Efficient liver segmentation in CT images based on graph cuts and bottleneck detection

Liver segmentation from abdominal computed tomography (CT) volumes is extremely important for computer-aided liver disease diagnosis and surgical planning of liver transplantation. Due to ambiguous edges, tissue adhesion, and variation in liver intensity and shape across patients, accurate liver segmentation is a challenging task. In this paper, we present an efficient semi-automatic method using intensity, local context, and spatial correlation of adjacent slices for the segmentation of healthy liver regions in CT volumes. An intensity model is combined with a principal component analysis (PCA) based appearance model to exclude complex background and highlight liver region. They are then integrated with location information from neighboring slices into graph cuts to segment the liver in each slice automatically. Finally, a boundary refinement method based on bottleneck detection is used to increase the segmentation accuracy. Our method does not require heavy training process or statistical model construction, and is capable of dealing with complicated shape and intensity variations. We apply the proposed method on XHCSU14 and SLIVER07 databases, and evaluate it by MICCAI criteria and Dice similarity coefficient. Experimental results show our method outperforms several existing methods on liver segmentation.     

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.     

Spot shape modelling and data transformations for microarrays

MOTIVATION: To study lowly expressed genes in microarray experiments, it is useful to increase the photometric gain in the scanning. However, a large gain may cause some pixels for highly expressed genes to become saturated. Spatial statistical models that model spot shapes on the pixel level may be used to infer information about the saturated pixel intensities. Other possible applications for spot shape models include data quality control and accurate determination of spot centres and spot diameters. RESULTS: Spatial statistical models for spotted microarrays are studied including pixel level transformations and spot shape models. The models are applied to a dataset from 50mer oligonucleotide microarrays with 452 selected Arabidopsis genes. Logarithmic, Box-Cox and inverse hyperbolic sine transformations are compared in combination with four spot shape models: a cylindric plateau shape, an isotropic Gaussian distribution and a difference of two-scaled Gaussian distribution suggested in the literature, as well as a proposed new polynomial-hyperbolic spot shape model. A substantial improvement is obtained for the dataset studied by the polynomial-hyperbolic spot shape model in combination with the Box-Cox transformation. The spatial statistical models are used to correct spot measurements with saturation by extrapolating the censored data. AVAILABILITY: Source code for R is available at http://www.matfys.kvl.dk/~ekstrom/spotshapes/     

A Statistical Skull Geometry Model for Children 0-3 Years Old

Head injury is the leading cause of fatality and long-term disability for children. Pediatric heads change rapidly in both size and shape during growth, especially for children under 3 years old (YO). To accurately assess the head injury risks for children, it is necessary to understand the geometry of the pediatric head and how morphologic features influence injury causation within the 0–3 YO population. In this study, head CT scans from fifty-six 0–3 YO children were used to develop a statistical model of pediatric skull geometry. Geometric features important for injury prediction, including skull size and shape, skull thickness and suture width, along with their variations among the sample population, were quantified through a series of image and statistical analyses. The size and shape of the pediatric skull change significantly with age and head circumference. The skull thickness and suture width vary with age, head circumference and location, which will have important effects on skull stiffness and injury prediction. The statistical geometry model developed in this study can provide a geometrical basis for future development of child anthropomorphic test devices and pediatric head finite element models.     

Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy

PurposeBiological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2) are needed for treatment planning and plan evaluation in carbon ion therapy. We present a model-independent, Monte Carlo based sensitivity analysis (SA) approach to quantify the impact of different uncertainties on the biological models.Methods and materialsThe Monte Carlo based SA is used for the evaluation of variations in biological parameters. The key property of this SA is the high number of simulation runs, each with randomized input parameters, allowing for a statistical variance-based ranking of the input variations. The potential of this SA is shown in a simplified one-dimensional treatment plan optimization. Physical properties of carbon ion beams (e.g. fragmentation) are simulated using the Monte Carlo code FLUKA. To estimate biological effects of ion beams compared to X-rays, we use the Local Effect Model (LEM) in the framework of the linear-quadratic (LQ) model. Currently, only uncertainties in the output of the biological models are taken into account.Results/conclusionsThe presented SA is suitable for evaluation of the impact of variations in biological parameters. Major advantages are the possibility to access and display the sensitivity of the evaluated quantity on several parameter variations at the same time. Main challenges for later use in three-dimensional treatment plan evaluation are computational time and memory usage. The presented SA can be performed with any analytical or numerical function and hence be applied to any biological model used in carbon ion therapy.     

