sims
sims.phantom
sims.voxel
GradientTable
sims
sims.phantom
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Add noise of specified distribution to a 4D array. |
|
numerical derivatives 2 eigenvectors |
|
Provide full paths to example or test datasets. |
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A general function for creating diffusion MR gradients. |
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Create a phantom based on a 3-D orbit |
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Simulate diffusion-weighted signals with a single tensor. |
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rotation matrix from 2 unit vectors |
sims.voxel
|
Diffusion gradient information |
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Add noise of specified distribution to the signal from a single voxel. |
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Given the principle tensor axis, return the array of all eigenvectors column-wise (or, the rotation matrix that orientates the tensor). |
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Calculates the perpendicular diffusion signal E(q) in a cylinder of radius R using the Soderman model [1]. |
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Calculates the three-dimensional signal attenuation E(q) originating from within a cylinder of radius R using the Soderman approximation [1]. |
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Construct B design matrix for DKI. |
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Simulated signal based on the diffusion and diffusion kurtosis tensors of a single voxel. |
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Dot product of two arrays. |
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Calculates the parallel Gaussian diffusion signal. |
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Computes the diffusion kurtosis tensor element (with indexes i, j, k and l) based on the individual diffusion tensor components of a multicompartmental model. |
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Simulate a Multi-Tensor signal. |
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Simulate the diffusion-weight signal, diffusion and kurtosis tensors based on the DKI model |
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Simulate a Multi-Tensor rtop. |
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Simulate a Multi-Tensor ODF. |
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Simulate a Multi-Tensor ODF. |
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Simulate a Multi-Tensor rtop. |
|
Simulate diffusion-weighted signals with a single tensor. |
|
Simulate a Multi-Tensor rtop. |
|
Simulated ODF with a single tensor. |
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Simulated ODF with a single tensor. |
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Simulate a Single-Tensor rtop. |
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Spherical to Cartesian coordinates |
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Simulate the signal for a Sticks & Ball model. |
|
rotation matrix from 2 unit vectors |
dipy.sims.phantom.
add_noise
(vol, snr=1.0, S0=None, noise_type='rician')Add noise of specified distribution to a 4D array.
Diffusion measurements in W directions at each (X, Y, Z)
voxel
position.
The desired signal-to-noise ratio. (See notes below.)
Reference signal for specifying snr (defaults to 1).
The distribution of noise added. Can be either ‘gaussian’ for Gaussian distributed noise, ‘rician’ for Rice-distributed noise (default) or ‘rayleigh’ for a Rayleigh distribution.
Volume with added noise.
Notes
SNR is defined here, following [1], as S0 / sigma
, where sigma
is
the standard deviation of the two Gaussian distributions forming the real
and imaginary components of the Rician noise distribution (see [2]).
References
Descoteaux, Angelino, Fitzgibbons and Deriche (2007) Regularized, fast and robust q-ball imaging. MRM, 58: 497-510
Gudbjartson and Patz (2008). The Rician distribution of noisy MRI data. MRM 34: 910-914.
Examples
>>> signal = np.arange(800).reshape(2, 2, 2, 100)
>>> signal_w_noise = add_noise(signal, snr=10, noise_type='rician')
dipy.sims.phantom.
get_fnames
(name='small_64D')Provide full paths to example or test datasets.
the filename/s of which dataset to return, one of: - ‘small_64D’ small region of interest nifti,bvecs,bvals 64 directions - ‘small_101D’ small region of interest nifti, bvecs, bvals
101 directions
‘aniso_vox’ volume with anisotropic voxel size as Nifti
‘fornix’ 300 tracks in Trackvis format (from Pittsburgh Brain Competition)
‘gqi_vectors’ the scanner wave vectors needed for a GQI acquisitions of 101 directions tested on Siemens 3T Trio
‘small_25’ small ROI (10x8x2) DTI data (b value 2000, 25 directions)
‘test_piesno’ slice of N=8, K=14 diffusion data
‘reg_c’ small 2D image used for validating registration
‘reg_o’ small 2D image used for validation registration
‘cb_2’ two vectorized cingulum bundles
filenames for dataset
Examples
>>> import numpy as np
>>> from dipy.io.image import load_nifti
>>> from dipy.data import get_fnames
>>> fimg, fbvals, fbvecs = get_fnames('small_101D')
>>> bvals=np.loadtxt(fbvals)
>>> bvecs=np.loadtxt(fbvecs).T
>>> data, affine = load_nifti(fimg)
>>> data.shape == (6, 10, 10, 102)
True
>>> bvals.shape == (102,)
True
>>> bvecs.shape == (102, 3)
True
dipy.sims.phantom.
gradient_table
(bvals, bvecs=None, big_delta=None, small_delta=None, b0_threshold=50, atol=0.01, btens=None)A general function for creating diffusion MR gradients.
It reads, loads and prepares scanner parameters like the b-values and b-vectors so that they can be useful during the reconstruction process.
an array of shape (N,) or (1, N) or (N, 1) with the b-values.
a path for the file which contains an array like the above (1).
an array of shape (N, 4) or (4, N). Then this parameter is considered to be a b-table which contains both bvals and bvecs. In this case the next parameter is skipped.
a path for the file which contains an array like the one at (3).
an array of shape (N, 3) or (3, N) with the b-vectors.
a path for the file which contains an array like the previous.
acquisition pulse separation time in seconds (default None)
acquisition pulse duration time in seconds (default None)
All b-values with values less than or equal to bo_threshold are considered as b0s i.e. without diffusion weighting.
