A parabolic–hyperbolic system modeling the tumor growth with angiogenesis

Shen, Haishuang; Wei, Xuemei

doi:10.1016/j.nonrwa.2021.103456

Nonlinear Analysis: Real World Applications

2022

DOI: 10.1016/j.nonrwa.2021.103456

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A parabolic–hyperbolic system modeling the tumor growth with angiogenesis

Haishuang Shen

Xuemei Wei

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2024

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Numerical and statistical approach on chemotaxis-haptotaxis model for cancer cell invasion of tissue

Pekmen,

Yirmili

2024

MMC

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<abstract><p>In this study, a one-dimensional chemotaxis-haptotaxis model of cancer cell invasion of tissue was numerically and statistically investigated. In the numerical part, the time dependent, nonlinear, triplet governing dimensionless equations consisting of cancer cell (CC) density, extracellular matrix (ECM) density, and urokinase plasminogen activator (uPA) density were solved by the radial basis function (RBF) collocation method both in time and space discretization. In the statistical part, mean CC density, mean ECM density, and mean uPA density were modeled by two different machine learning approaches. The datasets for modeling were originated from the numerical results. The numerical method was performed in a set of parameter combinations by parallel computing and the data in case of convergent combinations were stored. In this data, inputs consisted of selected time values up to a maximum time value and converged parameter values, and outputs were mean CC, mean ECM, and mean uPA. The whole data was divided randomly into train and test data. Trilayer neural network (TNN) and multilayer adaptive regression splines (Mars) model the train data. Then, the models were tested on test data. TNN modeling resulting in terms of mean squared error metric was better than Mars results.</p></abstract>

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Numerical and statistical approach on chemotaxis-haptotaxis model for cancer cell invasion of tissue

Pekmen,

Yirmili

2024

MMC

View full text Add to dashboard Cite

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A parabolic–hyperbolic system modeling the tumor growth with angiogenesis

Cited by 1 publication

References 24 publications

Numerical and statistical approach on chemotaxis-haptotaxis model for cancer cell invasion of tissue

Numerical and statistical approach on chemotaxis-haptotaxis model for cancer cell invasion of tissue

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