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Tisotumab vedotin is an investigational antibody-drug conjugate (ADC) for treatment of solid tumors expressing tissue factor with accelerated approval from the US Food and Drug Administration for treatment of recurrent or metastatic cervical cancer with disease progression during or after chemotherapy. This study describes development of a population pharmacokinetic (PK) model to assess the PK profile of tisotumab vedotin and microtubule-disrupting agent monomethyl auristatin E (MMAE) using data from 399 patients with solid tumors across four phase I/II trials. The ADC-MMAE model describes ADC and MMAE concentrations following intravenous administration of tisotumab vedotin. This four-compartment model comprises a two-compartment ADC model with parallel linear and Michaelis-Menten elimination, a delay compartment, and a one-compartment MMAE model. Nonspecific linear clearance of ADC was 1.42 L/day, central volume of distribution (V

This study aims to investigate pharmacokinetics (PK) and exposure-response parameters of the 400 mg once-daily venetoclax dose regimen in combination with obinutuzumab, which was approved for the first-line (1L) treatment of chronic lymphocytic leukemia (CLL) based on data from the phase 3 CLL14 study and the phase 1b dose-finding GP28331 study.Parameter estimates and uncertainty, which were estimated by a previously developed population PK (popPK) model, were used as informative priors for this analysis. They were re-estimated, and then used to evaluate additional covariate effects, describe venetoclax PK when administered with obinutuzumab, and provide empirical Bayes estimates of PK parameters and exposure. Exposure-progression-free survival (PFS) and exposure-safety relationships were assessed using data from CLL14, with steady-state nominal venetoclax exposure (CPK data from 274 patients (CLL14, n = 194; GP28331, n = 80) were included. The final model provided good fit of the observed data. Obinutuzumab co-administration, history of prior treatments, and disease severity at baseline had no appreciable influence on venetoclax steady-state exposure. No significant correlations were observed between venetoclax exposure and PFS, or between venetoclax exposure and the probability of treatment-emergent grade ≥ 3 neutropenia, grade ≥ 3 thrombocytopenia, grade ≥ 3 infections, and SAEs. Median dose intensities for venetoclax and obinutuzumab remained similar across venetoclax exposure tertiles.PopPK and exposure-efficacy, exposure-safety, and exposure-tolerability analyses support the 400 mg once-daily venetoclax dose plus obinutuzumab for 1L treatment in patients with CLL.ClinicalTrials.gov Identifiers NCT02242942 and NCT02339181.

Aim Pharmacologic effects were analysed to determine a dose recommendation for oseltamivir in immunocompromised (IC) adults with influenza. Methods Quantitative clinical pharmacology methods were applied to data from 160 adult IC patients (aged 18-78 years) from two studies (NV20234, 150 patients; NV25118, 10 patients) who received oseltamivir 75-200 mg twice daily for up to 10 days. An established population-pharmacokinetic (PK) model with additional effects on oseltamivir and oseltamivir carboxylate (OC) clearance described the PK characteristics of oseltamivir in IC patients versus otherwise healthy (OwH) patients from previous clinical trials. Estimated PK parameters were used to evaluate exposure-response relationships for virologic endpoints (time to cessation of viral shedding, viral load measures and treatment-emergent resistance). A drug-disease model characterized the viral kinetics of influenza accounting for the effect of OC on viral production. Results Oseltamivir clearance was 32.5% lower (95% confidence interval [CI], 26.1-38.8) and OC clearance was 33.7% lower (95% CI, 23.2-44.1) in IC versus OwH patients. No notable exposure-response relationships were identified for exposures higher than those achieved after conventional dose oseltamivir 75 mg, which appeared to be close to the maximum effect of oseltamivir. Simulations of the drug-disease model predicted that initiating treatment within 48 hours of symptom onset had maximum impact, and a treatment duration of 10 days was favourable over 3-5 days to limit viral rebound. Conclusions Our findings support the use of conventional-dose oseltamivir 75 mg twice daily for 10 days in the treatment of IC adult patients with influenza.

Purpose The CD79b-targeted antibody–drug conjugate polatuzumab vedotin (pola), alone and with chemoimmunotherapy, has clinical efficacy and a tolerable safety profile in B-cell non-Hodgkin lymphoma (B-NHL). We assessed (a) whether exposure from global studies of pola is comparable to Asian patients, and (b) if the recommended pola dose is appropriate in Asian patients based on exposure. Methods The pharmacokinetics (PK) of pola in Asian and global populations was characterized for three analytes (antibody-conjugated monomethyl auristatin E (MMAE) [acMMAE], total antibody, and unconjugated MMAE) in five phase 1b/2 single-agent and combination studies in B-NHL patients (JO29138 [JAPICCTI‐142580], DCS4968g [NCT01290549], GO27834 [NCT01691898], GO29044 [NCT01992653], and GO29365 [NCT02257567]). PK data were compared between Japanese phase 1 JO29138 (JAPICCTI‐142580) and global phase 1 DCS4968g (NCT01290549) studies and between Asian and non-Asian patients in the randomized relapsed/refractory B-NHL cohorts of the phase 1b/2 study GO29365 (NCT02257567). A population PK (popPK) model was used to assess the effects of Asian race and region on acMMAE and unconjugated MMAE exposure. Results PK non-compartmental analysis (NCA) parameters for the key analyte acMMAE in the Japanese JO29138 (JAPICCTI‐142580) and global phase 1 DCS4968g (NCT01290549) studies were similar. In GO29365 (NCT02257567), the phase 1b/2 combination study, mean exposure to the analytes was generally lower in Asian patients (by ~ 9.9 to 17.5%), but not to a clinically meaningful extent. Overall, the popPK model further suggested comparable PK in Asian patients with B-NHL (race or region) versus non-Asian patients. Conclusion Race has no clinically meaningful effect on pola PK. These results (and observations from efficacy/safety exposure–response analyses) support no pola dose adjustments are warranted for Asian patients with DLBCL.

Anti-neutrophil cytoplasmic antibody-associated vasculitides granulomatosis with polyangiitis (GPA) and microscopic polyangiitis (MPA) are rare, potentially organ- and life-threatening autoimmune conditions affecting adult and pediatric patients. An open-label phase II study was conducted to determine safe and effective dosing regimens of rituximab in pediatric patients with GPA/MPA. To determine the selection of an appropriate dose regimen in children for induction and maintenance, a population pharmacokinetic approach was used (nonlinear mixed-effect modeling), combining pediatric data with data from adults with GPA/MPA. The time course of B-cell depletion was assessed in both populations. The exposure-effect relationship was assessed by logistic regression. Twenty-five pediatric patients (80% female patients; age range, 6-17 years) were enrolled in the trial and received the induction regimen of intravenous rituximab 375 mg/m

Aims: To investigate pharmacokinetics (PK) and exposure-response of the 400 mg once daily venetoclax dose regimen in combination with obinutuzumab in the phase 3 CLL14 study approved for the treatment of first-line (1L) chronic lymphocytic leukaemia (CLL). Methods: Parameter estimates and uncertainty estimated by a previously developed population PK (popPK) model were used as informative priors for this analysis. They were re-estimated, then used to evaluate additional covariate effects, describe venetoclax PK when administered with obinutuzumab, and provide empirical Bayes estimates of PK parameters and exposure. Exposure-progression-free survival (PFS) and exposure-safety relationships were assessed using CLL14 data, with steady-state exposure at the nominal target dose (C) as the predictor variable. Exposure-safety analyses were conducted using logistic regression for selected treatment-emergent grade ≥3 adverse events (AEs) and serious AEs (SAEs). Dose intensities were summarized by tertiles of C. Results: PK data from 274 patients (CLL14, n=194; phase 1b dose-finding study GP28331, n=80) were included. The final model provided good fit of observed data. Obinutuzumab co administration, history of prior treatments, and disease severity at baseline had no appreciable influence on venetoclax steady-state exposure. No significant correlations were observed between venetoclax exposure and PFS, or between venetoclax exposure and the probability of treatment-emergent grade ≥3 neutropenia, grade ≥3 thrombocytopenia, grade ≥3 infections and SAEs. Median dose intensities for venetoclax and obinutuzumab remained similar across venetoclax exposure tertiles. Conclusion: PopPK and exposure efficacy, -safety and -tolerability analyses support the 400 mg once-daily venetoclax dose plus obinutuzumab in patients with 1L CLL.

