Image Processing Reference
In-Depth Information
developed a model-based approach for tracking tag intersections [77] and tag
stripes [81] * that has been validated using silicone gel phantoms [237]. A defor-
mation field that maps the first (undeformed) frame to a subsequent (deformed)
frame is modeled through a piecewise polynomial function. Two fitting steps are
involved in this method. First, the material points (tag intersections or stripes) in
each deformed frame, t > 0, are reconstructed in the coordinate system of the
undeformed state, t = 0 (reconstruction fit). In the latter frame, tag surfaces are
arranged in true planes because no motion has occurred as yet. In the second step,
the material points for t > 0, expressed in the reference frame ( t = 0), are used to
reconstruct a displacement field relative to t = 0 ( deformation fit ). **
A similar approach is followed by O'Dell et al. [177]. One-dimensional
displacements are obtained by three independent sets of tag lines: one in the
cardiac long axis and two orthogonal sets in the short-axis view. Reconstruction
of the deformation field is performed in two interpolation steps. The first step
assumes a global affine transformation between two time frames. This is done to
eliminate global bulk motion, and linear stretches and shear. In the second step,
the residual deformation is interpolated using a prolate spheroidal decomposition
to describe the curvilinear deformations expected in the heart.
Both Young et al. [77,81] and O'Dell et al. [177] assume that the reference frame
to which the strain analysis is related is the undeformed state. This is normally the
first frame in the sequence (planar tag surfaces). Although this simplifies the problem
by allowing decoupling of the motion component normal to the tagging plane, these
methods cannot be used to compute strains between two arbitrary frames. The latter
can be useful in order to retrospectively select the reference frame to coincide
precisely with the diastole or systole, or to compute strains over a subset of the
cardiac cycle. To circumvent this limitation, Moulton et al. [178] have proposed a
Lagrangian approach that explicitly computes the intersection of the tag surfaces in
two arbitrary frames. Tag surfaces are obtained by interpolating the tag curves that
are stacked in different imaging planes. Surface intersections define a set of material
lines for each time frame. These points were used to perform strain calculations
employing a p -version of FE basis functions.
Radeva, Amini, and Huang [179] use two coupled volumetric models: a tissue
deformation field and a model describing the LV geometry. The first model is
represented by a cubic trivariate B-spline (termed B-solid by the authors); the
second model is represented by two coupled surfaces (endocardium and epicardium)
fitted to boundary points. It is assumed that the boundaries are either manually
delineated or (semi)automatically detected from the tagged images. The B-solid
is deformed under thin-plate internal constraints and under two external forces.
* Related regularization schemes are the global and body-smoothing terms described in Young and
Axel [77] that act on the deformation gradient tensor. However, they are not directly interpretable as
an internal deformation energy.
** Amini et al. [235] have compared landmark-based (tag intersections) with curved-based tag (stripes)
tracking based on the simulator of Waks et al. [236]. They concluded that as the number of stripes
or landmarks increases, the two methods give similar performances. Under large deformations, the
degradation of the curve-based techniques is more graceful compared to landmark-based methods.
Search WWH ::




Custom Search