Background and Objective

Compartment models in pharmacokinetics are generally described for a single dose and can only simulate drug concentration as a function of the first dosing interval. Our objective was to create a one-compartment model for constant rate repetitive intravenous intermittent infusions where drug concentration can be simulated as a function of real time.

Methods

The analytical solutions to differential equations that were set for the time periods of drug infusion and elimination after an intermittent intravenous infusion were used to derive sequences patterns and determine the partial sums of mathematical series for multiple intermittent infusion doses.

Results

The model's original theory was supplemented with explicit solutions to the concentration and AUC, at non steady state conditions, with and without a loading dose, for both the infusion and elimination time periods after repetitive intermittent intravenous infusions. The validity and accuracy of these formulas in calculating drug concentration and AUC was verified by mathematical proofs, numerical methods and the principle of superposition.

Conclusions

Drug concentration and AUC can be simulated using the newly described one-compartment pharmacokinetic model in the entire time-domain of therapy after multiple and repetitive intermittent intravenous infusions and not just within the first dosing interval.

中文翻译：

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一室模型中多次间歇静脉输注的数学治疗

背景与目的

通常以单剂量描述药代动力学中的隔室模型，并且只能模拟作为第一给药间隔的函数的药物浓度。我们的目标是为恒定速率重复静脉间歇性输注创建一个单室模型，在该模型中可以将药物浓度模拟为实时函数。

方法

在间歇静脉输注后针对药物输注和消除的时间段设置的微分方程的解析解可用于得出序列模式，并确定多次间歇输注剂量的数学系列的部分和。

结果

该模型的原始理论还补充了在非稳态条件下（无论是否加载）有浓度和AUC的明确解决方案，适用于重复间歇性静脉内输注后的输注和消除时间段。通过数学证明，数值方法和叠加原理验证了这些公式在计算药物浓度和AUC时的有效性和准确性。

结论

可以在新的单室药代动力学模型中模拟药物浓度和AUC，该模型在治疗的整个时域中均经过多次重复性间歇静脉输注后，而不仅仅是在第一个给药间隔内。