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.

A quantitative approach to analysing cortisol response in the horse.

The cortisol response to glucocorticoid intervention has, in spite of several studies in horses, not been fully characterized with regard to the determinants of onset, intensity and duration of response. Therefore, dexamethasone and cortisol response data were collected in a study applying a constant rate infusion regimen of dexamethasone (0.17, 1.7 and 17 µg/kg) to six Standardbreds. Plasma was analysed for dexamethasone and cortisol concentrations using UHPLC-MS/MS. Dexamethasone displayed linear kinetics within the concentration range studied. A turnover model of oscillatory behaviour accurately mimicked cortisol data. The mean baseline concentration range was 34-57 µg/L, the fractional turnover rate 0.47-1.5 1/h, the amplitude parameter 6.8-24 µg/L, the maximum inhibitory capacity 0.77-0.97, the drug potency 6-65 ng/L and the sigmoidicity factor 0.7-30. This analysis provided a better understanding of the time course of the cortisol response in horses. This includes baseline variability within and between horses and determinants of the equilibrium concentration-response relationship. The analysis also challenged a protocol for a dexamethasone suppression test design and indicated future improvement to increase the predictability of the test.

Plasma concentration-dependent suppression of endogenous hydrocortisone in the horse after intramuscular administration of dexamethasone-21-isonicotinate.

Detection times and screening limits (SL) are methods used to ensure that the performance of horses in equestrian sports is not altered by drugs. Drug concentration-response relationship and knowledge of concentration-time profiles in both plasma and urine are required. In this study, dexamethasone plasma and urine concentration-time profiles were investigated. Endogenous hydrocortisone plasma concentrations and their relationship to dexamethasone plasma concentrations were also explored. A single dose of dexamethasone-21-isonicotinate suspension (0.03 mg/kg) was administered intramuscularly to six horses. Plasma was analysed for dexamethasone and hydrocortisone and urine for dexamethasone, using UPLC-MS/MS. Dexamethasone was quantifiable in plasma for 8.3 ± 2.9 days (LLOQ: 0.025 µg/L) and in urine for 9.8 ± 3.1 days (LLOQ: 0.15 µg/L). Maximum observed dexamethasone concentration in plasma was 0.61 ± 0.12 µg/L and in urine 4.2 ± 0.9 µg/L. Terminal plasma half-life was 38.7 ± 19 h. Hydrocortisone was significantly suppressed for 140 h. The plasma half-life of hydrocortisone was 2.7 ± 1.3 h. Dexamethasone potency, efficacy and sigmoidicity factor for hydrocortisone suppression were 0.06 ± 0.04 µg/L, 0.95 ± 0.04 and 6.2 ± 4.6, respectively. Hydrocortisone suppression relates to the plasma concentration of dexamethasone. Thus, determination of irrelevant plasma concentrations and SL is possible. Future research will determine whether hydrocortisone suppression can be used as a biomarker of the clinical effect of dexamethasone.

Animal Health Modeling & Simulation Society: a new society promoting model-based approaches in veterinary pharmacology.

The Animal Health Modeling & Simulation Society (AHM&S) is a newly founded association (2012) that aims to promote the development, application, and dissemination of modeling and simulation techniques in the field of Veterinary Pharmacology and Toxicology. The association is co-chaired by Pr. Johan Gabrielsson (Europe), Pr. Jim Riviere (USA), and secretary Dr. Jonathan Mochel (Switzerland). This short communication aims at presenting the membership, rationale and objectives of this group.

Quantitative pharmacology or pharmacokinetic pharmacodynamic integration should be a vital component in integrative pharmacology.

Pharmacodynamics (PD) examines the relationship between drug concentration and onset, intensity, and duration of the pharmacological effect. Pharmacokinetics (PK) is the science of the time course of drugs in the organism. The quantitative pharmacological approach focuses on concentration-response and response-time relationships, with special emphasis on the proposed impact of the drug on the disease. The review aims to raise awareness among pharmacologists with regard to why pharmacokinetic-pharmacodynamic (PKPD) integration is essential in basic pharmacology research to improve interpretation of data. Quantitative pharmacology is vital in drug discovery for target validation, optimizing the development of lead compounds, and scaling compounds to humans and has become mandatory for regulatory bodies. However, its use is still comparatively rare in experimental pharmacology, and its absence diminishes the interpretative value of published experimental data and can allow the presentation of misleading information. A primary requirement for PKPD integration is establishing the inter-relationships between in vitro and in vivo PK and PD properties and extrapolation to the known or possible future clinical use of a compound. This review examines the use of PKPD in experimental pharmacology by reviewing drug exposure measurements, plasma protein binding, exposure-effect relationships, and the measurement of active metabolites. It examines the significance of dosing schedules, the importance of target engagement, and problems in examining time-response relationships. It shows how quantitative pharmacology adds significant value to study design and examines why ignoring pharmacokinetics can lead to misleading results and conclusions. Finally, a guide list of points to be considered when performing studies is provided.

