Pharmacokinetic-pharmacodynamic modelling of insulin: comparison of indirect pharmacodynamic response with effect-compartment link models

Evaluating insulindysregulation in horses: A two-step insulin-tolerance test using porcine zinc insulin

In insulin dysregulation, hyperinsulinemia (HI) can be accompanied by peripheral insulin resistance (IR) in horses, which can be diagnosed with an insulin-tolerance test (ITT). The administration of 0.1 IU/kg body weight of recombinant regular human insulin (RHI) should elicit a 50 % reduction of the initial blood glucose concentration at 30 min after insulin administration in insulin sensitive horses. Compared to RHI, porcine zinc insulin (PZI) is veterinary-approved and therefore easier accessible for many practitioners. The aim of this study was to compare the insulin and glucose dynamics during a standard ITT with RHI to an ITT performed with PZI. Twelve Icelandic horses were subjected to an ITT with RHI (ITT-RHI) and with PZI (ITT-PZI) at same dosages in a randomised crossover design. The insulin and glucose dynamics that resulted from these tests were compared, and the consistency of classification into insulin-sensitive and IR categories was evaluated. No complications were observed with the use of either RHI or PZI in ITT. A good correlation of the test results was observed (r = 0.88; P < 0.001). The blood glucose concentrations and the percentage reduction in glucose concentration did not differ significantly between the two tests (P = 0.053), but four out of twelve horses were classified as IR in the ITT-RHI whereas with the ITT-PZI seven out of twelve horses were classified as IR with the 50 % glucose reduction from baseline. Based on the Youden index, when using the ITT-PZI, an adjusted cut-off value for blood glucose reduction of 40 % at 30 min resulted in better test performance. With consideration for the seemingly weaker effect of PZI and the adjusted cut-off value, PZI can be an appropriate substitute to RHI in an ITT.

Population pharmacokinetic modeling of flurbiprofen, the active metabolite of flurbiprofen axetil, in Chinese patients with postoperative pain

Background

Flurbiprofen axetil, a lipid-microsphere-carrier targeting preparation, is a non-steroidal anti-inflammatory drug indicated for the treatment of postoperative pain.

Aim

The aim of the study was to develop a population pharmacokinetic (PPK) model of flurbiprofen, the active metabolite of flurbiprofen axetil, and optimize the treatment of flurbiprofen axetil in Chinese patients.

Methods

A total of 144 therapeutic drug-monitoring samples of flurbiprofen axetil from 72 patients were included in this study. The pharmacologically active metabolite flurbiprofen was used as the analytical target and determined 5–45 minutes after intravenous administration. The PPK model for flurbiprofen was developed using Phoenix NLME 1.3 with a nonlinear mixed-effect model. Bootstrap and visual predictive checks were used simultaneously to validate the final PPK model. Potential covariates of age, sex, body weight, height, and body-mass index were tested for PK parameters.

Results

The PPK model of flurbiprofen was explained by a one-compartment model with first-order elimination, in which a hypothetical-effect compartment was linked to a PK compartment. Population mean values of PK parameters estimated in the final model were θ_Ke=0.0015/h, θ_Vd=7.91 L, and θ_CL=1.55 L/h. Analysis of covariates showed that height and weight influenced the K_e of flurbiprofen. The final model was proved to be robust.

Conclusion

The final PPK model was demonstrated to be appropriate and effective, and can be used to assess the PK parameters of flurbiprofen in Chinese patients with postoperative pain.

Pharmacokinetic-Pharmacodynamic Modeling to Study the Antipyretic Effect of Qingkailing Injection on Pyrexia Model Rats

Qingkailing injection (QKLI) is a modern Chinese medicine preparation derived from a well-known classical formulation, An-Gong-Niu-Huang Wan. Although the clinical efficacy of QKLI has been well defined, its severe adverse drug reactions (ADRs) were extensively increased. Through thorough attempts to reduce ADR rates, it was realized that the effect-based rational use plays the key role in clinical practices. Hence, the pharmacokinetic-pharmacodynamic (PK-PD) model was introduced in the present study, aiming to link the pharmacokinetic profiles with the therapeutic outcomes of QKLI, and subsequently to provide valuable guidelines for the rational use of QKLI in clinical settings. The PK properties of the six dominant ingredients in QKLI were compared between the normal treated group (NTG) and the pyrexia model group (MTG). Rectal temperatures were measured in parallel with blood sampling for NTG, MTG, model control group (MCG), and normal control group (NCG). Baicalin and geniposide exhibited appropriate PK parameters, and were selected as the PK markers to map the antipyretic effect of QKLI. Then, a PK-PD model was constructed upon the bacalin and geniposide plasma concentrations vs. the rectal temperature variation values, by a two-compartment PK model with a Sigmoid Emax PD model to explain the time delay between the drug plasma concentration of PK markers and the antipyretic effect after a single dose administration of QKLI. The findings obtained would provide fundamental information to propose a more reasonable dosage regimen and improve the level of individualized drug therapy in clinical settings.

