Incorporating target-mediated drug disposition in a minimal physiologically-based pharmacokinetic model for monoclonal antibodies

Target-mediated drug disposition (TMDD) usually accounts for nonlinear pharmacokinetics (PK) of drugs whose distribution and/or clearance are affected by their targets owing to high affinity and limited capacity. TMDD is frequently reported for monoclonal antibodies (mAb) for such reason. Minimal physiologically-based pharmacokinetic models (mPBPK), which accommodate the unique PK behaviors of mAb, provide a general approach for analyzing mAbs PK and predicting mAb interstitial concentrations in two groups of tissues. This study assessed the feasibility of incorporating TMDD into mPBPK models to consider target-binding in either plasma (cTMDD) or interstitial fluid (ISF) (pTMDD). The dose-related signature profiles of the pTMDD model reveal a parallel early decay phase, in contrast with the cTMDD model that exhibits a faster initial decline for low doses. The parallel early phase in the pTMDD model is associated with the slow perivascular extravasation of mAb, which restricts the initial decline regardless of interstitial target-mediated elimination. The cTMDD and pTMDD models both preserve the long terminal phase that is typically perceived in conventional two-compartment (2CM) and TMDD models. Having TMDD in ISF impacts the typical relationships between plasma concentrations and receptor occupancy, and between saturation of apparent nonlinear clearance and saturation of receptors. The vascular reflection coefficient (σ _v ) was found to affect receptor occupancy in ISF. In the cTMDD model, saturation of nonlinear clearance is equivalent to saturation of receptors. However, in the pTMDD model, they are no longer equal and all parameters pertaining to receptors or receptor binding (R _total , K _D , K _ss , k _int ) shifts such relationships. Different TMDD models were utilized in analyzing PK for seven mAbs from digitized literature data. When the target is in plasma, the cTMDD model performed similarly to the 2CM and TMDD models, but with one less system parameter. When the target exists in ISF, the pTMDD functioned well in analyzing only plasma data to reflect interstitial target binding properties. Assigning TMDD consistent with target-expressing tissues is important to obtain reliable characterizations of receptors and receptor binding. The mPBPK model exhibits excellent feasibility in integrating TMDD not only in plasma but also in ISF.     

Selection between Michaelis–Menten and target-mediated drug disposition pharmacokinetic models

Target-mediated drug disposition (TMDD) models have been applied to describe the pharmacokinetics of drugs whose distribution and/or clearance are affected by its target due to high binding affinity and limited capacity. The Michaelis–Menten (M–M) model has also been frequently used to describe the pharmacokinetics of such drugs. The purpose of this study is to investigate conditions for equivalence between M–M and TMDD pharmacokinetic models and provide guidelines for selection between these two approaches. Theoretical derivations were used to determine conditions under which M–M and TMDD pharmacokinetic models are equivalent. Computer simulations and model fitting were conducted to demonstrate these conditions. Typical M–M and TMDD profiles were simulated based on literature data for an anti-CD4 monoclonal antibody (TRX1) and phenytoin administered intravenously. Both models were fitted to data and goodness of fit criteria were evaluated for model selection. A case study of recombinant human erythropoietin was conducted to qualify results. A rapid binding TMDD model is equivalent to the M–M model if total target density R _tot is constant, and R _tot K _D /(K _D  + C) ²  ≪ 1 where K _D represents the dissociation constant and C is the free drug concentration. Under these conditions, M–M parameters are defined as: V _max  = k _int R _tot V _c and K _m  = K _D where k _int represents an internalization rate constant, and V _c is the volume of the central compartment. R _tot is constant if and only if k _int  = k _deg, where k _deg is a degradation rate constant. If the TMDD model predictions are not sensitive to k _int or k _deg parameters, the condition of R _tot K _D /(K _D  + C) ²  ≪ 1 alone can preserve the equivalence between rapid binding TMDD and M–M models. The model selection process for drugs that exhibit TMDD should involve a full mechanistic model as well as reduced models. The best model should adequately describe the data and have a minimal set of parameters estimated with acceptable precision.     

