Mathematical modeling of the circadian dynamics of the neuroendocrine-immune network in experimentally induced arthritis.

The circadian dynamics of important neuroendocrine-immune mediators have been implicated in progression of rheumatoid arthritis pathophysiology, both clinically as well as in animal models. We present a mathematical model that describes the circadian interactions between mediators of the hypothalamic-pituitary-adrenal (HPA) axis and the proinflammatory cytokines. Model predictions demonstrate that chronically elevated cytokine expression results in the development of adrenal insufficiency and circadian variability in paw edema. Notably, our model also predicts that an increase in mean secretion of corticosterone (CST) after the induction of the disease is accompanied by a decrease in the amplitude of the CST oscillation. Furthermore, alterations in the phase of circadian oscillation of both cytokines and HPA axis mediators are observed. Therefore, by incorporating the circadian interactions between the neuroendocrine-immune mediators, our model is able to simulate important features of rheumatoid arthritis pathophysiology.

Pharmacokinetic and pharmacodynamic analysis comparing diverse effects of detomidine, medetomidine, and dexmedetomidine in the horse: a population analysis.

The present study characterizes the pharmacokinetic (PK) and pharmacodynamic (PD) relationships of the α2-adrenergic receptor agonists detomidine (DET), medetomidine (MED) and dexmedetomidine (DEX) in parallel groups of horses from in vivo data after single bolus doses. Head height (HH), heart rate (HR), and blood glucose concentrations were measured over 6 h. Compartmental PK and minimal physiologically based PK (mPBPK) models were applied and incorporated into basic and extended indirect response models (IRM). Population PK/PD analysis was conducted using the Monolix software implementing the stochastic approximation expectation maximization algorithm. Marked reductions in HH and HR were found. The drug concentrations required to obtain inhibition at half-maximal effect (IC50 ) were approximately four times larger for DET than MED and DEX for both HH and HR. These effects were not gender dependent. Medetomidine had a greater influence on the increase in glucose concentration than DEX. The developed models demonstrate the use of mechanistic and mPBPK/PD models for the analysis of clinically obtainable in vivo data.

Development of translational pharmacokinetic-pharmacodynamic models.

Contemporary models in the field of pharmacokinetic-pharmacodynamic (PK-PD) modeling often incorporate the fundamental principles of capacity limitation and operation of turnover processes to describe the time course of pharmacological effects in mechanistic terms. This permits the identification of drug- and system-specific factors that govern drug responses. There is considerable interest in utilizing mechanism-based PK-PD models in translational pharmacology, whereby in silico, in vitro, and preclinical data may be effectively coupled with relevant models to streamline the discovery and development of new therapeutic agents. These translational PK-PD models form the subject of this review.

Extracting global system dynamics of corticosteroid genomic effects in rat liver.

One of the challenges in constructing biological models involves resolving meaningful data patterns from which the mathematical models will be generated. For models that describe the change of mRNA in response to drug administration, questions exist whether the correct genes have been selected given the myriad transcriptional effects that may occur. Oftentimes, different algorithms will select or cluster different groups of genes from the same data set. A new approach was developed that focuses on identifying the underlying global dynamics of the system instead of selecting individual genes. The procedure was applied to microarray genomic data obtained from rat liver after a large single dose of methylprednisolone in 52 adrenalectomized rats. Twelve clusters of at least 30 genes each were selected, reflecting the major changes over time. This method along with isolating the underlying dynamics of the system also extracts and clusters the genes that make up this global dynamic for further analysis as to the contributions of specific mechanisms affected by the drug.

Modeling and allometric scaling of s(+)-ketoprofen pharmacokinetics and pharmacodynamics: a retrospective analysis.

Interspecies scaling of pharmacokinetic (PK) parameters is commonplace in drug development. However, information about proportionality of pharmacodynamic (PD) parameters in different species is scarce. We investigated the feasibility of allometric scaling of PK and PD parameters of s(+)-ketoprofen (sKTP) using the literature data from several animal species. Two different indirect response models were proposed to characterize sKTP inhibitory effects on synthesis of thromboxane B(2) (TXB(2)) and prostaglandin E(2) (PGE(2)). Using the traditional allometric approach, the obtained PK and PD parameters were plotted against body weights (BW) on a log-log scale. For all species, values of systemic clearance (Cl), distribution clearance (Cl(D)), central volume of distribution (V(c)), and volume of distribution at steady-state (V(ss)) were highly correlated (r(2) = 0.89-0.99) with BW. The PD parameters for inhibition of TXB(2) synthesis were poorly correlated with BW (r(2) = 0.25-0.54) while most of the parameters for inhibition of PGE(2) synthesis lacked any correlation (r(2) approximately 0.05). In conclusion, indirect response models adequately described the time course of sKTP inhibitory effects on synthesis of TXB(2) and PGE(2). Allometrical scaling showed PK parameters to change proportionally to BW, whereas PD parameters had limited ranges and were essentially weight independent.

