Mechanism-Based Pharmacokinetic-Pharmacodynamic Modeling: Biophase Distribution, Receptor Theory, and Dynamical Systems Analysis

Engineering challenges for instrumenting and controlling integrated organ-on-chip systems

The sophistication and success of recently reported microfabricated organs-on-chips and human organ constructs have made it possible to design scaled and interconnected organ systems that may significantly augment the current drug development pipeline and lead to advances in systems biology. Physiologically realistic live microHuman (μHu) and milliHuman (mHu) systems operating for weeks to months present exciting and important engineering challenges such as determining the appropriate size for each organ to ensure appropriate relative organ functional activity, achieving appropriate cell density, providing the requisite universal perfusion media, sensing the breadth of physiological responses, and maintaining stable control of the entire system, while maintaining fluid scaling that consists of ~5 mL for the mHu and ~5 μL for the μHu. We believe that successful mHu and μHu systems for drug development and systems biology will require low-volume microdevices that support chemical signaling, microfabricated pumps, valves and microformulators, automated optical microscopy, electrochemical sensors for rapid metabolic assessment, ion mobility-mass spectrometry for real-time molecular analysis, advanced bioinformatics, and machine learning algorithms for automated model inference and integrated electronic control. Toward this goal, we are building functional prototype components and are working toward top-down system integration.

The mastermind approach to CNS drug therapy: translational prediction of human brain distribution, target site kinetics, and therapeutic effects

Despite enormous advances in CNS research, CNS disorders remain the world's leading cause of disability. This accounts for more hospitalizations and prolonged care than almost all other diseases combined, and indicates a high unmet need for good CNS drugs and drug therapies.Following dosing, not only the chemical properties of the drug and blood-brain barrier (BBB) transport, but also many other processes will ultimately determine brain target site kinetics and consequently the CNS effects. The rate and extent of all these processes are regulated dynamically, and thus condition dependent. Therefore, heterogenious conditions such as species, gender, genetic background, tissue, age, diet, disease, drug treatment etc., result in considerable inter-individual and intra-individual variation, often encountered in CNS drug therapy.For effective therapy, drugs should access the CNS "at the right place, at the right time, and at the right concentration". To improve CNS therapies and drug development, details of inter-species and inter-condition variations are needed to enable target site pharmacokinetics and associated CNS effects to be translated between species and between disease states. Specifically, such studies need to include information about unbound drug concentrations which drive the effects. To date the only technique that can obtain unbound drug concentrations in brain is microdialysis. This (minimally) invasive technique cannot be readily applied to humans, and we need to rely on translational approaches to predict human brain distribution, target site kinetics, and therapeutic effects of CNS drugs.In this review the term "Mastermind approach" is introduced, for strategic and systematic CNS drug research using advanced preclinical experimental designs and mathematical modeling. In this way, knowledge can be obtained about the contributions and variability of individual processes on the causal path between drug dosing and CNS effect in animals that can be translated to the human situation. On the basis of a few advanced preclinical microdialysis based investigations it will be shown that the "Mastermind approach" has a high potential for the prediction of human CNS drug effects.

Modeling NSCLC progression: recent advances and opportunities available

Non-small cell lung cancer (NSCLC) is one of the leading causes of death around the world with an estimated 5-year relative survival rate of 16% at diagnosis. Development of drugs treating NSCLC is not easy, and the success rate for an anticancer treatment to pass through the whole clinical development process is as low as 5%. Modeling and simulation lend themselves as tools which can potentially streamline drug development. A critical component of the models developed is a description of how the disease progresses over time and how a treatment would affect its trajectory. Our aim was to review the literature to present the models and growth functions which have been used for describing NSCLC dynamics, and how anticancer treatments can affect such dynamics, both in animals and in humans. Only a limited set of models were identified for such a purpose. Most of the models which have been used were descriptive of tumor growth, yet there were attempts to account for the underlying processes, especially in animals where it is more feasible to collect data needed for developing such models. Moreover, we discuss how modeling and simulation can aid in decision making across the different stages of drug development. Based on some encouraging results from trials of other cancer types where modeling tumor dynamics has played an important role, we propose further exploration of NSCLC using model-based techniques and further use of these techniques in designing and evaluating NSCLC trials.

Translational PK-PD modeling in pain

The current gap between animal research and clinical development of analgesic drugs presents a challenge for the application of translational PK-PD modeling and simulation. First, animal pain models lack predictive and construct validity to accurately reflect human pain etiologies and, secondly, clinical pain is a multidimensional sensory experience that can't always be captured by objective and robust measures. These challenges complicate the use of translational PK-PD modeling to project PK-PD data generated in preclinical species to a plausible range of clinical doses. To date only a few drug targets identified in animal studies have shown to be successful in the clinic. PK-PD modeling of biomarkers collected during the early phase of clinical development can bridge animal and clinical pain research. For drugs with novel mechanism of actions understanding of the target pharmacology is essential in order to increase the success of clinical development. There is a specific interest in the application of human pain models that can mimic different aspects of acute/chronic pain symptoms and serves as link between animal and clinical pain research. In early clinical development the main objective of PK-PD modeling is to characterize the relationship between target site binding and downstream biomarkers that have a potential link to the clinical endpoint (e.g. readouts from the human pain models) so as to facilitate the selection of doses for proof of concept studies. In patient studies, the role of PK-PD modeling and simulation is to characterize and confirm patient populations in terms of responder profiles with the aim to find the right dose for the right patient.

