New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants.

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new "Gamma isotherms" are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global "Gamma-Langmuir" isotherm retrieves Henry's law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global "Gamma-Hill" isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions.

Enhanced Sorption Performance of Natural Zeolites Modified with pH-Fractionated Humic Acids for the Removal of Methylene Blue from Water.

This work explores the effect of humic acids (HA) fractionation on the sorption ability of a natural zeolite (NYT)-HA adduct. HA were extracted from compost, fractionated via the pH fractionation method, and characterized via UV-Vis spectroscopy and gel permeation chromatography. The HA samples were immobilized onto NYT via thermal treatment. The resulting adducts (NYT-HA) were tested for their ability to remove methylene blue (MB) from an aqueous solution. It was found that the sorption performance of NYT-HA strongly depends on the chemical characteristics of humic acids. Sorption capacity increased with the molecular weight and hydrophobicity degree of the HA fractions. Hydrophobic and π-π interactions are likely the primary mechanisms by which MB interacts with HA. The sorption kinetic data conform to the pseudo-second-order model. The Freundlich isotherm model adequately described the sorption equilibrium and revealed that the uptake of MB onto NYT-HA is endothermic in nature.

Mycophenolate Mofetil Dose Adjustment in Pediatric Kidney Transplant Recipients.

BACKGROUND: The Immunosuppressant Bayesian Dose Adjustment web site aids clinicians and pharmacologists involved in the care of transplant recipients; it proposes dose adjustments based on the estimated area under the concentration-time curve (AUCs). Three concentrations (T 20 min , T 1 h , and T 3 h ) are sufficient to estimate mycophenolic acid (MPA) AUC 0-12 h in pediatric kidney transplant recipients. This study investigates mycophenolate mofetil (MMF) doses and MPA AUC values in pediatric kidney transplant recipients, and target exposure attainment when the proposed doses were followed, through a large-scale analysis of the data set collated since the inception of the Immunosuppressant Bayesian Dose Adjustment web site. METHODS: In this study, 4051 MMF dose adjustment requests, corresponding to 1051 patients aged 0-18 years, were retrospectively analyzed. AUC calculations were performed in the back office of the Immunosuppressant Bayesian Dose Adjustment using published Bayesian and population pharmacokinetic models. RESULTS: The first AUC request was posted >12 months posttransplantation for 41% of patients. Overall, only 50% had the first MPA AUC 0-12 h within the recommended 30-60 mg.h/L range. When the proposed dose was not followed, the proportion of patients with an AUC in the therapeutic range for MMF with cyclosporine or tacrolimus at the subsequent request was lower (40% and 45%, respectively) than when it was followed (58% and 60%, respectively): P = 0.08 and 0.006, respectively. Furthermore, 3 months posttransplantation, the dispersion of AUC values was often lower at the second visit when the proposed doses were followed, namely, P = 0.03, 0.003, and 0.07 in the 4 months-1 year, and beyond 1 year with <6-month or >6-month periods between both visits, respectively. CONCLUSIONS: Owing to extreme interindividual variability in MPA exposure, MMF dose adjustment is necessary; it is efficient at reducing such variability when based on MPA AUC.

Yesterday, Today, and Tomorrow. Evolution of a Sleeping Beauty: The Freundlich Isotherm.

The name of Herbert Freundlich is commonly associated with a power relationship for adsorbed amount of a substance (Cads) against the concentration in solution (Csln), such that Cads = KCslnn; this isotherm (together with the Langmuir isotherm) is considered to be the model of choice for correlating the experimental adsorption data of micropollutants or contaminants of emerging concern (pesticides, pharmaceuticals, and personal care products), but it also concerns the adsorption of gases on solids. However, Freundlich's 1907 paper was a "sleeping beauty", which only started to attract significant citations from the early 2000s onward; moreover, these citations were too often wrong. In this paper, the main steps in the historical developments of Freundlich isotherm are identified, along with a discussion of several theoretical points: (1) derivation of the Freundlich isotherm from an exponential distribution of energies, leading to a more general equation, based on the Gauss hypergeometric function, of which the power Freundlich equation is an approximation; (2) application of this hypergeometric isotherm to the case of competitive adsorption, when the binding energies are perfectly correlated; and (3) new equations for estimating the Freundlich coefficient KF from physicochemical properties such as the sticking surface or probability. From new data treatment of two examples from the literature, the influence of several parameters is highlighted, and the application of linear free-energy relationships (LFER) to the Freundlich parameters for different series of compounds is evoked, along with its limitations. We also suggest some ideas that may be worth exploring in the future, such as extending the range of applications of the Freundlich isotherm by means of its hypergeometric version, extending the competitive adsorption isotherm in the case of partial correlation, and exploring the interest of the sticking surfaces or probabilities instead of KF for LFER analysis.

