Interchangeability and predictive performance of empirical tolerance models

Physiological Indirect Response Model to Omics-Powered Quantitative Systems Pharmacology Model

Over the past several decades, mathematical modeling has been applied to increasingly wider scopes of questions in drug development. Accordingly, the range of modeling tools has also been evolving, as showcased by contributions of Jusko and colleagues: from basic pharmacokinetics/pharmacodynamics (PK/PD) modeling to today's platform-based approach of quantitative systems pharmacology (QSP) modeling. Aimed at understanding the mechanism of action of investigational drugs, QSP models characterize systemic effects by incorporating information about cellular signaling networks, which is often represented by omics data. In this perspective, we share a few examples illustrating approaches for the integration of omics into mechanistic QSP modeling. We briefly overview how the evolution of PK/PD modeling into QSP has been accompanied by an increase in available data and the complexity of mathematical methods that integrate it. We discuss current gaps and challenges of integrating omics data into QSP models and propose several potential areas where integrated QSP and omics modeling may benefit drug development.

A non-linear mixed effect model for innate immune response: In vivo kinetics of endotoxin and its induction of the cytokines tumor necrosis factor alpha and interleukin-6

Endotoxin, a component of the outer membrane of Gram-negative bacteria, has been extensively studied as a stimulator of the innate immune response. However, the temporal aspects and exposure-response relationship of endotoxin and resulting cytokine induction and tolerance development is less well defined. The aim of this work was to establish an in silico model that simultaneously captures and connects the in vivo time-courses of endotoxin, tumor necrosis factor alpha (TNF-α), interleukin-6 (IL-6), and associated tolerance development. Data from six studies of porcine endotoxemia in anesthetized piglets (n = 116) were combined and used in the analysis, with purified endotoxin (Escherichia coli O111:B4) being infused intravenously for 1–30 h in rates of 0.063–16.0 μg/kg/h across studies. All data were modelled simultaneously by means of importance sampling in the non-linear mixed effects modelling software NONMEM. The infused endotoxin followed one-compartment disposition and non-linear elimination, and stimulated the production of TNF-α to describe the rapid increase in plasma concentration. Tolerance development, observed as declining TNF-α concentration with continued infusion of endotoxin, was also driven by endotoxin as a concentration-dependent increase in the potency parameter related to TNF-α production (EC₅₀). Production of IL-6 was stimulated by both endotoxin and TNF-α, and four consecutive transit compartments described delayed increase in plasma IL-6. A model which simultaneously account for the time-courses of endotoxin and two immune response markers, the cytokines TNF-α and IL-6, as well as the development of endotoxin tolerance, was successfully established. This model-based approach is unique in its description of the time-courses and their interrelation and may be applied within research on immune response to bacterial endotoxin, or in pre-clinical pharmaceutical research when dealing with study design or translational aspects.

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.

Effects of the TRPV1 antagonist ABT-102 on body temperature in healthy volunteers: pharmacokinetic/ pharmacodynamic analysis of three phase 1 trials

AIM

To characterize quantitatively the relationship between ABT-102, a potent and selective TRPV1 antagonist, exposure and its effects on body temperature in humans using a population pharmacokinetic/pharmacodynamic modelling approach.

METHODS

Serial pharmacokinetic and body temperature (oral or core) measurements from three double-blind, randomized, placebo-controlled studies [single dose (2, 6, 18, 30 and 40 mg, solution formulation), multiple dose (2, 4 and 8 mg twice daily for 7 days, solution formulation) and multiple-dose (1, 2 and 4 mg twice daily for 7 days, solid dispersion formulation)] were analyzed. NONMEM was used for model development and the model building steps were guided by pre-specified diagnostic and statistical criteria. The final model was qualified using non-parametric bootstrap and visual predictive check.

