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.gitignore vendored Normal file
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venv/

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.vscode/settings.json vendored Normal file
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{
"python.formatting.provider": "black"
}

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LICENSE Normal file
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README.md Normal file
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pyproject.toml Normal file
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[build-system]
requires = ["hatchling"]
build-backend = "hatchling.build"
[tool.hatch.metadata]
allow-direct-references = true
[project]
name = "nqr_blochsimulator"
version = "0.0.1"
authors = [
{ name="Julia Pfitzer", email="git@jupfi.me" },
]
description = "Simple Python script to simulate NMR NQR Bloch equations"
readme = "README.md"
license = { file="LICENSE" }
requires-python = ">=3.8"
classifiers = [
"Programming Language :: Python :: 3",
"License :: OSI Approved :: MIT License",
"Operating System :: OS Independent",
]
dependencies = [
"matplotlib",
"numpy",
"scipy",
]

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src/nqr_blochsimulator/__init__.py Normal file
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src/nqr_blochsimulator/blochsimulator.py Normal file
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src/nqr_blochsimulator/classes/sample.py Normal file
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from math import pi, sqrt
class Sample:
"""
A class to represent a sample for NQR (Nuclear Quadrupole Resonance) Bloch Simulation.
"""
avogadro = 6.022e23
def __init__(
self,
name,
density,
molar_mass,
resonant_frequency,
gamma,
nuclear_spin,
spin_factor,
powder_factor,
filling_factor,
T1,
T2,
T2_star,
atom_density=None,
sample_volume=None,
):
"""
Constructs all the necessary attributes for the sample object.
Parameters
----------
name : str
The name of the sample.
density : float
The density of the sample (g/m^3 or kg/m^3).
molar_mass : float
The molar mass of the sample (g/mol or kg/mol).
resonant_frequency : float
The resonant frequency of the sample.
gamma : float
The gamma value of the sample.
nuclear_spin : float
The nuclear spin quantum number of the sample.
spin_factor : float
The spin factor of the sample.
powder_factor : float
The powder factor of the sample.
filling_factor : float
The filling factor of the sample.
T1 : float
The spin-lattice relaxation time of the sample.
T2 : float
The spin-spin relaxation time of the sample.
T2_star : float
The effective spin-spin relaxation time of the sample.
atom_density : float, optional
The atom density of the sample (atoms per cm^3). By default None.
sample_volume : float, optional
The volume of the sample (m^3). By default None.
"""
self.name = name
self.density = density
self.molar_mass = molar_mass
self.resonant_frequency = resonant_frequency
self.gamma = gamma
self.nuclear_spin = nuclear_spin
self.spin_factor = spin_factor
self.powder_factor = powder_factor
self.filling_factor = filling_factor
self.T1 = T1
self.T2 = T2
self.T2_star = T2_star
self.atom_density = atom_density
self.sample_volume = sample_volume
self.calculate_atoms()
def calculate_atoms(self):
"""
Calculate the number of atoms in the sample per volume unit.
If atom density and sample volume are provided, use these to calculate the number of atoms.
If not, use Avogadro's number, density, and molar mass to calculate the number of atoms.
"""
if self.atom_density and self.sample_volume:
self.atoms = (
self.atom_density
* self.sample_volume
/ 1e-6
/ (self.sample_volume * 6 / 3)
)
else:
self.atoms = self.avogadro * self.density / self.molar_mass