Machine learning algorithms to estimate everolimus exposure trained on simulated and patient pharmacokinetic profiles.

Everolimus is an immunosuppressant with a small therapeutic index and large between-patient variability. The area under the concentration versus time curve (AUC) is the best marker of exposure but measuring it requires collecting many blood samples. The objective of this study was to train machine learning (ML) algorithms using pharmacokinetic (PK) profiles from kidney transplant recipients, simulated profiles, or both types, and compare their performance for everolimus AUC0-12h estimation using a limited number of predictors, as compared to an independent set of full PK profiles from patients, as well as to the corresponding maximum a posteriori Bayesian estimates (MAP-BE). XGBoost was first trained on 508 patient interdose AUCs estimated using MAP-BE, and then on 500-10,000 rich interdose PK profiles simulated using previously published population PK parameters. The predictors used were: predose, ~1 h, and ~2 h whole blood concentrations, differences between these concentrations, relative deviations from theoretical sampling times, morning dose, patient age, and time elapsed since transplantation. The best results were obtained with XGBoost trained on 5016 simulated profiles. AUC estimation achieved in an external dataset of 114 full-PK profiles was excellent (root mean squared error [RMSE] = 10.8 µg*h/L) and slightly better than MAP-BE (RMSE = 11.9 µg*h/L). Using more profiles (n = 10,035) did not improve the ML algorithm performance. The contribution of mixing patient and simulated profiles was significant only when they were in balanced numbers, with ~500 for each (RMSE = 12.5 µg*h/L), compared with patient data alone (RMSE = 18.0 µg*h/L).

Mycophenolic Acid Exposure Prediction Using Machine Learning.

Therapeutic drug monitoring of mycophenolic acid (MPA) based on area under the curve (AUC) is well-established and machine learning (ML) approaches could help to estimate AUC. The aim of this work is to estimate the AUC of MPA in organ transplant patients using extreme gradient boosting (Xgboost R package) ML models. A total of 12,877 MPA AUC from 0 to 12 hours (AUC0-12 h ) requests from 6,884 patients sent to our Immunosuppressant Bayesian Dose Adjustment expert system (https://abis.chu-limoges.fr) for AUC estimation and dose recommendation based on MPA concentrations measured at least at three sampling times (~ 20 minutes, 1 and 3 hours after dosing) were used to develop two ML models based on two or three concentrations. Data were split into a training set (75%) and a test set (25%) and the Xgboost models in the training set with the lowest root mean squared error (RMSE) in a 10-fold cross-validation experiment were evaluated in the test set and in 4 independent full-pharmacokinetic (PK) datasets from renal or heart transplant recipients. ML models based on two or three concentrations, differences between these concentrations, relative deviations from theoretical times of sampling, presence of a delayed absorption peak, and five covariates (dose, type of transplantation, associated immunosuppressant, age, and time between transplantation and sampling) yielded accurate AUC estimation performances in the test datasets (relative bias < 5% and relative RMSE < 20%) and better performance than MAP Bayesian estimation in the four independent full-PK datasets. The Xgboost ML models described allow accurate estimation of MPA AUC0-12 h and can be used for routine exposure estimation and dose adjustment and will soon be implemented in a dedicated web interface.

Clinical Pharmacokinetics and Bayesian Estimators for the Individual Dose Adjustment of a Generic Formulation of Tacrolimus in Adult Kidney Transplant Recipients.

