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.

Human Papillomavirus, or HPV, is a viral pathogen that most commonly spreads through sexual contact. HPV strains 6 and 11 normally cause genital warts, while HPV strains 16 and 18 commonly cause cervical cancer, which causes cancerous cells to spread in the cervix. Physicians can detect those HPV strains, using a Pap smear, which is a diagnostic test that collects cells from the female cervix.

In the 1930s, George Beadle and Boris Ephrussi discovered factors that affect eye colors in developing fruit flies. They did so while working at the California Institute of Technology in Pasadena, California. (1) They took optic discs (colored fuchsia in the image) from fruit fly larvae in the third instar stage of development. Had the flies not been manipulated, they would have developed into adults with vermilion eyes. (2) Beadle and Ephrussi transplanted the donor optic discs into the bodies of several types of larvae, including those that would develop with normal colored eyes (brick red), and those that would develop eyes with other shades of red, such as claret, carmine, peach, and ruby (grouped together and colored black in the image). (3a) When implanted into normal hosts that would develop brick red eyes, the transplanted optic disc developed into an eye that also was brick red. (3b) When implanted into abnormal hosts that would develop eyes of some other shade of red, the transplanted optic discs developed into eyes that were vermilion. Beadle and Ephrussi concluded that there was a factor, such as an enzyme or some other protein, produced outside of the optic disc that influenced the color of the eye that developed from the disc.

This illustration shows George Beadle and Edward Tatum's experiments with Neurospora crassa that indicated that single genes produce single enzymes. The pair conducted the experiments at Stanford University in Palo Alto, California. Enzymes are types of proteins that can catalyze reactions inside cells, reactions that produce a number of things, including nutrients that the cell needs. Neurospora crassa is a species of mold that grows on bread. In the early 1940s, Beadle and Tatum conducted an experiment to discover the abnormal genes in Neurospora mutants, which failed to produce specific nutrients needed to survive. (1) Beadle and Tatum used X-rays to cause mutations in the DNA of Neurospora, and then they grew the mutated Neurospora cells in glassware. (2) They grew several strains, represented in four groups of paired test tubes. For each group, Neurospora was grown in one of two types of growth media. One medium contained all the essential nutrients that the Neurospora needed to survive, which Beadle and Tatum called a complete medium. The second medium was a minimal medium and lacked nutrients that Neurospora needed to survive. If functioning normally and in the right conditions, however, Neurospora can produce these absent nutrients. (3) When Beadle and Tatum grew the mutated mold strains on both the complete and on the minimal media, all of the molds survived on the complete media, but not all of the molds survived on the minimal media (strain highlighted in yellow). (4) For the next step, the researchers added nutrients to the minimal media such that some glassware received an amino acid mixture (represented as colored squares) and other glassware received a vitamin mixture (represented as colored triangles) in an attempt to figure out which kind of nutrients the mutated molds needed. The researchers then took mold from the mutant mold strain that had survived on a complete medium and added that mold to the supplemented minimal media. They found that in some cases the mutated mold grew on media supplemented only with vitamins but not on media supplemented only with amino acids. (5) To discover which vitamins the mutant molds needed, Beadle and Tatum used several tubes with the minimal media, supplementing each one with a different vitamin, and then they attempted to grow the mutant mold in each tube. They found that different mutant strains of the mold grew only on media supplemented with different kinds of vitamins, for instance vitamin B6 for one strain, and vitamin B1 for another. In experiments not pictured, Beadle and Tatum found in step (4) that other strains of mutant mold grew on minimal media supplemented only with amino acids but not on minimal media supplemented only with vitamins. When they repeated step (5) on those strains and with specific kinds of amino acids in the different test tubes, they found that the some mutated mold strains grew on minimal media supplemented solely with one kind of amino acid, and others strains grew only on minimal media supplemented with other kinds of amino acids. For both the vitamins and amino acid cases, Beadle and Tatum concluded that the X-rays had mutated different genes in Neurospora, resulting in different mutant strains of Neurospora cells. In a cell of a given strain, the X-rays had changed the gene normally responsible for producing an enzyme that catalyzed a vitamin or an amino acid. As a result, the Neurospora cell could no longer produce that enzyme, and thus couldn't catalyze a specific nutrient.