PBPK model was applied, while RIF was applied in a three-compartment PBPK model (absorption, distribution, and elimination).

2.2 Virtual Healthy Volunteers

A virtual cohort of 100 healthy individuals (50% female and 50% male) was created using a whole-body PBPK model. Virtual healthy volunteers aged between 18 and 60 years (39 ± 12 years), with a mean weight of 70 ± 17.6 kg and height of 1.75 ± 0.15 m were generated using equations that statistically described the physiological and anatomical parameters to represent the individuals from the observed clinical studies [22, 23] used to validate the model. Organ weights and volumes were calculated using anthropometric equations and organ density, previously described by Bosgra et al. [27] and Brown et al. [28], respectively. The regional blood flow and systemic circulation were based on the cardiac output [29]. Each simulation used random values based on the mean and standard deviation, ensuring variability among simulated individuals.

2.3 Oral Absorption

Oral absorption considered a seven-compartment transit model [30]. When an observed value was not available from the literature, the absorption constant rate (ka) was calculated using the effective permeability based on the Caco-2 cells in vitro permeability or using the polar surface area (PSA) and the number of HBDs [31]. PIs are known to be poorly water-soluble [32]; for this reason, the solubility of drugs in each intestinal compartment was considered to calculate the fraction absorbed in the model. Considering that RIF presents variability in both the rate and extent of absorption when administered orally, a lag time (tlag) was implemented in the model [33]. All parameters are presented in Table 1.

Table 1 Input parameters for the ATV/r and RIF models
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2.4 Intestinal Metabolism

The abundance of CYP3A4 in the intestine [34] and the in vitro intrinsic clearance (Clint,CYP3A4,gut) were used to calculate intestinal clearance (Clgut) [31]. The amount of the drug escaping intestinal metabolism (Fg) and arriving in the liver was determined by Eq. 1:

$$F_{\text{g}}= \frac{{Q}_{\mathrm{gut}}}{{Q}_{\mathrm{gut} }+ {(f}_{u,\mathrm{gut}} \times {Cl}_{\mathrm{gut}})}$$
(1)

where Qgut is the flow of blood to the gut (L/h) and fu,gut is the fraction unbound of the drug in the gut, considered to have a value of 1 in the model [35].

The total Clgut (L/h) incorporated the DDI effect on the intestinal CYP3A4, as described in Eqs. 2–4:

$${\text{Cl}}_{\text{gut}} = {\mathrm{Cl}}_{\mathrm{int},\mathrm{CYP}3\mathrm{A}4,\mathrm{gut}} \, {\times} \,\text{ Abundance }\,{\times} \, \frac{{\mathrm{Ind}}_{\mathrm{gut}}}{{\mathrm{Inhi}}_{\mathrm{gut}}}$$
(2)
$${\mathrm{Ind}}_{\mathrm{gut}}=1+ \frac{{E}_{\mathrm{max}} \times {I}_{\mathrm{gut}}}{{\mathrm{EC}}_{50}+ {I}_{\mathrm{gut}}}$$
(3)
$${\mathrm{Inhi}}_{\mathrm{gut}}={K}_{\mathrm{deg}}+ \frac{{(I}_{\mathrm{gut }\times } {K}_{\mathrm{inact}})}{{(I}_{\mathrm{gut} +} {K}_{i})}$$
(4)

where Clint,CYP3A4,gut, Emax, EC50, Kdeg, Kinact, Ki, and Igut represent the intrinsic clearance of each drug for the isoenzyme 3A4 (µL/min/pmol), maximum induction, the concentration of inducer producing 50% of Emax (µmol/L), the first-order degradation rate constant of CYP3A4, the maximal enzyme inactivation rate constant, the concentration of inhibitor producing 50% of maximum inhibition (µmol/L), and the unbound intestinal concentration of inducer or inhibitor (mg/L), respectively. The degradation rate constant of CYP3A4 was 0.02 h-1 (half-life time of 35 h) [36], and the total induction of CYP3A4 in the gut considered the sum of RTV and RIF induction. RTV was considered an irreversible inhibitor of CYP3A4.