BACKGROUND: Tacrolimus has a narrow therapeutic range and requires dose adjustment, usually based on the trough blood concentration but preferably on the area under the concentration-time curve over 12 h post-dose (AUC0-12h). The single-arm, multicentre, clinical study IMPAKT aimed: (i) to develop, in de novo kidney transplant recipients, pharmacokinetic models and maximum a-posteriori Bayesian estimators for a generic, immediate-release, oral formulation of tacrolimus to estimate tacrolimus AUC0-12h at different post-transplant periods using a limited sampling strategy, and considering the CYP3A5*3 polymorphism as a covariate and (ii) to compare the performance of these Bayesian estimators to those previously developed for the original formulation. METHODS: Thirty patients were enrolled and 29 provided nine blood samples over 9 h at day 7 and months 1 and 3 post-transplant. Tacrolimus blood profiles measured with liquid chromatography-tandem mass spectrometry were modelled using one-compartment, double gamma absorption, linear elimination models developed in-house. Different limited sampling strategies of three time-points within 4 h post-dose were tested for the maximum a-posteriori Bayesian estimator of tacrolimus AUC0-12h. The models and estimators were validated internally and their performance compared to that of models previously developed for the original formulation. RESULTS: The concentration-time curves, AUC0-12h/dose and trough blood concentration/dose exhibited wide inter-individual variability. The covariate-free pharmacokinetic models developed for the three post-transplant periods closely fitted the individual profiles. Maximum a-posteriori Bayesian estimators based on three different limited sampling strategies and no covariate yielded accurate AUC0-12h estimates, including for the five cytochrome P450 3A5 expressers and for the four patients without corticosteroids. The 0-1 h-3 h strategy finally chosen had very low bias (- 4.0 to - 2.5%) and imprecision (root mean square error 5.5-9.2%). The maximum a-posteriori Bayesian estimators previously developed for the reference product fitted the generic profiles with similar performance. CONCLUSIONS: We developed original pharmacokinetic models and accurate maximum a-posteriori Bayesian estimators to estimate patient exposure and adjust the dose of generic tacrolimus, and confirmed that the robust tools previously developed for the original formulation can be applied to this generic.

Tacrolimus Exposure Prediction Using Machine Learning.

The aim of this work is to estimate the area-under the blood concentration curve of tacrolimus (TAC) following b.i.d. or q.d. dosing in organ transplant patients, using Xgboost machine learning (ML) models. A total of 4,997 and 1,452 TAC interdose area under the curves (AUCs) from patients on b.i.d. and q.d. TAC, sent to our Immunosuppressant Bayesian Dose Adjustment expert system (www.pharmaco.chu-limoges.fr/) for AUC estimation and dose recommendation based on TAC concentrations measured at least at 3 sampling times (predose, ~ 1 and 3 hours after dosing) were used to develop 4 ML models based on 2 or 3 concentrations. For each model, data splitting was performed to obtain a training set (75%) and a test set (25%). The Xgboost models in the training set with the lowest root mean square error (RMSE) in a 10-fold cross-validation experiment were evaluated in the test set and in 6 independent full-pharmacokinetic (PK) datasets from renal, liver, and heart transplant patients. ML models based on two or three concentrations, differences between these concentrations, relative deviations from theoretical times of sampling, and four covariates (dose, type of transplantation, age, and time between transplantation and sampling) yielded excellent AUC estimation performance in the test datasets (relative bias < 5% and relative RMSE < 10%) and better performance than maximum a posteriori Bayesian estimation in the six independent full-PK datasets. The Xgboost ML models described allow accurate estimation of TAC interdose AUC and can be used for routine TAC exposure estimation and dose adjustment. They will soon be implemented in a dedicated web interface.

Tacrolimus Bayesian Dose Adjustment in Pediatric Renal Transplant Recipients.

BACKGROUND: Immunosuppressant Bayesian Dose Adjustment (ISBA) is an online expert system that estimates the area under the curve (AUC) of immunosuppressive drugs through pharmacokinetic modelling and Bayesian estimation to propose dose adjustments to reach predefined exposure targets. The ISBA database was retrospectively analyzed to describe tacrolimus pharmacokinetics and exposure, evaluate the efficiency of ISBA dose recommendations, and propose tacrolimus AUC0-12h target ranges for pediatric renal allograft recipients treated with immediate release tacrolimus. METHODS: The database included 1935 tacrolimus dose adjustment requests from 419 patients <19 years old who were treated with immediate-release tacrolimus and followed in 21 French hospitals. The tacrolimus exposure evolution with patient age and posttransplantation time, the correlation between trough tacrolimus concentration (C0) and AUC0-12h at different periods posttransplantation, and the efficiency of dose recommendations to avoid underexposure and overexposure and to decrease between-patient AUC variability were investigated. RESULTS: Tacrolimus AUC showed large between-patient variability (CV% = 40%) but moderate within-patient variability (median = 24.3% over a 3-month period). Dose-standardized exposure but not the AUC/C0 ratio significantly decreased with time posttransplantation and patient age. We derived AUC0-12h ranges from the consensual C0 ranges using linear regression equations. When the ISBA recommended dose was applied, the AUC distribution was narrower and a significantly higher proportion was within the targets (P < 0.0001). CONCLUSIONS: ISBA efficiently reduced tacrolimus underexposure and overexposure. The AUC0-12h target ranges for pediatric patients derived from the database were similar to those previously reported for adults. Estimating the AUC/C0 ratio could help determine personalized C0 targets.

