Mathématiques industrielles
(Industrie pharmaceutique)
Mercredi, 19 juin
Salle George V
Mathematical Characterization of In vivo Variability and Nonlinearity in Exposure-response Models
Nekka, Fahima
Faculté de Pharmacie. Université de Montréal

Pharmacometrics, based on advanced mathematical methods and simulation approaches, is being increasingly adopted by pharmaceutical industries in their drug development programs. This trend has been strengthened by the regulatory agencies which suggest exposure-response analysis in all new drug applications (NDA).

In this talk, I will report on the experience the team has developed in the area of biopharmaceutical research, fully supported by mathematical proof of concepts. I will illustrate with the particular project of optimal design regimen for antibiotics for which we have developed a more information loaded exposure-response formalism.

This project is in collaboration with Dr. J. Li

A user friendly tool to assist clinicians in the development of Limited Sampling Strategies
Barrière, Olivier
Faculté de Pharmacie. Université de Montréal

Limited sampling strategies (LSS) are widely used to estimate surrogates of drug exposure, such as the area under the concentration-time curve (AUC), which generally correlates with drug effect.

The aim of these LSS techniques is to reduce the inconvenient and frequent blood samplings, while keeping the precision of the derived estimates A regression procedure is usually proposed for the prediction of AUC  involving  only a small number of blood samples collected at specific times as dependent variables. Considering the trade off between the accuracy of the estimation and the clinical convenience, the challenge of LSS is to identify a suitable set of sample concentrations that can achieve this twofold goal. In this presentation, we will discuss the problematic and results around the multiple linear regression with confidence intervals computations, cross-validation methods, and appropriate performance criteria to solve this practical problem. As direct fallout, we have implemented a user friendly tool, with a graphical user interface, that can assist clinicians to set up LSS for their practical needs. In this talk, I will show how this software can be used to efficiently identify the best LSS and the associated statistics, as well as the evaluation of the performance of different LSSs based on various criteria. Such tools are very appreciated in drug development and clinical practice.

This work is in collaboration with J. Li, S. Sarem, F. Nekka and the Pharmacology Unit of Ste-Justine Hospital with C. Litalien, Y. Theoret and A.L Lepayreque.

Parametric optimization of nanoparticle therapeutic efficacy in the context of autoimmune type 1 diabetes.
Khadra, Anmar
Department of Physiology, McGill University

The use of nanoparticles (NPs) in the treatment of autoimmune type 1 diabetes has shown promising results. It was found that they can effectively expand a pool of autoregulatory T cells that can block disease progression to a therapeutic level in a dose-dependent manner. The structure (or valency) of these NPs is also a factor in determining their therapeutic efficacy. In this talk, we will present a mathematical model to explore the effects of compound design parameters (NP dose and valency) on disease progression. We will show, using bifurcation analysis, that the model exhibits a “resonance”-like behavior for a given range of NP-dose and valency and present a methodology to quantify the average valency-dependent minimal/optimal dose needed for effective therapy. We will also demonstrate how the model can generalize to other autoimmune diseases and serve as a computational tool to understand and optimize NP-based therapies.

Predictive Models of Type 1 Diabetes Progression
Jaberi-Douraki, Majid and Anmar Khadra
Centre of Nonlinear Dynamics, McGill University

The objective of this work is to predict the onset of type 1 diabetes progression by incorporating multiple risk factors such as the interaction of T-cell avidity with autoantibodies. We construct mathematical models in the form of differential equations, of the pathophysiology pertaining to diabetes development to address this issue. The goal is to examine, analytically and numerically, how the binding affinity of autoantibodies correlates with the pathogenic potential of T cells that are reactive to the same autoantigen. Based on our preliminary results, we expect these findings to have significant implications on the stability of autoimmunity and tolerance in the study of this disease.