tessl/pypi-dipy
Comprehensive Python library for diffusion MRI analysis including tensor imaging, tractography, and visualization
—
Pending
simulations.mddocs/
Simulations and Phantoms
Signal simulation tools for generating synthetic diffusion MRI data, phantoms, and testing algorithms with known ground truth. DIPY provides comprehensive simulation capabilities for method validation and algorithm development.
Capabilities
Single Tensor Simulation
Generate diffusion signals from single tensor models with specified diffusion properties.
def single_tensor(gtab, S0=1, evals=None, evecs=None, snr=None):
"""
Generate single tensor diffusion signal.
Parameters:
gtab (GradientTable): gradient table for simulation
S0 (float): baseline signal intensity
evals (array): tensor eigenvalues [lambda1, lambda2, lambda3]
evecs (array): tensor eigenvectors (3x3 matrix)
snr (float): signal-to-noise ratio (None for no noise)
Returns:
array: simulated diffusion signal
"""
def tensor(gtab, evals, evecs, S0=1, snr=None):
"""
Simulate tensor signal with specified parameters.
Parameters:
gtab (GradientTable): diffusion gradient table
evals (array): eigenvalues [AD, RD, RD] in mm²/s
evecs (array): eigenvector matrix
S0 (float): b=0 signal intensity
snr (float): signal-to-noise ratio
Returns:
array: tensor-based signal
"""
def design_matrix(gtab):
"""
Create design matrix for tensor fitting.
Parameters:
gtab (GradientTable): gradient table
Returns:
array: design matrix for linear fitting
"""Multi-Tensor Simulation
Simulate complex tissue with multiple fiber populations and crossing configurations.
def multi_tensor(gtab, mevals, angles, fractions, S0=100, snr=None):
"""
Multi-tensor signal simulation for crossing fibers.
Parameters:
gtab (GradientTable): gradient table
mevals (list): eigenvalues for each tensor
angles (list): fiber orientations [(theta1, phi1), (theta2, phi2), ...]
fractions (list): volume fractions for each tensor (sum to 100)
S0 (float): baseline signal
snr (float): signal-to-noise ratio
Returns:
array: multi-tensor signal
"""
def two_tensor(gtab, evals1, evals2, angles, fractions, S0=100, snr=None):
"""
Two-tensor crossing fiber simulation.
Parameters:
gtab (GradientTable): gradient information
evals1 (array): first tensor eigenvalues
evals2 (array): second tensor eigenvalues
angles (tuple): crossing angles (theta1, phi1, theta2, phi2)
fractions (list): volume fractions [f1, f2]
S0 (float): b=0 signal
snr (float): noise level
Returns:
array: two-tensor signal
"""
def multi_tensor_odf(mevals, angles, fractions, sphere, tau=1/4*pi):
"""
Generate multi-tensor ODF for visualization.
Parameters:
mevals (list): tensor eigenvalues
angles (list): fiber angles
fractions (list): volume fractions
sphere (Sphere): sampling sphere
tau (float): diffusion time parameter
Returns:
array: ODF values on sphere
"""Sticks and Ball Model
Simplified model with stick-like fibers in isotropic background for fast simulation.
def sticks_and_ball(gtab, d=0.0015, S0=1, angles=[(0, 0)], fractions=[100], snr=None):
"""
Sticks and ball model simulation.
Parameters:
gtab (GradientTable): gradient table
d (float): stick diffusivity (mm²/s)
S0 (float): baseline signal
angles (list): stick orientations [(theta, phi), ...]
fractions (list): volume fractions for each stick
snr (float): signal-to-noise ratio
Returns:
tuple: (signal, sticks) simulated signal and stick parameters
"""
def ball_and_stick_signal(gtab, d=0.0015, f=0.5, S0=1, angles=[(0, 0)], snr=None):
"""
Ball and stick model with isotropic and anisotropic components.
Parameters:
gtab (GradientTable): diffusion gradients
d (float): stick diffusivity
f (float): stick volume fraction (0-1)
S0 (float): baseline signal
angles (list): stick directions
snr (float): noise level
Returns:
array: ball and stick signal
"""Diffusion Kurtosis Simulation
Generate signals with non-Gaussian diffusion characteristics for DKI validation.
def kurtosis_signal(gtab, dt, kt, S0=1, snr=None):
"""
Simulate diffusion kurtosis signal.
