Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics

We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10^−9ms^−2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p&lt;0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p&lt;0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Investigation of the flowfield surrounding small photodriven flapping wings

The flowfield surrounding wings with a pure flapping motion was studied in quiescent air at a Reynolds number of approximately 200 using particle image velocimetry (PIV) in unusually thin illuminated planes (̃0.3 mm). Typical wing semi-spans were on the order of a few millimeters. The polymer cantilever wings consisting of monodomain liquid crystal polymers made from azobenzene (azo-LCN) were flapped at 30 Hz at a large amplitude (\u3e170⁰). Chordwise and spanwise planar slices of the flow across the wings were obtained and used to estimate the unsteady aerodynamic forces generated by the flapping wings. This study focuses on the flapping flight of small-scale wings in order to visualize the flowfield characteristics. The small-scale wings were, indeed, able to induce the surrounding flowfield and generate aerodynamic contribution, which was clearly observed in spanwise plane. Images at various spanwise and chordwise locations were acquired and processed. In terms of results, the spanwise flow was the dominant. The chordwise results were not conclusive useful due to the poor light filtering. The PIV displacement and velocity uncertainties were small quantitatives compared to the vorticity and circulation uncertaintie

Global variation in postoperative mortality and complications after cancer surgery: a multicentre, prospective cohort study in 82 countries

Background: 80% of individuals with cancer will require a surgical procedure, yet little comparative data exist on early outcomes in low-income and middle-income countries (LMICs). We compared postoperative outcomes in breast, colorectal, and gastric cancer surgery in hospitals worldwide, focusing on the effect of disease stage and complications on postoperative mortality. Methods: This was a multicentre, international prospective cohort study of consecutive adult patients undergoing surgery for primary breast, colorectal, or gastric cancer requiring a skin incision done under general or neuraxial anaesthesia. The primary outcome was death or major complication within 30 days of surgery. Multilevel logistic regression determined relationships within three-level nested models of patients within hospitals and countries. Hospital-level infrastructure effects were explored with three-way mediation analyses. This study was registered with ClinicalTrials.gov, NCT03471494. Findings: Between April 1, 2018, and Jan 31, 2019, we enrolled 15 958 patients from 428 hospitals in 82 countries (high income 9106 patients, 31 countries; upper-middle income 2721 patients, 23 countries; or lower-middle income 4131 patients, 28 countries). Patients in LMICs presented with more advanced disease compared with patients in high-income countries. 30-day mortality was higher for gastric cancer in low-income or lower-middle-income countries (adjusted odds ratio 3·72, 95% CI 1·70–8·16) and for colorectal cancer in low-income or lower-middle-income countries (4·59, 2·39–8·80) and upper-middle-income countries (2·06, 1·11–3·83). No difference in 30-day mortality was seen in breast cancer. The proportion of patients who died after a major complication was greatest in low-income or lower-middle-income countries (6·15, 3·26–11·59) and upper-middle-income countries (3·89, 2·08–7·29). Postoperative death after complications was partly explained by patient factors (60%) and partly by hospital or country (40%). The absence of consistently available postoperative care facilities was associated with seven to 10 more deaths per 100 major complications in LMICs. Cancer stage alone explained little of the early variation in mortality or postoperative complications. Interpretation: Higher levels of mortality after cancer surgery in LMICs was not fully explained by later presentation of disease. The capacity to rescue patients from surgical complications is a tangible opportunity for meaningful intervention. Early death after cancer surgery might be reduced by policies focusing on strengthening perioperative care systems to detect and intervene in common complications. Funding: National Institute for Health Research Global Health Research Unit

Global Incidence and Risk Factors Associated With Postoperative Urinary Retention Following Elective Inguinal Hernia Repair

Importance Postoperative urinary retention (POUR) is a well-recognized complication of inguinal hernia repair (IHR). A variable incidence of POUR has previously been reported in this context, and contradictory evidence surrounds potential risk factors.Objective To ascertain the incidence of, explore risk factors for, and determine the health service outcomes of POUR following elective IHR.Design, Setting, and Participants The Retention of Urine After Inguinal Hernia Elective Repair (RETAINER I) study, an international, prospective cohort study, recruited participants between March 1 and October 31, 2021. This study was conducted across 209 centers in 32 countries in a consecutive sample of adult patients undergoing elective IHR.Exposure Open or minimally invasive IHR by any surgical technique, under local, neuraxial regional, or general anesthesia.Main Outcomes and Measures The primary outcome was the incidence of POUR following elective IHR. Secondary outcomes were perioperative risk factors, management, clinical consequences, and health service outcomes of POUR. A preoperative International Prostate Symptom Score was measured in male patients.Results In total, 4151 patients (3882 male and 269 female; median [IQR] age, 56 [43-68] years) were studied. Inguinal hernia repair was commenced via an open surgical approach in 82.2% of patients (n = 3414) and minimally invasive surgery in 17.8% (n = 737). The primary form of anesthesia was general in 40.9% of patients (n = 1696), neuraxial regional in 45.8% (n = 1902), and local in 10.7% (n = 446). Postoperative urinary retention occurred in 5.8% of male patients (n = 224), 2.97% of female patients (n = 8), and 9.5% (119 of 1252) of male patients aged 65 years or older. Risk factors for POUR after adjusted analyses included increasing age, anticholinergic medication, history of urinary retention, constipation, out-of-hours surgery, involvement of urinary bladder within the hernia, temporary intraoperative urethral catheterization, and increasing operative duration. Postoperative urinary retention was the primary reason for 27.8% of unplanned day-case surgery admissions (n = 74) and 51.8% of 30-day readmissions (n = 72).Conclusions The findings of this cohort study suggest that 1 in 17 male patients, 1 in 11 male patients aged 65 years or older, and 1 in 34 female patients may develop POUR following IHR. These findings could inform preoperative patient counseling. In addition, awareness of modifiable risk factors may help to identify patients at increased risk of POUR who may benefit from perioperative risk mitigation strategies