Integrating experimentation and quantitative modeling to enhance discovery of Beta amyloid lowering therapeutics for Alzheimer's disease

Drug discovery can benefit from a proactive-knowledge-attainment philosophy which strategically integrates experimentation and pharmacokinetic/pharmacodynamic (PK/PD) modeling. Our programs for Alzheimer’s disease (AD) illustrate such an approach. Compounds that inhibit the generation of brain beta amyloid (Aβ), especially Aβ42, are being pursued as potential disease-modifying therapeutics. Complexities in the PK/Aβ relationship for these compounds have been observed and the data require an advanced approach for analysis. We established a semimechanistic PK/PD model that can describe the PK/Aβ data by accounting for Aβ generation and clearance. The modeling characterizes the in vivo PD (i.e., Aβ lowering) properties of compounds and generates insights about the salient biological systems. The learning from the modeling enables us to establish a framework for predicting in vivo Aβ lowering from in vitro parameters.

From pediatric covariate model to semiphysiological function for maturation: part I-extrapolation of a covariate model from morphine to Zidovudine

New approaches to expedite the development of safe and effective pediatric dosing regimens and first-in-child doses are urgently needed. Model-based approaches require quantitative functions on the maturation of different metabolic pathways. In this study, we directly incorporated a pediatric covariate model for the glucuronidation of morphine into a pediatric population model for zidovudine glucuronidation. This model was compared with a reference model that gave the statistically best description of the data. Both models had adequate goodness-of-fit plots and normalized prediction distribution errors (NPDE), similar population clearance values for each individual, and a Δobjective function value of 13 points (Δ2df). This supports our hypothesis that pediatric pharmacokinetic covariate models contain system-specific information that can be used as semiphysiological functions in pediatric population models. Further research should explore the validity of the semiphysiological function for other UDP-glucuronosyltransferase 2B7 substrates and patient populations and reveal how this function can be used for pediatric physiologically based pharmacokinetic models.CPT: Pharmacometrics & Systems Pharmacology (2012) 1, e9; doi:10.1038/psp.2012.11; advance online publication 3 October 2012.

Research priorities in pharmacokinetics

An opinion is expressed on the past, present and future roles of pharmacokinetic-pharmacodynamic research in the context of UK clinical pharmacology. On the basis of its current constitution, it seems unlikely that this area of research will be driven from within academic clinical pharmacology in the UK. Therefore, in order to bring its expertise and experience to bear effectively on the evolving emphasis on translational medicine and modelling and simulation, this community would need to reach out beyond its current preoccupations to increase interactions with the next generation of pharmacokineticists and pharmacometricians.

Individualization of drug therapy: history, present state, and opportunities for the future

Individualization of drug therapy, described as tailoring drug selection and drug dosing to a given patient, has been an objective of physicians and other health-care providers for centuries. An understanding of the pathogenesis of the disease, the mechanism of action of the drug, and exposure-response relationships provides the framework for individualization. There are many approaches to individualization: selecting an antibiotic based on minimum effective concentrations and bacterial sensitivity, population (sparse sample) pharmacokinetics, therapeutic drug monitoring and, more recently, pharmacogenomics. The goal of individualization is to optimize the efficacy of a drug, minimize its toxicity, or both. With the growth of technology and databases, drug-disease-trial models and simulation have become useful for integrating information from many different domains. Physiology-based pharmacokinetic (PBPK) models have provided a mechanistic approach to individualization, and clinical trial designs such as those involving enrichment have also enabled individualization. In the future, "-omics" technologies, vaccines, ex vivo gene therapy, and the so-called "diseases-in-a-dish" will provide additional strategies to achieve individualization.

Pharmacokinetic-pharmacodynamic modeling in acute and chronic pain: an overview of the recent literature

In acute and chronic pain, the objective of pharmacokinetic-pharmacodynamic (PKPD) modeling is the development and application of mathematical models to describe and/or predict the time course of the pharmacokinetics (PK) and pharmacodynamics (PD) of analgesic agents and link PK to PD. Performing population PKPD modeling using nonlinear mixed effects modeling allows, apart from the estimation of fixed effects (the PK and PD model estimates), the quantification of random effects as within- and between-subject variability. Effect-compartment models and mechanism-based biophase distribution models that incorporate drug-association and -dissociation kinetics are applied in PKPD modeling of pain treatment. Mechanism-based models enable the quantification of the rate-limiting factors in drug effect owing to drug distribution versus receptor kinetics (since receptor kinetics are nonlinear they are discernable from the linear effect-compartment kinetics). It is a helpful technique in understanding the complex behavior of specific analgesics, such as buprenorphine, but also morphine and its active metabolite morphine-6-glucuronide, especially with respect to the reversal of opioid-induced side effects, most importantly life-threatening respiratory depression. One approach in chronic pain studies is the application of mixture models. Mixture models do not necessarily need to take PK data into account and allow the objective differentiation of measured responses to analgesics into specific response subgroups, and as such, may play an important role in analyzing Phase I and II analgesia studies. Appropriate application of PKPD modeling leads to the improvement of current therapeutics with respect to dose design and outcome, understanding the interaction of analgesics within complex chronic pain disease processes and may play an important role in drug development. In the current article, novel observations using the aforementioned techniques on opioids, NSAIDs, epidural analgesia, ketamine and GABA-ergic drugs in acute and chronic pain are discussed.