Prednisolone pharmacokinetics and pharmacodynamics in relation to sex and race.

Prednisolone pharmacokinetics (PK) and pharmacodynamics (PD) were investigated in relation to sex and race in white males, black males, white females, and black females (n = 8/group) after a single oral dose (0.27 mg/kg) of prednisone. The study consisted of baseline and prednisone phases with 32-hour sampling in each phase. Women were studied during the luteal phase of their menstrual cycle. Total and free plasma prednisolone concentrations were assayed by HPLC and ultrafiltration, and pharmacokinetic data were analyzed by compartmental fitting using WinNonlin. Plasma cortisol concentrations were assayed by HPLC; T-helper, T-suppressor lymphocyte, and neutrophil cell counts were determined by FACS and hemocytometry, and these pharmacodynamic data were evaluated by basic and extended indirect response models using ADAPT II. Total body weight-normalized free prednisolone oral clearance and apparent volume of distribution were higher in men compared with women, regardless of race (by 22% in whites and 40% in blacks for oral clearance, p < 0.01; by32% in whites and 38% in blacks for apparent volume of distribution, p < 0.01). The 50% inhibitory concentration (IC50) values for T-suppressor cell-trafficking inhibition were higher in whites than in blacks, regardless of sex (by 125% in men and 208% in women, p < 0.01). The IC50 or SC50 values for effects of prednisolone on cortisol secretion and T-helper lymphocyte or neutrophil trafficking were not statistically different between men and women, blacks and whites. The findings of this study suggest that there are some prednisolone PK/PD differences related to sex and race. However, these differences do not suggest the need for dosage adjustments, and additional experiments with repeat dosing are needed to fully evaluate the clinical implication of these findings.

Effects of oral prasterone (dehydroepiandrosterone) on single-dose pharmacokinetics of oral prednisone and cortisol suppression in normal women.

This study sought to determine effects of multiple dosing of prasterone (DHEA, dehydroepiandrosterone) on the pharmacokinetics of prednisolone and endogenous cortisol secretion. These drugs are likely to be coadministered to patients with systemic lupus erythematosus. Fourteen normal women (ages 30.1 +/- 5.4 years) received single-dose oral prednisone (20 mg) before and after 200 mg/day of oral prasterone for one menstrual cycle (approximately 28 days). Identical assessments, timed to onset of menses, were conducted pretreatment (baseline) and at days 28 and 29 of prasterone treatment and included serum total and free prednisolone, prednisone, DHEA, DHEA-S (dehydroepiandrosterone sulfate), ACTH-stimulated cortisol, and sex hormones and 24-hour urine free cortisol. Pharmacokinetic parameters of prednisolone as assessed by Cmax, t 1/2, AUC, or serum protein binding were not affected by prasterone. The ACTH-stimulated plasma cortisol concentrations were mildly reduced, but 24-hour urinefree cortisol excretion was unchanged during prasterone administration. Serum androstenedione and testosterone increased, while no changes in serum estradiol or estrone occurred. The administration of 200 mg oral prasterone produced serum concentrations of DHEA and DHEA-S significantly greater than endogenous levels. Chronic dosing with 200 mg/day of prasterone did not alter either prednisolone pharmacokinetics or inhibition of cortisol secretion by prednisolone.

Interactions of aspirin and salicylic acid with prednisolone for inhibition of lymphocyte proliferation.

