Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

A Graph-Based Digital Pathology Approach To Describe Lymphocyte Clustering Patterns After Renal Transplantation

Introduction/ Background Renal transplantation (rTx) induces an adaptive immune response against foreign donor antigens mediated by lymphocytes of the recipient. Local accumulation of B- and T-cells is an important component of this response enabling and controlling immune cell interactions [1]. Combining digital microscopic images with network analysis [2][3] opens new perspectives to study the spa- tial dimension of lymphocyte clustering and to model their potential interactions.   Aims The aim of this study is to characterize the range of B- and T-lymphocytic infiltrates below the threshold of rejection defined by theBanffclassification [4][5] and to propose a mathematical description of immune cell clustering for use in systems medicine approaches.   Methods We established a workflow to comprehensively characterize lymphocyte clusters and compare their morphological features with organized structures such as secondary or tertiary lymphoid organs (TLO/SLO) [6]. 51 renal protocol and indication biopsies from 13 patients without evidence for severe rejection over 10 years were stained by CD3/CD20 duplex immunohisto- chemistry. Whole slide images (WSIs) were acquired to automatically detect biologically relevant regions of in- terest (ROIs) by means of density maps for lymphocytes (image analysis workflow illustrated in Fig. 1a). They are generated from single nuclei identification using an au- to-adaptive random forest pixelwise classifier (“nucleus container” module [7],Definiens,Germany). We imple- mented a graph-based tool in Java using individual cell coordinates to identify cell compartments (Fig. 1b) and applied it to each selected ROI. For this, a neighborhood graph is built by Delaunay triangulation and Euclidean distances. This analysis allows describing their specific clustering behavior based on features as described in [8]. The convex hull of the neighborhood graph allows a visualization of B- and T-cell compartments.   Results We identified B-cell rich compartments in about 55% of 150 ROIs in kidney tissue after successful transplantation (examples in Fig. 2). The B-cell compartments in rTx tended towards smaller overall size with on average about 90 cells in a B-cell cluster compared to more than 600 B-cells observed in mature TLOs and SLOs and they showed less prominent spatial organization (average degree on average 3.92 instead of 4.97; degree shows generally Poisson distribution as illustrated in Fig. 3A). Further, the graph analysis confirmed lower B-cell density (Fig. 3B displays the exponential character of the spatial B-cell distribution in a selected ROI), a different ratio between T- and B-cell compartments, and more frequent overlap between both regions than in mature lymphoid structures.   We conclude that the graph-based approach is feasible to distinguish relevant immune cell patterns in rTx and provides a useful mathematical description of neighborhood relationships between immune cells and their spatial organization. The workflow has the potential to improve throughput and robustness of immune cell evaluation for use in translational science

Investigation of pre-structured GaAs surfaces for subsequent site-selective InAs quantum dot growth

In this study, we investigated pre-structured (100) GaAs sample surfaces with respect to subsequent site-selective quantum dot growth. Defects occurring in the GaAs buffer layer grown after pre-structuring are attributed to insufficient cleaning of the samples prior to regrowth. Successive cleaning steps were analyzed and optimized. A UV-ozone cleaning is performed at the end of sample preparation in order to get rid of remaining organic contamination

Graph-based description of tertiary lymphoid organs at single-cell level

Our aim is to complement observer-dependent approaches of immune cell evaluation in microscopy images with reproducible measures for spatial composition of lymphocytic infiltrates. Analyzing such patterns of inflammation is becoming increasingly important for therapeutic decisions, for example in transplantation medicine or cancer immunology. We developed a graph-based assessment of lymphocyte clustering in full whole slide images. Based on cell coordinates detected in the full image, a Delaunay triangulation and distance criteria are used to build neighborhood graphs. The composition of nodes and edges are used for classification, e.g. using a support vector machine. We describe the variability of these infiltrates on CD3/CD20 duplex staining in renal biopsies of long-term functioning allografts, in breast cancer cases, and in lung tissue of cystic fibrosis patients. The assessment includes automated cell detection, identification of regions of interest, and classification of lymphocytic clusters according to their degree of organization. We propose a neighborhood feature which considers the occurrence of edges with a certain type in the graph to distinguish between phenotypically different immune infiltrates. Our work addresses a medical need and provides a scalable framework that can be easily adjusted to the requirements of different research questions