Neonatal pharmacology: extensive interindividual variability despite limited size

Providing safe and effective drug therapy to neonates requires knowledge of the impact of development on the pharmacokinetics and pharmacodynamics of drugs. Although maturational changes are observed throughout childhood, they are most prominent during the first year of life. Several of these processes overlap, making development an extremely dynamic system in the newborn compared with that in infants, children, or adults. Changes in body composition and porportions, liver mass, metabolic activity, and renal function collectively affect the pharmacokinetic behavior of medications. Instead of simply adapting doses by scaling adult or pediatric doses on the basis of a patient's weight and/or body surface area, integrated knowledge of clinical maturation and developmental pharmacology is critical to the safe and effective use of medications in neonates. Unfortunately, the effects of human ontogeny on both pharmacokinetics and pharmacodynamics have not been well established in these early stages of life, and information regarding the influence of developmental changes on the pharmacodynamics of medications is even more limited. Theoretically, age-dependent variations in receptor number and affinity for drugs have significant potential to influence an individual's response to drug therapy. In this review, some of the relevant covariates of pharmacokinetics and pharmacodynamics in neonates are reviewed and illustrated based on the published literature.

Impact of the pharmaceutical sciences on health care: a reflection over the past 50 years

During the last century, particularly the latter half, spectacular progress has been made in improving the health and longevity of people. The reasons are many, but the development of medicines has played a critical role. This report documents and reflects on the impressive contribution that those working in the pharmaceutical sciences have made to healthcare over the past 50 years. It is divided into six sections (drug discovery; absorption, distribution, metabolism, and excretion; pharmacokinetics and pharmacodynamics; drug formulation; drug regulation; and drug utilization), each describing key contributions that have been made in the progression of medicines, from conception to use. A common thread throughout is the application of translational science to the improvement of drug discovery, development, and therapeutic application. Each section has been coordinated by a leading scientist who was asked, after consulting widely with many colleagues across the globe, to identify "The five most influential ideas/concepts/developments introduced by 'pharmaceutical scientists' (in their field) over the past 50 years?" Although one cannot predict where the important breakthroughs will come in the future to meet the unmet medical needs, the evidence presented in this report should leave no doubt that those engaged in the pharmaceutical sciences will continue to make their contributions heavily felt.

Compartmental tissue distribution of antibody therapeutics: experimental approaches and interpretations

Monoclonal antibodies have provided many validated and potential new therapeutic candidates for various diseases encompassing the realms of neurology, ophthalmology, immunology, and especially oncology. The mechanism of action for these biological molecules typically involves specific binding to a soluble ligand or cell surface protein in order to block or alter a molecular pathway, induce a desired cellular response, or deplete a target cell. Many antigens reside within the interstitial space, the fluid-filled compartment that lies between the outer endothelial vessel wall and the plasma membranes of cells. This mini-review examines the concepts relevant to the kinetics and behavior of antibodies within the interstitium with a special emphasis on radiometric measurement of quantitative pharmacology. Molecular probes are discussed to outline chemical techniques, selection criteria, data interpretation, and relevance to the study of antibody pharmacokinetics. The importance of studying the tissue uptake of antibodies at a compartmental level is highlighted, including a brief overview of receptor occupancy and its interpretation in radiotracer studies. Experimental methods for measuring the spatial composition of tissues are examined in terms of relative vascular, interstitial, and cellular volumes using solid tumors as a representative example. Experimental methods and physiologically based pharmacokinetic modeling are introduced as distinct approaches to distinguish between free and bound fractions of interstitial antibody. Overall, the review outlines the available methods for pharmacokinetic measurements of antibodies and physiological measurements of the compartments that they occupy, while emphasizing that such approaches may not fully capture the complexities of dynamic, heterogeneous tumors and other tissues.

Pharmacokinetic-pharmacodynamic modeling of the D₂ and 5-HT (2A) receptor occupancy of risperidone and paliperidone in rats

PURPOSE

A pharmacokinetic-pharmacodynamic (PK-PD) model was developed to describe the time course of brain concentration and dopamine D₂ and serotonin 5-HT(2A) receptor occupancy (RO) of the atypical antipsychotic drugs risperidone and paliperidone in rats.

METHODS

A population approach was utilized to describe the PK-PD of risperidone and paliperidone using plasma and brain concentrations and D₂ and 5-HT(2A) RO data. A previously published physiology- and mechanism-based (PBPKPD) model describing brain concentrations and D₂ receptor binding in the striatum was expanded to include metabolite kinetics, active efflux from brain, and binding to 5-HT(2A) receptors in the frontal cortex.

RESULTS

A two-compartment model best fit to the plasma PK profile of risperidone and paliperidone. The expanded PBPKPD model described brain concentrations and D₂ and 5-HT(2A) RO well. Inclusion of binding to 5-HT(2A) receptors was necessary to describe observed brain-to-plasma ratios accurately. Simulations showed that receptor affinity strongly influences brain-to-plasma ratio pattern.

CONCLUSION

Binding to both D₂ and 5-HT(2A) receptors influences brain distribution of risperidone and paliperidone. This may stem from their high affinity for D₂ and 5-HT(2A) receptors. Receptor affinities and brain-to-plasma ratios may need to be considered before choosing the best PK-PD model for centrally active drugs.

