Diffusion-related meta data in Siemens files

Warning

This has been tested on Verio, Trio, Skyra and Prisma. Other models may or may not work.

Warning

The coordinate system of diffusion gradient direction has not yet been determined.

Private element

The diffusion-related meta-data is stored in a vendor-specific, binary-encoded, element, called CSA Image Header Info. The element tag is (0029,xx19), under the Private Creator value SIEMENS CSA HEADER. The DICOM Conformance Statements (e.g. for the Prisma) only describe it as manufacturer model dependent information but its precise format can be found on various websites. A parser for this format has been implemented in Dicomifier.

Fields in the private element

Once parsed, the CSA Image Header Info has four fields obviously related to diffusion MRI: B_value, DiffusionGradientDirection, DiffusionDirectionality, and B_matrix, which match the terms of the MR Diffusion module. Two examples are shown below, the first one for a diffusion-weighted image, the second one for a \(b=0\ s/mm^2\) image (other fields have been removed for readability).

meta_data = [
    {
        'B_value': [0],
        'DiffusionGradientDirection': [],
        'B_matrix': [],
        'DiffusionDirectionality': [b'DIRECTIONAL\x00'] },
    {
        'B_value': [1000],
        'DiffusionGradientDirection': [0.1977423, 0.17195807, -0.96505374],
        'B_matrix': [39.0, 34.0, -191.0, 30.0, -166.0, 932.0],
        'DiffusionDirectionality': [b'DIRECTIONAL\x00'] },
    {
        'B_value': [1000],
        'DiffusionGradientDirection': [-0.32412839, -0.94072425, 0.09989204],
        'B_matrix': [105.0, 305.0, -32.0, 885.0, -94.0, 11.0],
        'DiffusionDirectionality': [b'DIRECTIONAL\x00'] },
    {
        'B_value': [1000],
        'DiffusionGradientDirection': [-0.97839409, -0.17072155, 0.11661573],
        'B_matrix': [957.0, 167.0, -114.0, 29.0, -20.0, 14.0],
        'DiffusionDirectionality': [b'DIRECTIONAL\x00'] }
]

The b-value is always present and expressed in \(s/mm^2\). It appears to be the ideal b-value, i.e. not modulated by the imaging gradients. The direction of the diffusion gradient is not specified for non diffusion-weighted images, and neither is the b-matrix; when specified, the direction has norm 1.

The b-matrix has only six elements, and can thus be assumed to be the upper or the lower triangular part of the full b-matrix. However, looking at eigensystem of the b-matrix for both hypotheses, it appears that both the eigenvalues and the dot-product of the principal eigenvector with the direction of the diffusion gradient only match for the upper-triangular matrix.

import numpy

def from_upper(linear):
    return numpy.array([
        [linear[0], linear[1], linear[2]],
        [linear[1], linear[3], linear[4]],
        [linear[2], linear[4], linear[5]]])
def from_lower(linear):
    return numpy.array([
        [linear[0], linear[1], linear[3]],
        [linear[1], linear[2], linear[4]],
        [linear[3], linear[4], linear[5]]])

for item in meta_data:
    if not item["B_matrix"]:
        continue

    upper_eigensystem = numpy.linalg.eigh(from_upper(item["B_matrix"]))
    lower_eigensystem = numpy.linalg.eigh(from_lower(item["B_matrix"]))

    direction = item["DiffusionGradientDirection"]

    print(
        "Upper triangular matrix: ",
        upper_eigensystem[0].astype(int),
        numpy.dot(direction, upper_eigensystem[1][:,-1]),
        "\nLower triangular matrix: ",
        lower_eigensystem[0].astype(int),
        numpy.dot(direction, lower_eigensystem[1][:,-1]),
        "\n")

Upper triangular matrix:  [   0    0 1000] -1.0000001580676756
Lower triangular matrix:  [-220   43  956] -0.9739920011521168

Upper triangular matrix:  [   0    1 1000] 0.999999873698694
Lower triangular matrix:  [-916   31  969] 0.3232097831549061

Upper triangular matrix:  [  0   0 999] 1.0000000357323802
Lower triangular matrix:  [-143   17  983] 0.9894968101548527