On The Nield-Koznetsov Integral Function and Its Application to Airys Inhomogeneous Boundary Value Problem

In this work, we provide a solution to a two-point boundary value problem that involves an inhomogeneous Airys differential equation with a variable forcing function. The solution is expressed in terms of the recently introduced Nield-Koznetsov integral function, Ni(x), and another conveniently defined integral function, Ki(x). The resulting expressions involving these integral functions are then evaluated using asymptotic and ascending series

Diagnosis of obstructive coronary artery disease using computed tomography angiography in patients with stable chest pain depending on clinical probability and in clinically important subgroups: Meta-analysis of individual patient data

Objective To determine whether coronary computed tomography angiography (CTA) should be performed in patients with any clinical probability of coronary artery disease (CAD), and whether the diagnostic performance differs between subgroups of patients. Design Prospectively designed meta-analysis of individual patient data from prospective diagnostic accuracy studies. Data sources Medline, Embase, and Web of Science for published studies. Unpublished studies were identified via direct contact with participating investigators. Eligibility criteria for selecting studies Prospective diagnostic accuracy studies that compared coronary CTA with coronary angiography as the reference standard, using at least a 50% diameter reduction as a cutoff value for obstructive CAD. All patients needed to have a clinical indication for coronary angiography due to suspected CAD, and both tests had to be performed in all patients. Results had to be provided using 2 72 or 3 72 cross tabulations for the comparison of CTA with coronary angiography. Primary outcomes were the positive and negative predictive values of CTA as a function of clinical pretest probability of obstructive CAD, analysed by a generalised linear mixed model; calculations were performed including and excluding non-diagnostic CTA results. The no-treat/treat threshold model was used to determine the range of appropriate pretest probabilities for CTA. The threshold model was based on obtained post-test probabilities of less than 15% in case of negative CTA and above 50% in case of positive CTA. Sex, angina pectoris type, age, and number of computed tomography detector rows were used as clinical variables to analyse the diagnostic performance in relevant subgroups. Results Individual patient data from 5332 patients from 65 prospective diagnostic accuracy studies were retrieved. For a pretest probability range of 7-67%, the treat threshold of more than 50% and the no-treat threshold of less than 15% post-test probability were obtained using CTA. At a pretest probability of 7%, the positive predictive value of CTA was 50.9% (95% confidence interval 43.3% to 57.7%) and the negative predictive value of CTA was 97.8% (96.4% to 98.7%); corresponding values at a pretest probability of 67% were 82.7% (78.3% to 86.2%) and 85.0% (80.2% to 88.9%), respectively. The overall sensitivity of CTA was 95.2% (92.6% to 96.9%) and the specificity was 79.2% (74.9% to 82.9%). CTA using more than 64 detector rows was associated with a higher empirical sensitivity than CTA using up to 64 rows (93.4% v 86.5%, P=0.002) and specificity (84.4% v 72.6%, P<0.001). The area under the receiver-operating-characteristic curve for CTA was 0.897 (0.889 to 0.906), and the diagnostic performance of CTA was slightly lower in women than in with men (area under the curve 0.874 (0.858 to 0.890) v 0.907 (0.897 to 0.916), P<0.001). The diagnostic performance of CTA was slightly lower in patients older than 75 (0.864 (0.834 to 0.894), P=0.018 v all other age groups) and was not significantly influenced by angina pectoris type (typical angina 0.895 (0.873 to 0.917), atypical angina 0.898 (0.884 to 0.913), non-anginal chest pain 0.884 (0.870 to 0.899), other chest discomfort 0.915 (0.897 to 0.934)). Conclusions In a no-treat/treat threshold model, the diagnosis of obstructive CAD using coronary CTA in patients with stable chest pain was most accurate when the clinical pretest probability was between 7% and 67%. Performance of CTA was not influenced by the angina pectoris type and was slightly higher in men and lower in older patients. Systematic review registration PROSPERO CRD42012002780

Diagnosis of obstructive coronary artery disease using computed tomography angiography in patients with stable chest pain depending on clinical probability and in clinically important subgroups: Meta-analysis of individual patient data

