Laurent Bourguignon

The Hill equation: a review of its capabilities in pharmacological modelling.

The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug–receptor relationships. Many pharmacokinetic–pharmacodynamic models have used the Hill equation to describe nonlinear drug dose–response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill’s original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences.

Population Modeling and Monte Carlo Simulation Study of the Pharmacokinetics and Antituberculosis Pharmacodynamics of Rifampin in Lungs

ABSTRACT Little information exists on the pulmonary pharmacology of antituberculosis drugs. We used population pharmacokinetic modeling and Monte Carlo simulation to describe and explore the pulmonary pharmacokinetics and pharmacodynamics of rifampin (RIF; rifampicin). A population pharmacokinetic model that adequately described the plasma, epithelial lining fluid (ELF), and alveolar cell (AC) concentrations of RIF in a population of 34 human volunteers was made by use of the nonparametric adaptive grid (NPAG) algorithm. The estimated concentrations correlated well with the measured concentrations, and there was little bias and good precision. The results obtained with the NPAG algorithm were then imported into Matlab software to perform a 10,000-subject Monte Carlo simulation. The ability of RIF to suppress the development of drug resistance and to induce a sufficient bactericidal effect against Mycobacterium tuberculosis was evaluated by calculating the proportion of subjects achieving specific target values for the maximum concentration of drug (Cmax)/MIC ratio and the area under the concentration-time curve from time zero to 24 h (AUC0-24)/MIC ratio, respectively. At the lowest MIC (0.01 mg/liter), after the administration of one 600-mg oral dose, the rates of target attainment for Cmax/MIC (≥175) were 95% in ACs, 48.8% in plasma, and 35.9% in ELF. Under the same conditions, the target attainment results for the killing effect were 100% in plasma (AUC0-24/MIC ≥ 271) but only 54.5% in ELF (AUC0-24/MIC ≥ 665). The use of a 1,200-mg RIF dose was associated with better results for target attainment. The overall results suggest that the pulmonary concentrations obtained with the standard RIF dose are too low in most subjects. This work supports the need to evaluate higher doses of RIF for the treatment of patients with tuberculosis.

Exposure to anticholinergic and sedative drugs, risk of falls, and mortality: an elderly inpatient, multicenter cohort.

Abstract This study aimed to assess whether exposure to anticholinergic and sedative medications and its evolution was associated with increased risk of in-hospital falls and all-cause mortality. Furthermore, results were compared with 2 definitions of drug burden index (DBI) against the outcomes. This observational, multicentric, and longitudinal study was conducted among patients aged 65 years or older, in 3 geriatric hospitals, in Francheville, Lyon, and Villeurbanne, France (duration of follow-up, 11.6 months). The exposure to anticholinergic and sedative medications was quantified using a DBI, at admission and at the end of observation for 337 patients. The evolution of exposure was the absolute difference between the index at admission and at the end of observation. The outcomes were in-hospital falls and all-cause mortality. Overall, 5.9% of patients experienced a fall. The risk of fall was nearly 3-fold in patients whose DBI increased during hospital stay compared to those with stable or decreased DBI (hazard ratio, 2.9 [1.14–7.12]; P = 0.03), after adjustment for comorbidities. The overall proportion of mortality was 6.5%. The evolution of DBI during hospital stay was not related to the risk of mortality (hazard ratio, 1.9 [0.8–4.4]; P = 0.14). Results were similar with the 2 definitions of DBI. Increased exposure to anticholinergic and sedative medications during hospital stay is associated with a higher risk of in-hospital falls but not with mortality. The DBI could be implemented in hospital, to guide prescription and reduce anticholinergic and sedative drug exposure.