RESULTS

The developed body temperature model included additive components of baseline, circadian rhythm (cosine function of time) and ABT-102 effect (Emax function of plasma concentration) with tolerance development (decrease in ABT-102 Emax over time). Type of body temperature measurement (oral vs. core) was included as a fixed effect on baseline, amplitude of circadian rhythm and residual error. The model estimates (95% bootstrap confidence interval) were: baseline oral body temperature, 36.3 (36.3, 36.4)°C; baseline core body temperature, 37.0 (37.0, 37.1)°C; oral circadian amplitude, 0.25 (0.22, 0.28)°C; core circadian amplitude, 0.31 (0.28, 0.34)°C; circadian phase shift, 7.6 (7.3, 7.9) h; ABT-102 Emax , 2.2 (1.9, 2.7)°C; ABT-102 EC50 , 20 (15, 28) ng ml(-1) ; tolerance T50 , 28 (20, 43) h.

CONCLUSIONS

At exposures predicted to exert analgesic activity in humans, the effect of ABT-102 on body temperature is estimated to be 0.6 to 0.8°C. This effect attenuates within 2 to 3 days of dosing.

Phase I studies of sirolimus alone or in combination with pharmacokinetic modulators in advanced cancer patients

PURPOSE

Sirolimus is the eponymous inhibitor of the mTOR; however, only its analogs have been approved as cancer therapies. Nevertheless, sirolimus is readily available, has been well studied in organ transplant patients, and shows efficacy in several preclinical cancer models.

EXPERIMENTAL DESIGN

Three simultaneously conducted phase I studies in advanced cancer patients used an adaptive escalation design to find the dose of oral, weekly sirolimus alone or in combination with either ketoconazole or grapefruit juice that achieves similar blood concentrations as its intravenously administered and approved prodrug, temsirolimus. In addition, the effect of sirolimus on inhibition of p70S6 kinase phosphorylation in peripheral T cells was determined.

RESULTS

Collectively, the three studies enrolled 138 subjects. The most commonly observed toxicities were hyperglycemia, hyperlipidemia, and lymphopenia in 52%, 43%, and 41% of subjects, respectively. The target sirolimus area under the concentration curve (AUC) of 3,810 ng-h/mL was achieved at sirolimus doses of 90, 16, and 25 mg in the sirolimus alone, sirolimus plus ketoconazole, and sirolimus plus grapefruit juice studies, respectively. Ketoconazole and grapefruit juice increased sirolimus AUC approximately 500% and 350%, respectively. Inhibition of p70 S6 kinase phosphorylation was observed at all doses of sirolimus and correlated with blood concentrations. One partial response was observed in a patient with epithelioid hemangioendothelioma.

CONCLUSION

Sirolimus can be feasibly administered orally, once weekly with a similar toxicity and pharmacokinetic profile compared with other mTOR inhibitors and warrants further evaluation in studies of its comparative effectiveness relative to recently approved sirolimus analogs.

Comparison of two pharmacodynamic transduction models for the analysis of tumor therapeutic responses in model systems

Semi-mechanistic pharmacodynamic (PD) models that capture tumor responses to anticancer agents with fidelity can provide valuable insights that could aid in the optimization of dosing regimens and the development of drug delivery strategies. This study evaluated the utility and potential interchangeability of two transduction-type PD models: a cell distribution model (CDM) and a signal distribution model (SDM). The evaluation was performed by simulating dense and sparse tumor response data with one model and analyzing it using the other. Performance was scored by visual inspection and precision of parameter estimation. Capture of tumor response data was also evaluated for a liposomal formulation of paclitaxel in the paclitaxel-resistant murine Colon-26 model. A suitable PK model was developed by simultaneous fitting of literature data for paclitaxel formulations in mice. Analysis of the simulated tumor response data revealed that the SDM was more flexible in describing delayed drug effects upon tumor volume progression. Dense and sparse data simulated using the CDM were fit very well by the SDM, but under some conditions, data simulated using the SDM were fitted poorly by the CDM. Although both models described the dose-dependent therapeutic responses of Colon-26 tumors, the fit by the SDM contained less bias. The CDM and SDM are both useful transduction models that recapitulate, with fidelity, delayed drug effects upon tumor growth. However, they are mechanistically distinct and not interchangeable. Both fit some types of tumor growth data well, but the SDM appeared more robust, particularly where experimental data are sparse.

