The evaluation of analysis methods for diffusion tensor imaging (DTI) remains challenging due to the lack of gold standards and validation frameworks. Significant work remains in developing metrics for comparing fiber bundles generated from streamline tractography. We propose a set of volumetric and tract oriented measures for evaluating tract differences. The different methods developed for this assessment work are: an overlap measurement, a point cloud distance and a quantification of the diffusion properties at similar locations between fiber bundles. The application of the measures in this paper is a comparison of atlas generated tractography to tractography generated in individual images. For the validation we used a database of 37 subject DTIs, and applied the measurements on five specific fiber bundles: uncinate, cingulum (left and right for both bundles) and genu. Each measurments is interesting for specific use: the overlap measure presents a simple and comprehensive metric but is sensitive to partial voluming and does not give consistent values depending on the bundle geometry. The point cloud distance associated with a quantile interpretation of the distribution gives a good intuition of how close and similar the bundles are. Finally, the functional difference is useful for a comparison of the diffusion properties since it is the focus of many DTI analysis to compare scalar invariants. The comparison demonstrated reasonable similarity of results. The tract difference measures are also applicable to comparison of tractography algorithms, quality control, reproducibility studies, and other validation problems.

This paper presents a method for normalization of diffusion tensor images (DTI) to a fixed DTI template, a pre-processing step to improve the performance of full tensor based registration methods. The proposed method maps the individual tensors of the subject image in to the template space based on matching the cumulative distribution function and the fractional anisotrophy values. The method aims to determine a more accurate deformation field from any full tensor registration method by applying the registration algorithm on the normalized DTI rather than the original DTI. The deformation field applied to the original tensor images are compared to the deformed image without normalization for 11 different cases of mapping seven subjects (neonate through 2 years) to two different atlases. The method shows an improvement in DTI registration based on comparing the normalized fractional anisotropy values of major fiber tracts in the brain.

Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg- Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions.

Topology-based techniques are useful for multiscale exploration of the feature space of scalar-valued functions, such as those derived from the output of large-scale simulations. The Morse-Smale (MS) complex, in particular, allows robust identification of gradient-based features, and therefore is suitable for analysis tasks in a wide range of application domains. In this paper, we develop a two-stage algorithm to construct the 1-skeleton of the Morse-Smale complex in parallel, the first stage independently computing local features per block and the second stage merging to resolve global features. Our implementation is based on MPI and a distributed-memory architecture. Through a set of scalability studies on the IBM Blue Gene/P supercomputer, we characterize the performance of the algorithm as block sizes, process counts, merging strategy, and levels of topological simplification are varied, for datasets that vary in feature composition and size. We conclude with a strong scaling study using scientific datasets computed by combustion and hydrodynamics simulations.

Topological techniques have proven highly successful in analyzing and visualizing scientific data. As a result, significant efforts have been made to compute structures like the Morse-Smale complex as robustly and efficiently as possible. However, the resulting algorithms, while topologically consistent, often produce incorrect connectivity as well as poor geometry. These problems may compromise or even invalidate any subsequent analysis. Moreover, such techniques may fail to improve even when the resolution of the domain mesh is increased, thus producing potentially incorrect results even for highly resolved functions. To address these problems we introduce two new algorithms: (i) a randomized algorithm to compute the discrete gradient of a scalar field that converges under refinement; and (ii) a deterministic variant which directly computes accurate geometry and thus correct connectivity of the MS complex. The first algorithm converges in the sense that on average it produces the correct result and its standard deviation approaches zero with increasing mesh resolution. The second algorithm uses two ordered traversals of the function to integrate the probabilities of the first to extract correct (near optimal) geometry and connectivity. We present an extensive empirical study using both synthetic and real-world data and demonstrates the advantages of our algorithms in comparison with several popular approaches.

In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features. The flexibility and power of this approach is illustrated with examples showing novel features.