In Vivo Quantitative Prediction of the Effect of Gene Polymorphisms and Drug Interactions on Drug Exposure for CYP2C19 Substrates

We present a unified quantitative approach to predict the in vivo alteration in drug exposure caused by either cytochrome P450 (CYP) gene polymorphisms or CYP-mediated drug–drug interactions (DDI). An application to drugs metabolized by CYP2C19 is presented. The metrics used is the ratio of altered drug area under the curve (AUC) to the AUC in extensive metabolizers with no mutation or no interaction. Data from 42 pharmacokinetic studies performed in CYP2C19 genetic subgroups and 18 DDI studies were used to estimate model parameters and predicted AUC ratios by using Bayesian approach. Pharmacogenetic information was used to estimate a parameter of the model which was then used to predict DDI. The method adequately predicted the AUC ratios published in the literature, with mean errors of −0.15 and −0.62 and mean absolute errors of 0.62 and 1.05 for genotype and DDI data, respectively. The approach provides quantitative prediction of the effect of five genotype variants and 10 inhibitors on the exposure to 25 CYP2C19 substrates, including a number of unobserved cases. A quantitative approach for predicting the effect of gene polymorphisms and drug interactions on drug exposure has been successfully applied for CYP2C19 substrates. This study shows that pharmacogenetic information can be used to predict DDI. This may have important implications for the development of personalized medicine and drug development.

Comparison of Four Renal Function Estimation Equations for Pharmacokinetic Modeling of Gentamicin in Geriatric Patients

ABSTRACT Most aminoglycoside pharmacokinetic models include an index of renal function, such as creatinine clearance, to describe drug clearance. However, the best clinical descriptor of renal function for the pharmacokinetic modeling of aminoglycosides has not been established. This analysis was based on 412 gentamicin concentrations from 92 geriatric patients who received intravenous gentamicin for various infectious diseases. Four two-compartment population models were fitted to gentamicin concentrations in a learning set of 64 patients using the nonparametric adaptive grid (NPAG) algorithm. Each model included an index of renal function, namely, the Cockcroft-Gault (CG), Jelliffe (JEL), modification of diet in renal disease (MDRD), or modified MDRD (MDRDm; adjusted to individual body surface area) equation as a covariate influencing gentamicin serum clearance. Goodness of fit and predictive performance of the four models were compared using standard criteria in both the learning set and in a validation set of 28 patients. A final analysis was performed to estimate the population pharmacokinetic parameter values of the entire 92-patient group. In the learning set, the CG-based model best fit the data, followed by JEL-, MDRD-, and MDRDm-based models, with relative reductions of the Akaike information criterion of 29.4, 20.2, 14.2, and 4.2, respectively. Bias and precision of population predictions were significantly different among the four models. In the validation set, individual predictions from the four models showed marginally different biases. The final estimation confirmed the previous results. Specifically, the CG-based model showed predictive performance that was comparable to or better than that of the MDRD-based model at each stage of the analysis. This study shows that methods used to estimate renal function should not be considered interchangeable for the model-based estimation of gentamicin concentrations.

Mathematical modeling of pulmonary tuberculosis therapy: Insights from a prototype model with rifampin

There is a critical need for improved and shorter tuberculosis (TB) treatment. Current in vitro models of TB, while valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be useful to overcome the limitations of traditional approaches in TB research. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin, based on pharmacokinetic, pharmacodynamic and disease submodels. The full mathematical model can simulate the time-course of tuberculous disease from the first day of infection to the last day of therapy. Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of rifampin in lungs. The model reproduced some qualitative and quantitative properties of the bactericidal activity of rifampin observed in clinical data. The kill curves simulated with the model showed a typical biphasic decline in the number of extracellular bacteria consistent with observations in TB patients. Simulations performed with more simple pharmacokinetic/pharmacodynamic models indicated a possible role of a protected intracellular bacterial compartment in such a biphasic decline. This modeling effort strongly suggests that current dosage regimens of RIF may be further optimized. In addition, it suggests a new hypothesis for bacterial persistence during TB treatment.

Evaluation of fluoroquinolone reduced dosage regimens in elderly patients by using pharmacokinetic modelling and Monte Carlo simulations

