Comparison of four basic models of indirect pharmacodynamic responses

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

Drugs interact with their targets in different ways. A diversity of modeling approaches exists to describe the combination effects of two drugs. We investigate several combination effect terms (CET) regarding their underlying mechanism based on drug-receptor binding kinetics, empirical and statistical summation principles and indirect response models. A list with properties is provided and the interrelationship of the CETs is analyzed. A method is presented to calculate the optimal drug concentration pair to produce the half-maximal combination effect. This work provides a comprehensive overview of typically applied CETs and should shed light into the question as to which CET is appropriate for application in pharmacokinetic/pharmacodynamic models to describe a specific drug-drug interaction mechanism.

A cell-level model of pharmacodynamics-mediated drug disposition

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

Effect of vitamin K2 on the anticoagulant activity of warfarin during the perioperative period of catheter ablation: Population analysis of retrospective clinical data

BACKGROUND

Catheter ablation is a non-medication therapy for atrial fibrillation, and during the procedure, warfarin is withdrawn in the preoperative period to prevent the risk of bleeding. In case of emergency, vitamin K2 can be intravenously administered to antagonize the anticoagulant activity of warfarin. The aims of this study were to conduct population pharmacokinetic/pharmacodynamic modeling for retrospective clinical data and to investigate the effect of vitamin K2 on the anticoagulant activity of warfarin in the perioperative period of catheter ablation.

METHODS

A total of 579 international normalized ratio (INR) values of prothrombin time from 100 patients were analyzed using the nonlinear mixed-effects modeling program NONMEM. A 1-compartment model was adapted to the pharmacokinetics of warfarin and vitamin K2, and the indirect response model was used to investigate the relationship between plasma concentration and the pharmacodynamic response of warfarin and vitamin K2. Since no plasma concentration data for warfarin and vitamin K2 were available, 3 literally available pharmacokinetic parameters were used to simultaneously estimate 1 pharmacokinetic parameter and 5 pharmacodynamic parameters.

RESULTS

The population parameters obtained not only successfully explained the observed INR values, but also indicated an increase in sensitivity to warfarin in patients with reduced renal function. Simulations using these parameters indicated that vitamin K2 administration of more than 20 mg caused a slight dose-dependent decrease in INR on the day of catheter ablation and a delayed INR elevation after warfarin re-initiation.

CONCLUSIONS

A pharmacokinetic/pharmacodynamic model was successfully built to explain the retrospective INR data during catheter ablation. Simulation studies suggest that vitamin K2 should be administered with care and that more than 20 mg is unnecessary in the preoperative period of catheter ablation.

Feedback control indirect response models

A general framework is introduced for modeling pharmacodynamic processes that are subject to autoregulation, which combines the indirect response (IDR) model approach with methods from classical feedback control of engineered systems. The canonical IDR models are modified to incorporate linear combinations of feedback control terms related to the time course of the difference (the error signal) between the pharmacodynamic response and its basal value. Following the well-established approach of traditional engineering control theory, the proposed feedback control indirect response models incorporate terms proportional to the error signal itself, the integral of the error signal, the derivative of the error signal or combinations thereof. Simulations are presented to illustrate the types of responses produced by the proposed feedback control indirect response model framework, and to illustrate comparisons with other PK/PD modeling approaches incorporating feedback. In addition, four examples from literature are used to illustrate the implementation and applicability of the proposed feedback control framework. The examples reflect each of the four mechanisms of drug action as modeled by each of the four canonical IDR models and include: selective serotonin reuptake inhibitors and extracellular serotonin; histamine H2-receptor antagonists and gastric acid; growth hormone secretagogues and circulating growth hormone; β2-selective adrenergic agonists and potassium. The proposed feedback control indirect response approach may serve as an exploratory modeling tool and may provide a bridge for development of more mechanistic systems pharmacology models.

Pharmacokinetic and Pharmacodynamic Modeling Analysis of Intravenous Esomeprazole in Healthy Volunteers

Esomeprazole is one of the most commonly used drugs to treat gastroesophageal reflux disease and peptic ulcers, but the quantitative relationships among the pharmacokinetics (PK), pharmacodynamics (PD), and pharmacogenomics (PG) of the drug are not fully understood in special patient populations. A clinical PK/PD/PG study of intravenous (IV) esomeprazole in 5 dosing regimens was conducted in 20 healthy Chinese volunteers, who were categorized into Helicobacter pylori (HP)-negative and HP-positive subgroups. Plasma esomeprazole concentration and intragastric H(+) concentration were monitored for 24 hours postdosing. Population PK (PopPK) models were tested based on elimination characteristics and other data. For a single-dose IV esomeprazole regimen, a 2-compartment model with nonlinear elimination characteristics fitted the PK data well. The elimination of esomeprazole was found to be significantly linked to CYP2C19 genotype by 11% to 29%. A mechanism-based PD model was first tested to mimic the irreversible inhibition of H(+) /K(+) -ATPase by esomeprazole using a cell-killing mechanism and models of gastric H(+) secretion that included the effects of an asymmetric circadian rhythm and food effects. Results from this PD model showed that the turnover rate of H(+) /K(+) -ATPase was significantly different between HP-negative and HP-positive subgroups. In conclusion, the PopPK model quantitatively identified the effects of the CYP2C19 genotype on esomeprazole elimination in healthy subjects for the first time. In addition, the effects of HP status on drug effect, H(+) /K(+) -ATPase turnover, and circadian rhythm amplitude were preliminarily explored using a mechanism-based PD model.

Systems pharmacology - Towards the modeling of network interactions

Mechanism-based pharmacokinetic and pharmacodynamics (PKPD) and disease system (DS) models have been introduced in drug discovery and development research, to predict in a quantitative manner the effect of drug treatment in vivo in health and disease. This requires consideration of several fundamental properties of biological systems behavior including: hysteresis, non-linearity, variability, interdependency, convergence, resilience, and multi-stationarity. Classical physiology-based PKPD models consider linear transduction pathways, connecting processes on the causal path between drug administration and effect, as the basis of drug action. Depending on the drug and its biological target, such models may contain expressions to characterize i) the disposition and the target site distribution kinetics of the drug under investigation, ii) the kinetics of target binding and activation and iii) the kinetics of transduction. When connected to physiology-based DS models, PKPD models can characterize the effect on disease progression in a mechanistic manner. These models have been found useful to characterize hysteresis and non-linearity, yet they fail to explain the effects of the other fundamental properties of biological systems behavior. Recently systems pharmacology has been introduced as novel approach to predict in vivo drug effects, in which biological networks rather than single transduction pathways are considered as the basis of drug action and disease progression. These models contain expressions to characterize the functional interactions within a biological network. Such interactions are relevant when drugs act at multiple targets in the network or when homeostatic feedback mechanisms are operative. As a result systems pharmacology models are particularly useful to describe complex patterns of drug action (i.e. synergy, oscillatory behavior) and disease progression (i.e. episodic disorders). In this contribution it is shown how physiology-based PKPD and disease models can be extended to account for internal systems interactions. It is demonstrated how SP models can be used to predict the effects of multi-target interactions and of homeostatic feedback on the pharmacological response. In addition it is shown how DS models may be used to distinguish symptomatic from disease modifying effects and to predict the long term effects on disease progression, from short term biomarker responses. It is concluded that incorporation of expressions to describe the interactions in biological network analysis opens new avenues to the understanding of the effects of drug treatment on the fundamental aspects of biological systems behavior.

