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In this paper, the fuzzy Volterra integral equations' solutions are calculated using a hybrid methodology. The combination of the Elzaki transform and Adomian decomposition method results in the development of a novel regime. The precise fuzzy solutions are determined using Elzaki ADM after the fuzzy linear Volterra integral equations are first translated into two crisp integral equations utilizing the fuzzy number in parametric form. Three instances of the considered equations are solved to show the established scheme's dependability, efficacy, and application. The results have a substantial impact on the fuzzy analytical dynamic equation theory. The comparison of the data in a graphical and tabular format demonstrates the robustness of the defined regime. The lower and upper bound solutions' theoretical convergence and error estimates are highlighted in this paper. A tolerable order of absolute error is also obtained for this inquiry, and the consistency of the outcomes that are approximated and accurate is examined. The regime generated effective and reliable results. The current regime effectively lowers the computational cost, and a faster convergence of the series solution to the exact answer is signaled. [ABSTRACT FROM AUTHOR]

In the present study, time-fractional Schrödinger equations are dealt with for the analytical solution using an integral transform named Shehu Transform. Three kinds of time-fractional Schrödinger equations are discussed in the present study. Shehu transform is utilized to reduce the time-fractional PDE along with the fractional derivative in the Caputo sense. The present method is easy to implement in the search for an analytical solution. As no discretization or numerical program is required, the present scheme will surely be helpful in finding the analytical solution to some complex-natured fractional PDEs. [ABSTRACT FROM AUTHOR]

In the present paper, a Barycentric Lagrange interpolation polynomial-based Differential quadrature method is applied to get the numerical solution of non-linear coupled 2D But-gers' equation, For this process, first of all, the coupled Burgers' equation is dealt with generalized formula, By using the obtained generalized formula, required weighting coefficients in the differential quadrature method are easily calculated, Afterward, the reduced set of ordinary differential equations is solved by using the SSP-RK43 scheme, To test the efficiency of the newly applied method, the L., error norm has been computed, To test the stability of the proposed method, the Matrix stability analysis method is implemented, which shows that the developed method is unconditionally stable. [ABSTRACT FROM AUTHOR]

In this work, two numerical techniques are compared for solving one and two-dimensional convection-diffusion equations. First technique is referred as “MCUAT tension B-spline," and the second technique is labeled as “MCUAH tension B-spline." Various aspects are examined to validate the compatibility of results, including comparisons between numerical and exact solutions and evaluation of different error norms. Present errors are compared with existing literature, presenting a remarkable improvisation. Statistical validation of work is tested via a correlation matrix heatmap generated in Python. The order of convergence of the proposed work is also included. Via an observation of comparison of results, it is claimed that UAT results are slightly better than UAH results. Different aspects of correlation, such as strongly negative correlation and perfect positive correlation, are notified. The present work will introduce new dimensions to the field of numerical techniques. [ABSTRACT FROM AUTHOR]

In the present research paper, an iterative approach named the iterative Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These equations are the prominent ones in the field of physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested using a comparison of approximated and exact results in graphical form. Both 2D and 3D plots are provided to affirm the compatibility of approximated-exact results. The iterative Shehu transform method is a reliable and efficient tool to provide approximated and exact results to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization or linearization, and is free of errors. A convergence analysis is also provided in this research. [ABSTRACT FROM AUTHOR]

In this work, a numerical regime based upon the Non-Uniform Algebraic Hyperbolic Bspline is developed with the aid of the differential quadrature method named NUAH B-spline DQM to fetch the numerical approximation of non-linear coupled ZD Burgers equation. In the first step, the spatial discretization is mentioned using the NUAH B-spline of order 4: for improvised results, modified formulae are implemented, In the second step, the reduced system of ordinary differential equations is dealt using SSP-RK43 regime. The proposed regime is analyzed for stability also. Finally, the effectiveness and adaptability of the proposed regime are confirmed with the aid of numerical experiments, and fetched results are compared with the existing outcomes in the literature. It is observed that the present scheme is unconditionally stable by implementing the concept of the matrix stability analysis method. It is found that the present regime is easy to implement and produces accurate results. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach named Uniform Algebraic Hyperbolic (UAH) tension Bspline Differential quadrature me thod is implemented for the numerical approximation of 1 D Burgers' equation. In this work. UAH tension B-spline basis function is used for the spatial discretization. After finding the weighting coefficients. the original system is reduced to the system of ordinary differential equations, when SSP-RK 43 scheme is implemented. Accuracy of the present method is validated via & and l* error norms. Present results are compared with existing results and these results are acceptable. [ABSTRACT FROM AUTHOR]

