Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Matrix metalloproteinases in subjects with type 1 diabetes

<p>Abstract</p> <p>Background</p> <p>Nephropathy is serious complication of diabetes. We have previously shown that level of the proteoglycan syndecan-1 in blood is associated with ultrastructural kidney changes in young persons with type 1 diabetes. Dysregulation of matrix metalloproteinases (MMPs) and tissue inhibitors of matrix metalloproteinases (TIMPs) may contribute to the development of nephropathy. The aim of this study was to investigate if the levels of MMPs in blood samples are potential markers of early nephropathy in type 1 diabetes.</p> <p>Methods</p> <p>Blood samples were collected from type 1 diabetes patients after 11 years of diabetes (n = 15) and healthy volunteers (n = 12) and stored at ÷80°C until measurement. Levels and activities of serum MMP-2, MMP-9, TIMP-1 and TIMP- 2 were analyzed and compared to those of control individuals using ELISA, SDS-PAGE gelatin zymography, and Western blot analysis.</p> <p>Results</p> <p>The serum levels of both MMP-9 and MMP-2 were significantly higher in subjects with type 1 diabetes, compared to controls (p = 0.016 and p = 0.008 respectively). Western blotting revealed no differences between the two groups in the levels of TIMP-1 or TIMP-2, respectively.</p> <p>Conclusion</p> <p>Our MMP analysis of serum from a limited number of patients with type 1 diabetes suggest that such analysis is potentially useful as markers in studies of people at risk of progression to chronic kidney disease.</p

Gene Expression Programs of Mouse Endothelial Cells in Kidney Development and Disease

Endothelial cells are remarkably heterogeneous in both morphology and function, and they play critical roles in the formation of multiple organ systems. In addition endothelial cell dysfunction can contribute to disease processes, including diabetic nephropathy, which is a leading cause of end stage renal disease. In this report we define the comprehensive gene expression programs of multiple types of kidney endothelial cells, and analyze the differences that distinguish them. Endothelial cells were purified from Tie2-GFP mice by cell dissociation and fluorescent activated cell sorting. Microarrays were then used to provide a global, quantitative and sensitive measure of gene expression levels. We examined renal endothelial cells from the embryo and from the adult glomerulus, cortex and medulla compartments, as well as the glomerular endothelial cells of the db/db mutant mouse, which represents a model for human diabetic nephropathy. The results identified the growth factors, receptors and transcription factors expressed by these multiple endothelial cell types. Biological processes and molecular pathways were characterized in exquisite detail. Cell type specific gene expression patterns were defined, finding novel molecular markers and providing a better understanding of compartmental distinctions. Further, analysis of enriched, evolutionarily conserved transcription factor binding sites in the promoters of co-activated genes begins to define the genetic regulatory network of renal endothelial cell formation. Finally, the gene expression differences associated with diabetic nephropathy were defined, providing a global view of both the pathogenic and protective pathways activated. These studies provide a rich resource to facilitate further investigations of endothelial cell functions in kidney development, adult compartments, and disease

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

Solving ordinary differential equations with discontinuities

An algorithm is described that can detect and locate some discontinuities and provide information about their size, order and position. However, the success of the algorithm is strongly dependent on the location of the discontinuity with respect to the steps that straddle it. The major advantage of the scheme appears to be that a more reliable error estimate can be used when a discontinuity is present so that codes will be more robust. In some cases significant savings may accrue but it appears that a better restarting procedure than the one used will be necessary to realize most of those benefits