Kazuaki Nakane

A simple mathematical model utilizing topological invariants for automatic detection of tumor areas in digital tissue images

The number of diagnostic pathologists is significantly small in Japan with respect to the large number of clinical cases that require pathological diagnosis. Because of this individual diagnostic pathologists are overloaded in their daily work. To improve the situation development of computer assisted diagnostic system for a pathologist will be one of the effective solutions.

Persistent Homology for Fast Tumor Segmentation in Whole Slide Histology Images

Automated tumor segmentation in Hematoxylin & Eosin stained histology images is an essential step towards a computer-aided diagnosis system. In this work we propose a novel tumor segmentation approach for a histology whole-slide image (WSI) by exploring the degree of connectivity among nuclei using the novel idea of persistent homology profiles. Our approach is based on 3 steps: 1) selection of exemplar patches from the training dataset using convolutional neural networks (CNNs); 2) construction of persistent homology profiles based on topological features; 3) classification using variant of k-nearest neighbors (k-NN). Extensive experimental results favor our algorithm over a conventional CNN.

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

BackgroundA 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.MethodsUsing 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.ResultsThe 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.ConclusionsThe 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 SlideThe virtual slide(s) for this article can be found here: http://www.diagnosticpathology.diagnomx.eu/vs/7129390011429407.

Homology analysis of structures of high carbon bearing steel: effect of repeated quenching on prior austenite grain size

Abstract To estimate the effect of quenching on metal structures, the analysis process is very important. It was found that use of quenching reduced the prior austenite grain size greatly and the change in compressive stress at the surface of the material had a great effect on its strength. If we can estimate the change of the grains in the structure quantitatively, we can easily evaluate the effect of the quenching process. However, the structures are too complex to apply ordinary image analysis methods. In this paper, we propose a new method for analysing changes in steel structures. By use of this method, we confirm the effect of repeated quenching on the distribution of grains.

A numerical approach to the asymptotic behavior of solutions of a one-dimensional free boundary problem of hyperbolic type

A free boundary problem which arises from the physical model called “peeling” will be analyzed numerically. To obtain an equation which describes the motion of the free boundary, the fixed domain method is applied. By using the equation, numerical computations are carried out. Our numerical computations suggest that the peeling speed plays an important role in the existence of global solutions.

Application of the homology method for quantification of low-attenuation lung region in patients 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 Estimate of Grain Size Measurement Based on the JIS Samples

Test method for measuring austenite and martensite microscopic grain size of the steel is commonly done. Determination of average crystal density for the specimen is defined by JIS (Japanese Industrial Standards) in Japan. In general, this kind of determination is carried out by engineers. The results may depend on their skill, so automated tool to determine the grain size is needed. In this paper we try to apply homology method to analyze the structures. As the first trial, we apply this method to the figures on JIS. The result of homology is compared with the grain size defined in JIS. We can make sure the correlation between grain size and the homology value.

The Quantization of the Structure of Fisheyes via Homology Method

Martensitic high carbon high strength SAE 52100 bearing steel is one of the main alloys used for rolling contact applications where high wear resistance are required. Due to its high fatigue strength, SAE 52100 is recently being used not only for the production of bearings but also shafts. In this work, quenched SAE 52100 steel fatigue strength under rotating bending was investigated. Especially, we focus on “fisheye around inclusion” where the fatigue crack starts. Quantitative evaluation of its optical micrograph has not been enough carried out. In order to develop easy evaluation method for the fisheye area, we apply homology technique to the optical observation.

Influence of Repeated Quenching on Bearing Steel Martensitic Structure Investigated by Homology

JIS SUJ2 (high carbon high strength bearing steel) heat treated by repeated quenching was investigated. The microstructure of the bearing traces was observed after heat treatment by laser confocal microscope. In this paper, by mathematical methods, we try to evaluate quantitatively this change of the structure. Homology is a branch of mathematics that allows quantitative describing characteristics of a figure by replacing the figure with algebra. Applying homology we can express the degree of the connection of the figure. Here we use homology to quantify the change of structures by repeated quenching. Keyword: Homology, Rolling contact fatigue, SUJ2, repeated quenching

Homology Analysis of Prior Austenite Grain Size of SAE52100 Bearing Steel Processed by Cyclic Heat Treatment

Here, we introduce the mathematical methods to quantitatively evaluate the change of the tissue to quenching. SAE 52100 sample was repeatedly quenched and the influence of this cyclic heat treatment was investigated. The repeated quenching process increased the retained austenite content and had little influence on the materials hardness. The prior austenite grain size was decreased and consequently, refinement of the martensitic phase in the material occurred. The higher content of the retained austenite (higher fracture toughness) and the refinement of the microstructure accounted for the higher fatigue properties of the repeatedly quenched material. Here we use mathematical homology to quantify these features.