In this, research work. we present a novel technique named Hyperbolic B-spline based Differential quadrature method to get the numerical approximations of the 1 D and 2D coupled nonlinear Schrodinger equations. The coupled non-linear Schrodinger equation represents the range of physical phenomena with the aid of a model equation for the optical fiber with the linear birefringence. In present paper. Differential quadrature method is applied over the mentioned PDEs and reduced set of ordinary differential equations is solved by SSP-RK43 scheme. Accuracy and effectiveness of the proposed scheme is checked by L∞ error norm and conservation of mass properly is also tested. In present paper. elastic property is also checked. whether the wave amplitudes have restored their shapes or not for the different used parameters and stability of the proposed scheme is checked via matrix stability analysis method. which indicates that the present method has the property of unconditionally stable. [ABSTRACT FROM AUTHOR]

In this paper, a new numerical method named Barycentric Lagrange interpolation-based differential quadrature method is implemented to get numerical solution of 1D and 2D coupled nonlinear Schrödinger equations. In the present study, spatial discretization is done with the aid of Barycentric Lagrange interpolation basis function. After that, a reduced system of ordinary differential equations is solved using strong stability, preserving the Runge-Kutta 43 method. In order to check the accuracy of the proposed scheme, we have used the formula of L ∞ error norm. The matrix stability analysis method is implemented to test the proposed method's stability, which confirms that the proposed scheme is unconditionally stable. The present scheme produces better results, and it is easy to implement to obtain numerical solutions of a class of partial differential equations. [ABSTRACT FROM AUTHOR]

Epileptic seizure emergencies are life-threatening conditions, which in their most severe form, status epilepticus, have a high mortality rate if not quickly terminated. Treatment requires rapid delivery of anti-epileptics such as benzodiazepines to the brain. The nasal route is attractive due to its non-invasiveness, potential for direct nose to brain delivery, high vascularity, relatively large absorptive surface area, and avoidance of intestinal/liver metabolism. However, the limited volume of the nasal cavity and poor water solubility of anti-epileptics restrict absorption, leading to insufficient therapeutic brain levels. This review covers various formulation approaches adopted to improve nasal delivery of drugs, especially benzodiazepines, used to treat seizure emergencies. Other general topics such as nasal anatomy, challenges to nasal delivery, and drug/formulation considerations for nose to brain delivery are also discussed. [ABSTRACT FROM AUTHOR]

Water-soluble prodrugs can be rapidly converted by enzymes to hydrophobic drugs, whose aqueous thermodynamic solubilities are low, but are maintained in aqueous solution at supersaturated concentrations due to slow precipitation kinetics. Recently, we investigated avizafone (AVF) in combination with Aspergillus oryzae protease as a prodrug/enzyme system intended to produce supersaturated diazepam (DZP). Several fold enhancement of permeation of supersaturated DZP across Madin-Darby canine kidney II-wild type (MDCKII-wt) monolayers was observed, compared to saturated DZP solutions. However, prodrug conversion was incomplete, putatively due to partial racemization of AVF and stereoselectivity of A oryzae protease. Here we report synthesis of chirally pure AVF, and demonstrate complete conversion to supersaturated DZP followed by complete DZP permeation at enhanced rates across MDCKII-wt cell monolayers. We also synthesized, for the first time, a chirally pure prodrug of midazolam (MDZ-pro) and carried out the same sequence of studies. A oryzae protease was identified as a benign and efficient activating enzyme for MDZ-pro. The MDZ-pro/ A oryzae protease system showed greater than 25-fold increase in absorption rate of MDZ across MDCKII-wt monolayers, compared to saturated MDZ. Such chirally pure prodrug/enzyme systems are promising candidates for efficient intranasal delivery of benzodiazepine drugs used in the treatment of seizure emergencies. [ABSTRACT FROM AUTHOR]