The Øie-Tozer model of drug distribution and its suitability for drugs with different pharmacokinetic behavior

INTRODUCTION

Drug distribution is a major pharmacokinetic process that affects the time course of drug concentrations in tissues, biological fluids and the resulting pharmacological activities. Drug distribution may follow different pathways and patterns, and is governed by the drug's physicochemical properties and the body's physiology. The classical Øie-Tozer model is frequently used for predicting volume of drug distribution and for pharmacokinetic calculations.

AREAS COVERED

In this review, the suitability of the Øie-Tozer model for drugs that exhibit different distribution patterns is critically analyzed and illustrated. The method used is a pharmacokinetic modeling and simulation approach. It is demonstrated that the major limitation of the Øie-Tozer model stems from its focus on the total drug concentrations and not on the active (unbound) concentrations. Moreover, the Øie-Tozer model may be inappropriate for drugs with nonlinear or complex pharmacokinetic behavior, such as biopharmaceuticals, drug conjugates or for drugs incorporated into drug delivery systems. Distribution mechanisms and alternative distribution models for these drugs are discussed.

EXPERT OPINION

The Øie-Tozer model can serve for predicting unbound volume of drug distribution for 'classical' small molecular mass drugs with linear pharmacokinetics. However, more detailed mechanism-based distribution models should be used in preclinical and clinical settings for drugs that exhibit more complex pharmacokinetic behavior.

Role of computational methods in pharmaceutical sciences

Over the past two decades computational methods have eased up the financial and experimental burden of early drug discovery process. The in silico methods have provided support in terms of databases, data mining of large genomes, network analysis, systems biology on the bioinformatics front and structure-activity relationship, similarity analysis, docking, and pharmacophore methods for lead design and optimization. This review highlights some of the applications of bioinformatics and chemoinformatics methods that have enriched the field of drug discovery. In addition, the review also provided insights into the use of free energy perturbation methods for efficiently computing binding energy. These in silico methods are complementary and can be easily integrated into the traditional in vitro and in vivo methods to test pharmacological hypothesis.

A mechanism-based pharmacokinetic/pharmacodynamic model for CYP3A1/2 induction by dexamethasone in rats

AIM

To develop a pharmacokinetic/pharmacodynamic (PK/PD) model describing the receptor/gene-mediated induction of CYP3A1/2 by dexamethasone (DEX) in rats.

METHODS

A group of male Sprague-Dawley rats receiving DEX (100 mg/kg, ip) were sacrificed at various time points up to 60 h post-treatment. Their blood sample and liver were collected. The plasma concentration of DEX was determined with a reverse phase HPLC method. CYP3A1/2 mRNA, protein levels and enzyme activity were measured using RT-PCR, ELISA and the testosterone substrate assay, respectively. Data analyses were performed using a first-order conditional estimate (FOCE) with INTERACTION method in NONMEM version 7.1.2.

RESULTS

A two-compartment model with zero-order absorption was applied to describe the pharmacokinetic characteristics of DEX. Systemic clearance, the apparent volume of distribution and the duration of zero-order absorption were calculated to be 172.7 mL·kg(-1)·h(-1), 657.4 mL/kg and 10.47 h, respectively. An indirect response model with a series of transit compartments was developed to describe the induction of CYP3A1/2 via PXR transactivation by DEX. The maximum induction of CYP3A1 and CYP3A2 mRNA levels was achieved, showing nearly 21.29- and 8.67-fold increases relative to the basal levels, respectively. The CYP3A1 and CYP3A2 protein levels were increased by 8.02-fold and 2.49-fold, respectively. The total enzyme activities of CYP3A1/2 were shown to increase by up to 2.79-fold, with a lag time of 40 h from the Tmax of the DEX plasma concentration. The final PK/PD model was able to recapitulate the delayed induction of CYP3A1/2 mRNA, protein and enzyme activity by DEX.

CONCLUSION

A mechanism-based PK/PD model was developed to characterize the complex concentration-induction response relationship between DEX and CYP3A1/2 and to resolve the drug- and system-specific PK/PD parameters for the course of induction.

Uricases as therapeutic agents to treat refractory gout: Current states and future directions

Treatment of refractory gout remains a challenge on drug development. While pegloticase, a recombinant mammalian uricase modified with monomethoxyl-poly(ethylene glycol) (mPEG) is effective in treating refractory gout, after continued treatment for three months biweekly at a therapeutic dose of 0.14 mg/kg body weight, it elicits an immune response against mPEG in nearly 20% of patients. For continued treatment of refractory gout PEGylated uricases at monthly therapeutic doses below 4 μg/kg body weight have promise. To formulate uricases to achieve monthly therapeutic regimens requires pharmacodynamics simulation and experimentation including: (a) molecular engineering of uricases based on rational design and evolution biotechnology in combination to improve their inherent catalytic efficiency, thermostability and selectivity for urate over xanthine and; (b) optimization of the number and distribution of accessible reactive amino acid residues in native uricases for site-specific PEGylation with PEG derivatives with lower of immunogenicity than mPEG to retain activity, minimize immunogenicity and enhance the pharmacokinetics of the PEGylated uricase. These issues are briefly reviewed as a means to stimulate the development of safer uricase formulations for continued treatment of refractory gout.