Translational mixed-effects PKPD modelling of recombinant human growth hormone - from hypophysectomized rat to patients

BACKGROUND AND PURPOSE

We aimed to develop a mechanistic mixed-effects pharmacokinetic (PK)-pharmacodynamic (PD) (PKPD) model for recombinant human growth hormone (rhGH) in hypophysectomized rats and to predict the human PKPD relationship.

EXPERIMENTAL APPROACH

A non-linear mixed-effects model was developed from experimental PKPD studies of rhGH and effects of long-term treatment as measured by insulin-like growth factor 1 (IGF-1) and bodyweight gain in rats. Modelled parameter values were scaled to human values using the allometric approach with fixed exponents for PKs and unscaled for PDs and validated through simulations relative to patient data.

KEY RESULTS

The final model described rhGH PK as a two compartmental model with parallel linear and non-linear elimination terms, parallel first-order absorption with a total s.c. bioavailability of 87% in rats. Induction of IGF-1 was described by an indirect response model with stimulation of kin and related to rhGH exposure through an Emax relationship. Increase in bodyweight was directly linked to individual concentrations of IGF-1 by a linear relation. The scaled model provided robust predictions of human systemic PK of rhGH, but exposure following s.c. administration was over predicted. After correction of the human s.c. absorption model, the induction model for IGF-1 well described the human PKPD data.

CONCLUSIONS

A translational mechanistic PKPD model for rhGH was successfully developed from experimental rat data. The model links a clinically relevant biomarker, IGF-1, to a primary clinical end-point, growth/bodyweight gain. Scaling of the model parameters provided robust predictions of the human PKPD in growth hormone-deficient patients including variability.

Evaluation of estimation, prediction and inference for autocorrelated latent variable modeling of binary data-a simulation study

Longitudinal models of binary or ordered categorical data are often evaluated for adequacy by the ability of these to characterize the transition frequency and type between response states. Drug development decisions are often concerned with accurate prediction and inference of the probability of response by time and dose. A question arises on whether the transition probabilities need to be characterized adequately to ensure accurate response prediction probabilities unconditional on the previous response state. To address this, a simulation study was conducted to assess bias in estimation, prediction and inferences of autocorrelated latent variable models (ALVMs) when the transition probabilities are misspecified due to ill-posed random effects structures, inadequate likelihood approximation or omission of the autocorrelation component. The results may be surprising in that these suggest that characterizing autocorrelation in ALVMs is not as important as specifying a suitably rich random effects structure.

Establishing the Quantitative Relationship Between Lanreotide Autogel®, Chromogranin A, and Progression-Free Survival in Patients with Nonfunctioning Gastroenteropancreatic Neuroendocrine Tumors

The objective of this work was to establish the quantitative relationship between Lanreotide Autogel® (LAN) on serum chromogranin A (CgA) and progression-free survival (PFS) in patients with nonfunctioning gastroenteropancreatic neuroendocrine tumors (GEP-NETs) through an integrated pharmacokinetic/pharmacodynamic (PK/PD) model. In CLARINET, a phase III, randomized, double-blind, placebo-controlled study, 204 patients received deep subcutaneous injections of LAN 120 mg (n = 101) or placebo (n = 103) every 4 weeks for 96 weeks. Data for 810 LAN and 1298 CgA serum samples (n = 632 placebo and n = 666 LAN) were used to develop a parametric time-to-event model to relate CgA levels and PFS (76 patients experienced disease progression: n = 49 placebo and n = 27 LAN). LAN serum profiles were described by a one-compartment disposition model. Absorption was characterized by two parallel pathways following first- and zero-order kinetics. As PFS data were considered informative dropouts, CgA and PFS responses were modeled jointly. The LAN-induced decrease in CgA levels was described by an inhibitory E MAX model. Patient age and target lesions at baseline were associated with an increment in baseline CgA. Weibull model distribution showed that decreases in CgA from baseline reduced the hazard of disease progression significantly (P < 0.001). Covariates of tumor location in the pancreas and tumor hepatic tumor load were associated with worse prognosis (P < 0.001). We established a semimechanistic PK/PD model to better understand the effect of LAN on a surrogate endpoint (serum CgA) and ultimately the clinical endpoint (PFS) in treatment-naive patients with nonfunctioning GEP-NETs.

Pattern Recognition in Pharmacodynamic Data Analysis

Pattern recognition is a key element in pharmacodynamic analyses as a first step to identify drug action and selection of a pharmacodynamic model. The essence of this process is going from data to insight through exploratory data analysis. There are few formal strategies that scientists typically use when the experiment has been done and data collected. This report attempts to ameliorate this deficit by identifying the properties of a pharmacodynamic model via dissection of the pattern revealed in response-time data. Pattern recognition in pharmacodynamic analyses contrasts with pharmacokinetic analyses with respect to time course. Thus, the time course of drug in plasma usually differs markedly from the time course of the biomarker response, as a consequence of a myriad of interactions (transport to biophase, binding to target, activation of target and downstream mediators, physiological response, cascade and amplification of biosignals, homeostatic feedback) between the events of exposure to test compound and the occurrence of the biomarker response. Homing in on this important-but less often addressed-element, 20 datasets of varying complexity were analyzed, and from this, we summarize a set of points to consider, specifically addressing baseline behavior, number of phases in the response-time course, time delays between concentration- and response-time courses, peak shifts in response with increasing doses, saturation, and other potential nonlinearities. These strategies will hopefully give a better understanding of the complete pharmacodynamic response-time profile.

