A PBPK model for midazolam in four avian species

A physiologically based pharmacokinetic (PBPK) model was developed for midazolam in the chicken and extended to three other species. Physiological parameters included organ weights obtained from 10 birds of each species and blood flows obtained from the literature. Partition coefficients for midazolam in tissues vs. plasma were estimated from drug residue data obtained at slaughter. The avian models include separate compartments for venous plasma, liver, kidney, muscle, fat and all other tissues. An estimate of total body clearance from an earlier in vitro study was used as a starting value in the model, assuming almost complete removal of the parent compound by liver metabolism. The model was optimized for the chicken with plasma and tissue data from a pharmacokinetic study after intravenous midazolam (5 mg/kg) dose. To determine which parameters had the most influence on the goodness of fit, a sensitivity analysis was performed. The optimized chicken model was then modified for the turkey, pheasant and quail. The models were validated with midazolam plasma and tissue residue data in the turkey, pheasant and quail. The PBPK models in the turkey, pheasant and quail provided good predictions of the observed tissue residues in each species, in particular for liver and kidney.     

A physiologically based pharmacokinetic model for the prediction of the depletion of methyl‐3‐quinoxaline‐2‐carboxylic acid,the marker residue of olaquindox,in the edible tissues of pigs

To estimate the consumer exposure to olaquindox (OLA) residues in porcine edible tissues, a physiologically based pharmacokinetic (PBPK) model for methyl‐3‐quinoxaline‐2‐carboxylic acid (MQCA), the marker residue of OLA, was developed in pigs based on the assumptions of the flow‐limited distribution, hepatic metabolism, and renal excretion. The model included separate compartments corresponding to blood, muscle, liver, kidney, adipose, and an extra compartment representing the remaining carcass. Physiological parameters were determined from literatures. Plasma protein binding, partition coefficients, and renal clearance for MQCA were determined in in vitro and in vivo studies. The metabolic conversion of OLA to MQCA was assumed as a simple, one‐step process, and an apparent first‐order rate constant (k) was employed to describe this metabolic process. The PBPK model was optimized and validated with plasma and tissue data from literatures and our study. Sensitivity analysis and Monte Carlo simulation were also implemented to estimate the influence of model parameters on the goodness of fit. When compared with the observed data, the PBPK model underestimated the MQCA level in all compartments at the early time points, whereas gave excellent predictions of MQCA concentration in porcine edible tissues at later time points. The correlation coefficients between the predicted and observed values were over 0.88. The consistency between the model predictions and the real residues of OLA in pigs proved the good applicability of our model in food safety risk assessment.     

Development of a physiologically based pharmacokinetic model to predict tulathromycin distribution in goats

Physiologically based pharmacokinetic (PBPK) models, which incorporate species- and chemical-specific parameters, could be useful tools for extrapolating withdrawal times for drugs across species and doses. The objective of this research was to develop a PBPK model for goats to simulate the pharmacokinetics of tulathromycin, a macrolide antibiotic effective for treating respiratory infections. Model compartments included plasma, lung, liver, muscle, adipose tissue, kidney, and remaining poorly and richly perfused tissues. Tulathromycin was assumed to be 50% protein bound in plasma with first-order clearance. Literature values were compiled for physiological parameters, partition coefficients were estimated from tissue:plasma ratios of AUC, and the remaining model parameters were estimated by comparison against the experimental data. Three separate model structures were compared with plasma and tissue concentrations of tulathromycin in market age goats administered 2.5 mg/kg tulathromycin subcutaneously. The best simulation was achieved with a diffusion-limited PBPK model and absorption from a two-compartment injection site, which allowed for low persistent concentrations at the injection site and slower depletion in the tissues than the plasma as observed with the experimental data. The model with age-appropriate physiological parameters also predicted plasma concentrations in juvenile goats administered tulathromycin subcutaneously. The developed model and compilation of physiological parameters for goats provide initial tools that can be used as a basis for predicting withdrawal times of drugs in this minor species.     

