Progression patterns by motility phenotypes.

<p>Virtual magnetic resonance imaging of simulations reproducing progression by Expanding FLAIR (a and b), Expanding FLAIR + Necrosis (c and d), and Expanding Necrosis (e). Proliferative cells (P) show the size of the proliferating tumor, invasive cells (I) show the location of invasive cells, and B cells show normal brain cells and the location of necrosis (green arrows). In each simulation, the first time shot (treatment) is taken immediately prior to anti-angiogenesis treatment, the second time shot shows the 2-month follow-up, and the final time shot displays tumor appearance at the simulated time of death. Red arrows point to high-density proliferative cells. White arrows point to invasive cells and low-density proliferative cells in treated models. The tumor size at the start of treatment is as follows: 2.4% of the brain for (a) and (b), 2.6% of the brain for (c) and (d). For simulations (e) and (f), the tumor sizes are 1.1% for (e) and 0.08% for (f) with areas having 80% or more necrosis at the start of treatment are 0.3% and 0.4% of, respectively. The percents of the brain with 80% or more necrosis at time of death are: 1.5% (a and b), 4.2% (c and e), 5.0% (d), 1.3% (f). Finally, the percentages of brain occupied with FLAIR at the end of the simulations are: 84% (a and b), 26% (c), 23% (d), 6% (e), and 11% (f). The corresponding parameter choices for hypoxia-driven and concentration-driven motility may be found in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146617#pone.0146617.t004" target="_blank">Table 4</a>.</p

Population trial: effects of replication and motility rates on overall survival time.

<p>(a) plots the results of the population computational trial, that includes all three glioblastoma multiforme phenotypes and different mitotic rates. Each point corresponds to the median overall survival time of a group of 975 patients. The data fits into a bi-exponential model (red line), <i>f</i>(<i>x</i>) = <i>ae</i>^<i>bx</i> + <i>ce</i>^<i>dx</i>. The coefficients (with 95% confidence bounds) are: <i>a</i> = 2.584 (2.51, 2.657), <i>b</i> = 0.00889 (0.008012, 0.009768), <i>c</i> = 0.0005212 (1.322×10⁻⁵, 0.001029), <i>d</i> = 0.1047 (0.09417, 0.1152). Goodness of fit: SSE: 0.3315, R-square: 0.9975, Adjusted R-square: 0.9973, RMSE: 0.1034. (b) shows selected Kaplan-Meier survival curves from the population trial including all three glioblastoma multiforme phenotypes shown in (a). (c) plots the effects of the efficacy of a rate-reducing agent in each of the three glioblastoma multiforme phenotypes. (d) plots the computed factor of reduction in tumor mitotic rates generated by Tumor Treating Fields (<i>i.e</i>. efficacy rate ×0.01) in response to a spatial distribution of the electric field in the brain.</p

Tumor motility phenotypes.

<p>Tumor motility phenotypes.</p

Predicting patients response and survival times.

<p>(a) is a Kaplan-Meier analysis of the overall survival of the four tumor groups in the computational trial. There are three treatment groups: 30 highly-dispersive Tumors (blue), 25 moderately-dispersive (red), and 25 hypoxia-driven Tumors (Black). The control group (green) includes 75 untreated tumors from all three tumor groups. The difference in overall survival between the highly-dispersive tumors and all other groups is significant (Log-Rank <i>p</i> < 0.01); the differences between moderately-dispersive and both the hypoxia-driven and untreated groups is not significant. (b) is a cartoon that illustrates how the motility phenotypes can predict both the patterns of progression and the overall survival times (blue arrows).</p

A diagram of the components of the model, tumor phenotypes, progression patterns, and computational trials to predict overall survival times.

<p>A diagram of the components of the model, tumor phenotypes, progression patterns, and computational trials to predict overall survival times.</p

Dynamics of concentration-driven and hypoxia-driven motility.

<p>Cartoon depicting the differences between brain invasion by concentration-driven motility (a) and hypoxia-driven motility (b). The latter is triggered by necrosis and causes invasion and accumulation of <i>I</i> cells within a short distance of the tumor/healthy brain boundary. Concentration-driven motility causes dispersion of tumor cells away from the high density tumor mass such that the depth of invasion into healthy brain tissue is positively correlated with the intrinsic migratory ability of the tumor.</p

Hypoxia-driven versus concentration-driven motility: simulated progression patterns.

<p>Hypoxia-driven versus concentration-driven motility: simulated progression patterns.</p

Progression curves by motility phenotypes for glioblastoma multiforme treated and not treated by bevacizumab.

<p>Each plot displays the time evolution of the percent of the brain occupied by invasive cells (FLAIR, black curve), high density (HiDen) tumor mass (red curve), and necrosis (<i>i.e</i>. 80% or more brain death, blue curve) for treated (a, c, and e) and untreated (b,d, and f) tumors. Red arrows denote the time of treatment. Double-sided black arrows emphasize the expanding difference in percent FLAIR and percent necrosis in the treated highly-dispersive and moderately-dispersive models. Notice the closeness of the FLAIR and necrosis curves in hypoxia-driven tumors treated by bevacizumab (e). (a), (c) and (e) correspond to the progression pattern of Expanding FLAIR, Expanding FLAIR + Necrosis, and Expanding Necrosis, respectively. The parameter choices for highly-dispersive, moderately-dispersive, and hypoxia-driven tumors in these simulations correspond to the high concentration-driven/high hypoxia-driven, moderate concentration-driven/high hypoxia-driven, low concentration-driven/high hypoxia-driven, respectively (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146617#pone.0146617.t004" target="_blank">Table 4</a>).</p

Recurrence patterns.

<p>Recurrence patterns.</p

Hypoxia-driven versus concentration-driven motility.

<p>Hypoxia-driven versus concentration-driven motility.</p