Incorporating physiological and biochemical mechanisms into pharmacokinetic-pharmacodynamic models: a conceptual framework

The aim of this conceptual framework paper is to contribute to the further development of the modelling of effects of drugs or toxic agents by an approach which is based on the underlying physiology and pathology of the biological processes. In general, modelling of data has the purpose (1) to describe experimental data, (2a) to reduce the amount of data resulting from an experiment, e.g. a clinical trial and (2b) to obtain the most relevant parameters, (3) to test hypotheses and (4) to make predictions within the boundaries of experimental conditions, e.g. range of doses tested (interpolation) and out of the boundaries of the experimental conditions, e.g. to extrapolate from animal data to the situation in man. Describing the drug/xenobiotic-target interaction and the chain of biological events following the interaction is the first step to build a biologically based model. This is an approach to represent the underlying biological mechanisms in qualitative and also quantitative terms, thus being inherently connected in many aspects to systems biology. As the systems biology models may contain variables in the order of hundreds connected with differential equations, it is obvious that it is in most cases not possible to assign values to the variables resulting from experimental data. Reduction techniques may be used to create a manageable model which, however, captures the biologically meaningful events in qualitative and quantitative terms. Until now, some success has been obtained by applying empirical pharmacokinetic/pharmacodynamic models which describe direct and indirect relationships between the xenobiotic molecule and the effect, including tolerance. Some of the models may have physiological components built in the structure of the model and use parameter estimates from published data. In recent years, some progress toward semi-mechanistic models has been made, examples being chemotherapy-induced myelosuppression and glucose-endogenous insulin-antidiabetic drug interactions. We see a way forward by employing approaches to bridge the gap between systems biology and physiologically based kinetic and dynamic models. To be useful for decision making, the 'bridging' model should have a well founded mechanistic basis, but being reduced to the extent that its parameters can be deduced from experimental data, however capturing the biological/clinical essential details so that meaningful predictions and extrapolations can be made.

Opioid tolerance development: a pharmacokinetic/pharmacodynamic perspective

The opioids are commonly used to treat acute and severe pain. Long-term opioid administration eventually reaches a dose ceiling that is attributable to the rapid onset of analgesic tolerance coupled with the slow development of tolerance to the untoward side effects of respiratory depression, nausea and decreased gastrointestinal motility. The need for effective-long term analgesia remains. In order to develop new therapeutics and novel strategies for use of current analgesics, the processes that mediate tolerance must be understood. This review highlights potential pharmacokinetic (changes in metabolite production, metabolizing enzyme expression, and transporter function) and pharmacodynamic (receptor type, location and functionality; alterations in signaling pathways and cross-tolerance) aspects of opioid tolerance development, and presents several pharmacodynamic modeling strategies that have been used to characterize time-dependent attenuation of opioid analgesia.

Multiple-pool cell lifespan models for neutropenia to assess the population pharmacodynamics of unbound paclitaxel from two formulations in cancer patients

PURPOSE

Our objective was to build a mechanism-based pharmacodynamic model for the time course of neutropenia in cancer patients following paclitaxel treatment with a tocopherol-based Cremophor-free formulation (Tocosol Paclitaxel) and Cremophor EL-formulated paclitaxel (Taxol).

METHODS

A randomized two-way crossover trial was performed with 35 adult patients who received 175 mg/m(2) paclitaxel as either 15 min (Tocosol Paclitaxel) or 3 h (Taxol) intravenous infusions. Paclitaxel concentrations were measured by LC-MS/MS. NONMEM VI was used for population pharmacodynamics.

RESULTS

The cytotoxic effect on neutrophils was described by four mechanism-based models predicated on known properties of paclitaxel that used unbound concentrations in the central, deep peripheral or an intracellular compartment as forcing functions. Tocosol Paclitaxel was estimated to release 9.8% of the dose directly into the deep peripheral compartment (DPC). All models provided reasonable fitting of neutropenic effects. The model with the best predictive performance assumed that this dose fraction was released into 22.5% of the DPC which included the site of toxicity. The second-order cytotoxic rate constant was 0.00211 mL/ng per hour (variability: 52% CV). The relative exposure at the site of toxicity was 2.21 +/- 0.41 times (average +/- SD) larger for Tocosol Paclitaxel compared to Taxol. Lifespan was 11.0 days for progenitor cells, 1.95 days for maturating cells, and 4.38 days for neutrophils. Total drug exposure in blood explained half of the variance in nadir to baseline neutrophil count ratio.

