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Machine Learning (ML) is a fast-evolving field, integrated in many of today’s scientific disciplines. With the recent development of Neural Ordinary Differential Equations (NODEs), ML provides a new tool to model dynamical systems in the field of pharmacology and pharmacometrics, such as pharmacokinetics (PK) or pharmacodynamics. The novel and conceptionally different approach of NODEs compared to classical PK modeling creates challenges but also provides opportunities for its application. In this manuscript, we introduce the functionality of NODEs and develop specific NODE structures based on PK principles. We discuss two challenges of NODEs, overfitting and extrapolation to unseen data, and we provide practical solutions to these problems. We illustrate concept and application of our proposed NODE approach with several PK modeling examples, including multi-compartmental, target-mediated drug disposition and delayed absorption behavior. In all investigated scenarios, the NODEs were able to describe well the data and simulate data for new subjects within the observed dosing range. Finally, we briefly demonstrate how NODEs can be combined with mechanistic models. This research work enhances understanding of how NODEs can be applied in PK analyses and illustrates the potential for NODEs in the field of pharmacology and pharmacometrics.

Background Preterm neonates frequently experience hypernatremia (plasma sodium concentrations >145 mmol/l), which is associated with clinical complications, such as intraventricular hemorrhage. Study design In this single center retrospective observational study, the following 7 risk factors for hypernatremia were analyzed in very low gestational age (VLGA, below 32 weeks) neonates: gestational age (GA), delivery mode (DM; vaginal or caesarian section), sex, birth weight, small for GA, multiple birth, and antenatal corticosteroids. Machine learning (ML) approaches were applied to obtain probabilities for hypernatremia. Results 824 VLGA neonates were included (median GA 29.4 weeks, median birth weight 1170 g, caesarean section 83%). 38% of neonates experienced hypernatremia. Maximal sodium concentration of 144 mmol/l (interquartile range 142–147) was observed 52 hours (41–65) after birth. ML identified vaginal delivery and GA as key risk factors for hypernatremia. The risk of hypernatremia increased with lower GA from 22% for GA ≥ 31–32 weeks to 46% for GA Conclusion VLGA neonates with vaginal delivery and low GA have the highest risk for hypernatremia. Early identification of neonates at risk and early intervention may prevent extreme sodium excursions and associated clinical complications. Hintergrund Bei Fruhgeborenen tritt haufig eine Hypernatriamie (Natrium im Plasma > 145 mmol/l) auf, welche mit klinischen Komplikationen wie Hirnblutungen assoziiert ist. Patienten und MethodenDiese retrospektive Beobachtungsstudie untersuchte folgenden 7 Risikofaktoren fur Hypernatriamie bei Neugeborenen mit sehr niedrigem Gestationsalter (VLGA, unter 32 Wochen): Gestationsalter (GA), Entbindungsmodus (DM) (vaginal oder Kaiserschnitt), Geschlecht, Geburtsgewicht, klein fur GA, Mehrlingsgeburt und pranatale Lungenreife. Durch maschinelles Lernen (ML) wurden Risikofaktoren fur Hypernatriamie analysiert. Ergebnisse 824 VLGA-Neugeborene wurden eingeschlossen (GA Median 29,4 Wochen, Geburtsgewicht Median 1170 g, Kaiserschnitt 83%). 38% der Neugeborenen zeigten eine Hypernatriamie. Die maximale Natriumkonzentration von 144 mmol/l (Interquartilbereich 142–147) wurde 52 Stunden (41–65) nach der Geburt beobachtet. ML identifizierte vaginale Geburt und GA als Hauptrisikofaktoren fur Hypernatriamie. Die Haufigkeit stieg mit niedrigerem GA von 22% fur GA ≥31–32 Wochen auf 46% fur GA Schlussfolgerung VLGA-Neugeborene mit vaginaler Entbindung und niedrigem GA haben das hochste Risiko fur Hypernatriamie. Fruhes Identifizieren von Risikopatienten und fruhe Intervention konnten extreme Natriumexkursionen und damit verbundene klinische Komplikationen verhindern.

Modeling of retrospectively collected multi-center data of a rare disease in pediatrics is challenging because laboratory data can stem from several decades measured with different assays. Here we present a retrospective pharmacometrics (PMX) based data analysis of the rare disease congenital hypothyroidism (CH) in newborns and infants. Our overall aim is to develop a model that can be applied to optimize dosing in this pediatric patient population since suboptimal treatment of CH during the first 2 years of life is associated with a reduced intelligence quotient between 10 and 14 years. The first goal is to describe a retrospectively collected dataset consisting of 61 newborns and infants with CH up to 2 years of age. Overall, 505 measurements of free thyroxine (FT4) and 510 measurements of thyrotropin or thyroid-stimulating hormone were available from patients receiving substitution treatment with levothyroxine (LT4). The second goal is to introduce a scale/location-scale normalization method to merge available FT4 measurements since 34 different postnatal age- and assay-specific laboratory reference ranges were applied. This method takes into account the change of the distribution of FT4 values over time, i.e. a transformation from right-skewed towards normality during LT4 treatment. The third goal is to develop a practical and useful PMX model for LT4 treatment to characterize FT4 measurements, which is applicable within a clinical setting. In summary, a time-dependent normalization method and a practical PMX model are presented. Since there is no on-going or planned development of new pharmacological approaches for CH, PMX based modeling and simulation can be leveraged to personalize dosing with the goal to enhance longer-term neurological outcome in children with the rare disease CH. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09765-w.

