Biomedical Engineering Reference
In-Depth Information
analysis. Angles that describe different orientations of objects are often important
for the assessment of the severity of complex bone fractures (e.g., whether a surgical
intervention after fractures of the arm is required depends on the angle between the
bones).
Volume measurements
Volumetric measurements are essential to evaluate the success of a therapy [
49
].
Examples that illustrate this importance are the change of amalignant tumor's volume
in the course of chemotherapy which determines the success of the treatment and
wrist erosions' volume of a patient affected by RA, which determines the disease
progression and the success of the treatment. However, the 3D nature decreases
the reliability of traditional ruler-based in-slice measurements to an extreme level.
Hence, volumetric measurements can benefit tremendously from computer-based
methods.
In general, and particularly for volumetric measurements, the process of measure-
ments can be organized into two stages: first, we need to select the relevant structure
(volume selection), and second, we need to compute the respective volume of that
structure (volume approximation). Typically, the volume selection corresponds to
3D segmented elements. Once we have selected all voxels of a target structure, the
volume represented by these voxels can be approximated for volumetry.
A straightforward approach is to weight every voxel belonging to that selection
with the size of a respective volume cell. This method achieves a reasonable approx-
imation for interior core voxels. However, it does not reflect the boundary voxels
properly, where the separating isosurface may be closer or farther away from the
voxels, depending on the voxel values and the threshold. While this difference is
almost negligible for compact selections, which have a relatively small boundary,
it can be significant for small or elongated structures. Luft et al. [
50
] showed, for
example, that up to 50%of all volume cells of the cerebral ventricular system contain
a boundary. In [
51
], it was shown that 40% of all volume cells of such a ventricu-
lar system of a typical patient dataset contained a boundary representing more than
20% of the total volume. These facts clearly show that the straightforward weighted
counting of all voxels will compute a very inaccurate volume in too many cases.
Bartz et al. [
51
] describes a subdivision approach for these boundary voxels. First,
the boundary voxels are examined in their volume cell context, where a boundary
cell contains between one and seven selected voxels. Similar to the case table of the
Marching Cubes approach [
45
], the boundary cells are classified into simple (one
or seven voxels are selected) and complex cases (between two and six voxels are
selected). Simple cases can be resolved immediately by weighting the respective
volume with the interpolated isovalue parameter. The complex cases are recursively
subdivided into eight subcells using trilinear interpolation until either only simple
cases remain or the respective full voxel volume is below an error threshold.
Virtual endoscopy
Virtual endoscopy is a procedure inspired by real endoscopy, in which an endo-
scope is moved through air-filled or water-filled structures for diagnostic or thera-
peutic purposes [
48
]. Virtual endoscopy is based on CT or MRI data and simulates
