Li T, Park K
Purdue University, School of Pharmacy, West LaFayette, Indiana 47907, USA.
Pharm Res. 1998 Aug;15(8):1222-32. doi: 10.1023/a:1011939824353.
Reliable methods are needed to characterize the surface roughness of pharmaceutical solid particles for quality control and for finding the correlations with other properties. In this study, we used fractal analysis to describe the surface roughness.
Atomic force microscopy (AFM) was used to obtain three-dimensional surface profiles. The variation method was used to calculate fractal dimensions. We have measured fractal dimensions of four granule samples, four powders, and two freeze-dried powders.
A computer-program was written to implement the variation method. The implementation was verified using the model surfaces generated by fractional Brownian motion. The fractal dimensions of most particles and granules were between 2.1 and 2.2, and were independent of the scan size we measured. The freeze-dried samples, however showed wide variation in the values of fractal dimension, which were dependent on the scan size. As scan size increased, the fractal dimension also increased up to 2.5.
Fractal analysis can be used to describe surface roughness of pharmaceutical particles. The variation method allows calculation of reliable fractal dimensions of surface profiles obtained by AFM. Careful analysis is required for the estimation of fractal dimension, since the estimates are dependent on the algorithm and the digitized model size (i.e., number of data points of the measured surface profile) used. The fractal dimension of pharmaceutical materials is also a function of the observation scale i.e., the scan size) used in the profile measurement. The multi-fractal features and the scale-dependency of fractal dimension result from the artificial processes controlling the surface morphology.
需要可靠的方法来表征药用固体颗粒的表面粗糙度，以进行质量控制并找出其与其他性质的相关性。在本研究中，我们使用分形分析来描述表面粗糙度。
使用原子力显微镜（AFM）获取三维表面轮廓。采用变分法计算分形维数。我们测量了四种颗粒样品、四种粉末和两种冻干粉末的分形维数。
编写了一个计算机程序来实现变分法。使用分数布朗运动生成的模型表面对该实现进行了验证。大多数颗粒和微粒的分形维数在2.1至2.2之间，且与我们测量的扫描尺寸无关。然而，冻干样品的分形维数值显示出很大差异，这取决于扫描尺寸。随着扫描尺寸的增加，分形维数也增加，最高可达2.5。
分形分析可用于描述药用颗粒的表面粗糙度。变分法允许计算通过AFM获得的表面轮廓的可靠分形维数。由于估计值取决于所使用的算法和数字化模型尺寸（即测量表面轮廓的数据点数），因此在估计分形维数时需要仔细分析。药用材料的分形维数也是轮廓测量中所使用的观察尺度（即扫描尺寸）的函数。分形维数的多重分形特征和尺度依赖性源于控制表面形态的人工过程。
