A quantitative evaluation method utilizing the homology concept to assess the state of chromatin within the nucleus of lung cancer.

Homology is a mathematical tool to quantify "the contact degree", which can be expressed in terms of Betti numbers. The Betti numbers used in this study consisted of two numbers, b0 (a zero-dimensional Betti number) and b1 (a one-dimensional Betti number). We developed a chromatin homology profile (CHP) method to quantify the chromatin contact degree based on this mathematical tool. Using the CHP method we analyzed the number of holes (surrounded areas = b1 value) formed by the chromatin contact and calculated the maximum value of b1 (b1MAX), the value of b1 exceeding 5 for the first time or Homology Value (HV), and the chromatin density (b1MAX/ns2). We attempted to detect differences in chromatin patterns and differentiate histological types of lung cancer from respiratory cytology using these three features. The HV of cancer cells was significantly lower than that of non-cancerous cells. Furthermore, b1MAX and b1MAX/ns2 showed significant differences between small cell and non-small cell carcinomas and between adenocarcinomas and squamous cell carcinomas, respectively. We quantitatively analyzed the chromatin patterns using homology and showed that the CHP method may be a useful tool for differentiating histological types of lung cancer in respiratory cytology.

Development of "Mathematical Technology for Cytopathology," an Image Analysis Algorithm for Pancreatic Cancer.

Pancreatic ductal adenocarcinoma (PDAC) is a leading cause of cancer-related death worldwide. The accuracy of a PDAC diagnosis based on endoscopic ultrasonography-guided fine-needle aspiration cytology can be strengthened by performing a rapid on-site evaluation (ROSE). However, ROSE can only be performed in a limited number of facilities, due to a relative lack of available resources or cytologists with sufficient training. Therefore, we developed the Mathematical Technology for Cytopathology (MTC) algorithm, which does not require teaching data or large-scale computing. We applied the MTC algorithm to support the cytological diagnosis of pancreatic cancer tissues, by converting medical images into structured data, which rendered them suitable for artificial intelligence (AI) analysis. Using this approach, we successfully clarified ambiguous cell boundaries by solving a reaction-diffusion system and quantitating the cell nucleus status. A diffusion coefficient (D) of 150 showed the highest accuracy (i.e., 74%), based on a univariate analysis. A multivariate analysis was performed using 120 combinations of evaluation indices, and the highest accuracies for each D value studied (50, 100, and 150) were all ≥70%. Thus, our findings indicate that MTC can help distinguish between adenocarcinoma and benign pancreatic tissues, and imply its potential for facilitating rapid progress in clinical diagnostic applications.

Homology-Based Image Processing for Automatic Classification of Histopathological Images of Lung Tissue.

The purpose of this study was to develop a computer-aided diagnosis (CAD) system for automatic classification of histopathological images of lung tissues. Two datasets (private and public datasets) were obtained and used for developing and validating CAD. The private dataset consists of 94 histopathological images that were obtained for the following five categories: normal, emphysema, atypical adenomatous hyperplasia, lepidic pattern of adenocarcinoma, and invasive adenocarcinoma. The public dataset consists of 15,000 histopathological images that were obtained for the following three categories: lung adenocarcinoma, lung squamous cell carcinoma, and benign lung tissue. These images were automatically classified using machine learning and two types of image feature extraction: conventional texture analysis (TA) and homology-based image processing (HI). Multiscale analysis was used in the image feature extraction, after which automatic classification was performed using the image features and eight machine learning algorithms. The multicategory accuracy of our CAD system was evaluated in the two datasets. In both the public and private datasets, the CAD system with HI was better than that with TA. It was possible to build an accurate CAD system for lung tissues. HI was more useful for the CAD systems than TA.

Automated gleason grading on prostate biopsy slides by statistical representations of homology profile.

