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Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle

Figure 4

Host tissue RANKL and systemic OPG.

A Starting from the initial conditions described in Figure 3, the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) are shown at 30, 60 and 90 days, respectively. The outcomes for three different values of the host-RANKL level are shown. The computational domain is 15 mm long, but since the fields are symmetric, only the right half is shown. The y-axes have the following units: RANKL in pmol/mm; OC in cells/mm; tumor density is normalized between 0, when there is no tumor per unit length, and 1, when the unit space is fully occupied by tumor. The resorption fronts of osteoclasts either reach wave-like propagation () or die out (). B Starting from the initial conditions described in Figure 3, the evolution of the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) is shown after 45 and 90 days, respectively. The initial host-RANKL level is , and between 20 and 90 days, a uniform source of OPG is administered at (green) and (blue), respectively. Compared to the control at (red), the respective tumor burdens are reduced.

doi: https://doi.org/10.1371/journal.pcbi.1002703.g004