Olivier Barrière

Terrain modeling with multifractional Brownian motion and self-regulating processes

Approximate scale-invariance and local regularity properties of natural terrains suggest that they can be a accurately modeled with random processes which are locally fractal. Current models for terrain modeling include fractional and multifractional Brownian motion. Though these processes have proved useful, they miss an important feature of real terrains: typically, the local regularity of a mountain at a given point is strongly correlated with the height of this point. For instance, young mountains are such that high altitude regions are often more irregular than low altitude ones. We detail in this work the construction of a stochastic process called the Self-Regulated Multifractional Process, whose regularity at each point is, almost surely, a deterministic function of the amplitude. This property makes such a process a versatile and powerful model for real terrains. We demonstrate its use with numerical experiments on several types of mountains.

A Bayesian approach for the estimation of patient compliance based on the last sampling information.

Poor adherence to a drug prescription significantly impacts on the efficacy and safety of a planned therapy. The relationship between drug intake and pharmacokinetics (PK) is only partially known. In this work, we focus on the so-called “inverse problem”, concerned with the issue of retracing the patient compliance scenario using limited clinical knowledge. Using a reported Pop-PK model of imatinib, and accounting for the variability around its PK parameters, we were able to simulate a whole range of drug concentration values at a specific sampling point for a population of patients with all possible drug compliance profiles. Using a Bayesian decision rule, we developed a methodology for the determination of the associated compliance profile prior to a given sampling value. The adopted approach allows, for the first time, to quantitatively acquire knowledge about the compliance patterns having a causal effect on a given PK. Moreover, using a simulation approach, we were able to evaluate the evolution of success rate of the retracing process in terms of the considered time period before sampling as well as the model-inherited variability. In conclusion, this work allows, from a probability viewpoint, to propose a solution for this inverse problem of compliance determination.

Limited sampling strategies for estimating intravenous and oral cyclosporine area under the curve in pediatric hematopoietic stem cell transplantation.

Background: The optimal monitoring strategy for cyclosporine (CsA) in pediatric hematopoietic stem cell transplantation (HSCT) patients remains unclear. Although there is a growing interest in the use of the area under the concentration–time curve (AUC), measurement of AUC in clinical settings is often impractical. The objective of this study was to identify and validate limited sampling strategies (LSSs) for the prediction of CsA AUC after intravenous (IV) and oral (PO) administration in this population. Methods: Sixty-eight pediatric patients who underwent HSCT and received CsA were investigated. Twelve-hour pharmacokinetic profiles (n = 138) performed per standard of care were collected. Weighted multiple linear regression was used to investigate all possible LSSs consisting of 4 or less concentration–time points. Their predictive performance was evaluated by leave one out cross validation and external validation by measuring the root mean squared relative error (RMSE%) and the 95th percentile of the absolute relative error (AE%). Values less than 20% were considered clinically acceptable. Results: Nine LSSs (4 IV and 5 PO) convenient for clinical application proved to have clinically acceptable performance. Notably, LSS based on C0, C2, and C4 was found to be accurate for estimation of CsA exposure after both IV and PO administration with the 95th percentile of AE% of 19.7% and 17.5%, respectively. Conclusions: LSSs using 3 or 4 concentration–time points obtained within 4 hours postdose provide a convenient and reliable method to estimate CsA exposure in this population. These LSSs may facilitate future research aiming at better defining the relationship between AUC and clinical outcomes.

A Visual Representation of the Drug Input and Disposition Based on a Bayesian Approach

Compliance to a drug prescription describes the degree to which a patient correctly follows medical advice. Poor compliance significantly impacts on the efficacy and safety of a planned therapy, which can be summed up by the dictum: “a drug only works if it’s taken”. However, the relationship between drug intake and pharmacokinetics (PK) is only partially known, especially the so-called inverse problem, concerned with the issue of retracing the patient compliance scenario using limited clinical knowledge. Based on the Bayesian theory, we develop a decision rule to solve this problem. Given an observed concentration, we determine, among all possible compliance scenarios, which is the most probable one. Using a simulation approach, we are able to judge the quality of this retracing process by measuring its global performance. Since the sampling concentration is the result of both patient compliance (drug input) and patient PK characteristics (drug disposition), two natural questions arise here: first, given two different sampling concentration values, can we expect the same performance of the retracing process? Second, how is this performance affected by the PK variability between individuals? For this, we here design an heatmap-style image, called Compliance Spectrum, that provides an intuitive and interactive way to evaluate the relationship between drug input and drug disposition along with their consequences on PK profile. The current work provides a solution to this inverse problem of compliance determination from a probability viewpoint and uses it as a base to build a visual representation of drug input and disposition.

A Probabilistic Strategy for Group-Based Dose Adaptation

Individualized dose adaptation usually requires Therapeutic Drug Monitoring (TDM) based on patient blood samplings. However this invasive approach, generally accompanied with discomfort and cost, is not always justified since it may occur that the resulting dose adaptation does not significantly differ in a population whose individuals share similar characteristics. Inspired by the principle of maximum likelihood, we propose a probabilistic approach, based on population-pharmacokinetic modeling and simulation, to evaluate the therapeutic performance of a dosing regimen in terms of dose and time. Two types of therapeutic indicators, time-based and concentration-based, are suggested to assess quantitatively different drug regimens with the aim to identify the optimal one. For the population under investigation, our results identified a stable and robust optimal regimen and determined critical times including toxicity. Moreover, for a same therapeutic target, our approach enables to identify more than one corresponding regimen, giving thus a great flexibility in clinical practice.