Swansea University, Swansea, UK.
Medical University of Vienna, Vienna, Austria.
J Pharmacokinet Pharmacodyn. 2021 Feb;48(1):99-131. doi: 10.1007/s10928-020-09719-8. Epub 2020 Oct 10.
Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.
室模型产生线性常微分方程（ODE），为药代动力学（PK）分析提供了常用工具，对于低维室模型，很容易获得药物水平或浓度的精确解。精确解能够为这些系统提供有价值的见解和进一步的分析。转运室模型是一种流行的半机械方法，用于将简单的 PK 模型推广到允许延迟动力学的模型，但对于导致不同最终室的转运室系统的多次剂量输入，计算精确解并不简单。在这里，我们为在跟随吸收室和中央血液室的线性转运室级联之后的整个时间段内作为时间函数的药物水平找到精确解，对于 n 个转运室和到第一室的 M 个等剂量的情况。我们进一步展示了 PK ODE 模型的精确解在找到由规定的治疗范围施加的等剂量方案参数约束方面的用途。这导致了等剂量方案区域（EDRR）的构建，提供了新的、新颖的可视化效果，总结了安全有效的给药参数空间。对于具有二维和三维参数空间的经典和转运室模型，计算了 EDRR，并提出了作为告知药物剂量方案设计的有用图形工具。