Benzodiazepines (BZDs), including diazepam (DZP) and midazolam (MDZ), are drugs of choice for rapid treatment of seizure emergencies. Current approved use of these drugs involves administration via either intravenous or rectal routes. The former requires trained medical personnel, while the latter is socially unacceptable for many patients and caregivers. In recent years, efforts have been made to formulate BZDs for nasal administration. Because of the low solubility of these molecules, organic vehicles have been used to solubilize the drugs in the nasal products under development. However, organic solvents are irritating, potentially resulting in injury to nasal tissue. Here we report preliminary studies supporting a strategy in which water-soluble BZD prodrugs and a suitable converting enzyme are coadministered in an aqueous vehicle. Diazepam and midazolam prodrugs were synthesized and were readily converted to their active forms by a protease from Aspergillus oryzae . Using a permeation assay based on monolayers of Madin–Darby canine kidney II-wild type cells, we found that enzymatically produced BZDs could be maintained at high degrees of supersaturation, enabling faster transport across the membrane than can be achieved using saturated solutions. This strategy not only obviates the need for organic solvents, but it also suggests more rapid absorption and earlier peak concentrations than can be otherwise achieved. This article is part of a Special Issue entitled “Status Epilepticus”. [ABSTRACT FROM AUTHOR]

Purpose: To investigate cellular uptake pathways of novel anionic siRNA-lipoplexes as a function of formulation composition. Methods: Anionic formulations with anionic lipid/Ca/siRNA ratio of 1.3/2.5/1 (AF1) and 1.3/0.3/1 (AF2) were utilized. Uptake mechanisms were investigated using uptake inhibition and co-localization approaches in breast cancer cells. Actin-mediated uptake was investigated using actin polymerization and rearrangement assays. Silencing efficiency and endosomal escaping capability of lipoplexes were evaluated. The cationic formulation Lipofectamine-2000 was used as a control. Results: Anionic lipoplexes entered the breast cancer cells via endocytosis specifically via macropinocytosis or via both macropinocytosis and HSPG (heparin sulfate proteoglycans) pathways, depending on the Ca/siRNA ratio. Additionally, uptake of these lipoplexes was both microtubule and actin dependent. The control cationic lipid-siRNA complexes (Lipofectamine-2000) were internalized via both endocytic (phagocytosis, HSPG) and non-endocytic (membrane fusion) pathways. Their uptake was microtubule independent but actin dependent. Silencing efficiency of the AF2 formulation was negligible mainly due to poor endosomal release (rate-limiting step). Conclusions: Formulation composition significantly influences the internalization mechanism of anionic lipoplexes. Uptake mechanism together with formulation bioactivity helped in identification of the rate-limiting steps to efficient siRNA delivery. Such studies are extremely useful for formulation optimization to achieve enhanced intracellular delivery of nucleic acids. [ABSTRACT FROM AUTHOR]

Abstract: Novel formulations based on physiologically occurring anionic lipids have been designed to achieve safe and efficient siRNA delivery. Anionic liposomes (DOPG/DOPE) were complexed with siRNA using calcium ion bridges to prepare anionic lipoplexes. Various formulation parameters (liposome composition, lipid and calcium concentration) were evaluated and optimized to achieve efficient silencing and high cell viability in breast cancer cells. The optimal anionic lipoplexes composed of 1μg/mL lipid (40:60 (DOPG/DOPE m/m)), 2.4mM calcium and 10nM siRNA, showed maximum silencing (∼70% knockdown) without being cytotoxic. These lipoplexes also showed stability and high efficiency in the presence of serum. Additionally, optimal anionic lipoplexes showed efficient intracellular uptake and endosomal escape. Characterization studies indicated the optimal anionic formulations were 324.2±19.6nm with a surface charge of (−22.9±0.1)mV and 98.5±1.4% encapsulation efficiency. Control cationic lipoplexes (Lipofectamine 2000) showed silencing comparable to the anionic lipoplexes but were highly cytotoxic as indicated by IC50 values (cationic – 22.9μg/mL, compared to anionic – greater than 107 μg/mL). Calcium–siRNA complexes (without liposomes) showed low efficiency (∼50% silencing), and highly variable results. The optimized anionic formulations may offer a safer alternative to conventional cationic based systems for efficient in vitro as well as in vivo delivery of therapeutic siRNAs. [Copyright &y& Elsevier]