Pharmacometric Approaches to Guide Dose Selection of the Novel GPR40 Agonist TAK-875 in Subjects With Type 2 Diabetes Mellitus

The G-protein-coupled receptor 40 agonist (GPR40) TAK-875 is being developed as an adjunct to diet and exercise to improve glycemic control in patients with type 2 diabetes mellitus. Pharmacometric approaches such as model-based exposure-response and meta-analyses were applied to (i) characterize exposure/dose–efficacy responses of TAK-875, (ii) characterize the time course of glycosylated hemoglobin A1c (HbA1c) response with TAK-875 6.25 to 200 mg q.d. doses for 12 weeks, (iii) project and compare HbA1c response with dipeptidyl peptidase 4 (DPP-4) inhibitors and TAK-875 up to 24 weeks, and (iv) provide a quantitative rationale for dose selection in phase 3. On the basis of phase 2 data, relationships between TAK-875 concentrations and HbA1c were well characterized by exposure–response models. EC₅₀ and E_max of TAK-875 were estimated to be 3.16 µg/ml and 0.366, respectively. Model-based simulations over 24 weeks indicated that the 25- and 50-mg q.d. doses of TAK-875 achieve efficacy as comparable with or better than that of commonly used antidiabetic agents.

Pharmacokinetic/pharmacodynamic studies on exenatide in diabetic rats

AIM

To quantitatively evaluate the blood glucose-lowering effect of exenatide in diabetic rats.

METHODS

Male Harlan-Sprague-Dawley rats were treated with high-fat diet/streptozotocin to induce type 2 diabetes. After subcutaneous administration of a single dose of exenatide (4.2, 42, or 210 μg/kg), serum exenatide, insulin concentration and blood glucose were measured. The pharmacokinetics of exenatide was characterized by a two-compartment model with first-order absorption. Insulin turnover was characterized by an effect compartment and indirect response combined model. Glucose turnover was described using an indirect response model with insulin (in effect compartment) stimulating glucose disposition and insulin (in insulin compartment) inhibiting glucose production simultaneously. The model parameters were estimated using nonlinear mixed-effects model program. Visual predictive check and model evaluation were used to make assessments.

RESULTS

Exenatide exhibited rapid absorption with k(a)=4.45 h(-1), and the two-compartment model well described its pharmacokinetic profile. For the pharmacodynamic model, exenatide increased insulin release with the estimated S(m1) of 0.822 and SC(50) of 4.02 μg/L. It was demonstrated that insulin stimulated glucose dissipation (S(m2)=0.0513) and inhibited the production of glucose (I(m)=0.0381). Visual predictive check and model evaluation study indicated that a credible model was developed.

CONCLUSION

The glucose-lowering effect of exenatide in diabetic rats is reliably described and predicted by the combined effect compartment/indirect response model.

Pharmacology of intravenous insulin administration: implications for future closed-loop glycemic control by the intravenous/intravenous route

BACKGROUND

Our group is attempting to construct an artificial pancreas based on intravenous glucose monitoring and intravenous insulin delivery. To do so, the pharmacology of intravenous insulin administration must be studied. We used a pig model to determine the inherent lag time in the insulin/blood glucose system. The goal was to suggest a method that reduces the blood glucose level in a rapid and yet predictable manner.

METHODS

Six pigs received continuous intravenous insulin infusions at 0.04, 0.08, or 0.4 IU/kg/h for 60 min. Two pigs received short-term intravenous infusions at 0.4 IU/kg/h for 2 min, repeated five times at 60-min intervals. Four animals received five intravenous insulin bolus injections at 60-min intervals, two at 0.01 IU/kg and two 0.02 IU/kg, with a final dose of 0.04 IU/kg. The blood glucose level was measured every 1-5 min.