Methods of solving rapid binding target-mediated drug disposition model for two drugs competing for the same receptor

The target-mediated drug disposition (TMDD) model has been adopted to describe pharmacokinetics for two drugs competing for the same receptor. A rapid binding assumption introduces total receptor and total drug concentrations while free drug concentrations C _A and C _B are calculated from the equilibrium (Gaddum) equations. The Gaddum equations are polynomials in C _A and C _B of second degree that have explicit solutions involving complex numbers. The aim of this study was to develop numerical methods to solve the rapid binding TMDD model for two drugs competing for the same receptor that can be implemented in pharmacokinetic software. Algebra, calculus, and computer simulations were used to develop algorithms and investigate properties of solutions to the TMDD model with two drugs competitively binding to the same receptor. A general rapid binding approximation of the TMDD model for two drugs competing for the same receptor has been proposed. The explicit solutions to the equilibrium equations employ complex numbers, which cannot be easily solved by pharmacokinetic software. Numerical bisection algorithm and differential representation were developed to solve the system instead of obtaining an explicit solution. The numerical solutions were validated by MATLAB 7.2 solver for polynomial roots. The applicability of these algorithms was demonstrated by simulating concentration?Ctime profiles resulting from exogenous and endogenous IgG competing for the neonatal Fc receptor (FcRn), and darbepoetin competing with endogenous erythropoietin for the erythropoietin receptor. These models were implemented in ADAPT 5 and Phoenix WinNonlin 6.0, respectively.     

A physiologically based pharmacokinetic model to predict the pharmacokinetics of highly protein‐bound drugs and the impact of errors in plasma protein binding

Predicting the pharmacokinetics of highly protein‐bound drugs is difficult. Also, since historical plasma protein binding data were often collected using unbuffered plasma, the resulting inaccurate binding data could contribute to incorrect predictions. This study uses a generic physiologically based pharmacokinetic (PBPK) model to predict human plasma concentration–time profiles for 22 highly protein‐bound drugs. Tissue distribution was estimated from in vitro drug lipophilicity data, plasma protein binding and the blood: plasma ratio. Clearance was predicted with a well‐stirred liver model. Underestimated hepatic clearance for acidic and neutral compounds was corrected by an empirical scaling factor. Predicted values (pharmacokinetic parameters, plasma concentration–time profile) were compared with observed data to evaluate the model accuracy. Of the 22 drugs, less than a 2‐fold error was obtained for the terminal elimination half‐life (t_1/2, 100% of drugs), peak plasma concentration (C_max, 100%), area under the plasma concentration–time curve (AUC_0‐t, 95.4%), clearance (CL_h, 95.4%), mean residence time (MRT, 95.4%) and steady state volume (V_ss, 90.9%). The impact of f_up errors on CL_h and V_ss prediction was evaluated. Errors in f_up resulted in proportional errors in clearance prediction for low‐clearance compounds, and in V_ss prediction for high‐volume neutral drugs. For high‐volume basic drugs, errors in f_up did not propagate to errors in V_ss prediction. This is due to the cancellation of errors in the calculations for tissue partitioning of basic drugs. Overall, plasma profiles were well simulated with the present PBPK model. Copyright © 2016 John Wiley & Sons, Ltd.     

