Abstract
Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.
Highlights
It has been almost 50 years since pharmacokinetics was recognized as an independent scientific discipline, pharmacokinetic models are described exclusively only within the first dosing time interval [1]
Our results indicated that the time to reach peak concentration in the peripheral compartment t2,max depends on the dose and the drug concentration in the two compartments
As simulations imitate a process with another process, the predictive power of a pharmacokinetic compartment model can be unveiled only after you explain your model
Summary
It has been almost 50 years since pharmacokinetics was recognized as an independent scientific discipline, pharmacokinetic models are described exclusively only within the first dosing time interval [1]. One- and two-compartment models for intermittent intravenous infusion (IIV), lack mathematical expressions that can relate drug concentration as a function of real-time after administration of multiple IIV doses [2]. The development of these multi dosing expressions may have not been a priority, as the assessment of common pharmacokinetic parameters using compartmental and noncompartmental approaches and model selection is usually done after administration of a single drug dose to subjects [3] [4]. Series equations of drug concentration with time within each dosing interval were first developed and converted to real-time equations In this manuscript, using standard mathematical processes we have obtained particular solutions for the one- and two-compartment multiple IIV models in the form of piecewise functions. The time to reach peak time concentration in the peripheral compartment after a constant drug infusion period in the central com-
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