Physiologically Based Pharmacokinetic Model of Rifapentine and 25-Desacetyl Rifapentine Disposition in Humans

Abstract

Rifapentine (RPT) is a rifamycin antimycobacterial and, as part of a combination therapy, is indicated for the treatment of pulmonary tuberculosis (TB) caused by Mycobacterium tuberculosis. Although the results from a number of studies indicate that rifapentine has the potential to shorten treatment duration and enhance completion rates compared to other rifamycin agents utilized in antituberculosis drug regimens (i.e., regimens 1 to 4), its optimal dose and exposure in humans are unknown. To help inform such an optimization, a physiologically based pharmacokinetic (PBPK) model was developed to predict time course, tissue-specific concentrations of RPT and its active metabolite, 25-desacetyl rifapentine (dRPT), in humans after specified administration schedules for RPT. Starting with the development and verification of a PBPK model for rats, the model was extrapolated and then tested using human pharmacokinetic data. Testing and verification of the models included comparisons of predictions to experimental data in several rat tissues and time course RPT and dRPT plasma concentrations in humans from several single- and repeated-dosing studies. Finally, the model was used to predict RPT concentrations in the lung during the intensive and continuation phases of a current recommended TB treatment regimen. Based on these results, it is anticipated that the PBPK model developed in this study will be useful in evaluating dosing regimens for RPT and for characterizing tissue-level doses that could be predictors of problems related to efficacy or safety.

INTRODUCTION

Rifapentine (RPT) is a rifamycin-class antibiotic indicated for the treatment of pulmonary tuberculosis (TB) caused by Mycobacterium tuberculosis and in the treatment of latent TB infection in patients at high risk of progression to TB disease. RPT has a longer half-life, increased affinity to serum protein binding (1), and a lower MIC against M. tuberculosis than rifampin, which is currently used as part of several first-line TB treatment regimens (2, 3). Moreover, the primary metabolite for RPT, 25-desacetyl rifapentine (dRPT), has also been found to be active against M. tuberculosis, although at markedly lower MICs (1, 3, 4). Because of these characteristics, RPT has been the subject of a number of clinical pharmacology studies aimed at evaluating pharmacokinetics and developing effective therapies (5–15). Although data from these investigations are valuable in their own right, mathematical modeling offers a way to complement these studies, synthesize their disparate data, and provide the clinician an additional tool to characterize and predict the absorption, distribution, metabolism, and excretion (ADME) of RPT under dosing conditions of interest.

One of the very few such mathematical models was developed by Savic et al. (16), who used a classical compartmental modeling approach to assess human population pharmacokinetics of both RPT and dRPT. This model described the absorption, metabolism, and clearance of these two species and accurately predicted their time course plasma concentrations in healthy volunteers. Unfortunately, compartmental concentrations in this model were not directly relatable to those in actual tissues of interest (e.g., the lung and liver) because the effects of plasma protein binding and blood-tissue partitioning of the parent drug and metabolite were not included. Moreover, because the study utilized data from healthy subjects, the effects of the disease on pharmacokinetic outcomes could not be characterized.

A finer-grained approach that specifically includes relevant physiological and biochemical effects and processes and facilitates examination of organ or tissue-level pharmacokinetics is physiologically based pharmacokinetic (PBPK) modeling. Regrettably, few PBPK models have been developed for anti-TB drugs, let alone RPT. Using targeted experimental data in mice, Reisfeld et al. (17) developed a PBPK model to describe the biodistribution of the second-line TB agent capreomycin, and because capreomycin is nephrotoxic (18), PBPK modeling allowed for tissue-specific concentration predictions at both the site of action for the antibiotic effect, the lung, and the site of potential toxicity, the kidney. Subsequently, Lyons et al. (19) used a rich set of literature data to create a PBPK model to describe the disposition of rifampin, which, as noted earlier, is a first-line agent in current therapies for TB. Although the above models are useful in simulating and comparing the disposition of anti-TB drugs in tissues of interest, they were developed using data from rodents and currently have limited applicability to humans.