2.5 Liver Metabolism

The hepatic clearance (Clliver,CYP) considered the intrinsic clearance of a given CYP in µL/min/pmol (Clint,CYP,liver), the abundance of the CYP in the liver per milligram of microsomal protein per gram of liver (MPPGL), the liver weight in grams (WLiver), and the DDI effect on the given CYP. The MPPGL was calculated as described previously by Barter et al. [37]. The induction and inhibition of liver enzymes were integrated into the Clliver,CYP (L/h) as described in Eq. 5:

$${\text{Cl}}_{\text{liver,CYP}}\,=\, {\mathrm{Cl}}_{\mathrm{int},\mathrm{CYP},\mathrm{liver}} \, {\times}\,\text{ Abundance }\,\times\,\text{ MPPGL }\times{\text{W}}_{\text{Liver}}\,{\times}\,\frac{{\mathrm{Ind}}_{\mathrm{hep}}}{{\mathrm{Inhi}}_{\mathrm{hep}}}$$
(5)

The total hepatic clearance (Clhe) was considered as the sum of all enzymes involved in the metabolism. Additionally, Eqs. 6–8 were used when uptake and efflux transport was involved in ATV hepatic clearance:

$${\mathrm{Cl}}_{\mathrm{eff}}= {\mathrm{Cl}}_{\mathrm{int},\mathrm{eff}} \times \mathrm{Hepatocytes} \times {W}_{\mathrm{Liver}} \times \frac{{\mathrm{Ind}}_{\mathrm{eff}}}{{\mathrm{Inhi}}_{\mathrm{eff}}}$$
(6)
$${\mathrm{Cl}}_{\mathrm{up},\mathrm{act}}= {Cl}_{\mathrm{int},\mathrm{up},\mathrm{act}} \times \mathrm{Hepatocytes} \times {W}_{\mathrm{Liver}} \times \frac{{\mathrm{Ind}}_{\mathrm{uptake}}}{{\mathrm{Inhi}}_{\mathrm{uptake}}}$$
(7)
$${\mathrm{Cl}}_{\mathrm{up},\mathrm{pas}}= {\mathrm{Cl}}_{\mathrm{int},\mathrm{up},\mathrm{pas}} \times \mathrm{Hepatocytes} \times {W}_{\mathrm{Liver}}$$
(8)

where Clint,eff, Clint,up,act, Clint,up,pas, Hepatocytes, Indeff, Inhieff, Induptake and Inhiuptake represent the intrinsic efflux clearance of each drug for the given efflux transporter (µL/min/million hepatocytes), the intrinsic clearance of each drug for the given active uptake transporter (µL/min/million hepatocytes), the intrinsic clearance of each drug for the given passive uptake (µL/min/million hepatocytes), number of hepatocytes per gram of liver, induction and inhibition effect on the efflux transporter, and induction and inhibition effect on the active uptake transporter, respectively. The induction (\({\mathrm{Ind}}_{\mathrm{hep}})\) and inhibition (\({\text{Inhi}}_{\mathrm{hep}})\) of CYP3A4 hepatic enzymes were calculated the same way as described in Eqs. 3 and 4. As in the gut, the total induction of CYP3A4 in the liver was the sum of RTV and RIF induction. RTV was considered an irreversible inhibitor of CYP3A4.

