A mathematical model for dynamics of cardiovascular drug action: application to intravenous dihydropyridines in healthy volunteers

An Integrative Approach for Improved Assessment of Cardiovascular Safety Data

Cardiovascular adverse effects in drug development are a major source of compound attrition. Characterization of blood pressure (BP), heart rate (HR), stroke volume (SV), and QT-interval prolongation are therefore necessary in early discovery. It is, however, common practice to analyze these effects independently of each other. High-resolution time courses are collected via telemetric techniques, but only low-resolution data are analyzed and reported. This ignores codependencies among responses (HR, BP, SV, and QT-interval) and separation of system (turnover properties) and drug-specific properties (potencies, efficacies). An analysis of drug exposure-time and high-resolution response-time data of HR and mean arterial blood pressure was performed after acute oral dosing of ivabradine, sildenafil, dofetilide, and pimobendan in Han-Wistar rats. All data were modeled jointly, including different compounds and exposure and response time courses, using a nonlinear mixed-effects approach. Estimated fractional turnover rates [h^-1, relative standard error (%RSE) within parentheses] were 9.45 (15), 30.7 (7.8), 3.8 (13), and 0.115 (1.7) for QT, HR, total peripheral resistance, and SV, respectively. Potencies (nM, %RSE within parentheses) were IC ₅₀ = 475 (11), IC ₅₀ = 4.01 (5.4), EC ₅₀ = 50.6 (93), and IC ₅₀ = 47.8 (16), and efficacies (%RSE within parentheses) were I _max = 0.944 (1.7), I_max = 1.00 (1.3), E _max = 0.195 (9.9), and I_max = 0.745 (4.6) for ivabradine, sildenafil, dofetilide, and pimobendan. Hill parameters were estimated with good precision and below unity, indicating a shallow concentration-response relationship. An equilibrium concentration-biomarker response relationship was predicted and displayed graphically. This analysis demonstrates the utility of a model-based approach integrating data from different studies and compounds for refined preclinical safety margin assessment. SIGNIFICANCE STATEMENT: A model-based approach was proposed utilizing biomarker data on heart rate, blood pressure, and QT-interval. A pharmacodynamic model was developed to improve assessment of high-resolution telemetric cardiovascular safety data driven by different drugs (ivabradine, sildenafil, dofetilide, and pimobondan), wherein system- (turnover rates) and drug-specific parameters (e.g., potencies and efficacies) were sought. The model-predicted equilibrium concentration-biomarker response relationships and was used for safety assessment (predictions of 20% effective concentration, for example) of heart rate, blood pressure, and QT-interval.

A minimal model to describe short-term haemodynamic changes of the cardiovascular system

AIMS

Current pharmacokinetic-pharmacodynamic models describing the haemodynamic changes often do not include necessary feedback mechanisms. These models provide adequate description of current data but may fail to adequately extrapolate to additional scenarios. This study aims to develop a minimal model to describe the short-term changes of haemodynamics that can be used as the basis for model development by future researchers.

METHODS

A minimal haemodynamic model was developed to describe the influence of drugs on blood pressure components. The model structure was defined based on known mechanisms and previously published models. The model was evaluated under 2 different simulation settings. The model parameters were calibrated to describe (without estimation) the haemodynamics of 2 antihypertensive drugs with data extracted from the literature. Structural identifiability analysis was done using various combinations of the observed variable.

RESULTS

The proposed model structure includes mean arterial pressure, heart rate and stroke volume and is composed of 4 states described by differential equations. Model evaluation showed flexibility in describing the haemodynamics at different target perturbations. Overlay plots of model predictions and literature data showed a good description without data fitting. The structural identifiability analysis revealed all model parameters and initial conditions were identifiable only when heart rate, mean arterial pressure and cardiac output were measured together.

CONCLUSIONS

A minimal model of the haemodynamic system was developed and evaluated. The model accounted for short-term haemodynamic feedback processes. We propose that this model can be used as the basis for future pharmacometric analyses of drugs acting on the haemodynamic system.

Semi-mechanistic modelling platform to assess cardiac contractility and haemodynamics in preclinical cardiovascular safety profiling of new molecular entities

BACKGROUND AND PURPOSE

Cardiovascular safety is one of the most frequent causes of safety-related attrition both preclinically and clinically. Preclinical cardiovascular safety is routinely assessed using dog telemetry monitoring key cardiovascular functions. The present research was to develop a semi-mechanistic modelling platform to simultaneously assess changes in contractility (dPdt_max ), heart rate (HR) and mean arterial pressure (MAP) in preclinical studies.