The anti-inflammatory properties of salicylates and prednisolone were investigated using inhibition of in vitro phytohemagglutinin-stimulated lymphocyte proliferation in human whole blood from healthy male and female subjects. Steroids and salicylates are used in conjunction for the treatment of inflammatory disorders such as rheumatoid arthritis and inhibit the proinflammatory transcription factor, NFKB, by different mechanisms. Data generated using various combinations of these drugs were analyzed using isobolograms and the universal surface response approach based on the Loewe additivity principle. The interaction between aspirin and prednisolone was mildly antagonistic while that between salicylic acid and prednisolone was modestly synergistic at therapeutic concentrations. Further, aspirin was slightly more potent in males, but the nature of the steroid-salicylate interaction was similar across genders. This study helps rationalize part of the beneficial effects of steroids and salicylates in treatment of inflammatory disorders.

Approaches to pharmacokinetic/ pharmacodynamic modeling during pregnancy.

The modern approach in the field of pharmacokinetics/pharmacodynamics is the development of models based on the mechanisms of drug action and their alteration of physiologic processes. Such models often require consideration of the input and disposition kinetics of the drug, distribution to sites of action (biophase), processes controlling receptor binding or mediator turnover, mechanisms of drug activity, and signal transduction steps. Responses can often be categorized as: Direct (rapidly or slowly reversible), Indirect (inhibitory or stimulatory), or Irreversible. Further, there may be alterations in the system owing to tolerance, counter-regulation, pathophysiology, or physiological changes such as gender or pregnancy. Mathematical and computational tools are necessary for processing data. This article overviews many available pharmacodynamic models with an indication of the diverse approaches for quantitation of pharmacologic responses. Examples from the literature are illustrated with emphasis on changes occurring in kinetics and dynamics during pregnancy.

Pharmacodynamic modeling of lansoprazole using an indirect irreversible response model.

A mechanism-based pharmacokinetic/pharmacodynamic model was used to assess lansoprazole effects on gastric pH. The irreversible inactivation of the H+/K+-ATPase enzyme by lansoprazole controls the secretion rate of H+ ions and gastric pH values. The basal circadian rhythm of gastric acid production was taken into account as well as the effects of food intake. A model was applied to multiple-dose data from a crossover study of four dosage regimens of lansoprazole in two groups of normal male subjects. Model parameters were estimated by nonlinear regression and were compared to historical values reported in the literature. The predicted mean gastric ion concentration was 23.2 mM (pH 1.6) with the peak time at 12.6 hours (8:30 p.m.), and the half-time for H+ removal from the stomach averaged 1.7 hours. The estimated half-life of gastric food removal was 0.8 hours. The rate constant for normal H+/K+-ATPase degradation was 0.045 h(-1). The pharmacodynamic parameter describing lansoprazole action on gastric acid secretion was the second-order enzyme inactivation constant, which averaged 0.16 microg(-1) x L x h(-1). The parameters obtained for both the baseline and drug treatment data were consistent with the literature and physiologically relevant with the exception of effective food volume, which was large presumably due to buffer effects. The model successfully incorporated the physiological regulation of gastric acid production, the effects of food on gastric acid, and the effects of multiple-dosing regimens of lansoprazole on gastric acid production to give reasonable profiles of gastric pH.

Role of dosage regimen in controlling indirect pharmacodynamic responses.

The role of drug delivery in controlling indirect pharmacodynamic responses was assessed via computer simulations and literature review. Simulations of responses related to basic indirect response mechanisms were performed for various drug input rates which allowed the importance of drug delivery rate on the overall pharmacodynamic response to be evaluated. Response versus time profiles of integrated or net responses and efficiency were examined. Rate of drug input has the greatest influence on the area under the effect curve when doses are larger and target drug concentrations are above the IC(50)/SC(50). The pharmacodynamics of drugs which elicit indirect pharmacologic responses such as corticosteroids, diuretics, growth hormone, erythropoietin and insulin indicate that sustained drug delivery enhances the therapeutic efficiency and pharmacodynamic availability.

Indirect pharmacodynamic models for responses with multicompartmental distribution or polyexponential disposition.

