A mathematical model and numerical solution for brain tumor derived using fractional operator

Ganji, R.M.; Jafari, Hossein; Moshokoa, Seithuti P.; Nkomo, Ntando

doi:10.1016/j.rinp.2021.104671

Cited by 58 publications

(12 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other works, such as McNamara et al [11] shows this tendency of the neuronal circuits to stabilize different input signals, and its implication in diseases such as Parkinson. This stability also have implications in disorders generated by Glioblastoma multiforme [5], which generates a variation of the mechanical loads in certain regions of the brain. This tendency of the brain has been modelled [12] [3] to reproduce the stabilization of signals through noise inserted in the neuronal circuit.…”

Section: Methodology and Resultsmentioning

confidence: 99%

Numerical reproduction of the Sherrington-Adrian observations through a community of McCulloch-Pitts neurons with plastic remodelling

Irastorza-Valera,

Benítez,

Montans

et al. 2023

Preprint

View full text Add to dashboard Cite

Neurons form a highly complex network that produces cognition from simple associative rules. From previous results, this work shows the natural capability of the numerical network produced to modulate the output signal with independence of the intensity of the stimuli. Moreover, the plastic remodelling implemented in the model is capable to change the latency of a wide range of stimuli to synchronize them and adjust to a required delay of the signal.

show abstract

Section: Methodology and Resultsmentioning

confidence: 99%

Numerical reproduction of the Sherrington-Adrian observations through a community of McCulloch-Pitts neurons with plastic remodelling

Irastorza-Valera,

Benítez,

Montans

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…At present, the authors are investigating the possibility of applying the discussed method for solving the differentialintegral-algebraic equations and the integral equations with retarded argument. Many interesting and important problems are also described by means of the fractional differential equations (see for example [19,20]), possible to solve by applying the DTM method as well.…”

Section: Discussionmentioning

confidence: 99%

“…Similar to the previous example, the greatest attention should be paid to the DTM method. This time, by using, among others, the properties (3), ( 4), ( 6)- (10), we transform the system (20) with conditions (21) into the following system for k = 0, 1, 2, . .…”

Section: Examplementioning

confidence: 99%

Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

Hetmaniok

Pleszczyński

2022

Mathematics

View full text Add to dashboard Cite

Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat).

show abstract

“…The fractional approach has a better fit for COVID-19 modeling with real data of different cities [ 43 ]. Some other researchers have explored cancer, Covid19, drug resistance, tumor, and zooplankton dynamics modeling with fractional approach [ 44 – 48 ]. From this literature exploration, it is observed that the ORAI calcium flux is not taken into consideration to examine the neuronal calcium flux.…”

Section: Introductionmentioning

confidence: 99%

To study the effect of ER flux with buffer on the neuronal calcium

Vatsal,

Jha,

Singh

2023

Eur. Phys. J. Plus

View full text Add to dashboard Cite

Calcium signaling is decisive for cellular functions. This calcium random walk stipulates neuronal functions. Calcium concentration could provoke gene transcription, apoptosis, neuronal plasticity, etc. A malformation in calcium could change the neuron’s intracellular behavior. Calcium concentration balancing is a complex cellular mechanism. This occurrence can be handled with the Caputo fractional reaction–diffusion equation. In this mathematical modeling, we have included the STIM-Orai mechanism and Endoplasmic Reticulum (ER) flux, Inositol Triphosphate Receptor (IPR), SERCA, plasma membrane flux, voltage-gated calcium entry, and different buffer interactions. A hybrid integral transform and Green’s function approach were taken to solve the initial boundary problem. A closed-form solution of a Mittag-Leffler family function plotted using MATLAB software. Different parameters impact changes in the spatiotemporal behavior of the calcium concentration. Specific roles of organelles involved in Alzheimer’s disease-affected neurons are computed. Ethylene glycol tetraacetic acid (EGTA), 1,2-bis(o-aminophenoxy)ethane N,N,N,N-tetraacetic acid (BAPTA), and S100B protein effects are also observed. In all simulations, we can say S100B and the STIM-Orai effect cannot be neglected. This model lights up the different approaches for calcium signaling pathway simulation. As a consequence, we determine that a generalized reaction–diffusion approach is a better fit realistic model.

show abstract

A mathematical model and numerical solution for brain tumor derived using fractional operator

Cited by 58 publications

References 36 publications

Numerical reproduction of the Sherrington-Adrian observations through a community of McCulloch-Pitts neurons with plastic remodelling

Numerical reproduction of the Sherrington-Adrian observations through a community of McCulloch-Pitts neurons with plastic remodelling

Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

To study the effect of ER flux with buffer on the neuronal calcium

Contact Info

Product

Resources

About