134 RADIATION BIOLOGY 



are e~"'^, e~"^^, . . . , e~""^. The corresponding probabilities of occurrence are 



1 - e-"'», 1 - ?'«='», . . . , 1 - e-""^ 



The probability of occurrence of all events is the product of these separate 



probabilities : 



(1 - e-"'^){\ - e-^^-D) . . . (1 _ ^-a„D^ (54) 



This expression is the counterpart of Eq. (52) derived from a different working 

 model. The counterpart of Eq. (53) is 



N(D)/No = 1 - (1 - e-«'^)(l - e-"^^) •■•(!- e-""-^) (55) 



Tests have been devised (see, for example, Curie, 1929), and other tests could 

 probably be developed, to describe an experimental dose-effect curve by one or 

 the other of Eqs. (53) and (55) and to fix the appropriate value of n. However, 

 the fitting procedures are not critical. A reliable determination of the number 

 of hits and a discrimination between different types of equations, such as (53) and 

 (55), would require a higher experimental accuracy than is attained in practice. 



Possible inhomogeneities within the population, with regard to the response of 

 individual organisms to radiation, complicate the analysis of dose-efTect curves. 

 The effect of inhomogeneities tends to bend the curves of Fig. l-82b in the oppo- 

 site way, i.e., to reduce their net curvature and the apparent value of the number 

 of hits. 



5-4. "TIME-INTENSITY" FACTOR 



Thus far we have failed to consider the possible influence of the rate of 

 delivery of a radiation treatment upon the eventual effect of the treat- 

 ment. The dose of a treatment indicates the total amount of energy 

 absorbed by the treated material irrespective of the total duration of the 

 exposure to radiation and of possible variations of the radiation intensity 

 during the exposure. 



Equal doses can be delivered in very short and intense bursts or over 

 long periods of time at a very low intensity. For example, there can be 

 delivered within less than 1 microsecond an X-ray dose of the order of 

 10 r, which corresponds to the absorption of 1000 ergs per gram of tissue 

 and has appreciable biological effectiveness (see Slack and Thilo, 1944). 

 The same dose can be delivered at a steady rate by a weak radioactive 

 source of y rays over a period of weeks, months, or years. 



Control over the distribution of a radiation treatment in the course of 

 time offers, in principle, an opportunity for investigating the mechanism 

 of radiation effects. Studies in which this control is variously appHed 

 are often called studies of the "time-intensity factor," or simply of the 

 "time factor." These studies have yielded thus far only moderate 

 results. 



Two simple patterns of intensity distribution appear particularly con- 

 venient for investigating the influence of the time factor. The method 

 most commonly employed is to keep the intensity of irradiation constant 