A cell-level model of pharmacodynamics-mediated drug disposition

We aimed to develop a cell-level pharmacodynamics-mediated drug disposition (PDMDD) model to analyze in vivo systems where the PD response to a drug has an appreciable effect on the pharmacokinetics (PK). An existing cellular level model of PD stimulation was combined with the standard target-mediated drug disposition (TMDD) model and the resulting model structure was parametrically identifiable from typical in vivo PK and PD data. The PD model of the cell population was controlled by the production rate k _in and elimination rate k _out which could be stimulated or inhibited by the number of bound receptors on a single cell. Simulations were performed to assess the impact of single and repeated dosing on the total drug clearance. The clinical utility of the cell-level PDMDD model was demonstrated by fitting published data on the stimulatory effects of filgrastim on absolute neutrophil counts in healthy subjects. We postulated repeated dosing as a means of detecting and quantifying PDMDD as a single dose might not be sufficient to elicit the cellular response capable of altering the receptor pool to visibly affect drug disposition. In the absence of any PD effect, the model reduces down to the standard TMDD model. The applications of this model can be readily extended to include chemotherapy-induced cytopenias affecting clearance of endogenous hematopoietic growth factors, different monoclonal antibodies and immunogenicity effects on PK.     

Effects of bladder resorption on pharmacokinetic data analysis

In modern pharmacokinetic analysis, the urinary bladder is usually viewed as a nonreturning compartment or storage site for renally excreted compounds. Our previous studies have indicated appreciable bladder resorption of drugs. The present study used computer simulations to evaluate the quantitative importance of several potential determinants of bladder resorption, namely the bladder resorption rate constant (k _a), interval between bladder voiding (Δt _void),ratio of renal elimination rate constant to overall elimination rate constant (k _ex:k _el ratio), andk _el ort _1/2. The data identifiedk _a, Δt _void, andk _ex:k _el ratio as the three most important determinants of the rate and extent of bladder resorption. We further examined the errors introduced in the derived pharmacokinetic parameters due to omission of bladder resorption. Plasma concentration-time profiles and urinary excretion-time profiles were generated by simulations using different values ofk _a, Δt _void, andk _ex:k _el ratio. These profiles were used to derive the pharmacokinetic parameters, including the renal clearance (CL _renal), total body clearance (CL _total), nonrenal clearance (CL _nonrenal),t _1/2, mean residence time (MRT), amount and fraction of dose excreted in urine (A _ex andf _e), and volume of distribution at steady state (Vd _ss). Data show that resorption of drug from the bladder into the systemic circulation increased the area under the plama concentration-time profile,MRT andt _1/2, but decreasedCL _renal,CL _total,A _ex, andf _e.Vd _ss was relatively unchanged. Overestimation of MRT andt _1/2 was dependent onk _a,k _ex:k _el ratio,and Δt _void. Underestimation inCL _renal,A _ex, andf _e was not dependent on thek _ex:k _el ratio, but was affected by changes ink _a and Δt _void.CL _renal andf _e were the most sensitive pharmacokinetic parameters, with a≥50% underestimation at ak _a value that we reported previously, for the bladder absorption of antipyrine in rats with intact urothelium. In summary, these data indicate (i) alteration in the plasma concentration-time profiles and urinary excretion-time profiles due to bladder resorption, and (ii) substantial over-or underestimation in the derived pharmacokinetic parameters due to erroneous omission of bladder resorption. Supported in part by MERIT grant R37 CA-49816, and Research Career Development Award K04 CA-01497 for J. L-S. Au, from The National Cancer Institute, National Institutes of Health, Department of Health and Human Services.     

Dose correction for the Michaelis–Menten approximation of the target-mediated drug disposition model

The Michaelis–Menten (M–M) approximation of the target-mediated drug disposition (TMDD) pharmacokinetic (PK) model was derived based on the rapid binding (RB) or quasi steady-state (QSS) assumptions that implied that the target and drug binding and dissociation were in equilibrium. However, the initial dose for an IV bolus injection for the M–M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M–M approximation. We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant an identifiable parameter that was not for the original M–M model. Finally, we performed a simulation exercise to check if the correction will impact the model performance and the bias of the M–M parameter estimates. We used literature data to simulate plasma drug concentrations described by the RB/QSS TMDD model. The simulated data were refitted by both models. All the parameters estimated from the original M–M model were substantially biased. On the other hand, the corrected M–M is able to accurately estimate these parameters except for equilibrium constant K_m. Weighted sum of square residual and Akaike information criterion suggested a better performance of the corrected M–M model compared with the original M–M model. Further studies are necessary to determine the importance of this correction for the M–M model applications to analysis of TMDD driven PK data.     

