Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Identification of mutations in the PYRIN-containing NLR genes (NLRP) in head and neck squamous cell carcinoma

Head and Neck Squamous Cell Carcinoma (HNSCC) encompasses malignancies that arise in the mucosa of the upper aerodigestive tract. Recent high throughput DNA sequencing revealed HNSCC genes mutations that contribute to several cancer cell characteristics, including dysregulation of cell proliferation and death, intracellular proinflammatory signaling, and autophagy. The PYRIN-domain containing NLR (Nucleotide-binding domain, Leucine rich Repeats - containing) proteins have recently emerged as pivotal modulators of cell death, autophagy, inflammation, and metabolism. Their close physiologic association with cancer development prompted us to determine whether mutations within the NLRP (PYRIN-containing NLR ) gene family were associated with HNSCC genome instability and their clinicopathologic correlations. Catastrophic mutational events underlie cancer cell genome instability and mark a point-of-no-return in cancer cell development and generation of heterogeneity. The mutation profiles of 62 patients with primary conventional type HNSCC excluding other histologic variants were analyzed. Associations were tested using Fisher's Exact test or Mann-Whitney U test. Mutations in NLRP were associated with elevated genome instability as characterized by higher mutation rates. Clinically, NLRP mutations were more frequently found in HNSCC arising in the floor of mouth (50.0%) in comparison with HNSCC at other head and neck locations (14.8%). These mutations were clustered at the leucine rich repeats region of NLRP proteins, and affected NLRP genes were mostly localized at chromosomes 11p15.4 and 19q13.42-19q13.43. Twenty novel NLRP mutations were identified in HNSCC, and mutations in this group of genes were correlated with increased cancer cell genome mutation rates, and such features could be a potential molecular biomarker of HNSCC genome instability. © 2014 Lei et al

Glucocorticoid Effects on the Programming of AT1b Angiotensin Receptor Gene Methylation and Expression in the Rat

Adverse events in pregnancy may ‘programme’ offspring for the later development of cardiovascular disease and hypertension. Previously, using a rodent model of programmed hypertension we have demonstrated the role of the renin-angiotensin system in this process. More recently we showed that a maternal low protein diet resulted in undermethylation of the At1b angiotensin receptor promoter and the early overexpression of this gene in the adrenal of offspring. Here, we investigate the hypothesis that maternal glucocorticoid modulates this effect on fetal DNA methylation and gene expression. We investigated whether treatment of rat dams with the 11β-hydroxylase inhibitor metyrapone, could prevent the epigenetic and gene expression changes we observed. Offspring of mothers subjected to a low protein diet in pregnancy showed reduced adrenal Agtr1b methylation and increased adrenal gene expression as we observed previously. Treatment of mothers with metyrapone for the first 14 days of pregnancy reversed these changes and prevented the appearance of hypertension in the offspring at 4 weeks of age. As a control for non-specific effects of programmed hypertension we studied offspring of mothers treated with dexamethasone from day 15 of pregnancy and showed that, whilst they had raised blood pressure, they failed to show any evidence of Agtr1b methylation or increase in gene expression. We conclude that maternal glucocorticoid in early pregnancy may induce changes in methylation and expression of the Agtr1b gene as these are clearly reversed by an 11 beta-hydroxylase inhibitor. However in later pregnancy a converse effect with dexamethasone could not be demonstrated and this may reflect either an alternative mechanism of this glucocorticoid or a stage-specific influence

Role of the progesterone receptor for paclitaxel resistance in primary breast cancer