CONCLUSIONS

The relative exposure of unbound paclitaxel at the site of toxicity was twice as large for Tocosol Paclitaxel compared to Taxol. The proposed mechanism-based models explained the extent and time course of neutropenia jointly for both formulations.

Modeling Cardiac Uptake and Negative Inotropic Response of Verapamil in Rat Heart: Effect of Amiodarone

PURPOSE

To determine the effect of the P-glycoprotein (Pgp) modulator amiodarone on the pharmacokinetics and pharmacodynamics (PK/PD) of Pgp substrate verapamil in the perfused rat heart.

METHODS

In Langendorff-perfused rat hearts, the outflow concentration-time curve and inotropic response data were measured after a 1.5 nmol dose of [3H]-verapamil (infused within 1 min) in the absence and presence of the amiodarone (1 microM) in perfusate, as well as using a double dosing regimen (0.75 nmol in a 10 min interval). These data were analyzed by a PK/PD model.

RESULTS

Amiodarone failed to influence the rapid uptake and equilibrium partitioning of verapamil into the heart. The time course of the negative inotropic effect of verapamil, including the 'rebound' above the original baseline after the infusion of verapamil was stopped, could be described by a PK/PD tolerance model. Tolerance development (mean delay time, 12 min) led to a reduction in predicted steady-state effect (16%). The EC50 and Emax values as estimated in single dose experiments were 16.4+/-4.1 nM and 50.5+/-18.9 mmHg, respectively.

CONCLUSIONS

The result does not support the hypothesis that Pgp inhibition by amiodarone increases cardiac uptake of the Pgp substrate verapamil.

Dealing with time-dependent pharmacokinetics during the early clinical development of a new leukotriene B4 synthesis inhibitor

PURPOSE

The aim of this study was to explore the possibility of achieving a practical dosing regimen for 2,4,6-triiodophenol (AM-24), a new leukotriene B4 (LTB4) synthesis inhibitor. First, a model capable of dealing with the nonlinearity in its pharmacokinetic profile was built, and then it was combined with a pharmacodynamic model previously established with data from earlier phase I trials.

METHODS

One week after the first 240-, 350-, or 500-mg oral dose of AM-24, six additional doses were given to 24 healthy volunteers once daily. A total of 33 blood samples were obtained from each individual. Different models, including enzyme turnover models, were fitted to the data by using the software NONMEM.

RESULTS

Drug absorption was modeled with a first-order process. Drug disposition was described with a one-compartment model, and elimination with an (auto)inhibited and a noninhibited clearance. AM-24 inhibited the enzyme production rate to a maximum of 98%. Relative bioavailability was independent of the decrease in the amount of enzyme. The estimate of the enzyme turnover half-life was 8.5 h.

CONCLUSIONS

Simulations have shown that steady-state conditions eliciting 90% of maximal LTB4 synthesis inhibition can be reached after 3 weeks during an oral treatment with AM-24 administered at the dosage of 500 mg once daily.

Assessment of Basic Indirect Pharmacodynamic Response Models with Physiological Limits