To begin to address this gap, the principal aims of this study were to (i) develop a PBPK model to predict the ADME for rifapentine and its active metabolite in humans, (ii) test the model against available human study data, and (iii) make tissue-specific predictions of concentrations of RPT and dRPT in the lung and compare those to the MIC. The latter aim is particularly relevant because current dosing recommendations for anti-TB drugs are guided by knowledge of the unbound concentration of the agent in the plasma and by comparing this free fraction to the known MIC against M. tuberculosis (13). Because this plasma concentration may not accurately reflect that in the lung, the recommended dose may not provide the desired level of antibiotic effect.

MATERIALS AND METHODS

Approach.

To achieve the study aims, two PBPK models were developed, parameterized, and tested: one specific to the rat (R-PBPK) and another for humans (H-PBPK). The models shared the same compartmental structure and set of governing equations, with differences only in the parameter values, principally related to physiology and metabolism. Starting with development of the R-PBPK, tissue-specific pharmacokinetic data were used to compute key drug-tissue properties (e.g., partition coefficients) that were later utilized in the H-PBPK. Ultimately, both the R-PBPK and the H-PBPK were parameterized and verified using relevant sets of training and test data. Further details are given below.

Experimental data.

Pharmacokinetic data for RPT in rats were obtained from the work of Assandri et al. (20), which provided (i) drug concentrations in the plasma under multiple dosing conditions, (ii) concentrations obtained from homogenates of several relevant tissues after oral dosing, and (iii) the fraction of drug bound to plasma proteins over time. For development of the human model, a comprehensive review of the literature was conducted to identify pharmacokinetic studies where RPT was administered to adults as either a single dose or via repeated doses. Emphasis was placed on studies in which concentrations of both parent RPT and its metabolite dRPT were quantified because these coincident data could be used in the estimation of relevant metabolism and dRPT-specific parameters. As shown in Table 3, these data were divided into two parts: a “training” set used to determine unknown model parameters and a “validation” set, used to test and verify the model predictions.

TABLE 3.

Studies containing pharmacokinetic data for humans after oral dosing with rifapentine

Source (reference)	Dose (mg)	Regimena	TB infection	No. of subjects (sexb)
Data used for parameter estimation
Weiner et al. (12)	1,200	R (once weekly)	Yes	35 (M/F)
	900	R (once weekly)	Yes	35 (M/F)
	600	R (once weekly)	Yes	35 (M/F)
Data used for model testing/verification
Dooley et al. (14)	900	R (three times weekly)	No	15 (M/F)
Dooley et al. (6)	1,200	S	No	5 (M/F)
	900	R (daily dosing)	No	5 (M/F)
	600		No	5 (M/F)
Keung et al. (9)	600	S	No	20 (M/F)
Keung et al. (7)	600	S	No	20 (M)
Keung et al. (4)	600	S	No	15 (F)
Keung et al. (8)	600	S	No	23 (M)
	300	R (daily dosing)	No	23 (M)
	150	R (daily dosing)	No	23 (M)
Langdon et al. (10)	600	R (daily dosing, 4 days)	Yes	46 (M/F)
	750	R (daily dosing, 4 days)	Yes	46 (M/F)
	900	R (daily dosing, 4 days)	Yes	46 (M/F)
Reith et al. (13)	600	S	No	4 (M)

^aS, single dose; R, repeated dose.

^bM, male; F, female.

PBPK models.

The common PBPK model structure is shown in Fig. 1. The model comprises a set of compartments for RPT, identical to those used previously for rifampin (19), integrated with a simpler structure for the metabolite, dRPT, which consisted of only the lung and a “lumped” peripheral compartment. The compartmental species mass balance equations are similar to those used in this prior study (see the Appendix) with the exception of the description of oral absorption fraction for the parent compound and the explicit quantitation of the metabolite concentration over time described below.

FIG 1.

PBPK model structure.

Consistent with the experimental results from Assandri et al. (20), oral absorption was specified to be dose dependent. In particular, the following form was used to describe the oral fraction absorbed, F_a:

$$F_a=\frac{F_{a,k}}{D+F_{a,k}}$$ (1)

where D is the oral dose and F_a,k represents a constant to be fitted from the data.

