Relationship between tumor grade and computed architectural complexity in breast cancer specimens

Summary

Breast cancer is the leading form of cancer diagnosed in women, and the second leading cause of cancer mortality in this group. A commonly accepted grading system for breast cancer that has proven useful for guiding treatment strategy is the modified Bloom-Richardson system. However, this system is subject to interobserver variability, which can affect patient management and outcome. Hence, there is a need for an independent objective and reproducible breast cancer–grading tool to reduce interobserver variability. In this work, we hypothesized that architectural complexity of epithelial structures increases with decreasing differentiation in ductal carcinoma of the breast. To test this hypothesis, we explored the potential of a computer-based approach using fractal image analysis to quantitatively measure the complexity of breast histology specimens and investigate the relationship between increasing fractal dimension and tumor grade. More specifically, we developed an optimal staining and computational technique to compute the fractal dimensions of breast sections of grades 1, 2, and 3 tumors, assigned by a breast cancer pathologist, and compared the mean fractal dimensions between the tumor grades. We found that significant differences (P < .0005) exist between the mean fractal dimensions corresponding to the 3 tumor grades, and that the mean fractal dimension increases with increasing tumor grade. These results indicate that breast tumor differentiation can be characterized by the degree of architectural complexity of epithelial structures. They also indicate that fractal dimension has potential as an objective, reproducible, and automated measure of architectural complexity that may help reduce interobserver variability in grading.

Introduction

In 2007, breast cancer is expected to be the second leading cause of cancer deaths among women, resulting in an estimated 240 510 new cases diagnosed in the United States, and of these, 40 460 estimated deaths [1]. One of the factors that have proven useful for determining a patient's outcome and guiding the choice of treatment strategy in women with breast cancer is the assessment of histologic tumor grade [2], [3]. A commonly accepted grading system for breast cancer is the modified Bloom-Richardson system which is based on examining 3 features of a histology specimen: the mitosis count (a measure of cell division), nuclear pleomorphism (a measure of change in cell size and uniformity), and tubular formation (the percentage of cancer composed of tubular structures). Each of these features is assigned a score ranging from 1 to 3 (indicating the degree of departure from normal breast epithelium). The scores of each of the features are subsequently added together for a final sum that ranges between 3 and 9. A tumor with a final sum of 5 or less defines a grade 1 tumor (well-differentiated), a sum of 6 or 7 is a grade 2 tumor (moderately differentiated), and a sum of 8 or 9 is grade 3 tumor (poorly differentiated). Although the modified Bloom-Richardson grading scheme works reasonably well, significant interobserver variation in grading still exists [4], [5], [6]. This is not surprising as pathologists are assessing complex morphological characteristics of histologic structures in a semiquantitative manner. A more quantitative approach, which may aid in making pathology grading more reproducible, is to analyze images of histologic specimens using purely quantitative methods.

A quantitative method that lends itself particularly useful for characterizing complex irregular structures is fractal analysis. Although classical Euclidean geometry works well for describing properties of regular smooth-shaped objects such as circles or squares by using measures such as the length of the object's perimeter, these Euclidean descriptions are not adequate for complex irregular-shaped objects that occur in nature (eg, clouds, coastlines, and biological structures). These “non-Euclidean” objects are described better by fractal geometry, which has the ability to quantify the irregularity and complexity of objects with a measurable value called the fractal dimension. Fractal dimension differs from our intuitive notion of dimension (ie, topological dimension) in that it can be a noninteger value, and the more irregular and complex an object is, the higher its fractal dimension relative to its topological dimension (Fig. 1).

Recent studies have shown that fractal dimension can be useful for describing the complex pathologic architecture of tumors [7], [8], [9]. Given its potential for pathologic assessment, it is not surprising that fractal analysis has been investigated for its ability to discriminate between benign and malignant breast cells from fine-needle aspiration cytology smears [10], [11], [12]. However, to our knowledge, there have been no studies performed to assess the degree of tumor differentiation in histologic breast specimens. We have recently developed a fractal analysis technique for the examination of histologic breast specimens [13]. As a preliminary assessment of this technique and to test the hypothesis that architectural complexity of epithelial structures increases with decreasing degree of tumor differentiation, we apply it to specimens of grades 1, 2, and 3 ductal carcinoma of the breast.