Abstract To achieve the best treatment of mitral valve disease in a patient, surgeons aim to optimally combine complementary surgical techniques. Image‐based in silico simulation as well as visualization of the mitral valve dynamics can support the visual analysis of the patient‐specific valvular dynamics and enable an exploration of different therapy options. The usage in a time‐constrained clinical environment requires a mitral valve model that is cost‐effective, easy to set up, parameterize and evaluate. Working towards this goal, we develop a simplified model of the mitral valve and analyse its applicability for the sketched use‐case. We propose a novel approach to simulate the mitral valve with position‐based dynamics. The resulting mitral valve model can be deformed to simulate the closing and opening, and incorporate changes caused by virtual interventions in the simulation. Ten mitral valves were reconstructed from transesophageal echocardiogram sequences of patients with normal and abnormal physiology for evaluation. Simulation results showed good agreements with expert annotations of the original image data and reproduced valve closure in all cases. In four of five pathological cases, abnormal closing behaviour was correctly reproduced. In future research, we aim to improve the parameterization of the model in terms of biomechanical correctness and perform a more extensive validation.

Breast augmentation was the most commonly performed cosmetic surgery procedure in 2011 in the United States. Although aesthetically pleasing surgical results can only be achieved if the correct breast implant is selected from a large variety of different prosthesis sizes and shapes available on the market, surgeons still rely on visual assessment and other subjective approaches for operative planning because of lacking objective evaluation tools. In this paper, we present the development of a software prototype for augmentation mammaplasty simulation solely based on 3-D surface scans, from which patient-specific finite-element models are generated in a semiautomatic process. The finite-element model is used to preoperatively simulate the expected breast shapes using physical soft-tissue mechanics. Our approach uses a novel mechanism based on so-called displacement templates, which, for a specific implant shape and position, describe the respective internal body forces. Due to a highly efficient numerical solver we can provide immediate visual feedback of the simulation results, and thus, the software prototype can be integrated smoothly into the medical workflow. The clinical value of the developed 3-D computational tool for aesthetic breast augmentation surgery planning is demonstrated in patient-specific use cases.

We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions.

We demonstrate the application of advanced 3D visualization techniques to determine the optimal implant design and position in hip joint replacement planning. Our methods take as input the physiological stress distribution inside a patient's bone under load and the stress distribution inside this bone under the same load after a simulated replacement surgery. The visualization aims at showing principal stress directions and magnitudes, as well as differences in both distributions. By visualizing changes of normal and shear stresses with respect to the principal stress directions of the physiological state, a comparative analysis of the physiological stress distribution and the stress distribution with implant is provided, and the implant parameters that most closely replicate the physiological stress state in order to avoid stress shielding can be determined. Our method combines volume rendering for the visualization of stress magnitudes with the tracing of short line segments for the visualization of stress directions. To improve depth perception, transparent, shaded, and antialiased lines are rendered in correct visibility order, and they are attenuated by the volume rendering. We use a focus+context approach to visually guide the user to relevant regions in the data, and to support a detailed stress analysis in these regions while preserving spatial context information. Since all of our techniques have been realized on the GPU, they can immediately react to changes in the simulated stress tensor field and thus provide an effective means for optimal implant selection and positioning in a computational steering environment.

In this paper we present a technique for image deformation in which the user is given flexible control over what kind of deformation to perform. Freeform image extends available image deformation techniques in that it provides a palette of intuitive tools including interactive object segmentation, stiffness editing and force-based controls to achieve both a natural look and realistic animations of deforming parts. The model underlying our approach is physics-based and it is amenable to a variety of different kinds of image manipulations ranging from as-rigid- as-possible to fully elastic deformations. We have developed a multigrid solver for quadrangular finite elements, which achieves real-time performance for high resolution pixel grids. On recent CPUs this solver can handle about 16K co-rotated finite elements at roughly 60 ms.

Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics hardware architectures, large and deformable grids, as well as different rendering options. At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. Then, sampling requires minimum GPU memory and texture access operations, and it maps efficiently onto a feed-forward pipeline of multiple stages performing computation and geometry construction. We propose to spawn rendered elements from one single vertex. This makes the method amenable to upcoming Direct3D 10 graphics hardware which allows to create geometry on the GPU. By only modifying the algorithm slightly it can be used to render per-pixel iso-surfaces and to perform tetrahedral cell projection. As our method neither requires any pre-processing nor an intermediate grid representation it can efficiently deal with dynamic and large 3D meshes.