Pharmacokinetic-pharmacodynamic modelling in anaesthesia

Anaesthesiologists adjust drug dosing, administration system and kind of drug to the characteristics of the patient. They then observe the expected response and adjust dosing to the specific requirements according to the difference between observed response, expected response and the context of the surgery and the patient. The approach above can be achieved because on one hand quantification technology has made significant advances allowing the anaesthesiologist to measure almost any effect by using noninvasive, continuous measuring systems. On the other the knowledge on the relations between dosing, concentration, biophase dynamics and effect as well as detection of variability sources has been achieved as being the benchmark specialty for pharmacokinetic-pharmacodynamic (PKPD) modelling. The aim of the review is to revisit the most common PKPD models applied in the field of anaesthesia (i.e. effect compartmental, turnover, drug-receptor binding and drug interaction models) through representative examples. The effect compartmental model has been widely used in this field and there are multiple applications and examples. The use of turnover models has been limited mainly to describe respiratory effects. Similarly, cases in which the dissociation process of the drug-receptor complex is slow compared with other processes relevant to the time course of the anaesthetic effect are not frequent in anaesthesia, where in addition to a rapid onset, a fast offset of the response is required. With respect to the characterization of PD drug interactions different response surface models are discussed. Relevant applications that have changed the way modern anaesthesia is practiced are also provided.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems.

Physiologically-Based Pharmacokinetic-Pharmacodynamic Modeling of 1α,25-Dihydroxyvitamin D3 in Mice

1α,25-Dihydroxyvitamin D3 [1,25(OH)2D3] concentrations are regulated by renal CYP27B1 for synthesis and CYP24A1 for degradation. Published plasma and tissue 1,25(OH)2D3 concentrations and mRNA fold change expression of Cyp24a1 and Cyp27b1 following repetitive i.p. injections to C57BL/6 mice (2.5 μg × kg(-1) every 2 days for 4 doses) were fitted with a minimal and full physiologically-based pharmacokinetic-pharmacodynamic models (PBPK-PD). The minimal physiologically-based pharmacokinetic-pharmacodynamic linked model (mPBPK-PD) related Cyp24a1 mRNA fold changes to linear changes in tissue/tissue baseline 1,25(OH)2D3 concentration ratios, whereas the full physiologically-based pharmacokinetic-pharmacodynamic model (PBPK-PD) related measured tissue Cyp24a1 and Cyp27b1 fold changes to tissue 1,25(OH)2D3 concentrations with indirect response, sigmoidal maximal stimulatory effect/maximal inhibitory effect functions. Moreover, the intestinal segregated flow model (SFM) that describes a low and partial intestinal (blood/plasma) flow to enterocytes was nested within both models for comparison with the traditional model for intestine (TM) where the entire flow perfuses the intestine. Both the mPBPK(SFM)-PD and full PBPK(SFM)-PD models described the i.p. plasma and tissue 1,25(OH)2D3 concentrations and fold changes in mRNA expression significantly better than the TM counterparts with F test comparisons. The full PBPK(SFM)-PD fits showed estimates with good precision (lower percentage of coefficient of variation), and the model was more robust in predicting data from escalating i.v. doses (2, 60, and 120 pmol) and the rebound in 1,25(OH)2D3 tissue concentrations after dosing termination. The full PBPK(SFM)-PD model performed the best among the tested models for describing the complex pharmacokinetic-pharmacodynamic interplay among Cyp27b1, Cyp24a1, and 1,25(OH)2D3.

Improvement in latent variable indirect response joint modeling of a continuous and a categorical clinical endpoint in rheumatoid arthritis

Improving the quality of exposure-response modeling is important in clinical drug development. The general joint modeling of multiple endpoints is made possible in part by recent progress on the latent variable indirect response (IDR) modeling for ordered categorical endpoints. This manuscript aims to investigate, when modeling a continuous and a categorical clinical endpoint, the level of improvement achievable by joint modeling in the latent variable IDR modeling framework through the sharing of model parameters for the individual endpoints, guided by the appropriate representation of drug and placebo mechanism. This was illustrated with data from two phase III clinical trials of intravenously administered mAb X for the treatment of rheumatoid arthritis, with the 28-joint disease activity score (DAS28) and 20, 50, and 70% improvement in the American College of Rheumatology (ACR20, ACR50, and ACR70) disease severity criteria were used as efficacy endpoints. The joint modeling framework led to a parsimonious final model with reasonable performance, evaluated by visual predictive check. The results showed that, compared with the more common approach of separately modeling the endpoints, it is possible for the joint model to be more parsimonious and yet better describe the individual endpoints. In particular, the joint model may better describe one endpoint through subject-specific random effects that would not have been estimable from data of this endpoint alone.

Concentrations of MDPV in rat striatum correlate with the psychostimulant effect

3,4-methylenedioxypyrovalerone or MDPV is a synthetic cathinone with psychostimulant properties more potent than cocaine. We quantified this drug in the striatum after subcutaneous administration to rats. MDPV reached the brain around 5 min after its administration and peaked at 20-25 min later. The elimination half-life in the striatum (61 min) correlates with the decrease in the psychostimulant effect after 60 min. Around 11% of the administered dose reached the striatum and, considering a homogeneous brain distribution, we determined that around 86% of the plasma MDPV is distributed to the brain. MDPV induced a dose-dependent increase in locomotor activity, rearing behaviour and stereotypies, all prevented by haloperidol. A plot of locomotor activity or stereotypies versus MDPV striatal concentrations over time showed a direct relationship between factors. No free MDPV metabolites were detected in plasma, at any time, but hydrolysis with glucuronidase allowed us to identify mainly three metabolites, one of them for the first time in rat plasma. The present results contribute to evidence that MDPV induces hyperlocomotion mainly through a dopamine-dependent mechanism. Good correlation between behavioural effects and striatal levels of MDPV leads us to conclude that its psychostimulant effect is mainly due to a striatal distribution of the substance. The present research provides useful information on the pharmacokinetics of MDPV, and can help design new experiments with kinetics data as well as provide a better understanding of the effects of MDPV in humans and its potential interactions.

Development of a physiology-directed population pharmacokinetic and pharmacodynamic model for characterizing the impact of genetic and demographic factors on clopidogrel response in healthy adults

Clopidogrel (Plavix®), is a widely used antiplatelet agent, which shows high inter-individual variability in treatment response in patients following the standard dosing regimen. In this study, a physiology-directed population pharmacokinetic/pharmacodynamic (PK/PD) model was developed based on clopidogrel and clopidogrel active metabolite (clop-AM) data from the PAPI and the PGXB2B studies using a step-wise approach in NONMEM (version 7.2). The developed model characterized the in vivo disposition of clopidogrel, its bioactivation into clop-AM in the liver and subsequent platelet aggregation inhibition in the systemic circulation reasonably well. It further allowed the identification of covariates that significantly impact clopidogrel's dose-concentration-response relationship. In particular, CYP2C19 intermediate and poor metabolizers converted 26.2% and 39.5% less clopidogrel to clop-AM, respectively, compared to extensive metabolizers. In addition, CES1 G143E mutation carriers have a reduced CES1 activity (82.9%) compared to wild-type subjects, which results in a significant increase in clop-AM formation. An increase in BMI was found to significantly decrease clopidogrel's bioactivation, whereas increased age was associated with increased platelet reactivity. Our PK/PD model analysis suggests that, in order to optimize clopidogrel dosing on a patient-by-patient basis, all of these factors have to be considered simultaneously, e.g. by using quantitative clinical pharmacology tools.

