lib.dispersion.ns_r1rho

62 """The 2-site numerical solution to the Bloch-McConnell equation for R1rho data. 63 64 This function calculates and stores the R1rho values. 65 66 67 @keyword M0: This is a vector that contains the initial magnetizations corresponding to the A and B state transverse magnetizations. 68 @type M0: numpy float64, rank-1, 7D array 69 @keyword matrix: A numpy array to be populated to create the evolution matrix. 70 @type matrix: numpy rank-2, 6D float64 array 71 @keyword r1rho_prime: The R1rho_prime parameter value (R1rho with no exchange). 72 @type r1rho_prime: float 73 @keyword omega: The chemical shift for the spin in rad/s. 74 @type omega: float 75 @keyword offset: The spin-lock offsets for the data. 76 @type offset: numpy rank-1 float array 77 @keyword r1: The R1 relaxation rate. 78 @type r1: float 79 @keyword pA: The population of state A. 80 @type pA: float 81 @keyword pB: The population of state B. 82 @type pB: float 83 @keyword dw: The chemical exchange difference between states A and B in rad/s. 84 @type dw: float 85 @keyword k_AB: The rate of exchange from site A to B (rad/s). 86 @type k_AB: float 87 @keyword k_BA: The rate of exchange from site B to A (rad/s). 88 @type k_BA: float 89 @keyword spin_lock_fields: The R1rho spin-lock field strengths (in rad.s^-1). 90 @type spin_lock_fields: numpy rank-1 float array 91 @keyword relax_time: The total relaxation time period for each spin-lock field strength (in seconds). 92 @type relax_time: float 93 @keyword inv_relax_time: The inverse of the relaxation time period for each spin-lock field strength (in inverse seconds). This is used for faster calculations. 94 @type inv_relax_time: float 95 @keyword back_calc: The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies. 96 @type back_calc: numpy rank-1 float array 97 @keyword num_points: The number of points on the dispersion curve, equal to the length of the tcp and back_calc arguments. 98 @type num_points: int 99 """ 100 101 # Repetitive calculations (to speed up calculations). 102 Wa = omega # Larmor frequency [s^-1]. 103 Wb = omega + dw # Larmor frequency [s^-1]. 104 W = pA*Wa + pB*Wb # Population-averaged Larmor frequency [s^-1]. 105 dA = Wa - offset # Offset of spin-lock from A. 106 dB = Wb - offset # Offset of spin-lock from B. 107 d = W - offset # Offset of spin-lock from population-average. 108 109 # Loop over the time points, back calculating the R2eff values. 110 for i in range(num_points): 111 # The matrix that contains all the contributions to the evolution, i.e. relaxation, exchange and chemical shift evolution. 112 rr1rho_3d(matrix=matrix, R1=r1, r1rho_prime=r1rho_prime, pA=pA, pB=pB, wA=dA, wB=dB, w1=spin_lock_fields[i], k_AB=k_AB, k_BA=k_BA) 113 114 # The following lines rotate the magnetization previous to spin-lock into the weff frame. 115 theta = atan2(spin_lock_fields[i], dA) 116 M0[0] = sin(theta) # The A state initial X magnetisation. 117 M0[2] = cos(theta) # The A state initial Z magnetisation. 118 119 # This matrix is a propagator that will evolve the magnetization with the matrix R. 120 Rexpo = matrix_exponential(matrix*relax_time) 121 122 # Magnetization evolution. 123 MA = dot(M0, dot(Rexpo, M0)) 124 125 # The next lines calculate the R1rho using a two-point approximation, i.e. assuming that the decay is mono-exponential. 126 if MA <= 0.0 or isNaN(MA): 127 back_calc[i] = 1e99 128 else: 129 back_calc[i]= -inv_relax_time * log(MA)

Source Code for Module lib.dispersion.ns_r1rho_2site