Understanding time to peak effect of propofol as sole agent on bispectral index in children aged 2-12 years.

BACKGROUND: The pharmacodynamics of propofol in children have previously been described with the proprietary bispectral index (BIS) as an effect-site marker, and it has been suggested that the rate of onset of propofol might be age dependent, that is, a shorter time to peak effect in younger children. However, these analyses were potentially confounded by co-administered drugs, in particular opioids and benzodiazepines. Thus, the goal of this prospective study was to characterize the influence of age and weight on the onset of hypnotic effects from propofol, reflected by the time to peak of propofol effect-site concentration in the absence of additional drugs. METHODS: A total of 46 healthy children aged 2-12 years presenting for elective surgery were included in our observational cohort study. Solely propofol was administered via a target-controlled infusion pump programmed with the Paedfusor pharmacokinetic model. The BIS and infusion pump data were recorded. The effect of an induction "bolus" was recorded having stopped the pump once a propofol plasma target concentration of 7 µg.mL-1 was achieved. A direct-response and an indirect-response model in the context of nonlinear mixed-effects modeling was used to characterize and compare BIS data in children aged 2-6 years and older children aged 8-12 years. RESULTS: Time to peak of propofol effect-site concentration had a difference (p-value <.01) for age and weight, that is 84 [74, 96] (median [IQR] secs for children aged 2-6 years vs. 99 [91, 113] secs for children aged 8-12 years and 82 [71, 95] secs for weight 11-25 kg vs. 99 [91, 114] secs for weight 30-63 kg). The plasma effect-site equilibration rate constant for propofol had a heterogeneous distribution with a median of 2.36 (IQR: 2.05-2.93; range: 0.83-7.31) per minute but showed a weight-dependent effect in patients with weight below 45 kg. CONCLUSIONS: In children, the age and weight have an influence on time to peak effect of propofol. In the absence of opioids and benzodiazepines, time to peak effect was approximately 20% longer in children aged 8-12 years as compared to younger children. Such clinically relevant age and weight effects are an important consideration in the individualized titration of propofol dosing.

Low-dimensional neural ODEs and their application in pharmacokinetics.

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 low-dimensional NODE structures based on PK principles. We discuss two challenges of NODEs, overfitting and extrapolation to unseen data, and provide practical solutions to these problems. We illustrate concept and application of our proposed low-dimensional 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 the data well 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.

Computing optimal drug dosing regarding efficacy and safety: the enhanced OptiDose method in NONMEM.

Recently, an optimal dosing algorithm (OptiDose) was developed to compute the optimal drug doses for any pharmacometrics model for a given dosing scenario. In the present work, we enhance the OptiDose concept to compute optimal drug dosing with respect to both efficacy and safety targets. Usually, these are not of equal importance, but one is a top priority, that needs to be satisfied, whereas the other is a secondary target and should be achieved as good as possible without failing the top priority target. Mathematically, this leads to state-constrained optimal control problems. In this paper, we elaborate how to set up such problems and transform them into classical unconstrained optimal control problems which can be solved in NONMEM. Three different optimal dosing tasks illustrate the impact of the proposed enhanced OptiDose method.

Computing optimal drug dosing with OptiDose: implementation in NONMEM.

Determining a drug dosing recommendation with a PKPD model can be a laborious and complex task. Recently, an optimal dosing algorithm (OptiDose) was developed to compute the optimal doses for any pharmacometrics/PKPD model for a given dosing scenario. In the present work, we reformulate the underlying optimal control problem and elaborate how to solve it with standard commands in the software NONMEM. To demonstrate the potential of the OptiDose implementation in NONMEM, four relevant but substantially different optimal dosing tasks are solved. In addition, the impact of different dosing scenarios as well as the choice of the therapeutic goal on the computed optimal doses are discussed.

Delay differential equations based models in NONMEM.

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.

The rhythm of a preterm neonate's life: ultradian oscillations of heart rate, body temperature and sleep cycles.

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.

Modeling of levothyroxine in newborns and infants with congenital hypothyroidism: challenges and opportunities of a rare disease multi-center study.

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.

Clinical Pharmacology and Pharmacometrics to Better Understand Physiological Changes 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.

Enhanced early prediction of clinically relevant neonatal hyperbilirubinemia with machine learning.

BACKGROUND: Machine learning models may enhance the early detection of clinically relevant hyperbilirubinemia based on patient information available in every hospital. METHODS: 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. RESULTS: 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. CONCLUSION: 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.

Methadone dosing strategies in preterm neonates can be simplified.

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.

Delayed logistic indirect response models: realization of oscillating behavior.

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.

Caffeine Citrate Dosing Adjustments to Assure Stable Caffeine Concentrations in Preterm Neonates.

