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The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods., Competing Interests: The authors declare that they have no competing interests that could have appeared to influence the work reported in this paper., (Copyright: © 2024 Sherief et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

In this manuscript, the dynamic response of a long cylinder subjected to an asymmetric thermal shock is investigated within the framework of generalized micropolar thermoelasticity. The displacement and micro-rotation are assumed to vanish at the surface. Laplace transformation techniques are used to solve the problem. The solution is obtained in the transformed field using an innovative direct approach. Furthermore, we obtain the inverse transformations using a numerical method based on Fourier expansion. The obtained results are carefully presented through graphical representations and discussed extensively across different relaxation time values. It is evident that the relaxation time parameter significantly influences all the distributions. The displacement distributions are always continuous, whereas all other functions, including temperature variation, stress distribution, and micro-rotation, exhibit discontinuity at the wave front. The results obtained hold significant importance in various technological applications and in the manufacturing of mechanical components., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Sherief et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Nanostructured lipid carriers (NLCs) have been proven to significantly improve the bioavailability and efficacy of many drugs; however, they still have many limitations. These limitations could hinder their potential for enhancing the bioavailability of poorly water-soluble drugs and, therefore, require further amendments. From this perspective, we have investigated how the chitosanization and PEGylation of NLCs affected their ability to function as a delivery system for apixaban (APX). These surface modifications could enhance the ability of NLCs to improve the bioavailability and pharmacodynamic activity of the loaded drug. In vitro and in vivo studies were carried out to examine APX-loaded NLCs, chitosan-modified NLCs, and PEGylated NLCs. The three nanoarchitectures displayed a Higuchi-diffusion release pattern in vitro, in addition to having their vesicular outline proven via electron microscopy. PEGylated and chitosanized NLCs retained good stability over 3 months, versus the nonPEGylated and nonchitosanized NLCs. Interestingly, APX-loaded chitosan-modified NLCs displayed better stability than the APX-loaded PEGylated NLCs, in terms of mean vesicle size after 90 days. On the other hand, the absorption profile of APX (AUC 0-inf ) in rats pretreated with APX-loaded PEGylated NLCs (108.59 µg·mL -1 ·h -1 ) was significantly higher than the AUC 0-inf of APX in rats pretreated with APX-loaded chitosan-modified NLCs (93.397 µg·mL -1 ·h -1 ), and both were also significantly higher than AUC 0-inf of APX-Loaded NLCs (55.435 µg·mL -1 ·h -1 ). Chitosan-coated NLCs enhanced APX anticoagulant activity with increased prothrombin time and activated partial thromboplastin time by 1.6- and 1.55-folds, respectively, compared to unmodified NLCs, and by 1.23- and 1.37-folds, respectively, compared to PEGylated NLCs. The PEGylation and chitosanization of NLCs enhanced the bioavailability and anticoagulant activity of APX over the nonmodified NLCs; this highlighted the importance of both approaches.

Apixaban (Apx), an oral anticoagulant drug, is a direct factor Xa inhibitor for the prophylaxis against venous thromboembolism. Apx has limited oral bioavailability and poor water solubility. The goal of this study was to improve the formulation of an Apx-loaded nanostructured lipid carrier (NLC) to increase its bioavailability and effectiveness. As solid lipid, liquid lipid, hydrophilic, and lipophilic stabilizers, stearic acid, oleic acid, Tween 80, and lecithin were used, respectively. Utilizing Box-Behnken design, the effects of three factors on NLC particle size (Y 1 ), zeta potential (Y 2 ), and entrapment efficiency percent (Y 3 ) were examined and optimized. The optimized formula was prepared, characterized, morphologically studied, and pharmacokinetically and pharmacodynamically assessed. The observed responses of the optimized Apx formula were 315.2 nm, -43.4 mV, and 89.84% for Y 1 , Y 2 , and Y 3 , respectively. Electron microscopy revealed the homogenous spherical shape of the NLC particles. The in vivo pharmacokinetic study conducted in male Wistar rats displayed an increase in AUC and C max by 8 and 2.67 folds, respectively, compared to oral Apx suspension. Moreover, the half-life was increased by 1.94 folds, and clearance was diminished by about 8 folds, which makes the NLC formula a promising sustained release system. Interestingly, the pharmacodynamic results displayed the superior effect of the optimized formula over the drug suspension with prolongation in the cuticle bleeding time. Moreover, both prothrombin time and activated partial thromboplastin time are significantly increased. So, incorporating Apx in an NLC formula significantly enhanced its oral bioavailability and pharmacodynamic activity.