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Quantitiative Diffusion Measures

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Given the eigenvalues \lambda_1, \lambda_2, \lambda_3 and eigenvectors v_1, v_2, v_3 one can define many metrics.

Fractional anisotropy

Given a set of three eigenvalues \lambda_1, \lambda_2, \lambda_3  (variable ‘evalues’ in Matlab) the fractional anisotropy (FA) is calculated as:

FA = \frac{ \left(\lambda_1 - \lambda_2\right)^2+ \left( \lambda_1 - \lambda_3\right)^2 + \left( \lambda_2 - \lambda_3\right)^2}{2\left( \lambda_1^2 + \lambda_2^2 + \lambda_3^2 \right)}

which can be calculated using the following Matlab code:

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sum_sq_evalues = sum(evalues.^2);

sde = (evalues(1)-evalues(2))^2 + (evalues(2)-evalues(3))^2 + (evalues(1)-evalues(3))^2;
fa =  sqrt( sde / (2*sum_sq_evalues) );

For this, it doesn’t matter that the eigenvalues are sorted, though typically they are sorted from highest to lowest.

Apparent Diffusion Coefficient

Relative Anisotropy

Lambda Parallel

Lambda Perpendicular

Posted by craig at 11:49 am

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