The NS 2-site R1ρ model

This is the numerical model for 2-site exchange using 3D magnetisation vectors. It is selected by setting the model to `NS R1rho 2-site'. The simple constraint pA > pB is used to halve the optimisation space, as both sides of the limit are mirror image spaces.

For this model, the equations from Korzhnev et al. (2005b) have been used. The R1ρ value for state A magnetisation is defined as

R1ρ = - $\displaystyle {\frac{{1}}{{T_{\textrm{relax}}}}}$⋅ln$\displaystyle \left(\vphantom{ M_0^T \cdot e^{R \cdot T_{\textrm{relax}}} \cdot M_0 }\right.$M0TeR⋅TrelaxM0$\displaystyle \left.\vphantom{ M_0^T \cdot e^{R \cdot T_{\textrm{relax}}} \cdot M_0 }\right)$, (11.81)


M0 = $\displaystyle \begin{pmatrix}\sin{\theta} \\ 0 \\ \cos{\theta} \\ 0 \\ 0 \\ 0 \end{pmatrix}$, (11.82)
θ = arctan$\displaystyle \left(\vphantom{ \frac{\omega_1 }{\Omega_{\textrm{A}}} }\right.$$\displaystyle {\frac{{\omega_1 }}{{\Omega_{\textrm{A}}}}}$$\displaystyle \left.\vphantom{ \frac{\omega_1 }{\Omega_{\textrm{A}}} }\right)$. (11.83)

The relaxation evolution matrix is defined as

R = $\displaystyle \begin{pmatrix}-\mathrm{R}_{1\rho}'-\textrm{k}_{\textrm{AB}}& -\d...
...rm{AB}}& 0 & \omega_1 & -\mathrm{R}_1-\textrm{k}_{\textrm{BA}}\\  \end{pmatrix}$, (11.84)

where δA, B is defined in Equations 11.78a and 11.78b.

More information about the NS R1rho 2-site model is available from:

The relax user manual (PDF), created 2016-10-28.