A Pharmacodynamic Turnover Model Capturing Asymmetric Circadian Baselines of Body Temperature, Heart Rate and Blood Pressure in Rats: Challenges in Terms of Tolerance and Animal-handling Effects

Mathematical modeling of mammalian circadian clocks affecting drug and disease responses

To align with daily environmental changes, most physiological processes in mammals exhibit a time-of-day rhythmicity. This circadian control of physiology is intrinsically driven by a cell-autonomous clock gene network present in almost all cells of the body that drives rhythmic expression of genes that regulate numerous molecular and cellular processes. Accordingly, many aspects of pharmacology and toxicology also oscillate in a time-of-day manner giving rise to diverse effects on pharmacokinetics and pharmacodynamics. Genome-wide studies and mathematical modeling are available tools that have significantly improved our understanding of these nonlinear aspects of physiology and therapeutics. In this manuscript current literature and our prior work on the model-based approaches that have been used to explore circadian genomic systems of mammals are reviewed. Such basic understanding and having an integrative approach may provide new strategies for chronotherapeutic drug treatments and yield new insights for the restoration of the circadian system when altered by diseases.

Characterization of circadian blood pressure patterns using non-linear mixed effects modeling

Characterizing the time course of baseline or pre-drug blood pressure is important in acquiring unbiased estimates of antihypertensive drug effect. In this study, we recruited 23 healthy male volunteers and measured systolic (SBP) and diastolic blood pressure (DBP) over 24 hours on an hourly basis. Using a non-linear mixed effects model, circadian rhythm observed in blood pressure measurements was described by incorporating two cosine functions with periods 24 and 12 hours. A mixture model was applied to identify subgroups exhibiting qualitatively different circadian rhythms. Our results suggested that 78% of the study population, defined as ‘dippers’, demonstrated a typical circadian profile with a morning rise and a nocturnal dip. The remaining 22% of the subjects defined as ‘non-dippers’, however, were not adequately described using the typical profile and demonstrated an elevation of blood pressure during night-time. Covariate search identified weight as being positively correlated with mesor of SBP. Visual predictive checks using 1,000 simulated datasets were performed for model validation. Observations were in agreement with predicted values in ‘dippers’, but deviated slightly in ‘non-dippers’. Our work is expected to serve as a useful reference in assessing systematic intra-day blood pressure fluctuations and antihypertensive effects as well as assessing drug safety of incrementally modified drugs.

Application of the relationship between pharmacokinetics and pharmacodynamics in drug development and therapeutic equivalence: a PEARRL review

Objectives

The objective of this review was to provide an overview of pharmacokinetic/pharmacodynamic (PK/PD) models, focusing on drug-specific PK/PD models and highlighting their value added in drug development and regulatory decision-making.

Key findings

Many PK/PD models, with varying degrees of complexity and physiological understanding have been developed to evaluate the safety and efficacy of drug products. In special populations (e.g. paediatrics), in cases where there is genetic polymorphism and in other instances where therapeutic outcomes are not well described solely by PK metrics, the implementation of PK/PD models is crucial to assure the desired clinical outcome. Since dissociation between the pharmacokinetic and pharmacodynamic profiles is often observed, it is proposed that physiologically based pharmacokinetic and PK/PD models be given more weight by regulatory authorities when assessing the therapeutic equivalence of drug products.

Summary

Modelling and simulation approaches already play an important role in drug development. While slowly moving away from ‘one-size fits all’ PK methodologies to assess therapeutic outcomes, further work is required to increase confidence in PK/PD models in translatability and prediction of various clinical scenarios to encourage more widespread implementation in regulatory decision-making.

