A fractional order Covid-19 epidemic model with Mittag-Leffler kernel.

In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; ` ` S c ″ which denotes susceptible class, ` ` E c ″ represents exposed population, ` ` I c ″ is the class for infected people who have been developed with COVID-19 and can cause spread in the population. The recovered class is denoted by ` ` R c ″ and ` ` V c ″ is the concentration of COVID-19 virus in the area. The computational study shows us that the spread will be continued for long time and the recovery reduces the infection rate. The numerical scheme is based on the Lagrange's interpolation polynomial and the numerical results for the suggested model are similar to the integer order which gives us the applicability of the numerical scheme and effectiveness of the fractional order derivative.

Effect of preemptive intra-articular morphine and ketamine on pain after arthroscopic rotator cuff repair: a prospective, double-blind, randomized controlled study.

BACKGROUND: Rotator cuff tear is a leading etiology of shoulder pain and disability. Surgical treatment is indicated in patients with persistent pain who fail a trial of non-surgical treatment. Pain reduction following rotator cuff repair, particularly within the first 24-48 h, is a major concern to both doctors and patients. This study aimed to compare the postoperative antinociceptive additive effects of pre-incisional intra-articular (IA) ketamine when combined with morphine with two times the dose of morphine or saline. METHODS: In this prospective, randomized, double blind, controlled trial patients undergoing arthroscopic rotator cuff tear repair (ARCR) under general anesthesia were enrolled. Patients were randomly assigned to one of the three intervention groups. Twenty minutes prior to incision, morphine (20 mg/10 ml), ketamine (50 mg + morphine 10 mg/10 ml), or saline (0.9 % 10 ml) (n = 15/group), were administered to all patients. First 24 h postoperative analgesia consisted of intravenous patient controlled analgesia (IV-PCA) morphine and oral rescue paracetamol 1000 mg or oxycodone 5 mg. 24-h, 2-week and 3-month patient rated pain numeric rating scale (NRS) and analgesics consumption were documented. RESULTS: Patients' demographic and perioperative data were similar among all groups. The 24-h and the 2-week NRSs were significantly (p < 0.05) lower in both treatment groups compared to placebo, but were not significantly different between the two intervention groups. PCA-morphine and oral analgesics were consumed similarly among the groups throughout the study phases. CONCLUSIONS: Pre-incisional intra-articular morphine reduced pain in the first 2 weeks after arthroscopic rotator cuff repair. Further research is warranted to elucidate the optimal timing and dosing of IA ketamine and morphine for postoperative analgesic effects.

Lateral epicondylitis treatment: international survey of surgeons' preferences and literature review.

BACKGROUND: Lateral epicondylitis (LE) is a common cause of elbow pain. Despite a relatively high prevalence and morbidity, there is still no single effective ('gold standard') treatment for LE. We hypothesised that a surgeon's experience, country of origin and area of expertise would influence choices concerning patient management. The purpose of this survey was to describe the current trends and common practices in treating LE worldwide. MATERIAL AND METHODS: A total of 291 orthopaedic surgeons of 12 subspecialties from 57 countries were surveyed on their choice of LE treatment modalities. Their preferences were analysed according to country of origin, field of expertise and seniority. The results were compared with current published level-1 evidence. RESULTS: The most popular modalities of treatment among all of the surveyed orthopaedic surgeons were non-steroidal anti-inflammatory drugs (NSAIDs) and corticosteroid (CS) injection (38% of recommendations each). The most popular Modalities of treatment among the hand surgeons was NSAIDs (48%) and CS injection (30%). There was no significant difference in recommendations based on geography, seniority or specialisation (i.e., hand surgeons among others). CONCLUSIONS: Neither geography, seniority nor medical specialty affects surgeons' preferences in the treatment of LE. There appears to be little correlation between scientific evidence and therapeutic choices for managing LE. LEVEL OF EVIDENCE: Level V, Study.

A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model.

This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Our results show similar behavior as the classical order ones. This characteristic shows the applicability and usefulness of the derivative and our numerical scheme.

