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Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm3 to 62 mm3, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.
Gardner and Dr. Jones to model the surface brightness of astrophysical jets. We attempt to accomplish this goal by modeling the astrophysical jet HH30 in the spectral emission lines [SII] 6716Å, [OI] 6300Å, and [NII] 6583Å. In order to do so, we used the jet model to simulate the temperature and density of the jet to match observational data by Hartigan and Morse (2007). From these results, we derived the emissivities in these emission lines using Cloudy by Ferland et al. (2013). Then we used the emissivities to determine the surface brightness of the jet in these lines. We found that the simulated surface brightness agreed with the observational surface brightness and we conclude that the model could successfully be extended to model the surface brightness of a jet.