Structural models describing placebo treatment effects in schizophrenia and other neuropsychiatric disorders

Large variation in placebo response within and among clinical trials can substantially affect conclusions about the efficacy of new medications in psychiatry. Developing a robust placebo model to describe the placebo response is important to facilitate quantification of drug effects, and eventually to guide the design of clinical trials for psychiatric treatment via a model-based simulation approach. In addition, high dropout rates are very common in the placebo arm of psychiatric clinical trials. While developing models to evaluate the effect of placebo response, the data from patients who drop out of the trial should be considered for accurate interpretation of the results. The objective of this paper is to review the various empirical and semi-mechanistic models that have been used to quantify the placebo response in schizophrenia trials. Pros and cons of each placebo model are discussed. Additionally, placebo models used in other neuropsychiatric disorders like depression, Alzheimer's disease and Parkinson's disease are also reviewed with the objective of finding those placebo models that could be useful for clinical studies of both acute and chronic schizophrenic disease conditions. Better understanding of the patterns of dropout and the factors leading to dropouts are crucial in identifying the true placebo response. We therefore also review dropout models that are used in the development of models for treatment effects and in the optimization of clinical trials by simulation approaches. The use of an appropriate modelling strategy that is capable of identifying the potential sources of variable placebo responses and dropout rates is recommended for improving the sensitivity in discriminating between the effects of active treatment and placebo.

Coping with time scales in disease systems analysis: application to bone remodeling

In this study we demonstrate the added value of mathematical model reduction for characterizing complex dynamic systems using bone remodeling as an example. We show that for the given parameter values, the mechanistic RANK-RANKL-OPG pathway model proposed by Lemaire et al. (J Theor Biol 229:293-309, 2004) can be reduced to a simpler model, which can describe the dynamics of the full Lemaire model to very good approximation. The response of both models to changes in the underlying physiology and therapeutic interventions was evaluated in four physiologically meaningful scenarios: (i) estrogen deficiency/estrogen replacement therapy, (ii) Vitamin D deficiency, (iii) ageing, and (iv) chronic glucocorticoid treatment and its cessation. It was found that on the time scale of disease progression and therapeutic intervention, the models showed negligible differences in their dynamic properties and were both suitable for characterizing the impact of estrogen deficiency and estrogen replacement therapy, Vitamin D deficiency, ageing, and chronic glucocorticoid treatment and its cessation on bone forming (osteoblasts) and bone resorbing (osteoclasts) cells. It was also demonstrated how the simpler model could help in elucidating qualitative properties of the observed dynamics, such as the absence of overshoot and rebound, and the different dynamics of onset and washout.

Associating in vitro target binding and in vivo CNS occupancy of serotonin reuptake inhibitors in rats: the role of free drug concentrations

The present study aimed at investigating the theory that free (unbound) active site concentrations are the best predictors of target binding of compounds blocking the serotonin transporter (Sert) in the central nervous system (CNS). Thirteen serotonin reuptake inhibitors were evaluated for their Sert-binding affinities in vitro and in vivo in rats together with their unbound fractions in plasma and brain. Cortical Sert occupancy was used in vivo to acquire EC₅₀-estimates from total plasma, free plasma, whole brain, and free brain concentrations after acute drug administration. The in vitro-in vivo Sert occupancy analyses showed that the best correlation was achieved when unbound brain concentrations were employed. Unbound brain concentrations also provided a better correlation when compared with unbound plasma concentrations, which could be related to lack of equilibrium between plasma and brain at time of measurements or involvement of active brain efflux processes. In addition, brain-free fractions were shown to be directly correlated to the lipophilicity of the compounds. These data emphasize the use and impact of applying free fraction data in assessment of pharmacological in vitro-in vivo correlations and demonstrates its use to validate in vivo Sert occupancy as pharmacodynamic marker for serotonin reuptake inhibitors in rats.

Understanding the time course of pharmacological effect: a PKPD approach

The key concepts that underpin the choice of drug and dosing regimen are an understanding of the drugs' effectiveness, the potential for adverse effects, and the expected time course over which both desired and adverse effects are likely to occur. Research in clinical pharmacology should therefore address three fundamental questions: (1) What is the magnitude of drug effects (beneficial or adverse) from a given dose? (2) How quickly will any given effects occur? (3) How long will these effects last? Under steady-state conditions, only the magnitude of drug effects can be examined. This requires researchers to consider non-steady-state conditions, which require more complex models and an understanding of the mechanisms that drive the time course of drug effect. The aim of this review is to provide a conceptual framework for understanding the time course of drug effects using pharmacokinetic-pharmacodynamic models. Key examples will illustrate how this can inform the optimal use of drugs in the clinic.

Mechanism-based pharmacokinetic-pharmacodynamic modeling of the dopamine D2 receptor occupancy of olanzapine in rats

Purpose

A mechanism-based PK-PD model was developed to predict the time course of dopamine D₂ receptor occupancy (D₂RO) in rat striatum following administration of olanzapine, an atypical antipsychotic drug.

Methods

A population approach was utilized to quantify both the pharmacokinetics and pharmacodynamics of olanzapine in rats using the exposure (plasma and brain concentration) and D₂RO profile obtained experimentally at various doses (0.01–40 mg/kg) administered by different routes. A two-compartment pharmacokinetic model was used to describe the plasma pharmacokinetic profile. A hybrid physiology- and mechanism-based model was developed to characterize the D₂ receptor binding in the striatum and was fitted sequentially to the data. The parameters were estimated using nonlinear mixed-effects modeling .

Results

Plasma, brain concentration profiles and time course of D₂RO were well described by the model; validity of the proposed model is supported by good agreement between estimated association and dissociation rate constants and in vitro values from literature.

