Mixed Effects Modelling and Optimal Design of TNFα Response in LPS Challenge Studies - Methods and Applications in Drug Discovery

\u27\u27Endotoxin and mycoplasma are Nature’s darkest secrets. If they are ever solved, Hell itself will open.\u27\u27 - Lewis Thomas* Endotoxin, or lipopolysaccharides (LPS), are heterogeneous components from the cell wall of Gram-Negative bacteria and a common challenger in the field of drug discovery. In challenge studies a system is provoked by a challenger, such as LPS, which is a commonly used design when studying respiratory and immune-mediated diseases. Unfortunately, LPS challenge experiments with the purpose of determining the inhibiting effect of a drug on a biomarker, such as tumour necrosis factor alpha (TNFα), gives complex data from which it is difficult to determine the drug effect. This thesis is based on three papers and focuses on the complexity of TNFα response data from LPS challenge studies and how mathematical tools can simplify the estimation of the pharmacodynamic effect of the drug.The first paper presents a second-generation TNFα turnover model able to capture TNFα response data from an extensive data set, using the non-linear mixed effects (NLME) modelling framework. The second paper uses the developed second-generation model for improvement of the experimental design in LPS challenge studies, in order to make the TNFα response data from LPS challenge studies as informative as possible. The third and last paper describes a user-friendly software package in Mathematica for estimation and evaluation of NLME models, called NLMEModeling, where the dynamical systems can be described either as ordinary or stochastic differential equations.*K. Brigham, editor. Endotoxin and the lungs, volume 77. Marcel Dekker Inc., New York, 1994. ISBN 0-8247-9222-X

Pharmacokinetic/pharmacodynamic modelling approaches in paediatric infectious diseases and immunology.

Pharmacokinetic/pharmacodynamic (PKPD) modelling is used to describe and quantify dose-concentration-effect relationships. Within paediatric studies in infectious diseases and immunology these methods are often applied to developing guidance on appropriate dosing. In this paper, an introduction to the field of PKPD modelling is given, followed by a review of the PKPD studies that have been undertaken in paediatric infectious diseases and immunology. The main focus is on identifying the methodological approaches used to define the PKPD relationship in these studies. The major findings were that most studies of infectious diseases have developed a PK model and then used simulations to define a dose recommendation based on a pre-defined PD target, which may have been defined in adults or in vitro. For immunological studies much of the modelling has focused on either PK or PD, and since multiple drugs are usually used, delineating the relative contributions of each is challenging. The use of dynamical modelling of in vitro antibacterial studies, and paediatric HIV mechanistic PD models linked with the PK of all drugs, are emerging methods that should enhance PKPD-based recommendations in the future

Investigations of a compartmental model for leucine kinetics using nonlinear mixed effects models with ordinary and stochastic differential equations

Nonlinear mixed effects models represent a powerful tool to simultaneously analyze data from several individuals. In this study a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analyzed. We find that the interindividual variation of the model parameters is much smaller for the nonlinear mixed effects models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger, and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion nonlinear mixed effects models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies

Pemodelan Farmakokinetika Berbasis Populasi dengan R: Model Dua Kompartemen Ekstravaskuler: Population-Based Pharmacokinetics Modeling With R: Two Compartment Extravascular Model

A Tutorial of two-compartment extravascular population-based pharmacokinetics modeling was performed by differential equations and non-linear mixed effect model approach. First, three-level differential equations of two-compartment pharmacokinetics were generated. Then, covariate and non-covariate models were developed by nlmeODE and nlme packages installed in R. The best model was selected according to AIC, BIC, and LogLik value. A model without covariates model was selected as the best model. The selected model showed a goodness of fit with experimental dataset and residual plot of the model revealed that no violations of model assumtions.  In conclusion, nlme and nlmeODE is capable to generate an adequate predictive model of two-compartment population-based pharmacokinetics for extravascular rout

Accelerated Predictive Healthcare Analytics with Pumas, a High Performance Pharmaceutical Modeling and Simulation Platform