RESULTS

A high rate of intravenous insulin infusion led to rapid declines in blood glucose levels. The same rapid decline was achieved when the infusion was halted after 2 min. Using the latter method and with intravenous insulin boluses, blood glucose levels started to rise again after approximately 15-20 min. Insulin boluses led to a first detectable decrease in blood glucose level after 2-6 min and to a maximum rate of decrease shortly thereafter.

CONCLUSIONS

We found that intravenous bolus injections of insulin lowered blood glucose levels rapidly and predictably. Repetitive small intravenous insulin boluses together with an accurate and fast-responding intravascular continuous glucose monitor should be studied as a method of closed-loop glycemic control.

Pharmacokinetic/pharmacodynamic modeling of glucose clamp effects of inhaled and subcutaneous insulin in healthy volunteers and diabetic patients

The pharmacokinetics and pharmacodynamics (PK/PD) of inhaled insulin in humans have not been modeled previously. We rationalized a model for the effects of inhaled insulin on glucose infusion rate during a euglycemic clamp study based on the mechanism of insulin action and compared parameter estimates between subcutaneous and inhaled insulin in healthy and diabetic subjects. Published data from two studies in 11 healthy volunteers and 18 type 1 diabetes patients were digitized. The subjects received four different doses of inhaled insulin and one or three different doses subcutaneously at the start of a 10 h glucose clamp. All data were modeled simultaneously using NONMEM VI. Insulin pharmacokinetics were described by a one-compartment model with one (inhaled) or two (subcutaneous insulin) first-order absorption processes and first-order elimination. Insulin effects on glucose were described by an indirect response model. A biophase direct effect equation for the glucose infusion rate was implemented. Pharmacodynamic parameter estimates were 15.1 mg/min/kg for maximal glucose infusion rate (GIR(max)) and 88.0 mIU/L for SC(50) for diabetic patients and 62.9 mIU/L for healthy subjects. A PK/PD model based on fundamental principles of insulin action and glucose turnover suggests comparable potencies of inhaled and subcutaneous insulin.

Integrated pharmacokinetics and pharmacodynamics in drug development

Drug development is a complex, lengthy and expensive process. Pharmaceutical companies and regulatory authorities have recognised that the drug development process needs optimisation for efficiency in view of the return on investments. Pharmacokinetics and pharmacodynamics are the two main principles determining the relationship between dose and response. This article provides an update on integrated approaches towards drug development by linking pharmacokinetics, pharmacodynamics and disease aspects into mathematical models. Gradually, a transition is taking place from a rather empirical approach towards a modelling- and simulation-based approach to drug development. The main learning phases should be phases 0, I and II, whereas phase III studies should merely have a confirmatory purpose. In model-based drug development, mechanism-based mathematical models, which are iteratively refined along the path of development, incorporate the accumulating knowledge of the investigational drug, the disease and their mutual interference in different subsets of the target population. These models facilitate the design of the next study and improve the probability of achieving the projected efficacy and safety endpoints. In this article, several theoretical and practical aspects of an integrated approach towards drug development are discussed, together with some case studies from different therapeutic areas illustrating the application of pharmacokinetic/pharmacodynamic disease models at different stages of drug development.

Metallokinetic characteristics of antidiabetic bis(allixinato)oxovanadium(IV)-related complexes in the blood of rat

The antidiabetic effect of vanadium is a widely accepted phenomenon; some oxovanadium(IV) complexes have been found to normalize high blood glucose levels in both type 1 and type 2 diabetic animals. In light of the future clinical use of these complexes, the relationship among their chemical structures, physicochemical properties, metallokinetics, and antidiabetic activities must be closely investigated. Recently, we found that among bis(3-hydroxypyronato)oxovanadium(IV) [VO(3hp)(2)] related complexes, bis(allixinato)oxovanadium(IV) [VO(alx)(2)] exhibits a relatively strong hypoglycemic effect in diabetic animals. Next, we examined its metallokinetics in the blood of rats that received five VO(3hp)(2)-related complexes by the blood circulation monitoring-electron paramagnetic resonance method. The metallokinetic parameters were obtained from the blood clearance curves based on a two-compartment model; most parameters, such as area under the concentration curve and mean residence time, correlated significantly with the in vitro insulinomimetic activity in terms of 1/IC(50) (IC(50) is the 50% inhibitory concentration of the complex required for the release of free fatty acids in adipocytes) and the lipophilicity of the complex (log P (com)). The oxovanadium(IV) concentration was significantly higher and the species resided longer in the blood of rats that received VO(alx)(2) than in the blood of rats that received VO(3hp)(2) or bis(kojato)oxovanadium(IV); VO(alx)(2) also exhibited higher log P (com) and 1/IC(50) values. On the basis of these results, we propose that the introduction of lipophilic groups at the C2 and C6 positions of the 3hp ligand is an effective method to enhance the hypoglycemic effect of the complexes, as supported by the observed in vivo exposure and residence in the blood.

