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From early 20th, the homology have been studied as a branch of mathematics. It has been one of a major topic in mathematics and applied in many scientific fields. The homology can be regarded as a mathematical concept of quantifying the contact degree. Because it belongs to modern mathematics, advanced knowledge of mathematics are required to understand this concept. Fortunately, since the definition of the homology is very simple in two-dimensional case, we can easily apply this to image analyzing methods. Fracture surface is composed of a process that cracks grow. If these cracks contact one another, rupture occurs. Progress of the fracture would vary due to the effect of external force. We identify the rapid and the fatigue fracture surface by a homology method. By analyzing the state of fracture via a homology method, it is believed that the cause of fracture can be estimated.

Immunohistochemical data (IHC) plays an important role in clinical practice, and is typically gathered in a semi-quantitative fashion that relies on some degree of visual scoring. However, visual scoring by a pathologist is inherently subjective and manifests both intra-observer and inter-observer variability. In this study, we introduce a novel computer-aided quantification methodology for immunohistochemical scoring that uses the algebraic concept of persistent homology. Using 8 bit grayscale image data derived from 90 specimens of invasive ductal carcinoma of the breast, stained for the replicative marker Ki-67, we computed homology classes. These were then compared to nuclear grades and the Ki-67 labeling indices obtained by visual scoring. Three metrics for IHC staining were newly defined: Persistent Homology Index (PHI), center coordinates of positive and negative groups, and the sum of squares within groups (WSS). This study demonstrates that PHI, a novel index for immunohistochemical labeling using persistent homology, can produce highly similar data to that generated by a pathologist using visual evaluation. The potential benefits associated with our novel technology include both improved quantification and reproducibility. Since our method reflects cellularity and nuclear atypia, it carries a greater quantity of biologic data compared to conventional evaluation using Ki-67.

Frontotemporal lobar degeneration (FTLD) is a heterogeneous roup of disorders characterized by disturbances of behavior nd personality and different types of language impairment with r without concomitant features of motor neuron disease or arkinsonism [1]. FTLD is classified into three categories: fronotemporal dementia (FTD), progressive non-fluent aphasia (PNFA), nd semantic dementia (SD) [2]. Moreover, FTD is classified into wo categories: pick type and motor neuron disease (MND) type. TLD is also classified into four neuropathological categories: TLD-tau pathology type, FTLD-TDP43 pathology type, FTLD-FUS athology type, and FTLD-other type [2]. Clinical FTD-Pick type is ssociated with FTLD-tau, TDP, or FUS, and some FTLD is caused by arious genetic mutations. Limb girdle muscular dystrophy (LGMD) is a progressive myopahy with necrosis and regenerative changes in skeletal muscle. GMD Type 1D is caused by mutations in the DNAJB6 (DnaJ homolog

Primary mediastinal liposarcoma was observed in a 73-year-old man. Because of tight adhesions to adjacent tissues, neither complete resection nor surgical debulking of the tumor was possible. A T-tube was inserted into the patient's trachea for severe dyspnea, and he was treated with radiotherapy and an oral peroxisome proliferator-activated receptor-gamma agonist. The patient died 6 years after the initial diagnosis. Autopsy revealed liposarcoma composed of 3 subtypes in the primary tumor: well-differentiated, dedifferentiated, and round cell components. Round cell and dedifferentiated liposarcomas were predominantly observed in the metastatic nodules.

We describe an autopsy case of a patient with pandemic influenza (A/H1N1pdm) virus infection in Japan, who developed rapidly progressive viral pneumonia exhibiting diffuse alveolar damage. A 41-year-old female visited our hospital with a fever of 38.7C. She was a public health nurse with no underlying disease and had had contact with a group of elementary school students who had been infected with the influenza (A/H1N1pdm) virus 1 week earlier. She was prescribed oseltamivir and returned to the hotel where she was staying alone. The next day, she was found dead in her hotel room. At autopsy, both lungs were voluminous and microscopic examination revealed acute-stage, severe diffuse alveolar damage with remarkable mononuclear cell infiltration and hyaline membrane formation in the lungs. CD8-positive T lymphocytes were dominantly observed. Immunohistochemically, influenza A viral protein was confirmed in the damaged type II pneumocytes and also in the infiltrated macrophages. Real-time RT-PCR analysis of both pre- and post-mortem pharyngeal swabs confirmed a novel influenza (A/H1N1pdm) virus infection. This is the second autopsy case of influenza (A/H1N1pdm) virus infection in Japan, and the findings indicated that the patient died due to an exceptionally rapid progression of viral pneumonia. This case indicates that patients with influenza (A/H1N1pdm) virus infection should be carefully monitor for acute respiratory distress syndrome.

Simple characterizations of a pseudosphere or a time-like plane in Minkowski 3-space by the existence of light-like lines are given.

Simple characterizations of a pseudosphere or a plane in Minkowski 3-space by the existence of pseudocircles are given.

Lymphomatoid granulomatosis (LYG) in the CNS is an uncommon lymphoproliferative disease with characteristic angiocentric lymphoreticular proliferative and granulomatous lesions exhibiting low-grade malignant potential. Here we report a rare case of CNS-LYG, which disseminated to the lymph node and bone marrow. A 50-year-old man was diagnosed with CNS-LYG based on brain biopsy showing perivascular infiltration of CD3-positive small T-lymphocytes without overt nuclear atypism. Eight months after the initial neurological symptoms, inguinal lymph node swelling was found and histopathologically diagnosed as peripheral T-cell lymphoma. TCRgamma-gene rearrangement study using both paraffin-embedded specimens of brain and inguinal lymph node demonstrated an identical clonal band. Considering the clinical course, we concluded lymph node involvement of CNS-LYG, suggesting the malignant potential of CNS-LYG.

Sarcomatoid differentiation in renal cell carcinoma is thought to be the result of the dedifferentiation of the parent tumor, and it can be found in the chromophobe renal cell carcinoma just as other subtypes. We report a case of chromophobe renal cell carcinoma, which showed osteosarcoma-like differentiation. This is the first known case ever to be clearly identified as such. The patient was a 74-year-old man, and the CT scan revealed a huge retroperitoneal mass, which protruded from the lower half of the kidney and directly invaded the colon. Intraabdominal dissemination and metastases to the liver and lungs were also found. The resected tumor histologically showed sarcoma-like spindle cell proliferation and partly produced massive osteoid, which simulated the osteosarcoma. In addition, a typical histology of chromophobe renal cell carcinoma was found in part of the tumor. Immunohistochemically, spindle cells were reactive for epithelial membrane antigen, cytokeratin, and vimentin. The cell nests that were labeled by epithelial membrane antigen and cytokeratin were also found in the osteosarcoma-like area. We think that these phenomena were the result of "dedifferentiation" and metaplasia of the chromophobe renal cell carcinoma.