A physiologically based pharmacokinetic model for valnemulin in rats and extrapolation to pigs

A flow-limited, physiologically based pharmacokinetic (PBPK) model for predicting the plasma and tissue concentrations of valnemulin after a single oral administration to rats was developed, and then the data were extrapolated to pigs so as to predict withdrawal interval in edible tissues. Blood/tissue pharmacokinetic data and blood/tissue partition coefficients for valnemulin in rats and pigs were collected experimentally. Absorption, distribution and elimination of the drug were characterized by a set of mass-balance equations. Model simulations were achieved using a commercially available software program. The rat PBPK model better predicted plasma and tissue concentrations. The correlation coefficients of the predicted and experimentally determined values for plasma, liver, kidney, lung and muscle were 0.96, 0.94, 0.96, 0.91 and 0.91, respectively. The rat model parameters were extrapolated to pigs to estimate valnemulin residue withdrawal interval in edible tissues. Correlation (R(2) ) between predicted and observed liver, kidney and muscle were 0.95, 0.97 and 0.99, respectively. Based on liver tissue residue profiles, the pig model estimated a withdrawal interval of 10 h under a multiple oral dosing schedule (5.0 mg/kg, twice daily for 7.5 days). PBPK models, such as this one, provide evidence of the usefulness in interspecies PK data extrapolation over a range of dosing scenarios and can be used to predict withdrawal interval in pigs.     

Physiological parameter values for physiologically based pharmacokinetic models in food-producing animals. Part I: Cattle and swine

Physiologically based pharmacokinetic (PBPK) models for chemicals in food animals are a useful tool in estimating chemical tissue residues and withdrawal intervals. Physiological parameters such as organ weights and blood flows are an important component of a PBPK model. The objective of this study was to compile PBPK-related physiological parameter data in food animals, including cattle and swine. Comprehensive literature searches were performed in PubMed, Google Scholar, ScienceDirect, and ProQuest. Relevant literature was reviewed and tables of relevant parameters such as relative organ weights (% of body weight) and relative blood flows (% of cardiac output) were compiled for different production classes of cattle and swine. The mean and standard deviation of each parameter were calculated to characterize their variability and uncertainty and to allow investigators to conduct population PBPK analysis via Monte Carlo simulations. Regression equations using weight or age were created for parameters having sufficient data. These compiled data provide a comprehensive physiological parameter database for developing PBPK models of chemicals in cattle and swine to support animal-derived food safety assessment. This work also provides a basis to compile data in other food animal species, including goats, sheep, chickens, and turkeys.     

Diffusion‐limited PBPK model for predicting pulmonary pharmacokinetics of florfenicol in pig

For most bacterial lung infections, the concentration of unbound antimicrobial agent in lung interstitial fluid has been thought to be responsible for antimicrobial efficacy. In this study, a diffusion‐limited physiologically based pharmacokinetic (PBPK) model was developed to predict the pulmonary pharmacokinetics of florfenicol (FF) in pigs. The model included separate compartments corresponding to blood, diffusion‐limited lung, flow‐limited muscle, liver, and kidney and an extra compartment representing the remaining carcass. The absorption rate constant and renal and hepatic clearance of FF were determined in vivo. Other parameters were taken from the literature or optimized based on existing pharmacokinetic data. All mathematical operations during the development of the model were performed using acslXtreme version 3.0.2.1 (Aegis Technologies Group, Inc., Huntsville, AL, USA). The model accurately predicted the concentration–time courses of FF in lung interstitial fluid, serum, and plasma following different dosing schedules, except at the dose of 15 mg/kg. When compared with the tissue residue data, the model generally underestimated the FF concentration at the injection site, whereas it gave good predictions of FF concentrations in lung, liver, and kidney at early time points. The model predictions provide a scientific basis for the dosage regimen design of FF.     

In vivo release of oxytetracycline from a biodegradable controlled-release gel injected subcutaneously in Japanese quail (Coturnix coturnix japonica)

