58 research outputs found
Structural Derivative Model for Tissue Radiation Response
By means of a recently-proposed metric or structural derivative, called
scale-q-derivative approach, we formulate differential equation that models the
cell death by a radiation exposure in tumor treatments. The considered
independent variable here is the absorbed radiation dose D instead of usual
time. The survival factor, Fs, for radiation damaged cell obtained here is in
agreement with the literature on the maximum entropy principle, as it was
recently shown and also exhibits an excellent agreement with the experimental
data. Moreover, the well-known linear and quadratic models are obtained. With
this approach, we give a step forward and suggest other expressions for
survival factors that are dependent on the complex tumor structure.Comment: 6 pages, 2 collumn
Non-extensive radiobiology
The expression of survival factors for radiation damaged cells is based on
probabilistic assumptions and experimentally fitted for each tumor, radiation
and conditions. Here we show how the simplest of these radiobiological models
can be derived from the maximum entropy principle of the classical
Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy
and a cutoff hypothesis, motivated by clinical observations. A generalization
of the exponential, the logarithm and the product to a non-extensive framework,
provides a simple formula for the survival fraction corresponding to the
application of several radiation doses on a living tissue. The obtained
expression shows a remarkable agreement with the experimental data found in the
literature, also providing a new interpretation of some of the parameters
introduced anew. It is also shown how the presented formalism may has direct
application in radiotherapy treatment optimization through the definition of
the potential effect difference, simply calculated between the tumour and the
surrounding tissue.Comment: 8 pages, 1 figure. Sent to MaxEnt 2010. To be submitted for
publicatio
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