Biomedical Engineering Reference
In-Depth Information
difficult to acquire in a clinical context. The expectation is that anatomical shapes
can then be used to better understand physiology, or at least some of its pathologies.
The biological mechanisms involved in the formation and evolution of the shape
of organs are often too complex to model. Thus, one has to rely on robust statistical
approaches to produce generative models from data. Given the shapes of a number
of subjects, we can create a generalized model of an organ, called an atlas, which
can be used to distinguish normal from pathological organs or can be deformed
to give patient-specific models driven by the clinically available parameters of
interest. Such statistical analyses can both provide a predictive model and guide
the biophysical approach. However, computing statistics on dynamic 3D shapes
is very challenging. Traditional methods rely on point based parameterizations of
the shapes where the point-to-point correspondences can be an important limiting
factor for the usability of the method since the correspondences must be correct and
consistent over all the shapes. New approaches were recently developed to compute
such statistics without this limitation [
6
,
10
,
17
,
26
-
28
,
34
,
35
]. Here, the statistical
shape analysis tools are based on currents, a non-parametric representation of
shapes. These tools have a wide range of applications, and provide a well-posed
framework for statistical shape analysis of groups. Due to the fact that the methods
do not assume point correspondences between structures (and in fact assigning
landmarks to structures such as the heart are arbitrary), a wider range of data can be
used. For example, one can use surfaces to model organs such as the heart, brain,
and lungs, curves to model sulcal lines on the brain cortex, and sets of curves to
represent fibre bundles from diffusion MRI in the brain. The goal of this chapter
is to give an overview of this methodology in the context of a specific clinical
problem: the prediction of the cardiac shape remodeling in repaired tetralogy of
Fallot patients due to chronic regurgitation. The underlying assumption is that
changes in heart morphology may reveal structural abnormalities and dysfunctions
due to the pathology. In particular, we aim to establish which shape patterns are
related to the pathology in order to give further insights into the condition.
5.1.1
Repaired Tetralogy of Fallot
Tetralogy of Fallot (ToF) is a congenital heart defect that affects approximately 4 out
of every 10,000 babies [
9
]. The primary defect associated with this condition is a
ventricular-septal opening which allows blood to flow freely between the ventricles.
Secondary is stenosis in the pulmonary artery which restricts the blood flow from the
right ventricle to the lungs. Due to a misalignment of the aorta over the ventricular-
septal defect, the aorta is fed by both the left and right ventricle rather than just the
left ventricle. Patients may also have hypertrophy in the right ventricle that causes a
boot-like shape of the ventricle which is characteristic of this condition.
These abnormalities require open heart surgical repair early in infancy. As part
of this surgery, the stenosis in the pulmonary artery is cleared to allow blood
to flow more freely through the artery. As a consequence, the pulmonary valves
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