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Description: This article reflects the research of the last two decades in computational planning for cranio-maxillofacial surgery. Model-guided and computer-assisted surgery planning has tremendously developed due to ever increasing computational capabilities. Simulators for education, planning, and training of surgery are often compared with flight simulators, where maneuvers are also trained to reduce a possible risk of failure. Meanwhile, digital patient models can be derived from medical image data with astonishing accuracy and thus can serve for model surgery to derive a surgical template model that represents the envisaged result. Computerized surgical planning approaches, however, are often still explorative, meaning that a surgeon tries to find a therapeutic concept based on his or her expertise using computational tools that are mimicking real procedures. Future perspectives of an improved computerized planning may be that surgical objectives will be generated algorithmically by employing mathematical modeling, simulation, and optimization techniques. Planning systems thus act as intelligent decision support systems. However, surgeons can still use the existing tools to vary the proposed approach, but they mainly focus on how to transfer objectives into reality. Such a development may result in a paradigm shift for future surgery planning.

Description: The Ammonoidea is a group of extinct cephalopods ideal to study evolution through deep time. The evolution of the planispiral shell and complexly folded septa in ammonoids has been thought to have increased the functional surface area of the chambers permitting enhanced metabolic functions such as: chamber emptying, rate of mineralization and increased growth rates throughout ontogeny. Using nano-computed tomography and synchrotron radiation based micro-computed tomography, we present the first study of ontogenetic changes in surface area to volume ratios in the phragmocone chambers of several phylogenetically distant ammonoids and extant cephalopods. Contrary to the initial hypothesis, ammonoids do not possess a persistently high relative chamber surface area. Instead, the functional surface area of the chambers is higher in earliest ontogeny when compared to Spirula spirula. The higher the functional surface area the quicker the potential emptying rate of the chamber; quicker chamber emptying rates would theoretically permit faster growth. This is supported by the persistently higher siphuncular surface area to chamber volume ratio we collected for the ammonite Amauroceras sp. compared to either S. spirula or nautilids. We demonstrate that the curvature of the surface of the chamber increases with greater septal complexity increasing the potential refilling rates. We further show a unique relationship between ammonoid chamber shape and size that does not exist in S. spirula or nautilids. This view of chamber function also has implications for the evolution of the internal shell of coleoids, relating this event to the decoupling of soft-body growth and shell growth.

Description: Temperature-based estimation of time of death (ToD) can be per- formed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer mod- els. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We in- vestigate the impact of parameter variations and geometry representation on the estimated ToD based on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed to- mography (CT) data set, differentiating various organs and tissue types.

Description: Simulations and measurements of blood and air flow inside the human circulatory and respiratory system play an increasingly important role in personalized medicine for prevention, diagnosis, and treatment of diseases. This survey focuses on three main application areas. (1) Computational Fluid Dynamics (CFD) simulations of blood flow in cerebral aneurysms assist in predicting the outcome of this pathologic process and of therapeutic interventions. (2) CFD simulations of nasal airflow allow for investigating the effects of obstructions and deformities and provide therapy decision support. (3) 4D Phase-Contrast (4D PC) Magnetic Resonance Imaging (MRI) of aortic hemodynamics supports the diagnosis of various vascular and valve pathologies as well as their treatment. An investigation of the complex and often dynamic simulation and measurement data requires the coupling of sophisticated visualization, interaction, and data analysis techniques. In this paper, we survey the large body of work that has been conducted within this realm. We extend previous surveys by incorporating nasal airflow, addressing the joint investigation of blood flow and vessel wall properties, and providing a more fine-granular taxonomy of the existing techniques. From the survey, we extract major research trends and identify open problems and future challenges. The survey is intended for researchers interested in medical flow but also more general, in the combined visualization of physiology and anatomy, the extraction of features from flow field data and feature-based visualization, the visual comparison of different simulation results, and the interactive visual analysis of the flow field and derived characteristics.

Description: Volumetry of the cartilage of the knee, as needed for the assessment of knee osteoarthritis (KOA), is typically performed in a tedious and subjective process. We present an automated segmentation-based method for the quantification of cartilage volume by employing 3D Convolutional Neural Networks (CNNs). CNNs were trained in a supervised manner using magnetic resonance imaging data as well as cartilage volumetry readings given by clinical experts for 1378 subjects. It was shown that 3D CNNs can be employed for cartilage volumetry with an accuracy similar to expert volumetry readings. In future, accurate automated cartilage volumetry might support both, diagnosis of KOA as well as assessment of KOA progression via longitudinal analysis.

Description: Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.

Description: Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.

Description: Quantification of magnetic resonance (MR)-based relaxation parameters of tendons and ligaments is challenging due to their very short transverse relaxation times, requiring application of ultra-short echo-time (UTE) imaging sequences. We quantify both T1 and T2⁎ in the quadriceps and patellar tendons of healthy volunteers at a field strength of 3 T and visualize the results based on 3D segmentation by using bivariate histogram analysis. We applied a 3D ultra-short echo-time imaging sequence with either variable repetition times (VTR) or variable flip angles (VFA) for T1 quantification in combination with multi-echo acquisition for extracting T2⁎. The values of both relaxation parameters were subsequently binned for bivariate histogram analysis and corresponding cluster identification, which were subsequently visualized. Based on manually-drawn regions of interest in the tendons on the relaxation parameter maps, T1 and T2⁎ boundaries were selected in the bivariate histogram to segment the quadriceps and patellar tendons and visualize the relaxation times by 3D volumetric rendering. Segmentation of bone marrow, fat, muscle and tendons was successfully performed based on the bivariate histogram analysis. Based on the segmentation results mean T2⁎ relaxation times, over the entire tendon volumes averaged over all subjects, were 1.8 ms ± 0.1 ms and 1.4 ms ± 0.2 ms for the patellar and quadriceps tendons, respectively. The mean T1 value of the patellar tendon, averaged over all subjects, was 527 ms ± 42 ms and 476 ms ± 40 ms for the VFA and VTR acquisitions, respectively. The quadriceps tendon had higher mean T1 values of 662 ms ± 97 ms (VFA method) and 637 ms ± 40 ms (VTR method) compared to the patellar tendon. 3D volumetric visualization of the relaxation times revealed that T1 values are not constant over the volume of both tendons, but vary locally. This work provided additional data to build upon the scarce literature available on relaxation times in the quadriceps and patellar tendons. We were able to segment both tendons and to visualize the relaxation parameter distributions over the entire tendon volumes.

Description: We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.