Biomedical Engineering Reference
In-Depth Information
2D-ultrasound) do not provide sufficient information to compensate soft tissue
deformations. A promising approach to overcome this problem is to use a priori
knowledge about the mechanical behavior of soft tissues in the form of biomechan-
ical models.
Several groups have successfully applied this concept to compensate the “brain
shift” in neurosurgery applications [
1
]. Dumpuri et al. demonstrated how soft tissue
deformations during image-guided liver surgery can be compensated using an
intraoperative laser scanner and a linear elastic finite element (FE) model [
2
].
However, in this study the biomechanical model was not solved in real-time, but
in an offline process. Pratt et al. used a nonlinear FE model with explicit time
integration and endoscopic image data to perform real-time image registration for
laparoscopic cardiac interventions [
3
].
The major drawback of using biomechanical models for intraoperative registra-
tion is the high computational complexity of FE models. In order to be used for
intraoperative guidance, the model has to be robust and real-time capable while still
providing high registration accuracy. Several FE algorithms have been proposed for
real-time soft tissue simulation. The
total lagrangian explicit dynamics
(TLED)
algorithm relies on explicit time integration, precomputed spatial derivatives and
low-order elements to speed up the simulation [
4
]. While the method can naturally
handle nonlinearities and is easily parallelizable on the GPU [
5
], it requires very
small timesteps in order to remain numerically stable. It is in particular difficult to
robustly simulate instrument-induced deformations with this approach. The
multi-
plicative jacobian energy decomposition
(MJED) method proposed by Marchesseau
et al. overcomes this limitation by using an implicit time integration scheme [
6
]. The
approach allows a very efficient assembly of the stiffness matrix. It is considerably
faster than the standard nonlinear implicit finite element method (FEM), but it still
requires solving a nonlinear system of equations each time step. Both algorithms can
be used to solve the various hyper-, visco-, and poroelastic models that can be found
in the literature.
However, previous studies have shown that in the context of intraoperative
registration the material law and its parameterization has very little impact on the
registration accuracy as long as a geometrically nonlinear model is used [
7
,
8
]. This
motivates the use of corotated FEM models. The idea of this approach is to extract
the rotational component of the deformation gradient and then use a linear material
law [
9
]. As a result, the volume of the elements is preserved without having to solve
a nonlinear system for each time step.
In this paper, we present a fast, robust and accurate model for real-time soft
tissue registration. We first describe a corotational FEM with quadratic shape
functions based on the formulation proposed by Mezger et al. [
10
]. We then show
that the method performs significantly better than linear corotated FEM for high
resolution meshes and that it achieves nearly the same registration accuracy as a
complex nonlinear viscoelastic material model. Furthermore, we show by means
of a phantom experiment how the model can be used for intraoperative
registration.
