Diffuse domain approach for flexible needle insertion and relaxation.

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.

Real-time definition of single seed placement sensitivity in low-dose-rate prostate brachytherapy.

PURPOSE: In low-dose-rate brachytherapy, iodine-125 seeds are implanted based on a treatment plan, generated with respect to different dose constraints. The quality of the dose distribution depends on a precise seed placement, however, during treatment planning the impact on the dose parameters when certain seeds fail to be placed precisely is not clear. METHODS AND MATERIALS: We developed a method using automatic differentiation to calculate gradients of dose parameters with regard to the seeds' positions. Thus, we understand their sensitivity with respect to the seed placement. A statistical analysis is performed on a data set with 35 prostate brachytherapy patients. RESULTS: The most sensitive seeds regarding the dosimetric parameters of both rectum and urethra are close to the corresponding organ. Their gradient directions are mainly orthogonal to their surfaces. However, not all seeds close to the surface are equally sensitive with regard to the dose parameter. The most sensitive seeds regarding the prostate's dose parameters are distributed throughout the prostate and the direction of the gradients are mainly parallel to its surface. A linear regression with respect to different patient parameters shows that dose constraints which are barely fulfilled have large gradients and thus are additionally sensitive to misplacement. CONCLUSION: Automatic differentiation can be used to analyze dose parameter sensitivity with respect to seed placement. Integrating this into treatment planning systems is valuable as it speeds up the planning procedure, making it more robust and less dependent on user experience while showing the operating physician which needle placements require greater accuracy than others.