def predicted_signal(self, bvecs, bvals, axial_diffusivity,
radial_diffusivity):
"""
Compute the fiber contribution to the *relative signal* along its
coords.
Notes
-----
The calculation is based on a simplified Stejskal/Tanner equation:
.. math::
\frac{S/S_0} = exp^{-bval (\vec{b}*Q*\vec{b}^T)}
Where $S0$ is the unweighted signal and $\vec{b} * Q * \vec{b}^t$ is
the ADC for each tensor.
To get the diffusion signal measured, you will have to multiply back by
the $S_0$ in each voxel.
Parameters
----------
"""
# Gotta have those tensors:
tens = self.tensors(axial_diffusivity, radial_diffusivity)
# Preallocate:
sig = np.empty((tens.shape[0], len(bvals)))
for t_idx, ten in enumerate(tens):
ADC = ozt.apparent_diffusion_coef(bvecs, ten.reshape((3, 3)))
# Call S/T with the ADC as input:
sig[t_idx] = ozt.stejskal_tanner(1, bvals, ADC)
return sig
def predict(self, sphere, bvals=None):
"""
Predict the values of the signal on a novel sphere (not neccesarily
measured points) in every voxel
Parameters
----------
sphere : 3 x n array
"""
if self.verbose:
print("Predicting signal from TensorModel")
if bvals is None:
# Assume there's only one b value and you know where to find it:
bvals = self.bvals[self.b_idx][0] * np.ones(sphere.shape[-1])
else:
# If you gave them as input, you need to scale them:
bvals = bvals / float(self.scaling_factor)
pred_adc_flat = self.predict_adc(sphere)[self.mask]
predict_flat = np.empty(pred_adc_flat.shape)
out = ozu.nans(self.signal.shape[:3] + (sphere.shape[-1], ))
for ii in xrange(len(predict_flat)):
predict_flat[ii] = ozt.stejskal_tanner(self._flat_S0[ii], bvals,
pred_adc_flat[ii])
out[self.mask] = predict_flat
return out
def predict(self, sphere, bvals=None):
"""
Predict the values of the signal on a novel sphere (not neccesarily
measured points) in every voxel
Parameters
----------
sphere : 3 x n array
"""
if self.verbose:
print("Predicting signal from TensorModel")
if bvals is None:
# Assume there's only one b value and you know where to find it:
bvals = self.bvals[self.b_idx][0] * np.ones(sphere.shape[-1])
else:
# If you gave them as input, you need to scale them:
bvals = bvals/float(self.scaling_factor)
pred_adc_flat = self.predict_adc(sphere)[self.mask]
predict_flat = np.empty(pred_adc_flat.shape)
out = ozu.nans(self.signal.shape[:3] + (sphere.shape[-1], ))
for ii in xrange(len(predict_flat)):
predict_flat[ii] = ozt.stejskal_tanner(self._flat_S0[ii],
bvals,
pred_adc_flat[ii])
out[self.mask] = predict_flat
return out
def fit(self):
if self.verbose:
print("Predicting signal from TensorModel")
adc_flat = self.model_adc[self.mask]
fit_flat = np.empty(adc_flat.shape)
out = ozu.nans(self.signal.shape)
for ii in xrange(len(fit_flat)):
fit_flat[ii] = ozt.stejskal_tanner(self._flat_S0[ii],
self.bvals[self.b_idx],
adc_flat[ii])
out[self.mask] = fit_flat
return out
def fit(self):
if self.verbose:
print("Predicting signal from TensorModel")
adc_flat = self.model_adc[self.mask]
fit_flat = np.empty(adc_flat.shape)
out = ozu.nans(self.signal.shape)
for ii in xrange(len(fit_flat)):
fit_flat[ii] = ozt.stejskal_tanner(self._flat_S0[ii],
self.bvals[self.b_idx],
adc_flat[ii])
out[self.mask] = fit_flat
return out
def test_stejskal_tanner():
"""
Test the implementation of the S/T equation.
"""
bvecs = [[1,0,0],[0,1,0],[0,0,1]]
bvals = [1,1,1]
S0 = 1
ADC = np.random.rand(3)
Q = np.diag(ADC)
# Calculate explicitely:
st = S0 * np.exp(-1 * np.asarray(bvecs).T * Q * np.asarray(bvecs))
# These should give the same answer:
npt.assert_equal(mtt.stejskal_tanner(S0, bvals, ADC), np.diag(st))
def test_stejskal_tanner():
"""
Test the implementation of the S/T equation.
"""
bvecs = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
bvals = [1, 1, 1]
S0 = 1
ADC = np.random.rand(3)
Q = np.diag(ADC)
# Calculate explicitely:
st = S0 * np.exp(-1 * np.asarray(bvecs).T * Q * np.asarray(bvecs))
# These should give the same answer:
npt.assert_equal(mtt.stejskal_tanner(S0, bvals, ADC), np.diag(st))
def predicted_signal(self,
bvecs,
bvals,
axial_diffusivity,
radial_diffusivity):
"""
Compute the fiber contribution to the *relative signal* along its
coords.
Notes
-----
The calculation is based on a simplified Stejskal/Tanner equation:
.. math::
\frac{S/S_0} = exp^{-bval (\vec{b}*Q*\vec{b}^T)}
Where $S0$ is the unweighted signal and $\vec{b} * Q * \vec{b}^t$ is
the ADC for each tensor.
To get the diffusion signal measured, you will have to multiply back by
the $S_0$ in each voxel.
Parameters
----------
"""
# Gotta have those tensors:
tens = self.tensors(axial_diffusivity,
radial_diffusivity)
# Preallocate:
sig = np.empty((tens.shape[0], len(bvals)))
for t_idx, ten in enumerate(tens):
ADC = ozt.apparent_diffusion_coef(bvecs, ten.reshape((3,3)))
# Call S/T with the ADC as input:
sig[t_idx] = ozt.stejskal_tanner(1, bvals, ADC)
return sig