The objectives are to characterize oscillations of physiological functions such as heart rate and body temperature, as well as the sleep cycle from behavioral states in generally stable preterm neonates during the first 5 days of life. Heart rate, body temperature as well as behavioral states were collected during a daily 3-h observation interval in 65 preterm neonates within the first 5 days of life. Participants were born before 32 weeks of gestational age or had a birth weight below 1500 g; neonates with asphyxia, proven sepsis or malformation were excluded. In total 263 observation intervals were available. Heart rate and body temperature were analyzed with mathematical models in the context of non-linear mixed effects modeling, and the sleep cycles were characterized with signal processing methods. The average period length of an oscillation in this preterm neonate population was 159 min for heart rate, 290 min for body temperature, and the average sleep cycle duration was 19 min. Oscillation of physiological functions as well as sleep cycles can be characterized in very preterm neonates within the first few days of life. The observed parameters heart rate, body temperature and sleep are running in a seemingly uncorrelated pace at that stage of development. Knowledge about such oscillations may help to guide nursing and medical care in these neonates as they do not yet follow a circadian rhythm.

Clinical pharmacology is a multidisciplinary data sciences field that utilizes mathematical and statistical methods to generate maximal knowledge from data. Pharmacometrics (PMX) is a well‐recognized tool to characterize disease progression, pharmacokinetics, and risk factors. Because the amount of data produced keeps growing with increasing pace, the computational effort necessary for PMX models is also increasing. Additionally, computationally efficient methods, such as machine learning (ML) are becoming increasingly important in medicine. However, ML is currently not an integrated part of PMX, for various reasons. The goals of this article are to (i) provide an introduction to ML classification methods, (ii) provide examples for a ML classification analysis to identify covariates based on specific research questions, (iii) examine a clinically relevant example to investigate possible relationships of ML and PMX, and (iv) present a summary of ML and PMX tasks to develop clinical decision support tools., Clinical Pharmacology & Therapeutics, 107 (4), ISSN:0009-9236, ISSN:1532-6535

The field of medicine is undergoing a fundamental change, transforming towards a modern data-driven patient-oriented approach. This paradigm shift also affects perinatal medicine as predictive algorithms and artificial intelligence are applied to enhance and individualize maternal, neonatal and perinatal care. Here, we introduce a pharmacometrics-based mathematical-statistical computer program (PMX-based algorithm) focusing on hyperbilirubinemia, a medical condition affecting half of all newborns. Independent datasets from two different centers consisting of total serum bilirubin measurements were utilized for model development (342 neonates, 1,478 bilirubin measurements) and validation (1,101 neonates, 3,081 bilirubin measurements), respectively. The mathematical-statistical structure of the PMX-based algorithm is a differential equation in the context of non-linear mixed effects modeling, together with Empirical Bayesian Estimation to predict bilirubin kinetics for a new patient. Several clinically relevant prediction scenarios were validated, i.e., prediction up to 24 h based on one bilirubin measurement, and prediction up to 48 h based on two bilirubin measurements. The PMX-based algorithm can be applied in two different clinical scenarios. First, bilirubin kinetics can be predicted up to 24 h based on one single bilirubin measurement with a median relative (absolute) prediction difference of 8.5% (median absolute prediction difference 17.4 μmol/l), and sensitivity and specificity of 95.7 and 96.3%, respectively. Second, bilirubin kinetics can be predicted up to 48 h based on two bilirubin measurements with a median relative (absolute) prediction difference of 9.2% (median absolute prediction difference 21.5 μmol/l), and sensitivity and specificity of 93.0 and 92.1%, respectively. In contrast to currently available nomogram-based static bilirubin stratification, the PMX-based algorithm presented here is a dynamic approach predicting individual bilirubin kinetics up to 48 h, an intelligent, predictive algorithm that can be incorporated in a clinical decision support tool. Such clinical decision support tools have the potential to benefit perinatal medicine facilitating personalized care of mothers and their born and unborn infants.