Parameters:
gtab (GradientTable): multi-shell gradient table
dt (array): diffusion tensor (6-element vector)
kt (array): kurtosis tensor (15-element vector)
S0 (float): baseline signal
snr (float): signal-to-noise ratio
Returns:
array: kurtosis-based signal
"""
def gaussian_signal(gtab, dt, S0=1, snr=None):
"""
Generate Gaussian (tensor) signal for comparison.
Parameters:
gtab (GradientTable): gradient table
dt (array): diffusion tensor
S0 (float): b=0 signal
snr (float): noise level
Returns:
array: Gaussian diffusion signal
"""Phantom Generation
Create realistic phantom datasets with known ground truth for validation.
class SingleShellPhantom:
"""Single-shell diffusion phantom generator."""
def __init__(self, gtab, snr=None):
"""
Initialize phantom generator.
Parameters:
gtab (GradientTable): single-shell gradient table
snr (float): signal-to-noise ratio
"""
def create_voxel(self, tensor_params):
"""
Create single voxel with specified parameters.
Parameters:
tensor_params (dict): tensor parameters
Returns:
array: simulated voxel signal
"""
def create_volume(self, shape, tissue_map):
"""
Create full volume phantom.
Parameters:
shape (tuple): volume dimensions
tissue_map (array): tissue type labels
Returns:
array: 4D phantom volume
"""
class MultiShellPhantom:
"""Multi-shell phantom for advanced models."""
def __init__(self, gtab, snr=None):
"""Initialize multi-shell phantom."""
def add_crossing_region(self, center, radius, angles, fractions):
"""Add crossing fiber region to phantom."""
def add_single_fiber_region(self, center, radius, tensor_params):
"""Add single fiber region."""
def generate(self):
"""Generate complete phantom dataset."""
def spherical_phantom(gtab, sphere, angles, S0=100, snr=None):
"""
Create spherical phantom with specified fiber orientations.
Parameters:
gtab (GradientTable): gradient table
sphere (Sphere): sampling sphere
angles (list): fiber directions
S0 (float): baseline signal
snr (float): noise level
Returns:
array: spherical phantom data
"""Noise Models
Realistic noise models for diffusion MRI simulation including Rician and Gaussian noise.
def add_noise(signal, snr, S0=None, noise_type='rician'):
"""
Add noise to simulated signal.
Parameters:
signal (array): clean signal
snr (float): signal-to-noise ratio
S0 (float): reference signal for SNR calculation
noise_type (str): noise model ('rician', 'gaussian')
Returns:
array: noisy signal
"""
def rician_noise(signal, sigma):
"""
Add Rician noise to magnitude signal.
Parameters:
signal (array): magnitude signal
sigma (float): noise standard deviation
Returns:
array: Rician-distributed noisy signal
"""
def gaussian_noise(signal, sigma):
"""
Add Gaussian noise to signal.
Parameters:
signal (array): input signal
sigma (float): noise standard deviation
Returns:
array: Gaussian noisy signal
"""
def estimate_sigma(data, mask=None):
"""
Estimate noise level from background regions.
Parameters:
data (array): diffusion data
mask (array): brain mask
Returns:
float: estimated noise standard deviation
"""Ground Truth Generation
Tools for creating datasets with known ground truth for algorithm validation.
class GroundTruthDataset:
"""Generate datasets with known ground truth."""
def __init__(self, shape=(64, 64, 40), gtab=None):
"""
Initialize ground truth generator.
Parameters:
shape (tuple): volume dimensions
gtab (GradientTable): gradient table
"""
def add_bundle(self, streamlines, tensor_params):
"""
Add fiber bundle with known properties.
Parameters:
streamlines (list): bundle streamlines
tensor_params (dict): diffusion parameters
"""
def add_partial_volume(self, region_mask, tissue_fractions):
"""Add partial volume effects."""
def generate_data(self, snr=30):
"""
Generate complete dataset.
