630 HANDBOOK OF PHYSIOLOGY ^ CIRCULATION I 



10 



FIG. I. Analysis of data in a two-compartment system. In A, a semilogarithmic plot of hy- 

 pothetical specific activities in the two-compartment system is shown, with the equilibrium value, 

 xe, also indicated. In B, xe has been subtracted from the Xi values, giving the straight line (.Vi — xe), 

 and similarly (.vg — .vo) is another straight line having the same slope, which in both cases is meas- 

 ured by the half-time. An alternative method for getting the slope without using xg is shown in C, 

 where values of the lower curves are subtracted from those of the upper, giving tx[ — .vo). The use 

 of the constants thus established to calculate the flow rate, p, is discussed in the te.xt. 



If X20 = o, it is not necessary to collect data from 

 compartment 2 in order to calculate the turnover 

 rate constants for both compartments. Obviously, if 

 either ^i or S^ is known, p can be calculated from the 

 values of p/Si or p/Si- [In the corresponding equations 

 21 in reference (51), k^a and ksA were inadvertently 

 reversed.] 



Failure of the points (.vi — ^2), (xi — xe) or 

 {xe — X2) to fall on a straight line on semilogarithmic 

 paper suggests that some other model should be used 

 as the basis for interpreting the data. 



Three-Compartment and Multicompartment Systems 



As is true lor the simpler systems, the three-com- 

 partment systems have been completely solved in the 

 sense that formulas are available for deducing the 

 parameters of the system from data on the behavior 

 of a tracer in the system [Skinner et al. (62), Robertson 

 et al. (52), Solomon (64), Sheppard (59), Gellhorn 

 et al. (27), Cohn & Brues (15)]. Perl (48) gives 

 solutions for a four-compartment closed system. To 

 the best of this author's information, explicit formulas 

 have not been published for four-compartment open 

 systems or for systems having more than four com- 

 partments. 



The methods applicable to analysis of data in 

 multicompartment systems will be discussed in this 

 section and illustrated by application to the three- 

 compartment systems. 



Figure 2 illustrates the redistribution of an ex- 

 changeable substance which occurs in a three- 

 compartment closed system. 



EQUATIONS. A generalized form of equation i, equation 

 13 describes the change in the amount of tracer in 

 any compartment, ;', attributable to exchanges and or 

 transfers between it and another compartment, j: 



d{S, xd 

 dt 



= — P;i ■'^i -J- Pi) ''i 



(■3) 



In this notation, p,j is used to mean the rate of flow 

 into i from j. The reverse order of subscript notation 

 has been used by Solomon (64), the present author 

 (51, 52) and others, but the convention adopted here 

 conforms to usage in related fields, is favored by 

 Sheppard (60), Berman & Schoenfeld (7) and 

 Skinner et al. (62), and has some advantages which 

 appear below. In those systems in which p,y = p,i, 

 the two notations are interchangeable. 



Conversion from amount equations to specific 

 activity equations introduces many Pj,/S, and pu^'^i 