Tusamitamab ravtansine (SAR408701) is an antibody-drug conjugate (ADC), combining a humanized monoclonal antibody (IgG1) targeting carcinoembryonic antigen-related cell adhesion molecule 5 (CEACAM5) and a potent cytotoxic maytansinoid derivative, DM4, inhibiting microtubule assembly. SAR408701 is currently in clinical development for the treatment of advanced solid tumors expressing CEACAM5. It is administered intravenously as a conjugated antibody with an average Drug Antibody Ratio (DAR) of 3.8. During SAR408701 clinical development, four entities were measured in plasma: conjugated antibody (SAR408701), naked antibody (NAB), DM4 and its methylated metabolite (MeDM4), both being active. Average DAR and proportions of individual DAR species were also assessed in a subset of patients. An integrated and semi-mechanistic population pharmacokinetic model describing the time-course of all entities in plasma and DAR measurements has been developed. All DAR moieties were assumed to share the same drug disposition parameters, excepted for clearance which differed for DAR0 (i.e. NAB entity). The conversion of higher DAR to lower DAR resulted in a DAR-dependent ADC deconjugation and was represented as an irreversible first-order process. Each conjugated antibody was assumed to contribute to DM4 formation. All data were fitted simultaneously and the model developed was successful in describing the pharmacokinetic profile of each entity. Such a structural model could be translated to other ADCs and gives insight of mechanistic processes governing ADC disposition. This framework will further be expanded to evaluate covariates impact on SAR408701 pharmacokinetics and its derivatives, and thus can help identifying sources of pharmacokinetic variability and potential efficacy and safety pharmacokinetic drivers.

A mechanistic population‐pharmacokinetic model was developed to predict oseltamivir exposures in neonates and infants accounting for physiological changes during the first 2 years of life. The model included data from 13 studies, comprising 436 subjects with normal renal function (317 pediatric subjects (≥ 38 weeks postmenstrual age (PMA), ≥ 13 days old) and 119 adult subjects

BMS‐986184 is a human, second‐generation, anti–interferon‐γ–induced protein 10 (IP‐10) monoclonal antibody. In this study the pharmacokinetics and target engagement (TE) of BMS‐986184 in healthy participants were characterized using population‐based target‐mediated drug disposition (TMDD) modeling and data from a first‐in‐human study (NCT02864264). The results of the first‐in‐human study and the model generated were used to conduct stochastic simulations of a virtual population of healthy participants to predict pharmacokinetic exposures and TE responses for different dosage regimens. A 2‐compartment, 2‐target, TMDD structural model, assuming quasi‐steady‐state and stimulated production on treatment, was developed by simultaneous fitting of the total drug, serum‐free IP‐10, and serum total IP‐10 concentration data, with the second unobservable target contribution to drug elimination described by the Michaelis‐Menten elimination term. Model evaluation confirmed agreement between model predictions and observed data. Simulation of a virtual population of healthy individuals demonstrated that steady state was reached at the eighth dosing interval, and that around 150 mg subcutaneously every other week could be a suitable target dosage regimen for future clinical trials. Integrated modeling strategies such as this can be used to help guide rational clinical trial development of drugs with TMDD, leading to improved dose selection and greater patient benefits.

Aims Rituximab is standard care in a number of lymphoma subtypes, including follicular lymphoma (FL), although many patients are resistant to rituximab, or develop resistance with repeated treatment, and a high proportion relapse. Obinutuzumab is a novel anti-CD20 monoclonal antibody with improved efficacy over rituximab. It is approved for previously untreated chronic lymphocytic leukaemia (CLL), and for use with bendamustine in patients with rituximab-relapsed/refractory FL. Methods Using a previously described population pharmacokinetic (PK) model of obinutuzumab in patients with non-Hodgkin lymphoma and CLL, we conducted an exposure-response analysis using data from 6 clinical trials in patients with CD20+ B-cell malignancies (CLL11, GADOLIN, GATHER, GAUDI, GAUGUIN and GAUSS) to describe the PK properties of obinutuzumab, identify covariates influencing exposure, and explore how exposure affects safety, efficacy and pharmacodynamics. Results A 2-compartment model with linear and time-dependent clearance described obinutuzumab PK. Disease type and subtype, body weight, baseline tumour size, and sex had the largest effects on PK. Obinutuzumab exposure was not associated with occurrence or severity of adverse events, but higher exposure appeared to be associated with greater efficacy, particularly longer progression-free survival. However, in multivariate Cox regression analysis, progression-free survival benefit in the obinutuzumab plus bendamustine arm was independent of exposure. Conclusion The updated population PK model reported here accurately describes the PK of obinutuzumab patients with non-Hodgkin lymphoma and CLL. The selected obinutuzumab dosing regimen offers clinical benefit in a majority of rituximab-refractory FL patients treated with bendamustine, irrespective of variability in exposure, whilst minimising adverse events.

AIMS To optimise the dosing regimen of oseltamivir for immunocompromised (IC) paediatric patients (

Introduction Outcomes remain poor in patients with diffuse large B cell lymphoma (DLBCL) who overexpress BCL-2 protein. We present population pharmacokinetics (PopPK) and exposure–response (ER) analyses for venetoclax (a selective BCL-2 inhibitor) administered with rituximab-cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP) in patients with relapsed/refractory (R/R) and previously untreated (1L) non-Hodgkin lymphoma (NHL) from the phase 1b/2 CAVALLI study, to confirm dose selection for future studies. Methods Analyses included 216 patients with R/R or 1L NHL treated for eight 21-day cycles with 400–800 mg venetoclax (cycle 1: days 4–10; cycles 2–8: days 1–10) in combination with R for eight cycles and CHOP for 6–8 cycles. A legacy PopPK model for venetoclax was used to describe the observed data and provide post hoc PK parameters. Venetoclax steady-state exposure (AUCss) was used to predict clinical efficacy, safety, or tolerability. To isolate the effect of venetoclax, ER analyses referenced data from the R-CHOP arm of a historical control study, GOYA, in 1L DLBCL. Results There was no significant association between venetoclax AUCss and progression-free survival or complete response either for all-comers or the BCL-2-immunohistochemistry-positive subpopulation. No statistically significant trends were observed with venetoclax AUCss and the key grade ≥ 3 adverse events and serious adverse events. Similar dose intensities were observed for venetoclax and R-CHOP components across venetoclax exposures, suggesting venetoclax did not impact delivery of the R-CHOP backbone. Conclusions The PopPK and ER analyses, in addition to the positive benefit–risk observed in the clinical data, support the selection of 800 mg venetoclax given with R-CHOP for future studies in BCL-2-immunohistochemistry-positive patients with 1L DLBCL. Trial Registration ClinicalTrials.gov Identifier NCT02055820. Supplementary Information The online version contains supplementary material available at 10.1007/s12325-021-01919-z.

