Module m61b

The Meiboom (1961) 2-site on-resonance skewed population R1rho M61 skew model.

Description

This module is for the function, gradient and Hessian of the M61 skew model.

References

The model is named after the reference:

• 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:

                          pA^2.pB.delta_omega^2.kex
   R1rho = R1rho' + -------------------------------------- ,
                    kex^2 + pA^2.delta_omega^2 + omega_1^2

where 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 = omega_e is the effective field in the rotating frame.

Links

More information on the M61 skew model can be found in the:

• relax wiki,
• relax manual,
• relaxation dispersion page of the relax website.

Functions

r1rho_M61b(r1rho_prime=None, pA=None, dw=None, kex=None, spin_lock_fields2=None, back_calc=None)
Calculate the R1rho values for the M61 skew model.

Variables

__package__ = 'lib.dispersion'

Imports: any, isfinite, min, sum, fix_invalid, masked_where

Function Details

r1rho_M61b(r1rho_prime=None, pA=None, dw=None, kex=None, spin_lock_fields2=None, back_calc=None)

Calculate the R1rho values for the M61 skew 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).
• pA (float) - The population of state A.
• dw (numpy float array of rank [NE][NS][NM][NO][ND]) - The chemical exchange difference between states A and B in rad/s.
• 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.