Biomedical Engineering Reference
In-Depth Information
chosen geometric primitives for parameter assignment as well as the selected co-
ordinate systems were the most obvious.
The results show that, in the case of simulated data, the quadratic Cartesian-
based NURBS models either with a cylindrical or a prolate spheroidal parameter
assignment outperformed their counterparts in predicting normal strain. The de-
creased complexity associated with the cylindrical-parameterized model prompted
its use for subsequent calculation of Lagrangian and Eulerian strains for in vivo
data. We illustrated the capabilities of the methodology with results from three
canine studies, a normal human, and a patient with a history of myocardial infarc-
tion. The resulting strain values were plotted over the systolic phase of the cardiac
cycle. Qualitative results from right-ventricular analysis were also demonstrated
by displaying midventricular strain maps.
While a rigourous analysis explaining the disparity in performance between
the models is beyond the scope of this work, we posit that such a disparity is
to be expected based on the tagging pattern geometry. A significant portion of
the displacement data for nonrigidly registering the models is derived from the
tag plane normals in the three orthogonal directions (in addition to the tag plane
intersections and tag line/contour intersections). These three normal directions are
aligned with the Cartesian axes of the fitting coordinate system. For the Cartesian
models, this implies that each coordinate of the control points is solved from a
single set of tag plane normals, i.e., the
x
-value of each control point location
is solved only using the set of tag plane normals aligned in the
x
-direction and
the same for the
y
and
z
-values. However, for the non-Cartesian models, the
geometries of the tag plane normals and coordinate values of the control points
are not aligned, which, we believe, leads to a degradation in performance. For
example, the
r
-values of the control point locations of the cylindrical models are
solved using normal displacements from the two sets of tag plane normals that are
aligned along the
x
and
y
axes. A future area of possible research would be to
apply our approach to other MR tagging patterns (radial tags [9] and circular ring
tags [35]), and look at discrepancies in performance between the different model
formulations.
There are several additional areas for possible future development. As noted
previously, the current biventricular NURBS model does not encompass the most
apical regions of the LV/RV nor the outflow tracts, which would be important for
a more comprehensive analysis of myocardial deformation. One could perhaps
solve the degeneracy issue at the apical tip by clamping the B-spline volume at
the apex. However, that would impose certain limitations on the model's ability
to deform at the apex.
RV deformation analysis is challenging considering the sparseness of tag data
in the myocardial wall. Even in the LV, where the myocardial wall is thicker,
measurement of the radial strains is less tenable due to the paucity of displacement
information in the radial direction. This can be readily seen in Figure 30, where the
computed radial strains display unexpected irregularities. Increasing the density