Pharmacodynamic modeling of furosemide tolerance after multiple intravenous administration.

OBJECTIVE: Physiologic indirect-response models have been proposed to account for the pharmacodynamics of drugs with an indirect mechanism of action, such as furosemide. However, they have not been applied to tolerance development. The aim of this study was to investigate the development of tolerance after multiple intravenous dosing of furosemide in healthy volunteers. METHODS: Three repetitive doses of 30 mg furosemide were given as rapid intravenous infusions at 0, 4, and 8 hours to eight healthy volunteers. Urine samples were collected for a period up to 14 hours after the first dose. Volume and sodium losses were isovolumetrically replaced with an oral rehydration fluid. RESULTS: Tolerance was demonstrated as a significant decrease in diuretic and natriuretic response over time. Total mean diuresis was 35% lower (p < 0.01) and total mean natriuresis was 52% lower (p < 0.0001) after the third dose of furosemide compared with the first dose. However, there were considerable interindividual variations in the rate and extent of tolerance development for both diuresis and natriuresis. Pharmacokinetic-pharmacodynamic modeling of tolerance development was performed with use of an indirect-response model with an additional "modifier" compartment. This model gave an accurate description of the diuretic and natriuretic data after multiple dosing of furosemide and enabled the estimation of a lag-time for tolerance and a rate constant for tolerance development. Physiologic counteraction was demonstrated as a significant increase in plasma active renin levels (p < 0.00001) and a decrease in atrial natriuretic peptide levels (p < 0.005) during the day, concomitantly with the development of a negative sodium balance. This may be viewed as physiologic reflections of the modifier in our model. CONCLUSION: Indirect-response models may be successfully applied for tolerance modeling of drugs after multiple dosing.

Time course of enzyme induction in humans: effect of pentobarbital on nortriptyline metabolism.

To study the effect of induction we gave six male volunteers 10 mg nortriptyline three times a day for 4 weeks and 0.2 gm pentobarbital on days 8 to 21. Plasma and urinary levels of nortriptyline and metabolites were measured. The rate and extent of induction of the enzyme(s) were estimated by a model with use of nortriptyline concentrations. There was a marked decrease of nortriptyline levels after 2 days of pentobarbital treatment. Total clearance of nortriptyline increased more than twofold (range, 1.6-fold to 4.1-fold). Apparent metabolic clearance by 10-hydroxylation increased markedly. The decrease in nortriptyline levels was more rapid than the increase after pentobarbital cessation, fitting with the theory of the model. The induction of nortriptyline metabolism is probably mainly the result of an increase in a non-CYP 2D6 P450 isozyme, possibly CYP 3A4 or a CYP 2C form. More knowledge of induction characteristics of drugs should lead to better predictions of decreased effects and appearance of adverse effects. The kinetic model used for analysis of our data could then be useful.

Influence of CYP2D6 polymorphism on the pharmacokinetics and pharmacodynamic of tolterodine.

