Module lm63
source code
The Luz and Meiboom (1963) 2-site fast exchange LM63 model.
Description
This module is for the function, gradient and Hessian of the LM63 model.
References
The model is named after the reference:
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Luz, S. and Meiboom S., (1963) Nuclear Magnetic Resonance study of
protolysis of trimethylammonium ion in aqueous solution - order of
reaction with respect to solvent, J. Chem. Phys., 39,
366-370 (DOI: 10.1063/1.1734254).
Equations
The equation used is:
phi_ex / 4 * nu_cpmg / kex \ \
R2eff = R20 + ------ * | 1 - ----------- * tanh | ----------- | | ,
kex \ kex \ 4 * nu_cpmg / /
where:
phi_ex = pA * pB * delta_omega^2 ,
kex is the chemical exchange rate constant, pA and pB are the
populations of states A and B, and delta_omega is the chemical shift
difference between the two states.
Links
More information on the LM63 model can be found in the:
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r2eff_LM63(r20=None,
phi_ex=None,
kex=None,
cpmg_frqs=None,
back_calc=None)
Calculate the R2eff values for the LM63 model. |
source code
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__package__ = ' lib.dispersion '
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Imports:
isfinite,
min,
sum,
tanh,
fix_invalid,
masked_where
r2eff_LM63(r20=None,
phi_ex=None,
kex=None,
cpmg_frqs=None,
back_calc=None)
| source code
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Calculate the R2eff values for the LM63 model.
See the module docstring for details.
- Parameters:
r20 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R20 parameter value (R2 with no exchange).
phi_ex (numpy float array of rank [NE][NS][NM][NO][ND]) - The phi_ex parameter value (pA * pB * delta_omega^2).
kex (float) - The kex parameter value (the exchange rate in rad/s).
cpmg_frqs (numpy float array of rank [NE][NS][NM][NO][ND]) - The CPMG nu1 frequencies.
back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
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