Significance of ratios of different volumes of distribution in pharmacokinetics

Multicompartmental pharmacokinetics involves the four volumes: V_c = volume of the central compartment; V_ss = volume of distribution steady-state; V_β = volume of distribution beta; and V_ext = the extrapolated volume of distribution. The ratio V_c/V_ext is indicative of the degree of multicompartmental character of a set of data. The quantity (V_ext/V_β)?1 is the fractional error in the total clearance when one assumes a monoexponential rather than a polyexponential equation for disposition of a drug. The ratio V_ss/V_β indicates how well the one-compartment body model predicts average amounts of drug in the body when a multicompartmental model is actually operative. The quantity (V_ss/V_c)? 1 is equal to either k₁₂/k₂₁ or k₁₂/k₂₁ + k₁₃/k₃₁ of the two- and three-compartmental mammillary models. Examples from the literature are reported and discussed.     

A Full Target-Mediated Drug Disposition (TMDD) Model to Explain the Changes in Recombinant Human Erythropoietin (rhEpo) Pharmacokinetics in Patients with Different Bone Marrow Integrity Following Hematopoietic Transplantation

Our aim was to build a mechanistic full target-mediated drug disposition (TMDD) model for rhEpo to better understand rhEpo disposition, Epo receptor (EpoR) synthesis, and degradation in hematopoietic transplant patients with four distinct bone marrow conditions. All PK data were analyzed simultaneously using the nonlinear mixed effect modeling approach with NONMEM. The final model was a two-compartmental full TMDD model, which adequately characterizes rhEpo PK in patients and provides insight into the dynamics of free EpoR, rhEpo-EpoR, and total EpoR. The model predicted association rate constant (k_on), dissociation rate constant (k_off), and internalization rate constant (k_int) were 0.0276 pM^?1h^?1, 0.647 h^?1, and 0.255h^?1, respectively, which were supported by experimental data. Also, the EpoR degradation rate constant (k_deg) was estimated to be 0.461 h^?1. EpoR production rate was estimated to be 37.5 pM/h for adults at pre-ablation baseline and 5.91 pM/h, and 4.19 pM/h in the early post-transplant post-engraftment, and late post-transplant full engraftment. Our model provides extensive information on the dynamics of free EpoR, total EpoR and rhEpo-EpoR, and proven to be more robust and can provide more physiologically relevant binding parameters than previous models.     

Evaluation of the Clearance of a Sublingual Buprenorphine Spray in the Beagle Dog Using Gamma Scintigraphy

Purpose The aim of this study was to evaluate clearance from the buccal cavity and pharmacokinetic profiles of a sublingual spray formulation in the dog, to assist in interpretation of future pharmacokinetic studies. Methods Radiolabelled buprenorphine in a spray formulation (400 μg/100 μl in 30% ethanol) was administered sublingually to four beagle dogs, and the residence in the oral cavity was determined using gamma scintigraphy. Pharmacokinetic sampling was performed to facilitate correlation of location of dose with significant pharmacokinetic events. Results Scintigraphic imaging revealed that clearance of the formulation from the oral cavity was rapid, with a mean T _50% clearance of 0.86 ± 0.46 min, and T _80% clearance of 2.75 ± 1.52 min. In comparison, absorption of buprenorphine was relatively slow, with a T _max of 0.56 ± 0.13 h. Good buccal absorption despite short residence time can be explained by lipophilicity of buprenorphine enabling rapid sequestration into the oral mucosa, prior to diffusion and absorption directly into systemic circulation. Conclusion This study demonstrated rapid clearance of a sublingual solution from the canine oral cavity, with T _50% similar to results previously reported in man, providing initial confidence in using a conscious dog model to achieve representative residence times for a sublingual solution.     

