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.

Noise-robust breathing-phase estimation on marker-free, ultra low dose X-ray projections for real-time tumor localization via surrogate structures.

PURPOSE: This paper presents a novel strategy for feature-based breathing-phase estimation on ultra low-dose X-ray projections for tumor motion control in radiation therapy. METHODS: Coarse-scaled Curvelet coefficients are identified as motion sensitive but noise-robust features for this purpose. For feature-based breathing-phase estimation, an ensemble strategy with two classifiers is used. This consensus-based estimation substantially increases tracking reliability by rejection of false positives. The algorithm is evaluated on both synthetic and measured phantom data: Monte Carlo simulated ultra low dose projections for a C-arm X-ray and on the basis of 4D-chest-CTs of eight patients on one hand side and real measurements based on a motion phantom. RESULTS: To achieve an accuracy of breathing-phase estimation of more than 95% a fluence between 20 and 400 photons per pixel (open field) is required depending on the patient. Furthermore, the algorithm is evaluated on real ultra low dose projections from an XVI R5.0 system (Elekta AB, Stockholm, Sweden) using an additional lead filter to reduce fluence. The classifiers-consensus-based-gating method estimated the correct position of the test projections in all test cases at a fluence of ∼180 photons per pixel and 92% at a fluence of ∼40 photons per pixel. The deposited dose to patient per image is in the range of nGy. CONCLUSIONS: A novel method is presented for estimation of breathing-phases for real-time tumor localization at ultra low dose both on a simulation and a phantom basis. Its accuracy is comparable to state of the art X-ray based algorithms while the released dose to patients is reduced by two to three orders of magnitude compared to conventional template-based approaches. This allows for continuous motion control during irradiation without the need of external markers.

Diffuse domain method for needle insertion simulations.

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.

Conditional random fields for phase-based lung feature tracking with ultra-low-dose x-rays.

PURPOSE: During radiation therapy, a continuous internal tumor monitoring without additional imaging dose is desirable. In this study, a sequential feature-based position estimation with ultra-low-dose (ULD) kV x rays using linear-chain conditional random fields (CRFs) is performed. METHODS: Four-dimensional computed tomography (4D-CTs) of eight patients serve as a-priori information from which ULD projections are simulated using a Monte Carlo method. CRFs are trained with Local Energy-based Shape Histogram features extracted from the ULD images to estimate one out of ten breathing phases from the 4D-CT associated with the tumor position. RESULTS: Compared to a mean accuracy for ±1 breathing phase of 0.867 using a support vector machine (SVM), a mean accuracy of 0.958 results for the CRF with ten incident photons per pixel. This corresponds to a position estimation with a discretization error of 2.4-5.3 mm assuming a linear displacement relation between the breathing phases and a systematic error of 2.0-4.4 mm due to motion underestimation of the 4D-CT. CONCLUSIONS: The tumor position estimation is comparable to state-of-the-art methods despite its low imaging dose. Training CRFs further allows a prediction of the following phase and offers a precise post-treatment evaluation tool when decoding the full image sequence.