New Mathematical Methods in Pharmacokinetic Modeling

A Simple Method for the Prediction of Human Concentration-Time Profiles and Pharmacokinetics of Antibody-Drug Conjugates (ADC) from Rats or Monkeys

Knowledge of human concentration-time profiles from animal data can be useful during early drug development. The objective of this study is to predict human concentration-time profiles of antibody-drug conjugates (ADCs) and subsequently predict pharmacokinetic parameters in humans from rats or monkeys. Eight methods with different exponents of volume of distribution (0.8-1) as well as exponents of clearance (0.85), along with the exponents of volume of distribution for 5 ADCs, were used to predict human concentration-time profiles. The PK parameters were also scaled to humans from monkeys or rats using fixed exponents and compared with the PK parameters predicted from predicted human concentration-time profiles. The results of the study indicated that the exponent 0.9 and the combination of exponents of 0.9 and 0.8 (two exponents, 0.8 and 0.9, were used) were the best method to predict human concentration-time profiles and, subsequently, human PK parameters. The predicted PK parameters from fixed exponents were comparable with the predicted PK parameters estimated from human concentration-time profiles. The proposed methods are applicable to rats or monkeys with the same degree of accuracy. Overall, the proposed methods are robust, accurate, and cost- and time-effective.

Pharmacokinetics of Eltrombopag in Healthy Chinese Subjects and Effect of Sex and Genetic Polymorphism on its Pharmacokinetic and Pharmacodynamic Variability

BACKGROUND AND OBJECTIVE

Eltrombopag is the first oral, small-molecule, non-peptide thrombopoietin receptor agonist for the treatment of idiopathic thrombocytopenic purpura. This study investigated the pharmacokinetics of eltrombopag in healthy Chinese subjects and evaluated the effect of sex and genetic polymorphisms on its variability.

METHODS

Forty-eight healthy subjects were administered a single dose of eltrombopag (25 mg). Plasma concentrations of eltrombopag were determined using a validated liquid chromatography-tandem mass spectrometry method, and platelet counts were determined by blood tests. CYP1A2 rs762551, CYP2C8*3 rs10509681, CYP2C8*3 rs11572080, UGT1A1 rs887829, UGT1A3 rs3806596, and BCRP rs2231142 polymorphisms were genotyped by Sanger sequencing. A back-propagation artificial neural network (BP-ANN) model was constructed to predict pharmacokinetics based on physiological factors and genetic polymorphism data.

RESULTS

Compared with male subjects, female subjects who received a single 25-mg dose of eltrombopag exhibited a significantly increased mean maximum plasma concentration (C_max) and significantly decreased apparent clearance. Additionally, CYP1A2 rs762551 C>A single nucleotide polymorphism influenced distribution and elimination. C-allele carriers exhibited 30% higher systemic exposure and 20% lower apparent clearance compared with homozygous A-allele carriers. Mean percentage increases in platelet counts from baseline to Day 5 were 9.38% and 17.06% in male and female subjects, respectively. The BP-ANN model had a high goodness-of-fit index and good coherence between predicted and measured concentrations (R = 0.98979).

CONCLUSION

Sex and CYP1A2 rs762551 C>A were associated with the pharmacokinetic variability of eltrombopag in healthy Chinese subjects. Females exhibited a better platelet-elevating effect compared with males administered the same dosage. The developed BP-ANN model based on physiological factors and genetic polymorphism data could be promising for applications in pharmacokinetic studies.

TRIAL REGISTRATIONS

https://www.Chinadrugtrials.org.cn CTR20190898.

Therapeutic drug monitoring of anti-tumour necrosis factor-α agents in inflammatory bowel disease: Limits and improvements

AIMS

Since the publication of the American Gastroenterological Association's recommendations in 2017, there have been no significant changes in the biological monitoring recommendations in inflammatory bowel disease. Possible limitations are the lack of evidence to recommend proactive therapeutic drug monitoring (pTDM) over reactive TDM (rTDM), and the limited information about individualized dosing methods. This article aims to review the TDM strategy updates and the use of individualized dosing methods.

METHODS

For the analysis of the TDM strategies and individualized dosing method, a search was carried out in PubMed and Cochrane Central. In the TDM case, since August 2017.

RESULTS

A total of 263 publications were found, but only 7 related to proactive TDM. Five of these publications directly compared pTDM vs rTDM and 2 were randomized clinical trials. Six studies found benefits of pTDM and 1 found no differences. Regarding the individualized dosing method, 229 distinct results were found. Population pharmacokinetics was the most widely used method to develop individual dosage models and to analyse the influence of factors on drug concentrations (albumin concentration, weight, presence of anti-drug antibodies etc).