Comparison of the Pharmacokinetics and Pharmacodynamics of the Aldose Reductase Inhibitors,AL03152 (RS), AL03802 (R), and AL03803 (S)

The pharmacokinetics of AL03152 (RS) and its enantiomers, AL03802 (R) and AL03803 (S), were studied in the Sprague–Dawley rat following intravenous bolus administration. The enantiomers had differing pharmacokinetic profiles, while the racemic compound exhibited pharmacokinetic parameters approximating the mean values of the individual enantiomers. The total clearance (CL_T) values of the two enantiomers were similar, but the intrinsic clearance (Cl_int) was much greater for the S-enantiomer than for the R-enantiomer. The volume of distribution (V_ss) for AL03802 (R) was threefold greater than that for AL03803 (S). The stereoselectivity in V _ss could not be totally accounted for by the slight difference in serum protein binding of the isomers and resulted in a difference in the half-lives of the enantiomers. Only the R-isomer exhibited a persistent terminal elimination phase, consistent with more extensive tissue binding than the S-isomer. AL03152 enantiomers were equivalent in potency assessed from in vitro IC₅₀ values toward rat lens aldose reductase and rat kidney L-hexonate dehydrogenase and lens EC₅₀ values in diabetic rats.     

Verofylline pharmacokinetics in dietary-induced obese rats: Role of fat mass and protein binding in determining volume of distribution

1. Verofylline, a lipophilic polysubstituted methylxanthine, was utilized to examine how severely altered body composition in obesity affects drug disposition; the role of fat-free mass, fat mass and protein binding in determining the volume of distribution (V_ss) was investigated. Obesity was induced by feeding Sprague-Dawley rats for 8 months with a calorie-dense diet; the obese rats showed increases of 50% in total body mass and 150% in body fat.

2. Both the absolute V_ss and the clearance (Cl) in the obese rats increased 2-fold over control. Since Cl and V_ss increased similarly, the half-life of verofylline in obese rats did not change.

3. The increase of Cl in obese rats can be accounted for by metabolic function related to fat-free mass and decreased serum binding. Similarly, an increase in fraction unbound and in total body mass accounted for the increase in V_ss.

4. Based on in vitro measurements of muscle and fat tissue uptake of verofylline, and the assumed body spaces (from tritium dilution method), the predicted values for V_ss closely approximated those of observed values. The semi-physiological model proposed here appears adequate to relate changes of body composition and serum protein binding in obesity to V_ss.     

Effect of Receptor Up-Regulation on Insulin Pharmacokinetics in Streptozotocin-Treated Diabetic Rats

The present study investigated the mechanism by which the disposition of insulin is altered in streptozotocin (STZ)-treated diabetic rats as compared with 48-hr-fasted normal (control) rats. It was shown by an indocyanine green infusion method that the hepatic plasma flow rate (Q _H) in diabetic rats (1.64 ml/min/g liver) is significantly higher than that in control rats (0.982 ml/min/g liver). The portal injection technique revealed that the unidirectional clearance (CL_on), which represents the binding of A₁₄-¹²⁵ I-insulin to surface receptors in the liver, is significantly elevated in diabetic rats, suggesting an increase in the surface receptor number R _T), i.e., up-regulation in the liver. In both control and diabetic rats, the total-body clearance (CL_tot) and steady-state volume of distribution (Vd _ss) of labeled insulin decreased significantly with a simultaneous injection of unlabeled insulin (8 U/kg), confirming that the disposition of insulin is affected largely by specific, saturable receptor-mediated processes. The CL_tot and Vd _ss increased significantly in diabetic rats, while nonspecific portions of these parameters were not changed. From the increases in CL_tot (80%) and Q _H (67%) in diabetic rats, a pharmacokinetic analysis has revealed a 40% increase in the hepatic intrinsic clearance (CL_{int sp}) of A₁₄-¹²⁵ I-insulin via a specific mechanism in diabetic rats. In conclusion, we have provided in vivo evidence for a small increase in CL_{int sp} of insulin in STZ-diabetic rats compared with control rats, which may be caused by an increase in the surface receptor number in the livers of diabetic rats.     