Fasting Status and Circadian Variation Must be Considered When Performing AUC-based Therapeutic Drug Monitoring of Tacrolimus in Renal Transplant Recipients.

Therapeutic drug monitoring (TDM) is mandatory for the immunosuppressive drug tacrolimus (Tac). For clinical applicability, TDM is performed using morning trough concentrations. With recent developments making tacrolimus concentration determination possible in capillary microsamples and Bayesian estimator predicted area under the concentration curve (AUC), AUC-guided TDM may now be clinically applicable. Tac circadian variation has, however, been reported, with lower systemic exposure following the evening dose. The aim of the present study was to investigate tacrolimus pharmacokinetic (PK) after morning and evening administrations of twice-daily tacrolimus in a real-life setting without restrictions regarding food and concomitant drug timing. Two 12 hour tacrolimus investigations were performed; after the morning dose and the following evening dose, respectively, in 31 renal transplant recipients early after transplantation both in a fasting-state and under real-life nonfasting conditions (14 patients repeated the investigation). We observed circadian variation under fasting-conditions: 45% higher peak-concentration and 20% higher AUC following the morning dose. In the real-life nonfasting setting, the PK-profiles were flat but comparable after the morning and evening doses, showing slower absorption rate and lower AUC compared with the fasting-state. Limited sampling strategies using concentrations at 0, 1, and 3 hours predicted AUC after fasting morning administration, and samples obtained at 1, 3, and 6 hours predicted AUC for the other conditions (evening and real-life nonfasting). In conclusion, circadian variation of tacrolimus is present when performed in patients who are in the fasting-state, whereas flatter PK-profiles and no circadian variation was present in a real-life, nonfasting setting.

Pharmacogenetic-Whole blood and intracellular pharmacokinetic-Pharmacodynamic (PG-PK2-PD) relationship of tacrolimus in liver transplant recipients.

Tacrolimus (TAC) is the cornerstone of immunosuppressive therapy in liver transplantation. This study aimed at elucidating the interplay between pharmacogenetic determinants of TAC whole blood and intracellular exposures as well as the pharmacokinetic-pharmacodynamic relationship of TAC in both compartments. Complete pharmacokinetic profiles (Predose, and 20 min, 40 min, 1h, 2h, 3h, 4h, 6h, 8h, 12h post drug intake) of twice daily TAC in whole blood and peripheral blood mononuclear cells (PBMC) were collected in 32 liver transplanted patients in the first ten days post transplantation. A non-parametric population pharmacokinetic model was applied to explore TAC pharmacokinetics in blood and PBMC. Concurrently, calcineurin activity was measured in PBMC. Influence of donor and recipient genetic polymorphisms of ABCB1, CYP3A4 and CYP3A5 on TAC exposure was assessed. Recipient ABCB1 polymorphisms 1199G>A could influence TAC whole blood and intracellular exposure (p<0.05). No association was found between CYP3A4 or CYP3A5 genotypes and TAC whole blood or intracellular concentrations. Finally, intra-PBMC calcineurin activity appeared incompletely inhibited by TAC and less than 50% of patients were expected to achieve intracellular IC50 concentration (100 pg/millions of cells) at therapeutic whole blood concentration (i.e.: 4-10 ng/mL). Together, these data suggest that personalized medicine regarding TAC therapy might be optimized by ABCB1 pharmacogenetic biomarkers and by monitoring intracellular concentration whereas the relationship between intracellular TAC exposure and pharmacodynamics biomarkers more specific than calcineurin activity should be further investigated.

Population pharmacokinetics and Bayesian estimators for intravenous mycophenolate mofetil in haematopoietic stem cell transplant patients.

