In vitro simulation of in vivo pharmacokinetic model with intravenous administration via flow rate modulation

Abstract

The aim of this paper was to propose a method of flow rate modulation for simulation of in vivo pharmacokinetic (PK) model with intravenous injection based on a basic in vitro PK model. According to the rule of same relative change rate of concentration per unit time in vivo and in vitro, the equations for flow rate modulation were derived using equation method. Four examples from literature were given to show the application of flow rate modulation in the simulation of PK model of antimicrobial agents in vitro. Then an experiment was performed to confirm the feasibility of flow rate modulation method using levo-ornidazole as an example. The accuracy and precision of PK simulations were evaluated using average relative deviation (ARD), mean error and root mean squared error. In vitro model with constant flow rate could mimic one-compartment model, while the in vitro model with decreasing flow rate could simulate the linear mammillary model with multiple compartments. Zero-order model could be simulated using the in vitro model with elevating flow rate. In vitro PK model with gradually decreasing flow rate reproduced the two-compartment kinetics of levo-ornidazole quite well. The ARD was 0.925 % between in vitro PK parameters and in vivo values. Results suggest that various types of PK model could be simulated using flow rate modulation method without modifying the structure. The method provides uniform settings for the simulation of linear mammillary model and zero-order model based on in vitro one-compartment model, and brings convenience to the pharmacodynamic study.

Appendix

For the flow rate modulation formula of linear mammillary model, the Eq.(i) (Table 5) could be obtained by substituting Eq.(xi) (Table 1) into Eq. (2). The following equation could be derived by the definite integral of Eq.(i) (Table 5) at both sides during 0–t interval:

$$ \ln \frac{C}{{C_{0} }} = \ln \frac{{\sum\limits_{i = 1}^{l} {A_{i} e^{{ - k_{i} t}} } }}{{\sum\limits_{i = 1}^{l} {A_{i} } }} $$

(5)

Table 5 Summary of the formula for the verification of flow rate modulation equation

Making that $\sum\limits_{i = 1}^{l} {A_{i}}$, the Eq. (5) could be simplified as Eq.(vi) in Table 5, which had the same form as c-t equation of linear mammillary model in vivo.

For the simulation of one-compartment model in vitro, the Eq.(ii) (Table 5) could be obtained by substituting Eq.(xii) (Table 1) into Eq. (2). The Eq.(vii) (Table 5) could be yielded through the definite integral of Eq.(ii) (Table 5) during 0–t interval when C ₀ equals to c ₀. The Eq.(vii) (Table 5) had the same form as Eq.(ii) (Table 1).

As for the simulation for two-compartment model in vitro, similar method could be used to verify the formula of flow rate modulation when the initial value (C ₀) equals A + B. For three-compartment model in vitro, the formula for flow rate modulation could be demonstrated using the same method when C ₀ is the sum of A, B and R. The same process could be applied to verify the formula for flow rate modulation mimicking zero-order model when C ₀ equals to c ₀.