PK2 Two-Compartment PK model with absorption


Model used in : M. Prague, C. Commenges, J. Guedj, J. Drylewicz and R. Thiebaut. NIMROD: A Program for Inference via Normal Approximation of the Posterior in Models with Random effects based on Ordinary Differential Equations. (Submitted)

-----> Download here : PK2.zip

Mathematical model (ode.f90)


\[ \frac{d A_{GI}(t)}{dt}=-k_a A_{GI} \]

\[ \frac{d C_{P}(t)}{dt}= \frac{k_a}{V_0} A_{GI} - k_e C_P -k_{PT} C_P + \frac{k_{PT}}{V_0} C_T \]

\[ \frac{d C_{T}(t)}{dt}= \frac{k_{PT}}{V_T} C_P - k_{TP} C_T \]


\[ A_{GI}(0)=Dose(0) \]

\[ C_P(0)=0 \]

\[ C_T(0)=0 \]

Observational model (observationModelSpe.f90)

\[ Y^i_{1}(t_{ij})=C_P^i(X^i(t_{ij}))+\epsilon_{ij1}, \qquad \epsilon_{ij1}\sim \mathcal{N}\left(0,\sigma^2_{C_P}\right). \nonumber \]

Statistical model (parameterTransformation.f90)

All parameters are observed in log transformation. There is no additional covariates.

Data (inAndOutUser.f90 / pk.txt)

Data must be in this shape : "id" "time" "Cp" "dose(t=0)" (See the pk.txt file) If user want to account for multiple dosing, program must be modified. The input file used in this example is constituted of simulated data with a one compartment model with absorption, see PK1 : One-Compartment Pharmacokinetic model with absorption :

Priors (Input.txt)

Priors are choosen in accordance with the litterature with rather small standard deviation for V0 to avoid the flip-flop paradox.

\[\tilde{k}_a\sim \mathcal{N}(-4.5;0.1)\]

\[\tilde{k}_e\sim \mathcal{N}(-6.0;5.0)\]

\[\tilde{V}_0\sim \mathcal{N}(-4.6;5.0)\]

\[\tilde{k}_{TP}\sim \mathcal{N}(-4.0;1.0)\]

\[\tilde{k}_{PT}\sim \mathcal{N}(-4.0;1.0)\]

\[\tilde{V}_T\sim \mathcal{N}(-4.0;1.0)\]

\[\sigma_{k_a}\sim half-Cauchy(s=1.0)\]

\[\sigma_{k_e}\sim half-Cauchy(s=1.0)\]

\[\sigma_{V_0}\sim half-Cauchy(s=1.0)\]

\[\sigma_{C_P}\sim Jeffrey's\]