Biomedical Engineering Reference
In-Depth Information
(HF: panels C,D) is dilated relative to the normal heart (N: panels A,B); b) left-
ventricular (LV) wall thinning (average LV wall thickness over 3 hearts is 17.5
2.9 mm in N, and 12.9 2.8 mm in HF); (c) no change in RV wall thickness
(average RV wall thickness is 6.1 1.6 mm in N, and 6.3 2.1 mm in HF); (d)
increased septal wall thickness HF versus N (average septal wall thickness is
14.7 1.2 mm N, and 19.7 2.1 mm HF); (e) increased septal anisotropy in HF
versus N (average septal thickness is 0.71 0.15 N, and 0.82 0.15 HF); and (f)
changes in the transmural distribution of septal fiber orientation in HF versus N
(contrast panels B,D, particularly near the junction of the septum and RV).
3.3. Finite-Element Modeling of Cardiac Ventricular Anatomy
The structure of the cardiac ventricles can modeled be using the finite-
element modeling (FEM) methods developed by Nielson et al. (66). The geome-
try of the heart to be modeled is described initially using a predefined mesh with
6 circumferential elements and 4 axial elements. Elements use a cubic Hermite
interpolation in the transmural coordinate (I), and bilinear interpolation in the
longitudinal (N) and circumferential (R) coordinates. Voxels in the 3D DTMR
images identified as being on the epicardial and endocardial surfaces by the
semi-automated contouring algorithms described above are used to deform this
initial FEM template. Deformation of the initial mesh is performed to minimize
an objective function
F
(
n
):
2
D
¨
F(n)
=
H
v(
İ
)
v
+
{
B
2
n
+
ȕ
(
s
2
n) }
2
İ
,
[14]
d
d
d
2
}
d1
=
where
n
is a vector of mesh nodal values,
v
d
are the surface voxel data,
v
(F
d
) are
the projections of the surface voxel data on the mesh, and B and C are user-
defined constants. This objective function consists of two terms. The first de-
scribes the distance between each surface image voxel (
v
d
) and its projection
onto the mesh
v
(F
d
). The second, known as the weighted Sobelov norm, limits
the stretching (first-derivative terms) and bending (second-derivative terms) of
the surface. The parameters B and C control the degree of deformation of each
element. The weighted Sobelov norm is particularly useful in cases where there
is an uneven distribution of surface voxels across the elements. A linear least-
squares algorithm is used to minimize this objective function.
After the geometric mesh is fit to DTMRI data, the fiber field is defined for
the model. Principal eigenvectors lying within the boundaries of the mesh com-
puted above are transformed into the local geometric coordinates of the model
using the following transformation.
