Sager G
Institut für Meereskunde, Akademie der Wissenschaften der DDR, Rostock-Warnemünde.
Arch Geschwulstforsch. 1987;57(4):297-304.
A contribution by Krug and Taubert concerning the mathematical approximation of Ehrlich ascites tumor growth using logit transformation of the logistic function followed by an approximation of the prefinal decline of the cell number gives rise to further contemplations. The authors aimed at a rather simple method to be realised with programmable pocket computers. A proposal offered by Dr. Krug lead the author to further investigations into the problem in question. As one possibility the sigmoidal function is replaced by a special form of the Janoschek function whilst the multiplicative descending exponential function mainly responsible for the prefinal stage is given a more flexible character. As a result the ascending phase is only slightly altered whereas the stage of decline shows different behaviour partly due to the few and scattering input data for this branch of the growth curve. By this method linear deviations are reduced by about a quarter in the example treated.
克鲁格和陶伯特的一项贡献涉及使用逻辑函数的对数变换对艾氏腹水瘤生长进行数学近似，随后对细胞数量的最终下降前阶段进行近似，这引发了进一步的思考。作者旨在找到一种用可编程袖珍计算机实现的相当简单的方法。克鲁格博士提出的一项建议促使作者对该问题进行进一步研究。作为一种可能性，S形函数被扬诺谢克函数的一种特殊形式所取代，而主要负责最终前阶段的乘法递减指数函数则具有了更灵活的特性。结果，上升阶段仅略有改变，而下降阶段则表现出不同的行为，部分原因是该生长曲线分支的输入数据较少且分散。通过这种方法，在处理的示例中，线性偏差减少了约四分之一。
