A study of cryosurgery of lung cancer using Modified Legendre wavelet Galerkin method

Kumar, Mukesh; Upadhyay, Subrahamanyam; Rai, K.N.

doi:10.1016/j.jtherbio.2018.10.012

Cited by 18 publications

(5 citation statements)

References 20 publications

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“…Their theoretical study shows that large blood vessels (>4mm diameter) significantly affect the shape of the iceball, as the heat blood flow heat prevents the cold from propagating. Other studies describe advanced models validated in gel [12], or tailored to other organs, e.g., the prostate [13] and the lungs [14,15].…”

Section: State Of the Artmentioning

confidence: 99%

GPU-based 3D iceball modeling for fast cryoablation simulation and planning

et al. 2019

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Section: State Of the Artmentioning

confidence: 99%

GPU-based 3D iceball modeling for fast cryoablation simulation and planning

et al. 2019

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“…2021 ; Jaros and Kusano 2014 ; Kumar et al. 2018 ; Odibat 2019 ), the authors have investigated the fractional differential equations in different branches of sciences including mathematics, physics, bioscience, and engineering. Xu et al.…”

Section: Introductionmentioning

confidence: 99%

Optimal Approximation of Fractional Order Brain Tumor Model Using Generalized Laguerre Polynomials

et al. 2023

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A brain tumor occurs when abnormal cells form within the brain. Glioblastoma (GB) is an aggressive and fast-growing type of brain tumor that invades brain tissue or spinal cord. GB evolves from astrocytic glial cells in the central nervous system. GB can occur at almost any age, but the occurrence increases with advancing age in older adults. Its symptoms may include nausea, vomiting, headaches, or even seizures. GB, formerly known as glioblastoma multiforme, currently has no cure with a high rate of resistance to therapy in clinical treatment. However, treatments can slow tumor progression or alleviate the signs and symptoms. In this paper, a fractional order brain tumor model was considered. The optimal solution of the model was obtained using an optimization method based on operational matrices. The solution to the problem under study was expanded in terms of generalized Laguerre polynomials (GLPs). The study problem was shifted to a system of nonlinear algebraic equations by the use of Lagrange multipliers combined with operational matrices based on GLPs. The analysis of convergence was discussed. In the end, some numerical examples were presented to justify theoretical statements along with the patterns of biological behavior.

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“…Partial differential equations (PDE) are used to describe different types of phenomena in biosciences (Gupta et al 2013;Shangerganesh et al 2019). Recently, Kumar et al (2018) addressed initial-value boundary problems in hyperbolic PDE in the cryosurgery of lung cancer. The bio-heat transfer during cryosurgery of lung cancer was studied using the Lagrange wavelet Galerkin method to convert the problem into generalized systems of Sylvester equations.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

et al. 2020

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This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractionalorder partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

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A study of cryosurgery of lung cancer using Modified Legendre wavelet Galerkin method

Cited by 18 publications

References 20 publications

GPU-based 3D iceball modeling for fast cryoablation simulation and planning

GPU-based 3D iceball modeling for fast cryoablation simulation and planning

Optimal Approximation of Fractional Order Brain Tumor Model Using Generalized Laguerre Polynomials

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

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