Heron (Hero of Alexandria) was a Greek mathematician who defined multiple geometric equations including several for the triangle. This equation can be used to monitor proptosis if imaging studies are not available.
Heron's formula for the area of a triangle =
= SQRT(X*(X-a)*(X-b)*(X-c))
where:
• a, b, and c are sides of the formula.
• X is the perimeter (a+b+c) divided by 2.
The area of the triangle is also:
area =
= c * (height of the perpendicular line to the apex) / 2
Finally, proptosis is defined as the distance that the center of the cornea is beyond the lateral orbital margins. This is the height of the perpendicular line in the second area equation.
Parameters:
(1) c = distance in mm between the left and right lateral orbital margins
(2) a = distance from the center of the corneal surface to the closer orbital margin in mm
(3) b = distance from the center of the corneal surface to the further orbital margin in mm
Since the 2 area equations have the same value, they can be equated and then solved for the height.
NOTE: This requires a precise method for measuring the distances involved. The authors used a modified compass to take measurements, as demonstrated in Figure 3. An ultrasound probe was used in proximity to the cornea. Hopefully the clinician has a steady hand.
