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.
Here, I show that a Noonan Syndrome-linked gain-of-function mutation Raf1L613V, drives modest changes in astrocyte and oligodendrocyte progenitor cell (OPC) density in the mouse cortex and hippocampus. Raf1L613V mutant mice exhibited enhanced performance in hippocampal-dependent spatial reference and working memory and amygdala-dependent fear learning tasks. However, we observed normal perineuronal net (PNN) accumulation around mutant parvalbumin-expressing (PV) interneurons. Though PV-interneurons were minimally affected by the Raf1L613V mutation, other RASopathy mutations converge on aberrant GABAergic development as a mediator of neurological dysfunction.
I therefore hypothesized interneuron expression of the constitutively active Mek1S217/221E (caMek1) mutation would be sufficient to perturb GABAergic circuit development. Interestingly, the caMek1 mutation selectively disrupted crucial PV-interneuron developmental processes. During embryogenesis, I detected expression of cleaved-caspase 3 (CC3) in the medial ganglionic eminence (MGE). Interestingly, adult mutant cortices displayed a selective 50% reduction in PV-expressing interneurons, but not other interneuron subtypes. PV-interneuron loss was associated with seizure-like activity in mutants and coincided with reduced perisomatic synapses. Mature mutant PV-interneurons exhibited somal hypertrophy and a substantial increase in PNN accumulation. Aberrant GABAergic development culminated in reduced behavioral response inhibition, a process linked to ADHD-like behaviors. Collectively, these data provide insight into the mechanistic underpinnings of RASopathy neuropathology and suggest that modulation of GABAergic circuits may be an effective therapeutic option for RASopathy individuals.