BACKGROUND AND OBJECTIVE: Gleason grading system is currently the clinical gold standard for determining prostate cancer aggressiveness. Prostate cancer is typically classified into one of 5 different categories with 1 representing the most indolent disease and 5 reflecting the most aggressive disease. Grades 3 and 4 are the most common and difficult patterns to be discriminated in clinical practice. Even though the degree of gland differentiation is the strongest determinant of Gleason grade, manual grading is subjective and is hampered by substantial inter-reader disagreement, especially with regard to intermediate grade groups. METHODS: To capture the topological characteristics and the degree of connectivity between nuclei around the gland, the concept of Homology Profile (HP) for prostate cancer grading is presented in this paper. HP is an algebraic tool, whereby, certain algebraic invariants are computed based on the structure of a topological space. We utilized the Statistical Representation of Homology Profile (SRHP) features to quantify the extent of glandular differentiation. The quantitative characteristics which represent the image patch are fed into a supervised classifier model for discrimination of grade patterns 3 and 4. RESULTS: On the basis of the novel homology profile, we evaluated 43 digitized images of prostate biopsy slides annotated for regions corresponding to Grades 3 and 4. The quantitative patch-level evaluation results showed that our approach achieved an Area Under Curve (AUC) of 0.96 and an accuracy of 0.89 in terms of discriminating Grade 3 and 4 patches. Our approach was found to be superior to comparative methods including handcrafted cellular features, Stacked Sparse Autoencoder (SSAE) algorithm and end-to-end supervised learning method (DLGg). Also, slide-level quantitative and qualitative evaluation results reflect the ability of our approach in discriminating Gleason Grade 3 from 4 patterns on H&E tissue images. CONCLUSIONS: We presented a novel Statistical Representation of Homology Profile (SRHP) approach for automated Gleason grading on prostate biopsy slides. The most discriminating topological descriptions of cancerous regions for grade 3 and 4 in prostate cancer were identified. Moreover, these characteristics of homology profile are interpretable, visually meaningful and highly consistent with the rubric employed by pathologists for the task of Gleason grading.

Homology-based radiomic features for prediction of the prognosis of lung cancer based on CT-based radiomics.

PURPOSE: Radiomics is a new technique that enables noninvasive prognostic prediction by extracting features from medical images. Homology is a concept used in many branches of algebra and topology that can quantify the contact degree. In the present study, we developed homology-based radiomic features to predict the prognosis of non-small-cell lung cancer (NSCLC) patients and then evaluated the accuracy of this prediction method. METHODS: Four datasets were used: two to provide training and test data and two for the selection of robust radiomic features. All the datasets were downloaded from The Cancer Imaging Archive (TCIA). In two-dimensional cases, the Betti numbers consist of two values: b0 (zero-dimensional Betti number), which is the number of isolated components, and b1 (one-dimensional Betti number), which is the number of one-dimensional or "circular" holes. For homology-based evaluation, computed tomography (CT) images must be converted to binarized images in which each pixel has two possible values: 0 or 1. All CT slices of the gross tumor volume were used for calculating the homology histogram. First, by changing the threshold of the CT value (range: -150 to 300 HU) for all its slices, we developed homology-based histograms for b0 , b1 , and b1 /b0 using binarized images. All histograms were then summed, and the summed histogram was normalized by the number of slices. 144 homology-based radiomic features were defined from the histogram. To compare the standard radiomic features, 107 radiomic features were calculated using the standard radiomics technique. To clarify the prognostic power, the relationship between the values of the homology-based radiomic features and overall survival was evaluated using LASSO Cox regression model and the Kaplan-Meier method. The retained features with nonzero coefficients calculated by the LASSO Cox regression model were used for fitting the regression model. Moreover, these features were then integrated into a radiomics signature. An individualized rad score was calculated from a linear combination of the selected features, which were weighted by their respective coefficients. RESULTS: When the patients in the training and test datasets were stratified into high-risk and low-risk groups according to the rad scores, the overall survival of the groups was significantly different. The C-index values for the homology-based features (rad score), standard features (rad score), and tumor size were 0.625, 0.603, and 0.607, respectively, for the training datasets and 0.689, 0.668, and 0.667 for the test datasets. This result showed that homology-based radiomic features had slightly higher prediction power than the standard radiomic features. CONCLUSIONS: Prediction performance using homology-based radiomic features had a comparable or slightly higher prediction power than standard radiomic features. These findings suggest that homology-based radiomic features may have great potential for improving the prognostic prediction accuracy of CT-based radiomics. In this result, it is noteworthy that there are some limitations.

