Biomedical Engineering Reference
In-Depth Information
to pose queries (in standard query language, or SQL) on a wide range of cardiac
data sets by means of a graphical user interface (Figure 8). These data sets in-
clude: (a) DTMRI imaging data; (b) FEMs derived from DTMRI data; (c) elec-
trical mapping data obtained using epicardial electrode arrays; and (d) model
simulation data. Query results are either: (a) displayed on a 3D graphical repre-
sentation of the heart being analyzed; or (b) piped to data-processing scripts, the
results of which are then displayed visually. Queries may be posed by direct
entry of an SQL command into the Query Window (Figure 8B). This query is
executed, and the set of points satisfying this condition are displayed on a wire
frame model of the heart being studied (shown in green in Figure 8C). Queries
operating on a particular region of the heart may also be entered by graphically
selecting that region (Figure 8D). SQL commands specifying the coordinates of
the selected voxels are then automatically entered into the Query Window. One
example of such a predefined operation is shown in Figure 8E, which shows
computation of transmural inclination angle for the region enclosed by the box
in Figure 8D.
3.4. Generation of Computational Models from DTMRI Data
The bidomain equations describe the flow of electrical current within the
myocardium, between the intracellular and extracellular domains. This approach
treats each domain of the myocardial tissue as a continuum, rather than as being
composed of discrete cells connected by gap junctions and surrounded by the
extracellular milieu. Thus, quantities such as conductivity and transmembrane
voltage represent spatial averages. Several excellent reviews have been pub-
lished detailing the assumptions in, structure of, and solution methods for the
bidomain equations (68-70). The following is a brief review of the origins of
these equations.
The bidomain equations are derived by applying conservation of current
between the intra- and extracellular domains. The equations consist of parabolic
Eq. [16] and elliptic Eq. [17], equations that must be satisfied within the myo-
cardium, (a region designated as
H
):
¯
sO
1
1
¡
(
)
°
(,)
x t
=
I
(,)
x t
I
(,)
x t
¸
M
()
x
G
(,) ,
x t
x
in
H
, [16]
¡
°
ion
app
e
e
s
t
C
C
¢
±
m
/#
M
i
(
x
)/
v
(
x
,
t
) = -/#
M
(
x
)/G
e
(
x
,
t
), ~
x
in
H
,
[17]
and an additional elliptic equation, Eq. [18], that must be satisfied in the bath or
tissue surrounding the heart (a region designated as
B
):
