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Modeling invasion of metastasizing cancer cells to bone marrow utilizing ecological principles.

Chen KW, Pienta KJ - Theor Biol Med Model (2011)

Bottom Line: These modified equations allow a more flexible way to model the space competition between the two cell species.The ability to model initial density, metastatic seeding into the bone marrow and growth once the cells are present, and movement of cells out of the bone marrow niche and apoptosis of cells are all aspects of the adapted equations.These equations are currently being applied to clinical data sets for verification and further refinement of the models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Internal Medicine, The University of Michigan, 7308 CCC, 1500 E, Medical Center Drive, Ann Arbor, MI 48109, USA. kpienta@umich.edu

ABSTRACT

Background: The invasion of a new species into an established ecosystem can be directly compared to the steps involved in cancer metastasis. Cancer must grow in a primary site, extravasate and survive in the circulation to then intravasate into target organ (invasive species survival in transport). Cancer cells often lay dormant at their metastatic site for a long period of time (lag period for invasive species) before proliferating (invasive spread). Proliferation in the new site has an impact on the target organ microenvironment (ecological impact) and eventually the human host (biosphere impact).

Results: Tilman has described mathematical equations for the competition between invasive species in a structured habitat. These equations were adapted to study the invasion of cancer cells into the bone marrow microenvironment as a structured habitat. A large proportion of solid tumor metastases are bone metastases, known to usurp hematopoietic stem cells (HSC) homing pathways to establish footholds in the bone marrow. This required accounting for the fact that this is the natural home of hematopoietic stem cells and that they already occupy this structured space. The adapted Tilman model of invasion dynamics is especially valuable for modeling the lag period or dormancy of cancer cells.

Conclusions: The Tilman equations for modeling the invasion of two species into a defined space have been modified to study the invasion of cancer cells into the bone marrow microenvironment. These modified equations allow a more flexible way to model the space competition between the two cell species. The ability to model initial density, metastatic seeding into the bone marrow and growth once the cells are present, and movement of cells out of the bone marrow niche and apoptosis of cells are all aspects of the adapted equations. These equations are currently being applied to clinical data sets for verification and further refinement of the models.

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Competition among two species. The red (dash) line indicates the relative superior species (cancer cells); the green (solid) line indicates the relative inferior species (HSC). Superior species (cancer cells) can displace 90% of the inferior species (HSC). Inferior species (HSC) can displace 10% of the superior species (cancer cells). (A) Superior species (cancer cells) has colonization rate β1 = 0.2, mortality rate μ1 = 0.1 time-1 , and initial density = 0.0001. Inferior species (HSC) has colonization rate β2 = 0.8, mortality rate μ2 = 0.1 time-1 , and initial density = 0.5. (B) The superior species (cancer cells) has initial density = 0.01, and the inferior species (HSC) has initial density = 0.85; all other conditions remained the same as in (A). (C) The inferior species (HSC) has initial density = 0.84 and colonization rate β1 = 0.61 time-1 ; all other conditions remained the same as in (A).
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Figure 4: Competition among two species. The red (dash) line indicates the relative superior species (cancer cells); the green (solid) line indicates the relative inferior species (HSC). Superior species (cancer cells) can displace 90% of the inferior species (HSC). Inferior species (HSC) can displace 10% of the superior species (cancer cells). (A) Superior species (cancer cells) has colonization rate β1 = 0.2, mortality rate μ1 = 0.1 time-1 , and initial density = 0.0001. Inferior species (HSC) has colonization rate β2 = 0.8, mortality rate μ2 = 0.1 time-1 , and initial density = 0.5. (B) The superior species (cancer cells) has initial density = 0.01, and the inferior species (HSC) has initial density = 0.85; all other conditions remained the same as in (A). (C) The inferior species (HSC) has initial density = 0.84 and colonization rate β1 = 0.61 time-1 ; all other conditions remained the same as in (A).

Mentions: Hematopoietic stem cells (HSC) and cancer cells were modeled as the two species. Resuming the scenario at Figure 3, it was assumed that cancer cells are the relative superior species and HSC are the relative inferior species (Figure 4A, B and 4C). To reflect what happens in cancer in the body, the initial density for the inferior species (HSC) was set at a high level and a low initial density was set for the invading cancer cells. All values that generated the curves in Figure 4A, B and 4C are equivalent to the values in Figure 3A, B and 3C, respectively. To demonstrate the simulations clearly, the time maximum was changed to 1000 in Figure 4. The equations applied to Figure 4 are:


Modeling invasion of metastasizing cancer cells to bone marrow utilizing ecological principles.