Fast and accurate tumor segmentation of histology images using persistent homology and deep convolutional features.

Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles (PHPs). For a given image patch, the homology profiles are derived by efficient computation of persistent homology, which is an algebraic tool from homology theory. We propose an efficient way of computing topological persistence of an image, alternative to simplicial homology. The PHPs are devised to distinguish tumor regions from their normal counterparts by modeling the atypical characteristics of tumor nuclei. We propose two variants of our method for tumor segmentation: one that targets speed without compromising accuracy and the other that targets higher accuracy. The fast version is based on a selection of exemplar image patches from a convolution neural network (CNN) and patch classification by quantifying the divergence between the PHPs of exemplars and the input image patch. Detailed comparative evaluation shows that the proposed algorithm is significantly faster than competing algorithms while achieving comparable results. The accurate version combines the PHPs and high-level CNN features and employs a multi-stage ensemble strategy for image patch labeling. Experimental results demonstrate that the combination of PHPs and CNN features outperform competing algorithms. This study is performed on two independently collected colorectal datasets containing adenoma, adenocarcinoma, signet, and healthy cases. Collectively, the accurate tumor segmentation produces the highest average patch-level F1-score, as compared with competing algorithms, on malignant and healthy cases from both the datasets. Overall the proposed framework highlights the utility of persistent homology for histopathology image analysis.

Automated prediction of emphysema visual score using homology-based quantification of low-attenuation lung region.

OBJECTIVE: The purpose of this study was to investigate the relationship between visual score of emphysema and homology-based emphysema quantification (HEQ) and evaluate whether visual score was accurately predicted by machine learning and HEQ. MATERIALS AND METHODS: A total of 115 anonymized computed tomography images from 39 patients were obtained from a public database. Emphysema quantification of these images was performed by measuring the percentage of low-attenuation lung area (LAA%). The following values related to HEQ were obtained: nb0 and nb1. LAA% and HEQ were calculated at various threshold levels ranging from -1000 HU to -700 HU. Spearman's correlation coefficients between emphysema quantification and visual score were calculated at the various threshold levels. Visual score was predicted by machine learning and emphysema quantification (LAA% or HEQ). Random Forest was used as a machine learning algorithm, and accuracy of prediction was evaluated by leave-one-patient-out cross validation. The difference in the accuracy was assessed using McNemar's test. RESULTS: The correlation coefficients between emphysema quantification and visual score were as follows: LAA% (-950 HU), 0.567; LAA% (-910 HU), 0.654; LAA% (-875 HU), 0.704; nb0 (-950 HU), 0.552; nb0 (-910 HU), 0.629; nb0 (-875 HU), 0.473; nb1 (-950 HU), 0.149; nb1 (-910 HU), 0.519; and nb1 (-875 HU), 0.716. The accuracy of prediction was as follows: LAA%, 55.7% and HEQ, 66.1%. The difference in accuracy was statistically significant (p = 0.0290). CONCLUSION: LAA% and HEQ at -875 HU showed a stronger correlation with visual score than those at -910 or -950 HU. HEQ was more useful than LAA% for predicting visual score.

Homology analysis detects topological changes of Iba1 localization accompanied by microglial activation.