Conclusion

This model includes both receptor binding kinetics and pharmacokinetics as the basis for the prediction of the D₂RO in rats. Moreover, this modeling framework can be applied to scale the in vitro and preclinical information to clinical receptor occupancy.

Preclinical prediction of human brain target site concentrations: considerations in extrapolating to the clinical setting

The development of drugs for central nervous system (CNS) disorders has encountered high failure rates. In part, this has been due to the sole focus on blood-brain barrier permeability of drugs, without taking into account all other processes that determine drug concentrations at the brain target site. This review deals with an overview of the processes that determine the drug distribution into and within the CNS, followed by a description of in vivo techniques that can be used to provide information on CNS drug distribution. A plea follows for the need for more mechanistic understanding of the mechanisms involved in brain target site distribution, and the condition-dependent contributions of these mechanisms to ultimate drug effect. As future direction, such can be achieved by performing integrative cross-compare designed studies, in which mechanisms are systematically influenced (e.g., inhibition of an efflux transporter or induction of pathological state). With the use of advanced mathematical modeling procedures, we may dissect contributions of individual mechanisms in animals as links to the human situation.

Endpoints in pediatric pain studies

Assessing pain intensity in (preverbal) children is more difficult than in adults. Tools to measure pain are being used as primary endpoints [e.g., pain intensity, time to first (rescue) analgesia, total analgesic consumption, adverse effects, and long-term effects] in studies on the effects of analgesic drugs. Here, we review current and promising new endpoints used in pediatric pain assessment studies.

Individualized dosing regimens in children based on population PKPD modelling: are we ready for it?

Despite profound differences in response between children and adults, and between children of different ages, drugs are still empirically dosed in mg/kg in children. Since maturation of expression and function is typically a non-linear dynamic process which differs between biotransformation routes and pharmacological targets, paediatric dosing regimens should be based on the changing pharmacokinetic-pharmacodynamic (PKPD) relationship in children. In this respect, the population approach is essential, allowing for sparse sampling in each individual child. An example is presented on morphine glucuronidation, for which two covariates were identified and subsequently used to derive a model-based dosing algorithm for a prospective clinical trial in children. Using this novel dosing algorithm, similar morphine concentrations are expected while, depending on age, lower and higher morphine dosages are administered compared to mg/kg/h dosing. As the covariate functions may reflect system-specific information on the maturation of a specific drug-disposition pathway, its use for other drugs that share the same pathway is explored. For this purpose, prospective clinical trials and cross-validation studies are urgently needed. In conclusion, PKPD modelling and simulation studies are important to develop evidence-based and individualized dosing schemes for children, with the ultimate goal to improve drug safety and efficacy in this population.

Pharmacometrics 2020

This special issue of the Journal of Clinical Pharmacology is dedicated to pharmacometrics, covering topics related to methodological research, application to decisions, standardization, PhRMA survey, and growth strategy. Innovative methodological and technological advances in analyzing disease, drug, and trial data have equipped pharmacometricians with the know-how to influence high-level decisions, which in turn creates more pharmacometric opportunities. Pharmacometrics is revolutionizing drug development and regulatory decision making. To sustain the success and growth of this field, we need to up the ante. Strategic goals for pharmacometric groups in industry, regulatory agencies, and academia are proposed in this report. These goals should be of significance to all stakeholders who have a vested interest in drug development and therapeutics. The future of pharmacometrics depends on how well we all can deliver on the strategic goals.

What it takes to understand and cure a living system: computational systems biology and a systems biology-driven pharmacokinetics-pharmacodynamics platform

The utility of model repositories is discussed in the context of systems biology (SB). It is shown how such repositories, and in particular their live versions, can be used for computational SB: we calculate the robustness of the yeast glycolytic network with respect to perturbations of one of its enzyme activities and one transport system. The robustness with respect to perturbations in the key enzyme phosphofructokinase is surprisingly large. We then note the upcoming convergence of pharmacokinetics-pharmacodynamics (PK-PD) and bottom-up SB. In PK alone, quite a few one-, two- or more compartment models provide valuable initial guesses and insights into the absorption, distribution, metabolism and excretion of particular drugs. These models are phenomenological however, forbidding implementation of molecule-based tools and network information. In order to facilitate a fruitful synergy between SB and PK-PD, and between PK and PD, we present a new platform that combines standard phenomenological models used in the PK/PD field with mechanism-based SB models and approaches.

Application of quantitative pharmacology in development of therapeutic monoclonal antibodies

The advancement of therapeutic monoclonal antibodies during various stages of the drug development process can be effectively streamlined when appropriate translational strategies are applied. Design of successful translational strategies for development of monoclonal antibodies should allow for understanding of the dose- and concentration-response relationships with respect to both beneficial and toxic effects from early phases of drug development. Evaluation of relevant biomarkers during early stages of drug development should facilitate the successful design of safe and effective dosing strategies. Moreover, application of quantitative pharmacology is critical for translation of exposure-response relationships early on.

