Identifying a therapeutic target for vancomycin against staphylococci in young infants.

OBJECTIVES: To determine the therapeutic target of vancomycin in young infants with staphylococcal infections. METHODS: Retrospective data were collected for infants aged 0 to 90 days with CoNS or MRSA bacteraemia over a 4 year period at the Royal Children's Hospital Melbourne, Australia. Vancomycin broth microdilution MICs were determined. A published pharmacokinetic model was externally validated using the study dataset and a time-to-event (TTE) pharmacodynamic model developed to link the AUC of vancomycin with the event being the first negative blood culture. Simulations were performed to determine the trough vancomycin concentration that correlates with a 90% PTA of the target AUC24. RESULTS: Thirty infants, 28 with CoNS and 2 with MRSA bacteraemia, who had 165 vancomycin concentrations determined were included. The vancomycin broth microdilution MIC was determined for 24 CoNS and 1 MRSA isolate, both with a median MIC of 1 mg/L (CoNS range = 0.5-4.0). An AUC0-24 target of ≥300 mg/L·h or AUC24-48 of ≥424 mg/L·h. increased the chance of bacteriological cure by 7.8- and 7.3-fold, respectively. However, AUC0-24 performed best in the pharmacokinetic-pharmacodynamic model. This correlates with 24 to 48 h trough concentrations of >15-18 mg/L and >10-15 mg/L for 6- and 12-hourly dosing, respectively, and can be used to guide vancomycin therapy in this population. CONCLUSIONS: An AUC0-24 ≥300 mg/L·h or AUC24-48 ≥424 mg/L·h was associated with an increase in bacteriological cure in young infants with staphylococcal bloodstream infections.

A framework for simplification of quantitative systems pharmacology models in clinical pharmacology.

Quantitative systems pharmacology (QSP) is a relatively new discipline within modelling and simulation that has gained wide attention over the past few years. The application of QSP models spans drug-target identification and validation, through all drug development phases as well as clinical applications. Due to their detailed mechanistic nature, QSP models are capable of extrapolating knowledge to predict outcomes in scenarios that have not been tested experimentally, making them an important resource in experimental and clinical pharmacology. However, these models are complicated to work with due to their size and inherent complexity. This makes many applications of QSP models for simulation, parameter estimation and trial design computationally intractable. A number of techniques have been developed to simplify QSP models into smaller models that are more amenable to further analyses while retaining their accurate predictive capabilities. Different simplification techniques have different strengths and weaknesses and hence different utilities. Understanding the utilities of different methods is essential for selection of the best method for a particular situation. In this paper, we have created an overall framework for model simplification techniques that allows a natural categorisation of methods based on their utility. We provide a brief description of the concept underpinning the different methods and example applications. A summary of the utilities of methods is intended to provide a guide to modellers in their model endeavours to simplify these complicated models.

Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis-Menten model.

Nonlinear ordinary differential equations (ODEs) are common in pharmacokinetic-pharmacodynamic systems. Although their exact solutions cannot generally be determined via algebraic methods, their rapid and accurate solutions are desirable. Thus, numerical methods have a critical role. Inductive Linearization was proposed as a method to solve systems of nonlinear ODEs. It is an iterative approach that converts a nonlinear ODE into a linear time-varying (LTV) ODE, for which a range of standard integration techniques can then be used to solve (e.g., eigenvalue decomposition [EVD]). This study explores the properties of Inductive Linearization when coupled with EVD for integration of the LTV ODE and illustrates how the efficiency of the method can be improved. Improvements were based on three approaches, (1) incorporation of a convergence criterion for the iterative linearization process (for simulation and estimation), (2) creating more efficient step sizes for EVD (for simulation and estimation), and (3) updating the initial conditions of the Inductive Linearization (for estimation). The performance of these improvements were evaluated using single subject stochastic simulation-estimation with an application to a simple pharmacokinetic model with Michaelis-Menten elimination. The reference comparison was a standard non-stiff Runge-Kutta method with variable step size (ode45, MATLAB). Each of the approaches improved the speed of the Inductive Linearization technique without diminishing accuracy which, in this simple case, was faster than ode45 with comparable accuracy in the parameter estimates. The methods described here can easily be implemented in standard software programme such as R or MATLAB. Further work is needed to explore this technique for estimation in a population approach setting.

Evaluation of designs for renal drug studies based on the European Medicines Agency and Food and Drug Administration guidelines for drugs that are predominantly secreted.