All b-vectors need to be unit vectors up to a tolerance.
a string specifying the shape of the encoding tensor for all volumes in data. Options: ‘LTE’, ‘PTE’, ‘STE’, ‘CTE’ corresponding to linear, planar, spherical, and “cigar-shaped” tensor encoding. Tensors are rotated so that linear and cigar tensors are aligned with the corresponding gradient direction and the planar tensor’s normal is aligned with the corresponding gradient direction. Magnitude is scaled to match the b-value.
an array of strings of shape (N,), (N, 1), or (1, N) specifying encoding tensor shape for each volume separately. N corresponds to the number volumes in data. Options for elements in array: ‘LTE’, ‘PTE’, ‘STE’, ‘CTE’ corresponding to linear, planar, spherical, and “cigar-shaped” tensor encoding. Tensors are rotated so that linear and cigar tensors are aligned with the corresponding gradient direction and the planar tensor’s normal is aligned with the corresponding gradient direction. Magnitude is scaled to match the b-value.
an array of shape (N,3,3) specifying the b-tensor of each volume exactly. N corresponds to the number volumes in data. No rotation or scaling is performed.
A GradientTable with all the gradient information.
Notes
Often b0s (b-values which correspond to images without diffusion weighting) have 0 values however in some cases the scanner cannot provide b0s of an exact 0 value and it gives a bit higher values e.g. 6 or 12. This is the purpose of the b0_threshold in the __init__.
We assume that the minimum number of b-values is 7.
B-vectors should be unit vectors.
Examples
>>> from dipy.core.gradients import gradient_table
>>> bvals = 1500 * np.ones(7)
>>> bvals[0] = 0
>>> sq2 = np.sqrt(2) / 2
>>> bvecs = np.array([[0, 0, 0],
... [1, 0, 0],
... [0, 1, 0],
... [0, 0, 1],
... [sq2, sq2, 0],
... [sq2, 0, sq2],
... [0, sq2, sq2]])
>>> gt = gradient_table(bvals, bvecs)
>>> gt.bvecs.shape == bvecs.shape
True
>>> gt = gradient_table(bvals, bvecs.T)
>>> gt.bvecs.shape == bvecs.T.shape
False
dipy.sims.phantom.
orbital_phantom
(gtab=None, evals=array([0.0015, 0.0004, 0.0004]), func=None, t=array([0., 0.00628947, 0.01257895, 0.01886842, 0.0251579, 0.03144737, 0.03773685, 0.04402632, 0.0503158, 0.05660527, 0.06289475, 0.06918422, 0.0754737, 0.08176317, 0.08805265, 0.09434212, 0.1006316, 0.10692107, 0.11321055, 0.11950002, 0.1257895, 0.13207897, 0.13836845, 0.14465792, 0.15094739, 0.15723687, 0.16352634, 0.16981582, 0.17610529, 0.18239477, 0.18868424, 0.19497372, 0.20126319, 0.20755267, 0.21384214, 0.22013162, 0.22642109, 0.23271057, 0.23900004, 0.24528952, 0.25157899, 0.25786847, 0.26415794, 0.27044742, 0.27673689, 0.28302637, 0.28931584, 0.29560531, 0.30189479, 0.30818426, 0.31447374, 0.32076321, 0.32705269, 0.33334216, 0.33963164, 0.34592111, 0.35221059, 0.35850006, 0.36478954, 0.37107901, 0.37736849, 0.38365796, 0.38994744, 0.39623691, 0.40252639, 0.40881586, 0.41510534, 0.42139481, 0.42768429, 0.43397376, 0.44026323, 0.44655271, 0.45284218, 0.45913166, 0.46542113, 0.47171061, 0.47800008, 0.48428956, 0.49057903, 0.49686851, 0.50315798, 0.50944746, 0.51573693, 0.52202641, 0.52831588, 0.53460536, 0.54089483, 0.54718431, 0.55347378, 0.55976326, 0.56605273, 0.57234221, 0.57863168, 0.58492115, 0.59121063, 0.5975001, 0.60378958, 0.61007905, 0.61636853, 0.622658, 0.62894748, 0.63523695, 0.64152643, 0.6478159, 0.65410538, 0.66039485, 0.66668433, 0.6729738, 0.67926328, 0.68555275, 0.69184223, 0.6981317, 0.70442118, 0.71071065, 0.71700013, 0.7232896, 0.72957907, 0.73586855, 0.74215802, 0.7484475, 0.75473697, 0.76102645, 0.76731592, 0.7736054, 0.77989487, 0.78618435, 0.79247382, 0.7987633, 0.80505277, 0.81134225, 0.81763172, 0.8239212, 0.83021067, 0.83650015, 0.84278962, 0.8490791, 0.85536857, 0.86165805, 0.86794752, 0.87423699, 0.88052647, 0.88681594, 0.89310542, 0.89939489, 0.90568437, 0.91197384, 0.91826332, 0.92455279, 0.93084227, 0.93713174, 0.94342122, 0.94971069, 0.95600017, 0.96228964, 0.96857912, 0.97486859, 0.98115807, 0.98744754, 0.99373702, 1.00002649, 1.00631597, 1.01260544, 1.01889491, 1.02518439, 1.03147386, 1.03776334, 1.04405281, 1.05034229, 1.05663176, 1.06292124, 1.06921071, 1.07550019, 1.08178966, 1.08807914, 1.09436861, 1.10065809, 1.10694756, 1.11323704, 1.11952651, 1.12581599, 1.13210546, 1.13839494, 1.14468441, 1.15097389, 1.15726336, 1.16355283, 1.16984231, 1.17613178, 1.18242126, 1.18871073, 1.19500021, 1.20128968, 1.20757916, 1.21386863, 1.22015811, 