CONCLUSION

We have found no major changes in TDM strategies. There is a growing trend towards the use of pTDM because it has shown a longer duration of treatment response, lower rates of discontinuation and relapses. However, the available evidence is limited and of low quality. Despite the common use of population pharmacokinetic methods to analyse pharmacokinetic factors, they are not commonly used for personalized dosing.

Effect of Genetic Polymorphisms on the Pharmacokinetics of Deferasirox in Healthy Chinese Subjects and an Artificial Neural Networks Model for Pharmacokinetic Prediction

BACKGROUND AND OBJECTIVE

Deferasirox is an oral iron chelator used to reduce iron levels in iron-overloaded patients with transfusion-dependent anemia or non-transfusion-dependent thalassemia. This study investigated the effects of genetic polymorphisms on the pharmacokinetics of deferasirox in healthy Chinese subjects and constructed a pharmacokinetic prediction model based on physiologic factors and genetic polymorphism data.

METHODS

Twenty-eight subjects were enrolled in a randomized, open-label, two-period crossover study, and they received a single dose of one of two formulations of deferasirox (20 mg/kg) with a 7-day washout interval between the two periods. The plasma defersirox concentration was determined using a validated liquid chromatography-tandem mass spectrometry method, and pharmacokinetic parameters were calculated using the noncompartmental method. The polymorphisms of uridine diphosphate glucuronosyltransferase 1A1 (UGT1A1), UGT1A3, multidrug resistance protein 2 (MRP2), cytochrome P450 1A1 (CYP1A1), and breast cancer resistance protein 1 (BCRP1) were genotyped using Sanger sequencing. A back-propagation artificial neural network (BP-ANN) model was used to predict the pharmacokinetics.

RESULTS

The UGT1A1 rs887829 C > T single-nucleotide polymorphism (SNP) significantly influenced the area under the plasma concentration-time curve and the terminal half-life. Neither the MRP2 rs2273697 G > A SNP nor BCRP1 rs2231142 G > T SNP altered the absorption, disposition, and excretion of the drug. The BP-ANN model had a high goodness-of-fit index and good coherence between the predicted and measured concentrations (R² = 0.921).

CONCLUSION

Metabolic enzyme-related genetic polymorphisms were more strongly associated with the pharmacokinetics of deferasirox than membrane transporter-related genetic polymorphisms in the Chinese population.

TRIAL REGISTRATION

www.Chinadrugtrials.org.cn CTR20191164.

Short-term glucagon stimulation test of C-peptide effect on glucose utilization in patients with type 1 diabetes mellitus

This work aimed to evaluate the use of a four-point glucagon stimulation test of C-peptide effect on glucose utilization in type 1 diabetic patients using a new mathematical model. A group of 32 type 1 diabetic patients and a group of 10 healthy control subjects underwent a four-point glucagon stimulation test with blood sampling at 0, 6, 15 and 30 min after 1 mg glucagon bolus intravenous administration. Pharmacokinetic and pharmacokinetic/pharmacodynamic models of C-peptide effect on glucose utilization versus area under curve (AUC) were used. A two-sample t test and ANOVA with Bonferroni correction were used to test the significance of differences between parameters. A significant difference between control and patient groups regarding the coefficient of whole-body glucose utilization and AUC C-peptide/AUC glucose ratio (p ≪ 0.001 and p = 0.002, respectively) was observed. The high correlation (r = 0.97) between modeled coefficient of whole-body glucose utilization and numerically calculated AUC C-peptide/AUC glucose ratio related to entire cohort indicated the stability of used method. The short-term four-point glucagon stimulation test allows the numerically calculated AUC C-peptide/AUC glucose ratio and/or the coefficient of whole-body glucose utilization calculated from model to be used to diagnostically identify type 1 diabetic patients.

System approach to modeling of liver glucose metabolism with physiologically interpreted model parameters outgoing from [18F]FDG concentrations measured by PET

New mathematical models from physiologically interpreted parameters capable of evaluating glucose metabolism within the liver and/or the whole body were developed. The group of pigs in a fasting state and the group of pigs with euglycemic supraphysiological hyperinsulinemia were scanned by positron emission tomography after a single dose of [(18)F]FDG tracer. Simultaneously frequent sampling of the dynamic data of [(18)F]FDG plasma concentration in artery, portal vein and hepatic vein was obtained. A system approach to the liver and/or the whole-body system by the tools of linear dynamic sysztem theory was used. Three kinds of structural models, single input and single output or multiple outputs and multiple inputs and single output, were identified. Differences between the group of fasting pigs and the group of pigs in euglycemic supraphysiological hyperinsulinemia were identified by estimated parameters of the structural models. The suitability of the structural mathematical models for the estimation of physiologically interpreted parameters from PET was validated.