Induction and inhibition of hepatic uptake and efflux transporters by RTV and RIF were calculated as described in Eqs. 9 and 10:

$${\mathrm{Ind}}_{\mathrm{uptake}}\mathrm{ or }{\mathrm{Ind}}_{\mathrm{eff}}=1+ \frac{{E}_{\mathrm{max}} \times {I}_{\mathrm{liver}}}{{\mathrm{EC}}_{50}+ {I}_{\mathrm{liver}}}$$
(9)
$${\mathrm{Inhi}}_{\mathrm{uptake}}\mathrm{ or }{\mathrm{Inhi}}_{\mathrm{eff}}=1+ \frac{{I}_{\mathrm{liver}}}{{K}_{i}}$$
(10)

where Emax, EC50, Ki, and Iliver represent the maximum induction, the concentration of inducer producing 50% of Emax (µmol/L), the concentration of inhibitor producing 50% of maximum inhibition (µmol/L), and the unbound liver concentration of inducers or inhibitors (mg/L). RTV and RIF were considered reversible inhibitors of hepatic transporters.

Finally, the amount of the drug escaping the hepatic metabolism (Fh) and reaching the systemic circulation was determined by Eq. 11 for RTV.

$$F\mathrm{h}= \frac{{Q}_{\mathrm{he}}}{{Q}_{\mathrm{he} }+ \left(\frac{f\mathrm{up}}{R} \times {\mathrm{Cl}}_{\mathrm{he}}\right)}$$
(11)

where Qhe is the flow of blood to the liver (L/h), fup is the fraction unbound of the drug in the plasma, and R is the blood-to-plasma ratio.

2.6 Distribution

The volume of distribution (Vd) was calculated using the tissue-to-plasma ratio (TP) of each organ and the volume of each compartment [38], except for the liver, where a passive and active uptake and efflux transport was considered. A correction factor was applied to each organ TP in the ATV and RTV models to match observed Vd values of 109–187 L and 20–40 L, respectively [17, 39].

2.7 Drug Parameters

The PBPK model was developed using in vitro, in silico and in vivo data for ATV, RTV, and RIF. No renal clearance was considered in the simulation since all the drugs are metabolized almost entirely by the liver. The initial values of intrinsic hepatic passive uptake, active uptake, and P-gp efflux of ATV were based on a previous publication by Nicolaï et al. [40], however considering the limitations of in vitro/in vivo correlation, a correction factor of 0.4 and 0.02 was applied to Clint,up,act and Clint,eff, respectively, for the extrapolation of the in vitro transporter data via curve-fitting to reflect the observed ATV PK parameters area under the concentration time curve from time zero to 24 h (AUC24) and maximum concentration (Cmax) [12] (available in the electronic supplementary material [ESM]). RIF systemic clearance was used in the model as described in Table 1. All the physicochemical, in vitro parameters, and data describing the metabolism of the drugs by different enzyme isoforms are contained in Table 1.

2.8 Verification of the PBPK Model

To verify the model, simulated pharmacokinetic profiles of individual and coadministrated drugs were compared with clinical studies available in the literature [17, 22, 23]. The model verification was performed according to the European Medicines Agency (EMA) [41], and was considered validated when the mean of simulated PK parameters AUC24, Cmax, and Ctrough were less than twofold of the observed clinical mean and the absolute average fold error (AAFE) was below 2 [42]. The doses and regimens of the drugs were chosen to reflect the clinical studies used to validate the model [17, 22, 23]. The administration of the drugs was simulated considering a fed state, according to drug label recommendations [12, 17]. A sensitivity analysis of the model was performed considering the changes in simulated AUC24, Cmax, and Ctrough of ATV to a percentage range variation linearly spaced of 25%, 58%, and 75% in the gastrointestinal (GI) transit time, Emax and EC50 of RIF (CYP3A4), Kinact (CYP3A4) and Ki (efflux and active uptake transporters) of RTV, when simulating the administration of ATV/r 300/100 mg + RIF 600 mg once daily.