Because the metabolite dRPT is active against M. tuberculosis and its level has been measured in several studies in humans, the present model included equations to explicitly track its rate of formation and distribution over time. The deacetylation reaction to transform RPT to dRPT in the liver for humans was assumed to follow Michaelis-Menten kinetics (21),

$$v=\frac{V_M{C}_{\text{liver}}^{\text{RPT}}}{K_m+C_{\text{liver}}^{\text{RPT}}+\frac{{\left(C_{\text{liver}}^{\text{RPT}}\right)}^2}{K_I}}$$ (2)

where v is the rate of RPT deacetylation and V_M, K_m, and K_I represent the maximum reaction rate, the Michaelis-Menten constant, and the substrate inhibition constant for RPT deacetylation, respectively. Although its mechanism of action is currently unknown, in vitro studies have demonstrated the activity of dRPT against M. tuberculosis (4), and because this species may exhibit similar antibiotic effects in vivo, its disposition may be of interest when characterizing anti-TB therapies involving RPT. Interestingly, although the levels of dRPT are quantifiable in humans after RPT administration (6–11, 13–15), similar studies in rats have shown that this chemical is undetectable in the plasma (20). Consistent with this observation, the metabolic transformation of RPT to dRPT was not included in the R-PBPK. Lastly, rather than using in vitro results for RPT and dRPT protein binding, unbound fractions for this PBPK model were calculated using results from M. tuberculosis-infected patients after RPT dosing (22).

Parameter estimation.

Parameters in the governing PBPK model equations were taken from the literature or were estimated using the procedures described below.

Physiological parameters.

Physiological compartment volumes and blood flow rates for human and rat were obtained from a report by Brown et al. (23). Compartment volumes were scaled linearly with body weight, blood flow rates were scaled with body weight to the 0.75 power (24), and the coefficients of variation for each organ volume and the arterial blood flow rate were set at 0.2 and 0.3, respectively (19, 25). The resulting physiological parameters for each compartment are summarized in Table 1.

TABLE 1.

Physiological and anatomical parameters

Parameter (U) or site	Abbreviation	Mean		CVa
		Rat	Human
Parameter
Body wt (kg)	BW	0.23	65	0.16
Cardiac output (liters/h/kg0.75)	QCC	14.1	16.2	0.2
Site
Lung	QLUC	14.1	16.2	0.3
	VLUC	0.005	0.0076	0.2
Brain	QBRC	0.02	0.12	0.3
	VBRC	0.0057	0.02	0.2
Fat	QFC	0.07	0.0675	0.3
	VFC	0.07	0.2142	0.2
Heart	QHC	0.049	0.045	0.3
	VHC	0.0033	0.0047	0.2
Muscle	QMC	0.278	0.145	0.3
	VMC	0.4043	0.4	0.2
Bone	QBC	0.122	0.05	0.3
	VBC	0.073	0.1429	0.2
Skin	QSKC	0.058	0.05	0.3
	VSKC	0.1903	0.0371	0.2
Kidney	QKC	0.141	0.18	0.3
	VKC	0.0073	0.0044	0.2
Spleen	QSC	0.01	0.01	0.3
	VSC	0.002	0.0026	0.2
Gut	QGC	0.14	0.14	0.3
	VGC	0.027	0.0171	0.2
Liver	QLAC	0.024	0.06	0.3
	VLC	0.0366	0.0257	0.2
Carcass	QCRC	0.088	0.1325	0.3
	VCRC	0.1015	0.0448	0.2
Blood
Venous	VBLVC	0.0493	0.0526	0.2
Arterial	VBLAC	0.0247	0.0263	0.2

^aCV, coefficient of variation.

Partition coefficients.

With data for the free concentration of RPT in the plasma (20), mean values for the tissue-blood partition coefficient, P_T:blood, were determined using the following equation:

$$P_{T:\text{blood}}=\frac{1}{\text{BP}}\left(\frac{C_{\text{tissue}}^{\text{RPT}}}{C_{\text{plasma},f}^{\text{RPT}}}\right)$$ (3)

where BP is the blood-plasma partition coefficient, and C_tissue^RPT and C_plasma,f^RPT are the measured tissue and free plasma concentrations of RPT, respectively. Tissue-plasma partition coefficients were computed for all model compartments based on time course tissue concentration data (20) using points during the elimination phase at which equilibrium had been reached in drug concentration between the tissue and the venous blood.

