Mining polarization features from a Mueller matrix

Abstract

Recently, polarization technique has found more and more application prospects in the field of biomedicine, with the emergence of new light sources, polarization devices, and detectors, together with a rapid development in data processing and feature mining capability, and a prominent increase in polarization data measurement and interpretation methods. Muller matrix polarimetry has obvious advantages in exploring the characteristics of complex biomedical specimens [1-4]. Mueller matrix polarization analysis can be realized on other optical technologies by properly adding the polarization state generator and analyzer to the existing optical path in common optical devices, such as Mueller matrix microscopes and endoscopes [5,6]. In addition, Mueller matrix polarization method is more sensitive to the scattering of sub-wavelength microstructure. Compared with the traditional non-polarization optical method, Mueller matrix polarimetry can provide more information to characterize the samples, including the anisotropic optical properties, such as birefringence and diattenuation, as well as the distinctive features of various scattering particles and microstructures. At present, the main challenge of the application of Mueller matrix imaging methods in biomedical research is: how to analyze the obtained polarization data, that is, how to separate and derive specific polarization parameters to characterize target structures and meet the requirements in biomedical detection [7]. In order to break through this bottleneck, our research group has tried to develop a series of polarization feature extraction methods based on machine learning and shown preliminary application prospects in cancer pathological diagnosis.
The process of digitizing the Whole-Slide Images (WSI) of pathological tissues has led to the advent of Machine Learning (ML) tools in digital pathology to help with various tasks [8], including object recognition problems, and predicting disease diagnosis and prognosis of treatment response on patterns in the standard pathological image. Combined with polarimetry technique and data mining methods, we proposed a series of new methods that can derive new polarimetry feature parameters (PFPs) as linear or nonlinear combinations of polarimetry basis parameters (PBPs) to quantitatively and automatically identify the target microstructures in pathological sections, which can be used as a powerful tool in histopathological digitalization and computer-aided diagnosis [9].
In our research work, we took microscopic Mueller matrix images of H&E pathological sections of several typical breast tissues: healthy breast tissue, breast fibroma, breast ductal carcinoma, and breast mucinous carcinoma. Then sets of polarization parameters from Mueller matrix polar decomposition (MMPD) [10] and from our previous studies [7,11,12] were used as the PBPs for input data of training models. Then, a supervised learning method based on linear discriminant analysis (LDA) is used to derive new PFPs based on the polarization characteristics of the target microstructure, which are linear combinations of PBPs. Here, we obtained 12 PFPs to describe the three cancer-related pathological features in each typical breast pathological tissue, i.e. cell nuclei, aligned collagen, and disorganized collagen, as shown in Fig. 1. The training and testing of PFPs were completed in 224 regions of interests (ROIs). By the validation of the PFPs performance with the corresponding H&E images as ground truth, it can be concluded that: (1) the performance of PFPs in identifying the carcinogenesis related microstructures is satisfactory (AUC 0.87-0.94, accuracy 0.82-0.91, precision 0.81-0.95, and recall 0.80-0.98), which has the potential to automate the diagnosis process and predict patient survival and prognosis; (2) PFP is the simplified linear function of the PBPs with physical meanings, providing quantitative characterization for target pathological feature and allowing in-depth analysis of physical interpretation; (3) Benefitting from the advantages of polarization imaging (sensitive to sub-wavelength microstructures and less sensitive to imaging resolution), the outputs PFPs with high sensitivity has the potential to rapidly scan and quantitatively analyze the whole pathological section in the low-resolution and wide-field systems.
On the basis of the previous work, in order to quantitatively characterize more specific microstructures, we designed a neuron network according to the target microstructure characteristics and the corresponding polarization properties, output more complex nonlinear PFPs. Here, we took advantage of Bayesian decision theory and Conditional probability model to find the nonlinear combination from PBPs constrained under the increasing given conditions which correspond to more specific microstructures in breast pathology. The algorithm architecture for deriving nonlinear PFP is shown in Fig. 2. In the previous work, we derived PFP that can characterize all types of cell nuclei in breast tissue, as the simplest linear combination of PBP, denoted as P(Cell) here. In order to further extract the PFP that can characterize the cancerous cell nuclei, we used the Lasso regression method to extract an interim PFP as the linear combination of PBP under the given condition that all pixels are known to be cell denoted as P(Cancer cell | Cell), aiming to distinguish normal cell and cancerous cell. According to Bayesian theory, P(Cell) and P(Cancer cell | Cell) can be multiplied to get a final nonlinear PFP, namely P(Cancer cell), which can quantitatively characterize cancerous cell nuclei from complex breast tissue. Similarly, by continuing to add neurons (each neuron is a conditional probability model), we can separately extract two nonlinear PFPs which has great potential to quantitatively characterize highly differentiated cancerous cancer cells and low-differentiated cancer cells in breast tissues.

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Speaker

Hui Ma
Center for Precision Medicine and Healthcare, Tsinghua-Berkeley Shenzhen Institute, Tsinghua University
China

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