Stress tensor field visualization for implant planning in orthopedics

A Review of Three-Dimensional Medical Image Visualization

Importance. Medical images are essential for modern medicine and an important research subject in visualization. However, medical experts are often not aware of the many advanced three-dimensional (3D) medical image visualization techniques that could increase their capabilities in data analysis and assist the decision-making process for specific medical problems. Our paper provides a review of 3D visualization techniques for medical images, intending to bridge the gap between medical experts and visualization researchers.Highlights. Fundamental visualization techniques are revisited for various medical imaging modalities, from computational tomography to diffusion tensor imaging, featuring techniques that enhance spatial perception, which is critical for medical practices. The state-of-the-art of medical visualization is reviewed based on a procedure-oriented classification of medical problems for studies of individuals and populations. This paper summarizes free software tools for different modalities of medical images designed for various purposes, including visualization, analysis, and segmentation, and it provides respective Internet links.Conclusions. Visualization techniques are a useful tool for medical experts to tackle specific medical problems in their daily work. Our review provides a quick reference to such techniques given the medical problem and modalities of associated medical images. We summarize fundamental techniques and readily available visualization tools to help medical experts to better understand and utilize medical imaging data. This paper could contribute to the joint effort of the medical and visualization communities to advance precision medicine.

Visualization of 3D Stress Tensor Fields Using Superquadric Glyphs on Displacement Streamlines

Stress tensor fields play a central role in solid mechanics studies, but their visualization in 3D space remains challenging as the information-dense multi-variate tensor needs to be sampled in 3D space while avoiding clutter. Taking cues from current tensor visualizations, we adapted glyph-based visualization for stress tensors in 3D space. We also developed a testing framework and performed user studies to evaluate the various glyph-based tensor visualizations for objective accuracy measures, and subjective user feedback for each visualization method. To represent the stress tensor, we color encoded the original superquadric glyph, and in the user study, we compared it to superquadric glyphs developed for second-order symmetric tensors. We found that color encoding improved the user accuracy measures, while the users also rated our method the highest. We compared our method of placing stress tensor glyphs on displacement streamlines to the glyph placement on a 3D grid. In the visualization, we modified the glyph to show both the stress tensor and the displacement vector at each sample point. The participants preferred our method of glyph placement on displacement streamlines as it highlighted the underlying continuous structure in the tensor field.

Distance and force visualisations for improved simulation of intracranial aneurysm clipping

Purpose

The treatment of cerebral aneurysms shifted from microsurgical to endovascular therapy. But for some difficult aneurysm configurations, e.g. wide neck aneurysms, microsurgical clipping is better suited. From this combination of limited interventions and the complexity of these cases, the need for improved training possibilities for young neurosurgeons arises.

Method

We designed and implemented a clipping simulation that requires only a monoscopic display, mouse and keyboard. After a virtual craniotomy, the user can apply a clip at the aneurysm which is deformed based on a mass–spring model. Additionally, concepts for visualising distances as well as force were implemented. The distance visualisations aim to enhance spatial relations, improving the navigation of the clip. The force visualisations display the force acting on the vessel surface by the applied clip. The developed concepts include colour maps and visualisations based on rays, single objects and glyphs.

Results

The concepts were quantitatively evaluated via an online survey and qualitatively evaluated by a neurosurgeon. Regarding force visualisations, a colour map is the most appropriate concept. The necessity of distance visualisations became apparent, as the expert was unable to estimate distances and to properly navigate the clip. The distance rays were the only concept supporting the navigation appropriately.

Conclusion

The easily accessible surgical training simulation for aneurysm clipping benefits from a visualisation of distances and simulated forces.

Visualization of Human Spine Biomechanics for Spinal Surgery

We propose a visualization application, designed for the exploration of human spine simulation data. Our goal is to support research in biomechanical spine simulation and advance efforts to implement simulation-backed analysis in surgical applications. Biomechanical simulation is a state-of-the-art technique for analyzing load distributions of spinal structures. Through the inclusion of patient-specific data, such simulations may facilitate personalized treatment and customized surgical interventions. Difficulties in spine modelling and simulation can be partly attributed to poor result representation, which may also be a hindrance when introducing such techniques into a clinical environment. Comparisons of measurements across multiple similar anatomical structures and the integration of temporal data make commonly available diagrams and charts insufficient for an intuitive and systematic display of results. Therefore, we facilitate methods such as multiple coordinated views, abstraction and focus and context to display simulation outcomes in a dedicated tool. By linking the result data with patient-specific anatomy, we make relevant parameters tangible for clinicians. Furthermore, we introduce new concepts to show the directions of impact force vectors, which were not accessible before. We integrated our toolset into a spine segmentation and simulation pipeline and evaluated our methods with both surgeons and biomechanical researchers. When comparing our methods against standard representations that are currently in use, we found increases in accuracy and speed in data exploration tasks. in a qualitative review, domain experts deemed the tool highly useful when dealing with simulation result data, which typically combines time-dependent patient movement and the resulting force distributions on spinal structures.