Other model parameters.

To include the effects of data uncertainty and interstudy variability on model outputs, unknown parameters were estimated within a Bayesian hierarchical context (26–28). Within this context, parameters were estimated by first computing partition coefficients and other relevant parameters for the R-PBPK and then using these parameter distributions as “priors” in the estimation of the human-specific parameters.

Simulation methodology and computing platform.

Once the parameter distributions had been computed, a Monte Carlo approach was used to generate a large family of simulation results that would account for interstudy variability and data uncertainty. These results were then aggregated and processed to yield mean and 95% prediction intervals for pharmacokinetic outcomes of interest.

Data from the literature were digitized using DigitizeIt v.1.5.8 (29). Simulations of the PBPK governing equations, including the Bayesian Markov chain Monte Carlo, and resulting model evaluation were conducted in MCSim v5.4 (30). Processing, analysis, and visualization of data were carried out using scripts written in Python v2.7.2 (31) utilizing the numpy (32), scipy (33), and matplotlib (34) packages. All computations were performed on a compute cluster running the 64-bit CentOS Linux operating system on 6-GB-linked Dell 2950 servers, each containing two quad-core 2.5 GHz Xeon processors and 64 GB of RAM.

RESULTS

Model parameter values.

Using the procedures and data detailed above, distributions for unknown model parameters were estimated. The resulting parameters (posterior distributions) for both rat- and human-specific models are listed in Table 2.

TABLE 2.

Physicochemical, biochemical, and clearance-related parameters^a

Description	Parameter (U)	Rat			Human
		Prior	Posterior	Source	Prior	Posterior	Source
Fraction bound
RPT	fb,R		0.97	19		0.994	20
dRPT	fb,D					0.976	20
Absorption
Fractional absorption constant	Fa,k	U(1, 1000)	N(27, 0.21)		N(27, 0.21)	N(21.23, 0.16)	Rat
Oral absorption rate	kSG (1/h)	N(0.31, 0.2)	N(0.30, 0.06)	19	N(0.30, 0.06)	N(0.33, 0.18)	Rat
Gut lumen reabsorption	kGLG (1/h)	N(0.17, 0.3)	N(0.17, 0.06)	18	N(0.17, 0.06)	N(0.17, 0.06)	Rat
Total blood clearance
RPT	CLC_R (liters/h-BW0.75)	U(0.01, 10)	N(0.74, 0.31)		N(0.74, 0.31)	N(0.64, 0.18)	Rat
dRPT	CLC_D (liters/h-BW0.75)				U(0.001, 100)	N(0.07, 0.28)
Fractional renal clearance	fR		0.13	19		0.13	Rat
Deacetylation
	Vmax C (μmol/h-BW0.75)				U(0.01, 100)	N(0.97, 0.22)	37
	Km (μmol)				N(37.1, 0.2)	N(34.29, 0.16)	37
	KI (μmol)				N(174, 0.2)	N(168.07, 0.17)	37
Partition coefficients
Lung	PLU	N(48.9, 0.2)	N(48.48, 0.17)	19		N(48.48, 0.17)
Brain	PBR	N(5.93, 0.2)	N(5.81, 0.17)	19		N(5.81, 0.17)
Fat	PF	N(79.8, 0.2)	N(78.67, 0.17)	19		N(78.67, 0.17)
Heart	PH	N(63.9, 0.2)	N(62.02, 0.18)	19		N(62.02, 0.18)
Muscle	PM	N(38.1, 0.2)	N(37.39, 0.17)	19		N(37.39, 0.17)
Bone	PB	N(28.3, 0.2)	N(27.33, 0.18)	19		N(27.33, 0.18)
Skin	PSK	N(43.5, 0.2)	N(43.22, 0.17)	19		N(43.22, 0.17)
Kidney	PK	N(88.7, 0.2)	N(87.47, 0.17)	19		N(87.47, 0.17)
Spleen	PS	N(49.9, 0.2)	N(49.71, 0.17)	19		N(49.71, 0.17)
Gut	PG	N(42.1, 0.2)	N(38.69, 0.18)	19		N(38.69, 0.18)
Liver	PL	N(183.3, 0.2)	N(164.21, 0.18)	19		N(164.21, 0.18)
Carcass	PCR	N(28.3, 0.2)	N(29.04, 0.18)	19		N(29.04, 0.18)
Peripheral	PP				U(0.1, 200)	N(5.50, 0.29)

