Assessment of non-linear combination effect terms for drug-drug interactions

Thrombopoietin treats erythropoietin resistance by correcting EPO-induced progenitorcell depletion

Recombinant human erythropoietin (rHuEPO) is a prevalent treatment for anemia in patients with chronic kidney disease. However, up to 10% of these patients exhibit EPO resistance or hyporesponsiveness, which may be caused by the depletion of erythroid progenitor cells. Thrombopoietin (TPO) has the potential to promote the growth of early progenitor cells and correct the depletion. In this study, we investigate the efficacy and the underlying mechanism of the combination therapy of TPO and EPO to EPO resistance. First, the in vivo studies suggested that intensive EPO treatment induced progenitor cell depletion in the bone marrow, where the depletion was corrected by TPO. Then, colony assays showed that EPO and TPO synergistically enhanced the burst-forming unit-erythroid (BFU-E) production but antagonistically boosted the colony-forming units of megakaryocytes (CFU-MK) production. Also, we found TPO promoted hematopoietic stem and progenitor cells (HSPCs) production, while EPO drove HSPCs toward the erythroid lineage. Additionally, EPO induced more megakaryocytic-erythroid progenitors (MEPs) toward the erythroid output. Model-based simulations indicate the efficacy of this combination therapy for treating EPO-resistant anemia in rats. In conclusion, our study demonstrated the efficacy of combination therapy in addressing EPO-resistant anemia by correcting EPO-induced erythroid progenitor depletion.

Guiding model-driven combination dose selection using multi-objective synergy optimization

Despite the growing appreciation that the future of cancer treatment lies in combination therapies, finding the right drugs to combine and the optimal way to combine them remains a nontrivial task. Herein, we introduce the Multi-Objective Optimization of Combination Synergy - Dose Selection (MOOCS-DS) method for using drug synergy as a tool for guiding dose selection for a combination of preselected compounds. This method decouples synergy of potency (SoP) and synergy of efficacy (SoE) and identifies Pareto optimal solutions in a multi-objective synergy space. Using a toy combination therapy model, we explore properties of the MOOCS-DS algorithm, including how optimal dose selection can be influenced by the metric used to define SoP and SoE. We also demonstrate the potential of our approach to guide dose and schedule selection using a model fit to preclinical data of the combination of the PD-1 checkpoint inhibitor pembrolizumab and the anti-angiogenic drug bevacizumab on two lung cancer cell lines. The identification of optimally synergistic combination doses has the potential to inform preclinical experimental design and improve the success rates of combination therapies. Jel classificationDose Finding in Oncology.

A mechanistic assessment of the nature of pharmacodynamic drug-drug interaction in vivo and in vitro

Combination pharmacotherapy is becoming increasingly necessary because most diseases are pathophysiologically controlled at the subcellular level by target proteins in a combinatorial manner. We demonstrate the application of the stimulus-response mechanistic model in characterising the drug and physiological properties of pharmacodynamic drug-drug interactions (PDDI) using previously published in vitro and in vivo drug combination experiments. The in vitro experiment tested the effect of a combination of SCH66336 and 4-HPR on the survival of in squamous cell carcinoma cell lines, while the in vivo experiment tested the effect of a combination of cetuximab and cisplatin on tumour growth inhibition in female xenograft mice. The model adequately described both experiments, quantified both system and drug properties and predicted the nature of the PDDI mechanism. Strong baseline signals of 7.35 and 610 units existed in the in vitro and in vivo experiments respectively. An overall synergistic relationship (interaction index = 1.03E-8) was detected in the in vitro experiment. In the in vivo model, the overall interaction index was 70,139.45 implying an antagonistic interaction between the cisplatin and the cetuximab signals.

Drug Combination Modeling: Methods and Applications in Drug Development

Combination therapies have become increasingly researched and used in the treatment and management of complex diseases due to their ability to increase the chances for better efficacy and decreased toxicity. To evaluate drug combinations in drug development, pharmacokinetic and pharmacodynamic interactions between drugs in combination can be quantified using mathematical models; however, it can be difficult to deduce which models to use and how to use them to aid in clinical trial simulations to simulate the effect of a drug combination. This review paper aims to provide an overview of the various methods used to evaluate combination drug interaction for use in clinical trial development and a practical guideline on how combination modeling can be used in the settings of clinical trials.

