genomic data-guided mathematical modeling of...
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Genomic Data-Guided Mathematical Modeling of Cancer
Roxanne Casio – Rutgers University
Prof. De – Cancer Institute of New Jersey
Introduction
§ Cancer: The uncontrolled growth of abnormal cells in the body.
§ It is the second leading cause of deaths in the US.
§ In 2014, 2,626,418 deaths were recorded and 22.5 % of these deaths can be attributed to cancer.
§ Intra-tumor heterogeneity causes: 1. Spatial restrictions 2. Composition restrictions
§ Diagnoses depend heavily on biopsies, which may/may not accurately reflect the tumor as a whole.
Models Used
A. Tumor composed of discrete microlesions.The microlesions:
1. Increase in size2. Seed other microlesions
C. Volumetric Growth. Every cell replicates and pushes outward.
B. Surface Growth. Only a layer on the surface of the cell replicates radially outward.
§ Based on model and method from Waclaw (2016)
Formulas Used General Formula:
In the case of single-driver surface growth,
Where:
fn(a,t): The expected number of microlesions of age a at time t
Vn(a): Total volume of a microlesion of type n at age a
G: Asymptotic growth rate
M: Migration Probability
Vtot(t) Total volume of the tumor
n(t) Average number of drivers per cell
Figure 2. Using the single driver-surface growth method. Figure 2 is a plot of the relationship between volume and time when migration probabilities vary and velocity is constant.
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Figure 2. Volume vs Time using Single Driver-Surface Growth Method
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Figure 1. Volume vs Time using Single Driver-Surface Growth Method
v = 0.01v = 0.02v = 0.05v = 0.1
Figure 1. Using the single driver-surface growth method. Figure 1 is a plot of the relationship between volume and time when velocities vary and migration probability is constant.
Results Produced
Results Produced
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Figure 3. Volume vs. Time usingSingle Driver, Slow-Down Surface Growth Method
Figure 3. Using the single driver-slow-down surface growth method. Figure 3 is a plot of the relationship between volume and time with constant migration probability, constant velocity, and varying time scales of growth decrease.
Work in Progress
§ Total volume and fraction of cells with n drivers in the case of surface growth.
§ Colored lines represent subpopulations of cells within a tumor with nnumber of mutations.
Future Plan§ Research on cancer growth is limited to 2D. § 3D models of tumors, today, do not accurately represent the true
nature of the tumor.
Future Plan§ Research on cancer growth is limited to 2D. § 3D models of tumors, today, do not accurately represent the true
nature of the tumor.
Works Cited§ Marusyk,A. et al. “Intra-tumor heterogeneity : a looking glass for cancer?” Nature Reviews
Cancer, vol. 12, no. 5, 2012, pp. 323-334.
§ Nichols, Hannah. "The top 10 leading causes of death in the United States." Medical News Today. MediLexicon, Intl., 23 Feb. 2017. Web.11 Jul. 2017. http://www.medicalnewstoday.com/articles/282929.php
§ Paterson, C. et al. An exactly solvable, spatial model of mutation accumulation in cancer. Sci. Rep. 6, 39511; doi: 10.1038/srep39511 (2016).
§ Waclaw, Bartek. “Spatial models of cancer.” Homepage of Bartek Waclaw, https://bartekwaclaw.wordpress.com/biophysics/spatial-models-of-cancer/
Acknowledgements§ This work was funded by NSF.