AIMS: Intravenous mycophenolate mofetil (IV MMF), a prodrug of mycophenolic acid (MPA), is used during nonmyeloablative and reduced-intensity conditioning haematopoetic stem cell transplantation (HCT) to improve engraftment and reduce graft-versus-host disease. The aims of this study were to develop population pharmacokinetic models and Bayesian estimators based on limited sampling strategies to allow for individual dose adjustment of intravenous mycophenolate mofetil administered by infusion in haematopoietic stem cell transplant patients. METHODS: Sixty-three MPA concentration-time profiles (median [min-max] = 6 [4-7] samples) were collected from 34 HCT recipients transplanted for 14 (1-45) days and administered IV MMF every 8 hours, concomitantly with cyclosporine. The database was split into development (75%) and validation (25%) datasets. Pharmacokinetic models characterized by a single compartment with first-order elimination, combined with two gamma distributions to describe the transformation of MMF into mycophenolic acid, were developed using in parallel nonparametric (Pmetrics) and parametric (ITSIM) approaches. The performances of the models and the derived Bayesian estimators were evaluated in the validation set. RESULTS: The best limited sampling strategy led to a bias (min, max), root mean square error between observed and modeled interdose areas under the curve in the validation dataset of -11.72% (-31.08%, 5.00%), 14.9% for ITSIM and -2.21% (-23.40%, 30.01%), 12.4% for Pmetrics with three samples collected at 0.33, 2 and 3 hours post dosing. CONCLUSION: Population pharmacokinetic models and Bayesian estimators for IV MMF in HCT have been developed and are now available online (https://pharmaco.chu-limoges.fr) for individual dose adjustment based on the interdose area under the curve.

Population pharmacokinetic model and Bayesian estimator for 2 tacrolimus formulations in adult liver transplant patients.

AIMS: Tacrolimus is a narrow therapeutic range drug that requires fine dose adjustment, for which pharmacokinetic (PK) models have been amply proposed in renal, but not in liver, transplant recipients. This study aimed to build population PK models and Bayesian estimators (BEs) in adult de novo liver transplant patients receiving either the immediate-release (Prograf, twice daily, TD) or prolonged-release (Advagraf, once daily, OD) forms to help PK-guided dose individualization. METHODS: In total, 160 tacrolimus concentration-time profiles (1654 samples) were collected from 80 patients, at day 7 (D7) and week 6 (W6) post-transplant. Four population PK models were developed using in-parallel parametric and nonparametric approaches for each formulation and period post-transplant. The best limited sampling strategies for estimating the area-under-the-curve (AUC) were selected by comparing predicted values to an independent dataset. Finally, the doses required to reach AUC targets were estimated using each BE and compared to the doses obtained using the trapezoidal AUC. RESULTS: Tacrolimus PK was best described using a 1-compartmental model with first-order elimination and 2 γ-distributions to describe the absorption. In the validation datasets, Bayesian AUC estimates yielded mean bias/root mean squared prediction error of −5.06%/13.43% (OD D7), 2.25%/8.51% (OD W6), −2.36%/7.27% (TD D7) and 0.87%/9.07% (TD W6) for the in-parallel parametric approach; and 8.95%/17.84% (OD D7), −0.11%/10.13% (OD W6), 3.57%/18.40% (TD D7) and 4.48%/12.59% (TD W6) for the nonparametric approach. CONCLUSION: The BEs and limited sampling strategies proposed here are able to predict accurately and precisely tacrolimus AUC in liver patients using only 3 plasma concentrations. The dosing methods are available on our ImmunoSuppressive Bayesian dose Adjustment website (www.pharmaco.chu-limoges.fr).

A Limited Sampling Strategy to Estimate Exposure of Everolimus in Whole Blood and Peripheral Blood Mononuclear Cells in Renal Transplant Recipients Using Population Pharmacokinetic Modeling and Bayesian Estimators.

BACKGROUND AND OBJECTIVE: Intracellular exposure of everolimus may be a better marker of therapeutic effect than trough whole blood concentrations. We aimed to develop pharmacokinetic population models and Bayesian estimators based on a limited sampling strategy for estimation of dose interval exposures of everolimus in whole blood and peripheral blood mononuclear cells (PBMCs) in renal transplant recipients. METHODS: Full whole blood and PBMC concentration-time profiles of everolimus were obtained from 12 stable renal transplant recipients on two different occasions, 4 weeks apart. The dataset was treated as 24 individual profiles and split into a development dataset (n = 20) and a validation dataset (n = 4). The pharmacokinetic model was developed using non-parametric modeling and its performances and those of the derived Bayesian estimator were evaluated in the validation set. RESULTS: A structural two-compartment model with first-order elimination and two absorption phases described by a sum of two gamma distributions were developed. None of the tested covariates (age, sex, albumin, hematocrit, fat-free mass and genetic variants such as CYP3A5*1, ABCB1 haplotype, PPARA*42, PPARA*48, and POR*28) were retained in the final model. A limited sampling schedule of two whole blood samples at 0 and 1.5 h and one PBMC sample at 1.5 h post dose provided accurate estimates of the area under the plasma concentration-time curve (AUC) in comparison with the trapezoidal reference AUC (relative bias ± standard deviation = - 3.9 ± 10.6 and 4.1 ± 12.3% for whole blood and PBMC concentrations, respectively). CONCLUSION: The developed model allows simultaneous and accurate prediction of everolimus exposure in whole blood and PBMCs, and supplies a base for a feasible exploration of the relationships between intracellular exposure and therapeutic effects in prospective trials.