Clinically practical pharmacometrics computer model to evaluate and personalize pharmacotherapy in pediatric rare diseases: application to Graves' disease

Objectives

Graves' disease (GD) with onset in childhood or adolescence is a rare disease (ORPHA:525731). Current pharmacotherapeutic approaches use antithyroid drugs, such as carbimazole, as monotherapy or in combination with thyroxine hormone substitutes, such as levothyroxine, as block-and-replace therapy to normalize thyroid function and improve patients' quality of life. However, in the context of fluctuating disease activity, especially during puberty, a considerable proportion of pediatric patients with GD is suffering from thyroid hormone concentrations outside the therapeutic reference ranges. Our main goal was to develop a clinically practical pharmacometrics computer model that characterizes and predicts individual disease activity in children with various severity of GD under pharmacotherapy.

Methods

Retrospectively collected clinical data from children and adolescents with GD under up to two years of treatment at four different pediatric hospitals in Switzerland were analyzed. Development of the pharmacometrics computer model is based on the non-linear mixed effects approach accounting for inter-individual variability and incorporating individual patient characteristics. Disease severity groups were defined based on free thyroxine (FT4) measurements at diagnosis.

Results

Data from 44 children with GD (75% female, median age 11 years, 62% receiving monotherapy) were analyzed. FT4 measurements were collected in 13, 15, and 16 pediatric patients with mild, moderate, or severe GD, with a median FT4 at diagnosis of 59.9 pmol/l (IQR 48.4, 76.8), and a total of 494 FT4 measurements during a median follow-up of 1.89 years (IQR 1.69, 1.97). We observed no notable difference between severity groups in terms of patient characteristics, daily carbimazole starting doses, and patient years. The final pharmacometrics computer model was developed based on FT4 measurements and on carbimazole or on carbimazole and levothyroxine doses involving two clinically relevant covariate effects: age at diagnosis and disease severity.

Discussion

We present a tailored pharmacometrics computer model that is able to describe individual FT4 dynamics under both, carbimazole monotherapy and carbimazole/levothyroxine block-and-replace therapy accounting for inter-individual disease progression and treatment response in children and adolescents with GD. Such clinically practical and predictive computer model has the potential to facilitate and enhance personalized pharmacotherapy in pediatric GD, reducing over- and underdosing and avoiding negative short- and long-term consequences. Prospective randomized validation trials are warranted to further validate and fine-tune computer-supported personalized dosing in pediatric GD and other rare pediatric diseases.

Pharmacodynamics and Bactericidal Activity of Combination Regimens in Pulmonary Tuberculosis: Application to Bedaquiline-Pretomanid-Pyrazinamide

A critical barrier to codevelopment of tuberculosis (TB) regimens is a limited ability to identify optimal drug and dose combinations in early-phase clinical testing. While pharmacokinetic-pharmacodynamic (PKPD) target attainment is the primary tool for exposure-response optimization of TB drugs, the PD target is a static index that does not distinguish individual drug contributions to the efficacy of a multidrug combination. A PKPD model of bedaquiline-pretomanid-pyrazinamide (BPaZ) for the treatment of pulmonary TB was developed as part of a dynamic exposure-response approach to regimen development. The model describes a time course relationship between the drug concentrations in plasma and their individual as well as their combined effect on sputum bacillary load assessed by solid culture CFU counts and liquid culture time to positivity (TTP). The model parameters were estimated using data from the phase 2A studies NC-001-(J-M-Pa-Z) and NC-003-(C-J-Pa-Z). The results included a characterization of BPaZ activity as the most and least sensitive to changes in pyrazinamide and bedaquiline exposures, respectively, with antagonistic activity of BPa compensated by synergistic activity of BZ and PaZ. Simulations of the NC-003 study population with once-daily bedaquiline at 200 mg, pretomanid at 200 mg, and pyrazinamide at 1,500 mg showed BPaZ would require 3 months to attain liquid culture negativity in 90% of participants. These results for BPaZ were intended to be an example application with the general approach aimed at entirely novel drug combinations from a growing pipeline of new and repurposed TB drugs.

