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• W1978610706 abstract "I thank Drs. Elmehdi and Pistorius for their kind comments on my derivation of exact formulae to compensate for errors in the dose per fraction made early in a treatment ( 1 Joiner M.C. A simple α/β-independent method to derive fully isoeffective schedules following changes in dose per fraction. Int J Radiat Oncol Biol Phys. 2004; 58: 871-875 Abstract Full Text Full Text PDF Scopus (19) Google Scholar ). I note that there is no dispute about the validity of the formulae themselves, only a minor mathematical debate about the validity of the way that I carried out the derivation. First, Elmehdi and Pistorius state that Eq. 8 can (and should) be derived from a simple substitution of Eq. 7 into either Eq. 4 or 5. This is completely correct and would be the usual way of deriving the other variable in solving a pair of simultaneous equations. With hindsight, it might have been less controversial for me to have stated that. However, I elected to take the more elegant (in my opinion) shortcut of simply setting L in Eq. 4 (or T in Eq. 5) equal to zero, because the result can then be seen immediately with no further manipulation. In real life, although I would agree that T = 0 is unlikely, I see no reason why L could not be zero. However, in mathematical life, there is absolutely no reason at all why either L or T cannot be zero in these equations. Even the condition L = T can be accounted for if the equations are solved in the limit, because L − T tends to zero rather than L − T = 0. Also as I point out in my final paragraph on “Note on the meaning of L = T,” if L = T = α/β, then rather than the equations being insoluble as Elmehdi and Pistorius state, they are in fact valid for any combination of (D, d) that fits the relationship P(p+ α/β) − E(e+ α/β) = D(d+ α/β). My Eq. 7 and 8 are then seen as the unique solution that solves this relationship regardless of the value of α/β. The necessary conditions that E < P, and Ee < Pp, which Elmehdi and Pistorius also point out in their letter, were also stated in my article at the bottom of page 873. A simple α/β-independent method to derive fully isoeffective effective schedules following a change in dose per fraction: In regard to Joiner (Int J Radiat Oncol Biol Phys 2004;58:871–875)International Journal of Radiation Oncology, Biology, PhysicsVol. 63Issue 1PreviewWe applaud the effort by Joiner (1) in highlighting the necessity to derive formulae by which dosimetric errors in delivering the prescribed dose per fraction in a treatment can be corrected. The prescribed dose, the dose delivered in error, and compensating dose and their corresponding fractions are shown schematically in Fig. 1. In attempting to come up with formula for the compensating dose and its fraction values, the author made the following assumption: “because α/β can take any value, the dose per fraction to be given for the remainder of the treatment, d, can be derived from either Eq. Full-Text PDF" @default.
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• W1978610706 date "2005-09-01" @default.
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• W1978610706 title "In reply to Drs. Elmehdi and Pistorius" @default.
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• W1978610706 doi "https://doi.org/10.1016/j.ijrobp.2005.05.040" @default.
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