Quasi-Equilibrium Pharmacokinetic Model for Drugs Exhibiting Target-Mediated Drug Disposition

Purpose The aim of this study is to derive and evaluate an equilibrium model of a previously developed general pharmacokinetic model for drugs exhibiting target-mediated drug disposition (TMDD). Methods A quasi-equilibrium solution to the system of ordinary differential equations that describe the kinetics of TMDD was obtained. Computer simulations of the equilibrium model were carried out to generate plasma concentration-time profiles resulting from a large range of intravenous bolus doses. Additionally, the final model was fitted to previously published pharmacokinetic profiles of leukemia inhibitory factor (LIF), a cytokine that seems to exhibit TMDD, following intravenous administration of 12.5, 25, 100, 250, 500, or 750 μg/kg in sheep. Results Simulations show that pharmacokinetic profiles display steeper distribution phases for lower doses and similar terminal disposition phases, but with slight underestimation at early time points as theoretically expected. The final model well-described LIF pharmacokinetics, and the final parameters, which were estimated with relatively good precision, were in good agreement with literature values. Conclusions An equilibrium model of TMDD is developed that recapitulates the essential features of the full general model and eliminates the need for estimating drug-binding microconstants that are often difficult or impossible to identify from typical in vivo pharmacokinetic data.     

Use of a Target‐Mediated Drug Disposition Model to Predict the Human Pharmacokinetics and Target Occupancy of GC1118, an Anti‐epidermal Growth Factor Receptor Antibody

GC1118 is an anti‐epidermal growth factor receptor (EGFR) monoclonal antibody that is currently under clinical development. In this study, the pharmacokinetics (PK) of GC1118 were modelled in monkeys to predict human PK and receptor occupancy (RO) profiles. The serum concentrations of GC1118 and its comparator (cetuximab) were assessed in monkeys with a non‐compartmental analysis and a target‐mediated drug disposition (TMDD) model after intravenous infusion (3–25 mg/kg) of these drugs. The scaling exponent of the EGFR synthesis rate was determined using a sensitivity analysis. The human cetuximab exposures were simulated by applying different exponents (0.7–1.0) for the EGFR synthesis rate in the allometric monkey PK model. Simulated C_max and area under the curve values therein were compared with those previously reported in the literature to find the best exponent for the EGFR synthesis rate in human beings. The TMDD model appropriately described the monkey PK profile, which showed a decrease in clearance (CL; 1.2–0.4 ml/hr/kg) as the dose increased. The exponents for CL (0.75) and volume of distribution (Vd; 1.0) were used for the allometric scaling to predict human PK. The allometric coefficient for the EGFR synthesis rate chosen by the sensitivity analysis was 0.85, and the RO profiles that could not be measured experimentally were estimated based on the predicted concentrations of the total target and the drug–target complex. Our monkey TMDD model successfully predicts human PK and RO profiles of GC1118 and can be used to determine the appropriate dose for a first‐in‐human study investigating this drug.     

Population Pharmacokinetics of the Active Metabolite of Leflunomide in Pediatric Subjects with Polyarticular Course Juvenile Rheumatoid Arthritis