Context Copeptin is the C-terminal fragment of the arginine vasopressin (AVP) prohormone whose measurement is more robust than that of AVP. Similar release and clearance characteristics have been suggested promoting copeptin as a surrogate marker. Objective To characterize the physiology of osmotically regulated copeptin release and its half-life in direct comparison with plasma AVP. Design Ninety-one healthy volunteers underwent a standardized three-phase test protocol including (1) osmotic stimulation into the hypertonic range by hypertonic-saline infusion followed by osmotic suppression via (2) oral water load and (3) subsequent glucose infusion. Plasma copeptin, AVP, serum sodium, and osmolality levels were measured in regular intervals. Results In phase 1, an increase in median osmotic pressure [289 (286; 291) to 311 (309; 314) mOsm/kg H2O] caused similar release kinetics of plasma copeptin [4 (3.1; 6) to 29.3 (18.6; 48.2) pmol/L] and AVP [1 (0.7; 1.6) to 10.3 (6.8; 18.8) pg/mL]. Subsequent osmotic suppression to 298 (295; 301) mOsm/kg at the end of phase 3 revealed markedly different decay kinetics between both peptides—an estimated initial half-life of copeptin being approximately 2 times longer than that of AVP (26 vs 12 minutes). Conclusion Copeptin is released in equimolar amounts with AVP in response to osmotic stimulation, suggesting its high potential as an AVP surrogate for differentiation of osmotic disorders. Furthermore, we here describe the decay kinetics of copeptin in response to osmotic depression enabling to identify a half-life for copeptin in direct comparison with AVP.

We study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h𝕅0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.

We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale h ℕ 0 h $h\mathbb{N}_0^h$ , where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

Infliximab, an anti-tumour necrosis factor (TNF)-α monoclonal antibody, has been approved in chronic inflammatory disease, including rheumatoid arthritis, Crohn’s disease and ankylosing spondylitis. This study aimed to investigate and characterise target-mediated drug disposition of infliximab and antigen mass turnover during infliximab treatment. In this retrospective cohort of 186 patients treated with infliximab for rheumatoid arthritis, Crohn’s disease or ankylosing spondylitis, trough infliximab concentrations were determined from samples collected between weeks 0 and 22 after treatment initiation. Target-mediated pharmacokinetics of infliximab was described using target-mediated drug disposition modelling. Target-mediated elimination parameters were determined for rheumatoid arthritis and Crohn’s disease, assuming ankylosing spondylitis with no target-mediated elimination. The quasi-equilibrium approximation of a target-mediated drug disposition model allowed a satisfactory description of infliximab concentration–time data. Estimated baseline TNF-α amounts were similar in Crohn’s disease and rheumatoid arthritis (R0 = 0.39 vs 0.46 nM, respectively), but infliximab-TNF complex elimination was slower in Crohn’s disease than in rheumatoid arthritis (kint = 0.024 vs 0.061 day−1, respectively). Terminal elimination half-lives were 13.5, 21.5 and 16.5 days for rheumatoid arthritis, Crohn’s disease and ankylosing spondylitis, respectively. Estimated amounts of free target were close to baseline values before the next infusion suggesting that TNF-α inhibition may not be sustained over the entire dose interval. The present study is the first to quantify the influence of target antigen dynamics on infliximab pharmacokinetics. Target-mediated elimination of infliximab may be complex, involving a multi-scale turnover of TNF-α, especially in patients with Crohn’s disease. Additional clinical studies are warranted to further evaluate and fine-tune dosing approaches to ensure sustained TNF-α inhibition.

Delay differential equations (DDEs) are commonly used in pharmacometric models to describe delays present in pharmacokinetic and pharmacodynamic data analysis. Several DDE solvers have been implemented in NONMEM 7.5 for the first time. Two of them are based on algorithms already applied elsewhere, while others are extensions of existing ordinary differential equations (ODEs) solvers. The purpose of this tutorial is to introduce basic concepts underlying DDE based models and to show how they can be developed using NONMEM. The examples include previously published DDE models such as logistic growth, tumor growth inhibition, indirect response with precursor pool, rheumatoid arthritis, and erythropoiesis-stimulating agents. We evaluated the accuracy of NONMEM DDE solvers, their ability to handle stiff problems, and their performance in parameter estimation using both first-order conditional estimation (FOCE) and the expectation–maximization (EM) method. NONMEM control streams and excerpts from datasets are provided for all discussed examples. All DDE solvers provide accurate and precise solutions with the number of significant digits controlled by the error tolerance parameters. For estimation of population parameters, the EM method is more stable than FOCE regardless of the DDE solver. published

Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic–pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic–pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic–pharmacodynamic examples.