Additive manufacturing pertaining to bone: Hopes, reality and future challenges for clinical applications

For the past 20 years, the democratization of additive manufacturing (AM) technologies has made many of us dream of: low cost, waste-free, and on-demand production of functional parts; fully customized tools; designs limited by imagination only, etc. As every patient is unique, the potential of AM for the medical field is thought to be considerable: AM would allow the division of dedicated patient-specific healthcare solutions entirely adapted to the patients' clinical needs. Pertinently, this review offers an extensive overview of bone-related clinical applications of AM and ongoing research trends, from 3D anatomical models for patient and student education to ephemeral structures supporting and promoting bone regeneration. Today, AM has undoubtably improved patient care and should facilitate many more improvements in the near future. However, despite extensive research, AM-based strategies for bone regeneration remain the only bone-related field without compelling clinical proof of concept to date. This may be due to a lack of understanding of the biological mechanisms guiding and promoting bone formation and due to the traditional top-down strategies devised to solve clinical issues. Indeed, the integrated holistic approach recommended for the design of regenerative systems (i.e., fixation systems and scaffolds) has remained at the conceptual state. Challenged by these issues, a slower but incremental research dynamic has occurred for the last few years, and recent progress suggests notable improvement in the years to come, with in view the development of safe, robust and standardized patient-specific clinical solutions for the regeneration of large bone defects.

Robust and Fast Extraction of 3D Symmetric Tensor Field Topology

3D symmetric tensor fields appear in many science and engineering fields, and topology-driven analysis is important in many of these application domains, such as solid mechanics and fluid dynamics. Degenerate curves and neutral surfaces are important topological features in 3D symmetric tensor fields. Existing methods to extract degenerate curves and neutral surfaces often miss parts of the curves and surfaces, respectively. Moreover, these methods are computationally expensive due to the lack of knowledge of structures of degenerate curves and neutral surfaces. In this paper, we provide theoretical analysis on the geometric and topological structures of degenerate curves and neutral surfaces of 3D linear tensor fields. These structures lead to parameterizations for degenerate curves and neutral surfaces that can not only provide more robust extraction of these features but also incur less computational cost. We demonstrate the benefits of our approach by applying our degenerate curve and neutral surface detection techniques to solid mechanics simulation data sets.

Infill Optimization for Additive Manufacturing-Approaching Bone-Like Porous Structures

Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p-norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.

Glyphs for General Second-Order 2D and 3D Tensors

Glyphs are a powerful tool for visualizing second-order tensors in a variety of scientic data as they allow to encode physical behavior in geometric properties. Most existing techniques focus on symmetric tensors and exclude non-symmetric tensors where the eigenvectors can be non-orthogonal or complex. We present a new construction of 2d and 3d tensor glyphs based on piecewise rational curves and surfaces with the following properties: invariance to (a) isometries and (b) scaling, (c) direct encoding of all real eigenvalues and eigenvectors, (d) one-to-one relation between the tensors and glyphs, (e) glyph continuity under changing the tensor. We apply the glyphs to visualize the Jacobian matrix fields of a number of 2d and 3d vector fields.

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Visualizing Tensor Normal Distributions at Multiple Levels of Detail

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula

Patient-specific biomechanical models including patient-specific finite-element (FE) models are considered potentially important tools for providing personalized healthcare to patients with musculoskeletal diseases. A multi-step procedure is often needed to generate a patient-specific FE model. As all involved steps are associated with certain levels of uncertainty, it is important to study how the uncertainties of individual components propagate to final simulation results. In this study, we considered a specific case of this problem where the uncertainties of the involved steps were known and the aim was to determine the uncertainty of the predicted strain distribution. The effects of uncertainties of three important components of patient-specific models, including bone density, musculoskeletal loads and the parameters of the material mapping relationship on the predicted strain distributions, were studied. It was found that the number of uncertain components and the level of their uncertainty determine the uncertainty of simulation results. The 'average' uncertainty values were found to be relatively small even for high levels of uncertainty in the components of the model. The 'maximum' uncertainty values were, however, quite high and occurred in the areas of the scapula that are of the greatest clinical relevance. In addition, the uncertainty of the simulation result was found to be dependent on the type of movement analysed, with abduction movements presenting consistently lower uncertainty values than flexion movements.

Distance visualization for interactive 3D implant planning

An instant and quantitative assessment of spatial distances between two objects plays an important role in interactive applications such as virtual model assembly, medical operation planning, or computational steering. While some research has been done on the development of distance-based measures between two objects, only very few attempts have been reported to visualize such measures in interactive scenarios. In this paper we present two different approaches for this purpose, and we investigate the effectiveness of these approaches for intuitive 3D implant positioning in a medical operation planning system. The first approach uses cylindrical glyphs to depict distances, which smoothly adapt their shape and color to changing distances when the objects are moved. This approach computes distances directly on the polygonal object representations by means of ray/triangle mesh intersection. The second approach introduces a set of slices as additional geometric structures, and uses color coding on surfaces to indicate distances. This approach obtains distances from a precomputed distance field of each object. The major findings of the performed user study indicate that a visualization that can facilitate an instant and quantitative analysis of distances between two objects in interactive 3D scenarios is demanding, yet can be achieved by including additional monocular cues into the visualization.

Coherent Structures of Characteristic Curves in Symmetric Second Order Tensor Fields

This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglobal method for visualizing coherent structures in symmetric second order tensor fields. We demonstrate the usefulness by examples from DT-MRI, uncovering anatomical structures in linearly anisotropic regions not amenable to local feature criteria. To further exemplify the suitability of our concept, we also present its application to stress tensor fields. Last, an accelerated implementation utilizing GPUs is presented.

Superquadric glyphs for symmetric second-order tensors

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.