Purpose The established two-analyte integrated population pharmacokinetic model was applied to assess the impact of intrinsic/extrinsic factors on the pharmacokinetics (PK) of polatuzumab vedotin (pola) in patients with non-Hodgkin lymphoma (NHL) following bodyweight-based dosing. Methods Model simulations based on individual empirical Bayes estimates were used to evaluate the impact of intrinsic/extrinsic factors as patient subgroups on Cycle 6 exposures. Intrinsic factors included bodyweight, age, sex, hepatic and renal functions. Extrinsic factors included rituximab/obinutuzumab or bendamustine combination with pola and manufacturing process. The predicted impact on exposures along with the established exposure-response relationships were used to assess clinical relevance. Results No clinically meaningful differences in Cycle 6 pola exposures were found for the following subgroups: bodyweight 100–146 kg versus 38–versus versus male, mild hepatic impairment versus normal, mild-to-moderate renal impairment versus normal. Co-administration of rituximab/obinutuzumab or bendamustine, and change in the pola manufacturing process, also had no meaningful impact on PK. Conclusions In patients with NHL, bodyweight-based dosing is adequate, and no further dose adjustment is recommended for the heavier subgroup (100–146 kg). In addition, no dose adjustments are recommended for other subgroups based on intrinsic/extrinsic factors evaluated.

Exposure-response relationships were investigated to assess the risk/benefit of polatuzumab vedotin (pola) + bendamustine-rituximab (pola + BR) in relapsed/refractory diffuse large B-cell lymphoma (R/R DLBCL). Analyses were conducted in pivotal study GO29365 (NCT02257567; BR/pola + BR/pola + BG [BG: bendamustine-obinutuzumab]; 1.8 mg/kg pola, every 3 weeks [Q3W], six cycles), and supportive studies DCS4968g (NCT01290549) and GO27834 (NCT01691898) (pola/pola + R/pola + G; 0.1-2.4 mg/kg pola Q3W; eight-cycle landmark), separately. Exposure was characterized as simulated cycle-6 AUC and

Antibody-drug conjugates (ADCs) developed using the valine-citrulline-MMAE (vc-MMAE) platform, consist of a monoclonal antibody (mAb) covalently bound with a potent anti-mitotic toxin (MMAE) through a protease-labile vc linker. Recently, clinical data for a variety of vc-MMAE ADCs has become available. The goal of this analysis was to develop a platform model that simultaneously described antibody-conjugated MMAE (acMMAE) pharmacokinetic (PK) data from eight vc-MMAE ADCs, against different targets and tumor indications; and to assess differences and similarities of model parameters and model predictions, between different compounds. Clinical PK data of eight vc-MMAE ADCs from eight Phase I studies were pooled. A population PK platform model for the eight ADCs was developed, where the inter-compound variability (ICV) was described explicitly, using the third random effect level (ICV), and implemented using LEVEL option of NONMEM 7.3. The PK was described by a two-compartment model with time dependent clearance. Clearance and volume of distribution increased with body weight; volume was higher for males, and clearance mildly decreased with the nominal dose. Michaelis-Menten elimination had only minor effect on PK and was not included in the model. Time-dependence of clearance had no effect beyond the first dosing cycle. Clearance and central volume were similar among ADCs, with ICV of 15 and 5%, respectively. Thus, PK of acMMAE was largely comparable across different vc-MMAE ADCs. The model may be applied to predict PK-profiles of vc-MMAE ADCs under development, estimate individual exposure for the subsequent PK-pharmacodynamics (PD) analysis, and project optimal dose regimens and PK sampling times.

Exposure–response relationships from a phase 1b (M13-365) and phase 3 (MURANO) study were investigated to assess benefit/risk of venetoclax 400 mg daily plus rituximab in relapsed/refractory (R/R) chronic lymphocytic leukemia (CLL). Dose intensities were summarized by tertiles of predicted venetoclax steady-state average concentrations based on nominal venetoclax dose (CmeanSS,nominal) for tolerability; exposure–safety analyses used logistic regression. Exposure–progression-free survival (PFS) relationships were assessed using MURANO data, with CmeanSS,nominal as a grouping factor. Covariates were demographics, geographic region, study, baseline disease characteristics, ECOG performance status, responsiveness to prior therapy, and chromosomal abnormalities. There was no significant effect of covariates on grade ≥3 neutropenia/infection or PFS, and no relationship between venetoclax exposure and these endpoints, or venetoclax or rituximab dose intensity. These results support the recommended venetoclax 400 mg daily dose in combination with rituximab in patients with R/R CLL or small lymphocytic leukemia.

A two‐analyte integrated population pharmacokinetic (PK) model that simultaneously describes concentrations of antibody‐conjugated monomethyl auristatin E (acMMAE) and unconjugated MMAE following repeated administrations of polatuzumab vedotin (pola) was developed based on data from four clinical studies of pola in patients with non‐Hodgkin lymphoma. A two‐compartment model with a nonspecific, time‐dependent linear clearance, a linear time‐dependent exponentially declining clearance, and a Michaelis–Menten clearance provided a good fit of the acMMAE plasma PK profiles. All three acMMAE elimination pathways contributed to the input to the central compartment of unconjugated MMAE, which was also described by a two‐compartment model. Population PK parameters, covariate effects, and interindividual variability of model parameters were estimated. The impact of clinically relevant covariates on PK exposures of each analyte were quantified and reported to support key label claims.

An integrated pharmacokinetics (PK) model that simultaneously describes concentrations of total antibody (Tab) and antibody‐conjugated monomethyl auristatin E (acMMAE) following administration of monomethyl auristatin E (MMAE)‐containing antibody–drug conjugates (ADCs) was developed based on phase I PK data with extensive sampling for two ADCs. Two linear two‐compartment models that shared all parameters were used to describe the PK of Tab and acMMAE, except that the deconjugation rate was an additional clearance pathway included in the acMMAE PK model compared to Tab. Further, the model demonstrated its ability to predict Tab concentrations and PK parameters based on observed acMMAE PK and various reduced or eliminated Tab PK sampling schemes of phase II data. Thus, this integrated model allows for the reduction of Tab PK sampling in late‐phase clinical development without compromising Tab PK characterization.

End-stage renal disease (ESRD) patients receiving hemodialysis (HD) are at heightened risk for influenza, but the optimal oseltamivir dosage regimen for treating or preventing influenza in this high-risk population is still uncertain. Pharmacokinetic data for 24 adults with ESRD were pooled from a single-dose and a multiple-dose study to develop a population pharmacokinetic model using nonlinear mixed-effects modeling. The final model comprised five compartments, two each to describe the systemic pharmacokinetics of oseltamivir phosphate and its metabolite, oseltamivir carboxylate (OC), and a delay compartment to describe oseltamivir metabolism. Estimated OC clearance in the model was markedly faster during HD sessions (7.43 liters/min) than at other times (0.19 liter/min). Model simulations showed that 30 mg oseltamivir given after every HD session is the most suitable regimen for influenza treatment, producing trough OC concentrations above the median value achieved with the 75-mg twice-daily regimen in patients with normal renal function and peak concentrations below the highest oseltamivir exposures known to be well tolerated (median exposures after twice-daily dosing of 450 mg). Administration of the first dose following diagnosis of influenza need not wait until after the next HD session: addition of a single 30-mg dose during the 12 h before the next HD session raises OC exposures quickly without posing any safety risk. Further simulation showed that 30 mg oseltamivir given after every other HD session is the most suitable regimen for influenza prophylaxis.