Leflunomide is a pyrimidine synthesis inhibitor used in the treatment of rheumatoid arthritis. Data from two clinical studies were used to establish a population pharmacokinetic (PPK) model for the active metabolite (M1) of leflunomide in patients with juvenile rheumatoid arthritis (JRA) and determine appropriate pediatric doses. Seventy-three subjects 3–17 years of age provided 674 M1 concentrations. The PPK model was derived from nonlinear mixed-effects modeling and qualified by cross-study evaluation and predictive check. A one-compartment model with first-order input described M1 PPK well. Body weight (WT) correlated weakly with oral clearance (CL/F = 0.020·[WT/40]^0.430) and strongly with volume of distribution (V/F = 5.8·[WT/40]^0.769). Steady-state concentrations (C_ss) of M1 in JRA were compared for a variety of leflunomide dose regimens using Monte–Carlo simulation. To achieve comparable C_ss values in pediatric patients with JRA to that in adult patients, doses of leflunomide should be adjusted modestly: 10 mg/d for 10–20 kg, 15 mg/d for 20–40 kg, and 20 mg/d for > 40 kg.     

In vivo kinetic analysis of covalent binding between N-acetyl-L-cysteine and plasma protein through the formation of mixed disulfide in rats

Purpose. This investigation was undertaken to study the relationship between plasma drug clearance and covalent protein-binding kinetics of N-acetyl-L-cysteine (NAC). Methods. NAC was intravenously administered to rats via a bolus injection or continuous infusion. Plasma concentrations of protein-unbound and total NAC were analyzed using a compartment model, taking into consideration of the protein binding process, and the apparent first-order binding and dissociation rate constants (k_on and k_off) were obtained. Results. Plasma total NAC after a bolus injection showed biphasic elimination with an inflection point at 1 hr. After 1 hr, NAC was largely present in the covalent protein-bound form. During the steady state of the infusion, approximately 30%-40% of plasma NAC bound with protein covalently. The k_on, k_off, and the elimination rate constant of protein-unbound drug (k_e) were 0.23, 0.57, and 4.3 hr^-1. The dissociation half-life of NAC from protein estimated from k_off was in agreement with the elimination half-life of plasma total NAC. This suggests that the dissociation of NAC from protein rate-limited the drug elimination in plasma (k_off < k_e). Conclusion. We demonstrated that plasma total drug clearance is kinetically limited by covalent protein binding. The compartmental model described here is useful for analyzing its kinetics in vivo.     

Impact of dose selection on parameter estimation using a rapid binding approximation model of target-mediated drug disposition

The purpose of this study was to examine the role of dose selection on population pharmacokinetic (PK) parameter estimation using a rapid binding approximation of a target-mediated drug disposition (TMDD) model previously developed for interferon-β (IFN-β). A total of 50 replicate datasets each containing 100 subjects were created using NONMEM^®. The study design included IV injection of IFN-β followed by the SC route in a crossover manner, with each dose and route of administration separated by a 1,000 h washout period. Serial plasma PK samples were simulated up to 48 h for all subjects following each dose. Population mean PK parameters were re-estimated in NONMEM^® for each simulated dataset using the same TMDD model after including the following doses (MIU/kg): (A) 1, 3 and 10 (original study); (B) 1, 3 and 7; (C) 1, 3 and 5; (D) 1, 3 and 4; (E) 1 and 3; (F) 3 and 10; or (G) 10 MIU/kg only. Bias in the model fit was assessed by calculating the percent prediction error (PE%) for each of the population mean PK parameters relative to the estimates obtained from the fit to the 1, 3, and 10 MIU/kg doses (Case A). Relatively unbiased population mean PK parameter estimates (median PE% <8%) were obtained only when the study design included 1, 3 and a minimum higher dose of 7 MIU/kg. Bias increased for various parameters when the highest dose was less than 7 MIU/kg along with 1 and 3 MIU/kg being the low and intermediate dose levels. An increase in the bias for binding capacity, R_tot, and the equilibrium dissociation constant, K _D, was observed as the highest dose included in the dataset was reduced from 5 to 3 MIU/kg (median PE% ranged from ?4.71 to ?23.9% and ?4.76 to ?34.6%). Similar increases in the range of median PE% were also observed for other model parameters as the highest dose was reduced from 5 to 3 MIU/kg. Severely biased results were obtained from the study design that included only the 10 MIU/kg dose (Case G) suggesting that it is not sufficient to study just a high dose group. This bias was greatly reduced (median PE% <14%) for all parameters except K _D when the 3 and 10 MIU/kg doses were co-modeled (Case F). Plots of the PE% for R_tot and K _D versus the molar ratio of maximum dose to R_tot suggest that study designs should evaluate at least one IFN-β dose 3.5- to 4-fold higher than R_tot along with the 1 and 3 MIU/kg dose levels to obtain unbiased population PK parameter estimates. In summary, for the IFN-β model and study design, dose selection influences the ability to generate relatively unbiased population mean TMDD parameter estimates, which is based on maximum dose levels relative to R_tot. This simulation study highlights the role of dose selection in optimal study design strategies for drugs such as IFN-β that exhibit TMDD properties.     