Chen KW, Pienta KJ - Theor Biol Med Model (2011)

Competition among two species. The red (dash) line indicates the relative superior species (cancer cells); the green (solid) line indicates the relative inferior species (HSC). Superior species (cancer cells) can displace 90% of the inferior species (HSC). Inferior species (HSC) can displace 10% of the superior species (cancer cells). (A) Superior species (cancer cells) has colonization rate β1 = 0.2, mortality rate μ1 = 0.1 time-1 , and initial density = 0.0001. Inferior species (HSC) has colonization rate β2 = 0.8, mortality rate μ2 = 0.1 time-1 , and initial density = 0.5. (B) The superior species (cancer cells) has initial density = 0.01, and the inferior species (HSC) has initial density = 0.85; all other conditions remained the same as in (A). (C) The inferior species (HSC) has initial density = 0.84 and colonization rate β1 = 0.61 time-1 ; all other conditions remained the same as in (A).
© Copyright Policy - open-access
Related In: Results  -  Collection

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Figure 4: Competition among two species. The red (dash) line indicates the relative superior species (cancer cells); the green (solid) line indicates the relative inferior species (HSC). Superior species (cancer cells) can displace 90% of the inferior species (HSC). Inferior species (HSC) can displace 10% of the superior species (cancer cells). (A) Superior species (cancer cells) has colonization rate β1 = 0.2, mortality rate μ1 = 0.1 time-1 , and initial density = 0.0001. Inferior species (HSC) has colonization rate β2 = 0.8, mortality rate μ2 = 0.1 time-1 , and initial density = 0.5. (B) The superior species (cancer cells) has initial density = 0.01, and the inferior species (HSC) has initial density = 0.85; all other conditions remained the same as in (A). (C) The inferior species (HSC) has initial density = 0.84 and colonization rate β1 = 0.61 time-1 ; all other conditions remained the same as in (A).
Mentions: Hematopoietic stem cells (HSC) and cancer cells were modeled as the two species. Resuming the scenario at Figure 3, it was assumed that cancer cells are the relative superior species and HSC are the relative inferior species (Figure 4A, B and 4C). To reflect what happens in cancer in the body, the initial density for the inferior species (HSC) was set at a high level and a low initial density was set for the invading cancer cells. All values that generated the curves in Figure 4A, B and 4C are equivalent to the values in Figure 3A, B and 3C, respectively. To demonstrate the simulations clearly, the time maximum was changed to 1000 in Figure 4. The equations applied to Figure 4 are:

Bottom Line: These modified equations allow a more flexible way to model the space competition between the two cell species.The ability to model initial density, metastatic seeding into the bone marrow and growth once the cells are present, and movement of cells out of the bone marrow niche and apoptosis of cells are all aspects of the adapted equations.These equations are currently being applied to clinical data sets for verification and further refinement of the models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Internal Medicine, The University of Michigan, 7308 CCC, 1500 E, Medical Center Drive, Ann Arbor, MI 48109, USA. kpienta@umich.edu

ABSTRACT

Background: The invasion of a new species into an established ecosystem can be directly compared to the steps involved in cancer metastasis. Cancer must grow in a primary site, extravasate and survive in the circulation to then intravasate into target organ (invasive species survival in transport). Cancer cells often lay dormant at their metastatic site for a long period of time (lag period for invasive species) before proliferating (invasive spread). Proliferation in the new site has an impact on the target organ microenvironment (ecological impact) and eventually the human host (biosphere impact).

Results: Tilman has described mathematical equations for the competition between invasive species in a structured habitat. These equations were adapted to study the invasion of cancer cells into the bone marrow microenvironment as a structured habitat. A large proportion of solid tumor metastases are bone metastases, known to usurp hematopoietic stem cells (HSC) homing pathways to establish footholds in the bone marrow. This required accounting for the fact that this is the natural home of hematopoietic stem cells and that they already occupy this structured space. The adapted Tilman model of invasion dynamics is especially valuable for modeling the lag period or dormancy of cancer cells.

Conclusions: The Tilman equations for modeling the invasion of two species into a defined space have been modified to study the invasion of cancer cells into the bone marrow microenvironment. These modified equations allow a more flexible way to model the space competition between the two cell species. The ability to model initial density, metastatic seeding into the bone marrow and growth once the cells are present, and movement of cells out of the bone marrow niche and apoptosis of cells are all aspects of the adapted equations. These equations are currently being applied to clinical data sets for verification and further refinement of the models.

Show MeSH
Related in: MedlinePlus