The state of microglial activation provides important information about the central nervous system. However, a reliable index of microglial activation in histological samples has yet to be established. Here, we show that microglial activation induces topological changes of Iba1 localization that can be detected by analysis based on homology theory. Analysis of homology was applied to images of Iba1-stained tissue sections, and the 0-dimentional Betti number (b0: the number of solid components) and the 1-dimentional Betti number (b1: the number of windows surrounded by solid components) were obtained. We defined b1/b0 as the Homology Value (HV), and investigated its validity as an index of microglial activation using cerebral ischemia model mice. Microglial activation was accompanied by changes to Iba1 localization and morphology of microglial processes. In single microglial cells, the change of Iba1 localization increased b1. Conversely, thickening or retraction of microglial processes decreased b0. Consequently, microglial activation increased the HV. The HV of a tissue area increased with proximity to the ischemic core and showed a high degree of concordance with the number of microglia expressing activation makers. Furthermore, the HV of human metastatic brain tumor tissue also increased with proximity to the tumor. These results suggest that our index, based on homology theory, can be used to correctly evaluate microglial activation in various tissue images.

Application of the homology method for quantification of low-attenuation lung region inpatients with and without COPD.

BACKGROUND: Homology is a mathematical concept that can be used to quantify degree of contact. Recently, image processing with the homology method has been proposed. In this study, we used the homology method and computed tomography images to quantify emphysema. METHODS: This study included 112 patients who had undergone computed tomography and pulmonary function test. Low-attenuation lung regions were evaluated by the homology method, and homology-based emphysema quantification (b0, b1, nb0, nb1, and R) was performed. For comparison, the percentage of low-attenuation lung area (LAA%) was also obtained. Relationships between emphysema quantification and pulmonary function test results were evaluated by Pearson's correlation coefficients. In addition to the correlation, the patients were divided into the following three groups based on guidelines of the Global initiative for chronic Obstructive Lung Disease: Group A, nonsmokers; Group B, smokers without COPD, mild COPD, and moderate COPD; Group C, severe COPD and very severe COPD. The homology-based emphysema quantification and LAA% were compared among these groups. RESULTS: For forced expiratory volume in 1 second/forced vital capacity, the correlation coefficients were as follows: LAA%, -0.603; b0, -0.460; b1, -0.500; nb0, -0.449; nb1, -0.524; and R, -0.574. For forced expiratory volume in 1 second, the coefficients were as follows: LAA%, -0.461; b0, -0.173; b1, -0.314; nb0, -0.191; nb1, -0.329; and R, -0.409. Between Groups A and B, difference in nb0 was significant (P-value = 0.00858), and those in the other types of quantification were not significant. CONCLUSION: Feasibility of the homology-based emphysema quantification was validated. The homology-based emphysema quantification was useful for the assessment of emphysema severity.

Homology-based method for detecting regions of interest in colonic digital images.

BACKGROUND: A region of interest (ROI) is a part of tissue that contains important information for diagnosis. To use many image analysis methods efficiently, a technique that would allow for ROI identification is required. For the colon, ROIs are characterized by areas of stronger color intensity of hematoxylin. Since malignant tumors grow in the innermost layer, most ROIs will be located in the colonic mucosa and will be an accumulation of tumor cells and/or integrated cells with distorted architecture. METHODS: Using homology theory, our group proposed a method to estimate the contact degree of elements in a unit area of tissue. Homology is a concept that is used in many branches of algebra and topology, and it can quantify the contact degree. Due to the lack of contact inhibition of cancer cells, an area with unusual contact degree is expected to be a potential ROI. RESULTS: The current work verifies the accuracy of this method against the results of pathological diagnosis, based on 1825 colonic images provided by the Osaka Medical Center for Cancer and Cardiovascular Diseases. Although we have many false positives and there is a possibility of missing undifferentiated types of cancer, this system is very effective for detecting ROIs. CONCLUSIONS: The mathematical system proposed by our group successfully detects ROIs and is a potentially useful tool for differentiating tumor areas in microscopic examination very quickly. Because we use only the information from low-power field images, there is room for further improvement. This system could be used to screen for not only colon cancer but other cancers as well. More sophisticated and more efficient automated pathological diagnosis systems can be developed by integrating various techniques available today. VIRTUAL SLIDE: The virtual slide(s) for this article can be found here: http://www.diagnosticpathology.diagnomx.eu/vs/7129390011429407 .