Purpose: To provide a rabiobiological evaluation tool based on a mathematical model for control of metastases during treatment with the use of FDG beta emissions as therapeutic agent. Methods: Analytical and numerical solution of a nonlinear set of equations in order to describe the interaction between beta radiation and clonogenic transformed cells which are part of a primary tumor and related metastases. Under the consideration that beta emissions in this particular case can be taken as high LET radiation, the critical time and fraction number for local minima in the transformed cell population and can be found in closed form. Results: This theory can explain the observed behavior for the primary tumor and particularly for metastases in a mice‐melanoma experimental model, where 3 out of 7 of the treated animals showed no metastases. This result suggests the possibility of a fractionation scheme for total dose which can produce the same effect when repeated intravenous inoculations are provided at the proper critical time intervals. Conclusions: For metastases control with radionuclides, which are beta emitters like FDG as therapeutic agents, a treatment planning and follow up is possible from a quantitative point of view using a radiobiological kinetic model based on DNA damage mechanisms.Funding was provided by the School of Physics, Faculty of Science and Consejo de Desarrollo Científico y Humanístico, Universidad Central de Venezuela and Física Médica C. A.
Purpose: To develop a simple kinetic model for tumor survival curves which is able to describe their behavior for high and low LET clinical applications and at the same time can provide a relation to the mechanisms for DNA damage and repair. Method and Materials: Analytical and numerical solution of a nonlinear set of equations
urn:x-wiley:00942405:media:mp1994:mp1994-math-0001 where N is the number of clonogenic cells with undamaged DNA, NR is the number of cells with reversible DNA damage and NNR is the number of cells with irreversible DNA damage. At the same time α0 and N∞ are Gompertz model parameters and κREP is the probability per unit time for DNA repair. The probability per unit time for radiation reversible damage of DNA is given by κRAD (t), as well as γκRAD (t) is the probability per unit time for radiation irreversible DNA damage. A study of limit cases for the solution behaviour is made for several cases in order to find the relation between the linear‐quadratic model parameters and those of the proposed kinetic model, which is going to make easier its clinical application. Results: The proposed model is able to describe the proper behavior at low and high LET for V‐79 cells in late S phase. The values obtained for the new set of parameters and clinical applications related to fractionation are discussed. Conclusion: It is possible to develop simple microscopic models based on DNA damage and repair mechanisms in order to describe tumor survival curves. DNA damage has to be considered in two steps, one reversible and another irreversible. Its relation with the linear‐quadratic model can be helpful in order to implement its clinical application.
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