A long-acting, biodegradable, controlled-release formulation of oxytetracycline (CR-OTC) was evaluated in 18 adult Japanese quail (Coturnix coturnix japonica) following a single subcutaneous (s.c.) injection. Prior to characterizing the release of oxytetracycline (OTC) from the CR-OTC, the pharmacokinetic parameters of intravenously (i.v.) administered OTC were determined. Concentrations of free OTC were measured using a bioassay. The plasma concentration-time profile of OTC after a single i.v. injection at 20 mg/kg was best fit to an open two-compartmental model, with the following pharmacokinetic parameters: area under the curve (AUC) = 36.72 mg. h/L, terminal elimination half-life = 2.34 h, clearance (Cl) = 0.545 L/kg/h. Plasma [OTC] was >1.0 micro g/mL for at least 4 h following i.v. injection. The CR-OTC gel was well tolerated at a dosage of 1500 mg/kg s.c. Plasma [OTC] rose to >1.0 micro g/mL within 24 h; it remained >1.0 micro g/mL for at least 10 days in all birds sampled at that time point (n = 9) and for at least 18 days in two of nine birds. Using a deconvolution technique, it was determined that approximately 54.8% of the administered OTC was released from the CR-OTC over the 45-day observation period. This long-acting, biodegradable controlled-release OTC formulation may have potential for the treatment of chlamydophila infections and other OTC-sensitive bacteria in Japanese quail, however further studies are necessary to determine its safety and clinical application.     

磺胺二甲嘧啶生理药动学模型种间类推的应用

本研究应用磺胺二甲嘧啶在猪的生理药动学模型来预测其在绵羊体内的动力学过程。利用文献中已经建立的猪的生理模型,采用动物种间类推原理,将模型外推至绵羊,模拟磺胺二甲嘧啶在绵羊体内的血药和组织浓度,并估算可食性组织残留休药期。结果模拟休药期和文献休药期基本趋于一致,表明生理药动学模型种间类推是可行的。     

Serum pharmacokinetics of oxytetracycline in sheep and calves and tissue residues in sheep following a single intramuscular injection of a long-acting preparation

The pharmacokinetics of a long‐acting oxytetracycline (OTC) formulation (Liquamycin® LA‐200®) injected intramuscularly (i.m.) at a dose of 20 mg/kg were determined in four calves and 24 sheep to determine if the approved label dose for cattle provided a similar serum time/concentration profile in sheep. The AUC for the calves was 168±14.6 (μg ? h/mL) and was significantly less than the AUC for sheep (209±43 μg ? h/mL). Using the standard two‐stage approach and a one‐compartment model, the mean Cmax for the calves was 5.2±0.8 μg/mL, and for the sheep was 6.1±1.3 μg/mL. The mean terminal phase rate constants were 0.031 and 0.033 h, and the Vdss were 3.3 and 3.08 L/kg for the calves and sheep respectively. Analysis of the data using the standard two‐stage approach, the naive pooled‐data approach and a population model gave very similar results for both the cattle and sheep data. Sheep tissue residues of OTC in serum, liver, kidney, fat, muscle and injection site were measured at 1, 2, 3, 5, 7 and 14 days after a single i.m. injection of 20 mg/kg OTC. Half‐lives of OTC residues in the tissues were 38.6, 33.4, 28.6, 25.4, 21.3, and 19.9 h for injection site, kidney, muscle, liver, mesenteric fat and renal fat, respectively. The ratio of tissue to serum concentration was fairly consistent at all slaughter times, except for the fat and injection sites. The mean ratios were 1.72, 4.19, 0.11, 0.061, 0.84 and 827 for the liver, kidney, renal fat, mesenteric fat, muscle and injection sites, respectively. The tissue concentrations of OTC residues were below the established cattle tolerances for OTC in liver (6 p.p.m.), muscle (2 p.p.m.) and kidney (12 p.p.m.) by 48 h, and in injection site muscle by 14 days after the single i.m. injection of 20 mg/kg.     

The effects of experimentally induced bronchopneumonia on the pharmacokinetics and tissue depletion of gentamicin in healthy and pneumonic calves

The effects of a bovine bronchopneumonia model on the pharmacokinetics and tissue residue depletion profiles of gentamicin in calves weighing 90-140 kg was explored. Two groups of heifer calves were used. The first was a normal group, while the second group had bronchopneumonia induced. A scoring system was developed to evaluate the extent of disease in the groups. A bimodal distribution of the serum pharmacokinetic parameters in the pneumonic group was caused by the effects of dehydration. When the severely dehydrated calves were omitted from the analysis, serum clearance of gentamicin was significantly higher in the pneumonic group than in the normal group (P less than 0.05). The pharmacokinetic equations used to fit the tissue concentrations varied from tissue to tissue and between groups. Because the best equation of a particular tissue's concentrations varied between groups, withdrawal periods, which are normally determined in healthy animals, may be inappropriate in diseased animals. Addition of several parameters (serum creatinine, serum urea nitrogen, albumin, fibrinogen, and total protein concentrations, white blood cell counts, central fluid volume, volume of distribution at steady state, area under the serum concentration vs time curve, serum clearance, and elimination rate constant) to these tissue-depletion models using multiple regression improved the prediction of a concentration in a given tissue.     