Guiding dose adjustment of amlodipine after co-administration with ritonavir containing regimens using a physiologically-based pharmacokinetic/pharmacodynamic model

Amlodipine, a commonly prescribed anti-hypertensive drug, shows increased systemic exposure with cytochrome P450 (CYP) 3A inhibitors. Ritonavir (RTV) is a potent mechanism-based and reversible CYP3A inhibitor and moderate inducer that is used as a pharmacokinetic enhancer in several antiviral treatment regimens. Drug-drug interaction (DDI) between RTV and amlodipine is due to mixed inhibition and induction of CYP3A4, which is challenging to predict without a mechanistic model that accounts for the complexity of both mechanisms occurring simultaneously. A novel physiologically-based pharmacokinetic (PBPK) model was developed for amlodipine, and the model was verified using published clinical PK and DDI data. The verified amlodipine PBPK model was linked to a pharmacodynamics model that describes changes in systolic blood pressure (SBP) during and after co-administration with RTV. The magnitude and time course of RTV effects on amlodipine plasma exposures and SBP were evaluated, to provide guidance on dose adjustment of amlodipine during and after co-administration with RTV-containing regimens. Model simulations suggested that the increase in amlodipine's plasma exposure by RTV diminishes by approximately 80% within 5 days after the last dose of RTV. PBPK simulations suggested that resuming a full dose of amlodipine [5 mg once daily (QD)] immediately after RTV's last dose would decrease daily average SBP by a maximum of 3.3 mmHg, while continuing with the reduced dose (2.5 mg QD) for 5 days after the last dose of RTV would increase daily average SBP by a maximum of 5.8 mmHg. Based on these results, either approach of resuming amlodipine's full dose could be appropriate when combined with appropriate clinical monitoring.

Development of a mechanism-based pharmacokinetic/pharmacodynamic model to characterize the thermoregulatory effects of serotonergic drugs in mice

We have shown recently that concurrent harmaline, a monoamine oxidase-A inhibitor (MAOI), potentiates serotonin (5-HT) receptor agonist 5-methoxy-N,N-dimethyltryptamine (5-MeO-DMT)-induced hyperthermia. The objective of this study was to develop an integrated pharmacokinetic/pharmacodynamic (PK/PD) model to characterize and predict the thermoregulatory effects of such serotonergic drugs in mice. Physiological thermoregulation was described by a mechanism-based indirect-response model with adaptive feedback control. Harmaline-induced hypothermia and 5-MeO-DMT–elicited hyperthermia were attributable to the loss of heat through the activation of 5-HT_1A receptor and thermogenesis via the stimulation of 5-HT_2A receptor, respectively. Thus serotonergic 5-MeO-DMT–induced hyperthermia was readily distinguished from handling/injection stress-provoked hyperthermic effects. This PK/PD model was able to simultaneously describe all experimental data including the impact of drug-metabolizing enzyme status on 5-MeO-DMT and harmaline PK properties, and drug- and stress-induced simple hypo/hyperthermic and complex biphasic effects. Furthermore, the modeling results revealed a 4-fold decrease of apparent SC₅₀ value (1.88–0.496 µmol/L) for 5-MeO-DMT when harmaline was co-administered, providing a quantitative assessment for the impact of concurrent MAOI harmaline on 5-MeO-DMT–induced hyperthermia. In addition, the hyperpyrexia caused by toxic dose combinations of harmaline and 5-MeO-DMT were linked to the increased systemic exposure to harmaline rather than 5-MeO-DMT, although the body temperature profiles were mispredicted by the model. The results indicate that current PK/PD model may be used as a new conceptual framework to define the impact of serotonergic agents and stress factors on thermoregulation.

Sensitivity of pharmacokinetic-pharmacodynamic analysis for detecting small magnitudes of QTc prolongation in preclinical safety testing

INTRODUCTION

Preclinical concentration-effect (pharmacokinetic-pharmacodynamic, PKPD) modeling has successfully quantified QT effects of several drugs known for significant QT prolongation. This study investigated its sensitivity for detecting small magnitudes of QT-prolongation in a typical preclinical cardiovascular (CV) safety study in the conscious telemetered dog (crossover study in 4-8 animals receiving a vehicle and three dose levels). Results were compared with conventional statistical analysis (analysis of covariance, ANCOVA).

METHODS

A PKPD model predicting individual QTc was first developed from vehicle arms of 28 typical CV studies and one positive control study (sotalol). The model quantified between-animal, inter-occasion and within-animal variability and described QTc over 24h as a function of circadian variation and drug concentration. This "true" model was used to repeatedly (n = 500) simulate studies with typical drug-induced QTc prolongation (∆QTc) of 1 to 12 ms at high-dose peak concentrations. Simulated studies were re-analyzed by both PKPD analysis (with varying complexity) and ANCOVA. Sensitivity (power) was calculated as the percentage of studies in which a significant (α = 0.05) drug effect was found. One simulation scenario did not include a concentration-effect relationship and served to investigate false-positive rates. Exposure-effect relationships were derived from both PKPD analysis (linear concentration-effect) and ANCOVA (linear trend test for dose) and compared.