Global variation in postoperative mortality and complications after cancer surgery: a multicentre, prospective cohort study in 82 countries

© 2021 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY-NC-ND 4.0 licenseBackground: 80% of individuals with cancer will require a surgical procedure, yet little comparative data exist on early outcomes in low-income and middle-income countries (LMICs). We compared postoperative outcomes in breast, colorectal, and gastric cancer surgery in hospitals worldwide, focusing on the effect of disease stage and complications on postoperative mortality. Methods: This was a multicentre, international prospective cohort study of consecutive adult patients undergoing surgery for primary breast, colorectal, or gastric cancer requiring a skin incision done under general or neuraxial anaesthesia. The primary outcome was death or major complication within 30 days of surgery. Multilevel logistic regression determined relationships within three-level nested models of patients within hospitals and countries. Hospital-level infrastructure effects were explored with three-way mediation analyses. This study was registered with ClinicalTrials.gov, NCT03471494. Findings: Between April 1, 2018, and Jan 31, 2019, we enrolled 15 958 patients from 428 hospitals in 82 countries (high income 9106 patients, 31 countries; upper-middle income 2721 patients, 23 countries; or lower-middle income 4131 patients, 28 countries). Patients in LMICs presented with more advanced disease compared with patients in high-income countries. 30-day mortality was higher for gastric cancer in low-income or lower-middle-income countries (adjusted odds ratio 3·72, 95% CI 1·70–8·16) and for colorectal cancer in low-income or lower-middle-income countries (4·59, 2·39–8·80) and upper-middle-income countries (2·06, 1·11–3·83). No difference in 30-day mortality was seen in breast cancer. The proportion of patients who died after a major complication was greatest in low-income or lower-middle-income countries (6·15, 3·26–11·59) and upper-middle-income countries (3·89, 2·08–7·29). Postoperative death after complications was partly explained by patient factors (60%) and partly by hospital or country (40%). The absence of consistently available postoperative care facilities was associated with seven to 10 more deaths per 100 major complications in LMICs. Cancer stage alone explained little of the early variation in mortality or postoperative complications. Interpretation: Higher levels of mortality after cancer surgery in LMICs was not fully explained by later presentation of disease. The capacity to rescue patients from surgical complications is a tangible opportunity for meaningful intervention. Early death after cancer surgery might be reduced by policies focusing on strengthening perioperative care systems to detect and intervene in common complications. Funding: National Institute for Health Research Global Health Research Unit

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

© 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 licenseBackground: Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide. Methods: A multimethods analysis was performed as part of the GlobalSurg 3 study—a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital. Findings: Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3·85 [95% CI 2·58–5·75]; p<0·0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63·0% vs 82·7%; OR 0·35 [0·23–0·53]; p<0·0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer. Interpretation: Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised. Funding: National Institute for Health and Care Research

Pancreatic surgery outcomes: multicentre prospective snapshot study in 67 countries

Background: Pancreatic surgery remains associated with high morbidity rates. Although postoperative mortality appears to have improved with specialization, the outcomes reported in the literature reflect the activity of highly specialized centres. The aim of this study was to evaluate the outcomes following pancreatic surgery worldwide.Methods: This was an international, prospective, multicentre, cross-sectional snapshot study of consecutive patients undergoing pancreatic operations worldwide in a 3-month interval in 2021. The primary outcome was postoperative mortality within 90 days of surgery. Multivariable logistic regression was used to explore relationships with Human Development Index (HDI) and other parameters.Results: A total of 4223 patients from 67 countries were analysed. A complication of any severity was detected in 68.7 percent of patients (2901 of 4223). Major complication rates (Clavien-Dindo grade at least IIIa) were 24, 18, and 27 percent, and mortality rates were 10, 5, and 5 per cent in low-to-middle-, high-, and very high-HDI countries respectively. The 90-day postoperative mortality rate was 5.4 per cent (229 of 4223) overall, but was significantly higher in the low-to-middle-HDI group (adjusted OR 2.88, 95 per cent c.i. 1.80 to 4.48). The overall failure-to-rescue rate was 21 percent; however, it was 41 per cent in low-to-middle-compared with 19 per cent in very high-HDI countries.Conclusion: Excess mortality in low-to-middle-HDI countries could be attributable to failure to rescue of patients from severe complications. The authors call for a collaborative response from international and regional associations of pancreatic surgeons to address management related to death from postoperative complications to tackle the global disparities in the outcomes of pancreatic surgery (NCT04652271; ISRCTN95140761)

The value of open-source clinical science in pandemic response: lessons from ISARIC

International audienc