Abstract: Physicochemical characterization is a useful tool in understanding lipoplex assemblies and their correlation to biological activity. Anionic lipid-based ternary siRNA complexes composed of anionic liposomes (DOPG/DOPE), calcium ions and siRNA, have recently been shown to be safe and efficient in a breast cancer cell culture model. In the present work, the effects of various formulation parameters such as liposome composition (DOPG/DOPE ratio) and anionic lipid/Ca2+/siRNA molar charge ratio, on the physicochemical attributes (particle size, surface charge, siRNA loading efficiency and serum stability) of these ternary anionic lipoplexes were evaluated. Particle size, siRNA loading efficiency and serum stability correlated with the in vitro silencing efficiency of these lipoplexes. For example, large lipoplex particles (5/2.5/1 anionic lipid/Ca2+/siRNA molar charge ratio) showed less efficient silencing while absolute serum stability and high siRNA loading (1.3/2.5/1 anionic lipid/Ca2+/siRNA molar charge ratio), exhibited maximum silencing in breast cancer cells. The physicochemical properties also indicated that the siRNA exists in the complexed and/or encapsulated form within the lipoplexes, depending on the anionic lipid/siRNA charge ratio. Based on these studies a model representing lipid–siRNA association within the anionic lipoplexes prepared under various formulation conditions is proposed. Physicochemical attributes can be utilized to estimate in vitro activity of lipid–siRNA complexes and understand their morphology. [Copyright &y& Elsevier]

Abstract: siRNA based therapeutics is an emerging class of molecules with a high potential for fulfilling the promise of gene medicine. The high selectivity of siRNAs for their targets and subsequent gene ablation has been effectively demonstrated in a wide range of pre-clinical models. siRNA delivery in vivo has been most successfully achieved using lipid-based drug delivery systems. These lipid based formulations are designed to entrap siRNA molecules, ensure stability in in vitro and in vivo milieu, facilitate uptake, enhance cellular targeting, and facilitate delivery in the desired intracellular compartment. As more siRNA-based therapeutics enters the clinic with the associated regulatory scrutiny, there is a clear need to develop well-characterized systems that ensure consistent quality and thus reliable performance. Early clinical trials can be conducted using formulations with limited short-term stability manufactured on a small scale. However, a thorough understanding of the factors that influence the structure and stability of these particulate formulations is required to prevent any issues with optimization of large-scale industrial manufacturing, scale-up, and long-term shelf-life required to support large clinical trials and eventual market use. As newer targets for siRNA are identified and novel lipids are synthesized to optimize their in vivo efficiency, concomitant development of bio-physical methodologies that can improve understanding of the assembly and stability of these complex systems is critical. Along with bio-physical characterization, these assays are also required to reliably design, screen, develop and optimize formulations. Physicochemical characterization thus forms the basis of developing an effective analytical control strategy for siRNA delivery systems. In this review, analytical techniques used to characterize lipid-based siRNA delivery systems are discussed in detail. The importance of these physicochemical characterization techniques and analytical assays is explained. Case studies illustrating their use in siRNA formulation development and optimization are presented. [Copyright &y& Elsevier]

In this paper, we examine the time-dependent two-dimensional cable equation of fractional order in terms of the Caputo fractional derivative. This cable equation plays a vital role in diverse areas of electrophysiology and modeling neuronal dynamics. This paper conveys a precise semi-analytical method called the q-homotopy analysis transform method to solve the fractional cable equation. The proposed method is based on the conjunction of the q-homotopy analysis method and Laplace transform. We explained the uniqueness of the solution produced by the suggested method with the help of Banach’s fixed-point theory. The results obtained through the considered method are in the form of a series solution, and they converge rapidly. The obtained outcomes were in good agreement with the exact solution and are discussed through the 3D plots and graphs that express the physical representation of the considered equation. It shows that the proposed technique used here is reliable, well-organized and effective in analyzing the considered non-homogeneous fractional differential equations arising in various branches of science and engineering. [ABSTRACT FROM AUTHOR]

Highlights from the article: Transcatheter aortic valve implantation (TAVI) is a therapeutic option for patients with severe aortic stenosis (AS). Items on the TASQ capture QoL concerns reported by AS patients, suggesting this is a measure of relevant and meaningful outcomes for this patient population.