Returns:
tuple: (data, ground_truth_params)
"""
def create_qa_phantom(gtab, num_bundles=3, crossing_angle=60):
"""
Create quality assurance phantom with crossing bundles.
Parameters:
gtab (GradientTable): gradient table
num_bundles (int): number of fiber bundles
crossing_angle (float): angle between crossing fibers
Returns:
tuple: (phantom_data, bundle_masks, tensor_params)
"""Usage Examples
# Single tensor simulation
from dipy.sims.voxel import single_tensor, multi_tensor
from dipy.core.gradients import gradient_table
from dipy.core.sphere import get_sphere
import numpy as np
# Create gradient table
bvals = np.array([0, 1000, 1000, 2000, 2000])
bvecs = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0]])
bvecs = bvecs / np.linalg.norm(bvecs, axis=1, keepdims=True)
bvecs[0] = 0 # b=0 has no direction
gtab = gradient_table(bvals, bvecs)
# Simulate single tensor
evals = np.array([1.7e-3, 0.3e-3, 0.3e-3]) # AD, RD, RD
evecs = np.eye(3) # aligned with x-axis
signal = single_tensor(gtab, S0=100, evals=evals, evecs=evecs, snr=30)
print(f"Simulated signal shape: {signal.shape}")
print(f"b=0 signal: {signal[0]:.1f}")
print(f"DW signal mean: {signal[1:].mean():.1f}")
# Multi-tensor crossing simulation
from dipy.sims.voxel import sticks_and_ball
# 90-degree crossing
angles = [(0, 0), (90, 0)] # two perpendicular fibers
fractions = [50, 50] # equal volume fractions
crossing_signal, sticks = sticks_and_ball(
gtab, d=0.0015, S0=100, angles=angles, fractions=fractions, snr=25
)
# Create phantom volume
from dipy.sims.phantom import SingleShellPhantom
phantom = SingleShellPhantom(gtab, snr=30)
# Define tissue regions
shape = (32, 32, 20)
phantom_data = np.zeros(shape + (len(gtab.bvals),))
# Add single fiber region
center = (16, 16, 10)
for i in range(shape[0]):
for j in range(shape[1]):
for k in range(shape[2]):
# Distance from center
dist = np.sqrt((i-center[0])**2 + (j-center[1])**2 + (k-center[2])**2)
if dist < 8: # Within sphere
if dist < 4: # Inner core - single fiber
signal = single_tensor(gtab, S0=100, evals=evals, evecs=evecs, snr=30)
else: # Outer shell - partial volume
mixed_signal = 0.7 * single_tensor(gtab, S0=100, evals=evals, evecs=evecs) + \
0.3 * single_tensor(gtab, S0=100, evals=[0.7e-3]*3, evecs=evecs)
mixed_signal = add_noise(mixed_signal, snr=30)
phantom_data[i, j, k] = signal if dist < 4 else mixed_signal
print(f"Phantom shape: {phantom_data.shape}")
# Validation with known ground truth
from dipy.reconst.dti import TensorModel
# Fit tensor model to simulated data
tensor_model = TensorModel(gtab)
tensor_fit = tensor_model.fit(phantom_data)
# Compare with ground truth
estimated_fa = tensor_fit.fa
ground_truth_fa = 0.8 # Expected FA for our simulation
print(f"Ground truth FA: {ground_truth_fa:.3f}")
print(f"Estimated FA (center): {estimated_fa[16, 16, 10]:.3f}")
print(f"Estimation error: {abs(estimated_fa[16, 16, 10] - ground_truth_fa):.3f}")
# Noise analysis
from dipy.sims.voxel import add_noise, estimate_sigma
# Test different noise levels
snr_levels = [10, 20, 30, 50, 100]
clean_signal = single_tensor(gtab, S0=100, evals=evals, evecs=evecs)
for snr in snr_levels:
noisy_signal = add_noise(clean_signal, snr, noise_type='rician')
sigma_estimated = estimate_sigma(noisy_signal.reshape(1, 1, 1, -1))
sigma_true = 100 / snr # True noise level
print(f"SNR {snr}: True σ={sigma_true:.2f}, Estimated σ={sigma_estimated:.2f}")Install with Tessl CLI
npx tessl i tessl/pypi-dipy