EXPERIMENTAL APPROACH

Data from dPdt_max , HR, preload (left ventricular end-diastolic pressure [LVEDP]) and MAP were available from dog telemetry studies after dosing with atenolol (n = 27), salbutamol (n = 5), L-N^G -nitroarginine methyl ester (L-NAME; n = 4), milrinone (n = 4), verapamil (n = 12), dofetilide (n = 8), flecainide (n = 4) and AZ001 (n = 14). Literature model for rat CV function was used for the structural population pharmacodynamic model development. LVEDP was evaluated as covariate to account for the effect of preload on dPdt_max .

KEY RESULTS

The model was able to describe drug-induced changes in dPdt_max , HR and MAP for all drugs included in the developed framework adequately, by incorporating appropriate drug effects on dPdt_max , HR and/or total peripheral resistance. Consistent with the Starling's law, incorporation of LVEDP as a covariate on dPdt_max to correct for the preload effect was found to be statistically significant.

CONCLUSIONS AND IMPLICATIONS

The contractility and haemodynamics semi-mechanistic modelling platform accounts for diurnal variation, drug-induced changes and inter-animal variation. It can be used to hypothesize and evaluate pharmacological effects and provide a holistic cardiovascular safety profile for new drugs.

In vitro and in silico analysis of the effects of D2 receptor antagonist target binding kinetics on the cellular response to fluctuating dopamine concentrations

Background and Purpose

Target binding kinetics influence the time course of the drug effect (pharmacodynamics) both (i) directly, by affecting the time course of target occupancy, driven by the pharmacokinetics of the drug, competition with endogenous ligands and target turnover, and (ii) indirectly, by affecting signal transduction and homeostatic feedback. For dopamine D₂ receptor antagonists, it has been hypothesized that fast receptor binding kinetics cause fewer side effects, because part of the dynamics of the dopaminergic system is preserved by displacement of these antagonists.

Experimental Approach

Target binding kinetics of D₂ receptor antagonists and signal transduction after dopamine and D₂ receptor antagonist exposure were measured in vitro. These data were integrated by mechanistic modelling, taking into account competitive binding of endogenous dopamine and the antagonist, the turnover of the second messenger cAMP and negative feedback by PDE turnover.

Key Results

The proposed signal transduction model successfully described the cellular cAMP response for 17 D₂ receptor antagonists with widely different binding kinetics. Simulation of the response to fluctuating dopamine concentrations revealed that a significant effect of the target binding kinetics on the dynamics of the signalling only occurs at endogenous dopamine concentration fluctuations with frequencies below 1 min⁻¹.

Conclusions and Implications

Signal transduction and feedback are important determinants of the time course of drug effects. The effect of the D₂ receptor antagonist dissociation rate constant (k_off) is limited to the maximal rate of fluctuations in dopamine signalling as determined by the dopamine k_off and the cAMP turnover.

A tutorial on model informed approaches to cardiovascular safety with focus on cardiac repolarisation

Drugs can affect the cardiovascular (CV) system either as an intended treatment or as an unwanted side effect. In both cases, drug-induced cardiotoxicities such as arrhythmia and unfavourable hemodynamic effects can occur, and be described using mathematical models; such a model informed approach can provide valuable information during drug development and can aid decision-making. However, in order to develop informative models, it is vital to understand CV physiology. The aims of this tutorial are to present (1) key background biological and medical aspects of the CV system, (2) CV electrophysiology, (3) CV safety concepts, (4) practical aspects of development of CV models and (5) regulatory expectations with a focus on using model informed and quantitative approaches to support nonclinical and clinical drug development. In addition, we share several case studies to provide practical information on project strategy (planning, key questions, assumptions setting, and experimental design) and mathematical models development that support decision-making during drug discovery and development.

Systems pharmacology - Towards the modeling of network interactions

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

Modeling and Simulation Approaches for Cardiovascular Function and Their Role in Safety Assessment

Systems pharmacology modeling and pharmacokinetic-pharmacodynamic (PK/PD) analysis of drug-induced effects on cardiovascular (CV) function plays a crucial role in understanding the safety risk of new drugs. The aim of this review is to outline the current modeling and simulation (M&S) approaches to describe and translate drug-induced CV effects, with an emphasis on how this impacts drug safety assessment. Current limitations are highlighted and recommendations are made for future effort in this vital area of drug research.