Geographical differences in habitat relationships of cetaceans across an ocean basin

The distributions of highly mobile marine species such as cetaceans are increasingly modeled at basin scale by combining data from multiple regions. However, these basin-wide models often overlook geographical variations in species habitat relationships between regions. We tested for geographical variations in habitat relationships for a suite of cetacean taxa between the two sides of the North Atlantic basin. Using cetacean visual survey data and remote sensing data from the western and eastern basin in summer, we related the probability of presence of twelve cetacean taxa from three guilds to seafloor depth, sea surface temperature and primary productivity. In a generalized additive model framework, we fitted 1) basin-wide (BW) models, assuming a single global relationship, 2) region-specific intercepts (RI) models, assuming relationships with the same shape in both regions, but allowing a region-specific intercept and 3) region-specific shape (RS) models, assuming relationships with different shapes between regions. RS models mostly yielded significantly better fits than BW models, indicating cetacean occurrences were better modeled with region-specific than with global relationships. The better fits of RS models over RI models further provided statistical evidence for differences in the shapes of region-specific relationships. Baleen whales showed striking differences in both the shapes of relationships and their mean presence probabilities between regions. Deep diving whales and delphinoids showed contrasting relationships between regions with few exceptions (e.g. non-statistically different shapes of region-specific relationships for harbor porpoise and beaked whales with depth). Our findings stress the need to account for geographical differences in habitat relationships between regions when modeling species distributions from combined data at the basin scale. Our proposed hypotheses offer a roadmap for understanding why habitat relationships may geographically vary in cetaceans and other highly mobile marine species.     

Statistical shape modeling characterizes three-dimensional shape and alignment variability in the lumbar spine

The mechanics of the lumbar spine are heavily dependent on the underlying anatomy. Anatomical measures are used to assess the progression of pathologies related to low back pain and to screen patients for surgical treatment options. To describe anatomical norms and pathological differences for the population, statistical shape modeling, which uses full three-dimensional representations of bone morphology and relative alignment, can capture intersubject variability and enable comparative evaluations of subject to population. Accordingly, the objective of this study was to develop a comprehensive set of three-dimensional statistical models to characterize anatomical variability in the lumbar spine, by specifically describing the shape of individual vertebrae, and shape and alignment of the entire lumbar spine (L1-S1), with a focus on the L4-L5 and L5-S1 functional spinal units (FSU). Using CT scans for a cohort of 52 patients, lumbar spine geometries were registered to a template to establish correspondence and a principal component analysis identified the primary modes of variation. Scaling was the most prevalent mode of variation for all models. Subsequent modes of the statistical shape models of the individual bones characterized shape variation within the processes. Subsequent modes of variation for the FSU and entire spine models described alignment changes associated with disc height and lordosis. Quantification of anatomical variation in the spine with statistical models can inform implant design and sizing, assist clinicians in diagnosing pathologies, screen patients for treatment options, and support pre-operative planning.     

Modeling diurnal variation of marine populations

A number of marine populations exhibit diurnal variations in their behavioral pattern, and this phenomenon has been studied by several authors looking at a variety of species. But to our knowledge, fully adequate statistical tools have not been used in a comprehensive and systematic way. It is the goal of this article to bring forward relevant statistical techniques and to demonstrate how they can be used. Both parametric and nonparametric methods are employed, and we concentrate on such basic statistical issues as testing for the presence of diurnal variations using a nonparametric test and on estimating and testing the shape of diurnal oscillations. We indicate how this can be used to examine the effect of light on diurnal behavior. Our methods are illustrated using data from bottom trawl catches of cod (Gadus morhua) collected during winter surveys in the Barents Sea in the period 1985-1999.     

A Novel Atlas-Based Strategy for Understanding Cardiac Dysfunction in Patients with Congenital Heart Disease

Tetralogy of Fallot (TOF) is the most common form of cyanotic congenital heart disease. Infants diagnosed with TOF require surgical interventions to survive into adulthood. However, as a result of postoperative structural malformations and long-term ventricular remodeling, further interventions are often required later in life. To help identify those at risk of disease progression, serial cardiac magnetic resonance (CMR) imaging is used to monitor these patients. However, most of the detailed information on cardiac shape and biomechanics contained in these large four-dimensional (4D) data sets goes unused in clinical practice for lack of efficient and comprehensive quantitative analysis tools. While current global metrics of cardiac size and function, such as indexed ventricular mass and volumes, can identify patients at risk of further complications, they are not adequate to explain the underlying mechanisms causing the postoperative malfunctions, and help cardiologists plan optimal personalized treatments. We are proposing a novel approach that uses 4D ventricular shape models derived from CMR imaging exams to generate statistical atlases of ventricular shape and finite-element models of ventricular biomechanics to identify specific features of cardiac shape and biomechanical properties that explain variations in ventricular function. This study has the potential to discover novel biomarkers that precede adverse ventricular remodeling and dysfunction.     

Modeling regionalized volumetric differences in protein-ligand binding cavities

Identifying elements of protein structures that create differences in protein-ligand binding specificity is an essential method for explaining the molecular mechanisms underlying preferential binding. In some cases, influential mechanisms can be visually identified by experts in structural biology, but subtler mechanisms, whose significance may only be apparent from the analysis of many structures, are harder to find. To assist this process, we present a geometric algorithm and two statistical models for identifying significant structural differences in protein-ligand binding cavities. We demonstrate these methods in an analysis of sequentially nonredundant structural representatives of the canonical serine proteases and the enolase superfamily. Here, we observed that statistically significant structural variations identified experimentally established determinants of specificity. We also observed that an analysis of individual regions inside cavities can reveal areas where small differences in shape can correspond to differences in specificity.     