Basic indirect response models where drug alters the production (kin) of the response variable (R) based on the Hill function previously assumed one-compartment distribution of the response variable and simple first-order loss (kout) of R. These models were extended using convolution theory to consideration of two-compartment distribution of R and/or polyexponential loss of R. Theoretical equations and methods of data analysis were developed and simulations are provided to demonstrate expected response behavior based on biexponential response dissipation. The inhibition model was applied to our previous data for inhibition of circadian cortisol secretion by prednisolone. The presence of multicompartment response variables and/or polyexponential loss complicates the response patterns and resolution of pharmacologic parameters of indirect response models and requires careful experimental and data analysis approaches in order to properly evaluate such pharmacodynamic responses. The occurrence of these alternative distribution or disposition components does not alter the area under the effect curve (AUCE) which remains identical to the basic models. Model misselection was addressed by testing fittings comparing the basic and new models. Use of the former for these more complex models does not severely perturb the calculated cardinal dynamic parameters. These models may provide improved insights into indirect responses with complexities in distribution or disposition.

General pharmacokinetic model for drugs exhibiting target-mediated drug disposition.

Drugs that bind with high affinity and to a significant extent (relative to dose) to a pharmacologic target such as an enzyme, receptor, or transporter may exhibit nonlinear pharmacokinetic (PK) behavior. Processes such as receptor-mediated endocytosis may result in drug elimination. A general PK model for characterizing such behavior is described and explored through computer simulations and applications to several therapeutic agents. Simulations show that model predicted plasma concentration vs. time profiles are expected to be polyexponential with steeper distribution phases for lower doses and similar terminal disposition phases. Noncompartmental parameters always show apparent Vss and CL(D) decreasing with dose, but apparent clearance decreases only when the binding process produces drug elimination. The proposed model well captured the time-course of drug concentrations for the aldose reductase inhibitor imirestat, the endothelin receptor antagonist bosentan, and recombinant human interferon-beta 1a. This type of model has a mechanistic basis and considerable utility for fully describing the kinetics for various doses of relevant drugs.

Modeling of dose-response-time data: four examples of estimating the turnover parameters and generating kinetic functions from response profiles.

The most common approach to in vivo pharmacokinetic and pharmacodynamic modeling involves sequential analysis of the plasma concentration versus time and then response versus time data, such that the plasma kinetic model provides an independent function, driving the dynamics. However, response versus time data, even in the absence of measured drug concentrations, inherently contain useful information about the turnover characteristics of response (turnover rate, half-life of response), the drug's biophase kinetics (F, half-life) as well as the pharmacodynamic characteristics (potency, intrinsic activity). Previous analyses have assumed linear kinetics, linear dynamics, no time lag between kinetics and dynamics (single-valued response), and time constant parameters. However, this report demonstrates that the drug effect can be indirect (antinociception, cortisol/adrenocorticotropin (ACTH), body temperature), display nonlinear kinetics, display feedback mechanisms (nonstationarity, cortiso/ACTH) and exhibit hysteresis with the drug levels in the biophase (antinociception, body temperature). It is also demonstrated that crucial determinants of the success of modeling dose-response-time data are the dose selection, multiple dosing, and to some extent different input rates and routes. This report exemplifies the possibility of assigning kinetic forcing functions in pharmacodynamic modeling in both preclinical and clinical studies for the purpose of characterizing (discrimination between turnover and drug-specific parameters) response data and optimizing subsequent clinical protocols, and for identification of inter-individual differences.

Algorithm for application of Fourier analysis for biorhythmic baselines of pharmacodynamic indirect response models.

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate kin(t) and a first-order loss constant kout. If kin(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response Rb(t) to recover the equation for kin(t). Fourier analysis provides an approximate equation for Rb(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for kin(t), yielding the equation involving Rb(t). A computer program was developed to perform the square L2-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate kin(t) using ADAPT II. The pharmacodynamic parameters kout and IC50 were estimated from the model equation with kin(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of kin(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method.

Pharmacokinetics and pharmacodynamics of a humanized monoclonal antibody to factor IX in cynomolgus monkeys.

