A mean value for pairs of integrals

Se prueba que para dos funciones continuas reales, una determinada ecuación posee solució única. Se presenta también una generalización a integrales con peso.

Radiation induced apoptosis and initial DNA damage are inversely related in locally advanced breast cancer patients

[EN] Background: DNA-damage assays, quantifying the initial number of DNA double-strand breaks induced by radiation, have been proposed as a predictive test for radiation-induced toxicity. Determination of radiation-induced apoptosis in peripheral blood lymphocytes by flow cytometry analysis has also been proposed as an approach for predicting normal tissue responses following radiotherapy. The aim of the present study was to explore the association between initial DNA damage, estimated by the number of double-strand breaks induced by a given radiation dose, and the radio-induced apoptosis rates observed. Methods: Peripheral blood lymphocytes were taken from 26 consecutive patients with locally advanced breast carcinoma. Radiosensitivity of lymphocytes was quantified as the initial number of DNA double-strand breaks induced per Gy and per DNA unit (200 Mbp). Radio-induced apoptosis at 1, 2 and 8 Gy was measured by flow cytometry using annexin V/propidium iodide. Results: Radiation-induced apoptosis increased in order to radiation dose and data fitted to a semi logarithmic mathematical model. A positive correlation was found among radio-induced apoptosis values at different radiation doses: 1, 2 and 8 Gy (p < 0.0001 in all cases). Mean DSB/Gy/DNA unit obtained was 1.70 ± 0.83 (range 0.63-4.08; median, 1.46). A statistically significant inverse correlation was found between initial damage to DNA and radio-induced apoptosis at 1 Gy (p = 0.034). A trend toward 2 Gy (p = 0.057) and 8 Gy (p = 0.067) was observed after 24 hours of incubation. Conclusions: An inverse association was observed for the first time between these variables, both considered as predictive factors to radiation toxicity.