Generalized Bézier-like model and its applications to curve and surface modeling.

The subject matter of surfaces in computer aided geometric design (CAGD) is the depiction and design of surfaces in the computer graphics arena. Due to their geometric features, modeling of Bézier curves and surfaces with their shape parameters is the most well-liked topic of research in CAGD/computer-aided manufacturing (CAM). The primary challenges in industries such as automotive, shipbuilding, and aerospace are the design of complex surfaces. In order to address this issue, the continuity constraints between surfaces are utilized to generate complex surfaces. The parametric and geometric continuities are the two metrics commonly used for establishing connections among surfaces. This paper proposes continuity constraints between two generalized Bézier-like surfaces (gBS) with different shape parameters to address the issue of modeling and designing surfaces. Initially, the generalized form of C3 and G3 of generalized Bézier-like curves (gBC) are developed. To check the validity of these constraints, some numerical examples are also analyzed with graphical representations. Furthermore, for a continuous connection among these gBS, the necessary and sufficient G1 and G2 continuity constraints are also developed. It is shown through the use of several geometric designs of gBS that the recommended basis can resolve the shape and position adjustment problems associated with Bézier surfaces more effectively than any other basis. As a result, the proposed scheme not only incorporates all of the geometric features of curve design schemes but also improves upon their faults, which are typically encountered in engineering. Mainly, by changing the values of shape parameters, we can alter the shape of the curve by our choice which is not present in the standard Bézier model. This is the main drawback of traditional Bézier model.

An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions.

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions.

Investigation of the dynamical structures of double-chain deoxyribonucleic acid model in biological sciences.

The present research investigates the double-chain deoxyribonucleic acid model, which is important for the transfer and retention of genetic material in biological domains. This model is composed of two lengthy uniformly elastic filaments, that stand in for a pair of polynucleotide chains of the deoxyribonucleic acid molecule joined by hydrogen bonds among the bottom combination, demonstrating the hydrogen bonds formed within the chain's base pairs. The modified extended Fan sub equation method effectively used to explain the exact travelling wave solutions for the double-chain deoxyribonucleic acid model. Compared to the earlier, now in use methods, the previously described modified extended Fan sub equation method provide more innovative, comprehensive solutions and are relatively straightforward to implement. This method transforms a non-linear partial differential equation into an ODE by using a travelling wave transformation. Additionally, the study yields both single and mixed non-degenerate Jacobi elliptic function type solutions. The complexiton, kink wave, dark or anti-bell, V, anti-Z and singular wave shapes soliton solutions are a few of the creative solutions that have been constructed utilizing modified extended Fan sub equation method that can offer details on the transversal and longitudinal moves inside the DNA helix by freely chosen parameters. Solitons propagate at a consistent rate and retain their original shape. They are widely used in nonlinear models and can be found everywhere in nature. To help in understanding the physical significance of the double-chain deoxyribonucleic acid model, several solutions are shown with graphics in the form of contour, 2D and 3D graphs using computer software Mathematica 13.2. All of the requisite constraint factors that are required for the completed solutions to exist appear to be met. Therefore, our method of strengthening symbolic computations offers a powerful and effective mathematical tool for resolving various moderate nonlinear wave problems. The findings demonstrate the system's potentially very rich precise wave forms with biological significance. The fundamentals of double-chain deoxyribonucleic acid model diffusion and processing are demonstrated by this work, which marks a substantial development in our knowledge of double-chain deoxyribonucleic acid model movements.

A dynamical behavior of the coupled Broer-Kaup-Kupershmidt equation using two efficient analytical techniques.

The aim of the present study is to identify multiple soliton solutions to the nonlinear coupled Broer-Kaup-Kupershmidt (BKK) system, including beta, conformable, local-fractional, and M-truncated derivatives. The coupled Broer-Kaup-Kupershmidt system is employed for modelling nonlinear wave evolution in mathematical models of fluid dynamics, plasmic, optical, dispersive, and nonlinear long-gravity waves. The travelling wave solutions to the above model are found using the Unified and generalised Bernoulli sub-ODE techniques. By modifying certain parameter values, we may create bright soliton, squeezed bell-shaped wave, expanded v-shaped soliton, W-shaped wave, singular soliton, and periodic solutions. The four distinct kinds of derivatives are compared quite effectively using 2D line graphs. Also, contour plots and 3D graphics are given by using Mathematica 10. Lastly, any pair of propagating wave solutions has symmetrical geometrical forms.

