124 L. J. RiCHELLE, C. OnKELINX, J. -P. AUBERT 



gravity and chemical composition it had reached. Such a representation permits a 

 formal analysis of the system. 



Thanks to experimental data, obtained from combined kinetic analysis of calcium 

 metabolism and a technique of microsampling of bone tissue, the formal analysis 

 leads to the definition of mathematical expressions for the various functions. 



It is the purpose of this paper to establish and discuss a particular aspect of the 

 analysis, namely the kinetics of the process of mineralization in the rat. 



Experimental 



Material and methods 



All experiments were done Vv^ith female Wistar R rats. The animals were fed a 

 powder diet containing 0.65"'/o Ca, 0.690/0 P, 1 i. u. vitamin D per gram and distilled 

 water ad libitum. 



Every experimental animal was studied by the method of Aubert and Milhaud 

 (1960) to measure the parameters of calcium metabolism. This requires the determi- 

 nation of a chemical and radiochemical balance and the analysis of the serum dis- 

 appearance curve of a single dose of Ca'*^ injected intravenously. 



Diaphyseal bone samples from these animals were separated into fractions of 

 progressively increasing specific gravities by successive centrifugations in mixtures of 

 toluene and bromoforme (Herman and Richelle, 1961; Richelle, 1964). All the 

 chemical and radiochemical determinations were carried out, with the aid of auto- 

 matic machines. The experimental data as obtained from the records of the machines, 

 were transferred to punched cards and processed through an IBM 7040 digital com- 

 puter. The programme computed the individual data, analysed them statistically and 

 proceeded to the evaluation of the complete set of data, in terms of a logical analysis 

 based upon the selected model. All the methods and techniques are detailled elsewhere 

 (Onkelinx et al., 1965). 



Abh 



reviations 



The following abbreviations will be used: 

 t , time corresponding to the age of the animal; 

 0) , time corresponding to the age of an elementary volume of bone; 

 d ■, the specific gravity; 

 [Ca], mass of calcium per unit volume; 

 M , mass; Afc-, refers to mass of calcium, Af]> refers to mass of phosphorus, Mu 



refers to mass of bone; 

 N , number of elementary volumes which are present; 

 N( , number of elementary volumes which have been formed; 

 N,\ , number of elementary volumes which have been destroyed; 

 /m , frequency distribution of the mass; 

 /x , frequency distribution of the number of elementary volumes. 



All these parameters can be written as functions of one another; in this case, 

 the independent variable is written between parentheses. For example, the evolution 

 of the mass with time will be written M{t) and the value of the function at a given 

 time t\ will be referred to as M{t\). 