This work characterizes the pharmacokinetics (PK) of oseltamivir phosphate (OP) and its active metabolite, oseltamivir carboxylate (OC), and investigates oseltamivir i.v. dosing regimens for treatment of influenza in patients with normal renal function and with various degrees of renal impairment. Initially, data collected from 149 subjects with normal renal function and mild to severe renal impairment who were administered 40-200 mg oseltamivir i.v. were described by a four-compartment model. Two compartments described OP, one compartment described OC and one compartment described OP to OC metabolism. Then, data of 128 subjects administered 20-1,000 mg oseltamivir orally were added. The absorp- tion model included three first-order processes with direct (via first-pass) input in the OC compartment and two (di- rect and delayed) inputs in the OP compartment. Simula- tions and PK bridging were used to recommend i.v. dosing regimens. The analysis demonstrated that renal function had a major effect on OC clearance (CLM) and exposure. CLM for subjects with mild, moderate and severe renal impairment was 18, 50, and 84 % lower than for subjects with normal renal function. Simulations were used to select i.v. dosing regimens that provide OC Cmin coverage and exposures comparable to those achieved in subjects with normal renal function administered 75 mg b.i.d. orally. The oseltamivir dose depended on the degree of renal impair- ment and was independent of route of administration. Specifically, 75 mg b.i.d. is recommended for subjects with normal renal function or mild renal impairment, 30 mg b.i.d. for subjects with moderate renal impairment, and 30 mg q.d. for subjects with severe renal impairment. Recommended i.v. doses were the same as those recom- mended for oral administration in corresponding renal impairment groups.

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

The paper extended the TMDD model to drugs with two identical binding sites (2-1 TMDD). The quasi-steady-state (2-1 QSS), quasi-equilibrium (2-1 QE), irreversible binding (2-1 IB), and Michaelis-Menten (2-1 MM) approximations of the model were derived. Using simulations, the 2-1 QSS approximation was compared with the full 2-1 TMDD model. As expected and similarly to the standard TMDD for monoclonal antibodies (mAb), 2-1 QSS predictions were nearly identical to 2-1 TMDD predictions, except for times of fast changes following initiation of dosing, when equilibrium has not yet been reached. To illustrate properties of new equations and approximations, several variations of population PK data for mAbs with soluble (slow elimination of the complex) or membrane-bound (fast elimination of the complex) targets were simulated from a full 2-1 TMDD model and fitted to 2-1 TMDD models, to its approximations, and to the standard (1-1) QSS model. For a mAb with a soluble target, it was demonstrated that the 2-1 QSS model provided nearly identical description of the observed (simulated) free drug and total target concentrations, although there was some minor bias in predictions of unobserved free target concentrations. The standard QSS approximation also provided a good description of the observed data, but was not able to distinguish between free drug concentrations (with no target attached and both binding site free) and partially bound drug concentrations (with one of the binding sites occupied by the target). For a mAb with a membrane-bound target, the 2-1 MM approximation adequately described the data. The 2-1 QSS approximation converged 10 times faster than the full 2-1 TMDD, and its run time was comparable with the standard QSS model.

This work proposes and evaluates two methods (CM1 and CM2) for detecting non-compliance using concentration-time data and for obtaining estimates of population pharmacokinetic model parameters in a population with prevalent non-compliance. CM1 estimates individual residual variability (RV) and identifies subjects with higher than average RV as non-compliant. Exclusion of subjects with high RV from the analysis dataset reduces the bias in the estimates of the model parameters. Various methods of identification and exclusion of non-compliant subjects were tested, compared, and shown to reduce or eliminate bias in parameter estimates associated with non-compliance. The tested methods were (i) a pre-defined cutoff value of the random effect on RV, (ii) sequential exclusion of subjects with the highest RV percentiles, and (iii) use of a mixture model for RV. CM2 is applicable for the data with a specific sampling pattern that includes a potentially non-compliant outpatient part with several trough samples followed by a dense profile after the inpatient (compliant) dose. It relies only on the doses known to be administered (e.g., inpatient doses). In this method, all concentration measurements during the outpatient part of the study (except the trough value immediately preceding the inpatient dose) are removed from the dataset and an additional parameter (individual relative bioavailability of the outpatient doses) is introduced. For a number of simulated datasets with various sampling schemes and non-compliance patterns the proposed methods allowed to identify subjects with compliance problems and to reduce or eliminate bias in the estimates of the model parameters.

Fosamprenavir (FPV) is the phosphate ester prodrug of the HIV-1 protease inhibitor amprenavir (APV). A pediatric population pharmacokinetic model for APV was developed and simulation was used to identify dosing regimens for pediatric patients receiving FPV in combination with ritonavir (RTV) which resulted in concentrations similar to those in adults receiving FPV/RTV 700/100 mg BID. Pharmacokinetic data was obtained from HIV infected subjects aged 2 months to 18 years receiving either FPV or FPV/RTV. A two-compartment model with first order absorption and elimination was an appropriate structural model. Significant covariates in the model included RTV coadministration on clearance, fed status on bioavailability for the oral suspension, body weight on clearance and volume terms, black race on clearance, and age on clearance. The following FPV/RTV twice daily dosing regimens in pediatric patients delivered plasma APV exposure similar to adults: 45/7 mg/kg in patients weighing

Elotuzumab is a humanized, immunostimulatory anti-signaling lymphocytic activation molecule F7 (SLAMF7) IgG1 monoclonal antibody indicated in combination with lenalidomide and dexamethasone for patients with multiple myeloma (MM) who have received 1–3 prior therapies. We assessed the immunogenicity of elotuzumab as a monotherapy and in combination with bortezomib/dexamethasone and lenalidomide/dexamethasone in patients with MM in five clinical studies, including the pivotal ELOQUENT-2 trial (NCT01239797). Anti-drug antibody (ADA) prevalence was determined using a validated bridging assay. The prevalence of neutralizing antibodies (NAbs) was assessed in ADA-positive samples from ELOQUENT-2. Data from four trials of elotuzumab combined with lenalidomide/dexamethasone or bortezomib/dexamethasone (n = 390 evaluable patients) demonstrated that nine (2.3%) patients were ADA positive in baseline assays, 72 (18.5%) were ADA positive on-treatment or during follow-up, and two (0.5%) developed persistent ADAs. Patients treated with elotuzumab monotherapy had a higher incidence of elotuzumab ADAs than those on the combination therapy. In general, ADAs developed early and resolved after 2–4 months. Of 45 on-treatment ADA-positive patients in ELOQUENT-2, 19 had NAbs. Population pharmacokinetic modeling demonstrated an apparent increase in target-mediated elimination (higher V max, lower K M) in ADA-positive versus ADA-negative patients. ADAs were associated with lower elotuzumab steady-state exposure; however, this result may have been confounded by differential myeloma protein levels. ADAs/NAbs were not associated with hypersensitivity, infusion reactions, or loss of elotuzumab efficacy. Using a novel visualization, we also demonstrate that there is no clear relationship between the occurrence and titer values of ADA/NAbs and progression-free survival and best overall response status in patients treated with elotuzumab.

