Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

The Effects of Aging on the Molecular and Cellular Composition of the Prostate Microenvironment

Advancing age is associated with substantial increases in the incidence rates of common diseases affecting the prostate gland including benign prostatic hyperplasia (BPH) and prostate carcinoma. The prostate is comprised of a functional secretory epithelium, a basal epithelium, and a supporting stroma comprised of structural elements, and a spectrum of cell types that includes smooth muscle cells, fibroblasts, and inflammatory cells. As reciprocal interactions between epithelium and stromal constituents are essential for normal organogenesis and serve to maintain normal functions, discordance within the stroma could permit or promote disease processes. In this study we sought to identify aging-associated alterations in the mouse prostate microenvironment that could influence pathology.We quantitated transcript levels in microdissected glandular-adjacent stroma from young (age 4 months) and old (age 20-24 months) C57BL/6 mice, and identified a significant change in the expression of 1259 genes (p<0.05). These included increases in transcripts encoding proteins associated with inflammation (e.g., Ccl8, Ccl12), genotoxic/oxidative stress (e.g., Apod, Serpinb5) and other paracrine-acting effects (e.g., Cyr61). The expression of several collagen genes (e.g., Col1a1 and Col3a1) exhibited age-associated declines. By histology, immunofluorescence, and electron microscopy we determined that the collagen matrix is abundant and disorganized, smooth muscle cell orientation is disordered, and inflammatory infiltrates are significantly increased, and are comprised of macrophages, T cells and, to a lesser extent, B cells.These findings demonstrate that during normal aging the prostate stroma exhibits phenotypic and molecular characteristics plausibly contributing to the striking age associated pathologies affecting the prostate

Numerical studies of the lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

In vitro reconstruction of branched tubular structures from lung epithelial cells in high cell concentration gradient environment

We have succeeded in developing hollow branching structure in vitro commonly observed in lung airway using primary lung airway epithelial cells. Cell concentration gradient is the key factor that determines production of the branching cellular structures, as optimization of this component removes the need for heterotypic culture. The higher cell concentration leads to the more production of morphogens and increases the growth rate of cells. However, homogeneous high cell concentration does not make a branching structure. Branching requires sufficient space in which cells can grow from a high concentration toward a low concentration. Simulation performed using a reaction-diffusion model revealed that long-range inhibition prevents cells from branching when they are homogeneously spread in culture environments, while short-range activation from neighboring cells leads to positive feedback. Thus, a high cell concentration gradient is required to make branching structures. Spatial distributions of morphogens, such as BMP-4, play important roles in the pattern formation. This simple yet robust system provides an optimal platform for the further study and understanding of branching mechanisms in the lung airway, and will facilitate chemical and genetic studies of lung morphogenesis programs

Genetic polymorphism of the <it>OPG</it> gene associated with breast cancer

<p>Abstract</p> <p>Background</p> <p>The receptor activator of NF-κB (RANK), its ligand (RANKL) and osteoprotegerin (OPG) have been reported to play a role in the pathophysiological bone turnover and in the pathogenesis of breast cancer. Based on this we investigated the role of single nucleotide polymorphisms (SNPs) within <it>RANK</it>, <it>RANKL</it> and <it>OPG</it> and their possible association to breast cancer risk.</p> <p>Methods</p> <p>Genomic DNA was obtained from Caucasian participants consisting of 307 female breast cancer patients and 396 gender-matched healthy controls. We studied seven SNPs in the genes of <it>OPG</it> (rs3102735, rs2073618), <it>RANK</it> (rs1805034, rs35211496) and <it>RANKL</it> (rs9533156, rs2277438, rs1054016) using TaqMan genotyping assays. Statistical analyses were performed using the χ²-tests for 2 x 2 and 2 x 3 tables.</p> <p>Results</p> <p>The allelic frequencies (OR: 1.508 CI: 1.127-2.018, p=0.006) and the genotype distribution (p=0.019) of the <it>OPG</it> SNP rs3102735 differed significantly between breast cancer patients and healthy controls. The minor allele C and the corresponding homo- and heterozygous genotypes are more common in breast cancer patients (minor allele C: 18.4% vs. 13.0%; genotype CC: 3.3% vs. 1.3%; genotype CT: 30.3% vs. 23.5%). No significantly changed risk was detected in the other investigated SNPs. Additional analysis showed significant differences when comparing patients with invasive vs. non-invasive tumors (<it>OPG</it> rs2073618) as well as in terms of tumor localization (<it>RANK</it> rs35211496) and body mass index (<it>RANKL</it> rs9533156 and rs1054016).</p> <p>Conclusions</p> <p>This is the first study reporting a significant association of the SNP rs3102735 (<it>OPG</it>) with the susceptibility to develop breast cancer in the Caucasian population.</p