Context Copeptin is a surrogate marker for arginine vasopressin (AVP) release in response to hyperosmolal stimuli such as diabetic ketoacidosis (DKA). Objective The objective of this work is to characterize kinetics of copeptin and osmolality, and their dynamic relationship during rehydration and insulin therapy in children with type 1 diabetes (T1D) and DKA. Design and Setting A prospective, observational, multicenter study was conducted. Patients and Intervention Children with T1D admitted for DKA underwent serial serum copeptin and osmolality measurements from start of rehydration at 14 time points during 72 hours. Main Outcome Measures Measurements included temporal course of copeptin and osmolality (kinetics), relationship between both (dynamics), and association between-subject variability (BSV) (coefficient of variation, CV%). Results Twenty-eight children (20 newly diagnosed T1D) aged 1 to 16 years were included. Copeptin decreased from 95 pmol/L (95% CI, 55-136 pmol/L) (CV%, 158%) to 9.7 pmol/L (95% CI, 8.1-11.4 pmol/L) (CV%, 31%) with a 50% recovery time (t1/2) of 7.1 hours (range, 5.1-11.5 hours) (114%). Serum osmolality decreased from 321 mOsm/kg (range, 315-327 mOsm/kg) (4%) to 294 mOsm/kg (range, 292-296 mOsm/kg) (1%) with a t1/2 of 4.3 hours (range, 3.0-5.6 hours) (64%). Copeptin levels doubled with each osmolality increase by 15 mOsm/kg (range, 10-21 mOsm/kg) (59%), from 9.8 pmol/L (range, 7.3-12.3 pmol/L) (48%) to 280 mOsm/kg. Copeptin kinetics differed between newly diagnosed and known T1D patients (P = .001), and less between mild vs moderate-severe DKA (P = .04). Conclusions First, this study characterized for the first time copeptin kinetics and dynamics in the high hyperosmolar range in children with DKA. Second, it revealed significant differences in copeptin kinetics between newly diagnosed and known T1D patients that may be explained by changes at the osmoreceptor and renal AVP receptor level due to longstanding osmotic diuresis and DKA.

L-Thyroxine (L-T4) is the treatment of choice of congenital hypothyroidism (CH). Longitudinal measurements of free T4 (FT4) serum concentrations were collected over the first two years of life with oral L-T4 treatment in infants with CH. Purpose of this study was to develop an integrated mathematical model to characterize the kinetics of exogenous L-Thyroxine (L-T4) after multiple dosing in infants with CH, and the dynamics of residual endogenous FT4 synthesis under treatment in the context of severe, moderate and mild disease. A total of 200 FT4 concentrations from 30 patients were available for analysis. At start of treatment, mean (standard deviation [SD]) postnatal age and weight of the population were 11 (8) days and 3.9 (1.3) kg. Mean (SD) pretreatment FT4 concentration was 11.3 (7.4) pmol/L. Measured FT4 concentrations were modelled as sum of residual endogenous FT4 and exogenously administered FT4 (L-T4). The integrated mathematical model consists of an absorption compartment for the exogenous FT4 administration, and a central compartment for measured FT4 with linear elimination. Hence, for residual endogenous and exogenous FT4 the same elimination rate constant was assumed. For the residual endogenous synthesis, different approaches were tested: a constant production and typical time-dependent production functions. FT4 data were analyzed using nonlinear mixed-effects modeling. The integrated mathematical model with a time-dependent non-linear Emax function describing a decreasing residual endogenous FT4 synthesis for increasing time provided the best data fit in terms of Akaike value and various goodness-of-fit plots. This is in line with the expected progressive suppression of the thyroid stimulating hormone by the exogenous FT4, and the subsequent decrease of residual FT4 endogenous synthesis. The developed mathematical model allows simulation of FT4 pharmacokinetic profiles for different disease severities and different dosing regimens.

Caffeine is widely used in preterm neonates suffering from apnea of prematurity (AOP), and it has become one of the most frequently prescribed medications in neonatal intensive care units. Goal of this study is to investigate how caffeine citrate treatment affects sleep‐wake behavior in preterm neonates. The observational study consists of 64 preterm neonates during their first 5 days of life with gestational age (GA)

Ceftazidime is a parenteral cephalosporin frequently used in pregnant women for treatment of urinary tract or intrauterine infections. Despite its regular use in pregnant women, ceftazidime disposition in both mother and fetus is not well understood, and a pharmacokinetic (PK) model that allows characterization and simulation of both maternal and preterm neonatal ceftazidime disposition is not available. In this study, 10 pregnant women with suspected or proven intrauterine infections in the late second and early third trimester were treated with 1 g of ceftazidime intravenously every 6 hours. During ceftazidime treatment, one maternal and umbilical cord blood sample was taken at delivery to quantify ceftazidime concentrations in the mother and preterm neonate. Data showed that ceftazidime concentrations in the mother were comparable to those observed in the neonate. Based on these data, a PK model was developed to describe maternal disposition, ceftazidime distribution over the placenta, and elimination in the neonate. The maternal substructure of the model was parameterized according to a previously reported ceftazidime model with minor adjustments to account for pregnancy-related effects on renal elimination of ceftazidime. The expanded population PK model with an additional neonatal compartment was fitted to measured drug concentrations in the neonate. The neonatal elimination rate constant at delivery was close to that estimated for the mother. The presented results show that ceftazidime readily crosses the placenta and indicate that perinatal PK behavior of ceftazidime in preterm neonates can be expected to be similar to those observed in their mothers.