OBJECTIVE: To determine whether cytochrome P450 2D6 (CYP2D6) is involved in the metabolism of tolterodine by investigating potential differences in pharmacokinetics and pharmacodynamic (heart rate, accommodation, and salivation) of tolterodine and its 5-hydroxymethyl metabolite between poor metabolizers and extensive metabolizers of debrisoquin (INN, debrisoquine). METHODS: Sixteen male subjects (eight extensive metabolizers and eight poor metabolizers) received 4 mg tolterodine by mouth twice a day for 8 days followed by a single intravenous infusion of 1.8 mg tolterodine for 30 minutes after a washout period. Doses were given as the tartrate salt. The pharmacokinetics of tolterodine and 5-hydroxymethyl metabolite were determined, and the pharmacodynamic were measured. RESULTS: The mean systemic clearance of tolterodine was significantly lower (p < 0.001) among poor metabolizers (9.0 +/- 2.1 l/hr) compared with extensive metabolizers (44 +/- 13 L/hr), resulting in a fourfold longer elimination half-life (p < 0.001). The terminal half-life of the 5-hydroxymethyl metabolite (2.9 +/- 0.4 hours) was slightly longer than that of the parent compound (2.3 +/- 0.6 hours) among extensive metabolizers, but the 5-hydroxymethyl metabolite was undetectable in the serum of poor metabolizers. Only minor differences in pharmacodynamic effects after tolterodine dosage were observed between the groups. Tolterodine caused a similar decrease in salivation in both panels. The decrease occurred when the concentration of unbound tolterodine and 5-hydroxymethyl metabolite among extensive metabolizers was comparable with that of tolterodine among poor metabolizers. CONCLUSIONS: Tolterodine is extensively metabolized by CYP2D6 with high specificity. Despite the effect on pharmacokinetics, the CYP2D6 polymorphism does not appear to be of great importance in the antimuscarinic effect, probably because of the additive action of parent drug and active metabolite.

Neuroprotective efficacy of AR-A008055, a clomethiazole analogue, in a global model of acute ischaemic stroke and its effect on ischaemia-induced glutamate and GABA efflux in vitro.

We have investigated the neuroprotective properties of AR-A008055 [(+/-)-1-(4-methyl-5-thiazolyl-1-phenyl-methylamine], a novel compound structurally related to clomethiazole. Administration (i.p.) of (+/-)-AR-A008055 60 min after 5 min of global cerebral ischaemia in gerbils produced a dose-dependent protection of the hippocampus from damage. Both enantiomers [(R)-(+)-AR-A008055 and (S)-(-)- AR-A008055] at 600 micromol/kg produced similar protection to that following clomethiazole (600& micromol/kg) and both produced similar and sustained neuroprotection, at 4, 7 and 21 days post-insult. When infused intravenously over a 2-h period, both enantiomers produced concentration-dependent neuroprotection, with the enantiomers providing similar protection at every plasma concentration (50-200 nmol/ml). The efficacy of (S)-(-)-AR-A008055 was similar to clomethiazole, but it was slightly less potent. Ischaemia-induced glutamate efflux from rat brain cortical prisms in vitro was inhibited by both isomers (100 microM). The inhibitory effect of (R)-(+)-AR-A008055 was blocked by bicuculline (10 microM) and picrotoxin (100 microM), while the effect of (S)-(-)-AR-A008055 was only antagonised by picrotoxin. This indicated that (S)-(-)-AR-A008055, like clomethiazole, is able to open the GABA(A)-chloride channel in the absence of endogenous GABA. (R)-(+)-AR-A008055 was more potent than (S)-(-)-AR-A008055 in enhancing the concentration of GABA in the medium following 30 min exposure of tissue to the ischaemic conditions, suggesting that it is an effective GABA uptake inhibitor. This action may explain both its effect on glutamate efflux in vitro and its neuroprotective effect in vivo.

Effects of dietary sodium selenite supplementation on salicylate-induced embryo- and fetotoxicity in the rat.

The effects of dietary supplementation with sodium selenite (3.0 or 4.5 ppm Se) for 8 weeks prior to and throughout gestation on sodium salicylate induced embryo- and fetotoxicity (resorptions, fetal deaths, malformations, fetal weight reduction) have been studied in the rat. Salicylate was administered either as daily intragastric bolus doses of 250 mg/kg on gestation days 6-13 (maternal peak and trough salicylate levels of 222-120 micrograms/ml whole-blood) or via constant rate intravenous infusion of 150 mg/kg/day on the same gestation days via implanted osmotic minipumps (stable average maternal blood salicylate level of 120 micrograms/ml = human antirheumatic concentration). Both gavage and infusion of salicylate resulted in an increase of resorptions and fetal deaths as well as a decrease of fetal body weights. Gavage with salicylate also produced about 50% malformed fetuses. Selenite did not protect against the embryotoxic effects of salicylate administered as intragastric bolus doses. However, selenite was found to significantly increase fetal survival rate in the infusion experiment, although it did not counteract the decrease of fetal body weight. In animals fed selenite only, no negative effects on fetal body development were noted. The protective effect of selenite against salicylate induced embryotoxicity is difficult to explain, since very little is known about the mechanisms of salicylate embryotoxicity and the biological effects of selenium. However, an interaction between selenium, via glutathione peroxidase, and salicylate at the level of prostaglandin synthesis could be possible.