Management of chronic knee pain caused by postsurgical or posttraumatic neuroma of the infrapatellar branch of the saphenous nerve.

PURPOSE: Injury to the infrapatellar branch of the saphenous nerve (IBSN) is a relatively common complication after knee surgery, which can interfere with patient satisfaction and functional outcome. In some cases, injury to the IBSN can lead to formation of a painful neuroma. The purpose of this study was to report the results of surgical treatment in a series of patients with IBSN painful neuroma. METHODS: We retrospectively identified 37 patients who underwent resection of IBSN painful neuroma at our institution, after failure of non-operative treatment for a minimum of 6 months. Injury to the IBSN resulted from prior orthopedic surgery, vascular surgery, tumor resection, trauma, or infection. Leg pain and health-related quality of life were measured using the numeric rating scale (NRS) and EuroQol 5 dimensions (EQ-5D) questionnaire, respectively. Clinically meaningful improvement in leg pain was defined as reduction in NRS by at least 3 points. Predictors of favorable and unfavorable surgical outcome were investigated using multivariable logistic regression analysis. RESULTS: Patient-reported leg pain, health-related quality of life, and overall satisfaction with the surgical outcome were obtained at 94 ± 52.9 months after neuroma surgery. Postoperative patient-reported outcomes were available for 25 patients (68% of the cohort), of whom 20 patients (80.0%) reported improvement in leg pain, 17 patients (68.0%) reported clinically meaningful improvement in leg pain, and 17 patients (68%) reported improvement in health-related quality of life. The average NRS pain score improved from 9.43 ± 1.34 to 5.12 ± 3.33 (p < 0.01) and the average EQ-5D functional score improved from 10.48 ± 2.33 to 7.84 ± 2.19 (p < 0.01). Overall patient reported satisfaction with the surgical outcome was good to excellent for 18 patients (72.0%). Older age, multiple prior orthopedic knee surgeries, and failed prior attempts to resect an IBSN neuroma were associated with non-favorable surgical outcome. CONCLUSION: We conclude that surgical intervention is efficacious for appropriately selected patients suffering from IBSN painful neuroma.

A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller-Box scheme.

A novel hybrid nanofluid was explored in order to find an efficient heat-transmitting fluid to replace standard fluids and revolutionary nanofluids. By using tangent hyperbolic hybrid combination nanoliquid with non-Newtonian ethylene glycol (EG) as a basis fluid and a copper (Cu) and titanium dioxide (TiO2) mixture, this work aims to investigate the viscoelastic elements of the thermal transferring process. Flow and thermal facts, such as a slippery extended surface with magnetohydrodynamic (MHD), suction/injection, form factor, Joule heating, and thermal radiation effects, including changing thermal conductivity, were also integrated. The Keller-Box method was used to perform collective numerical computations of parametric analysis using governing equivalences. In the form of graphs and tables, the results of TiO2-Cu/EG hybrid nanofluid were compared to those of standard Cu/EG nanofluid in important critical physical circumstances. The entropy generation study was used to examine energy balance and usefulness for important physically impacting parameters. Detailed scrutiny on entropy development get assisted with Weissenberg number, magnetic parameter, fractional volumes, injection parameter, thermal radiation, variable thermal conductivity, Biot number, shape variation parameter, Reynolds and Brinkman number. Whereas the entropy gets resisted for slip and suction parameter. In this case, spotted entropy buildup with important parametric ranges could aid future optimization.

Galerkin finite element study for mixed convection (TiO2-SiO2/water) hybrid-nanofluidic flow in a triangular aperture heated beneath.

Fluidity and thermal transport across the triangular aperture with lower lateral inlet and apply placed at the vertical outlet of the chamber which filled with efficient TiO2-SiO2/water hybrid nanofluid under the parametrical influence. Several parameters are tested like the numbers of Hartmann ([Formula: see text]), Richardson ([Formula: see text]), and Reynolds ([Formula: see text]) were critiqued through streamlines, isotherms, and Nusselt number ([Formula: see text]). Numerical model has to be developed and solved through the Galerkin finite element method (GFEM) by discretized with 13,569 triangular elements optimized through grid-independent analysis. The Hartmann number ([Formula: see text]), exerts minimal impact over the flow and thermal aspects while the other parameters significantly manipulate the physical nature of the flowing and thermal aspects behaviors.

