Biomedical Engineering Reference
In-Depth Information
was as follows: order =
{
3
,
4
}
, spans in the
u
LV
direction =
{
1
}
, spans in the
{
order
,
order + 1
,
order + 2
,
order + 3
}
v
LV
direction =
, and spans in the
w
LV
{
1
,
2
,
3
,
4
}
direction =
, with the additional constraint that the span lengths in each
direction have similar Euclidean lengths. In addition, we varied the confidence
value for the tag plane intersections from the set
. This
variation led to 224 model variants for strain analysis. The governing parameters
of Arts' analytical model were varied so that the resulting analytical normal strains,
i.e., radial, circumferential, and longitudinal strains, followed the same systolic
evolutionary pattern in the basal and midventricular regions as those reported in
[33]. The simulated data consisted of eleven frames of eight short-axis images and
seven long-axis images. Sample images are shown in Figure 10.
The variation in the computational time is partly dependent upon the number
of control points and the number of data points. Associated with the data points is
the computational time to find the corresponding parametric values in the model
that are found via conjugate gradient descent. Associated with both the data points
and the number of control points is the matrix inversion involving the observation
matrix, which, as previously noted, is of size
s
{
1
,
1
.
5
,
2
,
2
.
5
,
5
,
10
,
50
}
n
, where
s
is the number of
data points and
n
the number of control points. For the models described in the
previous paragraph, the computational time took anywhere from 30 minutes and
1 hour and 15 minutes on a Sun Blade 100.
Bland-Altman methodology [34] was used for determining which model was
the optimal predictor of circumferential strain. The circumferential strains were
chosen for comparison due to the greater quantity of data in that direction as
compared with the radial and longitudinal directions. The strains predicted by
our model were averaged over 12 basal regions and 12 mid-cavity regions, and
compared with the corresponding strains predicted by Arts' model. This divi-
sion incorporated the previous segmentation described earlier (Section 5) with the
additional regional division separating the endocardium and epicardium as illus-
trated in Figure 11. The apical regions were not included since the model does
not extend sufficiently along the left-ventricular long-axis to encompass the entire
apical region. This division translates into 24
×
9 = 216 points for analysis of
each model from a total of eleven frames (only nine frames are available since the
very first and very last frames are identical and have zero strains everywhere). For
each of the 224 models we calculated the standard deviation and the mean of the
difference between Arts' model and the analyzed model. We then ranked the 224
models by the equation
×
|
µ
|
σ
σ
max
|
max
+
,
(48)
|
µ
where
µ
and
sigma
are the mean and standard deviation of the difference, re-
spectively. The use of this ranking measure is motivated by two factors used in
assessing predictive modelling — the need for accurate measurement and the min-
imization of variability in that measurement. The latter component is arguably the