^aN(a, b) denotes a normal distribution with a mean of a and fractional coefficient of variation (CV), b; U(a, b) represents a uniform distribution bounded by the minimum (a) and maximum (b). A single number in the posterior column represents no distribution. When “rat” is specified as the source, the posterior mean used in the R-PBPK (with a fractional CV of 0.3) was used as the prior distribution for the H-PBPK. BW, body weight.

Testing and verification of the rat-specific model (R-PBPK).

Using the computed parameters for the R-PBPK, simulations were conducted and compared to in vivo time course concentration values from a literature study (20) that detailed plasma and tissue pharmacokinetics after a single 10-mg/kg oral dose in the rat. This comparison is illustrated in Fig. 2, which shows experimental data (points) and predicted mean (solid line) and 95% prediction intervals (dashed lines) for the PBPK model.

FIG 2.

Simulations of rifapentine pharmacokinetics following a 10 mg/kg oral dose in the rat, showing concentration profiles in the plasma (A), lung (B), kidney (C), and spleen (D). Solid and dashed lines represent the simulated mean and 95% prediction intervals, respectively, whereas transparent circles represent the training set data from a study by Assandri et al. (20). C_PL, concentration in plasma; C_LU, concentration in lungs; C_K, concentration in kidneys; C_S, concentration in spleen.

Testing and verification of the human-specific model (H-PBPK) for single-dose scenarios.

Throughout the studies, training set data were used for parameter estimation (model calibration), while verification data were used for model evaluation (27). Using the set of parameters listed in Tables 1 and 3, simulations were run for 600-, 900-, and 1,200-mg single oral doses of RPT and compared to the corresponding dose training and verification data referenced in Table 3. Figure 3 shows the results of these comparisons for both RPT and dRPT in the plasma over multiple studies. The range of the experimental doses shown in this figure match those in a standard treatment regimen for TB treatment (1, 35). These comparisons show that the experimental data fall within the 95% prediction intervals, indicating that the model can accurately predict the pharmacokinetics of the drug and account for the variance in this measure across the population sampled.

FIG 3.

Comparison of simulation results to human plasma concentration data for RPT and dRPT following oral administration of 600-, 900-, and 1,200-mg oral RPT doses. Training set data are shown as open circles (○), whereas data from the validation set are shown as dark “×” symbols.

As an additional verification, pharmacokinetic measures for RPT (e.g., maximum concentration, area under the curve, and half-life) were computed from the model and compared to those from the literature. In particular, Table 4 shows the predicted values from simulations of time course plasma concentrations and those in a report by Langdon et al. (11), which were based on experimental data that were not used in the model parameterization.

TABLE 4.

Computed pharmacokinetic measures for rifapentine^a

Parameter	Symbol (U)	Model prediction	Expt (%CV)b
Maximum plasma concn	Cmax (μg/ml)	15.48 (21)	15.48 (30)
Drug half-life	t1/2	10.92 (14)	12.03 (20)
Area under the curve from time zero extrapolated to infinity	AUC0–∞ (μg·h/ml)	382.19 (25)	380.63 (31)
Apparent oral clearance	CL/F (liters/h)	1.69 (29)	1.92 (44)
Apparent vol of distribution	V/F (liters)	40.81 (29)	35.85 (47)

^aMeasures were derived from pharmacokinetic data (or simulation results) for a regimen consisting of a 900-mg dose administered repeatedly, 4 days apart. Shown are the median properties (%CV).

^bExpt, observed values reported from “occasion 2” in the study of Langdon et al. (10).

Testing and verification of the human-specific model (H-PBPK) for repeated dosing scenarios.

Relevant to standard treatments regimens for M. tuberculosis infection (36, 37), model simulations were conducted for three repeated dosing scenarios for which well-controlled experimental data were available: regimen A consisted of a 600-mg dose every day starting 3 days after an initial 600-mg dose (9), regimen B consisted of a 900-mg dose every 2 days (15), and regimen C consisted of a 600-mg dose every 3 days (9). Both the experimental data and corresponding simulation results are displayed in Fig. 4.