Serum pharmacokinetics and tissue and milk residues of oxytetracycline in goats following a single intramuscular injection of a long-acting preparation and milk residues following a single subcutaneous injection

Separate groups of goats were used to determine drug depletion patterns in serum (n=10), tissue (n=20) and milk (n=8) following a single intramuscular (i.m.) dose of 20 mg/kg of a long-acting oxytetracycline (OTC) formulation (Liquamycin LA-200). Milk residues were also determined following a subcutaneous (s.c.) administration of the same product at the same dose. Serum samples were taken for 24 h post-treatment and tissues (fat, liver, kidney, muscle and injection site) collected at 4, 7, 14, 21 and 28 days following injection. Milk from lactating goats was collected every 12 h for 8 days following both the i.m. and s.c. treatments utilizing an intervening 5-week washout period. Residues in serum and tissue were measured using a microbial inhibition assay, while milk residues were measured using both a microbial inhibition assay and a validated HPLC method. The serum pharmacokinetic parameters of OTC in goats were determined, with a mean AUC=67.4 microg h/mL, mean terminal half-life=14.4 h, and apparent clearance=0.33 L/kg h. Tissue half-lives could not be determined with confidence because the collection times provided only two points at which residues could be measured for most tissues. Oxytetracycline residues in all goat tissue samples measured less then cattle tissue tolerance by 96 h postdosing. One-compartment model describing milk depletion data for i.m. and s.c. dosing had terminal slope half-lives of 20.1 and 36.1 h, respectively. By 96 h post-treatment none of the milk samples contained OTC residues in excess of the cattle milk tolerance (0.3 p.p.m.). For both milk and tissue, the upper-bound 99% confidence intervals for the samples taken from goats 96 h postdosing were lower than approved cow milk and tissue tolerances.     

Investigation of Japanese quail (Coturnix japonica) as a pharmacokinetic model for cockatiels (Nymphicus hollandicus) and Poicephalus parrots via comparison of the pharmacokinetics of a single intravenous injection of oxytetracycline hydrochloride

The purpose of this study was to determine whether Japanese quail (Coturnix japonica) would serve as a pharmacokinetic animal model for two small companion parrots: cockatiels (Nymphicus hollandicus) and Poicephalus parrots. Oxytetracycline (OTC) was the pharmacologic agent chosen for this study as it is eliminated primarily by renal glomerular filtration and undergoes minimal metabolism. A single intravenous injection of 20 mg/kg oxytetracycline hydrochloride was administered to the three study groups and blood samples were obtained at 5, 10, 15, and 30 min post-OTC injection as well as 1, 2, 4, 8, 12 and 24 h post-OTC injection. Quantification of plasma OTC was accomplished using a standardized microbial inhibition assay. Naïve-pooled data (NPD) analysis of the plasma concentration–time profile of OTC best fit a two-compartment open model for all three avian species. Noncompartmental analysis of the mean data yielded the following parameters for quail, cockatiels and Poicephalus parrots respectively: λ_z = 3.14, 4.57, 3.71 h; AUC = 38.9, 42.7, 49.6 μg·h/mL; and Cl = 514, 468, 403 mL/h/kg. Based on the similarity of these pharmacokinetic parameters, it appears that quail could be used as a model species to predict the appropriate OTC dosing regimen for small psittacine birds. A bootstrap procedure was also applied to these sparse data sets for both compartmental and noncompartmental analysis. The bootstrap procedure allowed for the calculation of variability of parameters; however, the estimates of the parameters were very similar to those calculated using the NPD and the data mean values.     

A novel delivery of oxytetracycline in turkey breeder hens.

