Bone Mineral Metabolism in the R; 



125 



Results 



1. Functions M{t) 



It is possible to establish experimentally for given samples of bone (in this case, 

 the long bones of the rat), a series of functions M{t), namely M\,{t), Mc.^(t), Mi>(t), 

 for the diaphysis, the epiphysis or both. 



Between age 30 days and 120 days, these functions can be expressed by an equa- 

 tion of the following type: 



^(0: 



^"^ max. 



l+ae-W/n 



(1) 



where, Af„i:ix. is the limit value of the function when time becomes large. 



M, 



In 



1 =lna-kM, 



(2) 



a= - —1,Mq being the value of the function at time 0, 



Mq 



khz constant (units: M~^ t^^)- 



The numerical values of the parameters of Eq. 1, are derived from the linear 

 transformation of Eq. 1, that becomes: 



M{t) 



Since the value of A/,nax. is unknown, fitting the points to the best straight line was 

 realized by an iterative procedure, in which Mmax. was assigned values ranging 

 between ± 20''/o of the experimental value at time 150 days. The best fitted line was 

 selected by an analysis of 

 variances, based on the F test 

 of Snedecor. 



Table 1 gives in the dif- 

 ferent cases, the numerical 

 values of the parameters of 

 Eq. 1. Fig. 1 shows Afcn(0- 



In order to correlate ki- 

 netic data calculated from 

 measurements done in vivo, 

 with data derived from spe- 

 cific gravity separations of 

 diaphyseal samples, it is im- 

 portant to know whether or 

 not the diaphysis gives a 

 good picture of bone meta- 

 bolism, as a whole. 



One comparison which can be done is to relate the evolution with time of the 

 mass of calcium deposited in the diaphysis on one hand, and in the whole skeleton 

 on the other. These latter data exist in the literature (Sherman and MacLeod, 1925) 

 and can be expressed by an equation similar to Eq. 1 : 



Mc.it) =. .2100 (3) 



''^ ' 1 + 29.8 e-"'-055^ ^ ^ 



where Mc.,^ , the total mass of calcium in the body, is expressed in mg, and t, the age 

 of the rat, in days. This equation is valid for female rats between 30 and 120 days. 



Time [days] 



Fig. 1. Mass ot calcium (^/ca) 

 rats as a function of their age [t). 

 for groups of six animals. The de 

 standard deviations. The mass is nn 



the diaph 

 . The poi 



of the long bones of 

 represent mean values 

 ions shown correspond to two 

 red in mg and the age in days 



