  Extending deterministic compartments pharmacokinetic models as diffusions
seems not realistic on biological side because paths of these stochastic
processes are not smooth enough. In order to extend one compartment
intra-veinous bolus models, this paper suggests to modelize 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, an ergodic theorem for the concentration process and its
application to the estimation of the elimination constant, and consistent
estimators of the driving signal's Hurst parameter and of the volatility
constant.
  The second part of the paper provides applications of these theoretical
results on simulated concentration datas : a qualitative procedure for choosing
parameters on small sets of observations, and simulations of the estimators of
the elimination constant and of the driving signal's Hurst parameter. The
relationship between the estimations quality and the size/length of the sample
is discussed.
