A Pathwise Fractional one Compartment Intra-Veinous Bolus Model

Nicolas Marie (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 ESME - ESME - École spéciale de mécanique et d'électricité

To extend the deterministic compartments pharmacokinetics models as diffusions seems not realistic on the biological side because the paths of these stochastic processes are not smooth enough. In order to extend the one compartment intra-veinous bolus models, this paper suggests to model the concentration process $C$ by a class of stochastic differential equations driven by a fractional Brownian motion of Hurst parameter belonging to $]1/2,1[$. The first part of the paper provides probabilistic and statistical results on the concentration process $C$ : the distribution of $C$, a control of the uniform distance between $C$ and the solution of the associated ordinary differential equation, and consistent estimators of the elimination constant, of the Hurst parameter of the driving signal, and of the volatility constant. The second part of the paper provides applications of these theoretical results on simulated concentrations : a method to choose the parameters on small sets of observations, and simulations of the estimators of the elimination constant and of the Hurst parameter of the driving signal. The relationship between the quality of the estimations and the size/length of the sample is discussed.

Mots clés: Least-square estimation; Ergodicity; Pharmacokinetics; Fractional Brownian motion; One compartment bolus models; Fractional Ornstein-Uhlenbeck process

Domaines: Probabilités [math.PR]

Nicolas Marie. A Pathwise Fractional one Compartment Intra-Veinous Bolus Model. International Journal of Statistics and Probability, 2014, 3 (3), pp.65-79. ⟨10.5539/ijsp.v3n3p65⟩. ⟨hal-01519413⟩