Kinetics of drug action in disease states: towards physiology-based pharmacodynamic (PBPD) models

Gerhard Levy started his investigations on the "Kinetics of Drug Action in Disease States" in the fall of 1980. The objective of his research was to study inter-individual variation in pharmacodynamics. To this end, theoretical concepts and experimental approaches were introduced, which enabled assessment of the changes in pharmacodynamics per se, while excluding or accounting for the cofounding effects of concomitant changes in pharmacokinetics. These concepts were applied in several studies. The results, which were published in 45 papers in the years 1984-1994, showed considerable variation in pharmacodynamics. These initial studies on kinetics of drug action in disease states triggered further experimental research on the relations between pharmacokinetics and pharmacodynamics. Together with the concepts in Levy's earlier publications "Kinetics of Pharmacologic Effects" (Clin Pharmacol Ther 7(3): 362-372, 1966) and "Kinetics of pharmacologic effects in man: the anticoagulant action of warfarin" (Clin Pharmacol Ther 10(1): 22-35, 1969), they form a significant impulse to the development of physiology-based pharmacodynamic (PBPD) modeling as novel discipline in the pharmaceutical sciences. This paper reviews Levy's research on the "Kinetics of Drug Action in Disease States". Next it addresses the significance of his research for the evolution of PBPD modeling as a scientific discipline. PBPD models contain specific expressions to characterize in a strictly quantitative manner processes on the causal path between exposure (in terms of concentration at the target site) and the drug effect (in terms of the change in biological function). Pertinent processes on the causal path are: (1) target site distribution, (2) target binding and activation and (3) transduction and homeostatic feedback.

Pharmacodynamic models of age-structured cell populations

The purpose of this work is to review basic pharmacodynamic (PD) models describing drug effects on cell populations and expand them to age-structured models using the theory of physiologically structured populations. The plasma drug concentrations are interpreted as the environment affecting the cell production and mortality rates. An explicit solution to model equations provides the age density distribution that serves to establish a relationship between the cell lifespan distribution and the hazard of cell removal. Given the lifespan distributions, the age distributions for most commonly applied PD models of cell responses including basic cell turnover, transit compartments, and basic lifespan models have been derived both for the baseline conditions and drug treatment. The steady-state age distribution for basic indirect response models is exponential, and it is uniform for the basic lifespan model. As an example of more complex cell population, the age distribution of human red blood cells has been simulated based on a recent model of red blood cell survival. The age distribution for cells in the transit compartment model is the sum of the gamma functions. Means and variances of age distributions for all discussed models were calculated. A brief discussion of numerical challenges and possible future model developments is presented.

Pharmacodynamics and tolerability of repository corticotropin injection in healthy human subjects: A comparison with intravenous methylprednisolone

Repository corticotropin injection (porcine adrenocorticotropic hormone [ACTH] analog) and intravenous methylprednisolone (IVMP) are used to treat inflammatory conditions such as multiple sclerosis (MS) exacerbations and rheumatoid arthritis. This multiple‐dose, randomized, crossover, open‐label study evaluated and compared pharmacodynamic outcomes in subjects who received ACTH analog (80 U subcutaneously) or IVMP (1 g) daily for 5 days. Specific outcome measures included IVMP and cortisol concentrations, total cortisol‐equivalent exposure, immune cell population changes, and tolerability. IVMP and ACTH analog increased granulocyte numbers and decreased lymphocyte counts; effects on both were significantly less pronounced with ACTH analog. Based on total cortisol‐equivalent exposure (assuming linearity), administration of 80 U of ACTH analog equates to 30 mg IVMP. Because IVMP doses significantly higher than 30 mg are usually required to treat MS exacerbations, the lower cortisol‐equivalent exposure of 80 U ACTH analog supports the hypothesis that efficacy of ACTH analog results from both steroid‐dependent and ‐independent properties. Adverse events were mild in severity; subject incidence for adverse‐event reporting was similar following both regimens. The clinical relevance of these findings in autoimmune disease populations is unknown and requires further evaluation.

Physiologically-Based Pharmacokinetic and Pharmacodynamic Modeling for the Inhibition of Acetylcholinesterase by Acotiamide, A Novel Gastroprokinetic Agent for the Treatment of Functional Dyspepsia, in Rat Stomach

Purpose

Acotiamide, a gastroprokinetic agent used to treat functional dyspepsia, is transported to at least two compartments in rat stomach. However, the role of these stomach compartments in pharmacokinetics and pharmacodynamics of acotiamide remains unclear. Thus, the purpose of this study was to elucidate the relationship of the blood and stomach concentration of acotiamide with its inhibitory effect on acetylcholinesterase (AChE).

Methods

Concentration profiles of acotiamide and acetylcholine (ACh) were determined after intravenous administration to rats and analyzed by physiologically-based pharmacokinetic and pharmacodynamic (PBPK/PD) model containing vascular space, precursor pool and deep pool of stomach.

Results

Acotiamide was eliminated from the blood and stomach in a biexponential manner. Our PBPK/PD model estimated that acotiamide concentration in the precursor pool exceeded 2 μM at approximately 2 h after administration. Acotiamide inhibited AChE activity in vitro with a 50% inhibitory concentration of 1.79 μM. ACh reached the maximum concentration at 2 h after administration.

Conclusions

Our PBPK model well described the profile of acotiamide and ACh concentration in the stomach in the assumption that acotiamide was distributed by carrier mediated process and inhibited AChE in the precursor pool of stomach. Thus, Acotiamide in the precursor pool plays an important role for producing the pharmacological action.

Mechanism-based population pharmacokinetic and pharmacodynamic modeling of intravenous and intranasal dexmedetomidine in healthy subjects

PURPOSE

Dexmedetomidine is an α2-adrenoceptor agonist used for perioperative and intensive care sedation. This study develops mechanism-based population pharmacokinetic-pharmacodynamic models for the cardiovascular and central nervous system (CNS) effects of intravenously (IV) and intranasally (IN) administered dexmedetomidine in healthy subjects.

