6o2 



REGENERATION AND GROWTH 



IV. QUANTITATIVE ASPECTS OF REGENERATION 



The maximal rate of regeneration in the mammaUan Hver approaches that of 

 embryos and of maUgnant cancerous tissue (Christensen and Streicher, 1948). 

 The maximal absolute rate probably varies relatively little throughout the animal 

 kingdom (Table 6), though because the lower animals in general are small, they 



TABLE 6 



ABSOLUTE LINEAR RATES OF REGENERATION: REPRESENTATIVE EXAMPLES 



complete a regenerate of a particular relative size more rapidly than a larger ani- 

 mal (Table 7). Again the rate for intracellular regeneration, as in a nerve-fibre, is 

 about equal to that for a cellular structure such as a featherbud. 



The absolute rate of regeneration is not constant throughout one act, though 

 it is sometimes approximately so (Paulain, 1938), especially in Crustacean limbs; 

 however there is always an initial "lag" period, corresponding to the regressive- 

 phase, and usually the cessation of growth is far from abrupt, the rate declining 

 to zero according to an approximately exponential relation (Paulain, 1938). 

 Seddon et al. (1943) concluded that a number of very diverse algebraical relations 

 fitted, with equal approximation, this part of the curve of length/time, for a 

 regenerating mammalian nerve. A hyperbolic relation was most satisfactory on 

 empirical grounds. Here, as in a number of the examples given by Paulain, the 

 rate was virtually maximal once it did begin, after a long lag period. A relatively 

 abrupt onset is indicated also by the results of Ellis (1909), for the tadpole's tail, 

 of Du Noiiy (1936) for human skin, and of Needham (1949a), giving a composite 

 curve for limb-regeneration in a population of Asellus. Other instances show a 

 much more gradual onset (Ellis, 1909 Durbin, 1909; Paulain, 1938; Singer and 

 Craven, 1948) so that the complete curve is sigmoid (Fig. 2). In fact, no doubt, 

 all curves of regeneration and of other types of growth are essentially sigmoid since 

 the transition from zero to maximal speed and back can never be instantaneous 

 (see Thompson, 1942, p. 152). 



