tumor growth and radio therapy
DESCRIPTION
Tumor Growth and Radio Therapy. Bettina Greese Biomathematics, University of Greifswald Nuha Jabakhanji Bioinformatics , University of Alberta. Cancer: Background. A cancer tumor is a mass of cells with uncontrolled cell proliferation as a result of defective cell cycle control mechanisms. - PowerPoint PPT PresentationTRANSCRIPT
Tumor Growth and Radio Therapy
Bettina Greese Biomathematics, University of Greifswald Nuha Jabakhanji Bioinformatics , University of Alberta
Cancer: Background
A cancer tumor is a mass of cells with uncontrolled cell proliferation as a result of defective cell cycle control mechanisms.
How it results: point mutations, DNA rearrangements, gene amplification, translocation, mutations in tumor suppressor genes.
Cancer cells are genetically unstable and are able to become “worse” by accumulating mutations.
Why it’s important:
“An estimated 149,000 new cases of cancer and 69,500 deaths from cancer will occur in Canada in 2005.” National Cancer Institute of Canada
Mathematical Model: Simple Model
Two populations: Healthy and cancerous cells. Logistic growth with intrinsic growth rate. Competition for resources and space. Initial conditions: 100 healthy cells, 1 cancerous cell.
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Mathematical Model: Simple Model
Two populations: Healthy and cancerous cells. Logistic growth with intrinsic growth rate. Competition for resources and space. Natural mutations (healthy to cancerous cell).
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1)(2
22 thtc
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Mathematical Model: Simple Model
Two populations: Healthy and cancerous cells. Logistic growth with intrinsic growth rate. Competition for resources and space. Mutations: natural and radiation induced. Radiation induced death for cancerous and healthy cells.
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Simple Model: Analysis
Calculated the steady states and their stability. Plotted the phase plane for different parameter sets.
Extinction Coexistence
Simple Model: Analysis
Extinction Coexistence
Plots of healthy (red) and cancerous (green) cells versus time.
Simple Model: Analysis Thin lines: with effects of radiation and/or mutation. Left: The effect of natural mutation on the populations. Right: Cell deaths caused by constant radiation.
Simple Model: Analysis
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Left: Cell deaths caused by constant high radiation. Right: Cell deaths caused by pulsed radiation.
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Mathematical Model: Final Model Three populations: Healthy, cancerous and aggressive
cancerous cells. Logistic growth, competition, mutations, radiation induced
death are as before. Initial conditions: 100 healthy, 1 cancerous and 0 aggressive.
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Final Model: Analysis Plot of healthy (red), cancerous (green) and aggressive cancerous (blue) cells versus time. Thin lines: effect of natural mutation.
Final Model: Analysis Plot of healthy (red), cancerous (green) and aggressive cancerous (blue) cells versus time. Thin lines: effect of radiation induced mutations and death.
Final Model: Analysis Thick lines: natural mutations included. Thin lines: effect of radiation induced mutations and death in addition to natural mutations.
Conclusions and Limitations
Biologically meaningful parameters result in extinction of healthy cells.
Natural mutation accelerates extinction of healthy cells. Radiation delays extinction. High doses of radiation are needed to maintain a level of
healthy cells above cancer cells. Pulsed radiation allows higher doses of radiation, thus a
higher level of healthy cells is maintained for a significantly longer time.
Pulsed radiation includes breaks in radiation that result in the recovery of the cells.
Conclusions and Limitations
In the final model, the cancerous cells are driven to extinction by the aggressive cancerous cells when natural mutation is included.
Also, radiation does not change the qualitative behavior but results in lower levels of cell populations.
We used same mutation rates and carrying capacities for healthy and cancerous cells.
Pulsed radiation was not included in the final model. Initial cell populations were low. Further insight can be gained by varying parameters
within biological reason.
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