Target-mediated drug disposition and dynamics

Nonlinear pharmacokinetics and pharmacodynamics may result from several capacity-limited processes and often represent complicating factors in characterizing the pharmacological properties of drugs. Target-mediated drug disposition (TMDD) corresponds to a special case wherein a significant proportion of a drug (relative to dose) is bound with high affinity to a pharmacological target, such that this interaction is reflected in the pharmacokinetic properties of the drug. Dose-dependent effects on apparent pharmacokinetic parameters may manifest, including the steady-state volume of distribution and total systemic clearance. Although a few small molecular weight compounds have been identified to exhibit TMDD, the incidence of TMDD is likely to increase particularly among emerging biotechnology pharmaceuticals. The goal of this commentary is to describe the basic tenets of TMDD and discuss several mathematical modeling approaches for characterizing this phenomenon. Whereas traditional pharmacokinetic/pharmacodynamic models assume that the amount of the drug-target complex is negligible relative to the total amount of drug in the body, integrated mechanism-based models of TMDD incorporate the binding and stoichiometry of drug-target binding. These models may be utilized to infer the time-course of inaccessible system variables, such as the in vivo density of the drug-target complex, and provide a suitable platform for ascertaining the apparent pharmacodynamic implications of TMDD.     

Prediction of clinical pharmacokinetic parameters of linezolid using animal data by allometric scaling: applicability for the development of novel oxazolidinones

1.?Allometric scaling has previously been used as an effective tool for the prediction of human pharmacokinetic data. The pharmacokinetic data for linezolid, a novel oxazolidinone to treat Gram-positive pathogens, in mice, rats and dogs were subjected to simple allometric scaling. Generated allometric equations for parameters such as clearance (CL), volume of distribution (V_ss) and elimination rate constant (K₁₀) were used to predict human pharmacokinetic parameters including elimination half-lives. In addition, the human plasma concentration–time curve was simulated using a one-compartmental model.

2.?Application of simple allometry (Y?=?aW^b) for animal parameters such as CL, V_ss, and K₁₀ showed excellent allometric fit (r?≥?0.98). The allometric equations for CL, V_ss, and K₁₀ were??0.5465W^0.6595,??0.1369W^0.9246, and??0.4117W^–0.3139, respectively. The confidence in predictability of CL and V_ss parameters was particularly high since the allometric exponents of CL and V_ss almost approached the suggested values of 0.75 and 1.00, respectively.

3.?Animal pharmacokinetic parameters generated in the present authors’?laboratories for linezolid were in close agreement with reported literature values. The predicted human values for CL (4.68?l?h^?1), V_ss (37.07 litres), and K₁₀ (0.10?h^?1) were within the range observed for linezolid in the literature (CL?=?4?10.5 l?h^?1; V_ss?=?21???53 litres; K₁₀?=?0.09???0.3?h^?1). The human half-life (t_1/2) predicted using allometry (6.9?h) was similar to reported values in humans of 5?h. In summary, the retrospective analysis for linezolid suggests that allometric scaling can be used as a prospective tool for predicting human pharmacokinetic parameters of novel oxazolidinones.