Orcun Goksel

Modeling and simulation of flexible needles

Needle insertion is performed in many clinical and therapeutic procedures. Tissue displacement and needle bending which result from needle-tissue interaction make accurate targeting difficult. For performing physicians to gain essential needle targeting skills, needle insertion simulators can be used for training. An accurate needle bending model is essential for such simulators. These bending models are also needed for needle path planning. In this paper, three different models are presented to simulate the deformations of a needle. The first two models use the finite element method and take the geometric nonlinearity into account. The third model is a series of rigid bars connected by angular springs. The models were compared to recorded deformations during experiments of applying lateral tip forces on a brachytherapy needle. The model parameters were identified and the simulation results were compared to the experimental data. The results show that the angular spring model, which is computationally the most efficient model, is also the most accurate in modeling the bending of the brachytherapy needle.

3D needle-tissue interaction simulation for prostate brachytherapy

This paper presents a needle-tissue interaction model that is a 3D extension of a prior work based on the finite element method. The model is also adapted to accommodate arbitrary meshes so that the anatomy can effectively be meshed using third-party algorithms. Using this model a prostate brachytherapy simulator is designed to help medical residents acquire needle steering skills. This simulation uses a prostate mesh generated from clinical data segmented as contours on parallel slices. Node repositioning and addition, which are methods for achieving needle-tissue coupling, are discussed. In order to achieve realtime haptic rates, computational approaches to these methods are compared. Specifically, the benefit of using the Woodbury formula (matrix inversion lemma) is studied. Our simulation of needle insertion into a prostate is shown to run faster than 1 kHz.

3D simulation of needle-tissue interaction with application to prostate brachytherapy

This paper presents a needle-tissue interaction model that is a 3D extension of prior work based on needle and tissue models discretized using the Finite Element Method. The use of flexible needles necessitates remeshing the tissue during insertion, since simple mesh-node snapping to the tip can be detrimental to the simulation. In this paper, node repositioning and node addition are the two methods of mesh modification examined for coarse meshes. Our focus is on numerical approaches for fast implementation of these techniques. Although the two approaches compared, namely the Woodbury formula (matrix inversion lemma) and the boundary condition switches, have the same computational complexity, the Woodbury formula is shown to perform faster due to its cache-efficient order of operations. Furthermore, node addition is applied in constant time for both approaches, whereas node repositioning requires longer and variable computational times. A method for rendering the needle forces during simulated insertions into a 3D prostate model has been implemented. Combined with a detailed anatomical segmentation, this will be useful in teaching the practice of prostate brachytherapy. Issues related to discretization of such coupled (e.g., needle-tissue) models are also discussed.

B -Mode Ultrasound Image Simulation in Deformable 3-D Medium

This paper presents an algorithm for fast image synthesis inside deformed volumes. Given the node displacements of a mesh and a reference 3-D image dataset of a predeformed volume, the method first maps the image pixels that need to be synthesized from the deformed configuration to the nominal predeformed configuration, where the pixel intensities are obtained easily through interpolation in the regular-grid structure of the reference voxel volume. This mapping requires the identification of the mesh element enclosing each pixel for every image frame. To accelerate this point location operation, a fast method of projecting the deformed mesh on image pixels is introduced in this paper. The method presented was implemented for ultrasound B-mode image simulation of a synthetic tissue phantom. The phantom deformation as a result of ultrasound probe motion was modeled using the finite element method. Experimental images of the phantom under deformation were then compared with the corresponding synthesized images using sum of squared differences and mutual information metrics. Both this quantitative comparison and a qualitative assessment show that realistic images can be synthesized using the proposed technique. An ultrasound examination system was also implemented to demonstrate that real-time image synthesis with the proposed technique can be successfully integrated into a haptic simulation.

Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of the cross-correlation function