Indirect response (IDR) models are probably the most frequently applied tools relating the effect of a signal to a baseline response. A response modeled by such a classical IDR model will always return monotonously to its baseline after drug administration. We extend IDR models with a delay process, i.e. a retarded response state, that leads to oscillating response behavior. First, IDR models with a first-order production and second-order loss term based on the famous logistic equation are constructed. Second, a delay process similar to the delayed logistic equation is included. Relations of the classical IDR model with our extended IDR model concerning response and model parameters are revealed. Simulations of typical response profiles are presented and data fitting of a model for leptin and cholesterol dynamics after administration of methylprednisolone is performed. The influence of the delay parameter on the other model parameters is discussed.

Fentanyl and its derivatives sufentanil, alfentanil, and remifentanil are potent opioids. A comprehensive review of the use of fentanyl and its derivatives in the pediatric population was performed using the National Library of Medicine PubMed. Studies were included if they contained original pharmacokinetic parameters or models using established routes of administration in patients younger than 18 years of age. Of 372 retrieved articles, 44 eligible pharmacokinetic studies contained data of 821 patients younger than 18 years of age, including more than 46 preterm infants, 64 full-term neonates, 115 infants/toddlers, 188 children, and 28 adolescents. Underlying diagnoses included congenital heart and pulmonary disease and abdominal disorders. Routes of drug administration were intravenous, epidural, oral-transmucosal, intranasal, and transdermal. Despite extensive use in daily clinical practice, few studies have been performed. Preterm and term infants have lower clearance and protein binding. Pharmacokinetics was not altered by chronic renal or hepatic disease. Analyses of the pooled individual patients’ data revealed that clearance maturation relating to body weight could be best described by the Hill function for sufentanil (R 2 = 0.71, B max 876 mL/min, K 50 16.3 kg) and alfentanil (R 2 = 0.70, B max (fixed) 420 mL/min, K 50 28 kg). The allometric exponent for estimation of clearance of sufentanil was 0.99 and 0.75 for alfentanil clearance. Maturation of remifentanil clearance was described by linear regression to bodyweight (R 2 = 0.69). The allometric exponent for estimation of remifentanil clearance was 0.76. For fentanyl, linear regression showed only a weak correlation between clearance and bodyweight in preterm and term neonates (R 2 = 0.22) owing to a lack of data in older age groups. A large heterogeneity regarding study design, clinical setting, drug administration, laboratory assays, and pharmacokinetic estimation was observed between studies introducing bias into the analyses performed in this review. A limitation of this review is that pharmacokinetic data, based on different modes of administration, dosing schemes, and parameter estimation methods, were combined.

Fentanyl and its derivatives sufentanil, alfentanil, and remifentanil are potent opioids. A comprehensive review of the use of fentanyl and its derivatives in the pediatric population was performed using the National Library of Medicine PubMed. Studies were included if they contained original pharmacokinetic parameters or models using established routes of administration in patients younger than 18 years of age. Of 372 retrieved articles, 44 eligible pharmacokinetic studies contained data of 821 patients younger than 18 years of age, including more than 46 preterm infants, 64 full-term neonates, 115 infants/toddlers, 188 children, and 28 adolescents. Underlying diagnoses included congenital heart and pulmonary disease and abdominal disorders. Routes of drug administration were intravenous, epidural, oral-transmucosal, intranasal, and transdermal. Despite extensive use in daily clinical practice, few studies have been performed. Preterm and term infants have lower clearance and protein binding. Pharmacokinetics was not altered by chronic renal or hepatic disease. Analyses of the pooled individual patients’ data revealed that clearance maturation relating to body weight could be best described by the Hill function for sufentanil (R 2 = 0.71, B max 876 mL/min, K 50 16.3 kg) and alfentanil (R 2 = 0.70, B max (fixed) 420 mL/min, K 50 28 kg). The allometric exponent for estimation of clearance of sufentanil was 0.99 and 0.75 for alfentanil clearance. Maturation of remifentanil clearance was described by linear regression to bodyweight (R 2 = 0.69). The allometric exponent for estimation of remifentanil clearance was 0.76. For fentanyl, linear regression showed only a weak correlation between clearance and bodyweight in preterm and term neonates (R 2 = 0.22) owing to a lack of data in older age groups. A large heterogeneity regarding study design, clinical setting, drug administration, laboratory assays, and pharmacokinetic estimation was observed between studies introducing bias into the analyses performed in this review. A limitation of this review is that pharmacokinetic data, based on different modes of administration, dosing schemes, and parameter estimation methods, were combined.

Overdosing occurs frequently because of prescription errors in neonates, infants, children, adolescents, and adults. Currently there is no quantitative approach that can be used by clinicians to adjust dosing so that toxic drug concentrations can be brought back to levels observed with safe and efficacious therapeutic doses. We present a mathematical solution that offers the time between last overdosing and next therapeutic dose to achieve therapeutic drug concentrations as soon as possible. To facilitate applications of this solution in clinical practice, a minimal amount of information has to be provided, and no simulations are necessary to compute the optimal waiting time. For educational purposes, we provide access to an online decision support tool for overdosing situations (Time to next Dose Calculator) that (1) computes the waiting time after accidental overdosing in patients with normal elimination and (2) computes the waiting time and adjusted reference dosing for patients with abnormal elimination. This user-friendly online tool will help clinicians to quickly adjust a dosing schedule in overdosing situations to mitigate risk for negative clinical consequences.