Many physiological factors are regulated by homeostatic mechanisms to maintain normal body function. Empirical lower Rl (Model I and IV) or upper Rh limits (Model II and III) were included in current basic indirect response (IDR) models to account for the additional role of physiological limits (IDRPL). Various characteristics of these models were evaluated with simulations and explicit equations. The simulations reveal that the expanded models exhibit most properties of basic indirect response models, such as slow response initiation, lag time between the kinetic and dynamic peaks, a large dose plateau, and shift in Tmax with dose. The proposed models always produce lesser net responses than predicted by basic IDR models. Simulations demonstrate that addition of a parameter limit which is close to the baseline has a great influence on the overall and maximum responses and fitted model parameters. Only stimulatory IDRPL Models III and IV allow resolution of all model parameters in the absence of clear indications or predetermined values of the lower or upper limits. However, all four models are able to resolve model parameters when subgroups with different baselines are simultaneously fitted. These models create new interpretations of the determinants of baseline conditions which can be important in assessing inter-subject variability in responses. The applicability of IDRPL models is demonstrated using several examples from the published literature. Indirect response models with physiological limits will be useful in characterizing drug responses for turnover systems which are maintained within a certain range.

Modeling drug- and system-related changes in body temperature: application to clomethiazole-induced hypothermia, long-lasting tolerance development, and circadian rhythm in rats

The aim of the present investigation was to develop a pharmacokinetic-pharmacodynamic model for the characterization of clomethiazole (CMZ)-induced hypothermia and the rapid development of long-lasting tolerance in rats while taking into account circadian rhythm in baseline and the influence of handling. CMZ-induced hypothermia and tolerance was measured using body temperature telemetry in male Sprague-Dawley rats, which were given s.c. bolus injections of 0, 15, 150, 300, and 600 micromol kg(-1) and 24-h s.c. continuous infusions of 0, 20, and 40 micromol kg(-1) h(-1) using osmotic pumps. The duration of tolerance was studied by repeated injections of 300 micromol kg(-1) at 3- to 32-day intervals. Plasma exposure to CMZ was obtained in satellite groups of catheterized rats. Fitted population concentration-time profiles served as input for the pharmacodynamic analysis. The asymmetric circadian rhythm in baseline body temperature was successfully described by a novel negative feedback model incorporating external light-dark conditions. An empirical function characterized the transient increase in temperature upon handling of the animal. A feedback model for temperature regulation and tolerance development allowed estimation of CMZ potency at 30 +/- 1 microM. The delay in onset of tolerance was estimated via a series of four transit compartments at 7.6 +/- 2 h. The long-lasting tolerance was assumed to be caused by inactivation of a mediator with an estimated turnover time of 46 +/- 3 days. This multicomponent turnover model was able to quantify the CMZ-induced hypothermia, circadian rhythm in baseline, and rapid onset of a long-lasting tolerance to CMZ in rats.

Modelling a spontaneously reported side effect by use of a Markov mixed-effects model

AIMS

To present a method for analyzing side-effect data where change in severity is spontaneously reported during the experiment.

METHODS

A clinical study in 12 healthy volunteers aimed to investigate the concentration-response characteristics of a CNS-specific side-effect was conducted. After an open session where the subjects experienced the side-effect and where the individual pharmacokinetic parameters were evaluated they were randomized to a sequence of three different infusion rates of the drug in a double-blinded crossover way. The infusion rates were individualized to achieve the same target concentration in all subjects and different drug input rates were selected to mimic absorption profiles from different formulations. The occurrence of the specific side-effect and any subsequent change in severity was self-reported by the subjects. Severity was recorded as 0 = no side-effect, 1 = mild side-effect and 2 = moderate or severe side-effect.

RESULTS

The side-effect data were analyzed using a mixed-effects model for ordered categorical data with and without Markov elements. The former model estimated the probability of having a certain side-effect score conditioned on the preceding observation and drug exposure. The observed numbers of transitions between scores were from 0 -> 1: 24, from 0- > 2: 11, from 1 - >, 2: 23, from 2- > 1: 1, from 2- > 0: 32 and from 1 - >0: 2. The side-effect model consisted of an effect-compartment model with a tolerance compartment. The predictive performance of the Markov model was investigated by a posterior predictive check (PPC), where 100 datasets were simulated from the final model. Average number of the different transitions from the PPC was from 0 - > 1: 26, from 0 - > 2: 11, from 1 - > 2: 25, from 2 - >1: 1, from 2 - >0: 35 and from 1 - > 0: 1. A similar PPC for the model without Markov elements was at considerable disparity with the data.

