Description

Butz described the roundness index for an ellipse. This compares the area of an ellipse to a circle with the same circumference. This can be used to describe anatomic structures like the trachea.


 

Parameters:

(1) a = major diameter in mm

(2) b = minor diameter in mm

 

roundness index =

= 2 * (major diameter) * (minor diameter) / (((major diameter)^2) + ((minor diameter)^2))

 

This can be derived from the following relationships:

 

area of ellipse =

= PI() * (major diameter) * (minor diameter) / 4

 

circumference of the ellipse =

= PI() * SQRT((((major diameter)^2) + ((minor diameter)^2)) / 2)

 

circumference of a circle =

= PI() * 2 * (radius)

 

area of the circle =

= PI() * ((radius)^2)

 

PI() * 2 * (radius) =

= PI() * SQRT((((major diameter)^2) + ((minor diameter)^2)) / 2)

 

radius for circle with same circumference =

= (1/2) * SQRT((((major diameter)^2) + ((minor diameter)^2)) / 2)

 

area of the circle =

= (1/8) * (((major diameter)^2) + ((minor diameter)^2))

 


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