Determining individual glomerular proteinuria and periglomerular infiltration in a cleared murine kidney by a 3-dimensional fast marching algorithm.

Three-dimensional (3D) imaging has advanced basic research and clinical medicine. However, limited resolution and imperfections of real-world 3D image material often preclude algorithmic image analysis. Here, we present a methodologic framework for such imaging and analysis for functional and spatial relations in experimental nephritis. First, optical tissue-clearing protocols were optimized to preserve fluorescence signals for light sheet fluorescence microscopy and compensated attenuation effects using adjustable 3D correction fields. Next, we adapted the fast marching algorithm to conduct backtracking in 3D environments and developed a tool to determine local concentrations of extractable objects. As a proof-of-concept application, we used this framework to determine in a glomerulonephritis model the individual proteinuria and periglomerular immune cell infiltration for all glomeruli of half a mouse kidney. A correlation between these parameters surprisingly did not support the intuitional assumption that the most inflamed glomeruli are the most proteinuric. Instead, the spatial density of adjacent glomeruli positively correlated with the proteinuria of a given glomerulus. Because proteinuric glomeruli appear clustered, this suggests that the exact location of a kidney biopsy may affect the observed severity of glomerular damage. Thus, our algorithmic pipeline described here allows analysis of various parameters of various organs composed of functional subunits, such as the kidney, and can theoretically be adapted to processing other image modalities.

Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets.

BACKGROUND: The efficient and robust statistical analysis of the shape of plant organs of different cultivars is an important investigation issue in plant breeding and enables a robust cultivar description within the breeding progress. Laserscanning is a highly accurate and high resolution technique to acquire the 3D shape of plant surfaces. The computation of a shape based principal component analysis (PCA) built on concepts from continuum mechanics has proven to be an effective tool for a qualitative and quantitative shape examination. RESULTS: The shape based PCA was used for a statistical analysis of 140 sugar beet roots of different cultivars. The calculation of the mean sugar beet root shape and the description of the main variations was possible. Furthermore, unknown and individual tap roots could be attributed to their cultivar by means of a robust classification tool based on the PCA results. CONCLUSION: The method demonstrates that it is possible to identify principal modes of root shape variations automatically and to quantify associated variances out of laserscanned 3D sugar beet tap root models. The introduced approach is not limited to the 3D shape description by laser scanning. A transfer to 3D MRI or radar data is also conceivable.

Image Morphing in Deep Feature Spaces: Theory and Applications.

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller and Younes (Int J Comput Vis 41(1):61-84, 2001) and Trouvé and Younes (Found Comput Math 5(2):173-198, 2005). For this model, a variational time discretization of the Riemannian path energy is presented and the existence of discrete geodesic paths minimizing this energy is demonstrated. Furthermore, convergence of discrete geodesic paths to geodesic paths in the time continuous model is investigated. The spatial discretization is based on a finite difference approximation in image space and a stable spline approximation in deformation space; the fully discrete model is optimized using the iPALM algorithm. Numerical experiments indicate that the incorporation of semantic deep features is superior to intensity-based approaches.

Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data.

PURPOSE: Cancers are almost always diagnosed by morphologic features in tissue sections. In this context, machine learning tools provide new opportunities to describe tumor immune cell interactions within the tumor microenvironment and thus provide phenotypic information that might be predictive for the response to immunotherapy. METHODS: We develop a machine learning approach using variational networks for joint image denoising and classification of tissue sections for melanoma, which is an established model tumor for immuno-oncology research. The manual annotation of real training data would require substantial user interaction of experienced pathologists for each single training image, and the training of larger networks would rely on a very large number of such data sets with ground truth annotation. To overcome this bottleneck, we synthesize training data together with a proper tissue structure classification. To this end, a stochastic data generation process is used to mimic cell morphology, cell distribution and tissue architecture in the tumor microenvironment. Particular components of this tool are random placement and rotation of a large number of patches for presegmented cell nuclei, a stochastic fast marching approach to mimic the geometry of cells and texture generation based on a color covariance analysis of real data. Here, the generated training data reflect a large range of interaction patterns. RESULTS: In several applications to histological tissue sections, we analyze the efficiency and accuracy of the proposed approach. As a result, depending on the scenario considered, almost all cells and nuclei which ought to be detected are actually marked as classified and hardly any misclassifications occur. CONCLUSIONS: The proposed method allows for a computer-aided screening of histological tissue sections utilizing variational networks with a particular emphasis on tumor immune cell interactions and on the robust cell nuclei classification.

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies.

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.

Multiscale joint segmentation and registration of image morphology.

Multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa. In particular combined information of different image modalities makes segmentation significantly more robust. Indeed, fundamental tasks in image processing are highly interdependent. A variational approach is presented, which combines the detection of corresponding edges, an edge preserving denoising and the morphological registration via a non-rigid deformation for a pair of images with structural correspondence. The morphology of an image function is split into a singular part consisting of the edge set and a regular part represented by the field of normals on the ensemble of level sets. A Mumford-Shah type free discontinuity problem is applied to treat the singular morphology and the matching of corresponding edges under the deformation. The matching of the regular morphology is quantified by a second contribution which compares deformed normals and normals at deformed positions. Finally, a nonlinear elastic energy controls the deformation itself and ensures smoothness and injectivity. A multi scale approach that is based on a phase field approximation leads to an effective and efficient algorithm. Numerical experiments underline the robustness of the presented approach and show applications on medical images.