Effect of altered AGP plasma binding on heart rate changes by S(-)-propranolol in rats using mechanism-based estimations of in vivo receptor affinity (K(B,vivo))

In contrast to the impact of plasma protein binding on pharmacokinetics, no quantitative in vivo information is available on its impact on pharmacodynamics. The pharmacokinetic-pharmacodynamic relationship of the model drug S(-)-propranolol was evaluated using mechanism-based estimations of in vivo receptor affinity (K(B,vivo)), under conditions of altered plasma protein binding resulting from different levels of alpha-1-acid glycoprotein (AGP). Male Wistar Kyoto rats with isoprenaline-induced tachycardia received an intravenous infusion of S(-)-propranolol, on postsurgery day 2 (n = 7) and day 7 (n = 8) with elevated and normal plasma protein binding, respectively. Serial blood samples were taken in parallel to heart rate measurements. AGP concentrations at 2 and 7 days postsurgery were 708 +/- 274 and 176 +/- 111 microg/mL (mean +/- SE), respectively. Using nonlinear mixed effects modeling, AGP concentration was a covariate for intercompartmental clearance for the third compartment of the pharmacokinetic model of S(-)-propranolol. Individual values of AGP concentrations ranged between 110 and 1150 microg/mL, and were associated with K(B,vivo) values of S(-)-propranolol from 7.0 to 30 nM. Using the K(B,vivo) for S(-)-propranolol with correction for average values for normal and elevated plasma protein binding, nearly identical values were found. This confirms, strictly quantitative, earlier indications that plasma protein binding restricts the pharmacodynamics of S(-)-propranolol.

The time course of drug effects

This review aims to introduce the concepts and principles underpinning the time course of drug effects. Models describing the time course of drug concentrations (pharmacokinetic models) and the ensuing concentration-effect (pharmacodynamics models) as well as the linked time-effect (pharmacokinetic-pharmacodynamic models) are introduced. Different types of drug time-effects models are discussed with examples which aim to explain the time course of onset, duration, and maximal effect that occurs from any given dosing schedule. These drug effects are also described in relation to disease progression models.

Pharmacokinetic-pharmacodynamic analysis of the static allodynia response to pregabalin and sildenafil in a rat model of neuropathic pain

The objective of this study was to develop a pharmacokinetic-pharmacodynamic (PK-PD) model of the static allodynia response to pregabalin with and without sildenafil in a chronic constriction injury model of neuropathic pain. Six treatment groups were evaluated every 30 min for 6 h. Rats were treated with either 1) a saline infusion; 2) a 2-h pregabalin infusion at 4 mgxkg(-1)xh(-1); 3) a 2-h pregabalin infusion at 10 mgxkg(-1)xh(-1); 4) a 2.2-mg loading dose + 12 mgxkg(-1)xmin(-1) infusion of sildenafil; 5) a 2-h pregabalin infusion at 1.6 mgxkg(-1)xh(-1) with sildenafil; and 6) a 2-h infusion of pregabalin at 4 mgxkg(-1)xh with sildenafil. The static allodynia endpoint was modeled by using three population PD approaches: 1) the behavior of the injured paw using a three-category ordinal logistic regression model; 2) paw withdrawal threshold (PWT) (g) between the injured and uninjured paw using the Hill equation with a baseline function; and 3) the baseline normalized difference in PWT between the injured and uninjured paw. The categorical model showed a significant shift in the concentration-response relationship of pregabalin to lower concentrations with concomitant sildenafil. Likewise, the continuous PK-PD models demonstrated a reduction in the EC(50) of pregabalin necessary for PD response in the presence of sildenafil. The difference-transformed PD model resulted in a 54.4% (42.3-66.9%) decrease in EC(50), whereas the percentage-transformed PD model demonstrated a 53.5% (42.7-64.3%) shift. It is concluded from these studies that there is a synergistic PD interaction between pregabalin and sildenafil.

Morphine glucuronidation in preterm neonates, infants and children younger than 3 years

BACKGROUND AND OBJECTIVE

A considerable amount of drug use in children is still unlicensed or off-label. In order to derive rational dosing schemes, the influence of aging on glucuronidation capacity in newborns, including preterms, infants and children under the age of 3 years was studied using morphine and its major metabolites as a model drug.

METHODS

A population pharmacokinetic model was developed with the nonlinear mixed-effects modelling software NONMEM V, on the basis of 2159 concentrations of morphine and its glucuronides from 248 infants receiving intravenous morphine ranging in bodyweight from 500 g to 18 kg (median 2.8 kg). The model was internally validated using normalized prediction distribution errors.

RESULTS

Formation clearances of morphine to its glucuronides and elimination clearances of the glucuronides were found to be primarily influenced by bodyweight, which was parameterized using an allometric equation with an estimated exponential scaling factor of 1.44. Additionally, a postnatal age of less than 10 days was identified as a covariate for formation clearance to the glucuronides, independent of birthweight or postmenstrual age. Distribution volumes scaled linearly with bodyweight.

CONCLUSIONS

Model-based simulations show that in newborns, including preterms, infants and children under the age of 3 years, a loading dose in microg/kg and a maintenance dose expressed in microg/kg1.5/h, with a 50% reduction of the maintenance dose in newborns younger than 10 days, results in a narrow range of morphine and metabolite serum concentrations throughout the studied age range. Future pharmacodynamic investigations are needed to reveal target concentrations in this population, after which final dosing recommendations can be made.

