Delayed logistic indirect response models: realization of oscillating behavior

Formulation and Validation of an Extended Sigmoid Emax Model in Pharmacodynamics

PURPOSE OR OBJECTIVE

Drug concentration-response curves (DRCs) are crucial in pharmacology for assessing the drug effects on biological systems. The widely used sigmoid Emax model, which accounts for response saturation, relies heavily on the effective drug concentration ( E D 50 ). This reliance can lead to validation errors and inaccuracies in model fitting. The Emax model cannot generate multiple DRCs, raising concerns about whether the dataset is fully utilized.

METHODS

This study formulates an extended Emax (eEmax) model designed to overcome these limitations. The eEmax model generates multiple DRCs from a single dataset by using various estimatedα ' s ∈ 0,100 , while keeping E D α fixed, rather than estimating an E D 50 value as in the Emax model.

RESULTS

This model effectively captures a broader range of concentration-response behavior, including non-sigmoidal patterns, thus providing greater flexibility and accuracy compared to the Emax model. Validation using various drug-response data and PKPD frameworks demonstrates the eEmax model's improved accuracy and versatility in handling concentration-response data.

CONCLUSIONS

The eEmax model provides a robust and flexible method for drug concentration-response analysis, facilitating the generation of multiple DRCs from a single dataset and reducing the possibility of validation errors. This model is particularly valuable for its ease of use and its capability to fully utilize datasets, providing its potential in PKPD modeling and drug discovery.

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.

Leveraging Predictive Pharmacometrics-Based Algorithms to Enhance Perinatal Care-Application to Neonatal Jaundice

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.

Circadian rhythms: influence on physiology, pharmacology, and therapeutic interventions

Circadian rhythms are ubiquitous phenomena that recur daily in a self-sustaining, entrainable, and oscillatory manner, and orchestrate a wide range of molecular, physiological, and behavioral processes. Circadian clocks are comprised of a hierarchical network of central and peripheral clocks that generate, sustain, and synchronize the circadian rhythms. The functioning of the peripheral clock is regulated by signals from autonomic innervation (from the central clock), endocrine networks, feeding, and other external cues. The critical role played by circadian rhythms in maintaining both systemic and tissue-level homeostasis is well established, and disruption of the rhythm has direct consequence for human health, disorders, and diseases. Circadian oscillations in both pharmacokinetics and pharmacodynamic processes are known to affect efficacy and toxicity of several therapeutic agents. A variety of modeling approaches ranging from empirical to more complex systems modeling approaches have been applied to characterize circadian biology and its influence on drug actions, optimize time of dosing, and identify opportunities for pharmacological modulation of the clock mechanisms and their downstream effects. In this review, we summarize current understanding of circadian rhythms and its influence on physiology, pharmacology, and therapeutic interventions, and discuss the role of chronopharmacometrics in gaining new insights into circadian rhythms and its applications in chronopharmacology.

OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

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.

Estimating drug potency in the competitive target mediated drug disposition (TMDD) system when the endogenous ligand is included

Predictions for target engagement are often used to guide drug development. In particular, when selecting the recommended phase 2 dose of a drug that is very safe, and where good biomarkers for response may not exist (e.g. in immuno-oncology), a receptor occupancy prediction could even be the main determinant in justifying the approved dose, as was the case for atezolizumab. The underlying assumption in these models is that when the drug binds its target, it disrupts the interaction between the target and its endogenous ligand, thereby disrupting downstream signaling. However, the interaction between the target and its endogenous binding partner is almost never included in the model. In this work, we take a deeper look at the in vivo system where a drug binds to its target and disrupts the target's interaction with an endogenous ligand. We derive two simple steady state inhibition metrics (SSIMs) for the system, which provides intuition for when the competition between drug and endogenous ligand should be taken into account for guiding drug development.

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.

Pharmacometrics and Machine Learning Partner to Advance Clinical Data Analysis

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.

Indirect pharmacodynamic models for responses with circadian removal

Rhythmicity in baseline responses over a 24-h period for an indirect pharmacological effect R(t) can arise from either a periodic time-dependent input rate [Formula: see text] or a periodic time-dependent loss constant [Formula: see text]. If either [Formula: see text] or [Formula: see text] follows some nonstationary biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. Indirect response models assuming time-dependent input rates [Formula: see text] have been utilized to capture drug effects on various physiological responses such as hormone suppression, immune cell trafficking, and gene expression in tissues. This paradigm was extended to consider responses with circadian-controlled loss [Formula: see text] mechanisms. Theoretical equations describing this model are presented and simulations were performed to examine expected response behaviors. The model was able to capture the chronobiology and pharmacodynamics of applicable drug responses, including the uricosuric effects of lesinurad in humans, suppression of the beta amyloid (Aβ) peptide by a gamma-secretase inhibitor in mouse brain, and the modulation of extracellular dopamine by a dopamine transporter inhibitor in rat brain. This type of model has a mechanistic basis and shows utility for capturing drug responses displaying nonstationary baselines controlled by removal mechanism(s).