Fig 1.
Radio(chemo)-therapy schemes classified by the dose per fraction and the time spacing between fractions.
All schemes are defined in relation to the standard one.
Fig 2.
The increase of celularity may lead to the malignant transformation of LGGs.
Left and right images are immunohistochemical staining for Hematoxilyn and Eosin for LGG and HGG biopsies respectively.
Table 1.
Values of the biological and clinical parameters used in the mathematical model of LGG evolution.
Fig 3.
Results for the TMT under different fractionation schemes.
Stars and circles indicate the location of the standard and optimal treatments respectively on the (Dose, Δ) plane and their associated TMT. (a) ρ = 0.01 day−1. Optimal fractionation is dopt = 0.5 Gy every 6 days (Δopt = 6 days), and TMT = 2.9 years. (b) ρ = 0.005 day−1. Optimal fractionation is dopt = 0.5 Gy and Δopt = 16 days TMT = 5.7 years.
Fig 4.
Evolution of the tumor amplitude under standard and optimal therapies (black and gray curves respectively).
The value of the parameters used are: U0 = 0.3, U* = 0.65 and (a) ρ = 0.01 day−1 (a fast-growing virtual LGG) and (b) ρ = 0.005 day−1 (a slowly growth virtual LGG).
Fig 5.
Tumor amplitude evolution for eight virtual tumors under the effect of the optimal radiation treatment.
(a) ρ = 0.01 day−1, U* = 0.6. (b) ρ = 0.005 day−1, U* = 0.6. (c) ρ = 0.01 day−1, U0 = 0.3. (d) ρ = 0.005 day−1, U0 = 0.3. (a-b) Show the comparison between two simulations with U0 = 0.15 and U0 = 0.3 under optimal therapies. (c-d) Show the comparison between two simulations with U* = 0.5 and U* = 0.65 under optimal therapies.
Fig 6.
Dependence of the optimal Δ, (Δopt) and TMT on the initial and critical tumor cell densities for ρ = 0.005 day−1.
(a) Δopt as a function of U0 and U*. (b) TMT computed using the optimal Δopt(U0, U*). The insets show the curves for U0 = 0.3.
Fig 7.
Dependence of the TMT and Δopt on U* for U0 = 0.3.
(a) ρ = 0.01 day−1, (b) ρ = 0.005 day−1. In both cases, the optimal fractionation for each parameter set was used.
Fig 8.
The optimal protocol delays substantially the MT considering the optimal time between fractions Δopt for U0 = 0.3, U* = 0.5 and ρ ∈ [0.002, 0.01].
(a) Δopt 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.
Fig 9.
Comparison of four different fractionation schemes: Optimal fractionation (black line), best protracted scheme obtained for d = 1.8 Gy (grey line), best hypoprotracted treatment obtained with d = 3.2 Gy (light grey) and standard fractionation (dashed line).
In all cases the range 0.002 < ρ < 0.01 was studied. Pannel (a) shows the TMT as a function of ρ and (b) the value of Δ used for each of the schemes.
Fig 10.
Benefit quantification of the conservative suboptimal treatment, Δsubopt = 6 days, against the standard one for ρ ∈ [0.002, 0.01].