2.9 Predictions of Drug–Drug Interactions (DDIs) Between Rifampicin (RIF) and Ritonavir-Boosted Atazanavir (ATV/r)

Simulations were carried out to determine potential dose adjustments of ATV/r to overcome the DDI with RIF. Dosing regimens were selected based on the minimum concentration (Ctrough) necessary to observe the therapeutic efficacy of ATV, the protein binding-adjusted 90% inhibitory concentration (PBA-IC90) of 14 ng/mL [43, 44] and the established clinical ‘cut-off’ of 150 ng/mL [10]. Both were considered since the strains used for in vitro assays may present greater sensitivity than those observed in vivo. The pharmacokinetic parameters AUC24, Cmax, and Ctrough were calculated at steady state. The number of individuals below the PBA-IC90 and the clinical ‘cut-off’ were calculated as percentages.

3 Results

3.1 Verification of the PBPK Model

The simulated PKs at steady state of each drug and observed data are presented in Table 2. The PBPK model is assumed to be qualified for all drugs (alone or combined). Moreover, the simulated DDIs between RIF (600 mg once daily) and ATV and RTV (300 and 100 mg once daily, respectively) demonstrated results similar to those obtained clinically (an AUC24 reduction of 71.5% and 88.1% compared with 40–70% and 80%, and a Cmax decrease of 48.1% and 78.3% compared with 40–70% and 80% for ATV and RTV, respectively, were observed) [23]. A substantial decrease of > 90% (98.7%) and > 80% (85%) in the simulated Ctrough of ATV and RTV was predicted when coadministered with RIF, as reported in the clinical study [23]. Detailed pharmacokinetic plasma concentration-time plots are presented in the ESM.

Table 2 Verification of the PBPK model (simulated vs. observed data)
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The sensitivity analysis suggested that ATV plasma concentration is sensitive to changes in GI transit time, Emax and EC50 of RIF, and Kinact of RTV, but not for changes in Ki of RTV (Fig. 1). The AUC24 and Ctrough were more affected by changes of these parameters than the Cmax. In the fed state, AUC24 and Ctrough were higher compared with the fasted state (available in the ESM).

Fig. 1
figure 1

Sensitivity analysis of ATV plasma concentration to variations of ± 25, 58, and 75% of GI transit-time, Emax and EC50 of rifampicin for CYP3A4, Kinact of ritonavir for CYP3A4, Ki of ritonavir for efflux and active uptake transporter, respectively. The sensitivity analysis was performed at steady state, with simulation of administration of ATV/r 300/100 mg + 600 mg of RIF once daily. ATV atazanavir, GI gastrointestinal, Emax maximum induction, EC50 concentration of inducer producing 50% of maximum induction, CYP cytochrome P450, Kinact maximum inactivation rate (h−1), Ki concentration of inhibitor producing 50% of maximum inhibition, ATV/r ritonavir-boosted atazanavir, RIF rifampicin

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3.2 Predictions of DDIs Between RIF and ATV/r

To overcome the DDI between RIF and ATV/r, different dosing regimens were simulated (ATV 300–800 mg, RTV 100–300 mg, once or twice daily). The model predictions at steady-state are presented in Table 3. Simulations of different doses within a twice-daily regimen predicted a relevant increase of the ATV Ctrough depending on the dose (Table 3). Additionally, as demonstrated in Fig. 2 and Table 3, the number of individuals who presented Ctrough above PBA-IC90 of 14 ng/mL [43, 44] and the clinical ‘cut-off’ of 150 ng/mL [10] are 100% and > 95%, respectively, when ATV/r is administered twice daily at all the tested doses with RIF 600 mg once daily. When simulating a higher dose of RIF (1200 mg once daily), a slight reduction in the ATV Ctrough and > 64% of simulated individuals above the clinical ‘cut-off’ was observed (Table 3).

