# Mathematical model of the blocked breast duct

Eugeny P. Kolpak, Inna S. Frantsuzova, Elizaveta O. Evmenova

Research output

### Abstract

Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

Original language English 1554-1558 Drug Invention Today 12 7 Published - 1 Jul 2019

### Fingerprint

Breast
Theoretical Models
Growth
Breast Neoplasms
Recurrence
Neoplasms

### Scopus subject areas

• Drug Discovery

### Cite this

Kolpak, E. P., Frantsuzova, I. S., & Evmenova, E. O. (2019). Mathematical model of the blocked breast duct. Drug Invention Today, 12(7), 1554-1558.
Kolpak, Eugeny P. ; Frantsuzova, Inna S. ; Evmenova, Elizaveta O. / Mathematical model of the blocked breast duct. In: Drug Invention Today. 2019 ; Vol. 12, No. 7. pp. 1554-1558.
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Kolpak, EP, Frantsuzova, IS & Evmenova, EO 2019, 'Mathematical model of the blocked breast duct', Drug Invention Today, vol. 12, no. 7, pp. 1554-1558.

Mathematical model of the blocked breast duct. / Kolpak, Eugeny P.; Frantsuzova, Inna S.; Evmenova, Elizaveta O.

In: Drug Invention Today, Vol. 12, No. 7, 01.07.2019, p. 1554-1558.

Research output

TY - JOUR

T1 - Mathematical model of the blocked breast duct

AU - Kolpak, Eugeny P.

AU - Frantsuzova, Inna S.

AU - Evmenova, Elizaveta O.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

AB - Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

KW - Differential equations

KW - Mathematical model

KW - Numerical methods

KW - Stability

KW - Tumor

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M3 - Article

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VL - 12

SP - 1554

EP - 1558

JO - Drug Invention Today

JF - Drug Invention Today

SN - 0975-7619

IS - 7

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Kolpak EP, Frantsuzova IS, Evmenova EO. Mathematical model of the blocked breast duct. Drug Invention Today. 2019 Jul 1;12(7):1554-1558.