Mumford-Shah model for one-to-one edge matching.

This paper presents a new algorithm based on the Mumford-Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation. The optimization process is guided by an estimation minimization-type algorithm and an adaptive generalized gradient flow to guarantee a fast and smooth relaxation. The algorithm is tested on T1 and T2 magnetic resonance image data to study the parameter setting. We also present promising results of four applications of the proposed algorithm: interobject monomodal registration, retinal image registration, matching digital photographs of neurosurgery with its volume data, and motion estimation for frame interpolation.

Functional Thin Films on Surfaces.

The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering. Finally, we extend our method to incorporate non-linear van der Waals forcing terms which stabilize the motion of the film and allow additional effects such as pearling.

An adaptive level set method for interactive segmentation of intracranial tumors.

BACKGROUND: Meaningful segmentation of intracranial lesions can be of assistance for planning open navigated microneurosurgical procedures, as well as for radiotherapy. Meaningful segmentation, however, may be hampered by lack of computational power. The respective segmentation method should be based on state-of-the-art mathematical tools, and it should be suitable for real applications. METHODS: A three-dimensional computational method for interactive segmentation of intracranial tumors is presented. It is based on a front propagation method, in which the evolving front gradually approaches the boundary of a given segment. It generates and remembers the entire evolution of the interface. The segment boundary is chosen from a one parameter family. User interaction is realized by selecting "seed points" inside the object/lesion. External evolution velocity regulates the segmentation process, while approaching the boundary. Adaptively resolved grids ensure computational efficiency for larger segments. The resolution is steered by an image-based indicator, which allows coarse representation of the solution in low-frequency regions, but high resolution along suspected edges of the image. RESULTS: Model-based segmentation was performed on the imaging data of n = 12 patients and the results compared with manual segmentation of the same tumors. The method allowed for basic segmentation in all tumors <3 minutes. This increased 2-4 fold in four irregular tumors, where discrepancies existed in comparison with manually performed segmentation. DISCUSSION: The implicit formulations of this method establish methodical and topological flexibility in three dimensions. It is thus suitable for the segmentation of objects with non-sharp boundaries such as intracranial tumors.

Processing textured surfaces via anisotropic geometric diffusion.

A multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy, textured, parametric surfaces. The aim is to smooth noisy, triangulated surfaces and accompanying noisy textures-as they are delivered by new scanning technology-while enhancing geometric and texture features. For an initial textured surface a fairing method is described which simultaneously processes the texture and the surface. Considering an appropriate coupling of the two smoothing processes one can take advantage of the frequently present strong correlation between edge features in the texture and on the surface edges. The method is based on an anisotropic curvature evolution of the surface itself and an anisotropic diffusion on the processed surface applied to the texture. Here, the involved diffusion tensors depends on a regularized shape operator of the evolving surface and on regularized texture gradients. A spatial finite element discretization on arbitrary unstructured triangular grids and a semi-implicit finite difference discretization in time are the building blocks of the corresponding numerical algorithm. A normal projection is applied to the discrete propagation velocity to avoid tangential drifting in the surface evolution. Different applications underline the efficiency and flexibility of the presented surface processing tool.

Exploring invariant sets and invariant measures.

We propose a method to explore invariant measures of dynamical systems. The method is based on numerical tools which directly compute invariant sets using a subdivision technique, and invariant measures by a discretization of the Frobenius-Perron operator. Appropriate visualization tools help to analyze the numerical results and to understand important aspects of the underlying dynamics. This will be illustrated for examples provided by the Lorenz system. (c) 1997 American Institute of Physics.

A new software for prediction of femoral neck fractures.

Femoral neck fractures are an important clinical, social and economic problem. Even if many different attempts have been carried out to improve the accuracy predicting the fracture risk, it was demonstrated in retrospective studies that the standard clinical protocol achieves an accuracy of about 65%. A new procedure was developed including for the prediction not only bone mineral density but also geometric and femoral strength information and achieving an accuracy of about 80% in a previous retrospective study. Aim of the present work was to re-engineer research-based procedures and develop a real-time software for the prediction of the risk for femoral fracture. The result was efficient, repeatable and easy to use software for the evaluation of the femoral neck fracture risk to be inserted in the daily clinical practice providing a useful tool for the improvement of fracture prediction.

Robust feature detection and local classification for surfaces based on moment analysis.

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.

Co-registration of intra-operative brain surface photographs and pre-operative MR images.

