Biomedical Engineering Reference
In-Depth Information
regression and Akaike Information Criterion (AIC) model reduction [
1
] to detect
relevant modes and the direction of correlation.
To illustrate this method, in [
35
] we showed that these methods enable one to
identify shape features related to the severity of the regurgitation for a data-set
of 49 repaired ToF patients. The relationship between RV shape and pulmonary
regurgitation were investigated by relating the PCA shape vectors with tricuspid
regurgitation, trans-pulmonary valve regurgitation and pulmonary regurgitation
volume indices taken from color Doppler ultrasound and phase-contract magnetic
resonance images (PC-MRI).
90
% of the spectral energy was explained by 18 PCA
modes.
5.3.3
Building an Evolution Model
As explained beforehand, understanding and quantifying heart remodeling in these
patients is crucial for planning pulmonary valve replacement. Given that there
is a lack of longitudinal data available for these patients, we make use of the
atlas as the mean of the population and cross-sectional statistics to formulate a
generative growth model. Such a model could be used as reference, from which
the pathology evolution of one patient could be quantitatively compared. In cross-
sectional statistical design, one does not propagate the evolution over time for a
single patient but rather considers the image of each patient acquired at “time”
t
as an instance in the growth evolution of the group. In this way we can model the
growth of the population given these instances using regression analysis (Fig.
5.8
).
By making use of the initial velocities
v
0
that parametrize the deformations
φ
i
computed using the methods described in the previous sections, we can regress the
velocities against an index of patient growth using standard statistical techniques.
In order to obtain statistically significant results, we first need to reduce the
dimensionality of the problem to consider just the factors related to patient growth,
while also removing any co-linearity between factors. In the previous section the
model reduction was performed using PCA. In this case we chose instead to use
partial least squares (PLS) regression since it has the added advantage of computing
the components that are most related to a given external parameter (i.e. patient
growth). Using PLS allows us to compute the components that best describe the
variance of both the matrix of predictors (
X
) and the matrix of responses (
Y
),
as well as the covariance between
X
and
Y
, in a manner such that the regression
Y
is optimal.
In the case of ToF patients, we would ideally like to model the atlas deformation
of a patient as a function of growth (i.e.
deformation
=
f
(
X
)
,however
solving this problem is not possible due to the large number of deformation param-
eters that would need to be predicted with a single, one-dimensional, parameter
(growth). Rather, we revert the problem to be a function of the deformations:
growth
=
f
(
growth
)
which has a much lower number of parameters to
predict. The output values are then projected onto the reduced PLS subspace and
=
f
(
deformations
)
Search WWH ::
Custom Search