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Latest Published Articles

Generalizations of generating functions for basic hypergeometric orthogonal polynomials

OMS-Vol. 6 (2022), Issue 1, pp. 248 – 261 Open Access Full-Text PDF
Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang and Tanay V. Wakhare

Abstract: We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.

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Ultrasound guided anterior approach coeliac plexus ethanol neurolysis for pain relief in gastric and pancreatic malignancy

TCMS-Vol. 2 (2022), Issue 3, pp. 18 – 23 Open Access Full-Text PDF
D. Ashok Kumar, Ganesh Annamalai, Nadar Kalaivani Venkatasami and Sivabalan R G

Abstract: Background and Aim: Chronic cancer pain is one of the major challenges of palliative care and it is prevalent in 80\% of all the gastric and pancreatic malignancies. Adequate pain relief not only improves the drug compliance, but also alleviates depression among the cancer patients, thereby improving the quality of life. This study was carried out with the aim of evaluating the role of Coeliac Plexus ethanol Neurolysis (CPN) in pain relief among patients with gastric and pancreatic malignancy.
Methods and materials: This is an uncontrolled before-and-after non randomized trial. This bedside procedure was done in an ICU in chronic pain management centre. Trial coeliac plexus block was done after identification of coeliac trunk using ultrasound and 15 cc of 1% xylocard was given. After 30 minutes, pain relief was assessed with Numerical Rating Scale for pain (NRS). Patient was then given 20ml of 60% ethanol. Pain relief was documented using NRS immediately at 24hours, 72 hours,1 week and 3 months. Statistical analysis was done using Statistical Package for the Social Sciences version (SPSS) version 16.0. Paired t test was used to analyze the difference between variables.
Results: Our study shows statistically significant difference between pre-NRS and post immediate-NRS (mean 8.26\(\pm\)0.52 and 3.40 \(\pm\)0.47)(P value \(<0.0001\)) and significant decrease in NRS seen after 24 hours,72 hours,1 week and 3 months.
Conclusion: USG guided anterior approach coeliac plexus ethanol neurolysis is effective in decreasing pain associated with gastric and pancreatic malignancy.

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A study of 50 patients with acute kidney injury due to gastroenteritis

TCMS-Vol. 2 (2022), Issue 3, pp. 11 – 17 Open Access Full-Text PDF
A. Umakanth, Veera Purushotham, Renuka Devi Nalluri, Chennakesavulu Dara, Phani Krishna Telluri and Khizer

Abstract: Background: With an estimated 13.3 million cases each year, acute kidney injury (AKI) become a problem for world health. India has a high prevalence of AKI following volume depletion from gastrointestinal fluid loss. Due to poor socioeconomic situations, limited access to care, lack of awareness of personal cleanliness, crowding, and climatic factors that encourage the spread of infection, diarrheal illnesses are widespread in India. AKI following gastroenteritis is probably caused by a lack of medical facilities in rural areas and a delay in treating dehydration. Therefore, in order to come up with solutions to this issue, it is necessary to comprehend the disease’s clinical spectrum.
Materials and Methods: This is a prospective observational study conducted on 50 patients with AKI due to Acute Gastroenteritis admitted to Narayana medical college \& hospital, Nellore, Andhra Pradesh, over a period of 1 year. The diagnosis of acute kidney injury was used when there was evidence of kidney injury in some clinical settings without any kidney disease history. The term acute kidney injury was used when there was a rise in Serum creatinine \(\geq44 \mu mol/L (\geq0.5mg/dL)\) and the history of decreased urine output of less than \(0.5ml/kg/hr\) for more than 6hrs. The criteria used for AKI in the study was Risk, Injury, Failure, Loss of kidney function, and End-stage kidney disease (RIFLE) criteria (given by Acute Dialysis Quality Initiative Group 2004) and is as follows.
Results: Pre Renal Azotemia, which occurred in 58% of cases, was followed by Acute Tubular Necrosis, which occurred in 42% of cases in this study. The pre-renal group’s mean age was \(49.3 + 5.66\) years, while the ATN group’s was \(48.6 + 7.40\) years. The mean age of those who survived was 46.73 4.75, while that of those who did not survive was 65 6.034. On admission, Baseline creatinine with a mean of \(3.032+0.37mg/dl\). It was \(2.70+0.29\) and \(3.48\pm0.77\) inpre-renal and Acute Tubular Necrosis (ATN) groups. The mean peak creatine was \(4.73+0.48mg/dl\). It was 4.13+ 0.59 in pre-renal and 5.56\(\pm\) 0.66 in ATN groups, respectively. The Mean creatinine at the time of discharge 2.87 \(\pm\) \(0.39mg/dl\). The mean peak creatinine was 2.42 \(\pm\) 0.33 in pre-renal & 3.48+0.42 in ATN groups (In survivors) and 4.11\(\pm\) 0.79 in non-survivors.
Conclusion: Replacement of lost fluids, correction of electrolyte imbalances, and delivery of the proper antibiotics made up the course of treatment. Due to the frequent incidence of hypokalemia, ARF brought on by gastroenteritis differs from other ARF and has a better prognosis. An significant electrolyte disruption in AKI brought on by gastroenteritis is hypokalaemia. It was determined that the primary factor leading to death in AKI caused by gastroenteritis is septicemia.

