HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

A Pathwise Fractional one Compartment Intra-Veinous Bolus Model

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Friday, July 14, 2017 - 2:57:35 PM
Last modification on : Thursday, October 21, 2021 - 3:16:05 PM
Long-term archiving on: : Thursday, December 14, 2017 - 2:08:44 PM


Files produced by the author(s)



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



Record views


Files downloads