Kinetic Modeling of Time-Dependent Enzyme Inhibition by Pre-Steady-State Analysis of Progress Curves: The Case Study of the Anti-Alzheimer's Drug Galantamine

The Michaelis–Menten model of enzyme kinetic assumes the free ligand approximation, the steady-state approximation and the rapid equilibrium approximation. Analytical methods to model slow-binding inhibitors by the analysis of initial velocities have been developed but, due to their inherent complexity, they are seldom employed. In order to circumvent the complications that arise from the violation of the rapid equilibrium assumption, inhibition is commonly evaluated by pre-incubating the enzyme and the inhibitors so that, even for slow inhibitors, the binding equilibrium is established before the reaction is started. Here, we show that for long drug-target residence time inhibitors, the conventional analysis of initial velocities by the linear regression of double-reciprocal plots fails to provide a correct description of the inhibition mechanism. As a case study, the inhibition of acetylcholinesterase by galantamine, a drug approved for the symptomatic treatment of Alzheimer’s disease, is reported. For over 50 years, analysis based on the conventional steady-state model has overlooked the time-dependent nature of galantamine inhibition, leading to an erroneous assessment of the drug potency and, hence, to discrepancies between biochemical data and the pharmacological evidence. Re-examination of acetylcholinesterase inhibition by pre-steady state analysis of the reaction progress curves showed that the potency of galantamine has indeed been underestimated by a factor of ~100.

Exposure-response modeling improves selection of radiation and radiosensitizer combinations

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate.

Mathematical Modelling of the Molecular Mechanisms of Interaction of Tenofovir with Emtricitabine against HIV

The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these drugs are taken up by HIV-infected target cells, undergo intracellular phosphorylation and compete with natural deoxynucleoside triphosphates (dNTP) for incorporation into nascent viral DNA during reverse transcription. Once incorporated, they halt reverse transcription. In vitro studies have proposed that TDF and FTC act synergistically within an HIV-infected cell. However, it is unclear whether, and which, direct drug–drug interactions mediate the apparent synergy. The goal of this work was to refine a mechanistic model for the molecular mechanism of action (MMOA) of nucleoside analogues in order to analyse whether putative direct interactions may account for the in vitro observed synergistic effects. Our analysis suggests that depletion of dNTP pools can explain apparent synergy between TDF and FTC in HIV-infected cells at clinically relevant concentrations. Dead-end complex (DEC) formation does not seem to significantly contribute to the synergistic effect. However, in the presence of non-nucleoside reverse transcriptase inhibitors (NNRTIs), its role might be more relevant, as previously reported in experimental in vitro studies.

OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic-pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic-pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic-pharmacodynamic examples.

Pharmacodynamic Drug-Drug Interactions

Pharmacodynamic drug-drug interactions (DDIs) occur when the pharmacological effect of one drug is altered by that of another drug in a combination regimen. DDIs often are classified as synergistic, additive, or antagonistic in nature, albeit these terms are frequently misused. Within a complex pathophysiological system, the mechanism of interaction may occur at the same target or through alternate pathways. Quantitative evaluation of pharmacodynamic DDIs by employing modeling and simulation approaches is needed to identify and optimize safe and effective combination therapy regimens. This review investigates the opportunities and challenges in pharmacodynamic DDI studies and highlights examples of quantitative methods for evaluating pharmacodynamic DDIs, with a particular emphasis on the use of mechanism-based modeling and simulation in DDI studies. Advancements in both experimental and computational techniques will enable the application of better, model-informed assessments of pharmacodynamic DDIs in drug discovery, development, and therapeutics.

Pharmacokinetics of Fentanyl and Its Derivatives in Children: A Comprehensive Review

Fentanyl and its derivatives sufentanil, alfentanil, and remifentanil are potent opioids. A comprehensive review of the use of fentanyl and its derivatives in the pediatric population was performed using the National Library of Medicine PubMed. Studies were included if they contained original pharmacokinetic parameters or models using established routes of administration in patients younger than 18 years of age. Of 372 retrieved articles, 44 eligible pharmacokinetic studies contained data of 821 patients younger than 18 years of age, including more than 46 preterm infants, 64 full-term neonates, 115 infants/toddlers, 188 children, and 28 adolescents. Underlying diagnoses included congenital heart and pulmonary disease and abdominal disorders. Routes of drug administration were intravenous, epidural, oral-transmucosal, intranasal, and transdermal. Despite extensive use in daily clinical practice, few studies have been performed. Preterm and term infants have lower clearance and protein binding. Pharmacokinetics was not altered by chronic renal or hepatic disease. Analyses of the pooled individual patients' data revealed that clearance maturation relating to body weight could be best described by the Hill function for sufentanil (R ² = 0.71, B _max 876 mL/min, K ₅₀ 16.3 kg) and alfentanil (R ² = 0.70, B _{max (fixed)} 420 mL/min, K ₅₀ 28 kg). The allometric exponent for estimation of clearance of sufentanil was 0.99 and 0.75 for alfentanil clearance. Maturation of remifentanil clearance was described by linear regression to bodyweight (R ² = 0.69). The allometric exponent for estimation of remifentanil clearance was 0.76. For fentanyl, linear regression showed only a weak correlation between clearance and bodyweight in preterm and term neonates (R ² = 0.22) owing to a lack of data in older age groups. A large heterogeneity regarding study design, clinical setting, drug administration, laboratory assays, and pharmacokinetic estimation was observed between studies introducing bias into the analyses performed in this review. A limitation of this review is that pharmacokinetic data, based on different modes of administration, dosing schemes, and parameter estimation methods, were combined.