Denosumab (XGEVA®; AMG 162) is a fully human IgG2 monoclonal antibody, which binds to the receptor activator of nuclear factor κ-B ligand (RANKL) and prevents terminal differentiation, activation and survival of osteoclasts. We aimed to characterize the population pharmacokinetics of denosumab in patients with advanced solid tumours and bone metastases.A total of 14 228 free serum concentrations of denosumab from 1076 subjects (495 healthy subjects and 581 advanced cancer patients with solid tumours and bone metastases) included in 14 clinical studies were pooled. Denosumab was administered as either single intravenous (n = 36), single subcutaneous (n = 490) or multiple subcutaneous doses (n = 550) ranging from 30 to 180 mg (or from 0.01 to 3 mg/kg) and was given every 4 or 12 weeks for up to 3 years. An open two-compartment pharmacokinetic model with first-order absorption, linear distribution to a peripheral compartment, linear clearance and quasi-steady-state approximation of the target-mediated drug disposition was used to describe denosumab pharmacokinetics, using NONMEM Version 7.1.0 software. The influence of covariates (body weight, age, race, tumour type) was investigated using the full model approach. Model evaluation was performed through visual predictive checks. Model-based simulations were conducted to explore the role of covariates on denosumab serum concentrations and inferred RANKL occupancy.After subcutaneous administration, the dose-independent bioavailability and mean absorption half-life of denosumab were estimated to be 61% and 2.7 days, respectively. The central volume of distribution and linear clearance were 2.62 L/66 kg and 3.25 mL/h/66 kg, respectively. Clearance and volume parameters were proportional to body weight. Assuming 1 : 1 denosumab-RANKL binding, the baseline RANKL level, quasi-steady-state constant and RANKL degradation rate were inferred to be 4.46 nmol/L, 208 ng/mL and 0.00116 h-1, respectively. Between-subject variability in model parameters was moderate. Following 120 mg dosing every 4 weeks, the inferred RANKL occupancy at steady state exceeded 97% during the entire dosing interval in more than 95% of subjects, regardless of the patient covariates.The integration of pharmacokinetic data from 14 clinical studies demonstrated denosumab RANKL-mediated pharmacokinetics. Pharmacokinetics-based dosage adjustments on the basis of body weight, age, race and tumour type are not necessary in patients with bone metastases from solid tumours.

For AMG 317, a fully human monoclonal antibody to interleukin receptor IL-4Rα, we developed a population pharmacokinetic (PK) model by fitting data from four early phase clinical trials of intravenous and subcutaneous (SC) routes simultaneously, investigated important PK covariates, and explored the relationship between exposure and IgE response. Data for 294 subjects and 2183 AMG 317 plasma concentrations from three Phase 1 and 1 Phase 2 studies were analyzed by nonlinear mixed effects modeling using first-order conditional estimation with interaction. The relationship of IgE response with post hoc estimates of exposure generated from the final PK model was explored based on data from asthmatic patients. The best structural model was a two-compartment quasi-steady-state target-mediated drug disposition model with linear and non-linear clearances. For a typical 80-kg, 40-year subject, linear clearance was 35.0 mL/hr, central and peripheral volumes of distribution were 1.78 and 5.03 L, respectively, and SC bioavailability was 24.3%. Body weight was an important covariate on linear clearance and central volume; age influenced absorption rate. A significant treatment effect was observable between the cumulative AUC and IgE response measured. The population PK model adequately described AMG 317 PK from IV and SC routes over a 60-fold range of doses with two dosing strengths across multiple studies covering healthy volunteers and patients with mild to severe asthma. IgE response across a range of doses and over the sampling time points was found to be related to cumulative AMG 317 exposure.

Epithelial surfaces throughout the body continuously sample and respond to environmental stimuli. The accessibility of lung epithelium to inhaled therapies makes it possible to stimulate local antimicrobial defences with aerosolized innate immune ligands. This strategy has been shown to be effective in preclinical models, as delivery of innate immune ligands to the lungs of laboratory animals results in protection from subsequent challenge with microbial pathogens. Survival of the animal host in this setting correlates directly with killing of pathogens within the lungs, indicating the induction of a resistance mechanism. Resistance appears to be mediated primarily by activated epithelial cells rather than recruited leucocytes. Resistance reaches a peak within hours and persists for several days. Innate immune ligands can interact synergistically under some circumstances, and synergistic combinations of innate ligands delivered by aerosol are capable of inducing a high level of broad host resistance to bacteria, fungi and viruses. The induction of innate antimicrobial resistance within the lungs could have clinical applications in the prevention of lower respiratory tract infection in subjects transiently at high risk. These include cancer patients undergoing myeloablative chemotherapy, intubated patients being mechanically ventilated, vulnerable individuals during seasonal influenza epidemics, asthmatic subjects experiencing a respiratory viral infection, and healthy subjects exposed to virulent pathogens from a bioterror attack or emergent pandemic. In summary, stimulation of the lung epithelium to induce localized resistance to infection is a novel strategy whose clinical utility will be assessed in the near future.

Until recently, most therapeutic monoclonal antibodies (mAb) were designed to bind only one target. However, several existing mAbs bind to soluble and membrane forms of the same receptor. Moreover, design of bi-specific and multi-specific proteins that bind to more than one target is a promising direction of drug design. The pharmacokinetics and pharmacodynamics of these drugs may be described by the target-mediated drug disposition (TMDD). This work extended the TMDD model to drugs that bind more than one target. The quasi-steady-state (QSS) and Michaelis-Menten (MM) approximations of the model were also derived. Identifiability of model parameters was studied by simulations. The drug and target parameters used in simulations were chosen to imitate a monoclonal antibody that binds to the soluble (S) and membrane-bound (M) targets. The data were simulated for 224 subjects using the full TMDD model and dosing that mimicked typical Phase I and Phase II designs with rich sampling. Four population pharmacokinetic models were fitted to the free (unbound) drug and total (unbound and bound to the drug) S-target data: a one-target QSS model that simultaneously described the free drug and the total S-target (M1), a model with parallel linear and MM elimination that described the free drug combined with a separate S-target model that utilized the free drug concentrations but did not influence them (M2), a two-target QSS model where the S-target was described by the QSS approximation while the contribution of the M-target was described by the MM elimination term (M3), and a two-target full TMDD model (M4). The influence of relative contributions of the S and M-targets to target-mediated elimination on identifiability of the model parameters was investigated. The influence of assay sensitivity and availability of the total rather than free drug concentration measurements were also investigated. The results indicated that for the dosing regimens and system parameters investigated in this work the pharmacokinetic data alone did not allow to distinguish influences of the two targets. When the drug and S-target data were available, the model M1 described the data with the deficiencies of the fit visible only at the lowest dose level. However, the parameter estimates were strongly biased. The model M2 improved the fit and provided the precise estimates of the S-target parameters. However, no information concerning the M-target could be obtained from this model. The model M3 provided an excellent description of the data and the unbiased estimates of all the parameters. It also provided the unbiased estimates of change from baseline of the unobservable M-target concentrations. The models M1-M3 were robust while M4 was unstable despite the prohibitively long run time. The results were similar when the total rather than free drug was measured. The M-target parameters were estimated only when M-target elimination was at least comparable to S-target elimination. Improvement of the assay sensitivity has not resulted in marked improvement of the parameter estimates. In summary, for the cases investigated in this work the QSS approximation of the two-target TMDD model provided the unbiased and robust estimates of all the relevant TMDD parameters.