Image population analysis is the class of statistical methods that plays a central role in understanding the development, evolution and disease of a population. However, these techniques often require excessive computational power and memory that are compounded with a large number of volumetric inputs. Restricted access to supercomputing power limits its influence in general research and practical applications. In this paper we introduce ISP, an Image-Set Processing streaming framework that harnesses the processing power of commodity heterogeneous CPU/GPU systems and attempts to solve this computational problem. In ISP we introduce specially-designed streaming algorithms and data structures that provide an optimal solution for out-of-core multi-image processing problems both in terms of memory usage and computational efficiency. ISP makes use of the asynchronous execution mechanism supported by parallel heterogeneous systems to efficiently hide the inherent latency of the processing pipeline of out-of-core approaches. Consequently, with computationally intensive problems, the ISP out-of-core solution can achieve the same performance as the in-core solution. We demonstrate the efficiency of the ISP framework on synthetic and real datasets.

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Background and purpose
Acetabular retroversion may result in anterior acetabular over-coverage and posterior deficiency. It is unclear how standard radiographic measures of retroversion relate to measurements from 3D models, generated from volumetric CT data. We sought to: (1) compare 2D radiographic measurements between patients with acetabular retroversion and normal control subjects, (2) compare 3D measurements of total and regional femoral head coverage between patients and controls, and (3) quantify relationships between radiographic measurements of acetabular retroversion to total and regional coverage of the femoral head.

Patients and methods
For 16 patients and 18 controls we measured the extrusion index, crossover ratio, acetabular angle, acetabular index, lateral center edge angle, and a new measurement termed the "posterior wall distance". 3D femoral coverage was determined from volumetric CT data using objectively defined acetabular rim projections, head-neck junctions, and 4 anatomic regions. For radiographic measurements, intra-observer and inter-observer reliabilities were evaluated and associations between 2D radiographic and 3D model-based measures were determined.

Results
Compared to control subjects, patients with acetabular retroversion had a negative posterior wall distance, increased extrusion index, and smaller lateral center edge angle. Differences in the acetabular index between groups approached statistical significance. The acetabular angle was similar between groups. Acetabular retroversion was associated with a slight but statistically significant increase in anterior acetabular coverage, especially in the anterolateral region. Retroverted hips had substantially less posterior coverage, especially in the posterolateral region.

Interpretation
We found that a number of 2D radiographic measures of acetabular morphology were correlated with 3D model-based measures of total and regional femoral head coverage. These correlations may be used to assist in the diagnosis of retroversion and for preoperative planning.

Cam femoroacetabular impingement (FAI) is characterized by a malformed femoral head that may cause shearing between the femur and acetabulum, leading to intraarticular damage and early hip osteoarthritis. Radiographic measurements are used to diagnose cam FAI, but provide only a planar view of the femoral head and often assume the ideal femur shape to be spherical. Statistical shape modeling (SSM) can be used to objectively compare complex 3D morphology without the need to assume ideal geometry. The objective of this study was to generate accurate 3D reconstructions of femoral heads and apply statistical shape modeling to quantify 3D variation and morphologic differences between control and cam femurs. Femurs from 33 controls and 15 cam FAI patients were CT scanned and 3D surfaces were generated by image segmentation. Correspondence particles were optimally positioned upon each surface using a gradient descent energy function. Resulting particle configurations were used to generate mean shapes for each group. Morphological differences were calculated as the distance between mean control and patient geometries. Differences were consistent with the location and approximate shape of cam lesions found intra-operatively. Deviations in mean shape between groups were pronounced at the anterolateral headneck junction, where the mean cam femur protruded from the mean control femur by a maximum of 2.7mm. Sustained protrusions of ~1.0-2.5mm were distributed from the anterior-posterior midline of the femoral neck along the entire anterolateral head-neck junction and distally along the anterior section of the neck. Future work will refine our statistical shape modeling software to quantify, on a patient-specific basis, the severity of cam lesions for pre-operative planning.

Our objectives were to determine cartilage contact stress during walking, stair climbing, and descending stairs in a well-defined group of normal volunteers and to assess variations in contact stress and area among subjects and across loading scenarios. Ten volunteers without history of hip pain or disease with normal lateral center-edge angle and acetabular index were selected. Computed tomography imaging with contrast was performed on one hip. Bone and cartilage surfaces were segmented from volumetric image data, and subject-specific finite element models were constructed and analyzed using a validated protocol. Acetabular contact stress and area were determined for seven activities. Peak stress ranged from 7.52 ± 2.11 MPa for heel-strike during walking (233% BW) to 8.66 ± 3.01 MPa for heel-strike during descending stairs (261% BW). Average contact area across all activities was 34% of the surface area of the acetabular cartilage. The distribution of contact stress was highly non-uniform, and more variability occurred among subjects for a given activity than among activities for a single subject. The magnitude and area of contact stress were consistent between activities, although inter-activity shifts in contact pattern were found as the direction of loading changed. Relatively small incongruencies between the femoral and acetabular cartilage had a large effect on the contact stresses. These effects tended to persist across all simulated activities. These results demonstrate the diversity and trends in cartilage contact stress in healthy hips during activities of daily living and provide a basis for future comparisons between normal and pathologic hips.

