ABSTRACT
Needle insertion simulations play an important role in medical training and surgical planning. Most simulations require boundary conforming meshes, while the diffuse domain approach, currently limited to stiff needles, eliminates the need for meshing geometries. In this article the diffuse domain approach for needle insertion simulations is first extended to the use of flexible needles with bevel needle tips, which are represented by an Euler-Bernoulli beam. The model parameters are tuned and the model is evaluated on a real-world phantom experiment. Second, a new method for the relaxation of the needle-tissue system after the user releases the needle is introduced. The equilibrium state of the system is determined by minimizing the potential energy. The convergence rate of the coupled Laplace equations for solving the Euler-Bernoulli beam is 1.92 ± 0.14 for decreasing cell size. The diffuse penalty method for the application of Dirichlet boundary conditions results in a convergence rate of 0.73 ± 0.21 for decreasing phase field width. The simulated needle deviates on average by 0.29 mm compared to the phantom experiment. The error of the tissue deformation is below 1 mm for 97.5% of the attached markers. Two additional experiments demonstrate the feasibility of the relaxation process. The simulation method presented here is a valuable tool for patient-specific medical simulations using flexible needles without the need for boundary conforming meshing. To the best of the authors' knowledge this is the first work to introduce a relaxation model, which is a major step for simulating accurate needle-tissue positioning during realistic medical interventions.
Subject(s)
Needles , Humans , Computer Simulation , Phantoms, ImagingABSTRACT
A finite element cochain complex on Cartesian meshes of any dimension based on the H 1 -inner product is introduced. It yields H 1 -conforming finite element spaces with exterior derivatives in H 1 . We use a tensor product construction to obtain L 2 -stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.
ABSTRACT
We present a new strategy for needle insertion simulations without the necessity of meshing. A diffuse domain approach on a regular grid is applied to overcome the need for an explicit representation of organ boundaries. A phase field function captures the transition of tissue parameters and boundary conditions are imposed implicitly. Uncertainties of a volume segmentation are translated in the width of the phase field, an approach that is novel and overcomes the problem of defining an accurate segmentation boundary. We perform a convergence analysis of the diffuse elastic equation for decreasing phase field width, compare our results to deformation fields received from conforming mesh simulations and analyze the diffuse linear elastic equation for different widths of material interfaces. Then, the approach is applied to computed tomography data of a patient with liver tumors. A three-class U-Net is used to automatically generate tissue probability maps serving as phase field functions for the transition of elastic parameters between different tissues. The needle tissue interaction forces are approximated by the absolute gradient of a phase field function, which eliminates the need for explicit boundary parameterization and collision detection at the needle-tissue interface. The results show that the deformation field of the diffuse domain approach is comparable to the deformation of a conforming mesh simulation. Uncertainties of tissue boundaries are included in the model and the simulation can be directly performed on the automatically generated voxel-based probability maps. Thus, it is possible to perform easily implementable patient-specific elastomechanical simulations directly on voxel data.