Paclitaxel plays an important role in the treatment of primary breast cancer. However, a substantial proportion of patients treated with paclitaxel does not appear to derive any benefit from this therapy. We performed a prospective study using tumour cells isolated from 50 primary breast carcinomas. Sensitivity of primary tumour cells to paclitaxel was determined in a clinically relevant range of concentrations (0.85–27.2 μg ml−1 paclitaxel) using an ATP assay. Chemosensitivity data were used to study a possible association with immunohistochemically determined oestrogen and progesterone receptor (ER and PR) status, as well as histopathological parameters. Progesterone receptor (PR) mRNA expression was also determined by quantitative RT–PCR. We observed a clear association of the PR status with chemosensitivity to paclitaxel. Higher levels of immunohistochemically detected PR expression correlated with decreased chemosensitivity (P=0.008). Similarly, high levels of PR mRNA expression were associated with decreased paclitaxel chemosensitivity (P=0.007). Cells from carcinomas with T-stages 3 and 4 were less sensitive compared to stages 1 and 2 (P=0.013). Multiple regression analysis identified PR receptor status and T-stage as independent predictors of paclitaxel chemosensitivity, whereas the ER, N-stage, grading and age were not influential. In conclusion, in vitro sensitivity to paclitaxel was higher for PR-negative compared with PR-positive breast carcinoma cells. Thus, PR status should be considered as a possible factor of influence when designing new trials and chemotherapy protocols

Prenatal Stress and Balance of the Child's Cardiac Autonomic Nervous System at Age 5-6 Years

Objective: Autonomic nervous system (ANS) misbalance is a potential causal factor in the development of cardiovascular disease. The ANS may be programmed during pregnancy due to various maternal factors. Our aim is to study maternal prenatal psychosocial stress as a potential disruptor of cardiac ANS balance in the child. Methods: Mothers from a prospective birth cohort (ABCD study) filled out a questionnaire at gestational week 16 [IQR 12– 20], that included validated instruments for state anxiety, depressive symptoms, pregnancy-related anxiety, parenting daily hassles and job strain. A cumulative stress score was also calculated (based on 80 th percentiles). Indicators of cardiac ANS in the offspring at age 5–6 years are: pre-ejection period (PEP), heart rate (HR), respiratory sinus arrhythmia (RSA) and cardiac autonomic balance (CAB), measured with electrocardiography and impedance cardiography in resting supine and sitting positions. Results: 2,624 mother-child pairs, only single births, were available for analysis. The stress scales were not significantly associated with HR, PEP, RSA and CAB (p$0.17). Accumulation of maternal stress was also not associated with HR, PEP, RSA and CAB (p$0.07). Conclusion: Results did not support the hypothesis that prenatal maternal psychosocial stress deregulates cardiac AN

Rapid improvement in verbal fluency and aphasia following perispinal etanercept in Alzheimer's disease

<p>Abstract</p> <p>Background</p> <p>Recent clinical studies point to rapid and sustained clinical, cognitive, and behavioral improvement in both Alzheimer's disease and primary progressive aphasia following weekly perispinal administration of etanercept, a TNF-alpha inhibitor that acts by blocking the binding of this cytokine to its receptors. This outcome is concordant with recent basic science studies suggesting that TNF-alpha functions <it>in vivo </it>as a gliotransmitter that regulates synaptic function in the brain. We hypothesized that perispinal etanercept had the potential to improve verbal function in Alzheimer's disease, so we included several standarized measures of verbal ability to evaluate language skills in a clinical trial of perispinal etanercept for Alzheimer's disease.</p> <p>Methods</p> <p>This was a prospective, single-center, open-label, pilot study, in which 12 patients with mild-to-severe Alzheimer's disease were administered etanercept, 25–50 mg, weekly by perispinal administration for six months. Two additional case studies are presented.</p> <p>Results</p> <p>Two-tailed, paired t-tests were conducted comparing baseline performance to 6-month performance on all neuropsychological measures. Test batteries included the California Verbal Learning Test-Second Edition, Adult Version; Logical Memory I and II(WMS-LM-II) from the Wechsler Memory Scale-Abbreviated; the Comprehensive Trail Making Test (TMT); Boston Naming Test; and letter(FAS) and category verbal fluency. All measures revealed a significant effect except for the Boston Naming Test and the TMT-4, with WMS-LM-II being marginally significant at p = .05. The FAS test for letter fluency was most highly significant with a p < 0.0007. In addition, rapid improvement in verbal fluency and aphasia in two patients with dementia, beginning minutes after perispinal etanercept administration, is documented.</p> <p>Conclusion</p> <p>In combination with the previously reported results of perispinal etanercept in Alzheimer's disease and primary progressive aphasia, these results further argue that larger scale studies of this therapeutic intervention, including Phase 3 trials, are warranted in dementias. In addition, these results may provide insight into the basic pathophysiologic mechanisms underlying Alzheimer's disease and related forms of dementia, and suggest the existence of novel, rapidly reversible, TNF-mediated pathophysiologic mechanisms in Alzheimer's disease which are worthy of further investigation.</p

