Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique.

Impact of Removing Race Adjustment When Estimating GFR on Chronic Kidney Disease Staging

Introduction/Objective

Determination of glomerular filtration rate (GFR) is essential in assessment of kidney function, particularly in patients with chronic kidney disease (CKD). Formulas were developed to calculate estimated GFR (eGFR), as direct measurement is cumbersome and not amenable to routine monitoring. CKD-EPI is the most widely used formula for eGFR, using parameters of serum creatinine, gender, race, and age. A race adjustment was added from an unfounded assumption that Black patients have more muscle mass, increasing their eGFR by about 16%. There is concern on the impact of “correcting” for Black race on patient management, utility of eGFR, and its possible contribution to healthcare disparities. This study examined the impact of eliminating race adjustment from the CKD- EPI formula on CKD staging in patients at a large safety-net hospital in an academic medical center.

Methods/Case Report

80090 serum creatinine values from 56676 adult patients (31.4% Black, 67.5% female, median age 51 yrs) were collected from the electronic medical record (Epic, Verona, WI) over a 16-month timeframe. Values were excluded if they lacked age, gender, self-identified race, or serum creatinine. eGFR was calculated using the CKD-EPI equation with and without race modifier, and CKD staging was performed using 2012 Kidney Disease: Improving Global Outcomes guidelines.

Results (if a Case Study enter NA)

In our cohort, only 50.8% of Black patients are in CKD1, indicative of no CKD, compared to 67.9% of non-Black patients. Given that these two cohorts are demographically similar, this shows a discrepancy in kidney function even before removing the race adjustment. After removal of the race modifier, 28.1% of Black patients were reclassified into a more severe CKD stage. The most restaging occurred from CKD3A to 3B (39%).

Conclusion

Many Black patients in our study were reclassified to a more severe CKD stage, with the highest percentage of patients restaged to CKD3B, which would have attracted clinical attention for nephrology referral. We recommend removal of the race adjustment in eGFR, given its basis in the incorrect belief in biological differences between races. It perpetuates systemic racism and discrimination in healthcare, and its removal will provide more equitable care and reduce healthcare disparities. Future studies should examine the increase in resources required to provide adequate medical care to patients who will be placed into a more severe CKD stage.

Synergistic potential of propolis and vitamin e against sub-acute toxicity of AlCl(3) in albino mice: in vivo study

Current study evaluated the synergistic potential of propolis and vitamin E against sub-acute toxicity of aluminum chloride on different biochemical parameters and liver histology. Swiss albino mice (n=42) were randomly divided into seven groups. Group I received 0.2 ml of 0.9 % saline solution, Group II received Propolis (50 mg/kg b.w.), Group III received vitamin E (150 mg/kg b.w.), Group IV received AlCl(3) 50 mg/kg b.w., Group V received AlCl(3) + Propolis, Group VI received AlCl(3) + vitamin E and Group VII received AlCl(3) + propolis + vitamin E. Blood and tissue samples were collected after 7 and 21 days. The body weight of the animals significantly increased in all groups except Group IV. The concentration of serum high density lipoprotein significantly decreased in Group IV and increased in Group V, VI and VII. The level of aspartate aminotransferase, alanine transferase, alkaline phosphatase, triglycerides, total cholesterol, and low density lipoprotein significantly increased in AlCl(3) treated group and increased in Group V, VI and VII. Tissue sections were processed and stained by hematoxylin and eosin. Group II showed cellular necrosis. Group V, VI showed decreased number of vacuolization, sinusoidal spacing and macrophage cell infiltration. Group VI showed less degenerative changes in the third week. Vitamin E and propolis in combination with Al provides more protection against AlCl(3) induced toxicity.

MHD convective heat transfer in a discretely heated square cavity with conductive inner block using two-phase nanofluid model