PURPOSE: Brain shift, the change in configuration of the brain after opening the dura mater, is a significant problem for neuronavigation. Brain structures at intra-operative deformed positions must be matched with corresponding structures in the pre-operative 3D planning data. A method to co-register the cortical surface from intra-operative microscope images with pre-operative MRI-segmented data was developed and tested. METHODS: Automated classification of sulci on MRI-extracted cortical surfaces was tested by comparison with user guided marking of prominent sulci on an intra-operative photography. A variational registration method with a fidelity energy for 3D deformations of the cortical surface in conjunction with a higher-order, linear elastic prior energy was used for the actual registration. The minimization of this energy was performed with a regularized gradient descent scheme using finite elements for spatial discretization. The sulcal classification method was tested on eight different clinical MRI data sets by comparison of the deformed MRI scans with intra-operative photographs of the brain surface. RESULTS: User intervention was required for marking sulci on the photographs demonstrating the potential for incorporating an automatic classifier. The actual registration was validated first on an artificial testbed. The complete algorithm for the co-registration of actual clinical MRI data was successful for eight different patients. CONCLUSIONS: Pre-operative MRI scans can be registered to intra-operative brain surface photographs using a surface-to-surface registration method. This co-registration method has potential applications in neurosurgery, particularly during functional procedures.

Joint surface reconstruction and 4D deformation estimation from sparse data and prior knowledge for marker-less Respiratory motion tracking.

PURPOSE: The intraprocedural tracking of respiratory motion has the potential to substantially improve image-guided diagnosis and interventions. The authors have developed a sparse-to-dense registration approach that is capable of recovering the patient's external 3D body surface and estimating a 4D (3D + time) surface motion field from sparse sampling data and patient-specific prior shape knowledge. METHODS: The system utilizes an emerging marker-less and laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3D measurements in real-time. These sparse position measurements are registered with a dense reference surface extracted from planning data. Thereby a dense displacement field is recovered, which describes the spatio-temporal 4D deformation of the complete patient body surface, depending on the type and state of respiration. It yields both a reconstruction of the instantaneous patient shape and a high-dimensional respiratory surrogate for respiratory motion tracking. The method is validated on a 4D CT respiration phantom and evaluated on both real data from an AT prototype and synthetic data sampled from dense surface scans acquired with a structured-light scanner. RESULTS: In the experiments, the authors estimated surface motion fields with the proposed algorithm on 256 datasets from 16 subjects and in different respiration states, achieving a mean surface reconstruction accuracy of ± 0.23 mm with respect to ground truth data-down from a mean initial surface mismatch of 5.66 mm. The 95th percentile of the local residual mesh-to-mesh distance after registration did not exceed 1.17 mm for any subject. On average, the total runtime of our proof of concept CPU implementation is 2.3 s per frame, outperforming related work substantially. CONCLUSIONS: In external beam radiation therapy, the approach holds potential for patient monitoring during treatment using the reconstructed surface, and for motion-compensated dose delivery using the estimated 4D surface motion field in combination with external-internal correlation models.

Marker-less reconstruction of dense 4-D surface motion fields using active laser triangulation for respiratory motion management.

To manage respiratory motion in image-guided interventions a novel sparse-to-dense registration approach is presented. We apply an emerging laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3-D measurements in real-time. These sparse position measurements are registered with a dense reference surface extracted from planning data. Thereby a dense displacement field is reconstructed which describes the 4-D deformation of the complete patient body surface and recovers a multi-dimensional respiratory signal for application in respiratory motion management. The method is validated on real data from an AT prototype and synthetic data sampled from dense surface scans acquired with a structured light scanner. In a study on 16 subjects, the proposed algorithm achieved a mean reconstruction accuracy of +/- 0.22 mm w.r.t. ground truth data.

Restoring three-dimensional magnetic resonance angiography images with mean curvature motion.

OBJECTIVE: The management of neurovascular disease requires precise information on the cerebral vascular anatomy. Digital subtraction angiography (DSA) is the gold standard against which other imaging modalities have to be measured. To improve the quality of three-dimensional (3D) magnetic resonance angiography (MRA) images, we present a novel concept in 3D image analysis. METHODS: Five patients, harboring cerebral aneurysm, underwent DSA, computed tomography angiography (CTA) and MRA. MRA data were processed using a novel anisotropic curvature motion model. Three-dimensional reconstructions of CTA and MRA datasets were used for comparison. RESULTS: The 3D-reconstructed images accurately displayed all aneurysms. The anatomy of the anterior part of the circle of Willis was visualized reliably. The smoothened vessel surfaces enhanced the readability of the images. Regarding visual representation of the posterior part of the circle of Willis, the post-processed MRA showed the arterial segments less accurate than the standard modalities. CONCLUSIONS: This new approach is a promising tool for planning of neurovascular interventions and preoperative evaluation.

Statistical osteoporosis models using composite finite elements: a parameter study.

Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, numerous researchers employ micro-finite element models. To avoid disadvantages in setting up classical finite element models, composite finite elements (CFE) can be used. The aim of the study is to test the potential of CFE. For that, a parameter study on numerical lattice samples with statistically simulated, simplified osteoporosis is performed. These samples are subjected to compression and shear loading. Results show that the biggest drop of compressive stiffness is reached for transverse isotropic structures losing 32% of the trabeculae (minus 89.8% stiffness). The biggest drop in shear stiffness is found for an isotropic structure also losing 32% of the trabeculae (minus 67.3% stiffness). The study indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. The results further demonstrate the advantages of CFEs for simulating micro-structured samples.