Target-Mediated Drug Disposition Model for Bispecific Antibodies: Properties, Approximation, and Optimal Dosing Strategy

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target-mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented.

Assessment of Three-Drug Combination Pharmacodynamic Interactions in Pancreatic Cancer Cells

The pharmacodynamic interactions among trifluoperazine (TFP), gemcitabine (GEM), and paclitaxel (PTX) were assessed in pancreatic cancer cells (PANC-1). The phenothiazine TFP was chosen for its potential activity on cancer stem cells, while GEM and PTX cause apoptosis. Effects of each drug alone and in various combinations on cell growth inhibition of PANC-1 cells were studied in vitro to determine the drug-specific parameters and assess the nature of drug interactions. Joint inhibition (JI) and competitive inhibition (CI) equations were applied with a ψ interaction term. TFP fully inhibited growth of cells (I_max = 1) with an IC₅₀ = 9887 nM. Near-maximum inhibition was achieved for GEM (I_max = 0.825) and PTX (I_max= 0.844) with an IC₅₀ = 17.4 nM for GEM and IC₅₀ = 7.08 nM for PTX. Estimates of an interaction term ψ revealed that the combination of TFP-GEM was apparently synergistic; close to additivity, the combination TFP-PTX was antagonistic. The interaction of GEM-PTX was additive, and TFP-GEM-PTX was synergistic but close to additive. The combination of TFP IC₆₀-GEM IC₆₀-PTX IC₆₀ seemed optimal in producing inhibition of PANC-1 cells with an inhibitory effect of 82.1-90.2%. The addition of ψ terms to traditional interaction equations allows assessment of the degree of perturbation of assumed mechanisms.

A continuous-time multistate Markov model to describe the occurrence and severity of diarrhea events in metastatic breast cancer patients treated with lumretuzumab in combination with pertuzumab and paclitaxel

PURPOSE

To inform lumretuzumab and pertuzumab dose modifications in order to decrease the incidence, severity, and duration of the diarrhea events in metastatic breast cancer patients treated with a combination therapy of lumretuzumab (anti-HER3) in combination with pertuzumab (anti-HER2) and paclitaxel using quantitative clinical pharmacology modeling approaches.

METHODS

The safety and pharmacokinetic (PK) data from three clinical trials (lumretuzumab monotherapy n = 47, pertuzumab monotherapy n = 78, and the combination therapy of lumretuzumab, pertuzumab and paclitaxel n = 35) were pooled together to develop a continuous-time discrete states Markov model describing the dynamics of the diarrhea events.

RESULTS

The model was able to capture the time course of different severities of diarrhea reasonably well. The effect of lumretuzumab and pertuzumab was well described by an E_max function indicating an increased rate of transition from moderate to mild or more severe diarrhea with higher doses. The concentration needed to trigger or worsen diarrhea episodes was estimated to be 120-fold lower in combination therapy compared to monotherapy, suggesting strong synergy between the two monoclonal antibodies. The prophylactic effect of loperamide in a subset of patients was also well captured by the model with a clear tendency to reduce the occurrence of diarrhea events.

CONCLUSIONS

This work shows that PK-toxicity modeling provides insight into how the severity of key adverse events evolves over time and highlights the potential use to support decision making in drug development.

Quantitative systems pharmacology analysis of drug combination and scaling to humans: the interaction between noradrenaline and vasopressin in vasoconstriction

BACKGROUND AND PURPOSE

Development of combination therapies has received significant interest in recent years. Previously, a two-receptor one-transducer (2R-1T) model was proposed to characterize drug interactions with two receptors that lead to the same phenotypic response through a common transducer pathway. We applied, for the first time, the 2R-1T model to characterize the interaction of noradrenaline and arginine-vasopressin on vasoconstriction and performed inter-species scaling to humans using this mechanism-based model.

