Abstract
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.
Highlights
Glioblastoma multiforme (GBM) is an aggressive form of brain cancer with mean survival time following diagnosis ranging from about 4 months with supportive care only[1] to 15 months with standard treatment[2, 3]
The parameter D governs the rate of diffusion, and ρ, the growth rate of the tumor cell population. Swanson and her collaborators have explored the potential utility of equation (1) as a “patient specific” mathematical model to
glioblastoma multiforme (GBM) may arise de novo or as a malignant progression from a preexisting lower-grade lesion[13], and the extent of GBM invasion away from the main mass is difficult to ascertain from magnetic resonance (MR) images[14]
Summary
Glioblastoma multiforme (GBM) is an aggressive form of brain cancer with mean survival time following diagnosis ranging from about 4 months with supportive care only[1] to 15 months with standard treatment[2, 3]. Estimate patient survival[10] and to optimize treatment strategies[11] They have attempted to estimate the parameter ρ and the ratio ρ/D from successive magnetic resonance (MR) images of individual patients: small values of the latter ratio appear to correspond to especially “diffuse” growth patterns, and larger values to more “nodular” tumors[11]. Such characterizations may predict which patients are likely to derive the greatest benefit from surgical resection[12]. Equation (1) has the virtue of simplicity, given the limited frequency of clinical imaging data and the uncertainties surrounding many of the biological details of GBM growth, progression, and treatment
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