Table 3 Simulated pharmacokinetic parameters of atazanavir
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Fig. 2
figure 2

Box plot for atazanavir Ctrough plasma concentration (ng/mL) when different doses of ATV/r twice daily and RIF 600 mg once daily. The dashed line represents the clinical Ctrough cut-off (150 ng/mL) of ATV. *Simulation of RIF 1200 mg once daily, ATV atazanavir, Ctrough trough concentration, ATV/r ritonavir-boosted atazanavir, RIF rifampicin

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4 Discussion

The coadministration of RIF and the PIs ATV/r for the treatment of tuberculosis in PLWH is challenging, necessitating a switch to a less well-tolerated ART regimen with a higher pill burden and potential increased risk of therapeutic failure. There are currently no studies in the literature with RIF-mediated induction of both CYP3A4 and transporters incorporated in a PBPK model to predict the increased plasma clearance of boosted PIs. A PBPK model was developed herein to simulate the magnitude of the concurrent inhibition and induction of CYP3A4 and P-gp by the perpetrators RIF and RTV to determine the DDI effect on ATV. Virtual clinical studies were simulated, identifying dosing regimens of ATV/r to overcome the DDI magnitude. The selection of doses for further clinical investigation is based on a detailed evaluation of plasma concentrations concerning efficacy and toxicity. The simulation of a dose adjustment of ATV/r 300/100 mg to twice daily demonstrated a significant increase in the Ctrough of ATV (Fig. 3), with 100% of individuals above the PBA-IC90 of 14 ng/mL and 98% above the clinical cut-off of 150 ng/mL. A further dose increase to 600/200 mg twice daily was predicted to result in 100% of patients above the clinical cut-off of 150 ng/mL, but concomitantly expose the patients to a high Cmax and AUC24, increasing the potential risk of associated hepatotoxicity, as demonstrated previously with high doses of darunavir/ritonavir and RIF [45].

Fig. 3
figure 3

Simulated different regimens of ATV/r + RIF bid versus observed clinical data (ATV/r 300/100 + RIF mg od) [23]. Observed clinical data (solid dark circles), simulated mean: ATV/r 300/100 (dashed black line), ATV/r 300/200 (solid black line), ATV/r 400/100 (dashed dark grey line), ATV/r 400/100 (solid dark grey line), ATV/r 600/100 (dashed light grey line), ATV/r 600/200 (solid light grey line). ATV/r ritonavir-boosted atazanavir, RIF rifampicin, bid twice daily, od once daily

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The selection of dosing strategy was driven by the objective of minimizing the risk of having a Ctrough below the clinical cut-off, as well as reducing the risk of hepatotoxicity. The twice-daily dose seems to provide the most clinically sustainable opportunity to overcome the DDI, rather than opting for a higher once-daily dose. Our findings indicate that higher doses of ATV/r once daily do not minimize the risk of failure and are likely to increase the risk of hepatotoxicity. ATV/r 800/300 mg + RIF 600 mg once daily was simulated. Despite a threefold dose increase, and despite resulting in higher Ctrough values compared with ATV/r 300/100 mg + RIF 600 mg once daily, the simulation resulted in 58% of simulated patients below the clinical cut-off. Additionally, higher Cmax could contribute to the higher risk of hepatotoxicity. Ritonavir super-boosting represents a dosing strategy to increase the exposure of ART concomitantly administered with RIF, as demonstrated by Rabie et al. [46]; however, it has poor acceptability owing to the hepatotoxicity risk, and, in this case, is not suitable considering the commercially available formulations of ATV and RTV.

Model predictions suggest concentrations at 12 h with twice-daily dosing are likely to be higher compared with concentrations observed at 24 h in the case of a once-daily, higher-dose regimen. Although no data with higher doses of ATV are available in the literature, studies with other PIs have highlighted different scenarios. According to Kendall et al. [47], a double dose of lopinavir/ritonavir + RIF was not associated with hepatotoxicity, while Nijland et al. [45] showed a high incidence of adverse events when a higher than standard dose of lopinavir/ritonavir tablets was combined with RIF. According to Cleijsen et al. [48], ATV plasma trough concentrations above 750 ng/mL were significantly related to the occurrence of increased total bilirubin concentrations. Future clinical studies should include a comprehensive evaluation of early signs of liver toxicity (transaminase elevations and bilirubin) and potential associations with PIs and RIF pharmacokinetics. The model predictions were applied for the design of a clinical trial protocol (DERIVE study; ATV/r 300/100 mg twice daily concurrently with a double dose of RIF [1200 mg] once daily) to evaluate the efficacy and toxicity of ATV when administered concomitantly with RIF in adults and special populations (NCT 04121195). Finally, patient adherence is a major factor necessary to achieve ART efficacy; consequently, three-times daily regimens are unlikely to represent suitable options.