Keywords: hip, finite element, biomechanics, cartilage contact stresses, cartilage pressure

Objective: Brain enlargement has been observed in individuals with autism as early as two years of age. Studies using head circumference suggest that brain enlargement is a postnatal event that occurs around the latter part of the first year. To date, no brain imaging studies have systematically examined the period prior to age two. In this study we examine MRI brain volume in six month olds at high familial risk for autism.

Method: The Infant Brain Imaging Study (IBIS) is a longitudinal imaging study of infants at high risk for autism. This cross-sectional analysis examines brain volumes at six months of age, in high risk infants (N=98) in comparison to infants without family members with autism (low risk) (N=36). MRI scans are also examined for radiologic abnormalities.

Results: No group differences were observed for intracranial cerebrum, cerebellum, lateral ventricle volumes, or head circumference.

Conclusions: We did not observe significant group differences for head circumference, brain volume, or abnormalities of radiologic findings in a sample of 6 month old infants at highrisk for autism. We are unable to conclude that these changes are not present in infants who later go on to receive a diagnosis of autism, but rather that they were not detected in a large group at high familial risk. Future longitudinal studies of the IBIS sample will examine whether brain volume may differ in those infants who go onto develop autism, estimating that approximately 20\% of this sample may be diagnosed with an autism spectrum disorder at age two.

Background
No clear recommendations exist regarding optimal humeral component version and deltoid tension in reverse total shoulder arthroplasty (TSA).

Materials and methods
A biomechanical shoulder simulator tested humeral versions (0°, 10°, 20° retroversion) and implant thicknesses (-3, 0, +3 mm from baseline) after reverse TSA in human cadavers. Abduction and external rotation ranges of motion as well as abduction and dislocation forces were quantified for native arms and arms implanted with 9 combinations of humeral version and implant thickness.

Results
Resting abduction angles increased significantly (up to 30°) after reverse TSA compared with native shoulders. With constant posterior cuff loads, native arms externally rotated 20°, whereas no external rotation occurred in implanted arms (20° net internal rotation). Humeral version did not affect rotational range of motion but did alter resting abduction. Abduction forces decreased 30% vs native shoulders but did not change when version or implant thickness was altered. Humeral center of rotation was shifted 17 mm medially and 12 mm inferiorly after implantation. The force required for lateral dislocation was 60% less than anterior and was not affected by implant thickness or version.

Conclusion
Reverse TSA reduced abduction forces compared with native shoulders and resulted in limited external rotation and abduction ranges of motion. Because abduction force was reduced for all implants, the choice of humeral version and implant thickness should focus on range of motion. Lateral dislocation forces were less than anterior forces; thus, levering and inferior/posterior impingement may be a more probable basis for dislocation (laterally) than anteriorly directed forces.

Keywords: Shoulder, reverse arthroplasty, deltoid tension, humeral version, biomechanical simulator

Background
Lateral offset center of rotation (COR) reduces the incidence of scapular notching and potentially increases external rotation range of motion (ROM) after reverse total shoulder arthroplasty (rTSA). The purpose of this study was to determine the biomechanical effects of changing COR on abduction and external rotation ROM, deltoid abduction force, and joint stability.

Materials and methods
A biomechanical shoulder simulator tested cadaveric shoulders before and after rTSA. Spacers shifted the COR laterally from baseline rTSA by 5, 10, and 15 mm. Outcome measures of resting abduction and external rotation ROM, and abduction and dislocation (lateral and anterior) forces were recorded.

