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• W2026937948 abstract "It is found that tissue exhibits a property of “recovery from radiation effects.” The rate of recovery is generally assumed to be exponential (1 and 2). Due to this property of recovery, the effective radiation dose (sometimes called cumulative) tends toward an equilibrium value, that is, a value at which the rate of recovery of the tissue equals the rate of dosage. Assuming the fact of tissue recovery we will derive an expression for the effective (or cumulative) dose at the time just after it has been administered on the nth day. Since recovery begins the moment energy is absorbed by the tissue, we shall, for a first approximation, assume that the dose is administered instantaneously. To cover cases in which different doses are given on alternate days we shall take the case wherein Di, the initial dose, alternates with a dose Da on subsequent days. Let β be the recovery factor of the tissue for unit time. Thus β may be 4 per cent per day (3) as in the case of radium radiation filtered through 1 mm. of platinum, or it may be 8 per cent per day (2) as in the case of roentgen radiation of λeff = 0.16 Å. Let k = (1 − β), or the amount of radiation effect remaining after one day. First there is the case when n is odd. The contribution of the first day, A1 to the effective dose will be Dikn−1; the contribution of the second day, B2, will be Dakn−2, etc. Thus: The effective dose after n days is equal to the sum of the A's and B's, But: The series in the right-hand sides of Equations (1) and (1.1) are geometrical progressions of which the first term a is equal to 1; the common factor d = k2, and the number of terms are z = (n + 1)∕2. The sum of such a progression is Hence for the above series: The effective dose, De, is then When n is even; th ceorrtribtrtion of the first day, A1, is Dikn−1; that of the second day, B2, is Dakn−2, etc., whereas: And or The series in the parentheses of Equation (3) are geometrical; the first term is 1, the common factor is k2, and there are n∕2 terms in each. Thus: or" @default.
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• W2026937948 date "1934-12-01" @default.
• W2026937948 modified "2023-09-25" @default.
• W2026937948 title "Some Mathematical Aspects of Radiation Dosage" @default.
• W2026937948 doi "https://doi.org/10.1148/23.6.738" @default.
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