Constant rate of infusion--improvement of tests for teratogenicity and embryotoxicity.

Sodium salicylate was used as a model substance to investigate whether the embryotoxic effects on rat fetuses varies between two modes of administration. A marked increase in fetal adverse effects was observed at analgetic doses with the once-a-day bolus regimen compared to the constant rate input. The difference was less marked at antirheumatic levels.

New kinetic data on estradiol in light of the vaginal ring concept.

The principal estrogen produced by the functioning premenopausal ovary is 17 beta-estradiol. At the point of irreversible ovarian failure, at menopause, the production of estradiol decreases dramatically, which results in circulating serum levels less than 120 pmol/l. It is important to recognise the pharmacokinetic and metabolic outcomes associated with dosage and route of delivery of estrogen. One of the most promising methods of administering estrogen replacement therapy (ERT) for local effects is the estradiol vaginal ring designed for a controlled continuous low release (7.5 micrograms estradiol/24 h) over a period of 90 days. The present study was undertaken to characterise the basal endogenous turnover of estradiol in postmenopausal women. Information on the disposition of estradiol after an intravenous dose formed the base of the kinetic model. The rate of extent of absorption of estradiol was assessed after ring application. Individual serum concentrations of estradiol were analysed without subtraction of the basal estradiol levels. The results indicate a rapidly eliminated compound (plasma clearance 2 l/min) with a distribution of approximately 50 l, resulting in an efficient half-life of about 20 min. The endogenous production was highly variable (< 1-44 micrograms/24 h). The steady-state estradiol levels following ring application did not increase and were well within the normal basal estradiol range seen in untreated women. In light of the present findings, the low daily dose, the low availability of estradiol across the vaginal wall and the controlled local delivery, favour the use of the estradiol vaginal ring.

Pharmacodynamic modelling of reversible gastric acid pump inhibition in dog and man.

H 335/25, a 4-amino quinoline, belongs to a new class of reversible gastric acid pump inhibitors. A potential advantage of such drugs over the irreversible proton pump inhibitors (PPIs) is better control over the effect-time profile. Dose escalation studies were performed to characterize the effect on acid secretion in dogs (n=24) and healthy male subjects (n=12). The effect-time profile was delayed compared to the concentration-time profile. A model-based approach, using non-linear mixed effects modelling, was applied to quantify and elucidate the mechanism for the delayed effect. Three different models were investigated: (1) a slow equilibration preceding the formation of drug-enzyme complex, modelled by an effect-compartment, (2) a slow equilibration between free drug, free enzyme and drug-enzyme complex, described by a kinetic binding model, and (3) a delay between enzyme inhibition and the measured response, described by an indirect response model. Model 2 was shown to be superior to models 1 and 3, for both dog and human data. The dissociation rate constant, k(off), was estimated to be 0.85 and 0.88 h and the calculated equilibration constant, K(d), was 160 and 250 nM in dog and man, respectively. Simulations of the predicted time-course of the effect beyond the 4-5-h observation period was similar for the three models.

Pharmacokinetics and pharmacodynamics of tolterodine in man: a new drug for the treatment of urinary bladder overactivity.

The aim of this study was to determine the pharmacokinetics, pharmacodynamics, and safety of tolterodine following single oral and intravenous doses in healthy volunteers. A secondary aim was to identify major urinary metabolites and determine mass balance. Single oral doses of 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, and 12.8 mg of tolterodine (as the tartrate salt) were given to 17 healthy male volunteers. Two intravenous doses (0.64 and 1.28 mg) were administered to 8 of the volunteers and mass balance was studied after a single oral dose of 5 mg (14C)-tolterodine in 6 subjects. Tolterodine was rapidly absorbed following oral administration (time to peak serum concentration 0.9 +/- 0.4 h). The absolute bioavailability was highly variable, ranging from 10 to 70%. The volume of distribution at steady-state ranged from 0.9 to 1.6 l/kg and systemic clearance ranged from 0.23 to 0.52 l/h/kg, which resulted in a terminal half-life of 2-3 h. Tolterodine exhibited high first-pass metabolism and 2 hepatic metabolic pathways were identified: oxidation and dealkylation. Independent of route of administration, < 1% of the parent compound was excreted unchanged in urine. Five metabolites were structurally identified in urine. Following oral administration of (14C)-tolterodine, the excretion of radioactivity into urine and feces was 77 +/- 4.0% and 17 +/- 3.5%, respectively. Tolterodine decreased stimulated salivation after 3.2 mg, increased heart rate after 6.4 mg, and nearpoint of vision after 12.8 mg. Six of 8 subjects reported micturition difficulties after a dose of 12.8 mg. The lack of a direct relationship between tolterodine serum concentrations and effects on stimulated salivation suggested the presence of pharmacologically active metabolite(s).