1.22644758, 1.23273706, 1.23902653, 1.24531601, 1.25160548, 1.25789496, 1.26418443, 1.27047391, 1.27676338, 1.28305286, 1.28934233, 1.29563181, 1.30192128, 1.30821075, 1.31450023, 1.3207897, 1.32707918, 1.33336865, 1.33965813, 1.3459476, 1.35223708, 1.35852655, 1.36481603, 1.3711055, 1.37739498, 1.38368445, 1.38997393, 1.3962634, 1.40255288, 1.40884235, 1.41513183, 1.4214213, 1.42771078, 1.43400025, 1.44028973, 1.4465792, 1.45286867, 1.45915815, 1.46544762, 1.4717371, 1.47802657, 1.48431605, 1.49060552, 1.496895, 1.50318447, 1.50947395, 1.51576342, 1.5220529, 1.52834237, 1.53463185, 1.54092132, 1.5472108, 1.55350027, 1.55978975, 1.56607922, 1.5723687, 1.57865817, 1.58494765, 1.59123712, 1.59752659, 1.60381607, 1.61010554, 1.61639502, 1.62268449, 1.62897397, 1.63526344, 1.64155292, 1.64784239, 1.65413187, 1.66042134, 1.66671082, 1.67300029, 1.67928977, 1.68557924, 1.69186872, 1.69815819, 1.70444767, 1.71073714, 1.71702662, 1.72331609, 1.72960557, 1.73589504, 1.74218451, 1.74847399, 1.75476346, 1.76105294, 1.76734241, 1.77363189, 1.77992136, 1.78621084, 1.79250031, 1.79878979, 1.80507926, 1.81136874, 1.81765821, 1.82394769, 1.83023716, 1.83652664, 1.84281611, 1.84910559, 1.85539506, 1.86168454, 1.86797401, 1.87426349, 1.88055296, 1.88684243, 1.89313191, 1.89942138, 1.90571086, 1.91200033, 1.91828981, 1.92457928, 1.93086876, 1.93715823, 1.94344771, 1.94973718, 1.95602666, 1.96231613, 1.96860561, 1.97489508, 1.98118456, 1.98747403, 1.99376351, 2.00005298, 2.00634246, 2.01263193, 2.01892141, 2.02521088, 2.03150035, 2.03778983, 2.0440793, 2.05036878, 2.05665825, 2.06294773, 2.0692372, 2.07552668, 2.08181615, 2.08810563, 2.0943951, 2.10068458, 2.10697405, 2.11326353, 2.119553, 2.12584248, 2.13213195, 2.13842143, 2.1447109, 2.15100038, 2.15728985, 2.16357932, 2.1698688, 2.17615827, 2.18244775, 2.18873722, 2.1950267, 2.20131617, 2.20760565, 2.21389512, 2.2201846, 2.22647407, 2.23276355, 2.23905302, 2.2453425, 2.25163197, 2.25792145, 2.26421092, 2.2705004, 2.27678987, 2.28307935, 2.28936882, 2.2956583, 2.30194777, 2.30823724, 2.31452672, 2.32081619, 2.32710567, 2.33339514, 2.33968462, 2.34597409, 2.35226357, 2.35855304, 2.36484252, 2.37113199, 2.37742147, 2.38371094, 2.39000042, 2.39628989, 2.40257937, 2.40886884, 2.41515832, 2.42144779, 2.42773727, 2.43402674, 2.44031622, 2.44660569, 2.45289516, 2.45918464, 2.46547411, 2.47176359, 2.47805306, 2.48434254, 2.49063201, 2.49692149, 2.50321096, 2.50950044, 2.51578991, 2.52207939, 2.52836886, 2.53465834, 2.54094781, 2.54723729, 2.55352676, 2.55981624, 2.56610571, 2.57239519, 2.57868466, 2.58497414, 2.59126361, 2.59755308, 2.60384256, 2.61013203, 2.61642151, 2.62271098, 2.62900046, 2.63528993, 2.64157941, 2.64786888, 2.65415836, 2.66044783, 2.66673731, 2.67302678, 2.67931626, 2.68560573, 2.69189521, 2.69818468, 2.70447416, 2.71076363, 2.71705311, 2.72334258, 2.72963206, 2.73592153, 2.742211, 2.74850048, 2.75478995, 2.76107943, 2.7673689, 2.77365838, 2.77994785, 2.78623733, 2.7925268, 2.79881628, 2.80510575, 2.81139523, 2.8176847, 2.82397418, 2.83026365, 2.83655313, 2.8428426, 2.84913208, 2.85542155, 2.86171103, 2.8680005, 2.87428998, 2.88057945, 2.88686892, 2.8931584, 2.89944787, 2.90573735, 2.91202682, 2.9183163, 2.92460577, 2.93089525, 2.93718472, 2.9434742, 2.94976367, 2.95605315, 2.96234262, 2.9686321, 2.97492157, 2.98121105, 2.98750052, 2.99379, 3.00007947, 3.00636895, 3.01265842, 3.0189479, 3.02523737, 3.03152684, 3.03781632, 3.04410579, 3.05039527, 3.05668474, 3.06297422, 3.06926369, 3.07555317, 3.08184264, 3.08813212, 3.09442159, 3.10071107, 3.10700054, 3.11329002, 3.11957949, 3.12586897, 3.13215844, 3.13844792, 3.14473739, 3.15102687, 3.15731634, 3.16360582, 3.16989529, 3.17618476, 3.18247424, 3.18876371, 3.19505319, 3.20134266, 3.20763214, 3.21392161, 3.22021109, 3.22650056, 3.23279004, 3.23907951, 3.24536899, 3.25165846, 3.25794794, 3.26423741, 3.27052689, 3.27681636, 3.28310584, 3.28939531, 3.29568479, 3.30197426, 3.30826374, 3.31455321, 3.32084268, 3.32713216, 3.33342163, 3.33971111, 3.34600058, 3.35229006, 3.35857953, 3.36486901, 3.37115848, 3.37744796, 3.38373743, 3.39002691, 3.39631638, 3.40260586, 3.40889533, 3.41518481, 3.42147428, 3.42776376, 3.43405323, 3.44034271, 3.44663218, 3.45292166, 3.45921113, 3.4655006, 3.47179008, 3.47807955, 3.48436903, 3.4906585, 3.49694798, 3.50323745, 3.50952693, 3.5158164, 3.52210588, 3.52839535, 3.53468483, 3.5409743, 3.54726378, 3.55355325, 3.55984273, 3.5661322, 