A novel product (SQ12) for subcutaneous (SQ) injectable delivery of oxytetracycline (OTC) has been developed for use in livestock. SQ12 employs microfluidic spheres encasing OTC crystals, which allows for longer release of the OTC compared with other injectable antibiotics. The objectives of the study were to determine serum and tissue levels of SQ12 in turkey breeder hens to 14 days postinjection and to evaluate effects of SQ12 on reproductive status. Thirty photostimulated hens were housed in litter floor pens and provided with 14.5 hr of light per day in a curtain-sided facility. Six hens served as untreated controls. Twelve hens per treatment group received SQ injections in the neck with SQ12 at 11.4 (L dose group) or 22.7 mg/kg (H dose group) to assess low and high doses, respectively. Serum samples were obtained from each hen at predose and 6, 12, 24, 48, 72, 96, 168, 240, and 336 hr postinjection. All hens were euthanatized at 14 and 15 days postinjection. One-half of the hens in each treatment group were sampled (liver, lung, kidneys, and breast muscle) for tissue residue levels of OTC. The control group had no detectable OTC in serum or tissues at any sample collection time. There were no detectable serum levels of OTC in either treatment group prior to injection. The average serum concentrations of the L and H dose groups showed similar depletion curves although the H dose group was 42% higher at maximum concentration than the L group. Average tissue concentration of OTC for all tissues sampled from the H dose group was twice that of the L dose group. All tissue levels were below the OTC residue tolerance limit. SQ12 provided an extended source of OTC in serum of turkey breeder hens with no effect on reproductive status. SQ12 may provide for a novel treatment of bacterial infection in turkey breeder hens with longer lasting serum levels compared with other single injectable OTC products.     

A comparative study on irritation and residue aspects of five oxytetracycline formulations administered intramuscularly to calves, pigs and sheep

After intramuscular (IM) administration (dose 20 mg/kg) of three 20% (Terramycin/LA (product A), Alamycin LA (product B) and Terralon 20% LA (product C) and two 10% oxytetracycline (OTC) formulations (Engemycin 10% (product D) and Oxyject 10% (product E)), to calves, pigs and sheep, the OTC residue concentrations were determined in organs, muscle, fat, plasma, urine and at the injection sites at 10 days post injection (p.i.). At that time the irritation at the injection site was studied, too. The three 20%-formulations (products A, B, C) and one 10%-formulation (product E) induced considerable local irritation in and between the muscles. This was most pronounced in calves and pigs; in sheep the extent of irritation was limited. Ten days after administration of formulations A, B, C and E, OTC residues were found in organs and the OTC recovery at the injection sites varied widely among the three species. Following IM injection of product D minimal tissue irritation and no OTC residues could be detected at the injection site at 10 days p.i. The differences in local tissue irritation and the residue state of the carcass (including injection site) are related to the various solvent systems used in the formulations.     

Development of a multiroute physiologically based pharmacokinetic model for orbifloxacin in rabbits

To predict the orbifloxacin concentrations in rabbits after multiple routes of administration, a flow‐limited multiroute physiologically based pharmacokinetic (PBPK) model was developed. Three routes of administration (IV, IM, and PO) were incorporated into this model. Physiological parameters including tissue weights and blood flows through different tissues were obtained from the literature. The tissue/plasma partition coefficients (P_Xs) for noneliminating tissues were calculated according to the area method, while the P_Xs for kidney and the rest of the body compartment, together with other parameters for absorption and elimination, were optimized based on the published concentrations. The comparisons between predicted and observed orbifloxacin concentrations proved its validity, and the present model predicted available concentration data well, including those in liver, kidney, muscle, lung, heart, and plasma after oral, intravenous, or intramuscular administration. A local sensitivity analysis was also performed, which showed that the parameters for oral absorption were most influential on the orbifloxacin concentrations. This model was used to predict plasma and tissue concentrations after multiple oral or intramuscular administration. This study demonstrated the feasibility of predicting drug residues in minor species after multiple routes of administration in the extra‐label manner using the PBPK modeling.     

生理药动学模型及其在兽医药理学研究中的应用

生理药动学模型是一种模拟机体循环系统的血液流向,将各器官或组织相互联结起来而建立的整体模型,和经典房室模型与统计矩原理相比,生理模型有其独特的优越性.建立药动学生理模型的主要步骤包括收集资料、设计血流图、建立物质平衡方程组、验证和修订模型.目前,国内外学者已开展了数十种化合物在动物或人体内的生理药动学模型研究.生理模型在开展兽医药动-药效模型研究、指导兽药临床合理应用、指导新兽药的研发、评估兽药残留风险等方面具有良好的应用前景.     