AIMS: Dose adjustment for drugs eliminated by the kidneys generally assume a linear relationship between renal drug clearance (CLR ) and glomerular filtration rate (GFR). This assumption may not hold for drugs that undergo extensive tubular secretion where nonlinearity in drug handling is expected. The aim of this study is to determine if renal drug study designs recommended by the European Medicines Agency (EMA) and Food and Drug Administration (FDA) could distinguish linear from nonlinear renal drug handling. METHODS: In this simulation and estimation study, the study designs based on the EMA and FDA guidelines for Phase I renal drug studies were evaluated for their ability to discriminate a linear from a nonlinear relationship between CLR and GFR. The number of subjects for each simulated study ranged from 4 to 960. Power, relative standard error and bias were calculated. RESULTS: Study designs under the EMA and FDA guidelines required ≥8 and ≥48 subjects, respectively, to achieve ≥80% power to discriminate a linear from nonlinear relationship between CLR and GFR. The relative standard error of estimated parameters were 13-37 and 17-44% for the designs with 24 subjects under the EMA and FDA guidelines, respectively. The bias in parameter estimates under the EMA designs were not evident, however, they were biased (13-21%) under the FDA designs. CONCLUSION: The EMA design was found to require fewer subjects (n = 8) compared to the FDA (n = 48) to discriminate linear from nonlinear drug renal handling at ≥80% study power while both the designs perform poorly for the parameter precision.

Sulfate conjugation may be the key to hepatotoxicity in paracetamol overdose.

Paracetamol-induced hepatotoxicity is the leading cause of acute liver failure in many countries, including North America and the United Kingdom. Among the three dominant paracetamol metabolism pathways (i.e. glucuronidation, sulfation and oxidation), the importance of sulfation is often underestimated because of the general thinking that the sulfation pathway is saturated at therapeutic doses and ultimately accounts for a limited proportion of the fate of a paracetamol dose. We illustrate that insufficient sulfation leads to a shift in biotransformation of paracetamol to toxic oxidation pathways and patients with low sulfate reserves are at higher risk of paracetamol toxicity. Here, we propose that sulfation is of critical importance in understanding the risk of liver toxicity secondary to paracetamol overdose. Serum inorganic sulfate, a measurable substrate on the causal path of paracetamol-induced liver toxicity, should be considered a biomarker for potential toxicity as well as a target for treatment.

Does the intact nephron hypothesis provide a reasonable model for metformin dosing in chronic kidney disease?

This research explored the intact nephron hypothesis (INH) as a model for metformin dosing in patients with chronic kidney disease (CKD). The INH assumes that glomerular filtration rate (GFR) will account for all kidney drug handling even for drugs eliminated by tubular secretion like metformin. We conducted two studies: (1) a regression analysis to explore the relationship between metformin clearance and eGFR metrics, and (2) a joint population pharmacokinetic analysis to test the relationship between metformin renal clearance and gentamicin clearance. The relationship between metformin renal clearance and eGFR metrics and gentamicin clearance was found to be linear, suggesting that a proportional dose reduction based on GFR in patients with CKD is reasonable.

Reduction of quantitative systems pharmacology models using artificial neural networks.

Quantitative systems pharmacology models are often highly complex and not amenable to further simulation and/or estimation analyses. Model-order reduction can be used to derive a mechanistically sound yet simpler model of the desired input-output relationship. In this study, we explore the use of artificial neural networks for approximating an input-output relationship within highly dimensional systems models. We illustrate this approach using a model of blood coagulation. The model consists of two components linked together through a highly dimensional discontinuous interface, which creates a difficulty for model reduction techniques. The proposed approach enables the development of an efficient approximation to complex models with the desired level of accuracy. The technique is applicable to a wide variety of models and provides substantial speed boost for use of such models in simulation and control purposes.

A general model for cell death and biomarker release from injured tissues.

Cellular response to insults may result in the initiation of different cell death processes. For many cases the cell death process will result in an acute release of cellular material that in some circumstances provides valuable information about the process (i.e. may represent a biomarker). The characteristics of the biomarker release is often informative and plays critical roles in clinical practice and toxicology research. The aim of this study is to develop a general, semi-mechanistic model to describe cell turnover and biomarker release by injured tissue that can be used for estimation in pharmacokinetic and (toxicokinetic)-pharmacodynamic studies. The model included three components: (1) natural tissue turnover, (2) biomarker release from cell death and its movement from the cell through the tissue into the blood, (3) different target insult mechanisms of cell death. We applied the general model to biomarker release profiles for four different cell insult causes. Our model simulations showed good agreements with reported data under both delayed release and rapid release cases. Additionally, we illustrate the use of the model to provide different biomarker profiles. We also provided details on interpreting parameters and their values for other researchers to customize its use. In conclusion, our general model provides a basic structure to study the kinetic behaviour of biomarker release and disposition after cellular insult.

