INDICATOR SUBSTANCES AND FLOW ANALYSIS 



639 



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HG. 6. Four-compartment system specilic activity curves 

 generated by an analog computer and showing data points 

 displayed on same oscilloscope for convenience in curve-fitting. 



methods of programming and using digital computers 

 here. It will have to suffice to indicate that there are 

 several possible modes of use applicable to the analysis 

 of tracer data. 



One such use is at the stage of curve-fitting. 

 Largely because of the accumulated effect of the 

 random errors in real data, the attempts to achieve a 

 true least-squares fit for multi-exponential component 

 curves have not been entirely satisfactory. Of course, 

 a method similar to the peeling-off technique used in 

 graphical anahsis can be used, with the least-squares 

 method being used to give the best fit for each 

 component, but this has been objected to on the 

 grounds that it gives nonuniform v^eighting of the 

 data points. An entirely different procedure for 

 resolving curves into exponential components has 

 been published by Gardner et al. (26). The latter 

 method used a Fourier transform method with 

 numerical integration being achieved with an IBM- 

 650 computer. 



Another application of digital computers to 

 problems of compartmental analysis arises after the 

 necessary parameters describing the curve in terms of 

 exponential components have been achieved, and 

 consists of transforming the parameters of the data 

 into the parameters of the system, as indicated in 

 principle in equation 19. Alternatively, the computer 

 may be programmed to test a large number of possible 

 models systematically and to select those which best 

 fit the data. 



The general principles of programming digital 

 computers and some biological applications are 



FIG. 7. Curves fitted v^-ith analog computer to concentration 

 in plasma of creatinine injected intravenously at a constant rate 

 during first 30 min. (Data courtesy Dr. Paul Schloerb. ) 



discussed by Stacy (68). Sheppard (59) presents a 

 detailed program for solving three-compartment 

 nonsteady-state problems, written in FORTRANSIT, 

 a "language" for giving instructions to IBM-650 

 digital computers. The FORTRANSIT program 

 requires only slight modifications to FORTRAN, a 

 more general program for u.se with IBM-704, -7090, 

 Univac, and other modern high-speed machines. 

 Each of these machines requires a translation of the 

 FORTRAN program into its own "machine lan- 

 guage" (using binarv or octal instead of decimal 

 numbers, etc.), but this translation is achieved 

 automatically when cards punched to represent 

 F'ORTRAN statements are used as the input for the 

 appropriate translating machine. Herman et al. (9) 

 have developed a very general program suitable for, 

 but not restricted to, linear systems or even to com- 

 partmented systems. This program can handle up to 

 40 parameters, of which up to 25 may be unknowns, 

 in a system of up to 15 compartments. A set of IBM 

 cards with the FORTRAN statements or a set 

 suitable for direct use with the IBM-704 is available 

 upon request from Dr. Mones Berman, National 

 Institutes of Health, Bethesda, Md. A good example 

 of the kind of problem for which this program is 

 suited, involving finding a model giving the best fit to 

 a set of plasma and excretion data, is presented by 

 Lewallen et al. (42). 



