Numerical analysis of Galerkin meshless method for parabolic equations of tumor angiogenesis problem

Jahanshahi, Hadi; Shanazari, Kamal; Mesrizadeh, Mehdi; Soradi‐Zeid, Samaneh; Gómez-Aguilar, J. F.

doi:10.1140/epjp/s13360-020-00716-x

Cited by 26 publications

(3 citation statements)

References 38 publications

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“…Tumor angiogenesis refers to the formation of new blood vessels by the differentiation of endothelial cells from the already existing tumor vascular network. In the absence of tumor angiogenesis, the tumor grows only 1-2 mm in diameter and is in a dormant state (6). The progressive growth of solid tumors depends mainly on the tumor vascular network generated by their induction, and the microvascular network also provides the necessary pathway for tumor bloodstream metastasis (7).…”

Section: Original Articlementioning

confidence: 99%

Effects of Stellera chamaejasme on microvascular density and apoptosis of cancer cells in a rat bladder tumor model

Huang¹,

Zhang²,

Zhang³

et al. 2022

Transl Androl Urol

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Background: Investigate the effects of Stellera chamaejasme on microvascular density and apoptosis of cancer cells in rat bladder tumor models. Methods:The bladder tumor model of 75 specific pathogen-free (SPF)-grade Sprague-Dawley (SD) rats aged 5-6 weeks was established by n-methyl-N-nitrosourea (MNU) bladder perfusion induction, and the model rats were randomly divided into model group, low-dose (L-dose) group, medium-dose (M-dose) group, high-dose (H-dose) group, and positive drug (HCPT) group. L-dose group, M-Dose group, and H-dose group were treated with 5 g/kg, 10 g/kg, and 20 g/kg, respectively. The HCPT group was treated with 2 mg/kg hydroxycamptothecin at 1 mL/kg once a week and the model group were treated with the same amount of normal saline for 4 weeks. The quality of bladder cancer tissues in each group was measured.The pathological changes and microvascular density of bladder tissues were observed, and the apoptosis rate of vascular endothelial growth factor (VEGF), tumor tissue and the protein expression levels of factor associated suicide (Fas), factor associated suicide ligand (FasL) and Caspase3 in bladder tissues were detected.Results: Bladder cancer was induced 14 weeks after initial bladder perfusion with MNU. In the model group, epithelial cells of bladder tissue showed atypically hyperplasia with various sizes and disorders. After treatment with Stellera chamaejasme, the hematoxylin-eosin (HE) scores, bladder weight, microvascular density, and VEGF were significantly decreased, and the tumor inhibition rate, cell apoptosis, and the expression of apoptosis-related proteins Fas, FasL, and Caspase3 were significantly increased in the bladder tissue. The above changes were dose-dependent with Stellera chamaejasme.Conclusions: MNU can be used to prepare a rat bladder cancer model. Stellera chamaejasme has a good therapeutic effect on rat bladder cancer, which may inhibit the progression of bladder cancer by inhibiting micro-angiogenesis and inducing the apoptosis of bladder tumor cells.

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Section: Original Articlementioning

confidence: 99%

Effects of Stellera chamaejasme on microvascular density and apoptosis of cancer cells in a rat bladder tumor model

Huang¹,

Zhang²,

Zhang³

et al. 2022

Transl Androl Urol

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“…Mathematical models have been used as valuable tools in understanding the transmission dynamics of cancers [10]. Actually, mathematical modeling could play a pivotal role in the understanding of the disease's dynamics [11][12][13][14][15]. One common approach to modeling cancer is to use ordinary differential equations (ODEs), which are used to describe the time evolution of a system.…”

Section: Introductionmentioning

confidence: 99%

A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

et al. 2023

Self Cite

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A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–Fabrizio fractional-order model of cancer chemotherapy treatment was elaborated and analyzed. A fix-point theorem and an iterative method were implemented to prove the existence and uniqueness of the solutions of the proposed model. Afterward, in order to control cancer through chemotherapy treatment, a fuzzy-reinforcement learning-based control method that uses the State-Action-Reward-State-Action (SARSA) algorithm was proposed. Finally, so as to assess the performance of the proposed control method, the simulations were conducted for young and elderly patients and for ten simulated patients with different parameters. Then, the results of the proposed control method were compared with Watkins’s Q-learning control method for cancer chemotherapy drug dosing. The results of the simulations demonstrate the superiority of the proposed control method in terms of mean squared error, mean variance of the error, and the mean squared of the control action—in other words, in terms of the eradication of tumor cells, keeping normal cells, and the amount of usage of the drug during chemotherapy treatment.

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“…Also, in the current study, a new variable fractionalorder network is proposed for modeling of hepatitis B. By studying the factional order [45][46][47][48][49][50][51][52][53][54][55][56] or variable fractional-order network, we aim to consider the impact of the interaction between different communities on the disease rate in different societies. The relationships and travels between two countries, for instance, will definitely affect the rate of diseases in both of them.…”

Section: Introductionmentioning

confidence: 99%

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

Din

Yusuf

et al. 2022

Eur. Phys. J. Spec. Top.

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This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter Rs, followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get Rs less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have Rs > 1. For the case Rs > 1, adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

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Numerical analysis of Galerkin meshless method for parabolic equations of tumor angiogenesis problem

Cited by 26 publications

References 38 publications

Effects of Stellera chamaejasme on microvascular density and apoptosis of cancer cells in a rat bladder tumor model

Effects of Stellera chamaejasme on microvascular density and apoptosis of cancer cells in a rat bladder tumor model

A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

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