312 THE LANGUAGE AND CONCEPTS OF CONTROL 



fraction of injected Fe 59 diminishes in the plasma. The analysis was in- 

 tended to suggest why. 



Recollection of the content of Chapter 8 will permit verification that the 

 rates of the various steps in these two schemes (Figure 11-6) are given as 

 follows: 



du/dt = — k\u + k 2 v 



dv/dt = +k- [ u — (k n + k 3 )v + k A w 



dw/dt = +k 3 v - (k A + k 5 )w 

 for model, or scheme (a), and 



dx/dt = -k x x + k 2 y 



dy/dt = +A,.v - (k 2 + £ 3 + k 5 )y + k 4 z 



dz/di = + k- i y - k 4 z 



dm/dt = + k 5 y — k b m 



for model, or scheme (b) in Figure 1 1-6. 



The problem for the REAC C-302 analog computer, then, was to find a 

 set of solutions to these equations so that the concentrations u, v, w, and x, 

 y, z, and m (all in per cent remainder of radioactive iron added) could be ex- 

 pressed as a function of time, from time zero, when the tracer was added, out 

 to about ten days, the last of the measurements. More specifically stated, 

 the problem was: For what values of the rate constants, k, would the concen- 

 trations v and y, for example, have values which corresponded most closely 

 with the concentrations measured by sampling? If the k's could be so found, 

 then some knowledge would exist about the relative rates of the various 

 metabolic processes into which this added iron enters from the plasma. 



We shall not discuss how the computer was programmed, for this is in- 

 volved and would serve no useful purpose here. Suffice it to say that the 

 values of A could be adjusted as voltages on control potentiometers, much 

 like the volume control on a radio. They could be adjusted and readjusted 

 until the best fit of the experimental data was obtained. Some final, best-fit 

 values are given in Table 11-2, from which it can be seen that the rates of 

 the processes defined by Figure 11-6 do indeed change markedly from nor- 

 mal to diseased patients. Note, for instance that the slow step in the aplastic 

 anemia case is the synthesis of bone marrow (A 5 ), while this is just the proc- 

 ess that runs amok in polycythemia vera. 



This is only a first approach to this problem, and is described here pri- 

 marily to illustrate the method, and the power, of machine-aided analysis. 

 As the authors state, in future runs certain other experimentally measurable 



