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swayzak
05-02-2007, 05:31 PM
hi

I am a pathologist, involved in examination if cells to diagnose disease.

Forgive me if I over-simplify here but I want to make the problem clear.

As you may recall, a cell is the fundamental building block of most life.

Simply, it consists of a large circle, within which is a smaller circle (the nucleus).

Now in the cervical cancer screening program, we examine smears for signs of "pre-cancerous" cells & advise appropriate management (if abnormal, either early repeat smear or refer to gynaecologist for cervical examination depending on the severity of the abnormalities).

If the nucleus is abnormal ("dyskaryosis"), the larger it is (in relation to overall cell size), the more likely there is more advanced precancer present.

The original classification for these changes used the nuclear:cytoplasmic AREA ratio (cytoplasm = whole area of cell) where upto 1/3 = mild dysk, 1/3-2/3 = moderate and >2/3 = severe.

Howver, most pathologists found assessing the ratio using DIAMETER much easier & more reproducible.

Now instinct tells me that the ratios above are not equivalent when using area vs diameter.

So can someone translate the area ratios to diameter ratios ?

e.g. for mild, moderate & severe area ratios, what are the equivalent diameter ratios ?

My very rusty maths would suggest that, if the nuclear radius = z and cytoplasmic radius = y, then the solution relates to the ratio of pi x z squared & pi x y squared.

Advice would be much appreciated !

thanks

OfficeShredder
05-02-2007, 05:36 PM
If the ratio of the areas is < 1/3, then (let d be the diameter of the nucleus, D the diameter of the cell)

Pi*(d/2)^2 / Pi*(D/2)^2 <= 1/3

which cancels out to

(d/D)^2 < 1/3

or d*sqrt(3)<D

For an area between 1/3 and 2/3s you get

1/3<(d/D)^2)<2/3

D<sqrt(3)*d<sqrt(2)*D

And for over 2/3s,

sqrt(3)*d>sqrt(2)*D

swayzak
05-02-2007, 06:25 PM
Sorry but could you simplify that even further for a numpty like me ;)

equivalent ratio ranges to the area ones I gave (mild upto X, mod X to Y, sev > Y

thanks

OfficeShredder
05-03-2007, 08:07 AM
So mild would be < 1/sqrt(3),

moderate for the ratio between 1/sqrt(3) and sqrt(2/3)

and severe for the ratio above sqrt(2/3)