Directing Cluster Formation of Au Nanoparticles from Colloidal Solution

Discrete clusters of closely spaced Au nanoparticles can be utilized in devices from photovoltaics to molecular sensors because of the formation of strong local electromagnetic field enhancements when illuminated near their plasmon resonance. In this study, scalable, chemical self-organization methods are shown to produce Au nanoparticle clusters with uniform nanometer interparticle spacing. The performance of two different methods, namely electrophoresis and diffusion, for driving the attachment of Au nanoparticles using a chemical cross-linker on chemically patterned domains of polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) thin films are evaluated. Significantly, electrophoresis is found to produce similar surface coverage as diffusion in 1/6th of the processing time with an ~2-fold increase in the number of Au nanoparticles forming clusters. Furthermore, average interparticle spacing within Au nanoparticle clusters was found to decrease from 2-7 nm for diffusion deposition to approximately 1-2 nm for electrophoresis deposition, and the latter method exhibited better uniformity with most clusters appearing to have about 1 nm spacing between nanoparticles. The advantage of such fabrication capability is supported by calculations of local electric field enhancements using electromagnetic full-wave simulations from which we can estimate surface-enhanced Raman scattering (SERS) enhancements. In particular, full-wave results show that the maximum SERS enhancement, as estimated here as the fourth power of the local electric field, increases by a factor of 100 when the gap goes from 2 to 1 nm, reaching values as large as 10(10), strengthening the usage of electrophoresis versus diffusion for the development of molecular sensors

Image Analysis Approach To Distinguish Lobular Structures In The Mammary Gland From Well-Differentiated Breast Cancer With Tubule Formation

Introduction/ Background Automated detection of diagnostically relevant regions of interest (ROI) is one of the major challenges in medical image analysis. In digital pathology using whole slide images (WSI), the detection of certain biological structures is necessary, because the capacity for analysis of cells and subcellular structures at high resolution is limited by available processing time and computational power. For some applications it is also important to exclude irrelevant or misleading components of the image. One important challenge of this type is well differentiated (low-grade/G1) breast cancer. Aims We aim at automatically distinguishing non-malignant lobular tissue from well-differentiated breast cancer to avoid erroneous evaluation of normal tissue in the detection of nuclear hormone receptor expression. A second goal of lobule detection is to exclude inflammation of non-malignant pre-existing structures from tumor immune cell scoring of breast cancer in oncoimmunology. Methods Two approaches for lobule detection were applied: The first includes modules of own image analysis algorithms developed specifically for lobule detection combined with elements of a commercially available software platform (Definiens Developer®), and the second is a software package optimized for use with a multispectral camera system (Inform, Perkin-Elmer ®). Breast cancer samples were stained for estrogen receptor (ER), progesterone receptor (PR) and the lymphocyte marker CD8. The first approach starts with a texture-based supervised classification to detect lobule candidate regions and uses a nuclear density image to refine the candidate regions. The second approach uses a supervised machine learning method whose features and algorithm are not disclosed to the user. Manual annotations of lobular tissue by expert pathologists were used for evaluation of results. Results The accuracy of distinction between cancer areas and lobular structures decreased in cases with prominent glandular differentiation of the tumor. The major challenge was the separation of well-differentiated (G1) breast cancer with consistent hormone receptor expression from adjacent lobular areas. The second approach performed well on high-grade tumors and had advantages regarding speed and its convenient user interface. The modular first approach was superior on ER and PR images and successfully detected lobular areas even if the anatomical structure was disrupted by inflammation of infiltrating cancer cells. We conclude that modular approaches considering image context and allowing specific adjustments to the tissue of interest may be needed to overcome current limitations of automated ROI detection in clinical biopsy materials

In-silico insights on the prognostic potential of immune cell infiltration patterns in the breast lobular epithelium.

Scattered inflammatory cells are commonly observed in mammary gland tissue, most likely in response to normal cell turnover by proliferation and apoptosis, or as part of immunosurveillance. In contrast, lymphocytic lobulitis (LLO) is a recurrent inflammation pattern, characterized by lymphoid cells infiltrating lobular structures, that has been associated with increased familial breast cancer risk and immune responses to clinically manifest cancer. The mechanisms and pathogenic implications related to the inflammatory microenvironment in breast tissue are still poorly understood. Currently, the definition of inflammation is mainly descriptive, not allowing a clear distinction of LLO from physiological immunological responses and its role in oncogenesis remains unclear. To gain insights into the prognostic potential of inflammation, we developed an agent-based model of immune and epithelial cell interactions in breast lobular epithelium. Physiological parameters were calibrated from breast tissue samples of women who underwent reduction mammoplasty due to orthopedic or cosmetic reasons. The model allowed to investigate the impact of menstrual cycle length and hormone status on inflammatory responses to cell turnover in the breast tissue. Our findings suggested that the immunological context, defined by the immune cell density, functional orientation and spatial distribution, contains prognostic information previously not captured by conventional diagnostic approaches