FIG 4.

Model verification for repeated dosing: predictions of plasma RPT concentrations for the three dosing regimens described in the text. Solid and dashed lines represent the simulated mean and 95% prediction intervals, respectively, while the triangles denote experimental data from the test set.

Prediction of lung concentrations using the human-specific model.

Along with the predicted plasma concentrations shown in Fig. 4, simulations yielded the levels of RPT and dRPT in the lung over time. As an illustration of potential antibiotic effect, Fig. 5 shows the predicted levels of RPT, dRPT, and total rifamycin over time in the lung for the three RPT oral dosing scenarios described above.

FIG 5.

Model predictions of time course concentrations in the lungs after the three repeated oral regimens described in Fig. 4, showing concentrations of RPT (solid line), dRPT (dashed line), and total rifamycin (dot-dashed line).

There are a number of current and anticipated guidelines for the treatment of both active TB disease and latent TB infection involving rifapentine as part of a combination therapy (3, 38–41). Across these regimens, doses of RPT range from 600 to 1,200 mg with administration frequencies extending from daily to once weekly. To determine the pharmacokinetics and potential antibiotic effect of RPT and dRPT across these regimens, the model was used to predict lung concentrations of these species in a simulated population resulting from various doses of RPT at three administration frequencies: once weekly, twice weekly, and daily. The simulated population in these cases was the group of (virtual) individuals whose pharmacokinetics were predicted by Monte Carlo sampling across the estimated physiological and biochemical parameter distributions determined using the Bayesian procedure described earlier. Figure 6 depicts a cumulative distribution function of the dose response that indicates the probability that RPT or dRPT concentrations in the lungs are above their respective MICs, which were 0.063 mg/liter for RPT and 0.25 mg/liter for dRPT (4).

FIG 6.

Probability that the minimum steady-state concentration of RPT in the lung exceeds the MIC.

DISCUSSION

Methodology.

The PBPK models detailed herein utilized a system of biologically based physiological and biochemical descriptions and species mass balance equations to make tissue-specific pharmacokinetic predictions for RPT and its metabolite, dRPT, in relevant tissue compartments for both rats and humans. The values of unknown parameters in the model system were estimated within a hierarchical Bayesian framework to incorporate data uncertainties and interstudy variability, and Monte Carlo simulations were conducted using these distributions to quantify their effect on pharmacokinetic predictions.

Testing and verification.

Model predictions were generally in good agreement with data from the literature. As shown in Fig. 2, the experimental data corresponding to plasma and tissue (lung, kidney, and spleen) concentrations were within the 95% prediction intervals for the rat-specific PBPK model, demonstrating its ability to reasonably predict tissue-level RPT pharmacokinetics in this species. For the human-specific PBPK model, single-dose data from multiple studies for both RPT and dRPT concentrations were in reasonable concordance with results from simulations (Fig. 3). The relatively poorer agreement between predictions and data for dRPT is likely related to variability in metabolism between subjects, differences in analytical quantitation methods between studies, and/or an inadequate specification for RPT metabolism in the model. For repeated oral dosing, model predictions for RPT concentrations compare well with experimental data for all three dosing scenarios (Fig. 4). Finally, as shown in Table 4, there was reasonable to very good agreement between pharmacokinetic measures, such as C_max and area under the concentration-time curve (AUC_0–∞), computed from simulations and experimental data.

Model predictions.

A principal benefit of the PBPK approach is the ability to estimate internal doses that are generally not available in human subjects or patients. Figure 5 shows the predicted levels of RPT, dRPT, and total rifamycin over time in the lung for three repeated oral dosing scenarios for RPT. It should be noted that dRPT does not bind to plasma protein as readily as RPT. This decrease in fractional protein binding increases the bioavailability of dRPT and results in a higher predicted concentration of metabolite within the lungs. It is also notable that for all three dosing regimens, the predicted minimum concentrations for both RPT and dRPT in the lung are significantly above their in vitro MICs for M. tuberculosis of 0.063 and 0.25 μg/ml, respectively (4). Finally, the total rifamycin concentration is presented in this figure as an indication that there may be additional bactericidal effect owing to the presence of dRPT; however, because the mechanism of action of dRPT is not currently known, the overall pharmacodynamic effect cannot be assumed to be additive.

