R_i'(θ) gradients

A different partial derivative exists for the spectral density function parameter θ_j, the chemical exchange parameter ρ_ex, CSA parameter Δσ, and bond length parameter r. In model-free analysis the spectral density parameters include both the parameters of the diffusion tensor and the parameters of the various model-free models.

θ_j partial derivative

The partial derivatives of the relaxation equations with respect to the spectral density function parameter θ_j are

ρ_ex partial derivative

The partial derivatives of the relaxation equations with respect to the chemical exchange parameter ρ_ex are

Δσ partial derivative

The partial derivatives of the relaxation equations with respect to the CSA parameter Δσ are

r partial derivative

The partial derivatives of the relaxation equations with respect to the bond length parameter r are