Results
Resting abduction increased 20° vs native shoulders and was unaffected by COR lateralization. External rotation decreased after rTSA and was unaffected by COR lateralization. The deltoid force required for abduction significantly decreased 25% from native to baseline rTSA. COR lateralization progressively eliminated this mechanical advantage. Lateral dislocation required significantly less force than anterior dislocation after rTSA, and both dislocation forces increased with lateralization of the COR.

Conclusion
COR lateralization had no influence on ROM (adduction or external rotation) but significantly increased abduction and dislocation forces. This suggests the lower incidence of scapular notching may not be related to the amount of adduction deficit after lateral offset rTSA but may arise from limited impingement of the humeral component on the lateral scapula due to a change in joint geometry. Lateralization provides the benefit of increased joint stability, but at the cost of increasing deltoid abduction forces.

Keywords: Shoulder simulator, reverse arthroplasty, lateral offset, center of rotation

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.

In the context of long-range digital neural circuit reconstruction, this paper investigates an approach for registering axons across histological serial sections. Tracing distinctly labeled axons over large distances allows neuroscientists to study very explicit relationships between the brain's complex interconnects and, for example, diseases or aberrant development. Large scale histological analysis requires, however, that the tissue be cut into sections. In immunohistochemical studies thin sections are easily distorted due to the cutting, preparation, and slide mounting processes. In this work we target the registration of thin serial sections containing axons. Sections are first traced to extract axon centerlines, and these traces are used to define registration landmarks where they intersect section boundaries. The trace data also provides distinguishing information regarding an axon's size and orientation within a section. We propose the use of these features when pairing axons across sections in addition to utilizing the spatial relationships among the landmarks. The global rotation and translation of an unregistered section are accounted for using a random sample consensus (RANSAC) based technique. An iterative nonrigid refinement process using B-spline warping is then used to reconnect axons and produce the sought after connectivity information.

Expression analysis of ~omics data using microarrays has become a standard procedure in the life sciences. However, microarrays are subject to technical limitations and errors, which render the data gathered likely to be uncertain. While a number of approaches exist to target this uncertainty statistically, it is hardly ever even shown when the data is visualized using for example clustered heatmaps. Yet, this is highly useful when trying not to omit data that is "good enough" for an analysis, which otherwise would be discarded as too unreliable by established conservative thresholds. Our approach addresses this shortcoming by first identifying the margin above the error threshold of uncertain, yet possibly still useful data. It then displays this uncertain data in the context of the valid data by enhancing a clustered heatmap. We employ different visual representations for the different kinds of uncertainty involved. Finally, it lets the user interactively adjust the thresholds, giving visual feedback in the heatmap representation, so that an informed choice on which thresholds to use can be made instead of applying the usual rule-of-thumb cut-offs. We exemplify the usefulness of our concept by giving details for a concrete use case from our partners at the Medical University of Graz, thereby demonstrating our implementation of the general approach.

We propose a metamorphic geodesic regression approach approximating spatial transformations for image time-series while simultaneously accounting for intensity changes. Such changes occur for example in magnetic resonance imaging (MRI) studies of the developing brain due to myelination. To simplify computations we propose an approximate metamorphic geodesic regression formulation that only requires pairwise computations of image metamorphoses. The approximated solution is an appropriately weighted average of initial momenta. To obtain initial momenta reliably, we develop a shooting method for image metamorphosis.

Image-space line integral convolution (LIC) is a popular approach for visualizing surface vector fields due to its simplicity and high efficiency. To avoid inconsistencies or color blur during the user interactions in the image-space approach, some methods use surface parameterization or 3D volume texture for the effect of smooth transition, which often require expensive computational or memory cost. Furthermore, those methods cannot achieve consistent LIC results in both granularity and color distribution on different scales.

This paper introduces a novel image-space LIC for surface flows that preserves the texture coherence during user interactions. To make the noise textures under different viewpoints coherent, we propose a simple texture mapping technique that is local, robust and effective. Meanwhile, our approach pre-computes a sequence of mipmap noise textures in a coarse-to-fine manner, leading to consistent transition when the model is zoomed. Prior to perform LIC in the image space, the mipmap noise textures are mapped onto each triangle with randomly assigned texture coordinates. Then, a standard image-space LIC based on the projected vector fields is performed to generate the flow texture. The proposed approach is simple and very suitable for GPU acceleration. Our implementation demonstrates consistent and highly efficient LIC visualization on a variety of datasets.