3.57242168, 3.57871115, 3.58500063, 3.5912901, 3.59757958, 3.60386905, 3.61015852, 3.616448, 3.62273747, 3.62902695, 3.63531642, 3.6416059, 3.64789537, 3.65418485, 3.66047432, 3.6667638, 3.67305327, 3.67934275, 3.68563222, 3.6919217, 3.69821117, 3.70450065, 3.71079012, 3.7170796, 3.72336907, 3.72965855, 3.73594802, 3.7422375, 3.74852697, 3.75481644, 3.76110592, 3.76739539, 3.77368487, 3.77997434, 3.78626382, 3.79255329, 3.79884277, 3.80513224, 3.81142172, 3.81771119, 3.82400067, 3.83029014, 3.83657962, 3.84286909, 3.84915857, 3.85544804, 3.86173752, 3.86802699, 3.87431647, 3.88060594, 3.88689542, 3.89318489, 3.89947436, 3.90576384, 3.91205331, 3.91834279, 3.92463226, 3.93092174, 3.93721121, 3.94350069, 3.94979016, 3.95607964, 3.96236911, 3.96865859, 3.97494806, 3.98123754, 3.98752701, 3.99381649, 4.00010596, 4.00639544, 4.01268491, 4.01897439, 4.02526386, 4.03155334, 4.03784281, 4.04413228, 4.05042176, 4.05671123, 4.06300071, 4.06929018, 4.07557966, 4.08186913, 4.08815861, 4.09444808, 4.10073756, 4.10702703, 4.11331651, 4.11960598, 4.12589546, 4.13218493, 4.13847441, 4.14476388, 4.15105336, 4.15734283, 4.16363231, 4.16992178, 4.17621126, 4.18250073, 4.1887902, 4.19507968, 4.20136915, 4.20765863, 4.2139481, 4.22023758, 4.22652705, 4.23281653, 4.239106, 4.24539548, 4.25168495, 4.25797443, 4.2642639, 4.27055338, 4.27684285, 4.28313233, 4.2894218, 4.29571128, 4.30200075, 4.30829023, 4.3145797, 4.32086918, 4.32715865, 4.33344812, 4.3397376, 4.34602707, 4.35231655, 4.35860602, 4.3648955, 4.37118497, 4.37747445, 4.38376392, 4.3900534, 4.39634287, 4.40263235, 4.40892182, 4.4152113, 4.42150077, 4.42779025, 4.43407972, 4.4403692, 4.44665867, 4.45294815, 4.45923762, 4.4655271, 4.47181657, 4.47810604, 4.48439552, 4.49068499, 4.49697447, 4.50326394, 4.50955342, 4.51584289, 4.52213237, 4.52842184, 4.53471132, 4.54100079, 4.54729027, 4.55357974, 4.55986922, 4.56615869, 4.57244817, 4.57873764, 4.58502712, 4.59131659, 4.59760607, 4.60389554, 4.61018502, 4.61647449, 4.62276396, 4.62905344, 4.63534291, 4.64163239, 4.64792186, 4.65421134, 4.66050081, 4.66679029, 4.67307976, 4.67936924, 4.68565871, 4.69194819, 4.69823766, 4.70452714, 4.71081661, 4.71710609, 4.72339556, 4.72968504, 4.73597451, 4.74226399, 4.74855346, 4.75484294, 4.76113241, 4.76742188, 4.77371136, 4.78000083, 4.78629031, 4.79257978, 4.79886926, 4.80515873, 4.81144821, 4.81773768, 4.82402716, 4.83031663, 4.83660611, 4.84289558, 4.84918506, 4.85547453, 4.86176401, 4.86805348, 4.87434296, 4.88063243, 4.88692191, 4.89321138, 4.89950086, 4.90579033, 4.9120798, 4.91836928, 4.92465875, 4.93094823, 4.9372377, 4.94352718, 4.94981665, 4.95610613, 4.9623956, 4.96868508, 4.97497455, 4.98126403, 4.9875535, 4.99384298, 5.00013245, 5.00642193, 5.0127114, 5.01900088, 5.02529035, 5.03157983, 5.0378693, 5.04415878, 5.05044825, 5.05673772, 5.0630272, 5.06931667, 5.07560615, 5.08189562, 5.0881851, 5.09447457, 5.10076405, 5.10705352, 5.113343, 5.11963247, 5.12592195, 5.13221142, 5.1385009, 5.14479037, 5.15107985, 5.15736932, 5.1636588, 5.16994827, 5.17623775, 5.18252722, 5.1888167, 5.19510617, 5.20139564, 5.20768512, 5.21397459, 5.22026407, 5.22655354, 5.23284302, 5.23913249, 5.24542197, 5.25171144, 5.25800092, 5.26429039, 5.27057987, 5.27686934, 5.28315882, 5.28944829, 5.29573777, 5.30202724, 5.30831672, 5.31460619, 5.32089567, 5.32718514, 5.33347462, 5.33976409, 5.34605356, 5.35234304, 5.35863251, 5.36492199, 5.37121146, 5.37750094, 5.38379041, 5.39007989, 5.39636936, 5.40265884, 5.40894831, 5.41523779, 5.42152726, 5.42781674, 5.43410621, 5.44039569, 5.44668516, 5.45297464, 5.45926411, 5.46555359, 5.47184306, 5.47813254, 5.48442201, 5.49071148, 5.49700096, 5.50329043, 5.50957991, 5.51586938, 5.52215886, 5.52844833, 5.53473781, 5.54102728, 5.54731676, 5.55360623, 5.55989571, 5.56618518, 5.57247466, 5.57876413, 5.58505361, 5.59134308, 5.59763256, 5.60392203, 5.61021151, 5.61650098, 5.62279046, 5.62907993, 5.6353694, 5.64165888, 5.64794835, 5.65423783, 5.6605273, 5.66681678, 5.67310625, 5.67939573, 5.6856852, 5.69197468, 5.69826415, 5.70455363, 5.7108431, 5.71713258, 5.72342205, 5.72971153, 5.736001, 5.74229048, 5.74857995, 5.75486943, 5.7611589, 5.76744838, 5.77373785, 5.78002732, 5.7863168, 5.79260627, 5.79889575, 5.80518522, 5.8114747, 5.81776417, 5.82405365, 5.83034312, 5.8366326, 5.84292207, 5.84921155, 5.85550102, 5.8617905, 5.86807997, 5.87436945, 5.88065892, 5.8869484, 5.89323787, 5.89952735, 5.90581682, 5.9121063, 