Numerical investigation of the fractional diffusion wave equation with exponential kernel via cubic B-Spline approach.

Splines are piecewise polynomials that are as smooth as they can be without forming a single polynomial. They are linked at specific points known as knots. Splines are useful for a variety of problems in numerical analysis and applied mathematics because they are simple to store and manipulate on a computer. These include, for example, numerical quadrature, function approximation, data fitting, etc. In this study, cubic B-spline (CBS) functions are used to numerically solve the time fractional diffusion wave equation (TFDWE) with Caputo-Fabrizio derivative. To discretize the spatial and temporal derivatives, CBS with θ-weighted scheme and the finite difference approach are utilized, respectively. Convergence analysis and stability of the presented method are analyzed. Some examples are used to validate the suggested scheme, and they show that it is feasible and fairly accurate.

Mesenchymal stem cells derived from bone marrow and adipose tissue for repairing acute sciatic nerve injury in a rabbit model.

Peripheral nerve injury is one of the common disabling clinical conditions and around 50% of the cases end up in permanent impairment. Due to the lack of effective treatment options regenerative medicine employing stem cells is being evaluated. The presented study evaluated and compared regeneration potential of mesenchymal stem cells (MSCs) derived from bone marrow (BM) and adipose tissue (AD) in acute rabbit sciatic nerve injury (axonotmesis) model. A total of n = 54 grey giant rabbits were made subject of the study and divided equally into 3 groups: Control, BM-MSCs in Collagen I and AD-MSCs in Collagen I as per the treatment given. Iliac crest BM and omental AD was harvested from the same donor for isolation and culture of MSCs. The repair of sciatic nerve injury was evaluated on days 60 and 90. The clinical and histopathological scores and SEM morphology was better in cell treated groups as compared to the control. Morphology and histological studies revealed injured nerve in different levels of regenerative process. Gene expression was more than double for N-Cadherin in cell treated groups as compared to the control, especially at day 60. Between cell treated groups, BM-MSCs group showed better response as compared to the AD-MSCs, although statistically non-significant (p > 0.05). Incomplete nerve regeneration observed under various diagnostic parameters was in compliance to the incomplete clinical recovery at day 90. It was concluded that MSCs may improve sciatic nerve healing but fall short of complete regeneration at day 90, although BM-MSCs may have an edge over AD-MSCs.

An efficient technique based on cubic B-spline functions for solving time-fractional advection diffusion equation involving Atangana-Baleanu derivative.

The present paper deals with cubic B-spline approximation together with θ -weighted scheme to obtain numerical solution of the time fractional advection diffusion equation using Atangana-Baleanu derivative. To discretize the Atangana-Baleanu time derivative containing a non-singular kernel, finite difference scheme is utilized. The cubic basis functions are associated with spatial discretization. The current discretization scheme used in the present study is unconditionally stable and the convergence is of order O ( h 2 + Δ t 2 ) . The proposed scheme is validated through some numerical examples which reveal the current scheme is feasible and quite accurate.

Long COVID Syndrome and Takotsubo Cardiomyopathy: An Unwelcome Combination.