Physiologically based structure of mean residence time

A mean residence time (MRT) is an important pharmacokinetic parameter. To the author's knowledge, however, a physiologically based structure of MRT (thereafter MRT structure) has not been published so far. Primarily this is because MRT structures cannot be identified by traditional pharmacokinetic methods used for the determination of MRT. Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. The MRT structure identified is physiologically meaningful. Accordingly, it seems that the MRT structure identified may contribute to already established knowledge about MRT.

Assessment of exposure to PCB 153 from breast feeding and normal food intake in individual children using a system approach model

Investigators have typically relied on a single or few discrete time points as measures of polychlorinated biphenyl (PCB) body burden, however health effects are more likely to be the result of integrative exposure in time, optionally expressed as an area under the time curve (AUC) of PCB serum concentration. Using data from a subgroup of 93 infants from a birth cohort in eastern Slovakia-a region highly polluted by PCBs-we fit a system type model, customized to our longitudinal measures of serum PCB concentrations in cord, 6, 16, and 45 month blood specimens. The most abundant congener, PCB 153, was chosen for modeling purposes. In addition to currently used methods of exposure assessment, our approach estimates a concentration time profile for each subject, taking into account mean residence time of PCB 153 molecules in the body, duration of breast feeding, hypothetical PCB 153 concentration in steady-state without breast feeding and alternately without normal food intake. Hypothetical PCB 153 concentration in steady-state without normal food intake correlates with AUC (r=0.84, p<0.001) as well as with duration of breast feeding (r=0.64, p<0.001). It makes possible to determine each subject's exposure profile expressed as AUC of PCBs serum concentration with a minimum model parameters. PCB body burden in most infants was strongly associated with duration of breast feeding in most, but not all children, was apparent from model output.

A tentative taxonomy for predictive models in relation to their falsifiability

The growing importance of predictive models in biomedical research raises some concerns on the correct methodological approach to the falsification of such models, as they are developed in interdisciplinary research contexts between physics, biology and medicine. In each of these research sectors, there are established methods to develop cause-effect explanations for observed phenomena, which can be used to predict: epidemiological models, biochemical models, biophysical models, Bayesian models, neural networks, etc. Each research sector has accepted processes to verify how correct these models are (falsification). But interdisciplinary research imposes a broader perspective, which encompasses all possible models in a general methodological framework of falsification. The present paper proposes a general definition of 'scientific model' that makes it possible to categorize predictive models into broad categories. For each of these categories, generic falsification strategies are proposed, except for the so-called 'abductive' models. For this category, which includes artificial neural networks, Bayesian models and integrative models, the definition of a generic falsification strategy requires further investigation by researchers and philosophers of science.

Machine learning methods applied to pharmacokinetic modelling of remifentanil in healthy volunteers: a multi-method comparison

This study compared the blood concentrations of remifentanil obtained in a previous clinical investigation with the predicted remifentanil concentrations produced by different pharmacokinetic models: a non-linear mixed effects model created by the software NONMEM; an artificial neural network (ANN) model; a support vector machine (SVM) model; and multi-method ensembles. The ensemble created from the mean of the ANN and the non-linear mixed effects model predictions achieved the smallest error and the highest correlation coefficient. The SVM model produced the highest error and the lowest correlation coefficient. Paired t-tests indicated that there was insufficient evidence that the predicted values of the ANN, SVM and two multi-method ensembles differed from the actual measured values at alpha = 0.05. The ensemble method combining the ANN and non-linear mixed effects model predictions outperformed either method alone. These results indicated a potential advantage of ensembles in improving the accuracy and reducing the variance of pharmacokinetic models.

Novel approach to bioequivalence assessment based on physiologically motivated model

The study was conducted to exemplify an approach capable of obtaining a new insight into bioequivalence (BE) assessment, by the use of a physiologically motivated model. Data from an oral BE study of two piroxicam (PXM) products was used as an example. The BE study was carried out with 24 healthy European subjects according to a two-sequence crossover-randomized design. The test and reference formulations were a PXM generic formulation (LaborMed Pharma, Romania) and Feldene (Pfizer, USA), respectively. Plasma concentrations of PXM were monitored by a validated high-performance liquid chromatography over a period of 144 h after administration. After the structure of the optimal model was selected, parameters that characterized the whole-body disposition behavior of PXM in the subjects were derived. The paired Student's t-test and Wilkoxon's test were performed on the derived parameters. The null hypothesis of no differences in the parameters of the whole-body disposition behavior of PXM related to the test and reference product was not rejected at 5% level of significance. This result suggested that the compared products were bioequivalent and could be used interchangeably in clinical setting. The presented approach might show a new way, worth incorporating in future BE guidelines.

