Table 1.

Diffusion tensor imaging-derived tensor metric formulas

MD

MD = D = (λ1 + λ2 + λ3)/3

FA

FA = [(3/2) × (q/L)]1/2 = (3/2)1/2{[(λ1 - D)2+(λ2 - D)2+(λ3 - D)2]/(λ12 + λ22 + λ32)}1/2

RA

RA = q/p = {[(λ1 - D)2 + (λ2 - D)2+(λ3 - D)2]1/2}/[31/2D]

RD

RD = (λ2 + λ3)/2

AD

AD = λ1

Cs

Cs = 3λ3/(λ1 + λ2 + λ3)

p

p = 31/2D = (λ1 + λ2 + λ3)/31/2

q

q = [(λ1 - D)2 + (λ2 - D)2 + (λ3 - D)2]1/2

L

L = (p2 + q2)1/2 = (λ12 + λ22 + λ32)1/2

Cl

Cl = (λ1 - λ2)/(λ1 + λ2 + λ3)

Cp

Cp = 2(λ2 - λ3)/(λ1 + λ2 + λ3)

MD: Mean diffusivity; FA: Fractional anisotropy; RA: Relative anisotropy; RD: Radial diffusivity; AD: Axial diffusivity; Cs: Spherical tensor; p: Pure isotropic diffusion; q: Pure anisotropic diffusion; L: Total magnitude of the diffusion tensor; Cl: Linear tensor; Cp: Planar tensor.