Scalar and Vector Fields
Computing and mapping surface and volume anisotropy by magnitude and orientation as vector fields, and volume fraction as scalar values, can help identify heterogeneity and latent features to correlate form with function in bone specimens. The options for computing anisotropy maps with the MIL and Surface normals algorithms, as well as for computing volume fraction, are available in the Bone Analysis Wizard on the Scalar and Vector Fields page (see Computing Scalar and Vector Fields). Visualizations of vector-based anisotropy maps are available in the 3D view in the workspace, while the mapped scalar values of volume fractions can be examined in both 2D and 3D views.
Vector fields of anisotropy magnitude and orientation (left and middle respectively) and scalar-based map of volume fraction (right)
In the panel above, the image on the left shows anisotropy mapped by magnitude, with red being very anisotropic and blue isotropic. The image in the middle shows the same map replotted in such a way that the color corresponds to orientation.
Settings for Computing Anisotropy
Two mapping methods — MIL and Surface normals — are available in the Bone Analysis module for computing anisotropy, as well as the option to generate scalar-based maps of volume fraction. These mapping methods are described below.
MIL… This classic method of anisotropy measurement using the Mean Intercept Length (MIL) method combines both surface and volume anisotropy components and requires sampling volumes to be about 4-5 inter-trabecular spaces. The MIL algorithm can provide good information for evaluating orientation, but anisotropy values of magnitude can be overly noisy.
The settings for the MIL algorithm are listed in the table below.
| Description | |
|---|---|
| Sampling |
The resolution, or distance between subsequent samples along each vector (samplingDistance).
Recommendation The entered value should be about 4-5 inter-trabecular spaces. |
| Radius |
The radius of the sampling sphere, which determines the length of each sampling vector (lengthToAnalyze).
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| Orientations |
The number of lines to analyze per sampling sphere(countOrientations).
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Surface normals… The surface anisotropy measurement exclusive to Dragonfly is based on the construction of a surface mesh populated by a set of vectors perpendicular to the mesh faces with their magnitude being proportional to the local mesh face area. For each anisotropy evaluation point, the faces having their center at a distance smaller than the radius of influence are identified. A tensor of inertia is constructed using the normals of these faces, linearly weighted by their area and weighted on their distance to the evaluation point by the function: w(d) = 1 - (d2)/(r_max2). The eigenvectors and eigenvalues of the tensor of inertia are obtained. The eigenvector corresponding to the greatest eigenvalue, corresponding to the smallest moment of inertia (maximal elongation) is taken as the anisotropy orientation.
The Projection-based algorithm computes anisotropy as:
, where CA is the coefficient of anisotropy, S is the local mesh face area, n is the normal to the face, IO is the anisotropy orientation, DA is the degree of anisotropy. DA is a measure of how highly oriented substructures are within a volume. For an isotropic (perfectly oriented) system, the degree of anisotropy is equal to 0. As the system becomes more anisotropic (less well-oriented), the DA increases to some value less than or equal to 1.
The Eigenvalue-based algorithm gets anisotropy from the eigenvalues of the tensor of inertia, which is similar to the MIL algorithm.
The settings for the Surface normals algorithm are listed in the table below.
| Description | |
|---|---|
| Neighors | The Radius of Influence defines the kernel size, or elementary volume, within which anisotropy will be evaluated (radiusOfInfluence). You should note that a too small radius of influence may result in a low signal-to-noise ratio, while a too high radius can result in averaging and edge effects.
Recommendation The radius of influence can be as small as the size of a single trabeculae. |
| Anisotropy evaluation | Lets you choose an anisotropy evaluation method — Projection-based or Eigenvalue-based. You should note that both methods provide similar results, although you may find that the Projection-based method is slightly more sensitive. |
| Mesh smoothing (repetitions) | Determines number of times that the mesh obtained from the input ROI will be smoothed before computing anisotropy (meshSmoothingRepetitions).
Recommendation Selecting one or two iterations of smoothing usually provides for the most accurate result. |
Settings for Computing Volume Fraction
The computed output is the proportion of the sample volume that is mineralized bone, in which a scalar value — 1 for high and 0 for low — is assigned to every spatial position (labeled voxel) in the input region of interest.
The settings for the Volume fraction algorithm are listed in the table below.
| Description | |
|---|---|
| Radius | The distance from the analysis point to the last considered ROI element(radius).
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Global Settings for Computing Scalar and Vector Fields
The global settings for computing scalar and vector fields are described in the table below.
| Description | |
|---|---|
| Area box | Defines the analysis area for computing the selected mapping (areaOfAnalysisBox). The initial box shape can be resized and/or reoriented as required (see Adding and Editing Shapes).
Recommendation In cases in which you need very precise measurements and plan to use a small spacing value, you should reduce the area box as much as possible. You can also add multiple boxes to compute anisotropy and volume fraction maps in different orientations. |
| Spacing | Determines the distance between the random points in the analysis area (areaOfAnalysisSpacing).
Recommendation Although the highest resolution, or lowest spacing, is 0.085 mm, this is increased to reduce processing times as the entire 3D shape of the femoral head will be mapped Use single voxel in direction with smaller box length… If checked, computations will limited to a single voxel in the direction of the smallest length of the selected area box
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