Pharmacokinetic models to assist the prescriber in choosing the best tacrolimus dose.

Due to a high inter-individual variability in its pharmacokinetics, tacrolimus dose individualization is mandatory. Even though the expert opinion has defined the area under the curve (AUC) as the best marker to use when performing dose adjustment of tacrolimus, most centres only use trough levels. Multiple targets have been proposed for this parameter and physicians rely largely on their personal experience when making a decision about dose adjustment. Several population pharmacokinetics models (POPPK) allowing AUC determination have been developed, but only a few are actually used in routine practice for dose individualization. These POPPK models can also be used to perform Monte Carlo simulations that help to establish different dosing rules or to anticipate the pharmacokinetics of tacrolimus in particular populations, without conducting clinical trials. Various available applications of POPPK models to assist the prescriber in choosing the best tacrolimus dose are discussed in this paper as well as the difficulties in introducing them into routine therapeutic drug monitoring.

Population Pharmacokinetics and Bayesian Estimators for Refined Dose Adjustment of a New Tacrolimus Formulation in Kidney and Liver Transplant Patients.

BACKGROUND AND OBJECTIVES: A new once-daily formulation of tacrolimus (Envarsus®) has recently been developed, with alleged different pharmacokinetics from previous tacrolimus formulations. The objectives of this study were to develop population pharmacokinetic models and Bayesian estimators based on limited sampling strategies for Envarsus® in kidney and liver transplant recipients. MATERIALS AND METHODS: Full tacrolimus concentration-time profiles (13 samples) were drawn from 57 liver (113 profiles) and 49 kidney (97 profiles) graft recipients transplanted for at least 6 months and switched from Prograf® to Envarsus®. The two databases were split into a development (75%) and a validation (25%) dataset. Pharmacokinetic models characterised by a single compartment with first-order elimination and absorption in two phases described by a sum of two gamma distributions were developed using non-parametric (Pmetrics) and parametric (ITSIM) approaches in parallel. The best limited sampling strategy for each patient group was determined using the multiple model optimal algorithm. The performance of the models and derived Bayesian estimators was evaluated in the validation set. RESULTS: The best limited sampling strategy was 0, 8 and 12 h post-dose, leading to a relative bias ± standard deviation (root-mean-square error) between observed and modelled inter-dose area under the curve in the validation dataset of: 0.32 ± 6.86% (6.87%) for ITSIM and 3.4 ± 13.4% (13.2%) for Pmetrics in kidney transplantation; and 0.89 ± 7.32% (7.38%) for ITSIM and -2.62 ± 8.65% (8.89%) for Pmetrics in liver transplantation. CONCLUSION: Population pharmacokinetic models and Bayesian estimators for Envarsus® in kidney and liver transplantation were developed and are now available online for area under the curve-based tacrolimus dose adjustment.

A Time-Dependent Model Describes Methotrexate Elimination and Supports Dynamic Modification of MRP2/ABCC2 Activity.

