Time Series Analysis For Modeling Of Glioma Growth In Response To Radiotherapy

Jesus, Juliana Cunha de; Christo, Eliane da Silva; Garcia, Vanessa da Silva; Alvarez, Gustavo Benitez

doi:10.1109/tla.2016.7459646

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…In other words, it is observed that for the input data considered in these simulations, the saturation process in glioma growth starts approximately after 1 year, and this non-linear term can be crucial to adequately estimate the patient's survival time. Although this term was known to us, it had not been considered in our previous studies, since it was not included in the analyzes carried out by Barbosa et al (2019), Jesus et al (2014), Silva et al (2016) and Souza et al (2015).…”

Section: Influence Of the Nonlinear Term On Cell Proliferationmentioning

confidence: 99%

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Reactive-Advective-Diffusive Models for the Growth of Gliomas Treated with Radiotherapy

Machado

Alvarez

Lobão

2023

Semin., Ciênc. Exatas Tecnol.

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Gliomas are malignant brain tumors responsible for 50% of primary human brain cancer cases. They have a combination of rapid growth and invasiveness, and high fatality rates with a median survival time of one year. Mathematical models that describe its growth have helped to improve treatment. In this paper, a combined model formed by terms of two other models known in the literature is analyzed. The combined model is a Reactive-Advective-Diffusive partial differential equation, which is solved by combining the finite difference method, the Crank-Nicolson method and the upwind method. Logistic growth is used for cell proliferation ensuring a saturation threshold for glioma growth, which is crucial to properly estimate patient survival time. The well-known linear-quadratic radiobiological model is used to describe cell death due to radiotherapy treatment. Two initial conditions are compared in the simulations, indicating the need for further studies to have a model as close as possible to reality. Simulation results are shown for four scenarios: no radiotherapy, application of a single dose, and two dose fractionation schemes.

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Section: Influence Of the Nonlinear Term On Cell Proliferationmentioning

confidence: 99%

“…Two mathematical models that describe the growth of gliomas were proposed in Leder et al (2014), Rockne et al (2009) and Swanson et al (2003). Both models were analyzed in Barbosa et al (2019), Silva et al (2016) and Souza et al (2015), and new approaches based on time series were suggested in Jesus et al (2014) and Silva et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Reactive-Advective-Diffusive Models for the Growth of Gliomas Treated with Radiotherapy

Machado

Alvarez

Lobão

2023

Semin., Ciênc. Exatas Tecnol.

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Fault Location in Power Transmission Lines using Autocorrelation Function

Souza¹,

Christo²,

Almeida³

et al. 2018

IJAERS

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An electrical power system is subject to constant adversities due to its complexity, sensitivity and physical dimensions. Special emphasis is given to transmission lines (TL) that are the most vulnerable elements of an electrical system. Although most of the occurrences of distortions in the voltage signals from atmospheric discharges and overload are not detrimental to the energy supply, it is important to have control of these currents, since this allows the classification of the fault type and its geometric location on the transmission line. This study aims to compare different fault situations in a transmission line and to verify changes in time series models (TS). This study was carried out through computational tests performed with MatLAB®and RStudio® software. A total of 272faults were simulated in different situations. The obtained results were compared with the Traveling Wave Theory (TWT), another quite widespread fault localization technique. The above study revealed the applicability of time series in oscillographic data of fault situations in transmission lines with errors lower than 1.25%.

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Time series forecasting using ARIMA for modeling of glioma growth in response to radiotherapy

et al. 2021

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In present days, the growing number of people suffering from cancer has been a major cause for concern worldwide. Glioblastoma in particular, are primary tumors in glial cells located in the central nervous system. Because of this sensitive location, mathematical models have been studied and developed as alternative tools for analyzing tumor growth rates, assisting on the decision-making process for treatment dosage, without exposing the patient’s life. This paper presents two time series models to estimate the growth rate of glioblastoma in response to ionizing radiotherapy treatment. The results obtained indicate that the proposed time series methods attain predictions with a Mean Absolute Percentual Error (MAPE) of approximately 1% to 4%, and simulations show that the Autoregressive Integrated Moving Average (ARIMA) method surpasses the Holt method based on the Mean Square Error (MSE) and MAPE values obtained. Furthermore, the results show that the time series method is applicable to data from two different mathematical models for glioblastoma growth.

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Time Series Analysis For Modeling Of Glioma Growth In Response To Radiotherapy

Cited by 3 publications

References 12 publications

Reactive-Advective-Diffusive Models for the Growth of Gliomas Treated with Radiotherapy

Reactive-Advective-Diffusive Models for the Growth of Gliomas Treated with Radiotherapy

Fault Location in Power Transmission Lines using Autocorrelation Function

Time series forecasting using ARIMA for modeling of glioma growth in response to radiotherapy

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