Since the report of the first case from China in late 2019, the coronavirus disease (COVID-19) has spread very rapidly through the countries and regions leaving a trail of devastation in its path, everywhere. Although COVID-19 is primarily a respiratory illness mainly affecting the lungs; involvement of other organs including the cardiovascular system has been widely recognized. Whilst COVID-19 is an acute illness for a majority of cases; some of the debilitating virus-related symptoms can last for weeks and months, and are collectively termed as long COVID syndrome. Several published reports have described an association between acute COVID-19 illness and cardiac complications such as myocarditis and Takotsubo cardiomyopathy. However, little is known about any link between long COVID syndrome and the cardiac disease. We describe the case of a middle-aged woman with long COVID syndrome who presented with central chest pain and breathlessness. Her initial investigations showed an elevated cardiac troponin I and ischemic changes on 12 lead ECG. She was initially treated for non-ST elevation myocardial infarction. A subsequent coronary angiogram showed unobstructed coronary vessels and left ventricle (LV) gram demonstrated apical LV ballooning. She was managed conservatively and was discharged home following her clinical improvement. This case highlights the importance of holistic assessment of patients presenting with chest pain with the background of long COVID syndrome. It also outlines an emergent need to better understand pathophysiological mechanisms that underpin the development of cardiac complications in those with COVID-19 and long COVID syndrome.

Cerebral amyloid angiopathy: an underdiagnosed cause of recurrent neurological symptoms.

Cerebral amyloid angiopathy (CAA) is a common, yet frequently underdiagnosed pathology characterised by accumulation of amyloid ß proteins in the small blood vessels of the brain. As a result, cerebrovascular dysregulation follows, leading to cerebral microbleeds, lobar intracerebral haematomas and sulcal subarachnoid haemorrhages. Gradual motor and cognitive decline due to these brain injuries leads to significant functional limitation in patients. We describe the case of a 69-year-old man requiring multiple hospital admissions with a variety of neurological symptoms. Following imaging of the brain, he was eventually diagnosed with CAA. We present a brief up-to-date literature review on epidemiology, pathophysiology, clinical features, diagnosis and treatment options for CAA.

Trifascicular Block and Ventricular Standstill: A Late Complication of Mediastinal Radiotherapy in a Cancer Survivor.

Over the last half-century, radiation therapy has evolved to become one of the cornerstones of treatment for various types of cancers. It is estimated that more than 50% of patients with cancer are treated with radiotherapy. Patients with early stages of some cancers can even achieve a cure with radiotherapy alone. Radiation-induced heart disease is a well-recognized cause of mortality and morbidity in cancer survivors as a late complication of radiotherapy, often occurring more than a decade after radiotherapy. We describe a case of a middle-aged female who presented to the hospital with syncopal episodes. She was in remission from non-Hodgkin's lymphoma having received mediastinal radiotherapy 20 years, previously. Her initial workup such as laboratory investigations and 12 lead electrocardiogram were largely unremarkable. Cardiac monitoring over the course of the next few days was consistent with complete heart block with evidence of ventricular standstill. Her symptoms resolved following the implantation of a dual-chamber cardiac pacemaker. This case highlights the significance of clinical history taking and putting together all relevant facts to come to a differential diagnosis. In our case, this could have been easily overlooked as radiation therapy was given many years previously. We review and present an up-to-date albeit brief literature review on long-term cardiovascular complications of radiotherapy. Radiation-induced cardiac complications are an important cause of mortality and morbidity in cancer survivors. This article aims to raise awareness amongst clinicians of cardiac adverse effects occurring several years after the radiation therapy. This case also highlights the need for further research to better understand the pathophysiology of cardiovascular disease post-radiotherapy in order to develop effective prevention strategies and improve clinical outcomes.

Torn Between Caution and Compassion: a Dilemma for Clinicians from Black and Minority Ethnic Groups During the COVID-19 Pandemic.

The wide disparity in coronavirus disease (COVID-19)-related death rates based upon the ethnic origin is well established by now. The higher incidence of COVID-19 deaths amongst the healthcare staff belonging to black and minority ethnic (BAME) communities living in the United Kingdom has generated a great deal of concern and anxiety in clinicians. Public Health England (PHE) has outlined mitigation strategies after immense pressure from professional organisations and influential clinical leaders. Although seemingly well thought through, these measures fall short of addressing the professional, moral and emotional dilemma faced by the BAME clinicians who feel that they are being expected to choose between their duty towards their patients and the profession, and their responsibility to look after their own health.

Efficacy and Cardiovascular Safety of SGLT2 Inhibitors.

