Analytical solution and numerical model for the interface in a stratified long wave system

For a two layered long wave propagation, linearized governing equations, which were derived earlier from the Euler equations of mass and momentum assuming negligible friction and interfacial mixing are solved analytically using Fourier transform. For the solution, variations of upper layer water level is assumed to be sinosoidal having known amplitude and variations of interface level is solved. As the governing equations are too complex to solve it analytically, density of upper layer fluid is assumed as very close to the density of lower layer fluid to simplify the lower layer equation. A numerical model is developed using the staggered leap-forg scheme for computation of water level and discharge in one dimensional propagation having known amplitude for the variations of upper layer water level and interface level to be solved. For the numerical model, water levels (upper layer and interface) at both the boundaries are assumed to be known from analytical solution. Results of numerical model are verified by comparing with the analytical solutions for different time period. Good agreements between analytical solution and numerical model are found for the stated boundary condition. The reliability of the developed numerical model is discussed, using it for different a (ratio of density of fluid in the upper layer to that in the lower layer) and p (ratio of water depth in the lower layer to that in the upper layer) values. It is found that as ‘CX’ increases amplification of interface also increases for same upper layer amplitude. Again for a constant lower layer depth, as ‘p’ increases amplification of interface. also increases for same upper layer amplitude.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

Long-term risk stratification for survivors of acute coronary syndromes - Results from the long-term intervention with pravastatin in ischemic disease (LIPID) study

OBJECTIVES We developed a prognostic strategy for quantifying the long-term risk of coronary heart disease (CHD) events in survivors of acute coronary syndromes (ACS). BACKGROUND Strategies for quantifying long-term risk of CHD events have generally been confined to primary prevention settings. The Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) study, which demonstrated that pravastatin reduces CHD events in ACS survivors with a broad range of cholesterol levels, enabled assessment of long-term prognosis in a secondary prevention setting. METHODS Based on outcomes in 8,557 patients in the LIPID study, a multivariate risk factor model was developed for prediction of CHD death or nonfatal myocardial infarction. Prognostic indexes were developed based on the model, and low-, medium-, high- and very high-risk groups were defined by categorizing the prognostic indexes. RESULTS In addition to pravastatin treatment, the independently significant risk factors included: total and high density lipoprotein cholesterol, age, gender, smoking status, qualifying ACS, prior coronary revascularization, diabetes mellitus, hypertension and prior stroke. Pravastatin reduced coronary event rates in each risk level, and the relative risk reduction did not vary significantly between risk levels. The predicted five-year coronary event rates ranged from 5% to 19% for those assigned pravastatin and from 6.4% to 23.6% fur those assigned placebo. CONCLUSIONS Long-term prognosis of ACS survivors varied substantially according to conventional risk factor profile. Pravastatin reduced coronary risk within all risk levels; however, absolute risk remained high in treated patients with unfavorable profiles. Our risk stratification strategy enables identification of ACS survivors who remain at very high risk despite statin therapy. CT Am Coil Cardiol 2001;38:56-63) (C) 2001 by the American College of Cardiology.

Long-Term Effects of Specific Stabilizing Exercises for First-Episode Low Back Pain

Study Design. A randomized clinical trial with 1-year and 3-year telephone questionnaire follow-ups. Objective. To report a specific exercise intervention’s long-term effects on recurrence rates in acute, first-episode low back pain patients. Summary of Background Data. The pain and disability associated with an initial episode of acute low back pain (LBP) is known to resolve spontaneously in the short-term in the majority of cases. However, the recurrence rate is high, and recurrent disabling episodes remain one of the most costly problems in LBP. A deficit in the multifidus muscle has been identified in acute LBP patients, and does not resolve spontaneously on resolution of painful symptoms and resumption of normal activity. Any relation between this deficit and recurrence rate was investigated in the long-term. Methods. Thirty-nine patients with acute, first-episode LBP were medically managed and randomly allocated to either a control group or specific exercise group. Medical management included advice and use of medications. Intervention consisted of exercises aimed at rehabilitating the multifidus in cocontraction with the transversus abdominis muscle. One year and three years after treatment, telephone questionnaires were conducted with patients. Results. Questionnaire results revealed that patients from the specific exercise group experienced fewer recurrences of LBP than patients from the control group. One year after treatment, specific exercise group recurrence was 30%, and control group recurrence was 84% (P , 0.001). Two to three years after treatment, specific exercise group recurrence was 35%, and control group recurrence was 75% (P , 0.01). Conclusion. Long-term results suggest that specific exercise therapy in addition to medical management and resumption of normal activity may be more effective in reducing low back pain recurrences than medical management and normal activity alone. [Key Words: multifidus, low back pain, rehabilitation]

Effects of short- and long-term exposure to c-AMP and c-GMP on the noradrenaline transporter

The effects of short- and long-term exposure of cells to elevated cyclic adenosine monophosphate (c-AMP), using dibutyryl-c-AMP, 8-bromo-c-AMP, cholera toxin or forskolin, or cyclic guanosine monophosphate (c-GMP), using dibutyryl-c-GMP or 8-bromo-c-GMP, on the activity and expression of the noradrenaline transporter (NAT) were examined. Short- or long-term c-GMP elevation had no effects on H-3-noradrenaline uptake by rat PC12 phaeochromocytoma cells or human SK-N-SH-SY5Y neuroblastoma cells. Short-term c-AMP elevation (for 17 min experiment duration) caused a decrease in H-3-noradrenaline uptake by PC12 cells, but had no effects on SK-N-SH-SY5Y cells or COS-7 cells transfected with human or rat NAT cDNA. c-AMP did not affect H-3-nisoxetine binding to PC12 cells. Long-term (24 h) exposure to elevated c-AMP levels caused a decrease in H-3-noradrenaline uptake and NAT mRNA in PC12 cells, but had no effects on SK-N-SH-SY5Y cells and caused a small increase in H-3-noradrenaline uptake in COS-7 cells heterologously expressing rat or human NAT. Hence, c-AMP, but not c-GMP, causes a cell type-dependent reduction in NAT activity after short-term exposure and a reduction in NAT expression after long-term exposure. (C) 2001 Elsevier Science Ltd. All rights reserved.