EXPERIMENTAL APPROACH

Contractile data were obtained from in vitro rat small mesenteric arteries after exposure to single or combined challenges of noradrenaline and arginine-vasopressin with or without pretreatment with the irreversible α-adrenoceptor antagonist, phenoxybenzamine. Data were analysed using the 2R-1T model to characterize the observed exposure-response relationships and drug-drug interaction. The model was then scaled to humans by accounting for differences in receptor density.

KEY RESULTS

With receptor affinities set to published values, the 2R-1T model satisfactorily characterized the interaction between noradrenaline and arginine-vasopressin in rat small mesenteric arteries (relative standard error ≤20%), as well as the effect of phenoxybenzamine. Furthermore, after scaling the model to human vascular tissue, the model also adequately predicted the interaction between both agents on human renal arteries.

CONCLUSIONS AND IMPLICATIONS

The 2R-1T model can be of relevance to quantitatively characterize the interaction between two drugs that interact via different receptors and a common transducer pathway. Its mechanistic properties are valuable for scaling the model across species. This approach is therefore of significant value to rationally optimize novel combination treatments.

Feasibility of Exposure-Response Analyses for Clinical Dose-Ranging Studies of Drug Combinations

The exposure-response relationship of combinatory drug effects can be quantitatively described using pharmacodynamic interaction models, which can be used for the selection of optimal dose combinations. The aim of this simulation study was to evaluate the reliability of parameter estimates and the probability for accurate dose identification for various underlying exposure-response profiles, under a number of different phase II designs. An efficacy variable driven by the combined exposure of two theoretical compounds was simulated and model parameters were estimated using two different models, one estimating all parameters and one assuming that adequate previous knowledge for one drug is readily available. Estimation of all pharmacodynamic parameters under a realistic, in terms of sample size and study design, phase II trial, proved to be challenging. Inaccurate estimates were found in all exposure-response scenarios, except for situations where no pharmacodynamic interaction was present, with the drug potency and interaction parameters being the hardest to estimate. When previous knowledge of the exposure-response relationship of one of the monocomponents is available, such information should be utilized, as it enabled relevant improvements in parameter estimation and in correct dose identification. No general trends for classification of the performance of the tested study designs across different scenarios could be identified. This study shows that pharmacodynamic interactions models can be used for the exposure-response analysis of clinical endpoints especially when accompanied by appropriate dose selection in regard to the expected drug potencies and appropriate trial size and if information regarding the exposure-response profile of one monocomponent is available.

Release and Decay Kinetics of Copeptin vs AVP in Response to Osmotic Alterations in Healthy Volunteers

CONTEXT

Copeptin is the C-terminal fragment of the arginine vasopressin (AVP) prohormone whose measurement is more robust than that of AVP. Similar release and clearance characteristics have been suggested promoting copeptin as a surrogate marker.

OBJECTIVE

To characterize the physiology of osmotically regulated copeptin release and its half-life in direct comparison with plasma AVP.

DESIGN

Ninety-one healthy volunteers underwent a standardized three-phase test protocol including (1) osmotic stimulation into the hypertonic range by hypertonic-saline infusion followed by osmotic suppression via (2) oral water load and (3) subsequent glucose infusion. Plasma copeptin, AVP, serum sodium, and osmolality levels were measured in regular intervals.

RESULTS

In phase 1, an increase in median osmotic pressure [289 (286; 291) to 311 (309; 314) mOsm/kg H2O] caused similar release kinetics of plasma copeptin [4 (3.1; 6) to 29.3 (18.6; 48.2) pmol/L] and AVP [1 (0.7; 1.6) to 10.3 (6.8; 18.8) pg/mL]. Subsequent osmotic suppression to 298 (295; 301) mOsm/kg at the end of phase 3 revealed markedly different decay kinetics between both peptides-an estimated initial half-life of copeptin being approximately 2 times longer than that of AVP (26 vs 12 minutes).

CONCLUSION

Copeptin is released in equimolar amounts with AVP in response to osmotic stimulation, suggesting its high potential as an AVP surrogate for differentiation of osmotic disorders. Furthermore, we here describe the decay kinetics of copeptin in response to osmotic depression enabling to identify a half-life for copeptin in direct comparison with AVP.