Elevated basal concentrations of glucagon and reduced postprandial glucagon suppression are partly responsible for the increased hepatic glucose production seen in type 2 diabetic patients. Recently, it was demonstrated that an antagonistic human monoclonal antibody (mAb) blocking glucagon receptor (GCGR) has profound glucose-lowering effects in various animal models. To further understand the effects on glucose homeostasis mediated by such an antibody, a pharmacokinetic-pharmacodynamic (PK-PD) study was conducted in a diabetic ob/ob mouse model. Four groups of ob/ob mice were randomized to receive single intraperitoneal administration of placebo, 0.6, 1, or 3 mg/kg of mAb GCGR, a fully human mAb against GCGR. The concentration-time data were used for noncompartmental and compartmental analysis. A semi-mechanistic PK-PD model incorporating the glucose-glucagon inter-regulation and the hypothesized inhibitory effect of mAb GCGR on GCGR signaling pathway via competitive inhibition was included to describe the disposition of glucose and glucagon over time. The pharmacokinetics of mAb GCGR was well characterized by a two-compartment model with parallel linear and nonlinear saturable eliminations. Single injection of mAb GCGR caused a rapid glucose-lowering effect with blood glucose concentrations returning to baseline by 4 to 18 days with increasing dose from 0.6 to 3 mg/kg. Elevation of glucagon concentrations was also observed in a dose-dependent manner. The results illustrated that the feedback relationship between glucose and glucagon in the presence of mAb GCGR could be quantitatively described by the developed model. The model may provide additional understanding in the underlying mechanism of GCGR antagonism by mAb.

Models for drugs exhibiting target-mediated drug disposition (TMDD) play an important role in the investigation of biological products (Mager and Jusko 2001). These models are often overparameterized and difficult to converge. A simpler quasi-equilibrium (QE) approximation of the general model has been suggested (Mager and Krzyzanski 2005), but even this simpler form can be overparameterized when, for example, drug target level is not available. This work (a) introduces quasi-steady-state (QSS) and Michaelis-Menten (MM) approximations of the TMDD model, (b) derives the relationships between the parameters of the TMDD, QE, QSS and MM models, (c) investigates the parameter ranges where the simplified approximations are equivalent to the TMDD model, (d) proposes an algorithm for establishing identifiability of these models, and (e) tests this algorithm on simulated datasets. The proposed QSS approximation is more general than the QE approximation: it degenerates into the QE approximation when the internalization rate of the drug-target complex is much smaller than its dissociation rate. The proposed identifiability analysis algorithm may be applied to provide justification for use of simplified approximations, avoiding use of incorrect parameter estimates of over-parameterized TMDD models while simultaneously saving time and resources required for the pharmacokinetics analysis of drugs with TMDD. The utility of the derived approximations and of the identifiability algorithm was demonstrated on the examples of the simulated data sets. The simulation examples indicated that the QSS model may be preferable to the QE model when the internalization rate of the drug-target complex significantly exceeds its dissociation rate. The MM approximation may be adequate when the drug concentration significantly exceeds the target concentrations or when the target occupancy is close to 100%.

Actinomycin-D is an antineoplastic agent that inhibits RNA synthesis by binding to guanine residues and inhibiting DNA-dependent RNA polymerase. Although actinomycin-D has been used to treat rhabdomyosarcoma and Wilms tumor for more than 40 years, the dose/exposure relationship is not well characterized. The objective of this study was to develop an initial population pharmacokinetic model to describe actinomycin-D disposition in children and young adults from which a prospective study could be designed. A total of 165 actinomycin-D plasma concentration measurements from 33 patients, aged 1.6 to 20.3 years, were used for the analysis. The data were analyzed using nonlinear mixed-effects modeling with the NONMEM software system. Age, weight, and gender were examined as covariates for the ability to explain interindividual variability in actinomycin-D pharmacokinetics. The final model was qualified via predictive check and non-parametric bootstrap procedures. A 3-compartment model with first-order elimination was chosen as the structural model. Allometric expressions incorporating weight were used to describe the effects of body size on actinomycin-D pharmacokinetics. Age and gender had no discernible effects on actinomycin-D pharmacokinetics in the population studied. The predictive check showed that the developed model was able to simulate data in close agreement with the actual study observations. The availability of an initial population pharmacokinetic model to describe actinomycin-D pharmacokinetics will facilitate the development of a large-scale clinical trial to study the actinomycin-D dose/exposure relationship in pediatric patients with rhabdomyosarcoma and Wilms tumor. The covariate analysis described by the current data set suggests that indices of body size captured via allometric expressions improve the partition of variation in actinomycin-D pharmacokinetics from this pilot data set. Relationships between pharmacokinetics and toxicity will be examined in future prospective studies in which children less than 1 year old will be enrolled. Refereed/Peer-reviewed

Elotuzumab is a humanized immunoglobulin G1 monoclonal antibody in development for the treatment of patients with multiple myeloma who have received one or more prior therapies. In this work, 6958 elotuzumab serum concentrations from 375 patients enrolled in four Phase 1 to 3 clinical trials were used to analyze the pharmacokinetics (PK) of elotuzumab. A population PK model with parallel linear and Michaelis-Menten elimination from the central compartment and limited-capacity target-mediated elimination from the peripheral compartment described the elotuzumab concentration-time course. Clearance of elotuzumab increased with increasing body weight and weight-based dosing generated uniform exposures across a range of body weights. Coadministration of lenalidomide/dexamethasone background therapy decreased elotuzumab nonspecific clearance by 35 %. Target-mediated elimination of elotuzumab increased with increasing baseline serum M-protein, resulting in lower exposure in patients with high baseline serum M-protein concentration. Age, race, sex, renal and hepatic function, Eastern Cooperative Oncology Group performance status, lactate dehydrogenase, albumin and β2-microglobulin had less than 20 % effect on model parameters and are unlikely to have clinically meaningful effects. Impact of anti-drug antibodies (ADAs) on the PK of elotuzumab was assessed as an ad hoc analysis. In the majority of ADA-positive patients, immunogenicity started early, was transient and resolved by 2-4 months. Since the majority of patients had ADAs detected early, this resulted in a corresponding transient increase in nonspecific clearance at these time points. Nonspecific clearance appeared to return to baseline at later time points when ADAs were no longer detected.

Lampalizumab is an antigen-binding fragment of a humanized monoclonal antibody against complement factor D (CFD), a rate-limiting enzyme in the activation and amplification of the alternative complement pathway (ACP), which is in phase III clinical trials for the treatment of geographic atrophy. Understanding of the pharmacokinetics, pharmacodynamics, and biodistribution of lampalizumab following intravitreal administration in the ocular compartments and systemic circulation is limited but crucial for selecting doses that provide optimal efficacy and safety. Here, we sought to construct a semimechanistic and integrated ocular-systemic pharmacokinetic-pharmacodynamic model of lampalizumab in the cynomolgus monkey to provide a quantitative understanding of the ocular and systemic disposition of lampalizumab and CFD inhibition. The model takes into account target-mediated drug disposition, target turnover, and drug distribution across ocular tissues and systemic circulation. Following intravitreal administration, lampalizumab achieves rapid equilibration across ocular tissues. Lampalizumab ocular elimination is relatively slow, with a τ1/2 of approximately 3 days, whereas systemic elimination is rapid, with a τ1/2 of 0.8 hours. Target-independent linear clearance is predominant in the eye, whereas target-mediated clearance is predominant in the systemic circulation. Systemic CFD synthesis was estimated to be high (7.8 mg/day); however, the amount of CFD entering the eye due to influx from the systemic circulation was small (

