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.
etwork states to the structure of the signal itself. Under the common thread of characterizing the role of information, this dissertation investigates opportunistic scheduling, relaying and multicast in wireless networks. To assess the role of channel state information, the problem of opportunistic distributed opportunistic scheduling (DOS) with incomplete information is considered for ad-hoc networks in which many links contend for the same channel using random access. The objective is to maximize the system throughput. In practice, link state information is noisy, and may result in throughput degradation. Therefore, refining the state information by additional probing can improve the throughput, but at the cost of further probing. Capitalizing on optimal stopping theory, the optimal scheduling policy is shown to be threshold-based and is characterized by either one or two thresholds, depending on network settings. To understand the benefits of side information in cooperative relaying scenarios, a basic model is explored for two-hop transmissions of two information flows which interfere with each other. While the first hop is a classical interference channel, the second hop can be treated as an interference channel with transmitter side information. Various cooperative relaying strategies are developed to enhance the achievable rate. In another context, a simple sensor network is considered, where a sensor node acts as a relay, and aids fusion center in detecting an event. Two relaying schemes are considered: analog relaying and digital relaying. Sufficient conditions are provided for the optimality of analog relaying over digital relaying in this network. To illustrate the role of information about the signal structure in joint source-channel coding, multicast of compressible signals over lossy channels is studied. The focus is on the network outage from the perspective of signal distortion across all receivers. Based on extreme value theory, the network outage is characterized in terms of key parameters. A new method using subblock network coding is devised, which prioritizes resource allocation based on the signal information structure.