5.91839577, 5.92468524, 5.93097472, 5.93726419, 5.94355367, 5.94984314, 5.95613262, 5.96242209, 5.96871157, 5.97500104, 5.98129052, 5.98757999, 5.99386947, 6.00015894, 6.00644842, 6.01273789, 6.01902737, 6.02531684, 6.03160632, 6.03789579, 6.04418527, 6.05047474, 6.05676422, 6.06305369, 6.06934316, 6.07563264, 6.08192211, 6.08821159, 6.09450106, 6.10079054, 6.10708001, 6.11336949, 6.11965896, 6.12594844, 6.13223791, 6.13852739, 6.14481686, 6.15110634, 6.15739581, 6.16368529, 6.16997476, 6.17626424, 6.18255371, 6.18884319, 6.19513266, 6.20142214, 6.20771161, 6.21400108, 6.22029056, 6.22658003, 6.23286951, 6.23915898, 6.24544846, 6.25173793, 6.25802741, 6.26431688, 6.27060636, 6.27689583, 6.28318531]), datashape=(64, 64, 64, 65), origin=(32, 32, 32), scale=(25, 25, 25), angles=array([0., 0.2026834, 0.40536679, 0.60805019, 0.81073359, 1.01341699, 1.21610038, 1.41878378, 1.62146718, 1.82415057, 2.02683397, 2.22951737, 2.43220076, 2.63488416, 2.83756756, 3.04025096, 3.24293435, 3.44561775, 3.64830115, 3.85098454, 4.05366794, 4.25635134, 4.45903473, 4.66171813, 4.86440153, 5.06708493, 5.26976832, 5.47245172, 5.67513512, 5.87781851, 6.08050191, 6.28318531]), radii=array([0.2, 0.56, 0.92, 1.28, 1.64, 2. ]), S0=100.0, snr=None)Create a phantom based on a 3-D orbit f(t) -> (x,y,z)
.
Gradient table of measurement directions.
Tensor eigenvalues.
It could be desirable for -1=<x,y,z <=1
.
If None creates a circular orbit.
Represents time for the orbit. Default is
np.linspace(0, 2 * np.pi, 1000)
.
Size of the output simulated data
Define the center for the volume
Scale the function before applying to the grid
Density angle points, always perpendicular to the first eigen vector Default np.linspace(0, 2 * np.pi, 32).
Thickness radii. Default np.linspace(0.2, 2, 6)
.
angles and radii define the total thickness options
Maximum simulated signal. Default 100.
The signal to noise ratio set to apply Rician noise to the data. Default is to not add noise at all.
See also
Examples
>>> def f(t):
... x = np.sin(t)
... y = np.cos(t)
... z = np.linspace(-1, 1, len(x))
... return x, y, z
>>> data = orbital_phantom(func=f)
dipy.sims.phantom.
single_tensor
(gtab, S0=1, evals=None, evecs=None, snr=None)Simulate diffusion-weighted signals with a single tensor.
Table with information of b-values and gradient directions g. Note that if gtab has a btens attribute, simulations will be performed according to the given b-tensor B information.
Strength of signal in the presence of no diffusion gradient (also
called the b=0
value).
Eigenvalues of the diffusion tensor. By default, values typical for prolate white matter are used.
Eigenvectors of the tensor. You can also think of this as a rotation matrix that transforms the direction of the tensor. The eigenvectors need to be column wise.
Signal to noise ratio, assuming Rician noise. None implies no noise.
S(b, g) = S_0 e^(-b g^T R D R.T g)
, if gtab.tens=None
S(B) = S_0 e^(-B:D)
, if gtab.tens information is given
References
M. Descoteaux, “High Angular Resolution Diffusion MRI: from Local Estimation to Segmentation and Tractography”, PhD thesis, University of Nice-Sophia Antipolis, p. 42, 2008.
E. Stejskal and J. Tanner, “Spin diffusion measurements: spin echos in the presence of a time-dependent field gradient”, Journal of Chemical Physics, nr. 42, pp. 288–292, 1965.
dipy.sims.phantom.
vec2vec_rotmat
(u, v)rotation matrix from 2 unit vectors
u, v being unit 3d vectors return a 3x3 rotation matrix R than aligns u to v.
In general there are many rotations that will map u to v. If S is any rotation using v as an axis then R.S will also map u to v since (S.R)u = S(Ru) = Sv = v. The rotation R returned by vec2vec_rotmat leaves fixed the perpendicular to the plane spanned by u and v.
The transpose of R will align v to u.
Examples
>>> import numpy as np
>>> from dipy.core.geometry import vec2vec_rotmat
>>> u=np.array([1,0,0])
>>> v=np.array([0,1,0])
>>> R=vec2vec_rotmat(u,v)
>>> np.dot(R,u)
array([ 0., 1., 0.])
>>> np.dot(R.T,v)
array([ 1., 0., 0.])
GradientTable
dipy.sims.voxel.
GradientTable
(gradients, big_delta=None, small_delta=None, b0_threshold=50, btens=None)Bases: object
Diffusion gradient information
Diffusion gradients. The direction of each of these vectors corresponds to the b-vector, and the length corresponds to the b-value.
Gradients with b-value less than or equal to b0_threshold are considered as b0s i.e. without diffusion weighting.