AQUAVAN Injection (AQ) (GPI 15715; Guilford Pharmaceutical Inc., Baltimore, MD) is a water-soluble prodrug of propofol (PropofolGPI). This study aimed to explore the pharmacokinetics of AQ, PropofolGPI, and formate (a metabolite of AQ) and to compare them with the pharmacokinetics of propofol lipid emulsion (PropofolD).After ethics committee approval, 36 healthy volunteers were randomly allocated into six cohorts (male/female: 3/3) and given a single bolus of AQ (5, 10, 15, 20, 25, or 30 mg/kg). For comparison, an equipotent dose (as measured by the Bispectral Index) of PropofolD was given to the same subjects 1 week later. For both drugs, blood samples were collected (1-480 min) to analyze AQ, PropofolGPI, PropofolD, and formate concentrations. Noncompartmental pharmacokinetic analyses were performed for all analytes. A population compartmental model was developed for AQ and PropofolGPI using NONMEM. The models were evaluated using simulations and bootstraps.The noncompartmental pharmacokinetic comparison revealed different dispositions of PropofolGPI and PropofolD. The maximum plasma concentration was lower for PropofolGPI than for PropofolD at equipotent doses, and apparent clearance and distribution volume were much higher for PropofolGPI than for PropofolD. Formate concentrations were similar when injecting both drugs and were not higher than baseline. Compartmental modeling revealed that the pharmacokinetic behavior of AQ and its liberated PropofolGPI was best described by a nonlinear, six-compartment model, composed of two three-compartment models connected to each other by hydrolysis of AQ to PropofolGPI.PropofolGPI showed different noncompartmental pharmacokinetics from PropofolD, hereby revealing the influence of the formulation. The combined model for AQ and PropofolGPI was best modeled by a nonlinear, six-compartment model.

Background: AQUAVAN® Injection (AQ) (GPI 15715; Guilford Pharmaceuticals Inc., Baltimore, MD) is a water-soluble prodrug of propofol. The authors explored the pharmacodynamics and safety of AQ and compared it with propofol llpid emulsion (Propofol n ). Methods: After institutional review board approval, 36 volunteers with American Society of Anesthesiologists physical status of I were randomly allocated into six cohorts (male/female: 3/3 per cohort) and given a single bolus of AQ (5, 10, 15, 20, 25, or 30 mg/kg). A Bispectral Index® monitor (Aspect Medical Systems Inc., Newton, MA) measured the hypnotic effect. The lowest Bispectral Index level (BIS peak ) was recorded. One week later, Prcpofol D was given to the same subjects at 50 mg/min to reach a similar BIS peak . Heart rate, oxygen saturation measured by pulse oximetry, blood pressure, and side effects were monitored. Incidence and duration of apnea and loss (LOQ verbal ) and return of response to verbal command were measured. A population compartmental pharmacokinetic-phannacodynamic model was developed for AQ using NONMEM and evaluated using simulations, leverage, and bootstrap analyses. Results: In the higher dosages (cohorts 4-6), all subjects achieved LOCV verbal . Similar times until LOC verbal were seen for AQ and Prcpofol D . A dose-related increase in duration of LOCV verbal was longer for AQ than for Fropolol D . AQ BIS peak occurred later than with Prcpofol D . Pain on injection was only present with Propofol D (12 of 36). With AQ, transient paresthesias and pruritus were seen. Hemodynamic profiles were similar for both drugs, except for an initial tachycardia after AQ administration. Dose-dependent apnea was more pronounced with Propofol D than with AQ. The AQ combined phannacokinetic-phannacodynamic profile was best described by a nonlinear, six-compartment pharmacokinetic model and an effect site compartment. A dependency of the k e0 value on the Prcpofol GPI plasma concentration was noted. Conclusion: Bolus administration of AQ achieves LOC verbal at a similar time as an equipotent amount of Propofol D but shows a longer time to BIS peak and prolonged pharmacodynamics. For both drugs, excellent drug safety was achieved, although there was a tendency of fewer and shorter duration of apneas for AQ.

Treatment regimens involving obinutuzumab (GA101) demonstrated increased efficacy to rituximab in clinical trials for non-Hodgkin's lymphoma (NHL) and chronic lymphocytic leukemia (CLL). However, the pharmacokinetic (PK) properties and the exposure–response relationships of obinutuzumab still need to be fully described. Data from four clinical trials of obinutuzumab were analyzed to describe the PK properties in patients with NHL or CLL and the pharmacodynamic (PD) properties in patients with CLL. A population PK model with linear time-dependent clearance described the obinutuzumab concentration–time course. Diagnosis, baseline tumor size (BSIZ), body weight, and gender were the main covariates affecting obinutuzumab exposure. In patients with CLL, exposure was not associated with safety but showed positive trends of correlation with efficacy. Although efficacy correlated positively with exposure, since both efficacy and exposure correlated negatively with BSIZ, it was not possible to determine with certainty whether it would be beneficial to adjust the dose according to BSIZ.

This paper is devoted to the analytical and numerical study of isotropic elastic composites made of three or more isotropic phases. The ranges of their effective bulk and shear moduli are restricted by the Hashin–Shtrikman–Walpole (HSW) bounds. For two-phase composites, these bounds are attainable, that is, there exist composites with extreme bulk and shear moduli. For multiphase composites, they may or may not be attainable depending on phase moduli and volume fractions. Sufficient conditions of attainability of the bounds and various previously known and new types of optimal composites are described. Most of our new results are related to the two-dimensional problem. A numerical topology optimization procedure that solves the inverse homogenization problem is adopted and used to look for two-dimensional three-phase composites with a maximal effective bulk modulus. For the combination of parameters where the HSW bound is known to be attainable, new microstructures are found numerically that possess bulk moduli close to the bound. Moreover, new types of microstructures with bulk moduli close to the bound are found numerically for the situations where the aforementioned attainability conditions are not met. Based on the numerical results, several new types of structures that possess extremal bulk modulus are suggested and studied analytically. The bulk moduli of the new structures are either equal to the HSW bound or higher than the bulk modulus of any other known composite with the same phase moduli and volume fractions. It is proved that the HSW bound is attainable in a much wider range than it was previously believed. Results are readily applied to two-dimensional three-phase isotropic conducting composites with extremal conductivity. They can also be used to study transversely isotropic three-dimensional three-phase composites with cylindrical inclusions of arbitrary cross-sections (plane strain problem) or transversely isotropic thin plates (plane stress or bending of plates problems).

The translation and the Hashin–Shtrikman methods are used to provide bounds on the effective complex shear modulus of a two-phase two–dimensional viscoelastic composite. They are both given by inequalities that depend on six parameters. The best bounds are obtained by optimizing these parameters over the admissible set, which is larger for the translation method than for the Hashin–Shtrikman method. Consequently, the translation method generally leads to tighter bounds than would be obtained via the standard Hashin–Shtrikman approach. Equivalence classes of two–dimensional viscoelastic composites (directly analogous to similar classes for the pure elastic problem) are found. Combination of the simplified versions of the translation or the Hashin–Shtrikman–type bounds and this equivalency results in simple algorithms for computing tight bounds for any choice of phase moduli and volume fractions. The bounds constrain the effective shear modulus to lie inside a region of the complex plane bounded by arcs of circles. The four points which correspond to the Hashin–Shtrikman–Walpole bounds on the shear modulus of an elastic composite always lie inside or on the boundary of the bounding region. In many cases the bounding region tends to hug the corresponding parallelogram in the complex compliance plane having these four points as vertices.

