# Pharmacokinetics model

## Model description:

The pharmacokinetics model is a two compartment model that embodies the ligands of the macrophage mannose receptor, and it is represented mathematically as a system of differential equations of the form:

\begin{align*} \dot{x}_1 &= \alpha_1(x_2-x_1) - \dfrac{k_av_mx_1}{k_ck_a+k_cx_3+k_ax_1},\\ \dot{x}_2 &= \alpha_2(x_1-x_2),\\ \dot{x}_3 &= \beta_1(x_4-x_3) - \dfrac{k_av_mx_3}{k_ck_a+k_cx_3+k_ax_1}, \\ \dot{x}_4 &= \beta_2(x_3-x_4), \end{align*}

where $x_1(0) = c_0$, $x_2(0)=0$, $x_3(0) = \gamma x_4(0)=0$, $x_1$ represents the enzyme concentration in plasma, $x_2$ its concentration in compartment, $x_3$ is the plasma concentration of the mannosylated polymer that acts as a competitor of glucose oxidase for the mannose receptor of macrophages, and $x_4$ is the concentration of the same competitor in the part of the extravascular fluid of the organs accessible to this macromolecule.

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## Publication details:

 Title Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods Publication Type Journal Article Authors Chis, Oana-Teodora, Banga Julio R., and Balsa-Canto Eva Secondary Authors Jaeger, JohannesEditor