Studies show that breast cancer ranks first among all cancers affecting women in China. Additionally, its mortality rate is high and continues to increase. The five-year relative survival rate of patients with breast cancer who are detected at an early stage is ? 90%, whereas it is only 20% for those detected at an advanced stage. Therefore, early and effective diagnosis of breast cancer is crucial to patient recovery. Invasive ductal carcinoma is one of the most common types of breast cancer, and sclerosing adenopathy is a benign breast disease. These two diseases are similar both visually and microscopically and are susceptible to diagnostic errors. Immunohistochemical staining is typically required to identify these markers. It is a complicated and costly technique that can yield false-positive or false-negative results. Therefore, new methods for identifying sclerosing adenopathy and early invasive ductal carcinoma must be devised to reduce the misdiagnosis rates of both diseases. Polarimetric imaging can reflect the intricate microstructure of biological tissues and is promising for detecting biological tissues. Therefore, differential-tissue analysis for detecting sclerosing adenopathy and early invasive ductal carcinoma using polarization imaging methods is worth investigating.

Polarization imaging experiments were performed on sclerosing adenopathy and early invasive ductal carcinoma tissues. Subsequently, four vector parameters, i.e., the delay vector (R), dichroic vector (D), polarization vector (P), and scattering receding vector (Δ); six scalar parameters, i.e., the scattering receding matrix correlation parameter (Δ), phase-delay matrix correlation parameters (R, δ, θ, ψ), and dichroic correlation parameter (D) in the Mueller-matrix polarization decomposition (MMPD) method; and three scalar parameters (b, A, x) in the Mueller-matrix transformation (MMT) method were extracted. The vector parameters and the combination of scalar parameters were plotted in a three-dimensional (3D) scatter plot and a minimum enclosing sphere plot. The minimum enclosing sphere is the smallest sphere containing the Mueller-matrix parameter values from all the sample points, which reflects the spatial pattern of the parameter-value distribution. A quantitative analysis of the effect of the Mueller-matrix parameters in characterizing the difference between the two diseases was performed by analyzing the difference in the radius of the smallest enclosing sphere of the Mueller-matrix parameter values for the tissue sample points of the two diseases.

In this study, Mueller-matrix parameters were extracted via MMPD and MMT methods using breast sclerosing adenopathy and early invasive ductal carcinoma tissues, which are easily misdiagnosed in clinical practice. The effect of the Mueller-matrix parameters in characterizing the difference between the two diseases in two different structures, i.e., fibrotic mesenchyme and nucleus, was investigated based on the distribution range using the minimum enclosing sphere. The result shows that in the fibrotic interstitial region, the MMPD parameter R (Fig. 3) and the combinations of three-parameter (Fig. 4), i.e., R-θ-ψ, δ-θ-ψ, and R-δ-ψ, resulted in a better characterization of the difference between the two diseases. The relative radius difference of the smallest encircling sphere for the four abovementioned characterization parameters was 68.77%, 61.33%, 61.09%, and 61.04%, respectively (Table 2). This may be because different mechanisms and degrees of fibrotic mesenchymal proliferation occur in both diseases, to which phase-delay-related parameters are extremely sensitive. In the nucleus region, the MMPD parameter Δ (Fig. 6) and the combination of three-parameter Δ-δ-θ (Fig. 7) resulted in a better characterization of the difference between the two diseases. The difference in the relative radius of the smallest enclosing sphere was 57.36% and 49.35% for the two abovementioned characterization parameters, respectively (Table 3). This is attributable to the relatively rapid cell division and proliferation of early invasive ductal carcinoma cells, to which the scattering deviation correlation parameter is extremely sensitive.

Investigations into the differences between sclerosing adenopathy and early invasive ductal carcinoma are important in clinical applications. In this study, the variability of the two diseases was investigated using a biotissue Mueller-matrix imaging system. The results show that in the fibrotic mesenchymal region, the parameters related to the fundamental matrix of phase delays obtained using the MMPD method are the best for the differential characterization of sclerosing adenopathy and early invasive ductal carcinoma. They include the phase delay vector R; three-parameter combinations of four scalar parameters (the four parameters are the total phase delay values R, linear phase delay value δ, fast-axis orientation θ, and media spinority ψ, respectively), i.e. combination of R-θ-ψ, combination of δ-θ-ψ, and combination of R-δ-ψ. The relative radius differences of their minimum enclosing sphere are 68.77%, 61.33%, 61.09%, and 61.04%, respectively. In the nucleus region, the parameters associated with the scattering receding bias fundamental matrix MΔ obtained using the MMPD method are the best for the differential characterization of sclerosing adenopathy and early invasive ductal carcinoma. The parameters include the scattering receding bias vectors Δ and a three-parameter combination comprising scattering receding bias parameters Δ and phase-delay fundamental matrix MR correlation parameters δ and θ (Δ, δ and θ). The relative radius differences of their minimum enclosing spheres are 57.36% and 49.35%, respectively.

For both diseases, the Mueller-matrix parameters yielded better difference characterization in the fibrotic mesenchymal region than in the nucleus region. This study describes the development of clinical discriminators for both diseases. Only the differences in the distribution ranges of the Mueller-matrix parameters were examined, and only one variable, i.e., sample structure, was controlled. In future studies, the effect of the parameter values and variables such as the thickness of the sample slices shall be investigated.