METHOD

Single doses of 84 μg of dexmedetomidine were given once IV and once IN to six healthy men. Plasma dexmedetomidine concentrations were measured for 10 h along with plasma concentrations of norepinephrine (NE) and epinephrine (E). Blood pressure, heart rate, and CNS drug effects (three visual analog scales and bispectral index) were monitored to assess the pharmacological effects of dexmedetomidine. PK-PD modeling was performed for recently published data (Eur J Clin Pharmacol 67: 825, 2011).

RESULTS

Pharmacokinetic profiles for both IV and IN doses of dexmedetomidine were well fitted using a two-compartment PK model. Intranasal bioavailability was 82%. Dexmedetomidine inhibited the release of NE and E to induce their decline in blood. This decrease in NE was captured with an indirect response model. The concentrations of the mediator NE served via a biophase/transduction step and nonlinear pharmacologic functions to produce reductions in blood pressure and heart rate, while a direct effect model was used for the CNS effects.

CONCLUSION

The comprehensive panel of two biomarkers and seven response measures were well captured by the population PK/PD models. The subjects were more sensitive to the CNS (lower EC 50 values) than cardiovascular effects of dexmedetomidine.

A Systems Pharmacology Model of Erythropoiesis in Mice Induced by Small Molecule Inhibitor of Prolyl Hydroxylase Enzymes

Mammalian erythropoiesis is a conserved process tightly controlled by the hypoxia-inducible factor (HIF1) pathway. In this study, a small molecule inhibitor (PHI-1) of prolyl-hydroxylase-2 (PHD2) enzyme involved in regulating HIF1α levels was orally administered to male BALB/c mice at 10 and 30 mg/kg. A systems pharmacology model was developed based on the measured PHI-1 plasma exposures, kidney HIF1α, kidney erythropoietin (EPO) mRNA, plasma EPO, reticulocyte counts, red blood cells, and hemoglobin levels. The model fit resulted in the estimation of drug potency (IC₅₀: 1.7μM), and systems parameters such as EPO mRNA turnover (k_{deg_EPOmRNA}: 0.43 hr^-1) and mean lifespan of reticulocytes (T_r: 81 hours). The model correctly described the observed 30–40-fold increase in kidney HIF1α protein, ∼1,000 fold increase in EPO mRNA and 2–3-fold increase in the reticulocytes at 30 mg/kg. This study presents the first parsimonious systems model of erythropoiesis to quantitatively describe the in vivo effects of PHD2 inhibition.

Biomarker- versus drug-driven tumor growth inhibition models: an equivalence analysis

The mathematical modeling of tumor xenograft experiments following the dosing of antitumor drugs has received much attention in the last decade. Biomarker data can further provide useful insights on the pathological processes and be used for translational purposes in the early clinical development. Therefore, it is of particular interest the development of integrated pharmacokinetic-pharmacodynamic (PK-PD) models encompassing drug, biomarker and tumor-size data. This paper investigates the reciprocal consistency of three types of models: drug-to-tumor, such as established drug-driven tumor growth inhibition (TGI) models, drug-to-biomarker, e.g. indirect response models, and biomarker-to-tumor, e.g. the more recent biomarker-driven TGI models. In particular, this paper derives a mathematical relationship that guarantees the steady-state equivalence of the cascade of drug-to-biomarker and biomarker-to-tumor models with a drug-to-tumor TGI model. Using the Simeoni TGI model as a reference, conditions for steady-state equivalence are worked out and used to derive a new biomarker-driven model. Simulated and real data are used to show that in realistic cases the steady-state equivalence extends also to transient responses. The possibility of predicting the drug-to-tumor potency of a new candidate drug based only on biomarker response is discussed.

The method of averaging applied to pharmacokinetic/pharmacodynamic indirect response models

The computational effort required to fit the pharmacodynamic (PD) part of a pharmacokinetic/pharmacodynamic (PK/PD) model can be considerable if the differential equations describing the model are solved numerically. This burden can be greatly reduced by applying the method of averaging (MAv) in the appropriate circumstances. The MAv gives an approximate solution, which is expected to be a good approximation when the PK profile is periodic (i.e. repeats its values in regular intervals) and the rate of change of the PD response is such that it is approximately constant over a single period of the PK profile. This paper explains the basis of the MAv by means of a simple mathematical derivation. The NONMEM® implementation of the MAv using the abbreviated FORTRAN function FUNCA is described and explained. The application of the MAv is illustrated by means of an example involving changes in glycated hemoglobin (HbA1c%) following administration of canagliflozin, a selective sodium glucose co-transporter 2 inhibitor. The PK/PD model applied to these data is fitted with NONMEM® using both the MAv and the standard method using a numerical differential equation solver (NDES). Both methods give virtually identical results but the NDES method takes almost 8 h to run both the estimation and covariance steps, whilst the MAv produces the same results in less than 30 s. An outline of the NONMEM® control stream and the FORTRAN code for the FUNCA function is provided in the appendices.

PKPD modelling to predict altered disposition of 1α,25-dihydroxyvitamin D3 in mice due to dose-dependent regulation of CYP27B1 on synthesis and CYP24A1 on degradation

BACKGROUND AND PURPOSE

Concentrations of 1α,25-dihydroxyvitamin D3 [1,25(OH)2 D3 ], the active ligand of the vitamin D receptor, are tightly regulated by CYP27B1 for synthesis and CYP24A1 for degradation. However, the dose-dependent pharmacokinetic (PK)-pharmacodynamic (PD) relationship between these enzymes and 1,25(OH)2 D3 concentrations has not been characterized.

EXPERIMENTAL APPROACH

The pharmacokinetics of 1,25(OH)2 D3 were evaluated after administration of single (2, 60 and 120 pmol) and repeated (2 and 120 pmol q2d ×3) i.v. doses to male C57BL/6 mice. mRNA expression of CYP27B1 and CYP24A1 was examined by quantitative PCR and 1,25(OH)2 D3 concentrations were determined by enzyme immunoassay.

KEY RESULTS

CYP27B1 and CYP24A1 changes were absent for the 2 pmol dose and biexponential decay profiles showed progressively shorter terminal half-lives with increasing doses. Fitting with a two-compartment model revealed decreasing net synthesis rates and increasing total clearances with dose, consistent with a dose-dependent down-regulation of renal CYP27B1 and the induction of renal/intestinal CYP24A1 mRNA expression. Upon incorporation of PD parameters for inhibition of CYP27B1 and induction of CYP24A1 to the simple two-compartment model, fitting was significantly improved. Moreover, fitted estimates for the 2 pmol dose, together with the PD parameters as modifiers, were able to predict profiles reasonably well for the higher (60 and 120 pmol) doses. Lastly, an indirect response model, which considered the synthesis and degradation of enzymes, adequately described the PK and PD profiles.

