Nonlinear Modeling with Mammographic Evidence of Carcinoma

K. Drucis; M. Kolev; W. Majda; B. Zubik-Kowal

doi:10.1016/j.nonrwa.2010.05.017

Nonlinear Modeling with Mammographic Evidence of Carcinoma

K. Drucis, M. Kolev, W. Majda, B. Zubik-Kowal

Mathematics Department

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

The goal of this paper is to apply oncological data for mathematical modeling of breast cancer progression. The studied model is composed of nonlinear partial integro-differential equations, which are formulated with unknown parameters. It is demonstrated that it is possible to find such parameter values for the nonlinear model so that its solutions correspond to the oncological data, therefore showing the potential and extending the applications of the model to breast cancer. The nonlinear model equations are solved numerically and the numerical results confirm the oncological data.

Original language	American English
Pages (from-to)	4326-4334
Number of pages	9
Journal	Nonlinear Analysis: Real World Applications
Volume	11
Issue number	5
DOIs	https://doi.org/10.1016/j.nonrwa.2010.05.017
State	Published - Oct 2010

Keywords

Active particles
Breast tumor progression
Kinetic theory
Mammographic data
Mathematical model
Nonlinear integro-differential equations
Numerical simulations

EGS Disciplines

Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1016/j.nonrwa.2010.05.017

Cite this

@article{9e3c8c85ef20432da2384e1df3e9d56b,

title = "Nonlinear Modeling with Mammographic Evidence of Carcinoma",

abstract = " The goal of this paper is to apply oncological data for mathematical modeling of breast cancer progression. The studied model is composed of nonlinear partial integro-differential equations, which are formulated with unknown parameters. It is demonstrated that it is possible to find such parameter values for the nonlinear model so that its solutions correspond to the oncological data, therefore showing the potential and extending the applications of the model to breast cancer. The nonlinear model equations are solved numerically and the numerical results confirm the oncological data.",

keywords = "Active particles, Breast tumor progression, Kinetic theory, Mammographic data, Mathematical model, Nonlinear integro-differential equations, Numerical simulations",

author = "K. Drucis and M. Kolev and W. Majda and B. Zubik-Kowal",

year = "2010",

month = oct,

doi = "10.1016/j.nonrwa.2010.05.017",

language = "American English",

volume = "11",

pages = "4326--4334",

number = "5",

}

TY - JOUR

T1 - Nonlinear Modeling with Mammographic Evidence of Carcinoma

AU - Drucis, K.

AU - Kolev, M.

AU - Majda, W.

AU - Zubik-Kowal, B.

PY - 2010/10

Y1 - 2010/10

N2 - The goal of this paper is to apply oncological data for mathematical modeling of breast cancer progression. The studied model is composed of nonlinear partial integro-differential equations, which are formulated with unknown parameters. It is demonstrated that it is possible to find such parameter values for the nonlinear model so that its solutions correspond to the oncological data, therefore showing the potential and extending the applications of the model to breast cancer. The nonlinear model equations are solved numerically and the numerical results confirm the oncological data.

AB - The goal of this paper is to apply oncological data for mathematical modeling of breast cancer progression. The studied model is composed of nonlinear partial integro-differential equations, which are formulated with unknown parameters. It is demonstrated that it is possible to find such parameter values for the nonlinear model so that its solutions correspond to the oncological data, therefore showing the potential and extending the applications of the model to breast cancer. The nonlinear model equations are solved numerically and the numerical results confirm the oncological data.

KW - Active particles

KW - Breast tumor progression

KW - Kinetic theory

KW - Mammographic data

KW - Mathematical model

KW - Nonlinear integro-differential equations

KW - Numerical simulations

UR - http://www.scopus.com/inward/record.url?scp=77955509070&partnerID=8YFLogxK

UR - https://scholarworks.boisestate.edu/math_facpubs/32

U2 - 10.1016/j.nonrwa.2010.05.017

DO - 10.1016/j.nonrwa.2010.05.017

M3 - Article

SN - 1468-1218

VL - 11

SP - 4326

EP - 4334

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 5

ER -

Nonlinear Modeling with Mammographic Evidence of Carcinoma

Abstract

Keywords

EGS Disciplines

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this