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Awake craniotomy for brain tumors: Indications, benefits, types of anesthesia and surgical techniques

TCMS-Vol. 2 (2022), Issue 3, pp. 5 – 10 Open Access Full-Text PDF
Omar Al Awar, Patricia Nehmeh and Georgio Haddad

Abstract: Background: Awake brain surgery is used to treat brain tumors and epileptic seizures near areas that control language, movement or cognition, movement disorder, and recently during neurovascular surgery.
Methods: Preoperative airway evaluation should be performed in all patients. There are two commonly used anesthetic methods for awake craniotomy: monitored anesthesia care (MAC) and asleep-awake-asleep (AAA) technique, after the tumor resection, sedation is often sufficient until completion of the surgery. In our institution at Mount Lebanon hospital-Balamand university hospital, the combination of propofol and remifentanil has been considered as the standard protocol for sedation during the first stage of awake craniotomy because of the ease of use and reliability. The application of neuro-navigation, and intraoperative electrical mapping are a reliable method to minimize the risk of permanent deficit during surgery for brain tumors in eloquent areas.
Results: Whether sedation or an asleep-awake-asleep technique is chosen, it is crucial to apply adequate local anaesthesia on the skin incision what we call elliptic block using combinations of lidocaine and bupivacaine with epinephrine. If we perform awake-asleep-awake anesthesia type than similar to the pre-awake phase, one can also choose awake, spontaneous ventilation under light or deep sedation, or GA with airway control. Sedation often suffices. The patient usually requires lower rates of sedative infusions during the postawake phase than during the pre-awake phase as patients are often fatigued, and there is a lower level of painful stimuli during skull closure.
Conclusion: Patients receiving awake craniotomy have better outcomes in many aspects. The improvements in anesthetic agents and techniques, the application of neuro-navigation, and intraoperative electrical mapping are a reliable method to minimize the risk of permanent deficit during surgery. Appropriate patient selection, perioperative psychological support, and proper anesthetic management for individual patients in each stage of surgery are crucial for procedural safety, success, and patient satisfaction.

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Hyperbaric bupivacaine for spinal anaesthesia in adults patients: Comparison of isobaric bupivacaine 0.5% in 80mg/ml and 40mg/ml glucose solutions

TCMS-Vol. 2 (2022), Issue 3, pp. 1 – 4 Open Access Full-Text PDF
Patricia Wadih Nehme, Joseph Mounir Maalouli, Marie Tanios Merheb and Elie Mikhael Gharios

Abstract: Background: The Baricity of bupivacaine is one of the most important factors in influencing the distribution of the local anaesthetic and the spread of the blockade. Bupivacaine is rendered hyperbaric by adding glucose. The effect of differing degrees of hyperbaricity remains to be evaluated regarding spinal anesthesia blockade.
Methods: Hundred patients who underwent lower abdominal, hips, and lower extremity surgeries were randomized into two groups in a double-blind, randomised, parallel-group, prospective study. Group I received 0.5% isobaric bupivacaine with 80 mg/ml of glucose, while Group II received 0.5% isobaric bupivacaine with 40 mg/ml of glucose. The injection was made intrathecally in the midline position at L3-4 and L4-L5 interspace in the sitting position. The measured sensory blockade and motor blockade are the onset and duration. Duration of sensory block was the time measured from the time of the highest block for the regression to the S2 dermatome.
Results: Success rate, spread, and duration of sensory block were similar in both groups. The highest median level of sensory block was T3 (T2-T7) (median (10th/90th percentiles)) in both groups. The time to reach T10 did not differ between the groups. Power analysis suggested that a total number of 100 adults were required in both groups for a 90% chance at the 0.05 level of significance of detecting a 10% difference in success between groups. Categorical data were tested using the chi-square test. For continuous data, the Mann-Whitney test was used. Results are presented as median (10-90\(^{th}\) percentiles), number (%) of cases ,the significance was set as \(P< 0.05.\)
Conclusion: These results demonstrate that bupivacaine in 80mg/ml glucose provides reliable spinal anaesthesia of shorter duration and with less hypotension than bupivacaine in 40 mg/ml glucose. The recovery profile for ropivacaine may be of interest given that more surgery is being performed in the day-case setting.

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KG-Sombor index of Kragujevac trees

ODAM-Vol. 5 (2022), Issue 2, pp. 19 – 25 Open Access Full-Text PDF
Ivan Gutman, Izudin Redžepović and Veerabhadrappa R. Kulli

Abstract: The paper is concerned with the KG-Sombor index (\(KG\)), a recently introduced vertex-and-edge-degree-based version of the Sombor index, applied to Kragujevac trees (\(Kg\)). A general combinatorial expression for \(KG(Kg)\) is established. The species with minimum and maximum \(KG(Kg)\)-values are determined.

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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC