Mathématiques en biologie et médecine
Mercredi, 19 juin
Salle Du Manège
Branching process models for HIV and SIV infection
Coombs, Daniel
University of British Columbia

Differential equation models for HIV and SIV infection are of questionable validity when the numbers of a player in the model (virus or infected cell) are small. We have worked on branching process models for very early infection and successfully treated infection. Although direct simulation is always an option, analytic or mixed methods are often possible. I will summarize our progress and outline directions for future work.

Modelling pharmacological interventions in hematopoietic regulations
Bélair, Jacques
Université de Montréal

The production of human blood cells is regulated through a highly complex, coupled set of feedback mechanisms involving, among others, differentiation of cell lines from a common pool of stem cells and hormonal interactions between circulating cells and cells at different stages of maturation. As part of a global modeling project of the full hematopoietic system, we investigate possible pharmaceutical interventions using a structured model for the regulation of blood cells taking the form of a system of nonlinear delay differential equations. This model contains multiple time delays to incorporate maturation and lifespan times of the different cell species, together with feedback control mechanisms relating the circulating cells to the maturation process: some of the delays are therefore state-dependent. Concentrating on the regulation of neutrophils, we analyse the perturbative effects of different chemotherapeutic regimens on equilibrium solutions. We obtain dynamical interpretations for the neutropenic episodes: the influence of scheduling, as well as the remedial use of G-CSF, is particularly emphasized. Parameter estimation and compatibility of the behavior of the solutions of our model with clinical practice will be discussed. Supported by NSERC and FRQNT.

Nouvelles approches de modélisation et d’optimisation de diète animale
Dubeau, François (1), J.-P. Dussault (1), É. Joannopoulos (1) et C. Pomar (2)
(1) Université de Sherbrooke, (2) Agriculture et Agroalimentaire Canada, Sherbrooke (QC)

La production porcine est une activité très importante au Canada. Chaque année, environ 21 millions de porcs y sont produits. Le Québec est le plus gros producteur du Canada. Il produit à lui seul environ 8 millions de porcs par an, soit 38% de la production totale. Les coûts de l’alimentation représentent environ 70% du coût total de la production, ce qui en constitue une part importante. Il est donc primordial pour les producteurs de nourrir les animaux à moindre coût tout en ne négligeant aucun de leurs besoins. Depuis plusieurs années, les producteurs cherchent de nouvelles méthodes pour minimiser le coût de l’alimentation, mais également depuis peu à minimiser les effets environnementaux de leur production. Ce travail est principalement centré sur la diminution des coûts d’alimentation, tout en regardant l’impact environnemental, sans toutefois essayer de diminuer les rejets. Nous étudions trois types d’alimentation : l’alimentation traditionnelle, l’alimentation multiphase à énergie fixe et l’alimentation multiphase à énergie libre. Nous développerons les modèles correspondants à chaque type d’alimentation et nous les appliquerons plus précisément aux données du porc charcutier. Pour finir, nous analyserons les résultats obtenus à partir de ces données.

Numerical methods for modelling nematode and anguilliform swimming
Lapierre, David and Robert G. Owens
Département de mathématiques et de statistique, Université de Montréal

In the present work, we simulate the swimming of animal species such as lampreys, eels and nematodes which are naturally modelled as a one-dimensional flexible rod (see, for example, Fauci (1996) and Fauci and Peskin (1988)). Computations are performed with the Reissner-Simo model for the dynamics of beams, which is an extension of the Kirchhoff-Love model. The rod is immersed in a three-dimensional expanse of a viscous Newtonian fluid and fluid-structure interaction is handled using the immersed boundary method of Peskin (2002). We begin our presentation of the numerical results with a study of the computed three-dimensional dynamics of both the closed and open rod model under a variety of different conditions of twist and intrinsic curvature. These are verified by comparison with the results of Lim et al. (2008, 2010). We then proceed to represent the body of swimmers in two different Reynolds number regimes using the rod model. The first (at low Reynolds number ($Re < 1$)) is relevant to the swimming cycle of wildtype C. elegans and comparisons are made with some experimental data from the research group of Arratia (∼parratia) based upon their curvature data for three swimming cycles in a buffer solution of viscosity equal to 1mPa.s. The second set of simulations is performed at much higher Reynolds numbers ($O(10^4$)) and the computed results are compared with those for an eel-like robot by Boyer et al. (2008).