Early and Late Postnatal Myocardial and Vascular Changes in a Protein Restriction Rat Model of Intrauterine Growth Restriction

Intrauterine growth restriction (IUGR) is a risk factor for cardiovascular disease in later life. Early structural and functional changes in the cardiovascular system after IUGR may contribute to its pathogenesis. We tested the hypothesis that IUGR leads to primary myocardial and vascular alterations before the onset of hypertension. A rat IUGR model of maternal protein restriction during gestation was used. Dams were fed low protein (LP; casein 8.4%) or isocaloric normal protein diet (NP; casein 17.2%). The offspring was reduced to six males per litter. Immunohistochemical and real-time PCR analyses were performed in myocardial and vascular tissue of neonates and animals at day 70 of life. In the aortas of newborn IUGR rats expression of connective tissue growth factor (CTGF) was induced 3.2-fold. At day 70 of life, the expression of collagen I was increased 5.6-fold in aortas of IUGR rats. In the hearts of neonate IUGR rats, cell proliferation was more prominent compared to controls. At day 70 the expression of osteopontin was induced 7.2-fold. A 3- to 7-fold increase in the expression of the profibrotic cytokines TGF-β and CTGF as well as of microfibrillar matrix molecules was observed. The myocardial expression and deposition of collagens was more prominent in IUGR animals compared to controls at day 70. In the low-protein diet model, IUGR leads to changes in the expression patterns of profibrotic genes and discrete structural abnormalities of vessels and hearts in adolescence, but, with the exception of CTGF, not as early as at the time of birth. Invasive and non-invasive blood pressure measurements confirmed that IUGR rats were normotensive at the time point investigated and that the changes observed occurred independently of an increased blood pressure. Hence, altered matrix composition of the vascular wall and the myocardium may predispose IUGR animals to cardiovascular disease later in life

The PHF21B gene is associated with major depression and modulates the stress response

Major depressive disorder (MDD) affects around 350 million people worldwide; however, the underlying genetic basis remains largely unknown. In this study, we took into account that MDD is a gene-environment disorder, in which stress is a critical component, and used whole-genome screening of functional variants to investigate the 'missing heritability' in MDD. Genome-wide association studies (GWAS) using single- and multi-locus linear mixed-effect models were performed in a Los Angeles Mexican-American cohort (196 controls, 203 MDD) and in a replication European-ancestry cohort (499 controls, 473 MDD). Our analyses took into consideration the stress levels in the control populations. The Mexican-American controls, comprised primarily of recent immigrants, had high levels of stress due to acculturation issues and the European-ancestry controls with high stress levels were given higher weights in our analysis. We identified 44 common and rare functional variants associated with mild to moderate MDD in the Mexican-American cohort (genome-wide false discovery rate, FDR, <0.05), and their pathway analysis revealed that the three top overrepresented Gene Ontology (GO) processes were innate immune response, glutamate receptor signaling and detection of chemical stimulus in smell sensory perception. Rare variant analysis replicated the association of the PHF21B gene in the ethnically unrelated European-ancestry cohort. The TRPM2 gene, previously implicated in mood disorders, may also be considered replicated by our analyses. Whole-genome sequencing analyses of a subset of the cohorts revealed that European-ancestry individuals have a significantly reduced (50%) number of single nucleotide variants compared with Mexican-American individuals, and for this reason the role of rare variants may vary across populations. PHF21b variants contribute significantly to differences in the levels of expression of this gene in several brain areas, including the hippocampus. Furthermore, using an animal model of stress, we found that Phf21b hippocampal gene expression is significantly decreased in animals resilient to chronic restraint stress when compared with non-chronically stressed animals. Together, our results reveal that including stress level data enables the identification of novel rare functional variants associated with MDD.M-L Wong, M Arcos-Burgos, S Liu, J I Vélez, C Yu, B T Baune, M C Jawahar, V Arolt, U Dannlowski, A Chuah, G A Huttley, R Fogarty, M D Lewis, S R Bornstein, and J Licini