Spatiotemporally integrated fractionation involves finding a fluence-map and a number of treatment sessions that maximize tumor-kill subject to dose-limits on organs-at-risk (OAR). This problem was recently formulated using the linear-quadratic dose-response model. Owing to the uncertainty in dose-response parameters, however, a solution presumed optimal might be infeasible in practice. We addr...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

In 1989 the British Journal of Radiology published a review proposing the term biologically effective dose (BED), based on linear quadratic cell survival in radiobiology. It aimed to indicate quantitatively the biological effect of any radiotherapy treatment, taking account of changes in dose-per-fraction or dose rate, total dose and (the new factor) overall time. How has it done so far? Accept...

This paper introduces the concept of analytical probabilistic modeling (APM) to quantify uncertainties in quality indicators of radiation therapy treatment plans. Assuming Gaussian probability densities over the input parameters of the treatment plan quality indicators, APM enables the calculation of the moments of the induced probability density over the treatment plan quality indicators by an...

AIM To study the dose-response of stage I non-small-cell lung cancer (NSCLC) in terms of long-term local tumor control (LC) after conventional and hypofractionated photon radiotherapy, modeled with the linear-quadratic (LQ) and linear-quadratic-linear (LQ-L) approaches and to estimate the clinical α/β ratio within the LQ frame. MATERIAL AND METHODS We identified studies of curative radiothera...

PURPOSE To investigate whether rotational techniques (Volumetric Modulated Arc Therapy - VMAT) are associated with a higher risk for secondary primary malignancies compared to step-and-shoot Intensity Modulated Radiation Therapy (ss-IMRT). To this end, radiation therapy (RT) induced DNA double-strand-breaks and the resulting chromosomal damage were assessed in peripheral blood T-lymphocytes of ...

The authors developed mathematical models to quantify the impact of accidents on the U.S. nuclear power industry radionuclide air emissions incidence risk. Additionally, sensitivity analysis was performed on the terms in those models. The number of accidents of a given size needed to equilibrate the nuclear power industry leukemia incidence risk with the coal power industry leukemia incidence r...

This paper presents a review of several studies conducted in our laboratory to examine the carcinogenic effects in mice of high-LET radiation and, for comparison, of low-LET reference radiation. For some specific end-points the following conclusions can be formulated: i) the dose-response curves for myeloid leukemia and malignant lymphoma can be interpreted in terms of induction and inactivatio...

Background: The purpose of this paper is to establish an easy and reliable biodosimeter protocol to evaluate the biological effects of proton beams. Materials and Methods: Human peripheral blood lymphocytes were irradiated using proton beams (LET: 34.6 keV μm−1), and the chromosome aberrations induced were analyzed using cytokinesis-blocked (CB) micronucleus (MN) assay. To determine th...