574 Electronic Computers /3 1 : 3 



data, one could then compute an average density for the bone slice. 

 This process so far has used one analogy, that of the bone and wedge. 



Calculation, or even measurement, of all the points as described in the 

 last paragraph would make this so slow and laborious that it could be used 

 in only a limited number of experiments. No simple analytical rules exist 

 relating film darkening and wedge thickness. If broad-band X rays 

 from a clinical-type X-ray tube are used, the absorption of the wedge will 

 not increase exponentially with wedge thickness. The density of the 

 film will be a complex combination of emulsion sensitivity, developer 

 strength, and so on. 



To shorten the computing time, various electrical analogs are used. 

 The wedge is scanned with an optical densitometer, and the curve of 

 optical density versus wedge thickness is recorded with a potentiometer- 

 type recorder. The curve represents the functional relationship between 

 optical density of the film and wedge thickness. 



This function is then used to set up what is called a "function trans- 

 former." It operates so that, when a voltage is fed to it corresponding 

 to a given optical density, another voltage is produced which is then 

 proportional to the wedge thickness corresponding to that optical 

 density. (The function transformers used in several bone-density com- 

 puters are electromechanical function transformers which convert 

 the electrical input into a mechanical displacement and then into a new 

 voltage. However, this is purely fortuitous; completely electronic 

 function transformers could equally well be employed.) The output of 

 the function transformer represents equivalent wedge thickness. Thus, 

 if the wedge were traced at a constant velocity, a straight line graph 

 should be obtained for the output of the function transformer against 

 time. 



If, instead of retracing the wedge, the optical densitometer is set to 

 trace the photograph along a line across the image of the bone, then the 

 function transformer output against time is the analog of the equivalent 

 wedge thickness plotted against distance across the bone. To obtain 

 average values, this output is integrated electronically. A final output 

 number is obtained whose units are unrelated to bone mass, but whose 

 value is linearly proportional to the bone mass along the path traced. 

 Again, if one knows the cross-sectional area, this mass may be described 

 by an average bone density. 



Figure 1 shows an X-ray photograph of a rat and a wedge. Curves 

 of the optical density and of the equivalent wedge mass are shown in 

 Figures 2 and 3. In this computation, wedge thickness and bone mass 

 are considered to be analogs of one another, as also are optical density 

 and voltage, and distance and time. In addition, another voltage has 

 been made analogous to the mass of the calcium phosphate. 