See also
gradient_table
Notes
The GradientTable object is immutable. Do NOT assign attributes. If you have your gradient table in a bval & bvec format, we recommend using the factory function gradient_table
diffusion gradients
The b-value, or magnitude, of each gradient direction.
The q-value for each gradient direction. Needs big and small delta.
The direction, represented as a unit vector, of each gradient.
Boolean array indicating which gradients have no diffusion weighting, ie b-value is close to 0.
Gradients with b-value less than or equal to b0_threshold are considered to not have diffusion weighting.
The b-tensor of each gradient direction.
Methods
b0s_mask |
|
bvals |
|
bvecs |
|
gradient_strength |
|
qvals |
|
tau |
dipy.sims.voxel.
add_noise
(signal, snr, S0, noise_type='rician')Add noise of specified distribution to the signal from a single voxel.
The signal in the voxel.
The desired signal-to-noise ratio. (See notes below.) If snr is None, return the signal as-is.
Reference signal for specifying snr.
The distribution of noise added. Can be either ‘gaussian’ for Gaussian distributed noise, ‘rician’ for Rice-distributed noise (default) or ‘rayleigh’ for a Rayleigh distribution.
Signal with added noise.
Notes
SNR is defined here, following [1], as S0 / sigma
, where sigma
is
the standard deviation of the two Gaussian distributions forming the real
and imaginary components of the Rician noise distribution (see [2]).
References
Descoteaux, Angelino, Fitzgibbons and Deriche (2007) Regularized, fast and robust q-ball imaging. MRM, 58: 497-510
Gudbjartson and Patz (2008). The Rician distribution of noisy MRI data. MRM 34: 910-914.
Examples
>>> signal = np.arange(800).reshape(2, 2, 2, 100)
>>> signal_w_noise = add_noise(signal, 10., 100., noise_type='rician')
dipy.sims.voxel.
callaghan_perpendicular
(q, radius)Calculates the perpendicular diffusion signal E(q) in a cylinder of radius R using the Soderman model [1]. Assumes that the pulse length is infinitely short and the diffusion time is infinitely long.
q-space value in 1/mm
cylinder radius in mm
signal attenuation
References
dipy.sims.voxel.
cylinders_and_ball_soderman
(gtab, tau, radii=[0.005, 0.005], D=0.0007, S0=1.0, angles=[(0, 0), (90, 0)], fractions=[35, 35], snr=20)Calculates the three-dimensional signal attenuation E(q) originating from within a cylinder of radius R using the Soderman approximation [1]. The diffusion signal is assumed to be separable perpendicular and parallel to the cylinder axis [2]. This function is basically an extension of the ball and stick model. Setting the radius to zero makes them equivalent.
Signal measurement directions.
diffusion time in s
cylinder radius in mm
diffusion constant
Unweighted signal value.
List of K polar angles (in degrees) for the sticks or array of K sticks as unit vectors.
Percentage of each stick. Remainder to 100 specifies isotropic component.
Signal to noise ratio, assuming Rician noise. If set to None, no noise is added.
signal attenuation
References
Söderman, Olle, and Bengt Jönsson. “Restricted diffusion in cylindrical geometry.” Journal of Magnetic Resonance, Series A 117.1 (1995): 94-97.
Assaf, Yaniv, et al. “New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter.” Magnetic Resonance in Medicine 52.5 (2004): 965-978.
dipy.sims.voxel.
dki_design_matrix
(gtab)Construct B design matrix for DKI.
Measurement directions.
Design matrix or B matrix for the DKI model B[j, :] = (Bxx, Bxy, Bzz, Bxz, Byz, Bzz,
Bxxxx, Byyyy, Bzzzz, Bxxxy, Bxxxz, Bxyyy, Byyyz, Bxzzz, Byzzz, Bxxyy, Bxxzz, Byyzz, Bxxyz, Bxyyz, Bxyzz, BlogS0)
dipy.sims.voxel.
dki_signal
(gtab, dt, kt, S0=150, snr=None)Simulated signal based on the diffusion and diffusion kurtosis tensors of a single voxel. Simulations are preformed assuming the DKI model.
Measurement directions.
Elements of the diffusion tensor.
Elements of the diffusion kurtosis tensor.
Strength of signal in the presence of no diffusion gradient.
Signal to noise ratio, assuming Rician noise. None implies no noise.
Simulated signal based on the DKI model:
References
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.
dipy.sims.voxel.
dot
(a, b, out=None)Dot product of two arrays. Specifically,
If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).
If both a and b are 2-D arrays, it is matrix multiplication,
but using matmul()
or a @ b
is preferred.
If either a or b is 0-D (scalar), it is equivalent to multiply()
and using numpy.multiply(a, b)
or a * b
is preferred.
If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.
If a is an N-D array and b is an M-D array (where M>=2
), it is a
sum product over the last axis of a and the second-to-last axis of b:
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
First argument.
Second argument.
Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
If the last dimension of a is not the same size as the second-to-last dimension of b.
See also
vdot
Complex-conjugating dot product.
tensordot
Sum products over arbitrary axes.
einsum
Einstein summation convention.
matmul
‘@’ operator as method with out parameter.
Examples
>>> np.dot(3, 4)
12
Neither argument is complex-conjugated:
>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)
For 2-D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
[2, 2]])
>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128
dipy.sims.voxel.
kurtosis_element
(D_comps, frac, ind_i, ind_j, ind_k, ind_l, DT=None, MD=None)Computes the diffusion kurtosis tensor element (with indexes i, j, k and l) based on the individual diffusion tensor components of a multicompartmental model.
Diffusion tensors for all K individual compartment of the multicompartmental model.
Percentage of the contribution of each tensor. The sum of fractions should be equal to 100%.
Element’s index i (0 for x, 1 for y, 2 for z)
Element’s index j (0 for x, 1 for y, 2 for z)
Element’s index k (0 for x, 1 for y, 2 for z)
Elements index l (0 for x, 1 for y, 2 for z)
Voxel’s global diffusion tensor.
