def dki_signal(gtab, dt, kt, S0=150, snr=None):
r""" Simulated signal based on the diffusion and diffusion kurtosis
tensors of a single voxel. Simulations are preformed assuming the DKI
model.
Parameters
----------
gtab : GradientTable
Measurement directions.
dt : (6,) ndarray
Elements of the diffusion tensor.
kt : (15, ) ndarray
Elements of the diffusion kurtosis tensor.
S0 : float (optional)
Strength of signal in the presence of no diffusion gradient.
snr : float (optional)
Signal to noise ratio, assuming Rician noise. None implies no noise.
Returns
-------
S : (N,) ndarray
Simulated signal based on the DKI model:
.. math::
S=S_{0}e^{-bD+\frac{1}{6}b^{2}D^{2}K}
References
----------
.. [1] R. Neto Henriques et al., "Exploring the 3D geometry of the
diffusion kurtosis tensor - Impact on the development of robust
tractography procedures and novel biomarkers", NeuroImage (2015)
111, 85-99.
"""
dt = np.array(dt)
kt = np.array(kt)
A = dki_design_matrix(gtab)
# define vector of DKI parameters
MD = (dt[0] + dt[2] + dt[5]) / 3
X = np.concatenate((dt, kt * MD * MD, np.array([-np.log(S0)])), axis=0)
# Compute signals based on the DKI model
S = np.exp(dot(A, X))
S = add_noise(S, snr, S0)
return S
def DKI_signal(gtab, dt, kt, S0=150, snr=None):
r""" Simulated signal based on the diffusion and diffusion kurtosis
tensors of a single voxel. Simulations are preformed assuming the DKI
model.
Parameters
-----------
gtab : GradientTable
Measurement directions.
dt : (6,) ndarray
Elements of the diffusion tensor.
kt : (15, ) ndarray
Elements of the diffusion kurtosis tensor.
S0 : float (optional)
Strength of signal in the presence of no diffusion gradient.
snr : float (optional)
Signal to noise ratio, assuming Rician noise. None implies no noise.
Returns
--------
S : (N,) ndarray
Simulated signal based on the DKI model:
.. math::
S=S_{0}e^{-bD+\frac{1}{6}b^{2}D^{2}K}
References
----------
.. [1] R. Neto Henriques et al., "Exploring the 3D geometry of the
diffusion kurtosis tensor - Impact on the development of robust
tractography procedures and novel biomarkers", NeuroImage (2015)
111, 85-99.
"""
dt = np.array(dt)
kt = np.array(kt)
A = dki_design_matrix(gtab)
# define vector of DKI parameters
MD = (dt[0] + dt[2] + dt[5]) / 3
X = np.concatenate((dt, kt*MD*MD, np.array([np.log(S0)])), axis=0)
# Compute signals based on the DKI model
S = np.exp(dot(A, X))
S = add_noise(S, snr, S0)
return S
