Module m61
source code
The Meiboom (1961) 2-site fast exchange R1rho M61 model.
Description
This module is for the function, gradient and Hessian of the M61 model.
References
The model is named after the reference:
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Meiboom S. (1961). Nuclear magnetic resonance study of the proton
transfer in water. J. Chem. Phys., 34, 375-388. (DOI:
10.1063/1.1700960).
Equations
The equation used is:
phi_ex * kex
R1rho = R1rho' + ----------------- ,
kex^2 + omega_1^2
where:
phi_ex = pA * pB * delta_omega^2 ,
R1rho' is the R1rho value in the absence of exchange, kex is the
chemical exchange rate constant, pA and pB are the populations of
states A and B, delta_omega is the chemical shift difference between
the two states, and omega_1 is the spin-lock field strength.
Links
More information on the M61 model can be found in the:
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r1rho_M61(r1rho_prime=None,
phi_ex=None,
kex=None,
spin_lock_fields2=None,
back_calc=None)
Calculate the R2eff values for the M61 model. |
source code
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__package__ = ' lib.dispersion '
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Imports:
any,
isfinite,
min,
sum,
fix_invalid,
masked_where
r1rho_M61(r1rho_prime=None,
phi_ex=None,
kex=None,
spin_lock_fields2=None,
back_calc=None)
| source code
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Calculate the R2eff values for the M61 model.
See the module docstring for details.
- Parameters:
r1rho_prime (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho_prime parameter value (R1rho 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).
spin_lock_fields2 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho spin-lock field strengths squared (in rad^2.s^-2).
back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R1rho values. Each
element corresponds to the combination of spin lock field.
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