Pregnant women, fetuses, and newborns are particularly vulnerable patient populations. During pregnancy, the body is subject to physiological changes that influence the pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in pregnant women can result in sub-therapeutic or toxic effects, putting not only the pregnant woman but also her fetus at risk. During neonatal life, maturation processes also affect pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in newborns leads not only to short-term complications but can also have a negative impact on the long-term development of infants and children. For these reasons, it is crucial to characterize physiological changes in pregnant women, describe placental transfer kinetics of drugs, and describe physiological changes related to the transition from intrauterine to extrauterine life and maturation processes in preterm and term neonates. Quantitative pharmacological approaches such as pharmacometric and physiologically-based modeling and model-based simulations can be useful to better understand and predict such physiological changes and their effects on drug exposure and response. This review article (1) gives an overview of physiological changes in pregnant women, their fetuses, and (pre)term neonates, (2) presents case studies to illustrate applications of new modeling and simulation approaches, and (3) discusses challenges and opportunities in optimizing and personalizing treatments during pregnancy and neonatal life.

Pregnant women, fetuses, and newborns are particularly vulnerable patient populations. During pregnancy, the body is subject to physiological changes that influence the pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in pregnant women can result in sub-therapeutic or toxic effects, putting not only the pregnant woman but also her fetus at risk. During neonatal life, maturation processes also affect pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in newborns leads not only to short-term complications but can also have a negative impact on the long-term development of infants and children. For these reasons, it is crucial to characterize physiological changes in pregnant women, describe placental transfer kinetics of drugs, and describe physiological changes related to the transition from intrauterine to extrauterine life and maturation processes in preterm and term neonates. Quantitative pharmacological approaches such as pharmacometric and physiologically-based modeling and model-based simulations can be useful to better understand and predict such physiological changes and their effects on drug exposure and response. This review article (1) gives an overview of physiological changes in pregnant women, their fetuses, and (pre)term neonates, (2) presents case studies to illustrate applications of new modeling and simulation approaches, and (3) discusses challenges and opportunities in optimizing and personalizing treatments during pregnancy and neonatal life.

Aims A dramatic increase in newborn infants with neonatal abstinence syndrome has been observed and these neonates are frequently treated with complex methadone dosing schemes to control their withdrawal symptoms. Despite its abundant use, hardly any data on the pharmacokinetics (PK) of methadone is available in preterm neonates. Therefore we investigated developmental PK of methadone and evaluated current dosing strategies and possible simplification in this vulnerable population. Methods A single-centre open-label prospective study was performed to collect PK data after a single oral dose of methadone in preterm neonates. A population PK model was built to characterize developmental PK of (R)- and (S)-methadone. Model-based simulations were performed to identify a simplified dosing strategy to reach and maintain target methadone exposure. Results A total of 121 methadone concentrations were collected from 31 preterm neonates. A one-compartment model with first order absorption and elimination kinetics best described PK data for (R)- and (S)-methadone. Clearance increases with advancing gestational age and differs between R- and S-enantiomer, being slightly higher for the former (0.244 vs 0.167 L/h). Preterm neonates reached target exposure after 48 hours with currently used dosing schedules. Output from simulations revealed that target exposures can be achieved with a simplified dosing strategy during the first 4 days of treatment. Conclusion Methadone clearance in preterm neonates increases with advancing gestational age and its disposition is influenced by its chirality. Simulations that account for developmental PK changes indicate a shorter methadone dosing strategy can maintain target exposure to control withdrawal symptoms.

Machine learning models may enhance the early detection of clinically relevant hyperbilirubinemia based on patient information available in every hospital. We conducted a longitudinal study on preterm and term born neonates with serial measurements of total serum bilirubin in the first two weeks of life. An ensemble, that combines a logistic regression with a random forest classifier, was trained to discriminate between the two classes phototherapy treatment vs. no treatment. Of 362 neonates included in this study, 98 had a phototherapy treatment, which our model was able to predict up to 48 h in advance with an area under the ROC-curve of 95.20%. From a set of 44 variables, including potential laboratory and clinical confounders, a subset of just four (bilirubin, weight, gestational age, hours since birth) suffices for a strong predictive performance. The resulting early phototherapy prediction tool (EPPT) is provided as an open web application. Early detection of clinically relevant hyperbilirubinemia can be enhanced by the application of machine learning. Existing guidelines can be further improved to optimize timing of bilirubin measurements to avoid toxic hyperbilirubinemia in high-risk patients while minimizing unneeded measurements in neonates who are at low risk.

