Biomedical Engineering Reference
In-Depth Information
Table 2 Errors in comparison to a complex QLV model, respiratory deformation pattern
Mean error [mm]
Max error [mm]
Standard deviation [mm]
Corotated Model
0.13
0.47
0.08
Linear Model
0.76
3.1
0.48
Table 3 Errors in comparison to a complex QLV model, instrument indentation
Mean error [mm]
Max error [mm]
Standard deviation [mm]
Corotated model
0.09
0.55
0.08
Linear model
0.03
0.65
0.04
displacement of 11.07 mm. For the analysis we constructed a FE model (8,744
quadratic tetrahedral elements, 14,712 nodes) from a simple liver phantom. The
boundary conditions for both scenarios are shown in Fig. 2 .
The reference solution was calculated with the commercial FEM software
ABAQUS 6.10 using the QLV model by Raghunathan et al. [ 14 ].
For the respiratory deformation pattern, the maximal Euclidean distance
(measured at the nodes of the meshes) between the corotational model and the
QLV model is 0.47 mm. In contrast, a linear elastic model differs up to 3.1 mm from
the QLV reference solution (see Table 2 ). For the instrument indentation, the
corotated model and the linear model achieve a similar accuracy (Table 3 shows
that maximal distances are 0.55 mm and 0.65 mm).
The large errors of the linear model can be attributed to the fact that it cannot
adequately capture the large rotational components of the respiratory deformation
pattern. In both scenarios, the solution of the corotational model is very close to the
fully nonlinear QLV model.
It can be seen that the accurate solution of the displacement-zero traction
boundary value problem necessarily requires a geometric nonlinear formulation,
while the material nonlinearity is not that important.
It is important to point out that during surgery, the intraoperative navigation
system doesn't have to capture the very rapid soft tissue deformations in order to
provide a meaningful guidance. Thus, a corotational model with Rayleigh damping
delivers very accurate registration results. Also, the material nonlinearities only
have a negligible effect on the result, because the registration procedure can be
described as a displacement-zero traction problem. It is important to point out that
these assumptions do not hold for the application of biomechanical models in
surgical simulation. There, the biomechanical model has to be able to resolve the
feedback forces even for very fast instrument movements. Although the corotated
FE-model is very well suited for intraoperative registration, it is usually not
appropriate for surgical simulation.
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