1
|
Abbas I, SaifAlDien M, El-Bary AA, Egami RH, Elamin M. Theoretical estimation of the thermal damages of living tissues caused by laser irradiation in tumor thermal therapy. Heliyon 2024; 10:e29016. [PMID: 38617938 PMCID: PMC11015140 DOI: 10.1016/j.heliyon.2024.e29016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2023] [Revised: 02/29/2024] [Accepted: 03/28/2024] [Indexed: 04/16/2024] Open
Abstract
This article aims to provide theoretical predictions for the thermal reactions of human tissues during tumor thermotherapy when exposed to laser irradiation and an external heat source. For the construction of a theoretical study of bioheat transfer, the selection of a suitable thermal model capable of accurately predicting the required thermal responses is essential. The effect of heat production by heat treatment on a spherical multilayer tumor tissue is evaluated using this approach. Analytical solution for the non-homogenous differential equations is derived in the Laplace domain. The study examines the impact of thermal relaxation time on tissue temperature and the subsequent thermal damage. The numerical findings of thermal damage and temperatures are depicted in a graphical representation. This model explains laser treatment, physical events, metabolic support, and blood perfusion. The numerical outcomes of the recommended model are validated by comparing them to the literatures.
Collapse
Affiliation(s)
- Ibrahim Abbas
- Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt
| | - Mohamed SaifAlDien
- Department of Mathematics, Turabah University College, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia
| | - Alaa A El-Bary
- Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
| | - Ria H Egami
- Department of Mathematics, College of Science and Humanities in Sulail, Prince Sattam Bin Abdulaziz University, Saudi Arabia
| | - Mawahib Elamin
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
| |
Collapse
|
2
|
Farman M, Shehzad A, Nisar KS, Hincal E, Akgul A, Hassan AM. Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem. Sci Rep 2023; 13:22441. [PMID: 38105260 PMCID: PMC10725897 DOI: 10.1038/s41598-023-49806-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 12/12/2023] [Indexed: 12/19/2023] Open
Abstract
Marine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems.
Collapse
Affiliation(s)
- Muhammad Farman
- Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1107-2020, Lebanon.
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan.
| | - Aamir Shehzad
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
| | - Evren Hincal
- Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey
| | - Ali Akgul
- Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1107-2020, Lebanon
- Faculty of Arts and Science, Department of Mathematics, SIIRT University, Cyprus, Turkey
| | | |
Collapse
|
3
|
Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy. Symmetry (Basel) 2023. [DOI: 10.3390/sym15010250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods.
Collapse
|
4
|
Salihu N, Kumam P, Awwal AM, Sulaiman IM, Seangwattana T. The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery. PLoS One 2023; 18:e0281250. [PMID: 36928212 PMCID: PMC10019646 DOI: 10.1371/journal.pone.0281250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 01/17/2023] [Indexed: 03/18/2023] Open
Abstract
In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.
Collapse
Affiliation(s)
- Nasiru Salihu
- Center of Excellence in Theoretical and Computational Science, Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
- Department of Mathematics, Faculty of Sciences, Modibbo Adama University, Yola, Nigeria
- Gombe State University Mathematics for Innovative Research Group, Gombe State University, Gombe, Nigeria
| | - Poom Kumam
- Center of Excellence in Theoretical and Computational Science, Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
- KMUTT-Fixed Point Research Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- * E-mail:
| | - Aliyu Muhammed Awwal
- Center of Excellence in Theoretical and Computational Science, Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
- Gombe State University Mathematics for Innovative Research Group, Gombe State University, Gombe, Nigeria
- Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
| | - Ibrahim Mohammed Sulaiman
- School of Quantitative Sciences, Universiti Utara Malaysia, UUM Sintok, Kedah, Malaysia
- Institute of Strategic Industrial Decision Modelling, Universiti Utara Malaysia, Sintok, Kedah, Malaysia
| | - Thidaporn Seangwattana
- Faculty of Science Energy and Environment, King Mongkut’s University of Technology, North Bangkok, Rayong Campus, Rayong, Thailand
| |
Collapse
|
5
|
Khan NA, Sulaiman M, Alshammari FS. Analysis of heat transmission in convective, radiative and moving rod with thermal conductivity using meta-heuristic-driven soft computing technique. STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION : JOURNAL OF THE INTERNATIONAL SOCIETY FOR STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022; 65:317. [PMID: 36320454 PMCID: PMC9612628 DOI: 10.1007/s00158-022-03414-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 09/18/2022] [Accepted: 09/22/2022] [Indexed: 06/16/2023]
Abstract
ABSTRACT The present study analyzes the thermal attribute of conductive, convective, and radiative moving fin with thermal conductivity and constant velocity. The basic Darcy's model is utilized to formulate the governing equation for the problem, which is further nondimensionalized using certain variables. Moreover, an effective soft computing paradigm based on the approximating ability of the feedforword artificial neural networks (FANN's) and meta-heuristic approach of global and local search optimization techniques is developed to quantify the effect of variations in significant parameters such as ambient temperature, radiation-conduction number, Peclet number, nonconstant thermal conductivity, and initial temperature parameter on the temperature gradient of the rod. The results by the proposed FANN-AOA-SQP algorithm are compared with radial basis function approximation, Runge-Kutta-Fehlberg method and machine-learning algorithms. An extensive graphical and statistical analysis based on solution curves and errors such as absolute errors, mean square error, standard deviations in Nash-Sutcliffe efficiency, mean absolute deviations, and Theil's inequality coefficient are performed to show the accuracy, ease of implementation, and robustness of the design scheme.
Collapse
Affiliation(s)
- Naveed Ahmad Khan
- Department of Mathematics, Abdul Wali Khan University, Mardan, 23200 Pakistan
| | - Muhammad Sulaiman
- Department of Mathematics, Abdul Wali Khan University, Mardan, 23200 Pakistan
| | - Fahad Sameer Alshammari
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942 Saudi Arabia
| |
Collapse
|
6
|
Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling. Sci Rep 2022; 12:10761. [PMID: 35750796 PMCID: PMC9232503 DOI: 10.1038/s41598-022-14979-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 06/15/2022] [Indexed: 11/13/2022] Open
Abstract
The role of epidemiological models is crucial for informing public health officials during a public health emergency, such as the COVID-19 pandemic. However, traditional epidemiological models fail to capture the time-varying effects of mitigation strategies and do not account for under-reporting of active cases, thus introducing bias in the estimation of model parameters. To infer more accurate parameter estimates and to reduce the uncertainty of these estimates, we extend the SIR and SEIR epidemiological models with two time-varying parameters that capture the transmission rate and the rate at which active cases are reported to health officials. Using two real data sets of COVID-19 cases, we perform Bayesian inference via our SIR and SEIR models with time-varying transmission and reporting rates and via their standard counterparts with constant rates; our approach provides parameter estimates with more realistic interpretation, and 1-week ahead predictions with reduced uncertainty. Furthermore, we find consistent under-reporting in the number of active cases in the data that we consider, suggesting that the initial phase of the pandemic was more widespread than previously reported.
Collapse
|