Pharmacokinetic/pharmacodynamic modeling of biomarker response to sunitinib in healthy volunteers

A pharmacokinetic/pharmacodynamic (PK/PD) study of the tyrosine kinase inhibitor sunitinib was conducted in 12 healthy volunteers using blood pressure and circulating biomarker levels as PD markers. Blood pressure was measured, and plasma concentration-time courses of sunitinib, its major metabolite SU12662, vascular endothelial growth factors VEGF-A and VEGF-C, and soluble VEGF receptor-2 (sVEGFR-2) were studied in healthy subjects receiving 50 mg of sunitinib orally for 3-5 consecutive days. Using NONMEM, PK/PD models were established that predicted changes (expressed as multiples relative to baseline values) in systolic blood pressure, diastolic blood pressure, VEGF-A level, and sVEGFR-2 level, of 1.10, 1.18, 2.24, and 0.76, respectively, for a typical subject after 4 weeks of treatment with 50 mg/day. Simulated blood pressure-time courses compare excellently with published data in patients, whereas changes in circulating biomarkers were greater in patients than simulations suggest for healthy subjects. In conclusion, the tumor-independent pharmacological response to sunitinib could be described by PK/PD models, thereby facilitating model-based investigations with antiangiogenic drugs, using blood pressure and circulating proteins as biomarkers.

Basic PK/PD principles of drug effects in circular/proliferative systems for disease modelling

Disease progression modelling can provide information about the time course and outcome of pharmacological intervention on the disease. The basic PK/PD principles of proliferative and circular systems within the context of modelling disease progression and the effect of treatment thereupon are illustrated with the goal to better understand/predict eventual clinical outcome. Circular/proliferative systems can be very complex. To facilitate the understanding of how a dosing regimen can be defined in such systems we have shown the derivation of a system parameter named the Reproduction Minimum Inhibitory Concentration (RMIC) which represents the critical concentration at which the system switches from growth to extinction. The RMIC depends on two parameters (RMIC = (R₀ − 1) × IC₅₀): the basic reproductive ratio (R₀) a fundamental parameter of the circular/proliferative system that represents the number of offspring produced by one replicating species during its lifespan, and the IC₅₀, the potency of the drug to inhibit the proliferation of the system. The RMIC is constant for a given system and a given drug and represents the lowest concentration that needs to be achieved for eradication of the system. When exposure is higher than the RMIC, success can be expected in the long term. Time varying inhibition of replicating species proliferation is a natural consequence of the time varying inhibitor drug concentrations and when combined with the dynamics of the circular/proliferative system makes it difficult to predict the eventual outcome. Time varying inhibition of proliferative/circular systems can be handled by calculating the equivalent effective constant concentration (ECC), the constant plasma concentration that would give rise to the average inhibition at steady state. When ECC is higher than the RMIC, eradication of the system can be expected. In addition, it is shown that scenarios that have the same steady state ECC whatever the dose, dosage schedule or PK parameters have also the same average R₀ in the presence of the inhibitor (i.e. R_0-INH) and therefore lead to the same outcome. This allows predicting equivalent active doses and dosing schedules in circular and proliferative systems when the IC₅₀ and pharmacokinetic characteristics of the drugs are known. The results from the simulations performed demonstrate that, for a given system (defined by its RMIC), treatment success depends mainly on the pharmacokinetic characteristics of the drug and the dosing schedule.

Influence of plasma protein binding on pharmacodynamics: Estimation of in vivo receptor affinities of beta blockers using a new mechanism-based PK-PD modelling approach

The objective of this investigation was to examine in a systematic manner the influence of plasma protein binding on in vivo pharmacodynamics. Comparative pharmacokinetic-pharmacodynamic studies with four beta blockers were performed in conscious rats, using heart rate under isoprenaline-induced tachycardia as a pharmacodynamic endpoint. A recently proposed mechanism-based agonist-antagonist interaction model was used to obtain in vivo estimates of receptor affinities (K(B,vivo)). These values were compared with in vitro affinities (K(B,vitro)) on the basis of both total and free drug concentrations. For the total drug concentrations, the K(B,vivo) estimates were 26, 13, 6.5 and 0.89 nM for S(-)-atenolol, S(-)-propranolol, S(-)-metoprolol and timolol. The K(B,vivo) estimates on the basis of the free concentrations were 25, 2.0, 5.2 and 0.56 nM, respectively. The K(B,vivo)-K(B,vitro) correlation for total drug concentrations clearly deviated from the line of identity, especially for the most highly bound drug S(-)-propranolol (ratio K(B,vivo)/K(B,vitro) approximately 6.8). For the free drug, the correlation approximated the line of identity. Using this model, for beta-blockers the free plasma concentration appears to be the best predictor of in vivo pharmacodynamics.

Comparison of methods for evaluating drug-drug interaction

The goal of the present report is to compare several published methods of analyzing drug-drug interaction data. The compared methods are the curve-shift analysis, isobologram, combination index, and universal surface response analysis, and the comparison was based on analysis of published cytotoxicity data of combinations of two anti-folate agents. Major findings are as follows. The curve shift analysis enabled the inspection of the experimental data and visual evaluation of the approximate parallelism between the dose response curves. Isobologram analysis provided the range of concentration ratios where maximal synergy was obtained. The combination index analysis readily provided quantitative estimation of the extent of synergy or antagonism. The universal surface response method summarized drug-drug interaction in a single parameter, facilitating comparison of larger arrays of combinations. Only the curve shift analysis and the universal surface response method yielded a statistical estimate of differentiation between synergy, additivity, and antagonism. In summary, curve shift analysis, isobolograms, combination index analysis, and the universal response surface method are useful methods for analyzing drug-drug interaction, and provide complementary information.