In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

AimsA dramatic increase in newborn infants with neonatal abstinence syndrome has been observed and these neonates are frequently treated with complex methadone dosing schemes to control their withdrawal symptoms. Despite its abundant use, hardly any data on the pharmacokinetics of methadone is available in preterm neonates. Therefore we investigated developmental pharmacokinetics of methadone and evaluated current dosing strategies and possible simplification in this vulnerable population.MethodsA single center open-label prospective study was performed to collect pharmacokinetic data after a single oral dose of methadone in preterm neonates. A population pharmacokinetic model was built to characterize developmental pharmacokinetics of methadone and to assess the effects of weight and age on clearance and volume of distribution. In addition, simulation techniques were applied to evaluate reported dosing scenarios, investigate methadone exposure levels and examine the feasibility of simplified dosing recommendations.ResultsIn total, 121 methadone concentrations were collected from 31 preterm neonates. The median weight and gestational age amounted 1.6 kg and 32 weeks, respectively. A one-compartment model with first order absorption and elimination kinetics best described the data for (R)- and (S)-methadone. Clearance was observed to be higher for the (R)-enantiomer as compared to the (S)-enantiomer (0.244 versus 0.167 L/h). Target exposures, based on simulations, can be maintained with a simplified dosing strategy during the first four days of treatment. It is therefore questionable if there is a need for the currently used more extended dosing regimen of methadone in neonates.conclusionsThis clinical investigation demonstrates that the clearance of methadone increases with advancing gestational age and higher clearance values and volumes of distribution can be observed for (R)-methadone as compared to (S)-methadone in preterm neonates. Simulations that account for developmental pharmacokinetics indicate that a simplified methadone dosing strategy can maintain target exposure to control withdrawal symptoms in preterm neonates.Disclosure(s)Nothing to disclose

BackgroundThyroid hormones are essential for normal growth and puberty in children and adolescents. Graves’ disease (GD) is a rare autoimmune disorder associated with thyroid hormone over-production and occurs in 0.5–2:100’000 children (mostly females) in Europe. In contrast to adults, first line treatment of GD is long-term antithyroid drug (ATD) therapy, and radioiodine ablation is usually being reserved for patients after puberty. However, treatment of acquired hyperthyroidism with ATD is difficult since 1) paediatric patients differ considerable in age, weight and diseases severity and 2) minimal ATD dose should be used to avoid mild side effects (occurring in 6–35% of patients), and rare severe side effects such as agranulocytosis and liver failure.MethodsLongitudinal clinical and laboratory data from a Swiss multicentre cohort were analysed retrospectively. Non-linear mixed effects modelling was applied to characterize dynamics of free thyroxine (FT4) during the first 3 months of treatment with carbimazole. Sex, co-medications such as propranolol, and thyroid stimulating hormone receptor antibody were tested as covariates on model parameters. Reference range for FT4 was derived from target levels in clinical practice (12–22 pmol/L).ResultsStudy cohort comprised 45 children with GD, 78% females, median age 12.2 years (IQR = [8.7,13.6])) with a total of 181 visits. FT4 baseline at diagnosis of GD was 62.3 pmol/L (IQR = [45.7, 86.7]). None of the tested factors showed significant covariate effects. The model allows individual simulations of optimal ATD dosing strategies (starting and maintenance dose) for different GD severities, ages and weights at start of therapy. Personalized dosing examples will be presented.ConclusionsDeveloped pharmacometric model is able to predict dynamics of FT4 in children with GD depending on four parameters: ATD dose/kg/d, age, weight and disease severity, and can be applied to personalize dosing regimen to avoid over- or under dosing.Disclosure(s)Nothing to disclose

BackgroundSleep wake regulation undergoes distinctive maturational changes. Ultradian sleep wake rhythm predominates at preterm age and is mainly driven by the internal clock. Increased perinatal morbidity in preterm neonates often appears with breathing disorders, among which apnea of prematurity (AOP) is the most frequently observed. Pharmacological support with caffeine has been successfully employed in the treatment of AOP. Nowadays, caffeine citrate is administered to all preterm neonates suffering from AOP. Objective of our study was a quantitative investigation of whether caffeine citrate treatment for reduction of apnea and bradycardia of prematurity affects sleep-wake behavior in preterm neonates.MethodsObservational study of 64 preterm neonates during their first five days of life with gestational age (GA) < 32 weeks or very low birth weight of < 1500 g. Total of 52 patients treated with caffeine and 12 controls without caffeine were included. Sleep-wake behavior was scored in wakefulness (W), active sleep (AS), and quiet sleep (QS) associated with physical and cerebral regeneration. Individual caffeine concentration of every neonate was simulated with a pharmacokinetic model.ResultsFor increasing caffeine concentration, W increased, AS decreased, and QS was unchanged for GA > or = 28 weeks. No caffeine effect for GA < 28 weeks could be demonstrated. Maturational effects could be seen when comparing preterm neonates of GA >32 weeks with a birth weight of < 1500 g with very preterm neonates born of GA < 32: Neonates born >32 weeks had a significantly higher amount of W and lower percentage of AS.ConclusionsTreatment of apnea and bradycardia as well as stabilization of respiration with standard caffeine treatment is not at cost of QS, i.e. time for physical and cerebral regeneration during sleep remains unchanged. There is an increased fraction of W, alertness and most probably also arousability.Disclosure(s)Nothing to disclose