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

BACKGROUND AND PURPOSE

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

EXPERIMENTAL APPROACH

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

KEY RESULTS

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

CONCLUSIONS AND IMPLICATIONS

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

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

BACKGROUND AND PURPOSE

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

EXPERIMENTAL APPROACH

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

KEY RESULTS

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

CONCLUSIONS AND IMPLICATIONS

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

Structural identifiability analysis and reparameterisation (parameter reduction) of a cardiovascular feedback model

Structural identifiability should be considered when developing mathematical models. A globally or at least locally identifiable model has to be obtained in order to have some chance of obtaining unique parameter estimates when real data are available. An indicator of structural unidentifiability may be that some unknown parameter estimates are found to be not well determined from parameter estimation of a model. An example is discussed in this paper to illustrate the procedures involved when such situations arise. Problems with parameter estimation were observed for a PKPD model for an α1A/1L-adrenoceptor partial agonist developed for the treatment of stress urinary incontinence The regulation of the side effects of the increased peripheral resistance, induced by the constriction of the blood vessels, was modelled by adapting a previous cardiovascular nonlinear PKPD model proposed by Franchetau and co-workers. Structural identifiability analysis confirmed that the model was unidentifiable. The model was then reparameterised (parameter list reduction) to obtain a globally identifiable model. Simulation studies confirm the superiority of the reduced parameterisation with respect to parameter estimation. The simulation study also confirms the models behave indistinguishably with respect to the input-output behaviour. The example demonstrates the importance of recognising an unidentifiable model and illustrates step by step identifiability analysis, reparameterisation and validation of reparameterised model against the original model.

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.

Model-based decision making in early clinical development: minimizing the impact of a blood pressure adverse event

We describe how modeling and simulation guided program decisions following a randomized placebo-controlled single-rising oral dose first-in-man trial of compound A where an undesired transient blood pressure (BP) elevation occurred in fasted healthy young adult males. We proposed a lumped-parameter pharmacokinetic-pharmacodynamic (PK/PD) model that captured important aspects of the BP homeostasis mechanism. Four conceptual units characterized the feedback PD model: a sinusoidal BP set point, an effect compartment, a linear effect model, and a system response. To explore approaches for minimizing the BP increase, we coupled the PD model to a modified PK model to guide oral controlled-release (CR) development. The proposed PK/PD model captured the central tendency of the observed data. The simulated BP response obtained with theoretical release rate profiles suggested some amelioration of the peak BP response with CR. This triggered subsequent CR formulation development; we used actual dissolution data from these candidate CR formulations in the PK/PD model to confirm a potential benefit in the peak BP response. Though this paradigm has yet to be tested in the clinic, our model-based approach provided a common rational framework to more fully utilize the limited available information for advancing the program.

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.

Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling—A New Classification of Biomarkers

In recent years, pharmacokinetic/pharmacodynamic (PK/PD) modeling has developed from an empirical descriptive discipline into a mechanistic science that can be applied at all stages of drug development. Mechanism-based PK/PD models differ from empirical descriptive models in that they contain specific expressions to characterize processes on the causal path between drug administration and effect. Mechanism-based PK/PD models have much improved properties for extrapolation and prediction. As such, they constitute a scientific basis for rational drug discovery and development. In this report, a novel classification of biomarkers is proposed. Within the context of mechanism-based PK/PD modeling, a biomarker is defined as a measure that characterizes, in a strictly quantitative manner, a process, which is on the causal path between drug administration and effect. The new classification system distinguishes seven types of biomarkers: type 0, genotype/phenotype determining drug response; type 1, concentration of drug or drug metabolite; type 2, molecular target occupancy; type 3, molecular target activation; type 4, physiological measures; type 5, pathophysiological measures; and type 6, clinical ratings. In this paper, the use of the new biomarker classification is discussed in the context of the application of mechanism-based PK/PD analysis in drug discovery and development.

Pharmacokinetic-pharmacodynamic modelling of the cardiovascular effects of drugs - method development and application to magnesium in sheep

Background

There have been few reports of pharmacokinetic models that have been linked to models of the cardiovascular system. Such models could predict the cardiovascular effects of a drug under a variety of circumstances. Limiting factors may be the lack of a suitably simple cardiovascular model, the difficulty in managing extensive cardiovascular data sets, and the lack of physiologically based pharmacokinetic models that can account for blood flow changes that may be caused by a drug. An approach for addressing these limitations is proposed, and illustrated using data on the cardiovascular effects of magnesium given intravenously to sheep.

