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\begin{equation}
\mathrm{R}_{1\rho} = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
\end{equation}
For this model, the equations from \citet{Korzhnev05a} have been used.
The $\mathrm{R}_{1\rho}$ value for state A magnetisation is defined as
\begin{equation}
\mathrm{R}_{1\rho} = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
\end{equation}
where
\begin{align}
M_0 &= \begin{pmatrix} \sin{\theta} \\ 0 \\ \cos{\theta} \\ 0 \\ 0 \\ 0 \end{pmatrix}, \\
\theta &= \arctan \left( \frac{\omegaone}{\offsetA} \right).
\end{align}
The relaxation evolution matrix is defined as
\begin{equation}
R = \begin{pmatrix}
-\mathrm{R}_{1\rho}prime-\kAB & -\delta_A & 0 & \kBA & 0 & 0 \\
\delta_A & -\mathrm{R}_{1\rho}prime-\kAB & -\omegaone & 0 & \kBA & 0 \\
0 & \omegaone & -\Rone-\kAB & 0 & 0 & \kBA \\
\kAB & 0 & 0 & -\mathrm{R}_{1\rho}prime-\kBA & -\delta_B & 0 \\
0 & \kAB & 0 & \delta_B & -\mathrm{R}_{1\rho}prime-\kBA & -\omegaone \\
0 & 0 & \kAB & 0 & \omegaone & -\Rone-\kBA \\
\end{pmatrix},
\end{equation}