We present competitive and uncompetitive drug-drug interaction (DDI) with target mediated drug disposition (TMDD) equations and investigate their pharmacokinetic DDI properties. For application of TMDD models, quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are necessary to reduce the number of parameters. To realize those approximations of DDI TMDD models, we derive an ordinary differential equation (ODE) representation formulated in free concentration and free receptor variables. This ODE formulation can be straightforward implemented in typical PKPD software without solving any non-linear equation system arising from the QE or QSS approximation of the rapid binding assumptions. This manuscript is the second in a series to introduce and investigate DDI TMDD models and to apply the QE or QSS approximation. published

Target-mediated drug disposition (TMDD) describes drug binding with high affinity to a target such as a receptor. In application TMDD models are often over-parameterized and quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are essential to reduce the number of parameters. However, implementation of such approximations becomes difficult for TMDD models with drug–drug interaction (DDI) mechanisms. Hence, alternative but equivalent formulations are necessary for QE or QSS approximations. To introduce and develop such formulations, the single drug case is reanalyzed. This work opens the route for straightforward implementation of QE or QSS approximations of DDI TMDD models. The manuscript is the first part to introduce DDI TMDD models with QE or QSS approximations.

Combinations of gemcitabine and trabectedin exert modest synergistic cytotoxic effects on two pancreatic cancer cell lines. Here, systems pharmacodynamic (PD) models that integrate cellular response data and extend a prototype model framework were developed to characterize dynamic changes in cell cycle phases of cancer cell subpopulations in response to gemcitabine and trabectedin as single agents and in combination. Extensive experimental data were obtained for two pancreatic cancer cell lines (MiaPaCa-2 and BxPC-3), including cell proliferation rates over 0–120 h of drug exposure, and the fraction of cells in different cell cycle phases or apoptosis. Cell cycle analysis demonstrated that gemcitabine induced cell cycle arrest in S phase, and trabectedin induced transient cell cycle arrest in S phase that progressed to G2/M phase. Over time, cells in the control group accumulated in G0/G1 phase. Systems cell cycle models were developed based on observed mechanisms and were used to characterize both cell proliferation and cell numbers in the sub G1, G0/G1, S, and G2/M phases in the control and drug-treated groups. The proposed mathematical models captured well both single and joint effects of gemcitabine and trabectedin. Interaction parameters were applied to quantify unexplainable drug-drug interaction effects on cell cycle arrest in S phase and in inducing apoptosis. The developed models were able to identify and quantify the different underlying interactions between gemcitabine and trabectedin, and captured well our large datasets in the dimensions of time, drug concentrations, and cellular subpopulations.

Transit compartment models (TCM) are important tools in pharmacokinetic/pharmacodynamic (PKPD) modeling. In this work we investigate the relationship between TCMs with arbitrary initial values and lifespan models (LSM) with non-constant past and constant lifespan. We show that the total population in all transit compartments converges to a LSM, if the number of compartments n tends to infinity. The key to obtain this result is to establish a relationship between the initial values of the TCM and the non-constant past of the LSM. We apply the result to two already published PKPD models.

Drugs interact with their targets in different ways. A diversity of modeling approaches exists to describe the combination effects of two drugs. We investigate several combination effect terms (CET) regarding their underlying mechanism based on drug-receptor binding kinetics, empirical and statistical summation principles and indirect response models. A list with properties is provided and the interrelationship of the CETs is analyzed. A method is presented to calculate the optimal drug concentration pair to produce the half-maximal combination effect. This work provides a comprehensive overview of typically applied CETs and should shed light into the question as to which CET is appropriate for application in pharmacokinetic/pharmacodynamic models to describe a specific drug-drug interaction mechanism. published

This study investigates the combined effects of gemcitabine and trabectedin (ecteinascidin 743) in two pancreatic cancer cell lines and proposes a pharmacodynamic (PD) model to quantify their pharmacological interactions. Effects of gemcitabine and trabectedin upon the pancreatic cancer cell lines MiaPaCa-2 and BxPC-3 were investigated using cell proliferation assays. Cells were exposed to a range of concentrations of the two drugs, alone and in combination. Viable cell numbers were obtained daily over 5 days. A model incorporating nonlinear cytotoxicity, transit compartments, and an interaction parameter ψ was used to quantify the effects of the individual drugs and combinations. Simultaneous fitting of temporal cell growth profiles for all drug concentrations provided reasonable cytotoxicity parameter estimates (the cell killing rate constant K max and the sensitivity constant KC 50) for each drug. The interaction parameter ψ was estimated as 0.806 for MiaPaCa-2 and 0.843 for BxPC-3 cells, suggesting that the two drugs exert modestly synergistic effects. The proposed PD model enables quantification of the temporal profiles of drug combinations over a range of concentrations with drug-specific parameters. Based upon these in vitro studies, trabectedin may have augmented benefit in combination with gemcitabine. The PD model may have general relevance for the study of other cytotoxic drug combinations.