Department of Bioengineering and Therapeutic Sciences, Schools of Pharmacy and Medicine, University of California San Francisco, San Francisco, California, USA.
Department of Drug Metabolism and Pharmacokinetics, Septerna, South San Francisco, California, USA.
AAPS J. 2023 Apr 10;25(3):38. doi: 10.1208/s12248-023-00801-w.
In chemistry, rate processes are defined in terms of rate constants, with units of time, and are derived by differential equations from amounts. In contrast, when considering drug concentrations in biological systems, particularly in humans, rate processes must be defined in terms of clearance, with units of volume/time, since biological volumes, which are highly dependent on drug partition into biological tissues, cannot be easily determined. In pharmacology, pharmacokinetics, and in making drug dosing decisions, drug clearance and changes in drug clearance are paramount. Clearance is defined as the amount of drug eliminated or moved divided by the exposure driving that elimination or movement. Historically, all clearance derivations in pharmacology and pharmacokinetics have been based on the use of differential equations in terms of rate constants and amounts, which are then converted into clearance equations when multiplied/divided by a hypothesized volume of distribution. Here, we show that except for iv bolus dosing, multiple volumes may be relevant. We have recently shown that clearance relationships, as well as rate constant relationships, may be derived independent of differential equations using Kirchhoff's Laws from physics. Kirchhoff's Laws may be simply translated to recognize that when two or more rate-defining processes operate in parallel, the total value of the overall reaction parameter is equal to the sum of those rate-defining processes. In contrast, when two or more rate-defining processes operate in series, the inverse of the total reaction parameter is equal to the sum of the inverse of those rate-defining steps.
在化学中，速率过程是根据速率常数来定义的，其单位为时间，并通过微分方程从数量中推导出来。相比之下，当考虑生物系统（特别是人类）中的药物浓度时，必须根据清除率来定义速率过程，清除率的单位为体积/时间，因为生物体积高度依赖于药物在生物组织中的分配，而生物体积难以轻易确定。在药理学、药代动力学和制定药物剂量决策时，药物清除率及其变化至关重要。清除率定义为被消除或移动的药物量除以驱动该消除或移动的暴露量。从历史上看，药理学和药代动力学中的所有清除率推导都基于使用微分方程和速率常数以及数量，然后在乘以/除以假设的分布容积时将其转换为清除率方程。在这里，我们表明，除了静脉推注给药外，多个体积可能是相关的。我们最近表明，清除率关系以及速率常数关系可以独立于微分方程使用物理学中的基尔霍夫定律推导出来。基尔霍夫定律可以简单地翻译为，当两个或多个定义速率的过程同时进行时，总反应参数的值等于这些定义速率过程的值之和。相比之下，当两个或多个定义速率的过程串联进行时，总反应参数的倒数等于这些定义速率步骤的倒数之和。
