234 



GROWTH 



PRINCIPLES AND THEORY 



and a general physiological differential is the common cause for the differences in suscepti- 

 bility, metabolism and morphogenetic potencies. However, Child's theory is oversimplified 

 and neglects morphological as well as cytological and physiological characteristics. Even 

 in Child's classical example, the planaria, not only growth gradients and Child's gradients 

 have an opposite direction but even in the latter differences are found (Fig. 36). Hence 

 even in simple organisms such as planarians, there is not a uniform gradient but rather a 

 bundle of polar gradients that are only loosely correlated. (Bertalanffy, ig42b; Bertalanffy, 

 Hoffmann-Ostenhof and Schreier, 1946; Hoffmann-Ostenhof, Bertalanffy and Schreier^ 

 1948; Schreier, 1949). In hydroids, the growth gradient can be interpreted cytologically ; it 

 coincides with the distribution of undifferentiated I-cells and biochemically, with the 

 distribution of RNA which is connected with protein synthesis (Tardent, 1954). 



A mathematical theory of differentiation based on the concepts of open systems, physio- 

 logical dominance, competition, and gradients was developed by Spiegelman (1945). 



0% 100% 40% 



g 



Fig. 36. Comparison of gradients in Planarians. a Schema of body regions, b Gradient 

 of regenerative potency (head formation and total restitution) of the body when experi- 

 mentally cut into 8 pieces; after Child, c Gradient of regenerative potency of eights of the 

 postpharyngeal region; after Child, d Gradient of Oj-consumption; after Hyman. e Gradient 

 of susceptibility to distilled water; after Buchanan, y" Gradient of susceptibility to alcohol; 

 after Bertalanffy. g Growth gradient constructed from allometry constants of growth of 

 body regions; after Bertalanffy. After Bertalanffy, 1942b. 



{g) Growth of organs in time 



The growth-in-time of organs (except in a special case to be mentioned 

 presently) does not follow the formvdas valid for the growth of the organism as a 

 whole, both for biological and mathematical reasons. Biologically, the growth of 

 an organ whose existence and development depends on the body as a whole, 

 cannot be compared with that of an independent organism. Mathematically, a 

 sum of equations is formally identical with the summated terms only if these are 

 linear, which obviously is not the case either for growth of the total organism or 

 of its parts. 



Donaldson (1924) classified the organs of the rat in j groups showing a different 

 course of growth: organs with early rapid growth (brain, spinal cord, eyes); 

 organs with nearly constant increase following a phase of rapid growth (heart, 

 kidneys, liver, lungs, digestive tract, etc.); and organs the growth of which shows 