CONCLUSIONS AND IMPLICATIONS

The unique PK of exogenously administered 1,25(OH)2 D3 led to changes in PD of CYP27B1 and CYP24A1, which hastened the clearance of 1,25(OH)2 D3 .

A Joint Model for the Kinetics of CTC Count and PSA Concentration During Treatment in Metastatic Castration-Resistant Prostate Cancer

Assessment of treatment efficacy in metastatic castration-resistant prostate cancer (mCRPC) is limited by frequent nonmeasurable bone metastases. The count of circulating tumor cells (CTCs) is a promising surrogate marker that may replace the widely used prostate-specific antigen (PSA). The purpose of this study was to quantify the dynamic relationships between the longitudinal kinetics of these markers during treatment in patients with mCRPC. Data from 223 patients with mCRPC treated by chemotherapy and/or hormonotherapy were analyzed for up to 6 months of treatment. A semimechanistic model was built, combining the following several pharmacometric advanced features: (1) Kinetic-Pharmacodynamic (K-PD) compartments for treatments (chemotherapy and hormonotherapy); (2) a latent variable linking both marker kinetics; (3) modeling of CTC kinetics with a cell lifespan model; and (4) a negative binomial distribution for the CTC random sampling. Linked with survival, this model would potentially be useful for predicting treatment efficacy during drug development or for therapeutic adjustment in treated patients.

Population pharmacokinetic and pharmacodynamic analysis of tesamorelin in HIV-infected patients and healthy subjects

The objective of this analysis was to characterize the time course of selected pharmacodynamic (PD) markers of tesamorelin: growth hormone (GH) and insulin-like growth factor (IGF-1) concentrations in HIV-infected patients and healthy volunteers. A total of 41 subjects in Phase I trials receiving subcutaneous daily doses of 1 or 2 mg of tesamorelin during 14 consecutive days were included in this analysis. A previous pharmacokinetic (PK) model of tesamorelin was used as the input function for the PD model of GH. Tesamorelin was hypothesized to stimulate the secretion of GH in an "episodic" manner, i.e., for a finite duration of time. The resulting PK/PD model of GH was used to describe the time course of IGF-1. The effect of age, body weight, body mass index, sex, race, and health status on the model parameters was evaluated. The model was qualified using predictive checks and non-parametric bootstrap. Within the range of the values evaluated no covariates were significantly associated with GH or IGF-1 model parameters. Model evaluation procedures indicated accurate prediction of the selected pharmacodynamic markers. The time course of GH and IGF-1 concentrations following multiple doses of tesamorelin were well predicted by the sequential PK/PD model developed using Phase I data.

Data-driven modeling of pharmacological systems using endpoint information fusion

This study investigated the feasibility of deriving data-driven model of a class of pharmacological systems using the information fusion of endpoint responses. For a class of pharmacological systems subsuming conventional steady-state dose-response models, compartmental pharmacokinetic-pharmacodynamic models and indirect response models, a relation between multiple endpoint responses was formalized and analyzed to elucidate if this class of systems is identifiable, i.e., if the data-driven model of this class of systems can be derived from the endpoint responses alone. It was shown that this class of systems is fully identifiable in case all the responses involve effect compartments. However, it was also observed that persistently exciting dose profiles may be required in accurately deriving reliable data-driven model with low variance. The findings from the identifiability analysis were demonstrated using benchmark pharmacological system examples.

Tetrahydrobiopterin (BH4) responsiveness in neonates with hyperphenylalaninemia: a semi-mechanistically-based, nonlinear mixed-effect modeling

Neonatal loading studies with tetrahydrobiopterin (BH4) are used to detect hyperphenylalaninemia due to BH4 deficiency by evaluating decreases in blood phenylalanine (Phe) concentrations post BH4 load. BH4 responsiveness in phenylalanine hydroxylase (PAH)-deficient patients introduced a new diagnostic aspect for this test. In older children, a broad spectrum of different levels of responsiveness has been described. The primary objective of this study was to develop a pharmacodynamic model to improve the description of individual sensitivity to BH4 in the neonatal period. Secondary objectives were to evaluate BH4 responsiveness in a large number of PAH-deficient patients from a neonatal screening program and in patients with various confirmed BH4 deficiencies from the BIODEF database. Descriptive statistics in patients with PAH deficiency with 0-24-h data available showed that 129 of 340 patients (37.9%) had a >30% decrease in Phe levels post load. Patients with dihydropteridine reductase deficiency (n = 53) could not be differentiated from BH4-responsive patients with PAH deficiency. The pharmacologic turnover model, "stimulation of loss" of Phe following BH4 load, fitted the data best. Using the model, 193 of 194 (99.5%) patients with a proven BH4 synthesis deficiency or recycling defect were classified as BH4 sensitive. Among patients with PAH deficiency, 216 of 375 (57.6%) patients showed sensitivity to BH4, albeit with a pronounced variability; PAH-deficient patients with blood Phe <1200 μmol/L at time 0 showed higher sensitivity than patients with blood Phe levels >1200 μmol/L. External validation showed good correlation between the present approach, using 0-24-h blood Phe data, and the published 48-h prognostic test. Pharmacodynamic modeling of Phe levels following a BH4 loading test is sufficiently powerful to detect a wide range of responsiveness, interpretable as a measure of sensitivity to BH4. However, the clinical relevance of small responses needs to be evaluated by further studies of their relationship to long-term response to BH4 treatment.

The effect of plasmapheresis on blood pressure in voluntary plasma donors

BACKGROUND AND OBJECTIVES

Donor plasmapheresis involves the removal of a weight-adjusted volume of plasma and the return of cellular components to the donor. Although plasma volume generally returns to normal, some residual effect on vital signs may be possible. This analysis was performed to determine the possible effects of plasmapheresis on blood pressure.

MATERIALS AND METHODS

A 16-week study was conducted to evaluate the effects of plasma donations on cholesterol levels in healthy donors. From this study, the vital signs obtained prior to donation were analysed using statistical and dynamic analytical predictive models.