RESULTS

PKPD analysis/ANCOVA had a sensitivity of 80% to detect the effects of 7/13 ms (n = 4), 5/10 ms (n = 6) and 4.5/8 ms (n = 8), respectively. The false-positive rate was much higher using ANCOVA (40%) compared to PKPD analysis (1%). Typical drug effects were more precisely predicted using estimated concentration-effect slopes (± 1.5-2.8 ms) than dose-effect slopes (± 3.3-3.7 ms).

DISCUSSION

Preclinical PKPD analysis can increase the confidence in the quantification of small QTc effects and potentially allow reducing the number of animals while maintaining the required study sensitivity. This underscores the value of PKPD modeling in preclinical safety testing.

Modeling energy intake by adding homeostatic feedback and drug intervention

Energy intake (EI) is a pivotal biomarker used in quantification approaches to metabolic disease processes such as obesity, diabetes, and growth disorders. Eating behavior is however under both short-term and long-term control. This control system manifests itself as tolerance and rebound phenomena in EI, when challenged by drug treatment or diet restriction. The paper describes a model with the capability to capture physiological counter-regulatory feedback actions triggered by energy imbalances. This feedback is general as it handles tolerance to both increases and decreases in EI, and works in both acute and chronic settings. A drug mechanism function inhibits (or stimulates) EI. The deviation of EI relative to a reference level (set-point) serves as input to a non-linear appetite control signal which in turn impacts EI in parallel to the drug intervention. Three examples demonstrate the potential usefulness of the model in both acute and chronic dosing situations. The model shifts the predicted concentration-response relationship rightwardly at lower concentrations, in contrast to models that do not handle functional adaptation. A fourth example further shows that the model may qualitatively explain differences in rate and extent of adaptation in observed EI and its concomitants in both rodents and humans.

Differential analysis of transient increases of serum cTnI in response to handling in rats

Serum cardiac troponins are the key biomarkers of myocardial necrosis in humans and in preclinical species. The use of ultrasensitive assays for serum cardiac troponin I (cTnI) as a biomarker in safety studies is hampered by interindividual differences. In this study, we investigated the effect of handling procedures on serum cTnI and explored modeling and simulation approaches to mitigate the impact of these interindividual differences. Femoral-catheterized male Crl:WI(Han) rats (n = 16/group) were left undisturbed in their cages with no handling; subjected to 5 min of isoflurane/O₂ anesthesia (A); or placed into a rodent restrainer followed by simulated tail vein injection (RR). Serum cTnI concentrations were assessed over a 24-h period using an ultrasensitive assay, and the study was repeated for confirmation. The mean serum cTnI concentration pre-procedure was 4.2 pg/mL, and remained stable throughout the duration of the study in the rats submitted to the A procedure. Serum cTnI concentrations increased transiently after the RR procedure with a median time to maximum concentration (T_max), of 1 and 2 h and a mean maximum value concentration (C_max), of 53.0 and 7.2 pg/mL in the initial and repeat studies, respectively. A population pharmacodynamic model identified interindividual, procedure- and study-specific effects on serum cTnI concentrations in rats. It is concluded that a modeling and simulation approach more appropriately describes and statistically analyzes the data obtained with this ultrasensitive assays.

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.

