Sec. 16.6] I X TERN A L DOSIMETRY 431 



presumably the maximum gamma-ray dose is received. If the body were 

 actually a cylinder filled with soft tissue of unit density, the calculated dose 

 would be very nearly correct, but since the body contains large cavities and 

 an extensive bone structure consisting largely of minerals, it can be said only 

 that the computed values should be in the correct order of magnitude. 

 The dose received at any other point in the body should be less than at the 

 center, but it is difficult to make such calculations; at the surface of the skin, 

 for example, the gamma-ray dose may be from one-fourth to nearly one-half 

 that at the center. The necessity for uniform distribution of active material 

 is in this case entirely satisfied, at least initially, but in many other instances 

 it is not so certain. Finally, the contribution to the dose made by the beta 

 particles emitted by the isotope must, of course, also be computed. In most 

 cases, especially where small organs are involved, the beta-particle dose will 

 be many times greater than that produced by the gamma rays. 



16.6. Calculation of Radioactivity Density in Tissue. The dose delivered 

 to tissue or an organ that has taken up radioactive material in one form or 

 another depends directly on the number of atoms that disintegrate while 

 still within the tissue. The estimate of this number is, with a few notable 

 exceptions, complicated by the involved and often uncertain metabolism 

 of the radioactive isotope itself or the substance in which it is incorporated. 

 In most instances metabolic uptake and elimination of active material exhibit 

 rates that are comparable to and often very much smaller than the rate of 

 radioactive decay. Consequently, the number of atoms that decay while 

 in the particular organ under consideration usually is not equal to the number 

 of unstable atoms that pass through it; some atoms decay before entering 

 and many decay after leaving the organ. An estimate can be made, however, 

 when the metabolism of the isotope is known at least superficially, i.e., the 

 gross rates of uptake and elimination regardless of the chemical changes that 

 the isotope undergoes. 



To do this it is necessary to determine either empirically or by calculation 

 the activity density u expressed in microcuries per gram of tissue at any 

 instant, and the function 3.7 X 10 4 Z7, the number of disintegration per 

 gram of tissue in a given interval of time. 



It is to be expected that a mathematical description of metabolic processes 

 will often be impossible or else lead to inconveniently complicated expressions, 

 particularly where second- or higher order chemical reactions are involved. 

 If it is assumed, however, that uptake and elimination can be described by a 

 linear or exponential function of time, the calculations are reasonably 

 tractable and the results are valid for many biological processes and may serve 

 as a first approximation in more involved cases. In addition, it must be 

 assumed that the density of active material is uniform throughout the organ 



