130 



L. J. RiCHELLE, C. OnKELINX, J. "P. AuBERT 



points will be presented together with the refined solution of the model, unbiased by 

 the assumed identity of Eqs. 6 and 9. The line in Fig. 4 represents values of [Ca] 

 calculated from Eq. 17. 



0.60 





O.JO 

 0.20 



a/0 



10 20 30 W so 60 70 80 30 100 I/O 120 

 w [Days] 



Fig. 4. Function of calcification [Ca] (w). The calcium content [Ca] of an elementary volume is shown as a 

 function of the age of the elementary volume (w). The calcium content is expressed in mg/mm' and the age 



Discussion 



It is possible to proceed further with this type of analysis and distinguish for 

 instance in the v^^ as defined by kinetic analysis, the part due to the appearance of 

 new elementary volumes as opposed to the mineralization of already existing ones. 



We shall limit ourselves in the present paper to the discussion of the function 

 [Ca](..). 



The equation of the function of calcification is of the type 



[Ca] = [Ca]o+ (ICa]max^[Ca]> ^^g^ 



co + r 



where [CaJ^ is the calcium content of the elementary volume for to = 0; 



[Ca],i,ax. is the maximum calcium content of the elementary volume; 

 r is a constant, which is the time of half maximum calcium increase. 

 Such a function had been predicted and sketched with a good approximation by 

 Robinson in 1958 on the basis of autoradiographic and microradiographic observa- 

 tions. 



The rate of calcification, that is the derivative of Eq. 18 is given by 



d[Ca] _ r ([Ca] max.-[Ca]o) 

 {co + r)' 



dco 



(19) 



which is identical with 



d[Ca] 

 dco 



([Ca 



[Ca])2 



(20) 



r ([Ca]max.— [Ca]o) 



Eq. 19 and 20 show that the rate of calcification decreases rapidly as time and 

 calcification increase. This does not agree with the proposed diagramatic representa- 

 tion of Neuman and Neuman (1958), which assumed a constant rate of mineral 

 acquisition up to ZO^/o of maximum calcification. Eq. 20 characterizes the kinetics of 

 a reaction of the second order, the significance of which remains to be established. 



