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.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

Nanoparticle (NP) based therapeutic and theranostic agents have been developed for various diseases, yet application to neural disease/injury is restricted by the blood-brain-barrier (BBB). Traumatic brain injury (TBI) results in a host of pathological alterations, including transient breakdown of the BBB, thus opening a window for NP delivery to the injured brain tissue. This study focused on investigating the spatiotemporal accumulation of different sized NPs after TBI. Specifically, animal cohorts sustaining a controlled cortical impact injury received an intravenous injection of PEGylated NP cocktail (20, 40, 100, and 500 nm, each with a unique fluorophore) immediately (0 h), 2 h, 5 h, 12 h, or 23 h after injury. NPs were allowed to circulate for 1 h before perfusion and brain harvest. Confocal microscopy demonstrated peak NP accumulation within the injury penumbra 1 h post-injury. An inverse relationship was found between NP size and their continued accumulation within the penumbra. NP accumulation preferentially occurred in the primary motor and somatosensory areas of the injury penumbra as compared to the parietal association and visual area. Thus, we characterized the accumulation of particles up to 500 nm at different times acutely after injury, indicating the potential of NP-based TBI theranostics in the acute period after injury.

Background: Magnetic Resonance Spectroscopic Imaging (MRSI) has wide applicability for non-invasive biochemical assessment in clinical and pre-clinical applications but suffers from long scan times. Compressed sensing (CS) has been successfully applied to clinical H-1 MRSI, however a detailed evaluation of CS for conventional chemical shift imaging is lacking. Here we evaluate the performance of CS accelerated MRSI, and specifically apply it to accelerate Na-23-MRSI on mouse hearts in vivo at 9.4 T.

Methods: Synthetic phantom data representing a simplified section across a mouse thorax were used to evaluate the fidelity of the CS reconstruction for varying levels of under-sampling, resolution and signal-to-noise ratios (SNR). The amplitude of signals arising from within a compartment, and signal contamination arising from outside the compartment relative to noise-free Fourier-transformed (FT) data were determined. Simulation results were subsequently verified experimentally in phantoms and in three mouse hearts in vivo.

Results: CS reconstructed MRSI data are scaled linearly relative to absolute signal intensities from the fully-sampled FT reconstructed case (R-2 > 0.8, p-value < 0.001). Higher acceleration factors resulted in a denoising of the reconstructed spectra, but also in an increased blurring of compartment boundaries, particularly at lower spatial resolutions. Increasing resolution and SNR decreased cross-compartment contamination and yielded signal amplitudes closer to the FT data. Proof-of-concept high-resolution, 3-fold accelerated Na-23-amplitude maps of murine myocardium could be obtained within similar to 23 mins.

Conclusions: Relative signal amplitudes (i.e. metabolite ratios) and absolute quantification of metabolite concentrations can be accurately determined with up to 5-fold under-sampled, CS-reconstructed MRSI. Although this work focused on murine cardiac Na-23-MRSI, the results are equally applicable to other nuclei and tissues (e.g. H-1 MRSI in brain). Significant reduction in MRSI scan time will reduce the burden on the subject, increase scanner throughput, and may open new avenues for (pre-) clinical metabolic studies.