Lack of effect of tart cherry concentrate dose on serum urate in people with gout.

OBJECTIVES: Cherry concentrate has been suggested to reduce serum urate (SU) and gout flares. The aims of this study were to determine the magnitude of the effect of tart cherry concentrate on SU in people with gout, the most effective dose of tart cherry concentrate for lowering SU, and adverse effects. METHODS: Fifty people with gout and SU > 0.36 mmol/l were recruited. Half were on allopurinol and half were on no urate-lowering therapy. Participants were randomized to receive tart cherry juice concentrate: placebo, 7.5 ml, 15 ml, 22.5 ml or 30 ml twice daily for 28 days. Blood samples were taken at baseline, then at 1, 3 and 5 h post cherry and then on days 1, 3, 7, 14, 21 and 28. The area under the curve for SU was calculated over the 28-day study period. RESULTS: Cherry concentrate dose had no significant effect on reduction in SU area under the curve, urine urate excretion, change in urinary anthocyanin between day 0 and day 28, or frequency of gout flares over the 28-day study period (P = 0.76). There were 24 reported adverse events, with only one (hyperglycaemia) considered possibly to be related to cherry concentrate. Allopurinol use did not modify the effect of cherry on SU or urine urate excretion. CONCLUSION: Tart cherry concentrate had no effect on SU or urine urate excretion. If there is an effect of cherry concentrate on gout flares over a longer time period, it is not likely to be mediated by reduction in SU. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry (ANZCTR), https://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=368887, ANZCTR 12615000741583).

The pharmacokinetics of meropenem and piperacillin-tazobactam during sustained low efficiency haemodiafiltration (SLED-HDF).

OBJECTIVE: We analysed the pharmacokinetics of meropenem and piperacillin-tazobactam in patients undergoing a standardised session of sustained low efficiency haemodiafiltration (SLED-HDF) to inform the dosing of these drugs in an acute setting. PARTICIPANTS: Six stable patients with end-stage kidney disease. METHODS: An open-label pilot pharmacokinetic study of meropenem and piperacillin-tazobactam. SLED-HDF was undertaken for 4 h. Plasma drug concentrations were measured pre- and post-filter and in the effluent at multiple time points. The pharmacokinetic data was analysed using non-compartmental methods. The fraction of time that individual plasma concentration profiles were predicted to remain above the MIC break-points for commonly isolated gram-negative pathogens during a prolonged SLED-HDF session was assessed using two targets; fT > MIC (fraction of time above the MIC) and the more aggressive fT > 4 × MIC (fraction of time above 4 × MIC). RESULTS: Meropenem total and SLED-HDF clearance ranged from 141 to 180 mL/min and 126-205 mL/min, respectively. Piperacillin total and SLED-HDF clearance values ranged from 131 to 252 mL/min and 135-162 mL/min, respectively. Our results suggest that prolonged SLED-HDF (12 h) will only maintain a sufficient meropenem and piperacillin-tazobactam plasma concentration to achieve a target of fT > MIC for gram-negative pathogens (MIC 2 mg/L-meropenem, 8 mg/L-piperacillin-tazobactam) for less than 40% of the time. Plasma concentrations would be inadequate to achieve the more aggressive target of 100 % fT > 4xMIC target recommended for critically unwell patients. CONCLUSIONS: The pharmacokinetic data obtained from this pilot study demonstrate significant quantities of meropenem and piperacillin are removed during a SLED-HDF session. This may lead to subtherapeutic concentrations of piperacillin and meropenem over the duration of HDF session. TRIAL REGISTRATION: Australasian Clinical Trials Registry Network (ACTRN12616000078459).

The intact nephron hypothesis as a model for renal drug handling.