OBJECTIVES Fluoroquinolones are widely used in geriatric patients, but elderly patients are known to be at increased risk of decline in renal function. As fluoroquinolones usually exhibit a dominant renal elimination pathway, reduced dosage regimens are often used in geriatric patients. Our objective was to assess the capability to reach a pharmacokinetic-pharmacodynamic target of efficacy with such reduced dosage regimens of ofloxacin, levofloxacin and ciprofloxacin in elderly patients. METHODS Using Monte Carlo simulations, 1000 simulated elderly patients were created, based on published pharmacokinetic and pharmacodynamic data, and measured demographic data. Three usually proposed drug regimens taking renal function into account were evaluated using compartmental models. The probability of reaching an fAUC/MIC >100 was calculated for each regimen. RESULTS For MICs <1 mg/L, all simulated patients reach the efficacy target. However, with higher values of MIC, the proposed regimens were inefficient for patients with moderate or severe renal impairment: 3.4% and 30.2% of patients with moderate renal impairment reached the efficacy target for ciprofloxacin and ofloxacin, respectively, for an MIC of 2 mg/L. For ciprofloxacin, more than 80% of patients with severe renal impairment were unable to reach the target fAUC/MIC with an MIC as low as 1 mg/L, whereas for levofloxacin, all simulated patients reached the efficacy target until an MIC of 4 mg/L. CONCLUSIONS This suggests that the proposed dosage reduction does not allow the same exposure to be achieved in elderly patients with renal impairment, eventually leading to treatment failure or development of resistant strains.

Visual estimation of patients' body weight in hospital: the more observers, the better?

Objective Patients are not always weighed in hospitals. A visual estimate of patients’ body weight is often used. Little information exists about the validity of this practice. We assessed the visual estimation of body weight in a population of elderly hospitalised patients. Method Three observers performed a visual estimation of weight in 71 geriatric patients. Estimated body weights from each observer were compared to measured body weights. Various panels—three panels of two observers and two panels of three observers—were also evaluated. Results Overall results showed that a three observer panel gave better weight estimates than one or two individuals. Conclusion While further clinical studies are necessary to confirm these findings, using the mean or the median of several visual estimates may be a practical solution for body weight estimation when weighing patients is not possible.

Evaluation of various gentamicin dosage regimens in geriatric patients: a simulation study

The aim of this simulation study was to evaluate the ability of three regimens proposed in official French recommendations for gentamicin to hit defined pharmacokinetic (PK) and pharmacodynamic targets in a population of elderly patients. The first drug regimen tested consisted of a loading dose of 1 mg/kg and a maintenance dose weighted by creatininemia, every 8 h. The second regimen consisted of a fixed dose of 1 mg/kg at various intervals of time, calculated from creatinine clearance. The last regimen was a fixed dose of 3 mg/kg once a day. All regimens were for 5 days. We used a bicompartmental PK model and implemented a Monte Carlo simulation to generate a large sample of geriatric subjects. The analysis examined three ranges of creatinine clearance. Simulations showed that for the two regimens using multiple doses per day, neither was able to reach an efficacy level without significant toxicity after 5 days of treatment, regardless of the level of renal function. The use of creatininemia or creatinine clearance to adjust the drug dose did not alter these findings. The once‐a‐day dosing regimen gave better results both in efficacy and toxicity, except for patients with creatinine clearance lower than 60 mL/min, where the incidence of potential toxicity was above 25%. These results strongly suggest that official French recommendations about aminoglycoside dosage regimens in elderly patients with renal impairment should be updated, and that the frequent need for therapeutic drug monitoring and dosage individualization should be clearly stated.

The Case for Using Higher Doses of First Line Anti-Tuberculosis Drugs to Optimize Efficacy

Apart from new anti-tuberculosis drug development, another approach for tuberculosis (TB) treatment optimization is to derive maximum benefit from current agents. However, the dosage of current anti-TB drug regimens has never been optimized according to the exposure-effect relationships of each drug. The objective of this article is to review the latest pharmacokinetic, pharmacodynamic, experimental, and clinical data concerning the use of higher doses of first-line anti-TB drugs to improve the efficacy of pulmonary tuberculosis treatment. Exposure-effect relationships have been described for all first-line anti-TB agents. There is convincing evidence that patients would benefit from higher rifamycin exposure. This could be achieved by using higher daily doses of rifampin, or more frequent dosing of rifapentine. The dose-dependent activity of pyrazinamide observed in hollow-fiber and animal models suggests that higher doses of pyrazimamide might be more efficacious, but the tolerability of such higher doses needs to be investigated in humans. It is likely that higher doses of ethambutol would be associated with higher antibacterial effect, but the dose-related ocular toxicity of the drug precludes such practice. For isoniazid, dose individualization is required to optimize patient care. The use of higher than standard doses of isoniazid in fast acetylators should result in greater early bactericidal activity. To conclude, the use of higher doses for some of the firstline anti-TB agents has definite potential for shortening or improving TB treatment.