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parabolic flight.
The application of semi-automated image processing
procedures to detect endocardial boundaries and extract
LV dimensions can facilitate the data analysis and avoid
the introduction of subjective interpretations. Among the
border detection algorithms present in literature, level set
methods are numerical techniques used to track the
evolution of interfaces [5,6], which have been applied to
edge detection, shape recovery, representation and
recognition [7-9].
Aim of this study was to test the feasibility to semiautomatically
extract LV cavity dimensions from 2-D
echo data obtained during different gravity conditions by
means of level set techniques.
2. Materials and methods
2.1. Subjects
Seven healthy volunteers (mean age±SD, 45±10) were
0276−6547/02 $17.00 © 2002 IEEE 73 Computers in Cardiology 2002;29:73−76.
enrolled in this study. All subjects underwent special
flight physical examination and were not taking any
medication before and during flights. This study was
approved from an ethical point of view by the French
Space Agency (Centre National d’Etudes Spatiales
(CNES)).
Subjects were studied in the upright position and to
keep them in a near-standing position during microgravity,
they were fastened to a saddle with a seat belt.
2.2. Equipment and protocol
Parabolic flights were performed in the Airbus A-300
Zero G managed by Novespace for CNES and ESA in
Bordeaux. Flights were managed on three consecutive
days: each flight session lasted 2.5-3h and incorporated
30 parabolas.
Instantaneous gravity was measured continuously by
using the aircraft’s accelerometer. Gravity variations
during a parabolic flight profile include four consecutive
phases (Figure 1): normogravity (1 Gz), before the
parabola began; mild hypergravity (1.8 Gz) during the
ascending phase of the parabola (20-25 sec);
microgravity (0 Gz), lasting for 20 sec and corresponding
to the top of the parabola; a second period of mild
hypergravity (1.8 Gz) during the descending phase of the
parabola (20-25 sec), followed by a new steady state at
1Gz (1 min).
Figure 1. Schematic depicting different phases of
parabolic flight profile and corresponding variations in
gravity. Phase 1: normogravity (1 Gz); phase 2 and 4:
mild hypergravity (1.8 Gz); phase 3: microgravity (0 Gz).
Ultrasound images were obtained (frame rate 37 Hz)
in the apical 4-chamber view using an Aspen system
(Acuson, France Siemens Cie, France), opportunely
modified to digitally save on magneto-optical disk all the
images relevant to the whole parabolic flight profile
(about 1 minute of image acquisition per parabola).
2.3. Level set methods
Let's consider a 2-D space and a curve g(t) that is
propagating under the speed F in the normal direction: F
indicates how to move each point of the curve. A level set
function [5,6] is defined by taking the original curve g(t)
and generating a surface that intersects the xy plane
exactly where the curve g(t) sits. The intersection with the
xy plane is called zero level set because it represents the
set of points that are at height zero. To follow the
deformations in g(t), the level set function is modified, so
that the curve represents the moving zero level set of the
level set function. The evolution of the level set function
j(x,t)is defined by a partial differential equation:
+ Ñ = 0
¶
¶j j F
t
with the initial condition j (x,t) =j0.
If g(t)= j (0,t), g(t) moves with the desired speed function
F, that is used to control shape recovery process in the
image I(x) [7]:
j
e b j
Ñ
F = g K - Ñg × Ñ (1)
with
( )
( ) 2
1
1
÷ ÷ø
ö
ç çè
æ Ñ *
+
=
a
Gs I x
g x
( ) ( ) ( )2 1/ x / s
Gs x = s p e-
In (1), the first term on the right hand represents a surface
tension force that depends on the Euclidean curvature K;
the second term on the right hand describes a force that
attracts the surface towards the boundaries, with a
stabilizing effect. The edge indicator g is a nonincreasing
function of the gradient of a smoothed version
of the initial image. a selects the contrast of the objects to
be considered in the image during the motion of the
embedding, while s is the variance of the gaussian
determined by the size of the smallest features to be
detected. The parameter b is used to limit the
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