Biomedical Engineering Reference
In-Depth Information
sample comparing total bead displacement with 0 mm, 2 mm, and 5 mm ran-
dom perturbations on starting bead locations. The most striking feature of
Figure 15.5 is the fact that the bead trajectories are very similar across these
cases.
A mesh convergence study has also been performed on these pig brain cal-
culations in order to ensure that numerical discretization error is sufficiently
small that differences between predicted and measured bead locations can be
assigned to data model mismatch associated with physical conditions.
Shown in Figure 15.6 are results from a study involving computations in a pig
brain model where solutions are compared under increasing levels of discret-
ization with the goal of defining a solution-independent mesh resolution.
Figure 15.6 displays changes in displacement and pressure at several dis-
tances from the deformation source under increasing mesh discretization.
These surface plots are quite informative and indicate that the calculations
which produced the results in Figure 15.3 can be considered well resolved. In
these plots, six levels of mesh discretization are reported which illustrate a
maximum solution variance of 1 mm in displacement and 2 mm Hg in pres-
sure at the coarsest mesh scale (less than 5000 nodes) and less than 0.1 mm
and 0.3 mmHg at mesh resolutions of more than 16,000 nodes. The computa-
tions reported by Miga and colleagues have typically used meshes with res-
olutions in the 18,000 to 20,000 range, making them highly accurate from the
point of view of numerical discretization error.
Once valid model calculations have been obtained, their intraoperative value
depends on whether they can be utilized in a form that is familiar to the neuro-
surgeon. Towards this end, the Dartmouth group has developed a strategy to
deform the preoperative MR images based on the volumetric displacement field
computed with their model. Figure 15.7 dramatically illustrates the point by
showing a set of preoperative MR slices adjacent to their model-deformed coun-
terparts for a pig brain experiment where significant intraoperative tissue
motion has been induced. The algorithm in place is conceptualized in Figure 15.8
which shows that the displacement is computed at each image voxel using the
finite element basis functions expressed in the coordinate frame of the
deformed finite element mesh. These points are then undeformed to the origi-
nal image space in order to define the voxel intensity value, which should be
assigned to each image voxel in the deformed image space.
Within this framework, these investigators have defined a percent recap-
ture metric in order to quantify the accuracy of the model in the image-
guided setting. The percent recapture is the difference between the remaining
absolute total bead displacement error (difference between measured and
computed displacements) and the average total bead displacement, which
can be viewed as the amount of motion recovered by the model which would
have been unaccounted for if preoperative images were used as the basis for
image guidance. Across the series of
in vivo
pig brain experiments reported
by Miga et al.,
32
this percentage has ranged from 75 to 85% which is quite
encouraging, especially given that there are many ways in which the model-
ing can be enhanced.