Voxel’s global mean diffusivity.
kurtosis tensor element of index i, j, k, l
Notes
wijkl is calculated using equation 8 given in [1]
References
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.
dipy.sims.voxel.
multi_tensor
(gtab, mevals, S0=1.0, angles=[(0, 0), (90, 0)], fractions=[50, 50], snr=20)Simulate a Multi-Tensor signal.
Table with information of b-values and gradient directions. Note that if gtab has a btens attribute, simulations will be performed according to the given b-tensor information.
each tensor’s eigenvalues in each row
Unweighted signal value (b0 signal).
List of K tensor directions in polar angles (in degrees) or unit vectors
Percentage of the contribution of each tensor. The sum of fractions should be equal to 100%.
Signal to noise ratio, assuming Rician noise. If set to None, no noise is added.
Simulated signal.
Sticks in cartesian coordinates.
Examples
>>> import numpy as np
>>> from dipy.sims.voxel import multi_tensor
>>> from dipy.data import get_fnames
>>> from dipy.core.gradients import gradient_table
>>> from dipy.io.gradients import read_bvals_bvecs
>>> fimg, fbvals, fbvecs = get_fnames('small_101D')
>>> bvals, bvecs = read_bvals_bvecs(fbvals, fbvecs)
>>> gtab = gradient_table(bvals, bvecs)
>>> mevals=np.array(([0.0015, 0.0003, 0.0003],[0.0015, 0.0003, 0.0003]))
>>> e0 = np.array([1, 0, 0.])
>>> e1 = np.array([0., 1, 0])
>>> S = multi_tensor(gtab, mevals)
dipy.sims.voxel.
multi_tensor_dki
(gtab, mevals, S0=1.0, angles=[(90.0, 0.0), (90.0, 0.0)], fractions=[50, 50], snr=20)Simulate the diffusion-weight signal, diffusion and kurtosis tensors based on the DKI model
eigenvalues of the diffusion tensor for each individual compartment
Unweighted signal value (b0 signal).
List of K tensor directions of the diffusion tensor of each compartment in polar angles (in degrees) or unit vectors
Percentage of the contribution of each tensor. The sum of fractions should be equal to 100%.
Signal to noise ratio, assuming Rician noise. If set to None, no noise is added.
Simulated signal based on the DKI model.
elements of the diffusion tensor.
elements of the kurtosis tensor.
Notes
Simulations are based on multicompartmental models which assumes that tissue is well described by impermeable diffusion compartments characterized by their only diffusion tensor. Since simulations are based on the DKI model, coefficients larger than the fourth order of the signal’s taylor expansion approximation are neglected.
References
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.
Examples
>>> import numpy as np
>>> from dipy.sims.voxel import multi_tensor_dki
>>> from dipy.data import get_fnames
>>> from dipy.core.gradients import gradient_table
>>> from dipy.io.gradients import read_bvals_bvecs
>>> fimg, fbvals, fbvecs = get_fnames('small_64D')
>>> bvals, bvecs = read_bvals_bvecs(fbvals, fbvecs)
>>> bvals_2s = np.concatenate((bvals, bvals * 2), axis=0)
>>> bvecs_2s = np.concatenate((bvecs, bvecs), axis=0)
>>> gtab = gradient_table(bvals_2s, bvecs_2s)
>>> mevals = np.array([[0.00099, 0, 0],[0.00226, 0.00087, 0.00087]])
>>> S, dt, kt = multi_tensor_dki(gtab, mevals)
dipy.sims.voxel.
multi_tensor_msd
(mf, mevals=None, tau=0.025330295910584444)Simulate a Multi-Tensor rtop.
Percentages of the fractions for each tensor.
Eigen-values for each tensor. By default, values typical for prolate white matter are used.
diffusion time. By default the value that makes q=sqrt(b).
Mean square displacement.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
multi_tensor_odf
(odf_verts, mevals, angles, fractions)Simulate a Multi-Tensor ODF.
Vertices of the reconstruction sphere.
Eigen-values for each tensor.
Sequence of principal directions for each tensor in polar angles or cartesian unit coordinates.
Percentages of the fractions for each tensor.
Orientation distribution function.
Examples
Simulate a MultiTensor ODF with two peaks and calculate its exact ODF.
>>> import numpy as np
>>> from dipy.sims.voxel import multi_tensor_odf, all_tensor_evecs
>>> from dipy.data import default_sphere
>>> vertices, faces = default_sphere.vertices, default_sphere.faces
>>> mevals = np.array(([0.0015, 0.0003, 0.0003],[0.0015, 0.0003, 0.0003]))
>>> angles = [(0, 0), (90, 0)]
>>> odf = multi_tensor_odf(vertices, mevals, angles, [50, 50])
dipy.sims.voxel.
multi_tensor_pdf
(pdf_points, mevals, angles, fractions, tau=0.025330295910584444)Simulate a Multi-Tensor ODF.
Points to evaluate the PDF.
Eigen-values for each tensor. By default, values typical for prolate white matter are used.
Sequence of principal directions for each tensor in polar angles or cartesian unit coordinates.
Percentages of the fractions for each tensor.
diffusion time. By default the value that makes q=sqrt(b).
Probability density function of the water displacement.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
multi_tensor_rtop
(mf, mevals=None, tau=0.025330295910584444)Simulate a Multi-Tensor rtop.
Percentages of the fractions for each tensor.
Eigen-values for each tensor. By default, values typical for prolate white matter are used.
diffusion time. By default the value that makes q=sqrt(b).
Return to origin probability.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
single_tensor
(gtab, S0=1, evals=None, evecs=None, snr=None)Simulate diffusion-weighted signals with a single tensor.
Table with information of b-values and gradient directions g. Note that if gtab has a btens attribute, simulations will be performed according to the given b-tensor B information.
Strength of signal in the presence of no diffusion gradient (also
called the b=0
value).
Eigenvalues of the diffusion tensor. By default, values typical for prolate white matter are used.
