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The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannosereceptor, without knowing "a priori" the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without a priori parameter values. Then the resulting parameter estimate is improved by using the classical least-squares method.