PBPK modelling has been previously applied to predict DDIs between ART, anticancer, antimicrobial, and other classes of drugs [49,50,51,52,53,54]. Moreover, there is no study in the literature with RIF-mediated induction of CYP3A4 and transporter incorporated at the same time in a PBPK model to predict the increased plasma clearance of boosted PIs.

Although the model successfully predicted the PK of ATV, RTV and RIF, the model is characterized by some limitations. When assuming a well-stirred perfusion-limited model, instantaneous equilibrium of the drug concentration between blood and tissue into organs is considered [38]; however, during passive diffusion, a time lag for drugs to permeate across the membrane would be expected before achieving equilibrium, and this duration should not change the total exposure of the drug in the body (AUC24) but could impact the plasma concentration at a determined time. Moreover, membrane transporters can have a relevant impact on tissue distribution. The mechanisms involved in the uptake and efflux of drugs are complex and difficult to be determined in vitro. ATV distribution is not driven by passive diffusion alone and this could explain the underestimation of ATV Ctrough; partitioning into the tissue is difficult to model as well as some drug or organ-specific interactions. Another important point to consider is the administration with or without food, as demonstrated in the sensitivity analysis (see the ESM). The oral administration of ATV/r with food increases bioavailability and decreases pharmacokinetic variability. Furthermore, Ctrough is expected to be increased due to delayed absorption and an increase in time to reach maximum concentration [46], confirming how complex it is to predict Ctrough or the concentration at a specific time.

Although, in some cases the predicted ATV Ctrough was underestimated for the coadministration of ATV/r and RIF, the model suggests that sufficient Ctrough could be achieved with the 300/100 mg twice-daily regimen. The presented PBPK model does not provide a mechanistic description of toxicity due to the limited understanding of the underlying concentration-dependent mechanisms of hepatotoxicity. The described model was developed considering a population of healthy individuals, and pharmacokinetic differences have been described between HIV-positive patients and healthy volunteers [55]. Studies investigating the DDI between lopinavir and RIF showed a higher rate of hepatoxicity in healthy volunteers compared with HIV-infected individuals [56, 57]. For this purpose, clinical studies should include HIV-positive individuals to fully capture pharmacokinetic variability and potential differences in ADME processes.

The described PBPK approach could be applied in investigating DDIs between RIF and ART in special populations, such as children, elderly, and kidney and liver impairment since physiological and metabolic specificities of each population have been characterized and implemented in PBPK models previously [58,59,60,61]. Additionally, potential novel formulations of ART (long-acting) [62], different routes of administration (intramuscular, subcutaneous, etc.), and other tuberculosis agents (moderate inducers—rifabutin) [63] could be used in future studies to predict possible DDIs.

5 Conclusions

The simulations confirm that coadministration of RIF with ATV/r 300/100 mg once daily will result in subtherapeutic drug concentrations in PLWH coinfected with TB. The predicted data suggest an increased Ctrough of ATV/r 300/100 mg when administered twice daily compared with the once-daily regimen. However, a rational clinical evaluation of efficacy and toxicity should be considered in selecting sustainable dose adjustments, since, depending on the cut-off considered (PBA-IC90 = 14 ng/mL, or clinical = 150 ng/mL), some patients may present subtherapeutic Ctrough values.