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src/nqr_blochsimulator/classes/simulation.py Normal file
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import numpy as np
from numpy import pi
from scipy import signal
class Simulation:
def __init__(self) -> None:
pass
def blochsim(sim_points, sim_time, reference, isochrom, sample, pulse):
# PRE-SETTINGS
d = {"M0c": 1} # initial mag
NISO = 100
if isochrom > 0:
NISO = isochrom # number of isochromates
nsamples = (
sim_points # number of sample/rasterization points for the calculation
)
sim_length = sim_time # in s; Not larger than the repetition time!
modulation = "OFF" # select a optional modulation of the pulse ['OFF','SIN']
# Replace by the NWA power later
B1c_calc = np.sqrt(2 * 500 / 50) * pi * 4e-7 * 9 / 6e-3 # 17 od 8.5
d["B1c"] = 17.3e-3 # for Peak B1 T %12.5%14.3
# SAMPLE SETTINGS
d["T1"] = sample["T1"] # in s; T1, T2
d["T2"] = sample["T2"] #
T2STAR = sample["T2s"] # only used for some calculations
d["gamma"] = (
sample["gamma"] / (2 * pi) / 1e6
) # gamma in MHz/T eg 5e6 % sample.gamma in rad/(T s) eg 0.8
d["relax"] = 1 # Flag 1: with Relax, 0 without Relax
# Parameter preparation
# clear up some unit problems
# DO NOT CHANGE
d["B1c"] = d["B1c"] * 1e3
d["T1"] = d["T1"] * 1e3
d["T2"] = d["T2"] * 1e3
d["gamma"] = d["gamma"] * 2 * pi
d["Nx"] = NISO
d["M0"] = np.array(
[np.zeros(NISO), np.zeros(NISO), np.ones(NISO)]
) # initial magnetization
d["dt"] = sim_length / nsamples # time step width
d["dt"] = (
d["dt"] * 1e3
) # again unit correction. could be changed if necessary, but other time factors
# in later calculations would have to be changed too
# Pulse Designer
u = np.zeros((nsamples, 1))
v = np.zeros((nsamples, 1))
w = np.ones((nsamples, 1))
tt = (np.array(range(1, nsamples + 1)) * d["dt"] - d["dt"]).reshape(
-1, 1
) # time axis in ms
# PULSE TEMPLATES
pulse_dur_pow_pha = pulse
num_pulses, _ = pulse_dur_pow_pha.shape
# loop through every pulse
for count in range(num_pulses):
pulse_begin = pulse_dur_pow_pha[count, 0]
pulse_end = pulse_dur_pow_pha[count, 1]
pha = pulse_dur_pow_pha[count, 3] * (2 * pi / 360) # phase in rad
ind_begin = np.argmin(np.abs(tt * 1e-3 - pulse_begin)) # minValue is unused
ind_end = np.argmin(np.abs(tt * 1e-3 - pulse_end))
ind_end = ind_end - 1
u_pow, v_pow = np.pol2cart(
pha, pulse_dur_pow_pha[count, 2]
) # theta angle; rho abs
if modulation == "OFF":
u[ind_begin:ind_end, 0] = u_pow # set real pulse power
v[ind_begin:ind_end, 0] = v_pow # set imag pulse power
elif modulation == "SIN":
u[ind_begin:ind_end, 0] = u_pow * np.sin(
(pi * 1e-3 / (pulse_end - pulse_begin)) * tt[ind_begin:ind_end, 0]
)
v[ind_begin:ind_end, 0] = v_pow * np.sin(
(pi * 1e-3 / (pulse_end - pulse_begin)) * tt[ind_begin:ind_end, 0]
)
# Some sidenotes that can be ignored
for count in range(1):
d["G3"] = 1 # mT/m, fhwm of 2mm Gradient scaling
w = w * d["G3"] # Gradient in mT/m
# Isochromatic simulaten by modeling with Lorentz distribution
Df = 1 / pi / T2STAR # FWHF of Lorentzian in Hz
foffr = []
uu = np.random.rand(NISO, 1) - 0.5
foffr = Df / 2 * np.tan(pi * uu) # cauchy distributed frequency offset
d["xdis"] = np.linspace(-1, 1, NISO) # in m spatial resolution
d["xdis"] = (
np.array(foffr) * 1e-6 / (d["gamma"] / 2 / pi) / (d["G3"] * 1e-3)