Pharmacometric modeling establishes causal quantitative relationship between administered dose, tissue exposures, desired and undesired effects and patient’s risk factors. These models are employed to de-risk drug development and guide precision medicine decisions. Recent technological advances rendered collecting real-time and detailed data easy. However, the pharmacometric tools have not been designed to handle heterogeneous, big data and complex models. The estimation methods are outdated to solve modern healthcare challenges. We set out to design a platform that facilitates domain specific modeling and its integration with modern analytics to foster innovation and readiness to data deluge in healthcare. New specialized estimation methodologies have been developed that allow dramatic performance advances in areas that have not seen major improvements in decades. New ODE solver algorithms, such as coefficient-optimized higher order integrators and new automatic stiffness detecting algorithms which are robust to frequent discontinuities, give rise to up to 4x performance improvements across a wide range of stiff and non-stiff systems seen in pharmacometric applications. These methods combine with JIT compiler techniques and further specialize the solution process on the individual systems, allowing statically-sized optimizations and discrete sensitivity analysis via forward-mode automatic differentiation, to further enhance the accuracy and performance of the solving and parameter estimation process. We demonstrate that when all of these techniques are combined with a validated clinical trial dosing mechanism and non-compartmental analysis (NCA) suite, real applications like NLME parameter estimation see run times halved while retaining the same accuracy. Meanwhile in areas with less prior optimization of software, like optimal experimental design, we see orders of magnitude performance enhancements. Together we show a fast and modern domain specific modeling framework which lays a platform for innovation via upcoming integrations with modern analytics

Accelerated Predictive Healthcare Analytics with Pumas, a High Performance Pharmaceutical Modeling and Simulation Platform

Pharmacometric modeling establishes causal quantitative relationship between administered dose, tissue exposures, desired and undesired effects and patient’s risk factors. These models are employed to de-risk drug development and guide precision medicine decisions. Recent technological advances rendered collecting real-time and detailed data easy. However, the pharmacometric tools have not been designed to handle heterogeneous, big data and complex models. The estimation methods are outdated to solve modern healthcare challenges. We set out to design a platform that facilitates domain specific modeling and its integration with modern analytics to foster innovation and readiness to data deluge in healthcare. New specialized estimation methodologies have been developed that allow dramatic performance advances in areas that have not seen major improvements in decades. New ODE solver algorithms, such as coefficient-optimized higher order integrators and new automatic stiffness detecting algorithms which are robust to frequent discontinuities, give rise to up to 4x performance improvements across a wide range of stiff and non-stiff systems seen in pharmacometric applications. These methods combine with JIT compiler techniques and further specialize the solution process on the individual systems, allowing statically-sized optimizations and discrete sensitivity analysis via forward-mode automatic differentiation, to further enhance the accuracy and performance of the solving and parameter estimation process. We demonstrate that when all of these techniques are combined with a validated clinical trial dosing mechanism and non-compartmental analysis (NCA) suite, real applications like NLME parameter estimation see run times halved while retaining the same accuracy. Meanwhile in areas with less prior optimization of software, like optimal experimental design, we see orders of magnitude performance enhancements. Together we show a fast and modern domain specific modeling framework which lays a platform for innovation via upcoming integrations with modern analytics

Optimisation of congenital adrenal hyperplasia therapy in paediatric and foetal populations by leveraging pharmacometrics

