User:Asf45/Benchmark III: Results

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Figure 1

Figure 1 is to be completed for the final paper.

Figure 2

Figure 2 describes the cell population sizes of osteoclast, osteoblast and tumor cells under high myelomic paracrine activity (hCTSL=hBTSL=0.3) and low myelomic paracrine activity ((hCTSL=hBTSL=0.1) relative to their healthy values (hCTSL=hBTSL=0) as a function of the paracrine parameter gTC. This parameter represents the acuity of growth in myeloma cells due to the presence of osteoclast cells. In my recreation of Figure 2, blue=osteoblast, green=osteoclast, and red=myeloma.

Figure 2 in Koenders & Saso (2015)
Reproduction of Fig. 2 in Koenders & Saso (2015)

My figure implies the same overall result as the figure in the paper, namely that a combined increase in paracrine parameters leads to a worsening stability situation. Additionally, the sizes of the three cell populations relative to one another are the same as those in the original figure. However, my figure is slightly off from the one in the paper, because for both high and low myelomic paracrine activity, the lines extend further than they do in the actual figure from Koenders & Saso (2015). Since all equations were checked several times for errors, all parameters were exactly matched to those indicated in the paper, and altering the initial conditions did not change the figure very drastically, when I was recreating this figure I began to suspect that some parameter might be reported incorrectly in the paper. This suspicion was later confirmed when I attempted to replicate Figure 5 (see below). However, despite the fact that it is slightly off from the original figure, it does not affect the conclusions that can be made from it other than the values of gTC for which stability no longer exists.

Figure 3

Figure 3 is a time plot describing the restoration to equilibrium values of osteoclast, osteoblast and myeloma cells after a 10% perturbation from equilibrium at time t=0 when no myeloma is present. In my recreation of Figure 2, blue=osteoblast, green=osteoclast, and red=myeloma.

Fig. 3 in Koenders & Saso (2015)
Reproduction of Fig. 3 in Koenders & Saso (2015)

Successful replication of this figure indicates that, after 40-60 days, the natural bone repair process will return osteoclast and osteoblast cell population sizes to their equilibrium values after a small injury. Since myeloma is not present, the size of its population does not change, as indicated by the horizontal red line at y=1.00.

Figure 4

Figure 4 from Koenders & Saso (2015).
First attempt at recreating Figure 4 from Koenders & Saso (2015). All parameters are set for this figure as indicated by the authors in the paper.
Second attempt at recreating Figure 4 from Koenders & Saso (2015). All parameters are set for this figure as indicated by the authors in the paper except T[0] which is changed from 0.1 to 5.0.
Third attempt at recreating Figure 4 from Koenders & Saso (2015). All parameters are set for this figure as indicated by the authors in the paper except hCB and hBC which are changed from 0.012 to 0.0012 and gBC which is changed from 1.0 to 0.0.

Figure 5

Figure 5 is to be completed for the final paper.

Figure 6

Figure 6 is to be completed for the final paper.

Figure 7

Figure 7 is to be completed for the final paper.

Extension

For my model extension, I plan to conduct a sensitivity analysis. This will be particularly helpful for identifying which parameters may be causing my figures to differ slightly from those in the paper. I have already identified two parameters (gBC and gCB) whose values differ from those in the paper on which the authors base their model (Komarova et al. (2003)), and these parameters affect the behavior of the cell populations dramatically. To conduct this sensitivity analysis for all parameters, I will vary each parameter in the model by a fixed amount and calculate how much this perturbation affects the final equilibrium value of the cell populations.