Package lib :: Package dispersion :: Module ns_r1rho_3site
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Module ns_r1rho_3site

source code

The numerical solution for the 3-site Bloch-McConnell equations for R1rho-type data, the NS R1rho 3-site linear and NS R1rho 3-site model.

Description

This is the model of the numerical solution for the 3-site Bloch-McConnell equations. It originates from the funNumrho.m file from the Skrynikov & Tollinger code (the sim_all.tar file https://gna.org/support/download.php?file_id=18404 attached to https://gna.org/task/?7712#comment5).

References

The solution has been modified to use the from presented in:

Links

More information on the NS R1rho 3-site linear model can be found in the:

More information on the NS R1rho 3-site model can be found in the:

Functions [hide private]
 
ns_r1rho_3site(M0=None, matrix=None, r1rho_prime=None, omega=None, offset=None, r1=0.0, pA=None, pB=None, pC=None, dw_AB=None, dw_AC=None, k_AB=None, k_BA=None, k_BC=None, k_CB=None, k_AC=None, k_CA=None, spin_lock_fields=None, relax_time=None, inv_relax_time=None, back_calc=None, num_points=None)
The 3-site numerical solution to the Bloch-McConnell equation for R1rho data.
source code
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: atan2, cos, log, sin, dot, rr1rho_3d_3site, isNaN, matrix_exponential


Function Details [hide private]

ns_r1rho_3site(M0=None, matrix=None, r1rho_prime=None, omega=None, offset=None, r1=0.0, pA=None, pB=None, pC=None, dw_AB=None, dw_AC=None, k_AB=None, k_BA=None, k_BC=None, k_CB=None, k_AC=None, k_CA=None, spin_lock_fields=None, relax_time=None, inv_relax_time=None, back_calc=None, num_points=None)

source code 

The 3-site numerical solution to the Bloch-McConnell equation for R1rho data.

This function calculates and stores the R1rho values.

Parameters:
  • M0 (numpy float64, rank-1, 7D array) - This is a vector that contains the initial magnetizations corresponding to the A and B state transverse magnetizations.
  • matrix (numpy rank-2, 9D float64 array) - A numpy array to be populated to create the evolution matrix.
  • r1rho_prime (float) - The R1rho_prime parameter value (R1rho with no exchange).
  • omega (float) - The chemical shift for the spin in rad/s.
  • offset (numpy rank-1 float array) - The spin-lock offsets for the data.
  • r1 (float) - The R1 relaxation rate.
  • pA (float) - The population of state A.
  • pB (float) - The population of state B.
  • pC (float) - The population of state C.
  • dw_AB (float) - The chemical exchange difference between states A and B in rad/s.
  • dw_AC (float) - The chemical exchange difference between states A and C in rad/s.
  • k_AB (float) - The rate of exchange from site A to B (rad/s).
  • k_BA (float) - The rate of exchange from site B to A (rad/s).
  • k_BC (float) - The rate of exchange from site B to C (rad/s).
  • k_CB (float) - The rate of exchange from site C to B (rad/s).
  • k_AC (float) - The rate of exchange from site A to C (rad/s).
  • k_CA (float) - The rate of exchange from site C to A (rad/s).
  • spin_lock_fields (numpy rank-1 float array) - The R1rho spin-lock field strengths (in rad.s^-1).
  • relax_time (float) - The total relaxation time period for each spin-lock field strength (in seconds).
  • inv_relax_time (float) - The inverse of the relaxation time period for each spin-lock field strength (in inverse seconds). This is used for faster calculations.
  • back_calc (numpy rank-1 float array) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.
  • num_points (int) - The number of points on the dispersion curve, equal to the length of the tcp and back_calc arguments.