PubMed · 5857232
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R G Cornell. 1965. Spearman estimation for a simple exponential model.. https://pubmed.ncbi.nlm.nih.gov/5857232/
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PURPOSE: We address the question of whether or not, for the same average (or integral) dose, a smaller uniform dose to an entire normal tissue structure always results in a lower normal tissue complication probability (NTCP) than does a proportionally larger dose to a partial volume of the same structure. METHODS AND MATERIALS: A recent compilation of NTCP data and two theoretical formulations of the dependence of NTCP on dose and partial volume irradiated-the Lyman probit equation and the binomial model-are used to examine this question. Both models fit equally well available NTCP data. RESULTS: Empirical data indicate that for lung, kidney, and possibly liver (but not for esophagus, brain, or heart), given a fixed tumor dose and fixed integral dose, NTCP can be minimized by irradiating a partial volume fraction rather than the entire normal organ. The binomial model supports this interpretation, whereas the probit model predicts that for all organs uniform irradiation of the whole organ always results in the lowest possible NTCP. CONCLUSIONS: In contrast to what is commonly believed, this study suggests that for at least two normal tissues, namely lung and kidney, there may be situations where "a lot to a little" (i.e., fewer treatment ports) will result in higher tumor control probability and better treatment plan than "a little to a lot" (i.e., multifield treatment). This finding, which is independent of the binomial or probit models used here, depends only on the accuracy of the empirical NTCP data. It is also interesting to note that: a) lung and kidney are commonly classified as parallel tissues, while the others have more of a serial architecture; and b) the choice of the NTCP model can have a profound impact on treatment planning decisions.
We present a formalism to compute the probability of an amino acid sequence conformation being native-like, given a set of pairwise atom-atom distances. The formalism is used to derive three discriminatory functions with different types of representations for the atom-atom contacts observed in a database of protein structures. These functions include two virtual atom representations and one all-heavy atom representation. When applied to six different decoy sets containing a range of correct and incorrect conformations of amino acid sequences, the all-atom distance-dependent discriminatory function is able to identify correct from incorrect more often than the discriminatory functions using approximate representations. We illustrate the importance of using a detailed atomic description for obtaining the most accurate discrimination, and the necessity for testing discriminatory functions against a wide variety of decoys. The discriminatory function is also shown to be capable of capturing the fine details of atom-atom preferences. These results suggest that the all-atom distance-dependent discriminatory function will be useful for protein structure prediction and model refinement.
Conventional 3D dose calculations for stereotactic radiosurgery involve integration of individual static beams comprising a set of arcs. For iterative optimization of multiple isocentre treatment, which requires repetitive dose calculations at a large number of sample points, the conventional method is too slow. To overcome this problem spherically symmetric dose distributions are assumed. The authors describe a spherical dose model derived from a parametrized convolution of the collimator width and a dose spread kernel. The method is fast and easy to implement requiring just a single empirically derived value. Furthermore, the model is differentiable with respect to the parameters to be optimized. This property is useful when the optimization strategies rely on gradient information.