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The History and Clinical Usefulness of Pi

Richard A. Norton, MD
Arch Intern Med. 1971;128(6):991-992. doi:10.1001/archinte.1971.00310240145020.
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The clinician setting out to dilate a stricture needs to know what size instrument will pass through it. The trial-and-error method for catheters, endoscopes, and bougies will work, but there is an easier way. One need only measure the diameter in millimeters of the narrowed segment on the roentgenogram and multiply by pi to get the circumference. This gives the French number of the bougie that should pass snugly.

With an esophageal stricture, for example, the film should show the narrowed segment fully distended with barium sulfate, as in the Figure. The diameter (arrows) must be corrected for magnification by multiplying by 0.83 using films taken with an overhead tube and a target-to-film distance of at least 36 inches.1 In order to find the proper bougie, one employs the following formula:

C = π D

where C is the circumference to be found,π is 3.14, and D the diameter as


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