Difference between revisions of "CR72 full"

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<math>
 
<math>
\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\
+
\alpha_- = R_2^A - R_2^B + k_{\textrm{AB}} - k_{\textrm{BA}} \\
\Psi = (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}})^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\
+
\zeta = 2 \Delta \omega \, (R_2^A - R_2^B +k_{\textrm{AB}} - k_{\textrm{BA}} ) \\
\eta_+ = \frac{1}{\sqrt{2^3}\nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
+
\phantom{\zeta} = 2 \Delta \omega \, (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} ) \\
\eta_- = \frac{}{\sqrt{2^3}\nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
+
\phantom{\zeta} = 2 \Delta \omega \alpha_- \\
D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z^2}} \right) \\
+
\Psi = (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} )^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\
D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z^2}} \right)
+
\phantom{\Psi} = \alpha_-^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\
 +
\eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
 +
\eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
 +
D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\
 +
D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right)
 
</math>
 
</math>
  
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== Parameters ==
 
== Parameters ==
  
The CR72 full model has the parameters {$R_{2A}^0$, $R_{2B}^0$, $...$, $p_A$, $\Delta\omega$, $k_{ex}$}.
+
The CR72 full model has the parameters {{{:R2Azero}}, {{:R2Bzero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}.
  
 
== Reference ==
 
== Reference ==
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The reference for the CR72 full model is:
 
The reference for the CR72 full model is:
  
* Carver, J. and Richards, R. (1972).  General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. ''J. Magn. Reson.'', '''6'''(1), 89-105. ([http://dx.doi.org/10.1016/0022-2364(72)90090-X 10.1016/0022-2364(72)90090-X]).
+
* {{#lst:Citations|CarverRichards72}}
  
 
== Related models ==
 
== Related models ==
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The [[Relaxation dispersion citation for relax|implementation of the CR72 full model in relax]] can be seen in the:
 
The [[Relaxation dispersion citation for relax|implementation of the CR72 full model in relax]] can be seen in the:
* [http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html relax manual],  
+
* [http://www.nmr-relax.com/manual/The_full_CR72_2_site_CPMG_model.html relax manual],  
 
* [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation],
 
* [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation],
 
* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full relaxation dispersion page of the relax website].
 
* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full relaxation dispersion page of the relax website].
  
 
== See also ==
 
== See also ==
[[Category:Relaxation_dispersion]]
+
[[Category:Models]]
 +
[[Category:Dispersion models]]
 +
[[Category:Relaxation_dispersion analysis]]

Latest revision as of 16:44, 6 November 2015

The full Carver and Richards 1972 2-site relaxation dispersion model for SQ CPMG-type data for most time scales. This model is labelled as CR72 full in relax.

Equation

Please see the summary of the model parameters here.

[math] R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) [/math]

Which have the following definitions

[math] \alpha_- = R_2^A - R_2^B + k_{\textrm{AB}} - k_{\textrm{BA}} \\ \zeta = 2 \Delta \omega \, (R_2^A - R_2^B +k_{\textrm{AB}} - k_{\textrm{BA}} ) \\ \phantom{\zeta} = 2 \Delta \omega \, (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} ) \\ \phantom{\zeta} = 2 \Delta \omega \alpha_- \\ \Psi = (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} )^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ \phantom{\Psi} = \alpha_-^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ \eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ \eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\ D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) [/math]

[math]k_{\textrm{EX}}[/math] is the chemical exchange rate constant, [math]p_A[/math] and [math]p_B[/math] are the populations of states A and B, and [math]\Delta \omega[/math] is the chemical shift difference between the two states in ppm.

Parameters

The CR72 full model has the parameters {R2A0, R2B0, ..., pA, Δω, kex}.

Reference

The reference for the CR72 full model is:

  • Carver, J. P. and Richards, R. E. (1972). General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. J. Magn. Reson., 6(1), 89-105. (DOI: 10.1016/0022-2364(72)90090-X)

Related models

The CR72 model is a parametric restriction of this model.

Links

The implementation of the CR72 full model in relax can be seen in the:

See also