Model-Based Evaluation of Radiation and Radiosensitizing Agents in Oncology

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10-fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 μg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Correction to: Pharmacokinetics of Fentanyl and Its Derivatives in Children: A Comprehensive Review

Fentanyl and its derivatives sufentanil, alfentanil, and remifentanil are potent opioids. A comprehensive review of the use of fentanyl and its derivatives in the pediatric population was performed using the National Library of Medicine PubMed. Studies were included if they contained original pharmacokinetic parameters or models using established routes of administration in patients younger than 18 years of age. Of 372 retrieved articles, 44 eligible pharmacokinetic studies contained data of 821 patients younger than 18 years of age, including more than 46 preterm infants, 64 full-term neonates, 115 infants/toddlers, 188 children, and 28 adolescents. Underlying diagnoses included congenital heart and pulmonary disease and abdominal disorders. Routes of drug administration were intravenous, epidural, oral-transmucosal, intranasal, and transdermal. Despite extensive use in daily clinical practice, few studies have been performed. Preterm and term infants have lower clearance and protein binding. Pharmacokinetics was not altered by chronic renal or hepatic disease. Analyses of the pooled individual patients' data revealed that clearance maturation relating to body weight could be best described by the Hill function for sufentanil (R ² = 0.71, B _max 876 mL/min, K ₅₀ 16.3 kg) and alfentanil (R ² = 0.70, B _{max (fixed)} 420 mL/min, K ₅₀ 28 kg). The allometric exponent for estimation of clearance of sufentanil was 0.99 and 0.75 for alfentanil clearance. Maturation of remifentanil clearance was described by linear regression to bodyweight (R ² = 0.69). The allometric exponent for estimation of remifentanil clearance was 0.76. For fentanyl, linear regression showed only a weak correlation between clearance and bodyweight in preterm and term neonates (R ² = 0.22) owing to a lack of data in older age groups. A large heterogeneity regarding study design, clinical setting, drug administration, laboratory assays, and pharmacokinetic estimation was observed between studies introducing bias into the analyses performed in this review. A limitation of this review is that pharmacokinetic data, based on different modes of administration, dosing schemes, and parameter estimation methods, were combined.

Target mediated drug disposition with drug-drug interaction, Part II: competitive and uncompetitive cases

We present competitive and uncompetitive drug-drug interaction (DDI) with target mediated drug disposition (TMDD) equations and investigate their pharmacokinetic DDI properties. For application of TMDD models, quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are necessary to reduce the number of parameters. To realize those approximations of DDI TMDD models, we derive an ordinary differential equation (ODE) representation formulated in free concentration and free receptor variables. This ODE formulation can be straightforward implemented in typical PKPD software without solving any non-linear equation system arising from the QE or QSS approximation of the rapid binding assumptions. This manuscript is the second in a series to introduce and investigate DDI TMDD models and to apply the QE or QSS approximation.

Pharmacodynamic Modeling of Cell Cycle Effects for Gemcitabine and Trabectedin Combinations in Pancreatic Cancer Cells

Combinations of gemcitabine and trabectedin exert modest synergistic cytotoxic effects on two pancreatic cancer cell lines. Here, systems pharmacodynamic (PD) models that integrate cellular response data and extend a prototype model framework were developed to characterize dynamic changes in cell cycle phases of cancer cell subpopulations in response to gemcitabine and trabectedin as single agents and in combination. Extensive experimental data were obtained for two pancreatic cancer cell lines (MiaPaCa-2 and BxPC-3), including cell proliferation rates over 0-120 h of drug exposure, and the fraction of cells in different cell cycle phases or apoptosis. Cell cycle analysis demonstrated that gemcitabine induced cell cycle arrest in S phase, and trabectedin induced transient cell cycle arrest in S phase that progressed to G₂/M phase. Over time, cells in the control group accumulated in G₀/G₁ phase. Systems cell cycle models were developed based on observed mechanisms and were used to characterize both cell proliferation and cell numbers in the sub G₁, G₀/G₁, S, and G₂/M phases in the control and drug-treated groups. The proposed mathematical models captured well both single and joint effects of gemcitabine and trabectedin. Interaction parameters were applied to quantify unexplainable drug-drug interaction effects on cell cycle arrest in S phase and in inducing apoptosis. The developed models were able to identify and quantify the different underlying interactions between gemcitabine and trabectedin, and captured well our large datasets in the dimensions of time, drug concentrations, and cellular subpopulations.