Birchall A
Health Phys. 1986 Mar;50(3):389-97. doi: 10.1097/00004032-198603000-00005.
An algorithm for solving first-order non-recycling compartment models is described. Given the initial amounts of a radioactive material in each compartment and the fundamental transfer rate constants between each compartment, the algorithm gives both the amount of material remaining at any time t and the integrated number of transformations that would occur up to time t. The method is analytical, and consequently, is ideally suited for implementation on a microcomputer. For a typical microcomputer with 64 kilobytes of random access memory, a model containing up to 100 compartments, with any number of interconnecting translocation routes, can be solved in a few seconds; providing that no recycling occurs. An example computer program, written in 30 lines of Microsoft BASIC, is included in an appendix to demonstrate the use of the algorithm. A detailed description is included to show how the algorithm is modified to satisfy the requirements commonly encountered in compartment modelling, for example, continuous intake, partitioning of activity, and transformations from radioactive progeny. Although the algorithm does not solve models involving recycling, it is often possible to represent such cases by a non-recycling model which is mathematically equivalent.
本文描述了一种用于求解一阶非循环房室模型的算法。给定每个房室中放射性物质的初始量以及各房室之间的基本转移速率常数，该算法既能给出在任意时刻t剩余的物质量，又能给出直至时刻t发生的转化积分数。该方法是解析法，因此非常适合在微型计算机上实现。对于具有64千字节随机存取存储器的典型微型计算机，一个包含多达100个房室、具有任意数量相互连接的转运途径的模型，在不发生循环的情况下，几秒钟内即可求解。附录中包含一个用30行微软BASIC语言编写的示例计算机程序，以演示该算法的使用。文中还给出了详细描述，以说明如何修改该算法以满足房室建模中常见的要求，例如持续摄入、活度分配以及放射性子体的转化。虽然该算法不能求解涉及循环的模型，但通常可以用一个数学等效的非循环模型来表示此类情况。