Congenital adrenal hyperplasia (CAH) is a rare form of adrenal insufficiency causing deficiency of the highly regulated hormone cortisol and accumulation of its precursors such as 17α-hydroxyprogesterone (17-OHP) and subsequent androgen overproduction. Symptoms associated with CAH are premature pseudo puberty, earlier ending of longitudinal growth, and in female patients, virilisation and hirsutism. CAH patients require life-long cortisol replacement therapy, and dose optimisation through therapy monitoring is crucial to avoid potentially serious adverse events due to cortisol over- or underexposure. Paediatric CAH patients receive hydrocortisone (HC, synthetic cortisol) for cortisol replacement due to its lower risk for adverse effects whereas adult patients receive more potent glucocorticoids, e.g., dexamethasone (Dex). Especially in paediatrics, dried blood spot (DBS) sampling represents a highly advantageous alternative to plasma sampling. The major advantages include minimal invasiveness, low required blood volumes, stability of the analyte and easy storage of the matrix. Thus, DBS sampling has a high potential for facilitating CAH therapy monitoring routine. However, target concentrations of CAH biomarkers such as 17-OHP indicating a successful cortisol replacement are still unknown in DBS. To prevent in utero virilisation of female foetuses with CAH, prenatal therapy with Dex, administered to the pregnant women, has been conducted for decades. Yet, prenatal CAH therapy is still considered experimental since the traditionally administered Dex dose of 20 μg/kg/day is not based on a scientific rationale and is assumed to be too high, causing potential harm to the mother and foetus. In this regard, quantitative approaches such as pharmacometric modelling and simulation are powerful tools to provide a better understanding on pharmacokinetic (PK) and pharmacodynamic (PD) processes and to contribute to the optimisation of drug therapies. This work aimed at paving the way towards an optimised CAH therapy in paediatric and foetal populations by (1) providing insights into the quantitative relationship between cortisol concentrations measured in plasma and in DBS, (2) identifying paediatric target DBS concentrations for the commonly used biomarker 17-OHP and (3) suggesting a rational Dex dose in prenatal CAH therapy. To quantitatively link plasma and DBS cortisol concentrations, a semi-mechanistic nonlinear mixed-effects (NLME) PK model was developed based on data from paediatric CAH patients. The model characterised a nonlinear relationship between cortisol in plasma and DBS with plasma/DBS concentration ratios decreasing from approximately 8 to 2 with increasing DBS cortisol concentrations up to 800 nmol/L. These ratios decreased due to saturation of cortisol binding to corticosteroid-binding globulin and thus higher cortisol fraction associated with red blood cells. In future, more data from neonates and infants can be used to investigate a possible age effect, on the nonlinearity between plasma and DBS cortisol, in addition to the observed concentration effect. For the first time, a target morning DBS 17-OHP concentration range was determined for monitoring paediatric CAH patients. The DBS target range of 2.1-8.3 nmol/L was derived from simulations by applying a developed PK/PD model linking cortisol in plasma to 17-OHP in DBS and by leveraging healthy paediatric cortisol profiles. By extending the PK/PD model, and using the same simulation approach, circadian target concentration profiles, providing DBS biomarker targets for any time of the day, can be derived in future. Furthermore, in Bland-Altman and Passing-Bablok analyses, it was shown that capillary and venous DBS concentrations, which are both commonly obtained in clinical practice, are comparable to each other for cortisol and 17-OHP in paediatric CAH patients. For determining a reduced Dex dose which simultaneously decreases the risk for adverse events in prenatal CAH therapy and still shows sufficient efficacy in the foetus, a target Dex concentration range was identified from literature and a NLME model describing maternal Dex PK was developed. The Dex PK model was used to simulate maternal Dex concentration-time profiles following traditional or reduced Dex doses and to evaluate the tested dosing regimens with regard to the lowest effective dose. Based on the simulation results, a Dex dose of 7.5 μg/kg/day was suggested as a rational dose for prenatal CAH therapy, representing approximately a third of the traditional Dex dose. The suggested rational Dex dose should be evaluated in future clinical trials. In summary, this work provides quantitative insights into DBS measurements for CAH therapy monitoring, presents first target DBS concentrations for the biomarker 17-OHP in paediatrics, and suggests a first model-based dose rationale for Dex in prenatal CAH therapy. Ultimately, this work can help to improve CAH treatment with HC and Dex and therapy monitoring in the highly vulnerable paediatric and foetal populations

The role of population pharmacokinetic-pharmacodynamic modelling in antimalarial chemotherapy

Despite the high rates of mortality and morbidity associated with malaria very few new antimalarial drugs are being developed. Hence there is much to be gained by optimising currently available antimalarials. Using pharmacokinetic and pharmacodynamic data from field trials where mefloquine was administered either alone or in combination with artesunate important information regarding optimal dosing for the clinician has been obtained. The pharmacokinetics of mefloquine were influenced relatively little, or not at all, by factors such as age, sex, or measures of acute malaria severity. Splitting the 25 mglkg dose of mefloquine monotherapy was associated with a 50% increase in oral bioavailability, and bioavailability increased by 20% for the split dose on the combination treatment. Oral bioavailability was also observed to be associated with more rapid parasite clearance, a surrogate outcome measure for cure. A mechanistic mathematical model was developed that describes the change in total parasite burden with time in vivo, in the presence of mefloquine. Estimates for the pharmacokinetic and pharmacodynamic parameters were obtained from population modelling of pharmacokinetic and in vitro pharmacodynamic data, both derived from the same region. Model simulations confirmed that, early in the evolution of resistance, conventional assessments of the therapeutic response 28 days after treatment underestimate considerably the level of resistance. Longer follow-up is required. The model also indicates that initial deployment of a lower (l5-mglkg) dose of mefloquine provides a greater opportunity for the selection of resistant mutants and would be expected to lead more rapidly to resistance than de novo use of the higher (25-mglkg) dose. From the modelling of malaria therapy data it was observed that even in the absence of drugs the patient parasitaemia versus time profiles varied greatly between both patients and parasites. Parasite multiplication rate every 48 hours was estimated to be approximately 8 fold