The cardiovascular model was based on compartments for venous and arterial blood. Blood flowed from arterial to venous compartments via a passive flow through a systemic vascular resistance. Blood flowed from venous to arterial via a pump (the heart-lung system), the pumping rate was governed by the venous pressure (Frank-Starling mechanism). Heart rate was controlled via the difference between arterial blood pressure and a set point (Baroreceptor control). Constraints were made to pressure-volume relationships, pressure-stroke volume relationships, and physical limits were imposed to produce plausible cardiac function curves and baseline cardiovascular variables. "Cardiovascular radar plots" were developed for concisely displaying the cardiovascular status. A recirculatory kinetic model of magnesium was developed that could account for the large changes in cardiac output caused by this drug. Arterial concentrations predicted by the kinetic model were linked to the systemic vascular resistance and venous compliance terms of the cardiovascular model. The kinetic-dynamic model based on a training data set (30 mmol over 2 min) was used to predict the results for a separate validation data set (30 mmol over 5 min).

Results

The kinetic-dynamic model was able to describe the training data set. A recirculatory kinetic model was a good description of the acute kinetics of magnesium in sheep. The volume of distribution of magnesium in the lungs was 0.89 L, and in the body was 4.02 L. A permeability term (0.59 L min^-1) described the distribution of magnesium into a deeper (probably intracellular) compartment. The final kinetic-dynamic model was able to predict the validation data set. The mean prediction error for the arterial magnesium concentrations, cardiac output and mean arterial blood pressure for the validation data set were 0.02, 3.0 and 6.1%, respectively.

Conclusion

The combination of a recirculatory model and a simple two-compartment cardiovascular model was able to describe and predict the kinetics and cardiovascular effects of magnesium in sheep.

Modélisation numérique et simulation : nouvelles applications en pharmacologie

The complexity of pathophysiological mechanisms is beyond the capabilities of traditional approaches. Many of the decision-making problems in public health, such as initiating mass screening, are complex. Progress in genomics and proteomics, and the resulting extraordinary increase in knowledge with regard to interactions between gene expression, the environment and behaviour, the customisation of risk factors and the need to combine therapies that individually have minimal though well documented efficacy, has led doctors to raise new questions: how to optimise choice and the application of therapeutic strategies at the individual rather than the group level, while taking into account all the available evidence? This is essentially a problem of complexity with dimensions similar to the previous ones: multiple parameters with nonlinear relationships between them, varying time scales that cannot be ignored etc. Numerical modelling and simulation (in silico investigations) have the potential to meet these challenges. Such approaches are considered in drug innovation and development. They require a multidisciplinary approach, and this will involve modification of the way research in pharmacology is conducted.

Opioid-induced respiratory depression: a mathematical model for fentanyl

In this paper, respiratory depressant effects of fentanyl are described quantitatively by a mathematical model. The model is an extension of a previous one, which reproduces the human ventilatory control system on a physiological basis. It includes the following: three compartments for gas storage and exchange (lungs, body tissue, and brain tissue); the main mechanisms involved in ventilation control (peripheral chemoreceptors, central chemoreceptors, and the central hypoxic depression); and local blood flow regulation. The effects of fentanyl on the respiratory system include a decrease in peripheral and central chemoreceptor gains on ventilation and a direct inhibition of respiratory neural activity. All parameters in the model were chosen according to the literature. The model is able to reproduce the ventilatory effects of fentanyl in several conditions: 1) constant levels of fentanyl; 2) after a bolus injection; 3) at fixed levels of P(ETCO2); and 4) after artificial ventilation. According to the model, in spontaneously breathing subjects, minute ventilation depends on two opposing actions: fentanyl inhibitory influences, which depress ventilation, reducing oxygen tension and increasing CO2 tension, and the consequent activation of chemoreceptors, which stimulates ventilation. Simulations of anesthetized patients resuming spontaneous breathing after artificial ventilation demonstrate the risk of prolonged apnea and tissue hypoxemia. A safe transition can be achieved by increasing patient PCO2 toward the end of artificial ventilation, because an advanced chemoreceptor stimulation is produced, which promptly counteracts fentanyl-induced inhibition at cessation of artificial ventilation.

