Measuring Fractal Dimensions of Cell Contours: Practical Approaches and their Limitations

Abstract

We discuss practical methods to examine fractal properties of electron micrographs and outline a procedure to extract information from a gray scale image (EMM-image) by using different filtering methods. The data obtained from this reduction of information is used as a basis for numerical calculations of fractal dimensions D. To determine D of a given object, we use the yardstick, the box counting and the probabilistic methods. These three approaches will be critically discussed and the finite scaling range for natural objects such as cells will be examined. The method of digital image analysis as discussed here incorporates an algorithm that detects self-similar domains in the structure of cells. We apply this method to determine the fractal dimension of cell contours and we discuss advantages and limitations of these methods. As prototype examples, we investigate cellprofiles of lymphocytes and lymphocyte leukemic cells.