 # Fractional Anisotropy formula

Hi,
I have been trying to mathematically derive the formula to find FRACTIONAL ANISOTROPY
(Fractional anisotropy is a method that is used to emphasize and evaluate white matter fiber tracts)

The formula that is given in many textbooks and published paper is I understand the purpose of Lambda but unable to understand the need for SQUAREROOT (3/2)

Please do kindly explain the reason behind having SQUAREROOT(3/2) for the Fractional Anisotropy formula

The paper from which I found this formula is http://ac.els-cdn.com/S109078071100334X/1-s2.0-S109078071100334X-main.pdf?_tid=1a51f47e-3ca7-11e6-b075-00000aab0f26&acdnat=1467060088_0e9b31e7bbd5af7c0353a9eb06eae939

-Rahul Manay

I’m not a mathematician, I don’t know the formula and this is not a math forum, however I found that the FRACTIONAL ANISOTROPY is defined as the standard deviation of the eigenvalues divided by the mean of the squared Eigenvalues. If you put both formulas together you can derive the FRACTIONAL ANISOTROPY:

Look at the formula for the sample standard deviation: https://www.mathsisfun.com/data/standard-deviation-formulas.html where n -1 in our formula is 2.

The mean of the eigenvalues where we have 3 samples: If you put both formulas together (division of fractions) you can mathematically reorganize the formula and draw out the SQUAREROOT (3/2) as a multiplication.

Here is the same formula from the German wiki without the seperation of the SQUAREROOT (3/2)

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