Objective To determine whether coronary computed tomography angiography (CTA) should be performed in patients with any clinical probability of coronary artery disease (CAD), and whether the diagnostic performance differs between subgroups of patients. Design Prospectively designed meta-analysis of individual patient data from prospective diagnostic accuracy studies. Data sources Medline, Embase, and Web of Science for published studies. Unpublished studies were identified via direct contact with participating investigators. Eligibility criteria for selecting studies Prospective diagnostic accuracy studies that compared coronary CTA with coronary angiography as the reference standard, using at least a 50% diameter reduction as a cutoff value for obstructive CAD. All patients needed to have a clinical indication for coronary angiography due to suspected CAD, and both tests had to be performed in all patients. Results had to be provided using 2×2 or 3×2 cross tabulations for the comparison of CTA with coronary angiography. Primary outcomes were the positive and negative predictive values of CTA as a function of clinical pretest probability of obstructive CAD, analysed by a generalised linear mixed model; calculations were performed including and excluding non-diagnostic CTA results. The no-treat/treat threshold model was used to determine the range of appropriate pretest probabilities for CTA. The threshold model was based on obtained post-test probabilities of less than 15% in case of negative CTA and above 50% in case of positive CTA. Sex, angina pectoris type, age, and number of computed tomography detector rows were used as clinical variables to analyse the diagnostic performance in relevant subgroups. Results Individual patient data from 5332 patients from 65 prospective diagnostic accuracy studies were retrieved. For a pretest probability range of 7-67%, the treat threshold of more than 50% and the no-treat threshold of less than 15% post-test probability were obtained using CTA. At a pretest probability of 7%, the positive predictive value of CTA was 50.9% (95% confidence interval 43.3% to 57.7%) and the negative predictive value of CTA was 97.8% (96.4% to 98.7%); corresponding values at a pretest probability of 67% were 82.7% (78.3% to 86.2%) and 85.0% (80.2% to 88.9%), respectively. The overall sensitivity of CTA was 95.2% (92.6% to 96.9%) and the specificity was 79.2% (74.9% to 82.9%). CTA using more than 64 detector rows was associated with a higher empirical sensitivity than CTA using up to 64 rows (93.4% v 86.5%, P=0.002) and specificity (84.4% v 72.6%, P<0.001). The area under the receiver-operating-characteristic curve for CTA was 0.897 (0.889 to 0.906), and the diagnostic performance of CTA was slightly lower in women than in with men (area under the curve 0.874 (0.858 to 0.890) v 0.907 (0.897 to 0.916), P<0.001). The diagnostic performance of CTA was slightly lower in patients older than 75 (0.864 (0.834 to 0.894), P=0.018 v all other age groups) and was not significantly influenced by angina pectoris type (typical angina 0.895 (0.873 to 0.917), atypical angina 0.898 (0.884 to 0.913), non-anginal chest pain 0.884 (0.870 to 0.899), other chest discomfort 0.915 (0.897 to 0.934)). Conclusions In a no-treat/treat threshold model, the diagnosis of obstructive CAD using coronary CTA in patients with stable chest pain was most accurate when the clinical pretest probability was between 7% and 67%. Performance of CTA was not influenced by the angina pectoris type and was slightly higher in men and lower in older patients. Systematic review registration PROSPERO CRD42012002780

The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

A dusty gas flow model in porous media

AbstractThe differential equations governing the dusty fluid flow in porous media are developed based on Saffman's dusty gas flow equations. The model equations are cast in vorticity-streamfunction forms and applied to study the flow in a rectangular cavity. A numerical solution is obtained for the flow considered and the results are compared with the solution for a clean fluid flow in porous media

Standard numerical schemes for coupled parallel flow over porous layers

In this work, we develop finite difference schemes of various orders of accuracy that are suitable for the simulation of flow through and over porous layers. The flow through the porous layer is assumed to be governed by a Brinkman-type equation, and that through free-space by the Navier-Stokes equations. Matching conditions at the interface between layers are invoked to derive numerical expressions for the velocity and shear stress. Results are compared with the exact solution of flow through a channel bounded by a porous layer. © 2007 Elsevier Inc. All rights reserved

Analytical approach to the Darcy–Lapwood–Brinkman equation

Three exact solutions are obtained for flow through porous media, as governed by the Darcy–Lapwood–Brinkman model, for a given vorticity distribution. The resulting flow fields are identified as reversing flows; stagnation point flows; and flows over a porous flat plate with blowing or suction. Dependence of the flow Reynolds number on the permeability of the flow through the porous medium is illustrated