Biomedical Engineering Reference
In-Depth Information
Fig. 2 Liver model deformed by a respiratory motion pattern (
top
) and by a simulated contact
with surgical instruments (
bottom
). The boundary conditions for the respective models (
left
) are
shown along with the corresponding deformations (
right
)
However, for the same number of DOF, the solution time for the system matrix is
also slightly longer for the quadratic method. A possible reason for this is the higher
connectivity of the stiffness matrix.
We conclude that the quadratic corotated tetrahedral formulation is slightly less
efficient per DOF than a linear mesh. However, as the proposed method needs a lot
less DOF to achieve the same accuracy, it significantly outperforms the linear
tetrahedral formulation for both model problems.
The method achieves real-time performance (20 FPS) for model sizes up to
approximately 1300 DOF, if only a single CPU core is used. It is important to point
out that the method (especially the polar decomposition of each element) is easily
parallelizable. Thus, a straightforward parallel implementation should be able to
handle around 4000 DOF on the four core Intel i7-930.
4.2 Comparison with Nonlinear Viscoelastic Models
In order to compare the registration accuracy of the corotational model with the
accuracy of a more complex fully nonlinear QLV model, we consider a liver model
undergoing two different deformations. For the respiratory motion pattern, the liver
is linearly deformed over a timespan of three seconds with a maximum displace-
ment of 43.6 mm (Fig.
2
). The instrument indentation scenario features a maximal