Physiologically motivated time-delay model to account for mechanisms underlying enterohepatic circulation of piroxicam in human beings

The study was conducted to formulate a physiologically motivated time-delay (PM TD) mathematical model for human beings, which incorporates disintegration of a drug formulation, dissolution, discontinuous gastric emptying and enterohepatic circulation (EHC) of a drug. Piroxicam, administered to 24 European, healthy individuals in 20 mg capsules Feldene Pfizer, was used as a model drug. Plasma was analysed for piroxicam by a validated high-performance liquid chromatography method. The PM TD mathematical model was developed using measured plasma piroxicam concentration-time profiles of the individuals and tools of a computationally efficient mathematical analysis and modeling, based on the theory of linear dynamic systems. The constructed model was capable of (i) quantifying different fractions of the piroxicam dose sequentially disposable for absorption and (ii) estimating time delays between time when the piroxicam dose reaches stomach and time when individual of fractions of the piroxicam dose is disposable for absorption. The model verification was performed through a formal proof, based on comparisons of observed and model-predicted plasma piroxicam concentration-time profiles. The model verification showed an adequate model performance and agreement between the compared profiles. Accordingly, it confirmed that the developed model was an appropriate representative of the piroxicam fate in the individuals enrolled. The presented model provides valuable information on factors that control dynamic mechanisms of EHC, that is, information unobtainable with the models proposed for the EHC analysis previously.

Population pharmacokinetic and pharmacodynamic models of remifentanil in healthy volunteers using artificial neural network analysis

AIMS

An ordinary sigmoid E(max) model could not predict overshoot of electroencephalographic approximate entropy (ApEn) during recovery from remifentanil effect in our previous study. The aim of this study was to evaluate the ability of an artificial neural network (ANN) to predict ApEn overshoot and to evaluate the predictive performance of the pharmacokinetic model, and pharmacodynamic models of ANN with respect to data used.

METHODS

Using a reduced number of ApEn instances (n = 1581) to make NONMEM modelling feasible and complete ApEn data (n = 24 509), the presence of overshoot was assessed. A total of 1077 measured remifentanil concentrations and ApEn data, and a total of 24 509 predicted concentrations and ApEn data were used in the pharmacodynamic model A and B of ANN, respectively. The testing subset of model B (n = 7352) was used to evaluate the ability of ANN to predict overshoot of ApEn. Mean squared error (MSE) was calculated to evaluate the predictive performance of the ANN models.

RESULTS

With complete ApEn data, ApEn overshoot was observed in 66.7% of subjects, but only in 37% with a reduced number of ApEn instances. The ANN model B predicted 77.8% of ApEn overshoot. MSE (95% confidence interval) was 57.1 (3.22, 71.03) for the pharmacokinetic model, 0.148 (0.004, 0.007) for model A and 0.0018 (0.0017, 0.0019) for model B.

CONCLUSIONS

The reduced ApEn instances interfered with the approximation of true electroencephalographic response. ANN predicted 77.8% of ApEn overshoot. The predictive performance of model B was significantly better than that of model A.

Spline functions in convolutional modeling of verapamil bioavailability and bioequivalence. I: conceptual and numerical issues

A cubic spline function for describing the verapamil concentration profile, resulting from the verapamil absorption input to be evaluated, has been used. With this method, the knots are taken to be the data points, which has the advantage of being computationally less complex. Because of its inherently low algorhythmic errors, the spline method is less distorted and more suitable for further data analysis than others. The method has been evaluated using simulated verapamil delayed release tablet concentration data containing various degrees of random noise. The accuracy of the method was determined by how well the estimates of input rate and extent represented the true values. It was found that the accuracy of the method was of the same order of magnitude as the noise level of the data. Spline functions in convolutional modeling of verapamil formulation bioavailability and bioequivalence, as shown in the numerical simulation investigation, are very powerful additional tools for assessing the quality of new verapamil formulations in order to ensure that they are of the same quality as already registered formulations of the drug. The development of such models provides the possibility to avoid additional or larger bioequivalence and/or clinical trials and to thus help shorten the investigation time and registration period.