Eigenvectors of the tensor. You can also think of this as a rotation matrix that transforms the direction of the tensor. The eigenvectors need to be column wise.
Signal to noise ratio, assuming Rician noise. None implies no noise.
S(b, g) = S_0 e^(-b g^T R D R.T g)
, if gtab.tens=None
S(B) = S_0 e^(-B:D)
, if gtab.tens information is given
References
M. Descoteaux, “High Angular Resolution Diffusion MRI: from Local Estimation to Segmentation and Tractography”, PhD thesis, University of Nice-Sophia Antipolis, p. 42, 2008.
E. Stejskal and J. Tanner, “Spin diffusion measurements: spin echos in the presence of a time-dependent field gradient”, Journal of Chemical Physics, nr. 42, pp. 288–292, 1965.
dipy.sims.voxel.
single_tensor_msd
(evals=None, tau=0.025330295910584444)Simulate a Multi-Tensor rtop.
Eigen-values for the tensor. By default, values typical for prolate white matter are used.
diffusion time. By default the value that makes q=sqrt(b).
Mean square displacement.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
single_tensor_odf
(r, evals=None, evecs=None)Simulated ODF with a single tensor.
Measurement positions in (x, y, z), either as a list or on a grid.
Eigenvalues of diffusion tensor. By default, use values typical for prolate white matter.
Eigenvectors of the tensor, written column-wise. You can also think of these as the rotation matrix that determines the orientation of the diffusion tensor.
The diffusion probability at r
after time tau
.
References
Aganj et al., “Reconstruction of the Orientation Distribution Function in Single- and Multiple-Shell q-Ball Imaging Within Constant Solid Angle”, Magnetic Resonance in Medicine, nr. 64, pp. 554–566, 2010.
dipy.sims.voxel.
single_tensor_pdf
(r, evals=None, evecs=None, tau=0.025330295910584444)Simulated ODF with a single tensor.
Measurement positions in (x, y, z), either as a list or on a grid.
Eigenvalues of diffusion tensor. By default, use values typical for prolate white matter.
Eigenvectors of the tensor. You can also think of these as the rotation matrix that determines the orientation of the diffusion tensor.
diffusion time. By default the value that makes q=sqrt(b).
The diffusion probability at r
after time tau
.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
single_tensor_rtop
(evals=None, tau=0.025330295910584444)Simulate a Single-Tensor rtop.
Eigen-values for the tensor. By default, values typical for prolate white matter are used.
diffusion time. By default the value that makes q=sqrt(b).
Return to origin probability.
References
Cheng J., “Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI”, PhD Thesis, 2012.
dipy.sims.voxel.
sphere2cart
(r, theta, phi)Spherical to Cartesian coordinates
This is the standard physics convention where theta is the inclination (polar) angle, and phi is the azimuth angle.
Imagine a sphere with center (0,0,0). Orient it with the z axis running south-north, the y axis running west-east and the x axis from posterior to anterior. theta (the inclination angle) is the angle to rotate from the z-axis (the zenith) around the y-axis, towards the x axis. Thus the rotation is counter-clockwise from the point of view of positive y. phi (azimuth) gives the angle of rotation around the z-axis towards the y axis. The rotation is counter-clockwise from the point of view of positive z.
Equivalently, given a point P on the sphere, with coordinates x, y, z, theta is the angle between P and the z-axis, and phi is the angle between the projection of P onto the XY plane, and the X axis.
Geographical nomenclature designates theta as ‘co-latitude’, and phi as ‘longitude’
radius
inclination or polar angle
azimuth angle
x coordinate(s) in Cartesion space
y coordinate(s) in Cartesian space
z coordinate
Notes
See these pages:
for excellent discussion of the many different conventions possible. Here we use the physics conventions, used in the wikipedia page.
Derivations of the formulae are simple. Consider a vector x, y, z of length r (norm of x, y, z). The inclination angle (theta) can be found from: cos(theta) == z / r -> z == r * cos(theta). This gives the hypotenuse of the projection onto the XY plane, which we will call Q. Q == r*sin(theta). Now x / Q == cos(phi) -> x == r * sin(theta) * cos(phi) and so on.
We have deliberately named this function sphere2cart
rather than
sph2cart
to distinguish it from the Matlab function of that
name, because the Matlab function uses an unusual convention for the
angles that we did not want to replicate. The Matlab function is
trivial to implement with the formulae given in the Matlab help.
dipy.sims.voxel.
sticks_and_ball
(gtab, d=0.0015, S0=1.0, angles=[(0, 0), (90, 0)], fractions=[35, 35], snr=20)Simulate the signal for a Sticks & Ball model.
Signal measurement directions.
Diffusivity value.
Unweighted signal value.
List of K polar angles (in degrees) for the sticks or array of K sticks as unit vectors.
Percentage of each stick. Remainder to 100 specifies isotropic component.
Signal to noise ratio, assuming Rician noise. If set to None, no noise is added.
Simulated signal.
Sticks in cartesian coordinates.
References
Behrens et al., “Probabilistic diffusion tractography with multiple fiber orientations: what can we gain?”, Neuroimage, 2007.
dipy.sims.voxel.
vec2vec_rotmat
(u, v)rotation matrix from 2 unit vectors
u, v being unit 3d vectors return a 3x3 rotation matrix R than aligns u to v.
In general there are many rotations that will map u to v. If S is any rotation using v as an axis then R.S will also map u to v since (S.R)u = S(Ru) = Sv = v. The rotation R returned by vec2vec_rotmat leaves fixed the perpendicular to the plane spanned by u and v.
The transpose of R will align v to u.
Examples
>>> import numpy as np
>>> from dipy.core.geometry import vec2vec_rotmat
>>> u=np.array([1,0,0])
>>> v=np.array([0,1,0])
>>> R=vec2vec_rotmat(u,v)
>>> np.dot(R,u)
array([ 0., 1., 0.])
>>> np.dot(R.T,v)
array([ 1., 0., 0.])