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24MINING POLARIZATION FEATURES FROM A MUELLER MATRIX
DONG YANG1, JIACHENWAN2 AND HUI MA1,3
'Center for Precision Medicine and Healthcare, Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, China 2Department of Applied Physics, New York University, Tandon School of Engineering, USA 3Department of Physics, Tsinghua University, China
mahui@tsinghua. edu. cn
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 increasein polarization data measurement and interpretationmethods. 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 analyzerto the existing optical path in common optical devices, such as Mueller matrixmicroscopes 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 canprovide more information to characterize the samples, including the anisotropic optical properties, such as birefringence and diattenuation, as well as the distinctive features of various scatteringparticles 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 polarimetrytechnique 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 PFPsbased 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 sensitivityhas 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 PBPsconstrained 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 cellnuclei, 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 celldenoted as P(Cancer cell | Cell), aiming to distinguishnormal 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.
Cell nuclei label Aligned collagen label Disorganized collagen label Cell nuclei label Aligned collagen label Disorganized collagen label
Cell nuclei Aligned collagen Disorganized collagen Cell nuclei Aligned collagen Disorganized collage!
Figure 1:Quantitative characterization of cell nuclei (blue pixels), aligned collagen (red pixels), and disorganized collagen (orange pixels)using the PFPs in H&E pathological sections of different breast tissues: (a) healthy breast tissue; (b) breast fibroma; (c) breast ductal carcinoma; (d) breast mucinous carcinoma. The areas inside the black solid line and outside the red solid line in H&E images are the target microstructural features labelled by the breast pathologist. The image size is 800x 800 pixels[9].
Figure 2: Algorithm architecture for deriving nonlinear PFPs to characterize more specific microstructure feature in breast
pathological tissues.
Figure 3 summarizes the characterization results of these nonlinear PFPs derived by the proposed method. The cell nuclei with different pathological states in WSIs were labelled by pathologists under 40 x objectivemanually as ground truth, whereas, PBPs of breast pathological tissues, as the input data of designed ML model, were obtained under 4x objective. From Fig. 3, we can observe that the performance of these PFPs is satisfactory, which has the potential to quantitatively characterize more and more specific microstructures in breast tissues. Each neuron is a probability model composed of PBP according to the pathological structure, which has certain physical interpretability. In addition, in the low-resolution and wide-field systems, the PFPs are more sensitive than human vision to the cancer cells with different degrees of differentiation, and may provide quantitative evaluation for breast cancer diagnosis. This technique paves the way for cancer primaryscreeningin clinical practice.
Normal breast ccli Low level breast cancer cell High level breast cancer cell
Figure 3: For different breast pathological cells-normal breast cell, low level breast cancer cell, and high level breast cell, the characterization results of nonlinear PFPs: (a) P( Cancer cell); (b) P( Low level cancer cell); (c) P(High level cancer cell).
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