The contribution of the coronary concentrations of propofol to its cardiovascular effects in anesthetized sheep

Linking physiological pharmacokinetic models to models of the cardiovascular system requires knowledge of the sites in the body that mediate a drug's cardiovascular effects. We examined the role of the coronary concentrations of propofol. Nine sheep anesthetized with isoflurane (2%) were instrumented acutely for cardiovascular measurements. In a random crossover design, they were administered ramped coronary artery (CA) infusions of propofol to selectively enrich the myocardium (as indicated by the coronary sinus blood concentration) or IV infusions to achieve the same concentration range in all sites of the body. Reductions in left ventricular myocardial contractility (LV dP/dt(max)) and mean arterial blood pressure were linearly related to the propofol concentration. For the CA route, LV dP/dt(max) was reduced by 52 mm Hg/s for each milligram per liter increase in coronary sinus propofol concentration. For the IV route, the reduction in LV dP/dt(max) was equivalent to that with the CA route, showing that the coronary propofol concentration was the major contribution to this effect. For the CA route, mean arterial blood pressure was reduced by 0.6 mm Hg for each milligram per liter. There was a larger reduction (2.5 mm Hg x mg(-1) x L(-1)) for the IV route. Therefore, this effect was predominantly mediated by propofol concentrations elsewhere in the body.

IMPLICATIONS

With use of selective coronary artery infusions in sheep, the coronary concentrations of propofol were shown to be the major contributor to the cardiac depression caused by propofol but were a less significant contributor to the hypotension caused by this drug. Models of the cardiovascular effects of propofol should account for these relationships.

Clinical trial simulation using therapeutic effect modeling: application to ivabradine efficacy in patients with angina pectoris

Ivabradine is a new bradycardic agent with a potential indication for stable angina pectoris. To investigate the best compromise between efficacy, safety, drug regimen, and number of patients to include in a phase III study, we conducted Monte Carlo simulations using a full therapeutic model. The binary clinical outcome, chest pain, was simulated using a physiologic model in which the coronary reserve was derived from the heart rate. Safety was defined as being heart rate dependent. Using real data to build a pharmacokinetic-pharmacodynamic model controlling drug effect (i.e., heart rate decrease), and resampling heart rate profiles from the database, 100 clinical trials (N = 200) were simulated for five oral doses (2.5, 5, 10, 20, and 40 mg QD or BID) of ivabradine. Only 25% of the simulated trials showed a significant effect of ivabradine with doses up to 10 mg QD, and 48 and 55% of the trials with doses of 10 mg BID and 20 mg QD, respectively, and more than 80% of the trials with a 40 mg daily dose. For safety, 4% of patients had at least one adverse event in the untreated group, and from 5 to 13% in the treated groups for the lowest to the highest dose, respectively. The number of subjects to include in a future trial to obtain a 15% decrease in chest pain under the assumption of a 68% base risk, is 239 subjects per group with 10 mg BID or 196 with 20 mg QD. These results illustrate how clinical trial simulations including a PK/PD model as well as a physiopathologic mechanistic model, describing the relationship between the intermediate and clinical endpoint, and the resampling of real patients from a large database can help in designing future phase III trials.

A set-point model with oscillatory behavior predicts the time course of 8-OH-DPAT-induced hypothermia

Agonists for the 5-hydroxytryptamine (HT)(1A) receptor induce a hypothermic response that is believed to occur by lowering of the body's set-point temperature. We have developed a physiological model that can be used to predict the complex time course of the hypothermic response after administration of 5-HT(1A) agonists to rats. In the model, 5-HT(1A) agonists exert their effect by changing heat loss through a control mechanism with a thermostat signal that is proportional to the difference between measured and set-point temperature. Agonists exert their effect in a direct concentration-dependent manner, with saturation occurring at higher concentrations. On the basis of simulations, it is shown that, depending on the concentration and the intrinsic efficacy of a 5-HT(1A) agonist, the model shows oscillatory behavior. The model was successfully applied to characterize the complex hypothermic response profiles after administration of the reference 5-HT(1A) agonists R-8-hydroxy-2-(di-n-propylamino)tetralin (R-8-OH-DPAT) and S-8-OH-DPAT. This analysis revealed that the observed difference in effect vs. time profile for these two reference agonists could be explained by a difference in in vivo intrinsic efficacy.

