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Thesis

French

ID: <

10670/1.gmnxni

>

Where these data come from
Statistical contributions to the study of live kinetics: application to infusion and malaria

Abstract

Our work is a contribution to the development of statistical methods to assist in the understanding of two biological quantifiable phenomena through data from medical examinations. The first of these two biological phenomena is microcirculation in the general bloodstream system, the second is the sensitivity of parasite strains associated with malaria, for a therapeutic molecule. The goal is to collect information, extract from observations, to help physician to interpret more objectively/accurately the data collected from medical examinations. The medical device that exists today to display microcirculation is composed of a dynamic range imaging tool and injection of a contrast agent. The data collected are space-time series of volume images. For a given volume, and a unit of the image, we have access to observations dependant of medical examination times. Such a series of number is commonly known as « tissue enhancements ». The first objective of this thesis was to model a series of tissue enhancements using a non-parametric convolution model. The convolution product depends on an unknown constant, an unknown survival function and tissue enhancement observed in the artery afferent to the studied voxel. We have modeled the product between the constant and survival function, using a mixture of Gamma survival function with positive weight. The estimate of the parameters of Gamma and positive weight is performed using an iterative algorithm that we developed that aim to minimize the criterion of least squares associated. This algorithm is based on a non negativity test and non positivity that had been developed by Yannick Baraud, Sylvie Huet and Béatrice Laurent. One way to monitor the resistance of the parasite strains to the therapeutic molecules is to study the ex-vivo activity of the parasite for different concentrations of molecules. For a patient and a given therapeutic molecule, the activity of the parasite is measured using isotopic tests, observations related to these measures are generally reffered to as effects and are dependant of the concentrations of the tested molecule. The reference measurement for monitoring is the molecule concentration enabling to inhibit 50 % of the activity of the parasite. The assumption is generally established that a patient is infected with a detectable strain of parasite. Some biologists are making assumptions that patients are infected with more than one strain of parasite. We have modeled the effects of a therapeutic molecule in a sample of blood containing two different sensitivity of parasite strains using a nonlinear regression model assuming four parameters and set up a parameter estimation algorithm. In a second step we have been interested in developing a selection criteria for establishing, from observed data, if a patient is infected with a detectable strain of parasite or two parasite strains that have different sensitivity to the therapeutic molecule.

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