Patients with diabetes continued to exhibit a high risk for cardiovascular and renal events despite achieving satisfactory glycemic, blood pressure and lipid targets. Studies evaluating new diabetes medications focused on cardiovascular events, largely overlooking heart failure (HF). The latter has recently been recognised as a major cause of morbidity and mortality in patients with diabetes mellitus. There had been an unmet need for drugs with cardiovascular (including HF) and renal protection, with an expectation that an ideal diabetic drug should improve these endpoints. Moreover, an ideal drug should have weight reducing benefits. Recently published outcome trials have shown that sodium-glucose cotransporter 2 (SGLT2) inhibitors and glucagon-like peptide 1 receptor agonists (GLP-1RAs) can reduce cardiovascular and renal events, together with statistically significant weight reduction. As a result, many recently published international guidelines have recommended SGLT2 inhibitors and GLP-1RAs in patients with diabetes and pre-existing cardiovascular disease (CVD). In this review, we will critically analyse the efficacy and cardiovascular (CV) safety of SGLT2 inhibitors, based on the available literature to help position them in the clinical decision process.

Kawasaki Disease: An Unusual Case of a Retrospective Diagnosis in a 39-Year-Old Gentleman With Coronary Ectasias.

Kawasaki disease (KD) was first reported by Dr. Tomisaku Kawasaki in 1967 and is classified as an autoimmune vasculitis of small- and medium-sized arteries. It is usually a self-limited condition occurring in childhood, but it can have complications such as coronary artery aneurysms, myocardial ischemia, and arrhythmias with significant morbidity and mortality presenting later in life. We report a case of a KD presenting in adulthood with late cardiovascular sequelae managed with coronary artery bypass graft.

Cardiac amyloidosis-an underdiagnosed cause of heart failure in the elderly.

Amyloidosis is a rare, generally multisystem disease that can also involve the heart. Infiltration of the myocardium with amyloid proteins is an important and underappreciated cause of heart failure with preserved ejection fraction in the elderly. We present the case of an 84-year-old man with chest tightness, dyspnoea, and ascites. He had a history of dyslipidaemia and ischaemic heart disease. Initial investigations showed severe diastolic dysfunction and elevated pulmonary artery systolic pressure on echocardiogram along with elevated serum natriuretic peptides. Further evaluation by a magnetic resonance imaging scan of the heart and endomyocardial biopsy confirmed the diagnosis of senile systemic amyloidosis. He made good progress after treatment with conventional heart failure drugs and is currently under consideration to start on specific medications to slow down the progression of amyloidosis. This case aims to increase clinicians' awareness of senile amyloidosis as a cause of heart failure in the elderly.

Posterior circulation stroke: an easily overlooked complication of catheter ablation of atrial fibrillation.

Catheter ablation of atrial fibrillation (AF) has established itself as a safe and proven rhythm control strategy for selected patients with AF over the past decade. Thromboembolic complications of catheter ablation are becoming rare in anticoagulated patients with a risk of stroke reported as 0.3%. A particular challenge is posed by clinical presentation due to ischaemic stroke involving the posterior circulation following catheter ablation because of its substantial differences from the carotid territory stroke, making the timely diagnosis and treatment very difficult. It is crucial to keep an index of clinical suspicion in patients presenting with neurological deficits related to vertebrobasilar circulation following ablation. We describe the case of a man who presented with dizziness and palpitations after radiofrequency catheter ablation of AF. He was found to be in AF with a rapid ventricular response. His dizziness was initially attributed to the cardiac dysrhythmia. As his symptoms continued despite heart rate control, he underwent further investigations and was eventually diagnosed with a posterior circulation stroke resulting in left cerebellar infarction. He was treated with antiplatelet therapy and improved significantly over the following few days. We review and present an up-to-date brief literature review on the complications of catheter ablation of AF and describe pathophysiology, clinical features, diagnosis and treatment options for posterior circulation stroke after AF ablation. This case aims to raise awareness among clinicians about posterior circulation stroke after AF ablation.