PURPOSE: The intact nephron hypothesis (INH) states that impaired renal function results from a reduction in the number of complete (intact) nephrons. Under this model, renal drug clearance is assumed to be a linear function of glomerular filtration while tubular handling is ignored. The aims of this study were to systematically review published studies designed to test the INH and to assess the strength of the study designs used. METHODS: A systematic literature search was conducted in MEDLINE, EMBASE and Google Scholar. Studies specifically designed to understand the relationship between glomerular and tubular function across different levels of renal function were included. Studies that found a linear relationship between GFR and tubular clearance were deemed to support the INH while studies that found a non-linear relationship did not support the INH. Study design was accessed using a bespoke strength of evidence score. RESULTS: Thirty studies met the criteria for inclusion. Of these, 24 did not support the INH. Studies that did not support the INH used methods for measuring tubular clearance that were more robust and included subjects with a wider range of GFR values than studies that supported the INH. DISCUSSION: Our results suggest that the INH may not be a suitable general model for renal drug handling, particularly for drugs that are eliminated by tubular mechanisms. Further studies to assess the clinical importance of a non-linear relationship between drug clearance and GFR are warranted.

Automated proper lumping for simplification of linear physiologically based pharmacokinetic systems.

Physiologically based pharmacokinetic (PBPK) models are an important type of systems model used commonly in drug development before commencement of first-in-human studies. Due to structural complexity, these models are not easily utilised for future data-driven population pharmacokinetic (PK) analyses that require simpler models. In the current study we aimed to explore and automate methods of simplifying PBPK models using a proper lumping technique. A linear 17-state PBPK model for fentanyl was identified from the literature. Four methods were developed to search the optimal lumped model, including full enumeration (the reference method), non-adaptive random search (NARS), scree plot plus NARS, and simulated annealing (SA). For exploratory purposes, it was required that the total area under the fentanyl arterial concentration-time curve (AUC) between the lumped and original models differ by 0.002% at maximum. In full enumeration, a 4-state lumped model satisfying the exploratory criterion was found. In NARS, a lumped model with the same number of lumped states was found, requiring a large number of random samples. The scree plot provided a starting lumped model to NARS and the search completed within a short time. In SA, a 4-state lumped model was consistently delivered. In simplify an existing linear fentanyl PBPK model, SA was found to be robust and the most efficient and may be suitable for general application to other larger-scale linear systems. Ultimately, simplified PBPK systems with fundamental mechanisms may be readily used for data-driven PK analyses.

Development of a nonlinear hierarchical model to describe the disposition of deuterium in mother-infant pairs to assess exclusive breastfeeding practice.

The World Health Organization recommends exclusive breastfeeding (EBF) for the first 6 months after birth. The deuterium oxide dose-to-the-mother (DTM) technique is used to distinguish EBF based on a cut-off (< 25 g/day) of water intake from sources other than breastmilk. This value is based on a theoretical threshold and has not been verified in field studies. The aim of this study was to estimate the water intake cut-off value that can be used to define EBF practice. One hundred and twenty-one healthy infants, aged 2.5-5.5 months who were deemed to be EBF were recruited. After administration of deuterium to the mothers, saliva was sampled from mother and infant pairs over a 14-day period. Validation of infant feeding practices was conducted via home observation over six non-consecutive days with caregiver recall. A fully Bayesian framework using a gradient-based Markov chain Monte Carlo approach implemented in Stan was used to estimate the cut-off of non-milk water intake of EBF infants. From the original data set, 113 infants were determined to be EBF and provided 1500 paired mother-infant observations. The deuterium saliva concentrations were best described by two linked 1-compartment models (mother and infant), with body weight as a covariate on the mother's volume of distribution and infant's body weight on infant's water clearance rate. The cut-off value was based on the 90th percentile of the posterior distribution of non-milk water intake and was 86.6 g/day. This cut-off value can be used in future field studies in other geographic regions to determine exclusivity of breast feeding practices in order to determine their potential public health needs.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

A general empirical model for renal drug handling in pharmacokinetic analyses.

Dose adjustment in renal insufficiency is generally based on the assumption that renal drug clearance is related linearly to glomerular filtration rate. The theory underpinning this model is the intact nephron hypothesis, which says that impaired renal function is caused by a reduction in the number of complete (intact) nephrons. The purpose of the present commentary is to propose a general empirical model for renal drug handling. We will explore models for renal function under two scenarios: one that aligns with the intact nephron hypothesis, and one that relaxes the assumptions of this hypothesis. We propose that a nonlinear, non-intact nephron model will allow for differences in renal drug handling, while incorporating the intact nephron hypothesis model as a special case.

Assessing robustness of designs for random effects parameters for nonlinear mixed-effects models.

