Graphical methods for quantifying macromolecules through bright field imaging

Abstract

Bright field imaging of biological samples stained with antibodies and/or special stains provides a rapid protocol for visualizing various macromolecules. However, this method of sample staining and imaging is rarely employed for direct quantitative analysis due to variations in sample fixations, ambiguities introduced by color composition and the limited dynamic range of imaging instruments. We demonstrate that, through the decomposition of color signals, staining can be scored on a cell-by-cell basis. We have applied our method to fibroblasts grown from histologically normal breast tissue biopsies obtained from two distinct populations. Initially, nuclear regions are segmented through conversion of color images into gray scale, and detection of dark elliptic features. Subsequently, the strength of staining is quantified by a color decomposition model that is optimized by a graph cut algorithm. In rare cases where nuclear signal is significantly altered as a result of sample preparation, nuclear segmentation can be validated and corrected. Finally, segmented stained patterns are associated with each nuclear region following region-based tessellation. Compared to classical non-negative matrix factorization, proposed method: (i) improves color decomposition, (ii) has a better noise immunity, (iii) is more invariant to initial conditions and (iv) has a superior computing performance.

Fig. 1.

Computational steps in quantifying stained samples: in a single image, the user initializes the stained region associated with a signaling macromolecule. Learned parameters are subsequently used for the rest of the dataset.

Fig. 2.

Images of (a) human mammary fibroblasts and (b) mouse pre-adipocytes (positive control) grown under conditions that support adipocyte differentiation for 5–7 days before being fixed and stained with hematoxylin and Oil Red O.

Fig. 3.

An example of two-terminal (class) graph-cut segmentation: (a) an image grid (3 × 3), where ‘F’ and ‘B’ correspond to foreground and background seeds, respectively; (b) a graph constructed from image (a); (c) an optimum cut shown as a red line; and (d) a final labeling result where grid points are assigned to terminals S and T after the cut.

Fig. 4.

Noise is added to a synthetic image at 12 dB (a), 7 dB (b), 3 dB (c) and 0 dB (d), and the segmentation results based on graph cut (μ = 100) and NMF are shown in the second and third rows, respectively.

Fig. 5.

A comparison of signal decomposition by graph cut (μ = 100) (a) and NMF (b) indicates superior performance with the graph-cut method.

Fig. 6.

Decomposition (μ = 100) of color space when nuclear and antibody stains colocalize: (a) a bright field image of human mammary tissue stained for phosphorylated γH2AX and hematoxylin, and (b) its color decomposition.

Fig. 7.

Probability density functions corresponding to the fat content on a cell-by-cell basis for each of the two populations, where (a) corresponds to a population represented by Figure 8c and (b) corresponds to a population represented by Figure 8a. The KS test computes a P-value of 0.001 indicating that these two populations are different.

Fig. 8.

Segmentation and color decomposition from two images in the dataset indicate how region-based tessellation enables quantifying signal macromolecules on a cell-by-cell basis. (μ = 100, σ = 2.5)