The burgeoning field of statistical phylogeography

In the newly emerging field of statistical phylogeography, consideration of the stochastic nature of genetic processes and explicit reference to theoretical expectations under various models has dramatically transformed how historical processes are studied. Rather than being restricted to ad hoc explanations for observed patterns of genetic variation, assessments about the underlying evolutionary processes are now based on statistical tests of various hypotheses, as well as estimates of the parameters specified by the models. A wide range of demographical and biogeographical processes can be accommodated by these new analytical approaches, providing biologically more realistic models. Because of these advances, statistical phylogeography can provide unprecedented insights about a species' history, including decisive information about the factors that shape patterns of genetic variation, species distributions, and speciation. However, to improve our understanding of such processes, a critical examination and appreciation of the inherent difficulties of historical inference and challenges specific to testing phylogeographical hypotheses are essential. As the field of statistical phylogeography continues to take shape many difficulties have been resolved. Nonetheless, careful attention to the complexities of testing historical hypotheses and further theoretical developments are essential to improving the accuracy of our conclusions about a species' history.     

Assessment of scapular morphology and bone quality with statistical models

The design of total shoulder arthroplasty implants are guided by anatomy. The objective of this study was to develop statistical models to quantify shape and material property variation in the scapula. Material-mapped models were reconstructed from CT scans for a training set of subjects. Statistical shape (SSM) and intensity (SIM) models were created; SSM modes described scaling, changes in the medial border and acromial process, and elongation of the scapular blade. SIM modes captured bone quality changes in the anterior and inferior glenoid. Bone quality was independent of scapular morphology. Variation described by the statistical representations can inform implant design and sizing.     

Morphing methods to parameterize specimen-specific finite element model geometries

Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens.We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties.     

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.     

Modeling normal and altered human erythrocyte shapes by a new parametric equation: application to the calculation of induced transmembrane potentials

We present simple parametric equations in terms of Jacobi elliptic functions that provide a realistic model of abnormal variations in size which maintain the biconcave shape of a normal erythrocyte (anisocytosis) and abnormal variations in shape which maintain the original volume of the erythrocyte (poikilocytosis), as well as continuous deformations from the normal to the altered shapes. We illustrate our results with parameterizations of microcytes, macrocytes, and stomatocytes, and we apply these parameterizations to the numerical calculation of the induced transmembrane voltage in microcytes, macrocytes, and stomatocytes exposed to an external electromagnetic field of 1800 MHz.     

Biological clock mutants and parameter changes in mathematical models

A number of recent experiments have revealed the existence of mutants with different free run periods in their circadian rhythms. Parameter variations in mathematical models can be used to simulate such changes. In addition, phase response curves (PRC) are derived and the effect of parameter variation in their shape is studied. It is shown that changes in global parameters can also distort their shape. Therefore one cannot conclude that genetic experiments provide evidence in favor of “chronon” models since “kinetic” models can also simulate their outcome.     

Automatic methods for characterization of sexual dimorphism of adult femora: distal femur

Quantifying sex differences in femoral size and shape has extensive applications in forensics and prosthesis design. By applying strong statistical techniques such as principal component analysis (PCA), certain three-dimensional (3D) morphological variations of adult femora can be quantified over various femoral sizes. Coupling this statistical approach with a novel feature generation and extraction technique, localization of statistically significant (p<0.05) features are automatically defined and measured. Also, predefined anatomical landmarks and surgical axes have been calculated automatically. In all methods, femoral scale is controlled as a possible parameter of shape. By extensively comparing measurements across 92 male and 74 female femora, the dimorphic characteristics of the distal femur are shown. These differences have not been accounted for in many prosthetic systems and consequently these systems have limited sizing accuracy.     

Seed shape in model legumes: Approximation by a cardioid reveals differences in ethylene insensitive mutants of Lotus japonicus and Medicago truncatula

Seed shape in the model legumes Lotus japonicus and Medicago truncatula is described. Based in previous work with Arabidopsis, the outline of the longitudinal sections of seeds is compared with a cardioid curve. L. japonicus seeds adjust well to an unmodified cardioid, whereas accurate adjustment in M. truncatula is obtained by the simple transformation of scaling the vertical axis by a factor equal to the Golden Ratio. Adjustments of seed shape measurements with simple geometrical forms are essential tools for the statistical analysis of variations in seed shape under different conditions or in mutants. The efficiency of the adjustment to a cardioid in the model plants suggests that seed morphology may be related to genome complexity. Seeds of ethylene insensitive mutants present differences in size and shape as well as altered responses to imbibition. The biological implication and meaning of these relationships are discussed.     

Nested Sampling for Bayesian Model Comparison in the Context of Salmonella Disease Dynamics

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike''s Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.