The pharmacokinetics and pharmacodynamics (PK/PD) of a humanized anti-Factor IX IgG1 monoclonal antibody (SB 249417, FIX mAb) were studied in Cynomolgus monkeys. Single i.v. bolus doses of 1, 3, or 10 mg/kg of FIX mAb were administered. The total FIX mAb concentration, activated partial thromboplastin time (aPTT), and Factor IX activity were monitored for up to 4 weeks after dosing. In the monkey, FIX mAb had a plasma clearance of 0.6 ml/h/kg and a steady-state volume of distribution of approximately 70 ml/kg. The elimination phase half-life (3.8 days) was considerably less than other humanized IgG1 mAbs in the monkey, for which there is no binding to endogenous antigen. The suppression of Factor IX activity and the prolongation of aPTT were rapid and dose dependent. The time for aPTT values to return to basal levels (25-170 h) increased with increasing dose. A mechanism-based PK/PD model consistent with the stoichiometry of binding (2:1) was developed to describe the Factor IX activity and aPTT response time course. The model incorporated Factor IX synthesis and degradation rates that were interrupted by the sequestration of Factor IX by the antibody. aPTT values were related to free Factor IX activity. This model was able to describe the PD profiles from the three dose levels simultaneously. The estimated Factor IX half-life was 11 h and the third-order association rate constant was 3.96 x 10(3) microM(-2) h(-1). The PK/PD modeling was useful in summarizing the major determinants (endogenous and antibody-ligand binding) controlling FIX mAb-related effects.

Immunodynamics of methylprednisolone induced T-cell trafficking and deactivation using whole blood lymphocyte proliferation techniques in the rat.

Glucocorticoids have diverse effects on various components of the immune system and assessment of such activities in vivo often involves complex techniques and numerous animals. We developed a whole blood technique for determining proliferation rate of lymphocytes in minute amounts of rat blood (5 microL as opposed to a whole rat spleen) (Fasanmade AA, Jusko WJ. J Immunol Methods 1995; 184: 163-167). This method was used in assessment of in vivo T-cell deactivation by methylprednisolone (MP). The blockade of this process by the anti-glucocorticoid, RU 40555, also allows measurement of T-lymphocyte trafficking between vascular and extravascular pools. Blood samples were taken over several hours after iv MP administration to adrenalectomized rats, MP concentrations and lympho-proliferative activities were determined ex vivo after mitogen activation with and without blocking MP with RU 40555. MP disposition was mono-exponential with a t(1/2) of 34 min. The pharmacodynamics (PD) of T-cell trafficking was modeled with a physiological indirect model to generate the IC(50) (0.4 ng/mL) for the inhibitory action of MP on return of T-cells to blood as well as cell trafficking rate constants. The overall suppression of blood T-cells was modeled with an equation which accounts directly for inhibition of the proliferation activity of available blood T-cells with an DC(50) of 0.37 ng/mL. MP produced an initial influx of T-cells to blood within 1 h of infusion, a later marked T-cell depletion with a nadir at 4 h, and return to baseline by 9 h. Lymphocyte deactivation occurred within minutes of MP infusion and returned to baseline in 9 h. MP action was prolonged owing to the low IC(50). This approach for assessing dual features of corticosteroid effects on T-cell trafficking and deactivation allows quantitative PK/PD modeling in small animals such as the rat.

Pharmacokinetics and pharmacodynamics of cumulative single doses of inhaled salbutamol enantiomers in asthmatic subjects.

Objectives of this study were to compare the pharmacokinetics, pharmacodynamics and safety of single cumulative doses of active (R)-salbutamol given either as the single enantiomer or racemic mixture by inhalation to subjects with mild to moderate asthma. This was a double-blind, crossover, cumulative-dose, randomized study where all subjects received either four doses of 1.25 mg of (R)-salbutamol or 2.5 mg of racemic (RS-) salbutamol by nebulization. The pharmacokinetic parameters were determined by noncompartmental analysis and model-fitting. Changes in FEV(1), plasma potassium, plasma glucose, heart rate, and QTc interval were measured. The potassium and glucose data were fitted to indirect response pharmacodynamic models. The heart rate and QTc data were evaluated using data descriptors. No significant differences in pharmacokinetics of (R)-salbutamol given as either (R)- or (RS)-salbutamol were found with AUC values of 11.90 +/- 4.37 and 11. 47 +/- 2.88 ng.h/ml. The t(max)of about 2 h reflected serial dosing rather than delayed absorption. The t(1/2)averaged about 3.5 h. The (S)-salbutamol showed AUC of 48.46 +/- 12.11 ng.h/ml with a t(1/2)of about 5 h. The changes in FEV(1)reached a plateau after an initial increase and did not return to pre-drug values for 10 h. All pharmacodynamic parameters were similar whether (R)- or (RS)-salbutamol was given. The exposure to (R)-salbutamol was identical after inhalation of (R) -and (RS)-salbutamol by subjects with asthma. Several pharmacological responses including FEV(1)were also similar and there were no unique safety concerns with either treatment.