CONCLUSION

This approach of incorporating Markov elements in an analysis of spontaneously reported categorical side-effect data could adequately predict the observed side-effect time course and could be considered in analyses of categorical data where dependence between observations is an issue.

Pharmacokinetic/Pharmacodynamic Modellingof GnRH Antagonist Degarelix: A Comparisonof the Non-linear Mixed-Effects Programs NONMEM and NLME

In this paper, the two non-linear mixed-effects programs NONMEM and NLME were compared for their use in population pharmacokinetic/pharmacodynamic (PK/PD) modelling. We have described the first-order conditional estimation (FOCE) method as implemented in NONMEM and the alternating algorithm in NLME proposed by Lindstrom and Bates. The two programs were tested using clinical PK/PD data of a new gonadotropin-releasing hormone (GnRH) antagonist degarelix currently being developed for prostate cancer treatment. The pharmacokinetics of intravenous administered degarelix was analysed using a three compartment model while the pharmacodynamics was analysed using a turnover model with a pool compartment. The results indicated that the two algorithms produce consistent parameter estimates. The bias and precision of the two algorithms were further investigated using a parametric bootstrap procedure which showed that NONMEM produced more accurate results than NLME together with the nlmeODE package for this specific study.

Modelling acute tolerance to the EEG effect of two benzodiazepines

AIMS

We studied the development of acute tolerance to the EEG effect of midazolam and the new benzodiazepine Ro 48-6791.

METHODS

Nine young (24-28 years) and nine elderly (67-81 years) male volunteers received midazolam and Ro 48-6791 computer-controlled, targeting linearly increasing plasma concentrations for 30 min (targeted slopes: 40 and 20 ng ml-1 min-1 for midazolam, 3 and 1.5 ng ml-1 min-1 for Ro 48-6791, for young and elderly, respectively) and a constant concentration for the following 15 min. After recovery, the same infusion scheme was repeated. Plasma concentrations of midazolam, Ro 48-6791 and its metabolite Ro 48-6792 were determined from arterial blood samples. The hypnotic effect was assessed using the median frequency of the EEG power spectrum.

RESULTS

The concentration-effect relationship in each infusion cycle could be described by a sigmoid Emax model. The half-maximum concentration EC50 was higher in the second infusion cycle compared with the first one (midazolam, 47% (2.3-91.6%) and 37% (5.3-69.5%); Ro 48-6791, 22% (-2.8% to 44.6%) and 43% (3.4-82.4%) for young and elderly; mean and 95% confidence interval). The complete time course of the EEG median frequency could be described by an interaction between the parent drug in an effect compartment and a hypothetical competitive drug in an additional tolerance compartment. For Ro 48-6791, the use of its metabolite Ro 48-6792 as competitive compound also gave appropriate results.

CONCLUSION

Midzolam and Ro 48-6791 showed acute tolerance to the EEG effect which might be caused by competitive interaction with the metabolite.

Pharmacokinetic/pharmacodynamic modeling of the antinociceptive effects of (+)-tramadol in the rat: role of cytochrome P450 2D activity

In this study the role of cytochrome P450 2D (CYP2D) in the pharmacokinetic/pharmacodynamic relationship of (+)-tramadol [(+)-T] has been explored in rats. Male Wistar rats were infused with (+)-T in the absence of and during pretreatment with a reversible CYP2D inhibitor quinine (Q), determining plasma concentrations of Q, (+)-T, and (+)-O-demethyltramadol [(+)-M1], and measuring antinociception. Pharmacokinetics of (+)-M1, but not (+)-T, was affected by Q pretreatment: early after the start of (+)-T infusion, levels of (+)-M1 were significantly lower (P < 0.05). However, at later times during Q infusion those levels increased continuously, exceeding the values found in animals that did not receive the inhibitor. These results suggest that CYP2D is involved in the formation and elimination of (+)-M1. In fact, results from another experiment where (+)-M1 was given in the presence and in absence of Q showed that (+)-M1 elimination clearance (CL(ME0)) was significantly lower (P < 0.05) in animals receiving Q. Inhibition of both (+)-M1 formation clearance (CL(M10)) and CL(ME0) were modeled by an inhibitory E(MAX) model, and the estimates (relative standard error) of the maximum degree of inhibition (E(MAX)) and IC(50), plasma concentration of Q eliciting half of E(MAX) for CL(M10) and CL(ME0), were 0.94 (0.04), 97 (0.51) ng/ml, and 48 (0.42) ng/ml, respectively. The modeling of the time course of antinociception showed that the contribution of (+)-T was negligible and (+)-M1 was responsible for the observed effects, which depend linearly on (+)-M1 effect site concentrations. Therefore, the CYP2D activity is a major determinant of the antinociception elicited after (+)-T administration.