RESULTS

Preliminary analyses revealed a change in systolic and diastolic blood pressure from the corresponding baseline values (Pearson Coefficient -0.44 and -0.47, respectively). Statistical models predicted a marked decrease in systolic and diastolic blood pressure following multiple donations in donors with baseline pressure in the Stage 2 hypertension range with less pronounced decreases predicted in Stage 1 donors. Little or no change in blood pressure was predicted in donors with baseline normal blood pressure or prehypertension. Dynamic models including time between donations supported these results and predicted a recovery period of about 14 days without donation in donors with Stage 2 baseline levels.

CONCLUSIONS

Results suggest that systolic and diastolic blood pressure may be decreased following plasmapheresis used for plasma donations at intervals of <14 days in donors with high baseline blood pressure levels.

Prediction of Hemodynamic Response to Epinephrine via Model-Based System Identification

In this study, we present a system identification approach to the mathematical modeling of hemodynamic responses to vasopressor-inotrope agents. We developed a hybrid model called the latency-dose-response-cardiovascular (LDC) model that incorporated 1) a low-order lumped latency model to reproduce the delay associated with the transport of vasopressor-inotrope agent and the onset of physiological effect, 2) phenomenological dose-response models to dictate the steady-state inotropic, chronotropic, and vasoactive responses as a function of vasopressor-inotrope dose, and 3) a physiological cardiovascular model to translate the agent's actions into the ultimate response of blood pressure. We assessed the validity of the LDC model to fit vasopressor-inotrope dose-response data using data collected from five piglet subjects during variable epinephrine infusion rates. The results suggested that the LDC model was viable in modeling the subjects' dynamic responses: After tuning the model to each subject, the r (2) values for measured versus model-predicted mean arterial pressure were consistently higher than 0.73. The results also suggested that intersubject variability in the dose-response models, rather than the latency models, had significantly more impact on the model's predictive capability: Fixing the latency model to population-averaged parameter values resulted in r(2) values higher than 0.57 between measured versus model-predicted mean arterial pressure, while fixing the dose-response model to population-averaged parameter values yielded nonphysiological predictions of mean arterial pressure. We conclude that the dose-response relationship must be individualized, whereas a population-averaged latency-model may be acceptable with minimal loss of model fidelity.

Drug effects on the CVS in conscious rats: separating cardiac output into heart rate and stroke volume using PKPD modelling

BACKGROUND AND PURPOSE

Previously, a systems pharmacology model was developed characterizing drug effects on the interrelationship between mean arterial pressure (MAP), cardiac output (CO) and total peripheral resistance (TPR). The present investigation aims to (i) extend the previously developed model by parsing CO into heart rate (HR) and stroke volume (SV) and (ii) evaluate if the mechanism of action (MoA) of new compounds can be elucidated using only HR and MAP measurements.

EXPERIMENTAL APPROACH

Cardiovascular effects of eight drugs with diverse MoAs (amiloride, amlodipine, atropine, enalapril, fasudil, hydrochlorothiazide, prazosin and propranolol) were characterized in spontaneously hypertensive rats (SHR) and normotensive Wistar-Kyoto (WKY) rats following single administrations of a range of doses. Rats were instrumented with ascending aortic flow probes and aortic catheters/radiotransmitters for continuous recording of MAP, HR and CO throughout the experiments. Data were analysed in conjunction with independent information on the time course of the drug concentration following a mechanism-based pharmacokinetic-pharmacodynamic modelling approach.

KEY RESULTS

The extended model, which quantified changes in TPR, HR and SV with negative feedback through MAP, adequately described the cardiovascular effects of the drugs while accounting for circadian variations and handling effects.

CONCLUSIONS AND IMPLICATIONS

A systems pharmacology model characterizing the interrelationship between MAP, CO, HR, SV and TPR was obtained in hypertensive and normotensive rats. This extended model can quantify dynamic changes in the CVS and elucidate the MoA for novel compounds, with one site of action, using only HR and MAP measurements. Whether the model can be applied for compounds with a more complex MoA remains to be established.

PKPD modelling of the interrelationship between mean arterial BP, cardiac output and total peripheral resistance in conscious rats

BACKGROUND AND PURPOSE

The homeostatic control of arterial BP is well understood with changes in BP resulting from changes in cardiac output (CO) and/or total peripheral resistance (TPR). A mechanism-based and quantitative analysis of drug effects on this interrelationship could provide a basis for the prediction of drug effects on BP. Hence, we aimed to develop a mechanism-based pharmacokinetic-pharmacodynamic (PKPD) model in rats that could be used to characterize the effects of cardiovascular drugs with different mechanisms of action (MoA) on the interrelationship between BP, CO and TPR.

EXPERIMENTAL APPROACH

The cardiovascular effects of six drugs with diverse MoA, (amlodipine, fasudil, enalapril, propranolol, hydrochlorothiazide and prazosin) were characterized in spontaneously hypertensive rats. The rats were chronically instrumented with ascending aortic flow probes and/or aortic catheters/radiotransmitters for continuous recording of CO and/or BP. Data were analysed in conjunction with independent information on the time course of drug concentration using a mechanism-based PKPD modelling approach.

KEY RESULTS

By simultaneous analysis of the effects of six different compounds, the dynamics of the interrelationship between BP, CO and TPR were quantified. System-specific parameters could be distinguished from drug-specific parameters indicating that the model developed is drug-independent.

CONCLUSIONS AND IMPLICATIONS

A system-specific model characterizing the interrelationship between BP, CO and TPR was obtained, which can be used to quantify and predict the cardiovascular effects of a drug and to elucidate the MoA for novel compounds. Ultimately, the proposed PKPD model could be used to predict the effects of a particular drug on BP in humans based on preclinical data.

Lifespan based pharmacokinetic-pharmacodynamic model of tumor growth inhibition by anticancer therapeutics

Accurate prediction of tumor growth is critical in modeling the effects of anti-tumor agents. Popular models of tumor growth inhibition (TGI) generally offer empirical description of tumor growth. We propose a lifespan-based tumor growth inhibition (LS TGI) model that describes tumor growth in a xenograft mouse model, on the basis of cellular lifespan T. At the end of the lifespan, cells divide, and to account for tumor burden on growth, we introduce a cell division efficiency function that is negatively affected by tumor size. The LS TGI model capability to describe dynamic growth characteristics is similar to many empirical TGI models. Our model describes anti-cancer drug effect as a dose-dependent shift of proliferating tumor cells into a non-proliferating population that die after an altered lifespan T_A. Sensitivity analysis indicated that all model parameters are identifiable. The model was validated through case studies of xenograft mouse tumor growth. Data from paclitaxel mediated tumor inhibition was well described by the LS TGI model, and model parameters were estimated with high precision. A study involving a protein casein kinase 2 inhibitor, AZ968, contained tumor growth data that only exhibited linear growth kinetics. The LS TGI model accurately described the linear growth data and estimated the potency of AZ968 that was very similar to the estimate from an established TGI model. In the case study of AZD1208, a pan-Pim inhibitor, the doubling time was not estimable from the control data. By fixing the parameter to the reported in vitro value of the tumor cell doubling time, the model was still able to fit the data well and estimated the remaining parameters with high precision. We have developed a mechanistic model that describes tumor growth based on cell division and has the flexibility to describe tumor data with diverse growth kinetics.

