Volkmar Liebscher

Prior Shape Level Set Segmentation on Multistep Generated Probability Maps of MR Datasets for Fully Automatic Kidney Parenchyma Volumetry

Fully automatic 3-D segmentation techniques for clinical applications or epidemiological studies have proven to be a very challenging task in the domain of medical image analysis. 3-D organ segmentation on magnetic resonance (MR) datasets requires a well-designed segmentation strategy due to imaging artifacts, partial volume effects, and similar tissue properties of adjacent tissues. We developed a 3-D segmentation framework for fully automatic kidney parenchyma volumetry that uses Bayesian concepts for probability map generation. The probability map quality is improved in a multistep refinement approach. An extended prior shape level set segmentation method is then applied on the refined probability maps. The segmentation quality is improved by incorporating an exterior cortex edge alignment technique using cortex probability maps. In contrast to previous approaches, we combine several relevant kidney parenchyma features in a sequence of segmentation techniques for successful parenchyma delineation on native MR datasets. Furthermore, the proposed method is able to recognize and exclude parenchymal cysts from the parenchymal volume. We analyzed four different quality measures showing better results for right parenchymal tissue than for left parenchymal tissue due to an incorporated liver part removal in the segmentation framework. The results show that the outer cortex edge alignment approach successfully improves the quality measures.

Modeling the Hes1 Oscillator

Somitogenesis describes the segmentation of vertebrate embryonic bodies, which is thought to be induced by ultradian clocks (i.e., clocks with relatively short cycles compared to circadian clocks). One candidate for such a clock is the bHLH factor Hes1, forming dimers which repress the transcription of its own encoding gene. Most models for such small autoregulative networks are based on delay equations where a Hill function represents the regulation of transcription. The aim of the present paper is to estimate the Hill coefficient in the switch of an Hes1 oscillator and to suggest a more detailed model of the autoregulative network. The promoter of Hes1 consists of three to four binding sites for Hes1 dimers. Using the sparse data from literature, we find, in contrast to other statements in literature, that there is not much evidence for synergistic binding in the regulatory region of Hes1, and that the Hill coefficient is about three. As a model for the negative feedback loop, we use a Goodwin system and find sustained oscillations for systems with a large enough number of linear differential equations. By a suitable variation of the number of equations, we provide a rational lower bound for the Hill coefficient for such a system. Our results suggest that there exist additional nonlinear processes outside of the regulatory region of Hes1.

A matter of dispersal: REVEALSinR introduces state-of-the-art dispersal models to quantitative vegetation reconstruction

The REVEALS model is applied in quantitative vegetation reconstruction to translate pollen percentage data from large lakes and peatlands into regional vegetation composition. The model was first presented in 2007 and has gained increasing attention. It is a core element of the Landcover 6k initiative within the PAGES project. The REVEALS model has two critical components: the pollen dispersal model and pollen productivity estimates (PPEs). To study the consequences of model settings, we implemented REVEALS in R. We use a state-of-the-art Lagrangian stochastic dispersal model (LSM) and compare model outcomes with calculations based on a conventional Gaussian plume dispersal model (GPM). In the LSM turbulence causes pollen fall speed to have little effect on the dispersal pattern whereas fall speed is a major factor in the GPM. Dispersal models are also used to derive PPEs. The unrealistic GPM produces PPEs that do not describe actual pollen productivity, but rather serve as a basin specific correction factor. A test with pollen and vegetation data from NE Germany shows that REVEALS performs best when applied with the LSM. REVEALS applications with the GPM can produce realistic results, but only if unrealistic PPEs are used. We discuss the derivation of PPEs and further REVEALS applications. Our REVEALS implementation is freely available as the ‘REVEALSinR’ function within the R package DISQOVER. REVEALSinR offers an environment for experimentation and analysing model sensitivities. We encourage further experiments and welcome comments on our tool.

Time Evolution and Invariance of Boson Systems Given by Beam Splittings

Based on a model for general beam splittings we search for states of boson systems which are invariant under the combination of the evolution given by the splitting procedure and some inherent evolution. It turns out that for finite systems only trivial invariant normal states may appear. However, for locally normal states on a related quasilocal algebra representing states of infinite boson systems, one can find examples of nontrivial invariant states. We consider as example a beam splitting combined with a contraction compensating the loss of intensity caused by the splitting process. In general, we observe interesting connections between the splitting procedure and certain thinning operations in classical probability theory. Several applications to physics seem to be natural since these beam splitting models are used to describe measuring procedures on electromagentic fields.

An efficient level set method for simultaneous intensity inhomogeneity correction and segmentation of MR images.

