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Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation.

Vermolen FJ, Meijden RP, Es Mv, Gefen A, Weihs D - Ann Biomed Eng (2015)

Bottom Line: The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively.Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account.The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations.

View Article: PubMed Central - PubMed

Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands, F.J.Vermolen@tudelft.nl.

ABSTRACT
A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.

No MeSH data available.


Related in: MedlinePlus

Side view using confocal imaging of cells interacting with a impenetrable, polyacrylamide gel substrate with elastic modulus of 2300 Pa. The white are particles marking the gel surface location, green is microtubules, and blue is the cell nucleus. A A low metastatic potential breast cancer cell (MDA-MB-468) applies pressure to the substrate and indents it, likely in attempted penetration. B A benign breast cell (MCF-10A) will adhere to the substrate, flatten out slightly, but will not significantly deform the substrate. Scale bar is 10 μm.
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Fig11: Side view using confocal imaging of cells interacting with a impenetrable, polyacrylamide gel substrate with elastic modulus of 2300 Pa. The white are particles marking the gel surface location, green is microtubules, and blue is the cell nucleus. A A low metastatic potential breast cancer cell (MDA-MB-468) applies pressure to the substrate and indents it, likely in attempted penetration. B A benign breast cell (MCF-10A) will adhere to the substrate, flatten out slightly, but will not significantly deform the substrate. Scale bar is 10 μm.

Mentions: In addition to tumor initiation, the model is capable of monitoring the pressure applied by the tumor-cells on the small blood vessel walls. If the pressure exceeds a certain threshold value, then the cell is allowed to penetrate into the vessel wall, which is assigned a quantitative likelihood for the successful spreading of an initiated tumor at other organs in the body. Figure 11 shows that while cancer cells will attempt to invade a soft substrate, benign cells will simply attach to it.Figure 11


Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation.

Vermolen FJ, Meijden RP, Es Mv, Gefen A, Weihs D - Ann Biomed Eng (2015)

Side view using confocal imaging of cells interacting with a impenetrable, polyacrylamide gel substrate with elastic modulus of 2300 Pa. The white are particles marking the gel surface location, green is microtubules, and blue is the cell nucleus. A A low metastatic potential breast cancer cell (MDA-MB-468) applies pressure to the substrate and indents it, likely in attempted penetration. B A benign breast cell (MCF-10A) will adhere to the substrate, flatten out slightly, but will not significantly deform the substrate. Scale bar is 10 μm.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4495267&req=5

Fig11: Side view using confocal imaging of cells interacting with a impenetrable, polyacrylamide gel substrate with elastic modulus of 2300 Pa. The white are particles marking the gel surface location, green is microtubules, and blue is the cell nucleus. A A low metastatic potential breast cancer cell (MDA-MB-468) applies pressure to the substrate and indents it, likely in attempted penetration. B A benign breast cell (MCF-10A) will adhere to the substrate, flatten out slightly, but will not significantly deform the substrate. Scale bar is 10 μm.
Mentions: In addition to tumor initiation, the model is capable of monitoring the pressure applied by the tumor-cells on the small blood vessel walls. If the pressure exceeds a certain threshold value, then the cell is allowed to penetrate into the vessel wall, which is assigned a quantitative likelihood for the successful spreading of an initiated tumor at other organs in the body. Figure 11 shows that while cancer cells will attempt to invade a soft substrate, benign cells will simply attach to it.Figure 11

Bottom Line: The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively.Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account.The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations.

View Article: PubMed Central - PubMed

Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands, F.J.Vermolen@tudelft.nl.

ABSTRACT
A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.

No MeSH data available.


Related in: MedlinePlus