Biomedical Engineering Reference
In-Depth Information
of a human coronary artery. It has two materials, each representing separate lay-
ers of the arterial wall. Each layer was assigned material properties from the
literature that are appropriate for that specific layer [39]. The primary drawback
of irregular meshes is that, depending upon the geometry to be modeled, they
can be time consuming to construct.
12.2.9
Rezoning Regular Finite Element Meshes
The large deformations that occur in the context of many deformable image
registration problems can result in “element inversion” prior to complete regis-
tration. Element inversion is the generation, via deformation during the solution
process, of a finite element that has a negative Jacobian. Physically, for hexahe-
dral elements this implies an angle of greater than 180
◦
between two adjacent
edges of an element. This condition halts the solution process and thus must be
remedied in order to proceed.
To overcome this problem when regular meshes are used, an FE rezoning al-
gorithm has been implemented. The algorithm allows the tracking of large-scale
deformations using a relatively coarse computational mesh. When element in-
version is imminent, the FE mesh geometry is reset to its initial undeformed
configuration and the deformed template image intensity
T
and nodal displace-
ments
u
(
X
) are interpolated from the deformed mesh to the reset mesh. The
analysis then continues until the convergence criteria are met or another rezon-
ing is required. The rezoning process is illustrated graphically in Fig. 12.5.
The rezoning procedures require interpolation of
T
and
u
(
X
) from the nodes
of the deformed FE mesh to the nodes of the reset mesh. For each node
N
Figure 12.5:
Example of rezoning a regular mesh for 2-D Warping problem.
(A) Template image with a representation of the FE mesh superimposed on the
image. (B) The registration process causes large deformations in the Compu-
tational mesh. (C) The mesh is reset and the analysis continues. (D) Rezoning
allows for greater overall deformation during the registration process. (E) De-
formed template image at the end of the analysis.
