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The Baldwin 2014 2-site exact solution relaxation dispersion model for SQ CPMG-type data. This model is labelled as B14 in relax.

This model is not implemented yet

Equation

The paper main equation 50, needs following definitions

[math] v_{1c} = F_0\cosh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\cosh{\left(\tau_{\textrm{CP}}E_2\right)} \\ v_{1s} = F_0\sinh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\sinh{\left(\tau_{\textrm{CP}}E_2\right)} \\ v_{2}N = v_{1s}\left(O_B-O_A\right)+4O_B F_1^a \sinh{\left(\tau_{\textrm{CP}}E_1\right)} \\ p_D N = v_{1s} + \left(F_1^a+F_1^b\right)\sinh{\left(\tau_{\textrm{CP}}E_1\right)}\\ v_3 = \left( v_2^2 + 4 k_{\textrm{BA}} k_{\textrm{AB}} p_D^2 \right)^{1/2} \\ y = \left( \frac{v_{1c}-v_3}{v_{1c}+v_3} \right)^{N_{\textrm{CYC}}} [/math]

Equation compared to Carver Richards 72

Please see the relax summary of the model parameters here.

These definitions comes from the papers "Supplementary Section 4. Relation to Carver Richards equation".

[math] \tau_{\textrm{CP}} = \frac{1}{4\nu_\textrm{CPMG}} \\ \alpha_- = \Delta R_2 + k_{\textrm{AB}} - k_{\textrm{BA}} \\ \zeta = 2 \Delta \omega \, \alpha_- = h_1\\ \Psi = \alpha_-^2 + 4 k_{\textrm{BA}} k_{\textrm{AB}} - \Delta \omega^2 = h_2\\ \xi = \frac{2\tau_{\textrm{CP}}}{\sqrt{2}}\sqrt{\Psi + \sqrt{\Psi^2 + z^2}} = 2h_3 \tau_{\textrm{CP}} = \tau_{\textrm{CP}}E_0\\ \eta = \frac{2\tau_{\textrm{CP}}}{\sqrt{2}}\sqrt{-\Psi + \sqrt{\Psi^2 + z^2}} = 2h_4 \tau_{\textrm{CP}} = \tau_{\textrm{CP}}E_2\\ D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z^2}} \right) = F_0 \\ D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z^2}} \right) = F_2 [/math]

Physical meanings:
[math]\xi[/math] and [math]\eta[/math] are differences of the real and imaginary components of the free precession frequencies [math]f_{00}[/math] and [math]f_{11}[/math] (equation (41)).
[math]D_+[/math] and [math]D_-[/math] are the stay/stay ([math]F_{0}[/math]), and swap/swap ([math]F_{2}[/math]) coefficients (equation (36)).
[math]\zeta[/math] and [math]\Psi[/math] are parameters that enable the free precession frequencies to be written in a more concise form (equation (12)).
Note that in reference 2 (10.1016/S0076-6879(01)39315-1), in equation 25, the definition used for [math]\tau_{\textrm{CP}}[/math] is twice that used in this work but is otherwise identical.

Parameters

The B14 model has the parameters

Reference

The reference for the B14 model is:

  • A.J. Baldwin (2014). An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange. J. Magn. Reson., 2014. (10.1016/j.jmr.2014.02.023).

Related models

The B14 model is a linear correction to the CR72 model, and algorithms based on this have significant advantages in both precision and speed over existing formulaic approaches.

Links

See also