Package lib :: Package dispersion :: Module m61
[hide private]
[frames] | no frames]

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:

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:

Functions [hide private]
 
r1rho_M61(r1rho_prime=None, phi_ex=None, kex=None, spin_lock_fields2=None, back_calc=None, num_points=None)
Calculate the R2eff values for the M61 model.
source code
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: abs, array, isfinite, min, sum


Function Details [hide private]

r1rho_M61(r1rho_prime=None, phi_ex=None, kex=None, spin_lock_fields2=None, back_calc=None, num_points=None)

source code 

Calculate the R2eff values for the M61 model.

See the module docstring for details.

Parameters:
  • r1rho_prime (float) - The R1rho_prime parameter value (R1rho with no exchange).
  • phi_ex (float) - 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 rank-1 float array) - The R1rho spin-lock field strengths squared (in rad^2.s^-2).
  • back_calc (numpy rank-1 float array) - The array for holding the back calculated R1rho values. Each element corresponds to the combination of spin lock field.
  • num_points (int) - The number of points on the dispersion curve, equal to the length of the spin_lock_fields and back_calc arguments.