The apparent stiffness tensors of two-dimensional elastic composite samples smaller thanthe representative volume element (RVE) are studied as a function of system size. Numericalexperiments are used to investigate how the apparent properties of the composite converge withincreasing scale factor n, defined to be the ratio between the linear size of the composite and thelinear size of the unit cell. Under affine (Dirichlet-type) or homogeneous stress (Neumann-type) boundary conditions, the apparent elastic moduli overestimate orunderestimate, respectively, the effective elastic moduli of the infinitely periodic system. Theresults show that the difference between the Dirichlet, Neumann and the effective stiffnesstensors depends strongly on the phase stiffness contrast ratio. Dirichlet boundary conditionsprovide a more accurate estimate of the effective elastic properties of stiff matrix composites,whereas Neumann boundary conditions provide a more accurate estimate for compliant matrixstructures. It is shown that the apparent bulk and shear moduli may lie outside of theHashin–Shtrikman bounds. However, these bounds provide good upper and lower estimates forthe apparent bulk and shear moduli of structures with a scale factor n ⩾ 2. A similar approach isused to study hierarchical composites containing two distinct structural levels with a finiteseparation of length scales. It is shown, numerically, that the error associated with replacing thesmallest-scale regions by an equivalent homogeneous medium is very small, even when the ratiobetween the length scales is as low as three.

By using similar techniques that were employed in an earlier article on nonlinear conductivity [L. V. Gibiansky and S. Torquato, J. Appl. Phys. 84, 301 1998], we find approximations for the effective energy of nonlinear, isotropic, elastic dispersions in arbitrary space dimension d. We apply our results for incompressible dispersions with rigid or liquid inclusions and, more generally, with a power-law-type shear energy. It is shown that the new approximations lie within the best available rigorous upper and lower bounds on the effective energy. We also develop bounds on the effective energy of nonlinear conducting media with voids or cracks, purely in terms of the effective and phase elastic moduli of the media.

Rigorous cross-property bounds that connect the effective thermal conductivity κ * (or the electrical conductivity σ * ) and the effective bulk modulus K * of any isotropic, two-phase composite were recently derived by the authors. Here we reformulate these bounds and apply them to porous rocks with dry or fluid-filled pores. It is shown that knowledge of the effective conductivity can yield sharp estimates of the effective bulk modulus (and vice versa), even in cases where there is a wide disparity in the phase properties. The bounds yield, in particular, relations between the formation factor and the bulk modulus of the porous medium. By using the same approach we obtain new relations between the bulk moduli of a dry porous material and the bulk modulus of the same material with fluid-filled pores that are more general than the traditional Gassmann equation. The Gassmann formula for the bulk modulus of the fluid-saturated porous medium is shown to correspond to a lower bound on this quantity. Limiting cases that we consider include cracked materials with dry and fluid-saturated pores. Theoretical results are tested against experimental measurements of the effective bulk modulus of dry and water-saturated Westerly granite and sandstone samples. We found good agreement between our cross-property bounds and the experimental data, even when the experimental data depart from the Gassmann formula. Our results add new insight to understanding of the properties of the porous media. They show that the Gassmann approximation works well for rocks with high porosity but needs to be corrected for rocks with high crack-type porosity.

Approximations for the effective energy and, thus, effective conductivity of nonlinear, isotropic conducting dispersions are developed. This is accomplished by using the Ponte Castaneda variational principles [Philos. Trans. R. Soc. London Ser. A 340, 1321 (1992)] and the Torquato approximation [J. Appl. Phys. 58, 3790 (1985)] of the effective conductivity of corresponding linear composites. The results are obtained for dispersions with superconducting or insulating inclusions, and, more generally, for phases with a power-law energy. It is shown that the new approximations lie within the best available rigorous upper and lower bounds on the effective energy.

The general goal of this paper is to develop a new approach for bounding the effective moduli (e.g. elastic moduli, conductivity, or thermal expansion coefficients) of composite materials. Specifically, this paper aims to : (1) formulate a procedure that combines the translation method and the Beran procedure into one powerful method that has the advantages of both approaches ; and (2) apply the new method to study effective properties of viscoelastic composites. The new method enables one to get the most restrictive three-point geometrical-parameter bounds. In particular, we obtain new three-point bounds on the complex bulk modulus of an isotropic viscoelastic composite. The new bounds are given by the outermost of several circular arcs in the complex bulk modulus plane. They take into account three-point statistical information and thus are much more restrictive than previously known two-point bounds.

Recently, Grabovsky and Milton have studied effective properties of plane polycrystals made of a crystal with a rank-one local compliance tensor and a positive definite ‘weak’ direction. This paper continues their investigation. By using several complementary approaches, it is proved that the effective compliance tensor of such a polycrystal has exactly one weak direction. The new proofs clarify the link of the degenerate polycrystal problem with previously obtained results on the polycrystal properties. Investigation of the phase boundary conditions has allowed us to find theL-closure set of the effective properties of all polycrystals that can be constructed by sequential laminations of the original degenerate crystals. Bounds on theG-closure, i.e. a set of the effective properties of all the polycrystals that can be built from the given set of degenerate crystals, are found. They are given by a polygonal set in the plane of two linear invariants of the effective compliance tensors. The effective moduli of the polycrystals made from crystals with non-definite ‘weak’ directions are also studied.

We utilize two different approaches, homogenization theory and discrete network analyses, to study the mechanical and transport properties of two-dimensional cellular solids (honeycombs) consisting of either hexagonal, triangular, square or Voronoi cells. We exploit results from homogenization theory for porous solids (in the low-density limit) to establish rigorous bounds on the effective thermal conductivity of honeycombs in terms of the elastic moduli and vice versa. It is shown that for hexagonal, triangular or square honeycombs, the cross-property bound relating the bulk modulus to the thermal conductivity turns out to be an exact and optimal result. The same is true for the cross-property bound linking the shear or Young's modulus of the triangular honeycomb to its conductivity. For low-density honeycombs, we observe that all of the elastic moduli do not depend on the Poisson's ratio of the solid phase. The elastic-viscoelastic correspondence principle enables us to conclude that all of the viscoelastic moduli of honeycombs in the low-density limit are proportional to the complex Young's modulus of the solid phase. Such structures have real Poisson's ratios and the loss tangent is the same for any load.

Infants are at increased risk for morbidity and mortality due to influenza. Until recently, few data were available with which to optimize oseltamivir dosing in this high-risk population. Here, data for 133 infants were pooled from two prospective pharmacokinetic/pharmacodynamic safety studies to develop a population pharmacokinetic model. A three-compartment model with allometric scaling of all clearance and volume parameters described the disposition of oseltamivir and its carboxylate metabolite (OC). Weight dependence, OC clearance, and volume of distribution increased linearly with age. Analyses showed no association between OC exposure and viral clearance, the development of resistance (phenotypic/genotypic), normalization of body temperature, or safety endpoints. Pharmacokinetic bridging showed that a 3 mg/kg dose yielded acceptable OC exposure and good tolerability while minimizing the risk of underexposure and resistance/treatment failure. These pharmacological analyses formed the basis of the US Food and Drug Administration's recent approval of oseltamivir treatment for infants with influenza aged as young as 2 weeks.

Sharp bounds on the effective thermal expansion coefficients of isotropic multiphase composites and isotropic polycrystals are obtained by using classical variational principles and the translation method. Our bounds are appreciably narrower than the known Schapery-Rosen-Hashin bounds. Conditions are formulated that guarantee a one-to-one correspondence between the bulk modulus and thermal expansion coefficient of a polycrystal. All of our results can be readily applied to the poroelasticity problem. Generalizations of the results to treat anisotropic composites comprised of anisotropic phases are discussed.