Takimoto M, Yoshioka H
Jpn J Antibiot. 1979 May;32(5):627-30.
Intending to improve the accuracy of determination of antibiotics, a two-dimensional diffusion method using large agar plate was introduced. Three antimicrobial agents, ampicillin, PC-904, and tobramycin, were used. Inhibition zones of B. subtilis on the agar plate were measured which were formed as a result of diffusion of these agents. The relationship between the concentration of antimicrobials and the size of inhibition zones was studied. Plotting the data-points on the graph, it was predicted that there might be a relationship of quadratic equation between the diameter of inhibition zone and the logarithm of concentration of the agents. On the other hand, mathematical considerations were taken to find out a physical principle or an equation which governs the diffusion of antibiotics in the agar. Assuming that antibiotics spreads in the agar after the principle of simple diffusion, an equation was lead which shows how the antibiotics distributes in the agar in relation to time. The equation was written as, (formula: see text) where, S is amount of antibiotics, D diffusion constant, r distance from the center of diffusion, t period during which the diffusion proceeds. As a result of the mathematical calculations mentioned, it was confirmed that the relation between the size of zones and the logarithm of concentration of antibiotics is described by a quadratic equation as predicted on the basis of experimental data.
为提高抗生素测定的准确性，引入了一种使用大琼脂平板的二维扩散法。使用了三种抗菌剂，氨苄青霉素、PC - 904和妥布霉素。测量了琼脂平板上由于这些药剂扩散而形成的枯草芽孢杆菌的抑菌圈。研究了抗菌剂浓度与抑菌圈大小之间的关系。将数据点绘制在图表上，预计抑菌圈直径与药剂浓度对数之间可能存在二次方程关系。另一方面，从数学角度进行考量以找出控制抗生素在琼脂中扩散的物理原理或方程。假设抗生素按照简单扩散原理在琼脂中扩散，推导出一个方程，该方程表明抗生素在琼脂中相对于时间的分布情况。该方程写为，（公式：见原文）其中，S是抗生素的量，D是扩散常数，r是距扩散中心的距离，t是扩散进行的时间段。通过上述数学计算，证实了抑菌圈大小与抗生素浓度对数之间的关系如基于实验数据所预测的那样由二次方程描述。