Pharmacokinetics and renal clearance of oxytetracycline after intravenous and intramuscular administration to dairy cows

Following intravenous administration of an oxytetracycline-HC1 and an oxytetracycline-dihydrate formulation to dairy cows, no statistical difference could be found between the pharmacokinetic parameters, derived from the three-compartment model, of these preparations. Urinary recovery was continued for a period of 72 h following intravenous or intramuscular OTC administration. The recovery of OTC in the urine in the 72-h period was in the range of 73% to 96% of the available dose administered. The renal OTC clearance, the renal creatinine clearance, the urinary flow, and the interrelationships of these were determined on the basis of urine and plasma data. The mean OTC renal clearance ranged from 482 to 1050 ml/min and the creatinine clearance from 651 to 1304 ml/min. The OTC and creatinine clearances were significantly correlated to the urine flow up to 30 ml/min. The total body clearance and renal clearance values were of the same order of magnitude, and along with the urine recovery data they provided evidence of predominantly renal route of OTC elimination in dairy cows. The renal OTC elimination is the net result of mainly glomerular filtration, partly tubular secretion, minus reabsorption in the urogenital tract.     

Irritation, bioavailability, and residue aspects of ten oxytetracycline formulations administered intramuscularly to pigs

After intramuscular administration to pigs (dosage 20-35 mg/kg) great differences were found among 10 injectable oxytetracycline (OTC) formulations with respect to irritation and persistence at the injection site and to the residue state of edible tissues. The OTC recovery percentages at the injection site 7-10 days after injection ranged from less than 0.001 to 0.15 per cent for three 10 per cent-formulations and from 0.12 to 20.5 per cent for seven 20 per cent-formulations. The OTC recovery percentage was obvious related to the extent of tissue irritation at the injection site, which was particularly evident for the 20 per cent-formulations. Serious doubt is expressed about advantages of so-called 'long-acting' formulations.     

Pharmacokinetics and renal clearance of oxytetracycline after intravenous and intramuscular administration to dairy cows

Summary

Following intravenous administration of an oxytetracycline‐HC 1 and an oxytetracycline‐dihydrate formulation to dairy cows, no statistical difference could be found between the pharmacokinetic parameters, derived from the three‐compartment model, of these preparations. Urinary recovery was continued for a period of 72 h following intravenous or intramuscular OTC administration.

The recovery of OTC in the urine in the 72‐h period was in the range of 73% to 96% of the available dose administered.

The renal OTC clearance, the renal creatinine clearance, the urinary flow, and the interrelationships of these were determined on the basis of urine and plasma data. The mean OTC renal clearance ranged from 482 to 1050 ml/min and the creatinine clearance from 651 to 1304 ml/min. The OTC and creatinine clearances were significantly correlated to the urine flow up to 30 ml/min. The total body clearance and renal clearance values were of the same order of magnitude, and along with the urine recovery data they provided evidence of predominantly renal route of OTC elimination in dairy cows. The renal OTC elimination is the net result of mainly glomerular filtration, partly tubular secretion, minus reabsorption in the urogenital tract.     

A physiologically based pharmacokinetic model for quinoxaline‐2‐carboxylic acid in rats,extrapolation to pigs

A multi‐compartment physiologically based pharmacokinetic (PBPK) model to describe the disposition of cyadox (CYX) and its metabolite quinoxaline‐2‐carboxylic acid (QCA) after a single oral administration was developed in rats (200 mg/kg b.w. of CYX). Considering interspecies differences in physiology and physiochemistry, the model efficiency was validated by pharmacokinetic data set in swine. The model included six compartments that were blood, muscle, liver, kidney, adipose, and a combined compartment for the rest of tissues. The model was parameterized using rat plasma and tissue concentration data that were generated from this study. Model simulations were achieved using a commercially available software program (ACSLX_Libero version 3.0.2.1). Results supported the validity of the model with simulated tissue concentrations within the range of the observations. The correlation coefficients of the predicted and experimentally determined values for plasma, liver, kidney, adipose, and muscles in rats were 0.98, 0.98, 0.98, 0.99, and 0.95, respectively. The rat model parameters were then extrapolated to pigs to estimate QCA disposition in tissues and validated by tissue concentration of QCA in swine. The correlation coefficients between the predicted and observed values were over 0.90. This model could provide a foundation for developing more reliable pig models once more data are available.