BACKGROUND: Multidrug resistance protein-2 encoded by the ABCC2 gene (MRP2/ABCC2), an efflux transporter expressed at the proximal renal tubule, is rate-limiting for urine excretion of coproporphyrin (UCP) isomers I and III, translating in high UCP [I/(I + III)] ratio in MRP2-deficient patients presenting with the Dubin-Johnson Syndrome. MRP2 is also a major contributor to methotrexate (MTX) clearance. As MTX is both a substrate and an inhibitor of MRP2, time course of the concentrations of MTX in blood could induce functional modification of MRP2 over time, which in turn can modify its own elimination rate. METHODS: A 3-parameter time-dependent MTX population pharmacokinetic (PK) model based on a power function accounting for nonlinearity in its clearance was developed using Pmetrics in a first cohort of 41 patients (76 PK profiles) and compared with a previously published 2-compartment model developed with NONMEM and a 3-compartment model developed with ITSIM. In a second cohort (62 patients and 62 PK profiles), the association between the UCP [I/(I + III)] ratio at 3 periods [before MTX administration (P1), at the end of infusion (P2), and at hospital discharge (P3)] and the time-dependent PK parameters of MTX was investigated. Effects of genetic polymorphisms and of coadministered drugs were also studied. RESULTS: The model developed tightly fitted the data in both cohorts. A significant inverse correlation was found between log (k1) (ie, the rate constant explaining MTX concentration decrease) and the difference in UCP [I/(I + III)] ratio between P3 and P2 (DP3) (ß ± SD = -0.025 ± 0.008, P = 0.00443). CONCLUSIONS: Self-inhibition of the MRP2-dependent secretion of MTX is a plausible explanation for the time-dependent PKs of this drug. Additional studies specifically designed to evaluate this hypothesis are required.

Modeling of Tacrolimus Exposure in Kidney Transplant According to Posttransplant Time Based on Routine Trough Concentration Data.

OBJECTIVES: The aim of this study was to develop a pharmacokinetics model allowing the description of the evolution of tacrolimus exposure in kidney transplant patients over the first months after transplant, using trough concentrations of routinely collected blood. MATERIALS AND METHODS: The authors performed a retrospective analysis of trough concentration data collected from adult kidney transplant recipients (from 2008 to 2013). The total data set was divided into a building data set, used to build the structural model, and a validation data set, used to validate the structural model. (C0 = 133; 26 patients). A pharmacokinetics analysis was carried out by applying a nonparametric adaptive grid approach. The structural model parameters were tacrolimus clearance and volume of distribution. RESULTS: In patients in the building set group, estimated clearance was 3.6 ± 0.57 L/h and estimated volume of distribution was 9.9 ± 1.14 L. No covariate was significantly associated with tacrolimus clearance or volume of distribution. The model adequately described tacrolimus dose-normalized trough concentration evolution after transplant (the plot of individual model predicted versus observed concentrations resulted in r = 0.84). The prediction performance in the validation group yielded 2.3% mean prediction error and 21.4% root mean squared error. CONCLUSIONS: This model could be highly useful in the optimization of tacrolimus prescription at any posttransplant time in kidney transplant patients.

Pharmacokinetic tools for the dose adjustment of ciclosporin in haematopoietic stem cell transplant patients.

AIMS: Ciclosporin A (CsA) is used in the prophylaxis and treatment of acute and chronic graft vs. host disease after haematopoietic stem cell (HSCT) transplantation. Our objective was to build and compare three independent Bayesian estimators of CsA area under the curve (AUC) using a limited sampling strategy (LSS), to assist in dose adjustment. METHODS: The Bayesian estimators were developed using in parallel: two independent parametric modelling approaches (nonmem® and iterative two stage (ITS) Bayesian modelling) and the non-parametric adaptive grid method (Pmetrics®). Seventy-two full pharmacokinetic profiles (at pre-dose and 0.33, 0.66, 1, 2, 3, 4, 6, 8 and 12h after dosing) collected from 40 HSCT patients given CsA were used to build the pharmacokinetic models, while 15 other profiles (n = 7) were kept for validation. For each Bayesian estimator, AUCs estimated using the full profiles were compared with AUCs estimated using three samples. RESULTS: The pharmacokinetic profiles were well fitted using a two compartment model with first order elimination, combined with a gamma function for the absorption phase with ITS and Pmetrics or an Erlang distribution with nonmem. The derived Bayesian estimators based on a C0-C1 h-C4 h sampling schedule (best LSS) accurately estimated CsA AUC(0,12 h) in the validation group (n = 15; nonmem: bias (mean ± SD)/RMSE 2.05% ± 13.31%/13.02%; ITS: 4.61% ± 10.56%/11.20%; Pmetrics: 0.30% ± 10.12%/10.47%). The dose chosen confronting the three results led to a pertinent dose proposal. CONCLUSIONS: The developed Bayesian estimators were all able to predict ciclosporin AUC(0,12 h) in HSCT patients using only three blood with minimal bias and may be combined to increase the reliability of CsA dose adjustment in routine.