Role of modelling and simulation in Phase I drug development

Although the use of pharmacokinetic/pharmacodynamic modelling and simulation (M&S) in drug development has increased during the last decade, this has most notably occurred in patient studies using the population approach. The role of M&S in Phase I, although of longer history, does not presently have the same impact on drug development. However, trends such as the increased use of biomarkers and clinical trial simulation as well as adoption of the learn/confirm concept can be expected to increase the importance of modelling in Phase I. To help identify the role of M&S, its main advantages and the obstacles to its rational use, an expert meeting was organised by COST B15 in Brussels, January 10-11, 2000. This article presents the views expressed at that meeting. Although it is clear that M&S occurs in only a minority of Phase I clinical trials, it is used for a large number of different purposes. In particular, M&S is considered valuable in the following situations: censoring because of assay limitation, characterisation of non-linearity, estimating exposure-response relationship, combined analyses, sparse sampling studies, special population studies, integrating PK/PD knowledge for decision making, simulation of Phase II trials, predicting multiple dose profile from single dose, bridging studies and formulation development. One or more of the following characteristics of M&S activities are often present and severely impede its successful integration into clinical drug development: lack of trained personnel, lack of protocol and/or analysis plan, absence of pre-specified objectives, no timelines or budget, low priority, inadequate reporting, no quality assurance of the modelling process and no evaluation of cost-benefit. The early clinical drug development phase is changing and if these implementation aspects can be appropriately addressed, M&S can fulfill an important role in reshaping the early trials by more effective extraction of information from studies, better integration of knowledge across studies and more precise predictions of trial outcome, thereby allowing more informed decision making.

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.

Interchangeability and predictive performance of empirical tolerance models

Models of tolerance are commonly derived on empirical grounds, because of lack of knowledge about the mechanism of tolerance or because of the difficulty of appropriately simplifying complex physiological processes. The present study was performed to evaluate the interchangeability of tolerance models used in the literature and to address some determinants for selection of an appropriate design and data analysis strategy. Seven models were chosen (noncompetitive antagonist model, partial agonist model, reverse agonist model, direct moderator model, indirect moderator model, pool model and adaptive pool model) along with their corresponding parameter estimates, representing a wide range of empirical models. The performance of the models on various data sets was evaluated. Data were simulated from each original model and were further analysed by the other models. The effect-time course of each and every data set could be described well by at least 2 different empirical tolerance models, but no model could describe all the data sets adequately. However, all models could adequately describe at least 2 different data sets. This indicates that, without additional knowledge or assumptions, it is unlikely that reliable mechanistic information can be deduced from the mere fact that 1 (or more) of these models can describe the data. Generally, data expressing only limited tolerance can be described by a wide variety of models, whereas few models will be appropriate for data characterised by extensive tolerance. The models that gave an adequate description of a data set were selected for further study that investigated their predictive capacity based on the parameters previously determined. Predictions were made for 4 different administration schemes. The selected models gave similar predictions for the extended designs of 3 data sets for which the original study designs characterised tolerance well. For the other 4 data sets, the selected models gave disparate predictions, although the models described the original data set well. Thus, the predictive capability of a model was linked to the original study design, whereas the correlation between predictive performance and the type of model was weak or absent. Based on the results, factors of importance for the design and evaluation of studies of tolerance were identified and discussed.

Pharmacokinetic-haemodynamic relationships of 2-chloroadenosine at adenosine A1 and A2a receptors in vivo

1. The purpose of the present study was to develop an experimental strategy for the quantification of the cardiovascular effects of non-selective adenosine receptor ligands at the adenosine A1 and A2a receptor in vivo. 2-Chloroadenosine (CADO) was used as a model compound. 2. Three groups of normotensive conscious rats received an short intravenous infusion of 1.4 mg kg-1 CADO during constant infusions of the A1-selective antagonist, 8-cyclopentyltheophylline (CPT; 20 micrograms min-1 kg-1), the A2a-selective antagonist, 8-(3-chlorostyryl) caffeine (CSC; 32 micrograms min-1 kg-1) or the vehicle. The heart rate (HR) and mean arterial blood pressure (MAP) were recorded continuously during the experiment and serial arterial blood samples were taken for analysis of drug concentrations. The ratio MAP/HR was also calculated, which may reflect changes in total peripheral resistance on the assumption that no changes in stroke volume occur. 3. During the infusion of CPT, CADO produced a reduction in both blood pressure and MAP/HR by activation of the A2a receptor. The concentration-effect relationships were described according to the sigmoidal Emax model, yielding potencies based on free drug concentrations (EC50,u) of 61 and 68 ng ml-1 (202 and 225 nM) for the reduction of blood pressure and MAP/HR, respectively. During the infusion of CSC, an EC50,u value of 41 ng ml-1 (136 nM) was observed for the A1 receptor-mediated reduction in heart rate. The in vivo potencies correlated with reported receptor affinities (Ki(A1) = 300 nM and Ki(A2a) = 80 nM). The maximal reductions in MAP/HR and heart rate were comparable to those of full agonists, with the Emax values of -12 +/- 1 x 10(-2) mmHg b.p.m.-1 and -205 b.p.m. respectively. 4. It is concluded that this integrated pharmacokinetic-pharmacodynamic approach can be used to obtain quantitative information on the potency and intrinsic activity of new non-selective adenosine receptor agonists at different receptor subtypes in vivo.