Optimal designs for nonlinear models are dependent on the choice of parameter values. Various methods have been proposed to provide designs that are robust to uncertainty in the prior choice of parameter values. These methods are generally based on estimating the expectation of the determinant (or a transformation of the determinant) of the information matrix over the prior distribution of the parameter values. For high dimensional models this can be computationally challenging. For nonlinear mixed-effects models the question arises as to the importance of accounting for uncertainty in the prior value of the variances of the random effects parameters. In this work we explore the influence of the variance of the random effects parameters on the optimal design. We find that the method for approximating the expectation and variance of the likelihood is of potential importance for considering the influence of random effects. The most common approximation to the likelihood, based on a first-order Taylor series approximation, yields designs that are relatively insensitive to the prior value of the variance of the random effects parameters and under these conditions it appears to be sufficient to consider uncertainty on the fixed-effects parameters only.

Deterministic identifiability of population pharmacokinetic and pharmacokinetic-pharmacodynamic models.

Identifiability is an important component of pharmacokinetic-pharmacodynamic (PKPD) model development. Structural identifiability is concerned with the uniqueness of the model parameters for a set of perfect input-output data and deterministic identifiability with the precision of parameter estimation given imperfect input-output data. We introduce two subcategories of deterministic identifiability, external and internal, and consider factors that distinguish between these forms. We define external deterministic identifiability as a function of externally controllable variables, i.e., the design, and internal deterministic identifiability as a function of the model and its parameter values. The concepts are explored using three common PK and PKPD models, and verified for their precision for the selected set of parameter values under optimal design.

Pharmacokinetic-Pharmacodynamic Model for the Effect of l-Arginine on Endothelial Function in Patients with Moderately Severe Falciparum Malaria.

Impaired organ perfusion in severe falciparum malaria arises from microvascular sequestration of parasitized cells and endothelial dysfunction. Endothelial dysfunction in malaria is secondary to impaired nitric oxide (NO) bioavailability, in part due to decreased plasma concentrations of l-arginine, the substrate for endothelial cell NO synthase. We quantified the time course of the effects of adjunctive l-arginine treatment on endothelial function in 73 patients with moderately severe falciparum malaria derived from previous studies. Three groups of 10 different patients received 3 g, 6 g, or 12 g of l-arginine as a half-hour infusion. The remaining 43 received saline placebo. A pharmacokinetic-pharmacodynamic (PKPD) model was developed to describe the time course of changes in exhaled NO concentrations and reactive hyperemia-peripheral arterial tonometry (RH-PAT) index values describing endothelial function and then used to explore optimal dosing regimens for l-arginine. A PK model describing arginine concentrations in patients with moderately severe malaria was extended with two pharmacodynamic biomeasures, the intermediary biochemical step (NO production) and endothelial function (RH-PAT index). A linear model described the relationship between arginine concentrations and exhaled NO. NO concentrations were linearly related to RH-PAT index. Simulations of dosing schedules using this PKPD model predicted that the time within therapeutic range would increase with increasing arginine dose. However, simulations demonstrated that regimens of continuous infusion over longer periods would prolong the time within the therapeutic range even more. The optimal dosing regimen for l-arginine is likely to be administration schedule dependent. Further studies are necessary to characterize the effects of such continuous infusions of l-arginine on NO and microvascular reactivity in severe malaria.

Evidence for the changing regimens of acetylcysteine.

Paracetamol overdose prior to the introduction of acetylcysteine was associated with significant morbidity. Acetylcysteine is now the mainstay of treatment for paracetamol poisoning and has effectively reduced rates of hepatotoxicity and death. The current three-bag intravenous regimen with an initial high loading dose was empirically derived four decades ago and has not changed since. This regimen is associated with a high rate of adverse effects due mainly to the high initial peak acetylcysteine concentration. Furthermore, there are concerns that the acetylcysteine concentration is not adequate for 'massive' overdoses and that the dose and duration may need to be altered. Various novel regimens have been proposed, looking to address these issues. Many of these modified regimens aim to decrease the rate of adverse reactions by slowing the loading dose and thereby decrease the peak concentration. We used a published population pharmacokinetic model of acetylcysteine to simulate these modified regimens. We determined mean peak and 20 h acetylcysteine concentrations and area under the under the plasma concentration-time curve to compare these regimens. Those regimens that resulted in a lower peak acetylcysteine concentration have been shown in studies to have a lower rate of adverse events. However, these studies were too small to show whether they are as effective as the traditional regimen. Further research is still needed to determine the optimum dose and duration of acetylcysteine that results in the fewest side-effects and treatment failures. Indeed, a more patient-tailored approach might be required, whereby the dose and duration are altered depending on the paracetamol dose ingested or paracetamol concentrations.