Intensity inhomogeneity (bias field) is a common artefact in magnetic resonance (MR) images, which hinders successful automatic segmentation. In this work, a novel algorithm for simultaneous segmentation and bias field correction is presented. The proposed energy functional allows for explicit regularization of the bias field term, making the model more flexible, which is crucial in presence of strong inhomogeneities. An efficient minimization procedure, attempting to find the global minimum, is applied to the energy functional. The algorithm is evaluated qualitatively and quantitatively using a synthetic example and real MR images of different organs. Comparisons with several state-of-the-art methods demonstrate the superior performance of the proposed technique. Desirable results are obtained even for images with strong and complicated inhomogeneity fields and sparse tissue structures.

A level set based framework for quantitative evaluation of breast tissue density from MRI data.

Breast density is a risk factor associated with the development of breast cancer. Usually, breast density is assessed on two dimensional (2D) mammograms using the American College of Radiology (ACR) classification. Magnetic resonance imaging (MRI) is a non-radiation based examination method, which offers a three dimensional (3D) alternative to classical 2D mammograms. We propose a new framework for automated breast density calculation on MRI data. Our framework consists of three steps. First, a recently developed method for simultaneous intensity inhomogeneity correction and breast tissue and parenchyma segmentation is applied. Second, the obtained breast component is extracted, and the breast-air and breast-body boundaries are refined. Finally, the fibroglandular/parenchymal tissue volume is extracted from the breast volume. The framework was tested on 37 randomly selected MR mammographies. All images were acquired on a 1.5T MR scanner using an axial, T1-weighted time-resolved angiography with stochastic trajectories sequence. The results were compared to manually obtained groundtruth. Dices Similarity Coefficient (DSC) as well as Bland-Altman plots were used as the main tools for evaluation of similarity between automatic and manual segmentations. The average Dices Similarity Coefficient values were and for breast and parenchymal volumes, respectively. Bland-Altman plots showed the mean bias () standard deviation equal for breast volumes and for parenchyma volumes. The automated framework produced sufficient results and has the potential to be applied for the analysis of breast volume and breast density of numerous data in clinical and research settings.

Piecewise-deterministic Markov processes as limits of Markov jump processes

A classical result about Markov jump processes states that a certain class of dynamical systems given by ordinary differential equations are obtained as the limit of a sequence of scaled Markov jump processes. This approach fails if the scaling cannot be carried out equally across all entities. In the present paper we present a convergence theorem for such an unequal scaling. In contrast to an equal scaling the limit process is not purely deterministic but still possesses randomness. We show that these processes constitute a rich subclass of piecewise-deterministic processes. Such processes apply in molecular biology where entities often occur in different scales of numbers.

Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes

In the present work we propose an alternative approach to model autocatalytic networks, called piecewise-deterministic Markov processes. These were originally introduced by Davis in 1984. Such a model allows for random transitions between the active and inactive state of a gene, whereas subsequent transcription and translation processes are modeled in a deterministic manner. We consider three types of autoregulated networks, each based on a positive feedback loop. It is shown that if the densities of the stationary distributions exist, they are the solutions of a system of equations for a one-dimensional correlated random walk. These stationary distributions are determined analytically. Further, the distributions are analyzed for different simulation periods and different initial concentration values by numerical means. We show that, depending on the network structure, beside a binary response also a graded response is observable.

Hybrid Modeling of Noise Reduction by a Negatively Autoregulated System

We analyze the reduction of intrinsic noise caused by transition of a promoter between its active and inactive state in a negatively regulated genetic network, i.e., transcription of the gene is inhibited by its own gene product. To measure the noise attenuation, we compare its behavior to an inducible gene for which activation and deactivation of the gene take place at constant rates.As a model, we choose a hybrid approach in which some of the reaction channels are modeled as discrete events, and other reactions are modeled as continuous processes. Such a model is appropriate for investigations of noise caused by low reactant numbers. By focusing on intrinsic noise originating from the switching behavior of the regulatory system of a particular gene, we model only the transition between two different promoter states as a discrete event.We show that the stationary distributions of the unregulated and the autoregulated system are given as a solution of two coupled ordinary differential equations. Also, beside the distribution densities, the first two central moments are derived in closed analytical forms. We give conditions on the parameters when one or the other system shows lower fluctuations.

An algebraic analysis of the two state Markov model on tripod trees.

Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such a model. This type of investigation has been undertaken before by several scientists from different fields of research. In contrast to other work we fully analyse the model, presenting conditions under which one can infer a model from the observation or at least get support for the tree-shaped interdependence of the leaves considered. We also present all conditions under which the results can be extended from tripod trees to quartet trees, a step necessary to reconstruct at least a topology. Apart from finding conditions under which such an extension works we discuss example cases for which such an extension does not work.