) # Conversion factors: foffr from Hz/T to MHz/T as required for d.gamma/2/pi, conversion from Hz-Gamma to radian gamma, and gradient must be scaled from mT/m to T/m
# USE BLOCH EQUATIONS
# M_sy1 = bloch_symmetric_strang_splitting_vectorised(u, v, w, d) # This function would need to be defined or imported
# Z-Component
# Mlong = np.squeeze(M_sy1[2, :, :]) # Coordinates M: space components - location(isochromat) - time
# Mlong_avg = np.mean(Mlong, 1)
# Mlong_avg = Mlong_avg[:-1]
# siglong = np.abs(Mlong_avg)
# XY-Component
# Mtrans = np.squeeze(M_sy1[0, :, :] + 1j*M_sy1[1, :, :]) # Coordinates M: space components - location(isochromat) - time
# Mtrans_avg = np.mean(Mtrans, 1)
# Mtrans_avg = Mtrans_avg[:-1]
# sigtrans = Mtrans_avg * reference
# return sigtrans
def bloch_symmetric_strang_splitting_vectorised(u, v, w, d):
"""Vectorised version of bloch_symmetric_strang_splitting
Parameters
----------
u : array_like
Real part of pulse
v : array_like
Imaginary part of pulse
w : array_like
Gradient
d : dict
"""
xdis = d["xdis"]
Nx = d["Nx"]
Nu = len(u)
M0 = d["M0"]
dt = d["dt"]
gadt = d["gamma"] * dt / 2
B1 = np.tile(gadt * np.transpose(u - 1j * v) * d["B1c"], (Nx, 1))
K = gadt * xdis * np.transpose(w) * d["G3"]
phi = -np.sqrt(np.abs(B1) ** 2 + K**2)
cs = np.cos(phi)
si = np.sin(phi)
n1 = np.real(B1) / np.abs(phi)
n2 = np.imag(B1) / np.abs(phi)
n3 = K / np.abs(phi)
n1[np.isnan(n1)] = 1
n2[np.isnan(n2)] = 0
n3[np.isnan(n3)] = 0
Bd1 = n1 * n1 * (1 - cs) + cs
Bd2 = n1 * n2 * (1 - cs) - n3 * si
Bd3 = n1 * n3 * (1 - cs) + n2 * si
Bd4 = n2 * n1 * (1 - cs) + n3 * si
Bd5 = n2 * n2 * (1 - cs) + cs
Bd6 = n2 * n3 * (1 - cs) - n1 * si
Bd7 = n3 * n1 * (1 - cs) - n2 * si
Bd8 = n3 * n2 * (1 - cs) + n1 * si
Bd9 = n3 * n3 * (1 - cs) + cs
M = np.zeros((3, Nx, Nu))
M[:, :, 0] = M0
Mt = M0
D = np.diag(
[
np.exp(-1 / d["T2"] * d["relax"] * dt),
np.exp(-1 / d["T2"] * d["relax"] * dt),
np.exp(-1 / d["T1"] * d["relax"] * dt),
]
)
b = np.array([0, 0, d["M0c"]]) - np.array(
[0, 0, d["M0c"] * np.exp(-1 / d["T1"] * d["relax"] * dt)]
)
for n in range(Nu): # Time loop
Mrot = np.array(
[
Bd1[:, n] * Mt[0, :] + Bd2[:, n] * Mt[1, :] + Bd3[:, n] * Mt[2, :],
Bd4[:, n] * Mt[0, :] + Bd5[:, n] * Mt[1, :] + Bd6[:, n] * Mt[2, :],
Bd7[:, n] * Mt[0, :] + Bd8[:, n] * Mt[1, :] + Bd9[:, n] * Mt[2, :],
]
)
Mt = np.dot(D, Mrot) + np.tile(b, (Nx, 1)).transpose()
Mrot = np.array(
[
Bd1[:, n] * Mt[0, :] + Bd2[:, n] * Mt[1, :] + Bd3[:, n] * Mt[2, :],
Bd4[:, n] * Mt[0, :] + Bd5[:, n] * Mt[1, :] + Bd6[:, n] * Mt[2, :],
Bd7[:, n] * Mt[0, :] + Bd8[:, n] * Mt[1, :] + Bd9[:, n] * Mt[2, :],
]
)
Mt = Mrot
M[:, :, n + 1] = Mrot
return M

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tests/simulation.py Normal file
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import unittest
from nqr_blochsimulator.classes.sample import Sample
from nqr_blochsimulator.classes.simulation import Simulation
class TestSimulation(unittest.TestCase):
def setUp(self):
self.sample = Sample(
"Ammonium nitrate",
1720,
80.0433
* 1e-3
/ Simulation.avogadro, # molar mass in kg/mol
1.945e6,
2 * 3.436e8,
1.5,
0.5,
1,
0.1,
0.1,
0.1,
0.1,
)
self.simulation = Simulation(self.sample, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6)