Dependence of the TMT and Δ_opt on <i>U</i>_* for <i>U</i>₀ = 0.3.

<p>(a) <i>ρ</i> = 0.01 day⁻¹, (b) <i>ρ</i> = 0.005 day⁻¹. In both cases, the optimal fractionation for each parameter set was used.</p

Tumor amplitude evolution for eight virtual tumors under the effect of the optimal radiation treatment.

<p>(a) <i>ρ</i> = 0.01 day⁻¹, <i>U</i>_* = 0.6. (b) <i>ρ</i> = 0.005 day⁻¹, <i>U</i>_* = 0.6. (c) <i>ρ</i> = 0.01 day⁻¹, <i>U</i>₀ = 0.3. (d) <i>ρ</i> = 0.005 day⁻¹, <i>U</i>₀ = 0.3. (a-b) Show the comparison between two simulations with <i>U</i>₀ = 0.15 and <i>U</i>₀ = 0.3 under optimal therapies. (c-d) Show the comparison between two simulations with <i>U</i>_* = 0.5 and <i>U</i>_* = 0.65 under optimal therapies.</p

The increase of celularity may lead to the malignant transformation of LGGs.

<p>Left and right images are immunohistochemical staining for Hematoxilyn and Eosin for LGG and HGG biopsies respectively.</p

Dependence of the optimal Δ, (Δ_opt) and TMT on the initial and critical tumor cell densities for <i>ρ</i> = 0.005 day⁻¹.

<p>(a) Δ_opt as a function of <i>U</i>₀ and <i>U</i>_*. (b) TMT computed using the optimal Δ_opt(<i>U</i>₀, <i>U</i>_*). The insets show the curves for <i>U</i>₀ = 0.3.</p

Comparison of four different fractionation schemes: Optimal fractionation (black line), best protracted scheme obtained for <i>d</i> = 1.8 Gy (grey line), best hypoprotracted treatment obtained with <i>d</i> = 3.2 Gy (light grey) and standard fractionation (dashed line).

<p>In all cases the range 0.002 < <i>ρ</i> < 0.01 was studied. Pannel (a) shows the TMT as a function of <i>ρ</i> and (b) the value of Δ used for each of the schemes.</p

The optimal protocol delays substantially the MT considering the optimal time between fractions Δ_opt for <i>U</i>₀ = 0.3, <i>U</i>_* = 0.5 and <i>ρ</i> ∈ [0.002, 0.01].

<p>(a) Δ_opt and TMT obtained with the optimal protocol. (b) TMT for both the optimal (black curve) and the standard protocols (dark gray curve). The light gray curve represents the differences between their TMTs. The later provides a quantification of the benefit obtained from the optimal fractionation over the standard one.</p

Results for the TMT under different fractionation schemes.

<p>Stars and circles indicate the location of the standard and optimal treatments respectively on the (Dose, Δ) plane and their associated TMT. (a) <i>ρ</i> = 0.01 day⁻¹. Optimal fractionation is <i>d</i>_opt = 0.5 Gy every 6 days (Δ_opt = 6 days), and TMT = 2.9 years. (b) <i>ρ</i> = 0.005 day⁻¹. Optimal fractionation is <i>d</i>_opt = 0.5 Gy and Δ_opt = 16 days TMT = 5.7 years.</p

Scatter plot of log IGF-I serum levels and log of DL-PCB 156 (A), PCB 167 (B), ∑DL-PCBs (C), and ∑TEQs serum levels (D).

<p>Scatter plot of log IGF-I serum levels and log of DL-PCB 156 (A), PCB 167 (B), ∑DL-PCBs (C), and ∑TEQs serum levels (D).</p

Distribution of IGF-I and IGFBP-3 (ng/ml) in the studied population.

<p><i>Abbreviations:</i> p5 represents the 5th percentile and p95 represents the 95th percentile.</p><p><i>P</i> values correspond to comparison between characteristics, for IGF-I and IGFBP-3 (Kruskal-Wallis test).</p

Distribution of DL-PCBs concentrations (ng/g lipid) and TEQs (pg/g lipid) in adult blood serum in the population of the Canary Islands.

<p><i>Abbreviations:</i> LOQ, limit of quantification; N.A., not applicable. p5 and p95 represent the 5^th and 95^th percentiles respectively. ∑DL-PCB: sum over the dioxin-like PCB levels (IUPAC numbers 77, 81, 105, 114, 118, 123, 126, 156, 157, 167, 169, and 189). ∑TEQs: sum over TEQs for the DL-PCBs.</p