Surface & Lenght Density 
Buffon Needles Problem  
Georges Louis Leclerc,Count of Buffon
(1707 – 1788)
He was a French naturalist, mathematician
 cosmologist and encyclopedic author.
Surface Density
Sv=2 ΣI/ Σ(l/p)

where "S v " or surface density is defined as the surface area of a structure per unit volume of the reference space.
"Sv "   is equal to two times the intersections of the structure surface with the test lines. 
Length Density

Lv= 2A =  ΣQ/ Σ(a/f)

where "L v "  is the length of a tubular structure per unit volume of the reference space,


"A "
  is the number of profiles of the tubular structures per unit area.
Length Estimation in Thick Vertical Section:

Estimation of  the microvessels length of muscle         
Lv=2 . I / L
Lv=2. I / P. (l/p)
Thick section: >20 μm
Vertical section
Major axis of the cycloids should be parallel to the vertical direction
Combined length and number estimation:

Estimation of the length of neurites or spermatozoa tail in 2-D space                 
L=π/2. (a/l) . (1/asf). ΣI
asf (L)=the area of Merz grid / the area of the basic tile (x.y)
 asf(N)= The area of counting frame / the area of the basic tile (x.y)
Estimation of length of dendrites

1-   Thick sectioning
2-   Counting intersections

 Histomorphometry & Stereology Research Center
Shiraz University Medical Sciences
Postal code: 71348 - 45794
Tel & Fax: + 98 71 32304372    

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