OBJECTIVE: To identify dosing strategies that will assure stable caffeine concentrations in preterm neonates despite changing caffeine clearance during the first 8 weeks of life. METHODS: A 3-step simulation approach was used to compute caffeine doses that would achieve stable caffeine concentrations in the first 8 weeks after birth: (1) a mathematical weight change model was developed based on published weight distribution data; (2) a pharmacokinetic model was developed based on published models that accounts for individual body weight, postnatal, and gestational age on caffeine clearance and volume of distribution; and (3) caffeine concentrations were simulated for different dosing regimens. RESULTS: A standard dosing regimen of caffeine citrate (using a 20 mg/kg loading dose and 5 mg/kg/day maintenance dose) is associated with a maximal trough caffeine concentration of 15 mg/L after 1 week of treatment. However, trough concentrations subsequently exhibit a clinically relevant decrease because of increasing clearance. Model-based simulations indicate that an adjusted maintenance dose of 6 mg/kg/day in the second week, 7 mg/kg/day in the third to fourth week and 8 mg/kg/day in the fifth to eighth week assures stable caffeine concentrations with a target trough concentration of 15 mg/L. CONCLUSIONS: To assure stable caffeine concentrations during the first 8 weeks of life, the caffeine citrate maintenance dose needs to be increased by 1 mg/kg every 1-2 weeks. These simple adjustments are expected to maintain exposure to stable caffeine concentrations throughout this important developmental period and might enhance both the short- and long-term beneficial effects of caffeine treatment.

Disease Progression Modeling to Evaluate the Effects of Enzyme Replacement Therapy on Kidney Function in Adult Patients with the Classic Phenotype of Fabry Disease.

BACKGROUND/AIMS: Fabry disease (FD) is a rare inherited lysosomal storage disease with common and serious kidney complications. Enzyme replacement therapies (ERT) with agalsidase-α and -ß were investigated to characterize their therapeutic effect on kidney function in FD patients with Classic phenotype. METHODS: The prospective FD cohort consisted of 98 genetically confirmed patients (females, n = 61, males, n = 37). The median [interquartile range] follow-up time (time difference from first to last visit) was 9 [6, 12] years. The median age of ERT start was 36 [21 - 54] years for females and 39 [28 - 49] years for males. RESULTS: A disease progression model was developed to (i) characterize the time course of estimated glomerular filtration rate (eGFR) and (ii) evaluate therapeutic effects of ERT on kidney function. Change in eGFR over time was best described by the linear model. Females had stable kidney function with and without ERT (eGFR slopes of -0.07 ml/min/1.73m^2 per year and 0.52 ml/min/1.73m^2 per year, respectively). Males with ERT showed an eGFR decrease of -3.07 ml/min/1.73m^2 per year. CONCLUSION: Mathematical disease progression modeling indicates that there is no clear therapeutic effect of ERT on kidney function in adult patients with Classic Phenotype of FD. Interpretation of these findings should take into account that the study is not randomized and lacks a placebo controlled group. Further investigations are warranted to clarify whether earlier ERT initiation before 18 years of age, higher ERT dose or more intensive therapies can preserve kidney function.

Target-mediated drug disposition with drug-drug interaction, Part I: single drug case in alternative formulations.

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.

Target mediated drug disposition with drug-drug interaction, Part II: competitive and uncompetitive cases.

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.

Assessment of non-linear combination effect terms for drug-drug interactions.

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.

Distributed transit compartments for arbitrary lifespan distributions in aging populations.

Transit compartment models (TCM) are often used to describe aging populations where every individual has its own lifespan. However, in the TCM approach these lifespans are gamma-distributed which is a serious limitation because often the Weibull or more complex distributions are realistic. Therefore, we extend the TCM concept to approximately describe any lifespan distribution and call this generalized concept distributed transit compartment models (DTCMs). The validity of DTCMs is obtained by convergence investigations. From the mechanistic perspective the transit rates are directly controlled by the lifespan distribution. Further, DTCMs could be used to approximate the convolution of a signal with a probability density function. As example a stimulatory effect of a drug in an aging population with a Weibull-distributed lifespan is presented where distribution and model parameters are estimated based on simulated data.

Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.

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.

Applying Neural ODEs to Derive a Mechanism-Based Model for Characterizing Maturation-Related Serum Creatinine Dynamics in Preterm Newborns.

Serum creatinine in neonates follows complex dynamics due to maturation processes, most pronounced in the first few weeks of life. The development of a mechanism-based model describing complex dynamics requires high expertise in pharmacometric (PMX) modeling and substantial model development time. A recently published machine learning (ML) approach of low-dimensional neural ordinary differential equations (NODEs) is capable of modeling such data from newborns automatically. However, this efficient data-driven approach in itself does not result in a clinically interpretable model. In this work, an approach to deriving an interpretable model with reasonable PMX-type functions is presented. This "translation" was applied to derive a PMX model for serum creatinine in neonates considering maturation processes and covariates. The developed model was compared to a previously published mechanism-based PMX model whereas both models had similar mechanistic structures. The developed model was then utilized to simulate serum creatinine concentrations in the first few weeks of life considering different covariate values for gestational age and birth weight. The reference serum creatinine values derived from these simulations are consistent with observed serum creatinine values and previously published reference values. Thus, the presented NODE-based ML approach to model complex serum creatinine dynamics in newborns and derive interpretable, mathematical-statistical components similar to those in a conventional PMX model demonstrates a novel, viable approach to facilitate the modeling of complex dynamics in clinical settings and pediatric drug development.