MHD darcy-forchheimer nanofluid flow and entropy optimization in an odd-shaped enclosure filled with a (MWCNT-Fe3O4/water) using galerkin finite element analysis.

MHD nanoliquid convective flow in an odd-shaped cavity filled with a multi-walled carbon nanotube-iron (II, III) oxide (MWCNT-Fe3O4) hybrid nanofluid is reported. The side walls are adiabatic, and the internal and external borders of the cavity are isothermally kept at high and low temperatures of Th and Tc, respectively. The governing equations obtained with the Boussinesq approximation are solved using Galerkin Finite Element Method (GFEM). Impact of Darcy number (Da), Hartmann number (Ha), Rayleigh number (Ra), solid volume fraction (ϕ), and Heated-wall length effect are presented. Outputs are illustrated in forms of streamlines, isotherms, and Nusselt number. The impact of multiple parameters namely Rayleigh number, Darcy number, on entropy generation rate was analyzed and discussed in post-processing under laminar and turbulent flow regimes.

Neurolysis for the treatment of sciatic nerve palsy associated with total hip arthroplasty.

Sciatic nerve palsy following total hip arthroplasty (THA) is a relatively rare yet potentially devastating complication. The purpose of this case series was to report the results of patients with a sciatic nerve palsy who presented between 2000 and 2010, following primary and revision THA and were treated with neurolysis. A retrospective review was made of 12 patients (eight women and four men), with sciatic nerve palsy following THA. The mean age of the patients was 62.7 years (50 to 72; standard deviation 6.9). They underwent interfascicular neurolysis for sciatic nerve palsy, after failing a trial of non-operative treatment for a minimum of six months. Following surgery, a statistically and clinically significant improvement in motor function was seen in all patients. The mean peroneal nerve score function improved from 0.42 (0 to 3) to 3 (1 to 5) (p < 0.001). The mean tibial nerve motor function score improved from 1.75 (1 to 4) to 3.92 (3 to 5) (p = 0.02).The mean improvement in sensory function was a clinically negligible 1 out of 5 in all patients. In total, 11 patients reported improvement in their pain following surgery. We conclude that neurolysis of the sciatic nerve has a favourable prognosis in patients with a sciatic nerve palsy following THA. Our findings suggest that surgery should not be delayed for > 12 months following injury.

Accurate determination of solid and liquid dispersions from spectra channeled with the Fabry-Perot interferometer.

The band spacing of the fringes of equal chromatic order of a thin Fabry-Perot interferometer is compared when this interferometer contains air, a solid, or a liquid. This comparison enables the dispersion of the group velocity of light in these media to be known accurately to 2.4 parts in one thousand. The Sellmeier dispersion function is used to deduce the refractive indices with the same degree of accuracy. The order-transformation method is used to find the exact order values from the roughly known optical thickness. The exact order values for air and the sample are used to find the refractive index accurately to approximately 3 x 10(-5). A least-squares fitting of the accurate experimental data to the Sellmeier dispersion function enables the coefficients of the latter to be more precisely defined for solids such as glass and mica and for liquids such as glycerin and distilled water. The atomic parameters such as the density of states and the absorption wavelengths in the ultraviolet region of the spectrum for the given samples are deduced from the more precisely found Sellmeier coefficients.

Accurate measurement of the refractive indices of solids and liquids by the double-layer interferometer.

The rings of equal inclination of the double-layer interferometer disappear in their common center if a plane-parallel glass plate is rotated inside one of the interferometer gaps that is filled with a liquid. Knowledge of the ring count and the rotated angle allows the refractive indices of both the rotated plate and the liquid to be found from a new analytical formula accurate to ?0.0004. The experimental results for glass, distilled water, and methanol are fitted to the Sellmeier dispersion function to determine their quantum parameters such as the absorption wavelengths in the ultraviolet side of the spectrum and the atomic number densities contributing to these absorption bands.