Finally, the model was used to assess the potential efficacy of regimens spanning current recommended anti-TB therapies that include RPT (35, 38–41). This assessment was conducted by computing lung tissue concentrations and comparing those to the MIC for M. tuberculosis. These results are depicted in Fig. 6, which shows the probability of the minimum steady-state drug concentration in the lungs exceeding the MIC for M. tuberculosis for three distinct administration frequencies. For illustration, this figure also contains an example probability threshold of 0.98 from which a minimum protective dose (MPD) can be found. Using this probability threshold, the MPD was seen to be 26 mg for once-daily dosing, 225 mg for the twice-weekly regimen, and 910 mg for the once-weekly administration (see Fig. 6). Based on these estimates, anti-TB regimens that include daily administration of 1,200 mg of RPT (39) for active TB disease exceed the predicted MPD, whereas those that reduce this dose and frequency for the treatment of latent TB infection to 750 mg once weekly (40) fall below the predicted MPD. It is important to note that these results do not include the antimicrobial effects of other anti-TB drugs given as part of the regimen; however, depending on the margin of safety, they could suggest possible adjustments to the dosing schedule.

Novel features and advantages of the present model.

Unlike previous PBPK models for anti-TB drugs (17, 19), the present model was developed to make predictions of pharmacokinetics in humans. To quantify and illustrate uncertainty in simulation outputs, model development and testing included a Bayesian approach to parameter estimation and Monte Carlo simulations. These features allowed the verified model to be used to assess a current treatment regimen by comparing lung-specific predictions of antibiotic concentrations with the MIC for M. tuberculosis. In addition, because administration of certain rifamycins (including rifapentine) has resulted in signs of drug-induced liver injury (42), liver-specific predictions of drug levels could help inform treatments that minimize the potential for hepatotoxicity. Like most PBPK models, the one described here allowed prediction of species concentrations in tissues and/or organs of interest and provided a systematic way to extrapolate across doses and between species. With these features, the model has the potential to aid in dose optimization and in the determination of how pharmacokinetic endpoints depend on alterations to anatomical, physiological, and biochemical parameters.

Limitations and deficiencies of the present model.

The present H-PBPK approach currently suffers from several limitations and deficiencies: (i) it is not immediately applicable to the analysis of combination drug therapies; (ii) the pharmacokinetic predictions, while expected to be valid and useful for a population or subpopulation, may contain too much uncertainty for individualized applications like personalized medicine; (iii) parameters for the R-PBPK were estimated using relatively few data points, and inaccuracies in some of these parameters were propagated to the human-specific model; and (iv) the specification used for RPT metabolism is biologically plausible but, owing to a lack of data, has not been adequately verified.

Future directions.

Using the present model as a foundation, efforts are under way to add additional anti-TB agents (e.g., isoniazid or bedaquiline) to simulate combination therapies and quantify pharmacokinetic drug-drug interactions. Other enhancements include integration of pharmacodynamic descriptions that include M. tuberculosis growth and drug-induced killing kinetics (43, 44) and descriptions of RPT-induced hepatotoxicity (5, 42).

APPENDIX

The following are the governing equations for the PBPK model, which mathematically specify the species mass balances and relevant biological phenomena in each compartment. In these equations, a superscript “i” corresponds to either parent RPT or the dRPT metabolite. Although RPT disposition is described in all of the discrete tissue compartments, dRPT is modeled within only two compartments: lung and peripheral. Individual tissue blood flow rates, Q_T, were computed using total cardiac flow as Q_T = Q_C × Q_TC and Q_C = Q_CC × BW^0.75. Q_TC values for the percentages of cardiac flow to each tissue are given in Table 1. Finally, the drug concentration entering tissues in the arterial blood is the free concentration of drug, C_A,fⁱ, and concentrations leaving the tissues are calculated using the concentrations within the tissue compartment along with the respective partition coefficients: C_T,venⁱ = C_Tⁱ/P_T.