Diversity of mechanism-based pharmacodynamic models

Pharmacodynamics is the study of the time course of pharmacological effects of drugs. The field of pharmacodynamic modeling has made many advances, due in part to the relatively recent development of basic and extended mechanism-based models. The purpose of this article is to describe the classic as well as contemporary approaches, with an emphasis on pertinent equations and salient model features. In addition, current methods of integrating various system complexities into these models are discussed. Future pharmacodynamic models will most likely reflect an assembly of the basic components outlined in this review.

Influence of arterial vs. venous sampling site on nicotine tolerance model selection and parameter estimation

In this modeling study we utilize previously published nicotine pharmacokinetic (PK) and pharmacodynamic (PD, heart rate) data to investigate the influence of PK sampling site (venous vs. arterial) on the selection of a specific PD tolerance model and estimation of its parameters. We describe a general model for tolerance which includes as special cases feedback (TF), and kinetic based tolerance (TK) models. A TK model has arterial plasma drug concentrations (Ca) driving (hypothetical) effect (Ce) and antagonist (Cm) site concentrations, which drive a non-feedback effect (Enf): tolerance depends on the relative rate of equilibration of Ce and Cm with Ca. The TF model adds feedback which makes tolerance depend on Enf, not just on drug kinetics for nicotine. The arterial-sampling-analysis (PKPDa) has Ca driving Ce and Cm. The venous-sampling-analysis (PKPDv) does the same but estimates Ca from venous data by means of deconvolution. A TF model (with Cm = Ce) was always selected in the PKPDa. According to this model tolerance developed rapidly with a median half-life of 6.6 min, and median decrease of effect due to tolerance of 31%. Different variants of the TF or TK models were selected in the PKPDv. Parameter estimates for PKPDv show higher variability, and, for the TF model, lower rate and extent of tolerance development and threefold increase in EC50. The study shows that (i) TF models are more appropriate than TK models to describe nicotine effect data, (ii) venous sampling may lead to incorrect model selection and inaccurate and imprecise parameter estimation in respect to arterial sampling, and (iii) arterial sampling should be preferred for accurate (non-steady-state) PD modeling.

Considerations on pharmacodynamics and pharmacokinetics: Can everything be explained by the extent of drug binding to its receptor?

It is frequently assumed that pharmacological responses depend solely on the extent of drug binding to its receptor according to the occupational theory. It is therefore presumed that the intensity of the effect is determined by drug concentration at its receptor site, yielding a unique concentration-effect relationship. However, when dependence, abstinence, and tolerance phenomena occur, as well as for pharmacological responses in vivo that are modulated by homeostatic mechanisms, the rate of drug input shifts the concentration-effect relationship. Hence, such responses cannot be explained on the sole basis of the extent of drug binding to its receptor. Information on the cellular and molecular processes involved in the generation of abstinence, dependence, and tolerance will undoubtedly result in the development of pharmacodynamic models allowing a satisfactory explanation of drug effects modulated by these phenomena. Notwithstanding, integrative physiology concepts are required to develop pharmacokinetic-pharmacodynamic models allowing the description of drug effects in an intact organism. It is therefore important to emphasize that integrative physiology cannot be neglected in pharmacology teaching and research, but should be considered as an equally valuable tool as molecular biology and other biomedical disciplines for the understanding of pharmacological effects.Key words: pharmacodynamics, pharmacokinetics, drug-receptor binding, occupational theory.