Pharmacokinetic/pharmacodynamic modeling of corticosterone suppression and lymphocytopenia by methylprednisolone in rats

Adrenal suppression and lymphocytopenia are commonly monitored pharmacological responses during systemic exposure to exogenously administered corticosteroids. The pharmacodynamics of plasma corticosterone (CS) and blood lymphocytes were investigated in 60 normal rats which received either 50 mg/kg methylprednisolone (MPL) or vehicle intramuscularly. Blood samples were collected between 0.5 and 96 h following treatment. Plasma CS displayed a transient suppression with re-establishment of a normal circadian rhythm 24 h following drug treatment. An indirect response model with suppression of production well captured plasma CS profiles. An early stress-induced rise in CS was also factored into the model. Blood lymphocyte numbers exhibited a sharp decline and then returned to a new circadian rhythm which was half of the original baseline level. An integrated pharmacodynamic (PD) model with inhibition of lymphocyte trafficking from tissue to blood by both MPL and CS and induction of cell apoptosis by MPL reasonably captured this lymphocytopenia. Rats and humans differ in lymphocyte responses with humans showing full recovery of baselines. Modeling provides a valuable tool in quantitative assessment of dual, complex drug responses.

A flexible nonlinear feedback system that captures diverse patterns of adaptation and rebound

An important approach to modeling tolerance and adaptation employs feedback mechanisms in which the response to the drug generates a counter-regulating action which affects the response. In this paper we analyze a family of nonlinear feedback models which has recently proved effective in modeling tolerance phenomena such as have been observed with SSRI's. We use dynamical systems methods to exhibit typical properties of the response-time course of these nonlinear models, such as overshoot and rebound, establish quantitive bounds and explore how these properties depend on the system and drug parameters. Our analysis is anchored in three specific in vivo data sets which involve different levels of pharmacokinetic complexity. Initial estimates for system (k(in), k(out), k(tol)) and drug (EC(50)/IC(50), E(max)/I(max), n) parameters are obtained on the basis of specific properties of the response-time course, identified in the context of exploratory (graphical) data analysis. Our analysis and the application of its results to the three concrete examples demonstrates the flexibility and potential of this family of feedback models.

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

Mechanism-based PK-PD models differ from conventional PK-PD models in that they contain specific expressions to characterize, in a quantitative manner, processes on the causal path between drug administration and effect. This includes target site distribution, target binding and activation, pharmacodynamic interactions, transduction, and homeostatic feedback mechanisms. As the final step, the effects on disease processes and disease progression are considered. Particularly through the incorporation of concepts from receptor theory and dynamical systems analysis, important progress has been made in the field of mechanism-based PK-PD modeling. This has yielded models with much-improved properties for extrapolation and prediction. These models constitute a theoretical basis for rational drug discovery and development.

Mechanistic model of acute autoinhibitory feedback action after administration of SSRIs in rats: Application to escitalopram-induced effects on brain serotonin levels

This study presents the development and evaluation of a feedback turnover model that mimics drug-induced effects on brain extracellular levels of serotonin (5-HT) after acute administration of the selective serotonin reuptake inhibitor (SSRI) escitalopram (S-citalopram) in rats. The extracellular 5-HT output in the hippocampus was continuously monitored by intracerebral microdialysis in conjunction with serial arterial blood sampling for evaluation of escitalopram pharmacokinetics. 5-HT levels were significantly increased following administration of 2.5, 5 and 10 mg/kg of escitalopram and the 5-HT levels gradually declined to its baseline value within 360 min. However, at 5 and 10 mg/kg, the response-time curves were almost identical. This might be explained by activation of serotonergic autoreceptors exerting negative feedback, leading to a reduced release of new 5-HT into the synapse. The dynamics of escitalopram-evoked changes of 5-HT response was characterized by a turnover model, which included an inhibitory feedback moderator component. Thus, the response acted linearly on the production of the moderator, which acted inversely on the production of response. The plasma kinetics served as input to an inhibitory function acting on the loss of response. Simultaneous fitting of the model after three constant rate infusions demonstrated the flexibility of the system. The efficacy (I(max)) and potency (IC(50)) of inhibition of reuptake were 0.9+/-0.03 and 4.4+/-1.4 ng/ml, respectively, corresponding to an EC(50) of escitalopram about 30 ng/ml. In conclusion, the model lends itself to 'what-if' predictions at different drug exposure scenarios, and has potential for extrapolation of the pharmacodynamics of SSRIs in man.

PKPD Model of Interleukin-21 Effects on Thermoregulation in Monkeys—Application and Evaluation of Stochastic Differential Equations

PURPOSE

To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling.

METHODS

A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM.

RESULTS

The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function.

CONCLUSIONS

The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

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.