(i) Lung:

$$\frac{d{A}_{\text{lung}}^i}{dt}=Q_C\left(C_{\text{venous}}^i-C_{L,\text{ven}}^i\right)$$

(ii) Kidney:

$$\frac{d{A}_K^{\text{RPT}}}{dt}=Q_K\cdot \left(C_{A,f}^{\text{RPT}}-C_{K,\text{ven}}^{\text{RPT}}\right)-f_R\cdot C{L}^{\text{RPT}}\cdot C_{\text{Art}}^{\text{RPT}}$$

where CL and f_R are the total blood clearance and fractional renal clearance, respectively.

(iii) Liver and metabolism:

$$v=\frac{V_M{C}_{\text{liver}}^{\text{RPT}}}{K_m+C_{\text{liver}}^{\text{RPT}}+\frac{{\left(C_{\text{liver}}^{\text{RPT}}\right)}^2}{K_I}}$$

$$\frac{d{A}_L^{\text{RPT}}}{dt}=Q_{\text{LA}}{C}_{A,f}^{\text{RPT}}+Q_S{C}_S^{\text{RPT}}+Q_G{C}_G^{\text{RPT}}-Q_L{C}_{L,\text{ven}}^{\text{RPT}}-\begin{array}{c}\left(1-f_R\right)\cdot \text{CL}\cdot \left(Q_{\text{LA}}{C}_{\text{Art}}^i+Q_S{C}_S^i+Q_G{C}_G^i\right)/Q_L-v\end{array}$$

where Q_L is the total blood flow leaving the liver and is the sum of the spleen, gut, and inlet liver blood flow rates. Biliary clearance for RPT occurs in the liver where the fraction of total blood clearance is equal to 1 − f_R.

(iv) Gut:

$$\frac{d{A}_G^{\text{RPT}}}{dt}=Q_G\left(C_{A,f}^{\text{RPT}}-C_{G,\text{ven}}^{\text{RPT}}\right)+k_{\text{GLG}}{A}_{\text{GL}}^{\text{RPT}}+k_{\text{SG}}{A}_{\text{RPT}}^{\text{stom}}$$

(v) Stomach:

$$\frac{d{A}_{\text{Stom}}^{\text{RPT}}}{dt}=F_{a}D\cdot d(t)-k_{\text{SG}}{A}_{\text{Stom}}^{\text{RPT}}$$

where F_a is the fractional absorption, D is the ingested dose, and d(t) describes the time dependence of the dosing schedule.

(vi) Remaining tissues:

$$\frac{d{A}_T^i}{dt}=Q_T\hspace{0.17em}(C_{A,f}^i-C_{T,\text{ven}}^i)$$

(vii) Arterial blood:

$$\frac{d{A}_A^i}{dt}=Q_C\left(C_{L,\text{ven}}^i-C_{A,f}^i\right)-{\alpha }^i{f}_R\cdot \mathrm{C}{\mathrm{L}}^{\text{dRTP}}\cdot C_{A,f}^{dRPT}$$

Renal clearance for dRPT occurs based on the free concentration of dRPT in the arterial blood and is removed from the arterial blood compartment; therefore, α^RPT = 0 and α^dRPT = 1.

(viii) Venous blood:

$$\frac{d{A}_V^i}{dt}=\sum _j^{N_T}{Q}_j{C}_{j,\text{ven}}^i+{\beta }^{i}v$$

All concentrations exiting the tissues are pooled in the venous blood compartment. Because there is no liver compartment for the dRPT submodel, any generation of dRPT is within the venous blood; therefore, β^RPT = 0 and β^dRPT = 1.

(ix) Peripheral compartment:

$$\frac{d{A}_P^{\text{dRPT}}}{dt}=Q_C\left(C_{A,f}^{\text{dRPT}}-C_{P,\text{ven}}^{\text{dRPT}}\right)-\left(1-f_R\right)\cdot C{L}^{\text{dRPT}}\cdot C_{P,\text{ven}}^{\text{dRPT}}$$

Biliary clearance occurs within the peripheral compartment where the fraction of total clearance is equal to 1 − f_R.

Funding Statement

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.