Prediction of disease progression, treatment response and dropout in chronic obstructive pulmonary disease (COPD)

Purpose

Drug development in chronic obstructive pulmonary disease (COPD) has been characterised by unacceptably high failure rates. In addition to the poor sensitivity in forced expiratory volume in one second (FEV₁), numerous causes are known to contribute to this phenomenon, which can be clustered into drug-, disease- and design-related factors. Here we present a model-based approach to describe disease progression, treatment response and dropout in clinical trials with COPD patients.

Methods

Data from six phase II trials lasting up to 6 months were used. Disease progression (trough FEV₁ measurements) was modelled by a time–varying function, whilst the treatment effect was described by an indirect response model. A time-to-event model was used for dropout

Results

All relevant parameters were characterised with acceptable precision. Two parameters were necessary to model the dropout patterns, which was found to be partly linked to the treatment failure. Disease severity at baseline, previous use of corticosteroids, gender and height were significant covariates on disease baseline whereas disease severity and reversibility to salbutamol/salmeterol were significant covariates on E_max for salmeterol active arm.

Conclusion

Incorporation of the various interacting factors into a single model will offer the basis for patient enrichment and improved dose rationale in COPD.

Electronic supplementary material

The online version of this article (doi:10.1007/s11095-014-1490-4) contains supplementary material, which is available to authorized users.

Time lapse investigation of antibiotic susceptibility using a microfluidic linear gradient 3D culture device

This study reports a novel approach to quantitatively investigate the antibacterial effect of antibiotics on bacteria using a three-dimensional microfluidic culture device. In particular, our approach is suitable for studying the pharmacodynamics effects of antibiotics on bacterial cells temporally and with a continuous range of concentrations in a single experiment. The responses of bacterial cells to a linear concentration gradient of antibiotics were observed using time-lapse photography, by encapsulating bacterial cells in an agarose-based gel located in a commercially available microfluidics chamber. This approach generates dynamic information with high resolution, in a single operation, e.g., growth curves and antibiotic pharmacodynamics, in a well-controlled environment. No pre-labelling of the cells is needed and therefore any bacterial sample can be tested in this setup. It also provides static information comparable to that of standard techniques for measuring minimum inhibitory concentration (MIC). Five antibiotics with different mechanisms were analysed against wild-type Escherichia coli, Staphylococcus aureus and Salmonella Typhimurium. The entire process, including data analysis, took 2.5-4 h and from the same analysis, high-resolution growth curves were obtained. As a proof of principle, a pharmacodynamic model of streptomycin against Salmonella Typhimurium was built based on the maximal effect model, which agreed well with the experimental results. Our approach has the potential to be a simple and flexible solution to study responding behaviours of microbial cells under different selection pressures both temporally and in a range of concentrations.

Pharmacokinetic and pharmacodynamic analysis comparing diverse effects of detomidine, medetomidine, and dexmedetomidine in the horse: a population analysis

The present study characterizes the pharmacokinetic (PK) and pharmacodynamic (PD) relationships of the α2-adrenergic receptor agonists detomidine (DET), medetomidine (MED) and dexmedetomidine (DEX) in parallel groups of horses from in vivo data after single bolus doses. Head height (HH), heart rate (HR), and blood glucose concentrations were measured over 6 h. Compartmental PK and minimal physiologically based PK (mPBPK) models were applied and incorporated into basic and extended indirect response models (IRM). Population PK/PD analysis was conducted using the Monolix software implementing the stochastic approximation expectation maximization algorithm. Marked reductions in HH and HR were found. The drug concentrations required to obtain inhibition at half-maximal effect (IC50 ) were approximately four times larger for DET than MED and DEX for both HH and HR. These effects were not gender dependent. Medetomidine had a greater influence on the increase in glucose concentration than DEX. The developed models demonstrate the use of mechanistic and mPBPK/PD models for the analysis of clinically obtainable in vivo data.

Translational pharmacokinetic-pharmacodynamic modeling for an orally available novel inhibitor of anaplastic lymphoma kinase and c-Ros oncogene 1

An orally available macrocyclic small molecule, PF06463922 [(10R)-7-amino-12-fluoro-2,10,16-trimethyl-15-oxo-10,15,16,17-tetrahydro-2H-8,4-(metheno)pyrazolo[4,3-h][2,5,11]benzoxadiazacyclotetradecine-3-carbonitrile], is a selective inhibitor of anaplastic lymphoma kinase (ALK) and c-Ros oncogene 1 (ROS1). The objectives of the present study were to characterize the pharmacokinetic-pharmacodynamic relationships of PF06463922 between its systemic exposures, pharmacodynamic biomarker (target modulation), and pharmacologic response (antitumor efficacy) in athymic mice implanted with H3122 non-small cell lung carcinomas expressing echinoderm microtubule-associated protein-like 4 (EML4)-ALK mutation (EML4-ALK(L1196M)) and with NIH3T3 cells expressing CD74-ROS1. In these nonclinical tumor models, PF06463922 was orally administered to animals with EML4-ALK(L1196M) and CD74-ROS1 at twice daily doses of 0.3-20 and 0.01-3 mg/kg per dose, respectively. Plasma concentration-time profiles of PF06463922 were adequately described by a one-compartment pharmacokinetic model. Using the model-simulated plasma concentrations, a pharmacodynamic indirect response model with a modulator sufficiently fit the time courses of target modulation (i.e., ALK phosphorylation) in tumors of EML4-ALK(L1196M)-driven models with EC50,in vivo of 36 nM free. A drug-disease model based on an indirect response model reasonably fit individual tumor growth curves in both EML4-ALK(L1196M)- and CD74-ROS1-driven models with the estimated tumor stasis concentrations of 51 and 6.2 nM free, respectively. Thus, the EC60,in vivo (52 nM free) for ALK inhibition roughly corresponded to the tumor stasis concentration in an EML4-ALK(L1196M)-driven model, suggesting that 60% ALK inhibition would be required for tumor stasis. Accordingly, we proposed that the EC60,in vivo for ALK inhibition corresponding to the tumor stasis could be considered a minimum target efficacious concentration of PF06463922 for cancer patients in a phase I trial.