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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

The number of tumor cells in the tissue vs. time for a ‘good’ and ‘bad’ (with adjusted immune system parameters). For the ‘bad’ immune system case, we show two different runs.
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Fig4: The number of tumor cells in the tissue vs. time for a ‘good’ and ‘bad’ (with adjusted immune system parameters). For the ‘bad’ immune system case, we show two different runs.

Mentions: We start illustrating the method in two spatial dimensions. In Fig. 2 we show a snapshot of the considered tissue where we consider a domain with radius of 40 micrometer that is initially filled with endothelial cells. On four points of the domain, we assume that T-cells can invade the region where they neutralize the tumor cells. The epithelial cells are depicted as green cicles, whereas the tumor cells and T-cells, respectively, are represented by red and blue circles. We use the data from Tables 1 and 2 as input data, and we adjust the data for the immune system, where we increase the T-cell mobility, and appearance rate on the small blood vessels. To this extent, we model a ‘good’ immune system response by taking , and . The results for the T-cell counts are given in Fig. 3. It is clear that the T-cell counts are significantly higher for the ‘good’ case. Further, it is also clear to see that the number of tumor cells significantly reduces with a ‘good’ immune system response as to be expected. The ‘good’ immune system is able to battle the tumor in its early stages and the tumor cells disappear completely. It is further clear to see that the number of epithelial cells stays more or less constant with a ‘good’ immune system response, whereas if the immune system is poor then the number of epithelial cells decreases due to enhanced cell death as a result of the pressure that is experienced by the epithelial cells. To show the variation from the uncertainty in the model, we show the tumor cell fraction for two runs with identical parameters for the ‘bad’ immune system response, and one run with a ‘good’ immune system in Fig. 4. Although the variations between the two ‘bad’ immune system response are considerable, we see that the fraction ranges up to about 30 percent in both runs. Hence qualitatively the runs mimic similar behavior. The results for the ‘good’ immune system mimic a totally different behavior for the tumor cell fraction. The fraction stays around zero at all times. From these calculations, it is shown that a good immune system response could prevent cancers to initiate.Figure 2


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)

The number of tumor cells in the tissue vs. time for a ‘good’ and ‘bad’ (with adjusted immune system parameters). For the ‘bad’ immune system case, we show two different runs.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4495267&req=5

Fig4: The number of tumor cells in the tissue vs. time for a ‘good’ and ‘bad’ (with adjusted immune system parameters). For the ‘bad’ immune system case, we show two different runs.
Mentions: We start illustrating the method in two spatial dimensions. In Fig. 2 we show a snapshot of the considered tissue where we consider a domain with radius of 40 micrometer that is initially filled with endothelial cells. On four points of the domain, we assume that T-cells can invade the region where they neutralize the tumor cells. The epithelial cells are depicted as green cicles, whereas the tumor cells and T-cells, respectively, are represented by red and blue circles. We use the data from Tables 1 and 2 as input data, and we adjust the data for the immune system, where we increase the T-cell mobility, and appearance rate on the small blood vessels. To this extent, we model a ‘good’ immune system response by taking , and . The results for the T-cell counts are given in Fig. 3. It is clear that the T-cell counts are significantly higher for the ‘good’ case. Further, it is also clear to see that the number of tumor cells significantly reduces with a ‘good’ immune system response as to be expected. The ‘good’ immune system is able to battle the tumor in its early stages and the tumor cells disappear completely. It is further clear to see that the number of epithelial cells stays more or less constant with a ‘good’ immune system response, whereas if the immune system is poor then the number of epithelial cells decreases due to enhanced cell death as a result of the pressure that is experienced by the epithelial cells. To show the variation from the uncertainty in the model, we show the tumor cell fraction for two runs with identical parameters for the ‘bad’ immune system response, and one run with a ‘good’ immune system in Fig. 4. Although the variations between the two ‘bad’ immune system response are considerable, we see that the fraction ranges up to about 30 percent in both runs. Hence qualitatively the runs mimic similar behavior. The results for the ‘good’ immune system mimic a totally different behavior for the tumor cell fraction. The fraction stays around zero at all times. From these calculations, it is shown that a good immune system response could prevent cancers to initiate.Figure 2

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