Pharmacokinetics of quinacrine after intrapleural instillation in rabbits and man.

Quinacrine was given by intrapleural instillation or intravenous infusion to 10 rabbits. The uptake of quinacrine from the pleural space was rapid and complete. The mean absorption half-life was approximately 7 min and the mean bioavailability was slightly in excess of 100%. Similar absorption characteristics generally applied in man, in a pilot study on four patients. In three of them, peak quinacrine plasma concentrations were reached that were far above the normal therapeutic range. Known systemic side-effects of quinacrine comprise CNS stimulation, toxic psychosis and convulsions. In view of the high bioavailability and the large doses used for pleural sclerosing (pleurodesis) in patients, neurological disease and psychiatric disturbances that predispose to CNS toxicity should be considered as contraindications to intrapleural quinacrine.

Translational neuropharmacology and the appropriate and effective use of animal models.

This issue of the British Journal of Pharmacology is dedicated to reviews of the major animal models used in neuropharmacology to examine drugs for both neurological and psychiatric conditions. Almost all major conditions are reviewed. In general, regulatory authorities require evidence for the efficacy of novel compounds in appropriate animal models. However, the failure of many compounds in clinical trials following clear demonstration of efficacy in animal models has called into question both the value of the models and the discovery process in general. These matters are expertly reviewed in this issue and proposals for better models outlined. In this editorial, we further suggest that more attention be made to incorporate pharmacokinetic knowledge into the studies (quantitative pharmacology). We also suggest that more attention be made to ensure that full methodological details are published and recommend that journals should be more amenable to publishing negative data. Finally, we propose that new approaches must be used in drug discovery so that preclinical studies become more reflective of the clinical situation, and studies using animal models mimic the anticipated design of studies to be performed in humans, as closely as possible.

Constant-rate infusion of nicotine and cotinine. I. A physiological pharmacokinetic analysis of the cotinine disposition, and effects on clearance and distribution in the rat.

The tissue partition of cotinine was measured by a GC-MS method following a 6-day constant-rate input of nicotine and cotinine to male rats by means of an osmotic minipump. The tissue-to-blood partition coefficients of cotinine were calculated for adipose (0.08), brain (0.48), heart muscle (0.51), following the cotinine infusion. When nicotine was infused the tissue partitioning of cotinine increased by a factor of 2.3-4.9, depending on the tissue sampled. Another group of animals were killed at timed intervals from 10 min to 30 hr, after having received a single intravenous bolus dose of 0.5 mg cotinine, and the washout of cotinine was traced in blood and tissues. A physiological model was used to simulate the disposition of cotinine. Generally, the model-predicted concentrations were consistent with those found experimentally. The fractional uptake of cotinine into various tissues was simulated. Blood, intestinal, and skeletal muscle tissues embodied more than 70% of the total body load of the drug. Clearance (Cl), volume of distribution (Vd), and the biological half-life (t1/2) were calculated both from the infusion study and by fitting a monoexponential model to the iv blood data of the rat. Significant differences were found in the apparent clearance calculated from the single iv bolus dose compared to the constant rate infusion. The volume of distribution was, however, consistent from both studies. The impact of a change in clearance was also simulated.

An extended physiological pharmacokinetic model of methadone disposition in the rat: validation and sensitivity analysis.

An extended physiological model of methadone disposition in the rat was constructed and evaluated in various tests of model validity. A separate circulation model of the fetus was included due to the large tissue concentration differences obtained after a constant rate infusion but also to propose the use of this type of model for optimization of toxicological tests. Simulations were performed with the animal model and scaled-up models of humans to elucidate the determinants of methadone disposition. The rationale of the use of an extended model for methadone was also discussed.