Preliminary Study of Cell Survival Modelling Considering Stochastic Fluctuations in Cell Survival Rates During Radiation Therapy

Abstract

To establish a cell survival model considering stochastic fluctuations in cell survival rates during radiotherapy and calculate local control rates (LCR). The hypothesis of this model is that LCR after radiotherapy can be calculated by counting the number of events that no cell is alive in a large number of trials on computer simulations considering stochastic fluctuations in cell survival rates. Cell survival rates after irradiation was considered a random variable and determined by the proprietary multi-paradigm numerical computing environment function betarnd (α, β), with the values of α and β shown in the Table. The reason for using a beta distribution is that the normal distribution may produce negative values, which are difficult to interpret as cell survival rates after radiotherapy. Scenario A: 1,000,000,000 (=N0) cells were assumed to be present at the start. Cell survival rates after irradiation (=Ps) were determined by betarnd (α, β). The number of surviving cells after the first irradiation (=N1) was the number of the “success” Bernoulli trials with n = 1,000,000,000 (=N0) with the success probability = Ps. The number of surviving cells after the second irradiation (=N2) was the “success” number in the results of the Bernoulli trials for n=N1 with success probability = Ps. The Ps was considered constant during the continuing radiotherapy with 33 irradiations, and so iterations until N33 were calculated. If N33 became 0, it was considered that all cells were dead and that local control was achieved. If N33 was not 0, it was considered to show local failure. The calculation was repeated 10,000 times. The Ps was sampled in each repeated calculation and the LCR was the number of events where all cells were dead after the radiotherapy divided by 10,000. Scenario B: The difference of Scenario B from Scenario A is that Ps is changed in each irradiation during the continuing radiotherapy, making the number of surviving cells after the second irradiation (=N2) the summation of the “success” number in the Bernoulli trials with n=N1 and success probability = Ps that was resampled before the second irradiation. The Ps of all irradiations is different in general in Scenario B. Other details are as in Scenario A. The LCR are shown in the Table. The effect of different probability distributions appears to lessen the local control rate when the mean cell survival rate ≥ 0.5. This primitive stochastic cell survival model was able to calculate LCR.Abstract MO_34_2791; Table 1Mean Survival RateVariance≅0.001≅0.002≅0.005≅0.01≅0.020.3Scenario A100%100%99.9%98.0%92.8%Scenario B100%100%100%100%100%(α, β)(50, 116.7)(25, 58.33)(15, 35)(6, 14)(3, 7)0.4Scenario A99.8%99.0%95.7%89.1%79.8%Scenario B100%100%99.99%100%99.99%(α, β)(80, 120)(40, 60)(20, 30)(10, 15)(4, 6)0.5Scenario A74.6%69.7%63.9%59.5%55.8%Scenario B89.1%90.0%89.1%89.9%92.2%(α, β)(100, 100)(60, 60)(25, 25)(12, 12)(5, 5)0.6Scenario A3.1%7.9%14.9%22.7%30.7%Scenario B0%0%0%0.2%5.0%(α, β)(120, 80)(60, 40)(30, 20)(15, 10)(6, 4) Open table in a new tab