Mathematical modeling of carcinoma growth with a dynamic change in the phenotype of cells

Krasnyakov, Ivan; Bratsun, Dmitry; Pismen, L. M.

doi:10.20537/2076-7633-2018-10-6-879-902

Cited by 2 publications

(3 citation statements)

References 29 publications

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“…В работах [14,15] авторы исследовали развитие гетерогенной опухоли. Для этого все клетки опухоли были классифицированы на разные фенотипы в зависимости от того, какое положение эти клетки занимали в опухоли.…”

Section: дискретная модель эпителия с индивидуальной динамикой клетокunclassified

“…Наиболее современные модели деформируемой клетки принимают во внимание геометрию и возможность ее деформации, обусловленную как внешними, так и внутренними силами [1,[12][13][14][15][16]. Учитывается также возможность появления активной силы, которая может быть результатом белковой команды, генерируемой экспрессией генов.…”

Section: Introductionunclassified

“…Задача о заживлении раны была рассмотрена в [13]. В работах [1,[14][15][16] авторами было изучено структурообразование при росте карциномы при помощи модели деформируемой клетки. При численной реализации использовались массивы из тысяч и десятков тысяч индивидуальных клеток.…”

Section: Introductionunclassified

See 2 more Smart Citations

Microscopic simulation of the chemomechanics of squamous cell tissue

Bratsun¹,

Bratsun²,

Krasnyakov³

2022

DREAM

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The development of computer technologies makes it possible to implement a mathematical model of tissue dynamics, which includes the behavior of individual cells. The paper describes a mathematical model of a quasi-two-dimensional tissue, which consists of cells represented by dynamically changing polygons. The model includes two important processes that mimic the properties of real cells, namely mitotic division and intercalation. An equation of motion based on the elastic potential energy is written for each vertex of the polygonal cell. In the course of evolution, the tissue tends to take a position corresponding to the minimum of potential energy. The model allows a simple extension to the case of the feedback between the biomechanical and chemical properties of the medium and the introduction of several competing tissue types. The results of numerical simulation of heterogeneous carcinoma of the solid type are given as an example. The prospects for the development of this approach to simulation are discussed.

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Section: дискретная модель эпителия с индивидуальной динамикой клетокunclassified

Section: Introductionunclassified

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Microscopic simulation of the chemomechanics of squamous cell tissue

Bratsun¹,

Bratsun²,

Krasnyakov³

2022

DREAM

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Mathematical Modeling of Invasive Carcinoma: Biomechanics of Small Groups of Cancer Cells

Krasnyakov

Bratsun

Pismen

2021

J. Phys.: Conf. Ser.

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According to the latest research, cancer is a complex biological system that evolves over time and space. This means that cancer cells differ from each other in their functions in the tumor. They engage in various interactions with the microenvironment and compete for available nutrients to survive. The main problem of mathematical modeling in oncology today is the heterogeneity of a typical malignant neoplasm. In this work, we propose a chemomechanical model of the pattern formation of small groups of cancer cells of invasive carcinoma of a non-special type (IC NST). The model assumes that carcinoma is a heterogeneous formation, which consists of cells of different phenotypes performing different tasks to maintain the existence of the tumor. In the model, each cell is represented as a deformable polygon that changes its shape and size as the tissue develops. Numerical modeling implements various subtypes of IC NST structures. These patterns are compared with morphological structures identified in clinical studies.

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Mathematical modeling of carcinoma growth with a dynamic change in the phenotype of cells

Cited by 2 publications

References 29 publications

Microscopic simulation of the chemomechanics of squamous cell tissue

Microscopic simulation of the chemomechanics of squamous cell tissue

Mathematical Modeling of Invasive Carcinoma: Biomechanics of Small Groups of Cancer Cells

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