Pharmacokinetic-pharmacodynamic modeling of telmisartan using an indirect response model in spontaneously hypertensive rats

AIM

To investigate the pharmacokinetic (PK) and the pharmacodynamic (PD) properties of telmisartan in spontaneously hypertensive (SH) rats using an indirect response and effect-compartment link models, and compare two PK-PD models fitting quality.

METHODS

The SH rats received a single oral dose of 2, 4, and 8 mg/kg of telmisartan. The plasma concentrations of telmisartan were determined by the liquid chromatography-mass spectrum method. The mean arterial blood pressure was measured to characterize the pharmacodynamics of telmisartan by tail-cuff manometry. The relationship for the telmisartan concentration-hypotensive effect in the SH rats was characterized using an indirect response model.

RESULTS

The PK parameters showed dose proportionality, with a long terminal half-life of 16 h, a clearance of 0.15 Lxkg( -1) xh( -1), and a volume of distribution of 5.36 Lxkg( -1) in the study. For the indirect response PD model, the estimated K(in) were 36.6, 34.1, and 32.8 %.h( -1), K(out) were 36.7, 34.6, and 31.9 h( -1); the IC(50) values were 86.2, 95.8, and 91.1 ngxmL( -1); and the area under the effect curve (AUEC) were 762.8, 1490.5, and 2086.2 mmHg.h at three doses, respectively. For the effect-compartment model, the K(eo) were 29.4, 33.8, and 28.7 h( -1); the IC(50) values were 78.2, 85.7, and 80.9 ngxmL(-1), and the AUEC were 781.5, 1602.8, and 2215.7 mmHg.h at three doses, respectively.

CONCLUSION

According to Akaike's information criterion values, the proposed indirect response model provided a more appropriate and good-fitting PK/PD characterization of telmisartan than the effect-compartment link model in SH rats.

Population Pharmacokinetic–Pharmacodynamic Modeling of Subcutaneous and Pulmonary Insulin in Rats

PURPOSE

To develop a population pharmacokinetic-pharmacodynamic (PKPD) model for insulin in rats.

METHODS

Rats were administered insulin either subcutaneously (s.c) (0.26,1.3,2.6 U/kg) or by pulmonary route (spray-instillation (s.i)) (0.26,1.3,2.6,13,26 U/kg). Insulin (0.26,1.3,2.6 U/kg) combined with different combinations of hydroxy methyl amino propionic acid (HMAP: 5,10,16,25 mg/kg) was also administered by spray-instillation. Plasma insulin and glucose concentrations at pre-determined time points were measured. Population pharmacokinetic-pharmacodynamic modeling was performed using NONMEM.

RESULTS

Insulin exhibited dose-disproportional PK across formulations and routes of administration. The kinetic model suggested monoexponential disposition with simultaneous first order (64%-dimeric form of insulin) - zero order (36%-hexameric form of insulin) absorption. Maximum relative bioavailability (relative to s.c - 0.26 U/kg) of spray-instilled insulin was 46%. Addition of HMAP increased the relative bioavailability of insulin administered via spray-instilled route by 40%. The insulin-glucose relationship was characterized using an indirect response model, wherein, insulin stimulation of glucose uptake into muscle cells was assumed. The basal zero order production rate of glucose (k(G, prod)) was estimated as 0.98 mg/dl/min. The SC50 was fixed at 80 mu U/ml based on literature reports and the S(max) was estimated to be 6.

CONCLUSIONS

The proposed PKPD model satisfactorily describes insulin disposition and glucose concentrations across range of doses with and without HMAP.