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

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

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

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

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

Values of several textural features (normalized to the maximum value obtained in each subplot) for different spatial resolutions (432x432 ST 1mm, 432x432 ST 2 mm, 256x256 ST 1 mm, 256x256 ST 2 mm) and dynamic range values (16, 32 and 64 grey levels).

<p>Shown are results for a) co-occurence (CM) Entropy, b) CM Homogeneity, c) run-length matrix (RLM) SRE, d) RLM LRE.</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

Mean (and standard deviation) of the CV of the 20 patients’ regarding each dynamic range considered.

<p>CV was computed for each feature considering different combinations of matrix size and slice thickness, that is, matrix sizes of 432x432 and 256x256 pixels and slice thickness of 1 mm and 2 mm. Shaded cells correspond to those combinations obtaining a CV below 10%.</p

Mean (and standard deviation) of the CV computed for the 20 patients.

<p>Results are shown for each combination of spatial resolution and slice thickness considered. CV was computed for each feature considering different dynamic range values, i.e. 16, 32 and 64 grey levels.</p