The problem of steady, laminar natural convection in a discretely heated and cooled square cavity filled by an alumina/water nanofluid with a centered heat-conducting solid block under the effects of inclined uniform magnetic field, Brownian diffusion and thermophoresis is studied numerically by using the finite difference method. Isothermal heaters and coolers are placed along the vertical walls and the bottom horizontal wall, while the upper horizontal wall is kept adiabatic. Water-based nanofluids with alumina nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number (10³ ≤ Ra ≤ 10⁶), the Hartmann number (0 ≤ Ha ≤ 50), thermal conductivity ratio (0.28 ≤ k_w ≤ 16), centered solid block size (0.1 ≤ D ≤ 0.7) and the nanoparticles volume fraction (0 ≤ ϕ ≤ 0.04). The developed computational code is validated comprehensively using the grid independency test and numerical and experimental data of other authors. The obtained results reveal that the effects of the thermal conductivity ratio, centered solid block size and the nanoparticles volume fraction are non-linear for the heat transfer rate. Therefore, it is possible to find optimal parameters for the heat transfer enhancement in dependence on the considered system. Moreover, high values of the Rayleigh number and nanoparticles volume fraction characterize homogeneous distributions of nanoparticles inside the cavity. High concentration of nanoparticles can be found near the centered solid block where thermal plumes from the local heaters interact.

Orientational and Microstructural Evolution During Epitaxial Growth of Cu on Si(001) by Sputter Deposition

Epitaxial Cu thin films have been grown on H-terminated Si(OOl) substrates at room temperature by D.C. ion-beam sputter deposition in ultrahigh vacuum. The development of orientation and microstructure during epitaxial growth from the initial stages of Cu growth up to Cu thicknesses of few hundred nm has been investigated. Analysis by in-situ reflection high energy electron diffraction, thin film x-ray diffraction, and plan-view and cross-sectional transmission electron microscopy indicates that the films are well textured with Cu(001)∥ Si(001) and Cu[100]∥ Si[110]. Interestingly, it is found that a distribution of orientations occurs at the early stages of Cu epitaxy on Si(001) surface, and that a (001) texture emerges gradually with increasing Cu thickness. The effect of silicide formation and deposition conditions on the crystalline quality of Cu epitaxy is also discussed.

Bochdalek diaphragmatic hernia presenting with acute gastric dilatation

Congenital diaphragmatic hernia through the foramen of Bochdalek may present after infancy. A 21/2-year-old Malay girl presented with acute respiratory distress. Chest examination showed reduced chest expansion and decreased breath sounds on the left side. Chest radiograph showed a large "cyst" in the left chest, which was thought to be a lung cyst under tension. Tube thoracostomy resulted in clinical improvement. Results of a barium study showed that the cyst perforated by the thoracostomy tube was the stomach, which had herniated through a Bochdalek diaphragmatic defect. Surgical repair of the diaphragmatic defect and closure of the perforated stomach was performed successfully. Congenital diaphragmatic hernia should be included in the differential diagnosis of respiratory distress in young children. Nasogastric tube placement must be considered as an early diagnostic or therapeutic intervention when the diagnosis is suspected.

Lung abscess: an unusual presentation of congenital tracheoesophageal fistula without atresia

Tracheoesophageal fistula (TEF) without atresia is rare and usually presents with symptoms from birth. In this report, a 9-year-old boy presented with productive cough of 4 month's duration and was shown to have a right lung abscess seen on chest radiograph. His parents denied earlier respiratory symptoms or illnesses. Rigid bronchoscopy showed a fistulous opening of about 1 mm in diameter in the posterior wall of the trachea about 16 cm from the upper incisor teeth. Cannulation with a ureteral catheter demonstrated that the fistulous opening communicated with the esophageal lumen. The tracheoesophageal fistula was 1 cm long and was divided through a right supraclavicular incision. The postoperative period was uneventful, and the patient was discharged on the third postoperative day. This case demonstrated that TEF should be considered in any patient presenting with chronic respiratory problems even after a prolonged symptom-free period.

Serum prolactin bioactivity and immunoactivity in hyperprolactinaemic states

Serum prolactin concentrations were measured using a sensitive bioassay (Nb2 assay) and by radioimmunoassay in 11 patients with prolactin-secreting pituitary tumours (median serum immunoactive prolactin 5150 mU/L), and in 58 normal control subjects (median prolactin 190 mU/L). The mean ratio of serum prolactin bioactivity to immunoactivity was significantly lower in patients with prolactinomas than in normoprolactinaemic controls. Ten lactating women in the early post-partum period (median prolactin 3800 mU/L), studied as a model of physiological hyperprolactinaemia, also had reduced bioactivity to immunoactivity ratios. Overall, there was a significant negative correlation between bioactivity:immunoactivity ratio and serum immunoactive prolactin. The change in relative bioactivity of prolactin in serum samples from patients with prolactinomas and in women with physiological hyperprolactinaemia may reflect changes in the molecular heterogeneity of the hormone. Such changes may affect activity in both bioassays and radioimmunoassays.