A widely used time-domain technique for motion or delay estimation between digitized ultrasound RF signals involves the maximization of a discrete pattern-matching function, usually the cross-correlation. To achieve sub-sample accuracy, the discrete pattern-matching function is interpolated using the values at the discrete maximizer and adjacent samples. In prior work, only 1-D fit, applied separately along the axial, lateral, and elevational axes, has been used to estimate the sub-sample motion in 1-D, 2-D, and 3-D. In this paper, we explore the use of 2-D and 3-D polynomial fitting for this purpose. We quantify the estimation error in noise-free simulations using Field II and experiments with a commercial ultrasound machine. In simulated 2-D translational motions, function fitting with quartic spline polynomials leads to maximum bias of 0.2% of the sample spacing in the axial direction and 0.4% of the sample spacing in the lateral direction, corresponding to 38 nm and 1.31 μm, respectively. The maximum standard deviations were approximately 1% of the sample spacing in both the axial and the lateral directions, corresponding to 193 nm axially and 4.43 μm laterally. In simulated 1% axial strain, the same function fitting leads to mean absolute displacement estimation errors of 255 nm in the axial direction and 4.77 ?m in the lateral direction. In experiments with a linear array transducer, 2-D quartic spline fitting leads to maximum bias of 458 nm and 6.27 μm in the axial and the lateral directions, respectively. These results are more than one order of magnitude smaller than those obtained with separate 1-D fit when applied to the same data set. Simulations and experiments in 3-D yield similar results when comparing 3-D polynomial fitting with 1-D fitting along the axial, lateral, and elevational directions.

Haptic Simulator for Prostate Brachytherapy with Simulated Needle and Probe Interaction

This paper presents a haptic simulator for prostate brachytherapy. Both needle insertion and the manipulation of the transrectal ultrasound (TRUS) probe are controlled via haptic devices. Tissue interaction forces that are computed by a deformable tissue model based on the finite element method (FEM) are rendered to the user by these devices. The needle insertion simulation employs 3D models of needle flexibility and asymmetric tip bevel. The needle-tissue simulation allows a trainee to practice needle insertion and targeting. The TRUS-tissue interaction simulation allows a trainee to practice the 3D intraoperative TRUS placement for registration with the preoperative volume study and to practice TRUS axial translation and rotation for imaging needles during insertions. Approaches to computational acceleration for realtime haptic performance are presented. Trade-offs between accuracy and speed are discussed. A graphics-card implementation of the numerically intensive mesh-adaptation operation is also presented. The simulator can be used for training, rehearsal, and treatment planning.

Cloud-Based Evaluation of Anatomical Structure Segmentation and Landmark Detection Algorithms: VISCERAL Anatomy Benchmarks

Variations in the shape and appearance of anatomical structures in medical images are often relevant radiological signs of disease. Automatic tools can help automate parts of this manual process. A cloud-based evaluation framework is presented in this paper including results of benchmarking current state-of-the-art medical imaging algorithms for anatomical structure segmentation and landmark detection: the VISCERAL Anatomy benchmarks. The algorithms are implemented in virtual machines in the cloud where participants can only access the training data and can be run privately by the benchmark administrators to objectively compare their performance in an unseen common test set. Overall, 120 computed tomography and magnetic resonance patient volumes were manually annotated to create a standard Gold Corpus containing a total of 1295 structures and 1760 landmarks. Ten participants contributed with automatic algorithms for the organ segmentation task, and three for the landmark localization task. Different algorithms obtained the best scores in the four available imaging modalities and for subsets of anatomical structures. The annotation framework, resulting data set, evaluation setup, results and performance analysis from the three VISCERAL Anatomy benchmarks are presented in this article. Both the VISCERAL data set and Silver Corpus generated with the fusion of the participant algorithms on a larger set of non-manually-annotated medical images are available to the research community.

Image-Based Variational Meshing

In medical simulations involving tissue deformation, the finite element method (FEM) is a widely used technique, where the size, shape, and placement of the elements in a model are important factors that affect the interpolation and numerical errors of a solution. Conventional model generation schemes for FEM consist of a segmentation step delineating the anatomy followed by a meshing step generating elements conforming to this segmentation. In this paper, a single-step model generation technique is proposed based on optimization. Starting from an initial mesh covering the domain of interest, the mesh nodes are adjusted to minimize an objective function which penalizes intra-element intensity variations and poor element geometry for the entire mesh. Trade-offs between mesh geometry quality and intra-element variance are achieved by adjusting the relative weights of the geometric and intensity variation components of the cost function. This meshing approach enables a more accurate rendering of shapes with fewer elements and provides more accurate models for deformation simulation, especially when the image intensities represent a mechanical feature of the tissue such as the elastic modulus. The use of the proposed mesh optimization is demonstrated in 2-D and 3-D on synthetic phantoms, MR images of the brain, and CT images of the kidney. A comparison with previous meshing techniques that do not account for image intensity is also provided demonstrating the benefits of our approach.

Isotropic Total Variation Regularization of Displacements in Parametric Image Registration.

Spatial regularization is essential in image registration, which is an ill-posed problem. Regularization can help to avoid both physically implausible displacement fields and local minima during optimization. Tikhonov regularization (squared

Simultaneous Segmentation and Multiresolution Nonrigid Atlas Registration

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