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

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

Characteristics of patients with GBM at first recurrence.

<p>Necrosis (+) and (-) indicate that the tumor showed, respectively, the presence or absence of expanding area of necrosis (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115018#pone-0115018-g002" target="_blank">Fig. 2</a>). M =  Male. F =  Female. Age  =  age at initial diagnosis in years. Initial Therapy  =  therapy given prior to first recurrence. Surgery  =  initial surgical procedure at the time of diagnosis. Chemo + Bev  =  chemotherapy given with bevacizumab. XRT  =  radiation therapy. Tem  =  Temozolomide. XRT/Tem  =  radiation therapy with concurrent Temozolomide. XRT, Tem  =  radiation therapy followed by Temozolomide. CCNU  =  Lomustine. CPT-11 =  Irinotecan. STR  =  subtotal resection. ICT-107 =  ICT-107 vaccine. Gliadel  =  Gliadel wafers. GTR  =  gross total resection. R =  craniotomy surgical details unknown. ** =  This patient had a diagnosis of gliosarcoma. The mean age of patients 1–11 is 48.4 years. The mean age of patients 12–23 is 54.7 years.</p><p>Characteristics of patients with GBM at first recurrence.</p

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

Hypoxia-driven versus concentration-driven motility.

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

Summary of the phenotypes of glioblastoma multiforme and their predicted response to anti-angiogenesis, anti-mitotic, and anti-hypoxia driven motility agents.

<p>Summary of the phenotypes of glioblastoma multiforme and their predicted response to anti-angiogenesis, anti-mitotic, and anti-hypoxia driven motility agents.</p

Effects of replication rates on overall survival time.

<p>(a)—(c) plot the results of computational trials studying the effects of titrating the motility rate (/hr) on the overall survival of patients with highly-dispersive, moderately-dispersive, and hypoxia-driven glioblastoma multiforme (GBM), respectively. Each dot corresponds to the median overall survival of a group of 25 patients (Log-Rank <i>p</i> < 0.05). The red arrows in (a) and (b) indicate the highest mitotic rates that generate statistically significant prolongation of overall survival as compared to baseline rate of 0.35/hr. (d) and (e) show selected Kaplan-Meier survival curves from the computational trials (a) and (b), respectively. (f) plots the relationship between the efficacy of a motility-reducing agent and overall survival times in patients with hypoxia-driven GBM; each dot represents the median overall survival time of a group of 25 patients.</p