Pharmacokinetic modelling of the haemodynamic effects of the A2a adenosine receptor agonist CGS 21680C in conscious normotensive rats

1. The aim of the present investigation was to determine the relationship between the blood concentration and haemodynamic effects of the adenosine A2a receptor agonist, CGS 21680C (the sodium salt of 2-p-(2-carboxyethyl)phenylethylamino-5'-N-ethylcarboxamidoadeno sin e) in conscious normotensive rats. 2. Chronically cannulated rats were randomly assigned to three groups which received 300, 1000 or 3000 micrograms kg-1 (0.56, 1.9 or 5.6 mumol kg-1) of CGS 21680C intravenously over 15 min. The mean arterial blood pressure (MAP) and heart rate (HR) were monitored continuously during the experiment and serial arterial blood samples were taken for analysis of drug concentration. The ratio MAP/HR was also calculated, which may reflect changes in total peripheral resistance on the assumption that no changes in stroke volume occur. 3. For each individual rat the reduction in mean arterial pressure was related to the blood concentration according to the sigmoidal Emax model. The concentration-effect relationships were consistent for the different treatment groups. The potency based on free drug concentrations (EC50,u) was 5.8 ng ml-1 (11 nM) (mean +/- s.e.; n = 19) and correlated well with the reported adenosine A2a receptor affinity (Ki 19 nM). In comparison with the reduction in blood pressure, CGS 21680C exhibited a greater potency for the reduction of the ratio MAP/HR. 4. It is concluded that estimates can be obtained for the potency and intrinsic activity of adenosine A2a receptor agonists in vivo by pharmacokinetic-pharmacodynamic analysis of mean arterial pressure data in a rat model. In future studies, total peripheral resistance may also be useful as a pharmacodynamic parameter for A24 activation, provided that possible changes of the stroke volume are also assessed.

Relationship between hypoglycaemic response and plasma concentrations of BTS 67 582 in healthy volunteers

The relationships between blood glucose, plasma insulin and plasma BTS 67 582 concentrations were studied in a randomised, placebo-controlled, four-way crossover study involving 16 healthy male volunteers aged between 19 and 43 years. Single oral doses of 125, 250 and 500 mg BTS 67 582 were studied. Fasting blood samples were taken pre-dose and half-hourly for 8 h post-dose. Mean peak plasma concentrations of BTS 67 582 were 518, 1076 and 2435 ng ml-1 for doses of 125, 250 and 500 mg, respectively. Mean maximum reductions in blood glucose were 1.13, 1.59 and 1.78 mmol l-1, and mean maximum increases in plasma insulin were 26, 14 and 21 muu ml-1 for the three doses, respectively. Changes in incremental area under the curve (AUC) of blood glucose were correlated with changes in plasma BTS 67 582 AUC. The maximum reduction in blood glucose was correlated with the peak plasma BTS 67 582 concentration. No correlations between plasma insulin and plasma BTS 67 582 concentrations were observed. Anticlockwise hysteresis was evident in concentration-effect curves, but less evident following subtraction of placebo data, and was mainly due to an underlying downward trend in fasted blood glucose levels with time evident under placebo treatment. This suggests that hypoglycaemic effects were related to systemic BTS 67 582 concentrations, suggesting that active metabolites of the drug do not make a major contribution to acute hypoglycaemic effects. A log-linear model described the relationship between blood glucose and plasma BTS 67 582 concentrations for 14 of the 16 volunteers.(ABSTRACT TRUNCATED AT 250 WORDS)