Tobias Preusser

Anisotropic diffusion in vector field visualization on Euclidean domains and surfaces

Vector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data on two and three-dimensional domains and on surfaces in an intuitively understandable way. Here, a new approach based on anisotropic nonlinear diffusion is introduced. It enables an easy perception of vector field data and serves as an appropriate scale space method for the visualization of complicated flow pattern. The approach is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. Here, an initial noisy image intensity is smoothed along integral lines, whereas the image is sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem. It is discretized only in the final implementational step. Therefore, many important qualitative aspects can already be discussed on a continuous level. Applications are shown for flow fields in 2D and 3D, as well as for principal directions of curvature on general triangulated surfaces. Furthermore, the provisions for flow segmentation are outlined.

High-intensity focused ultrasound: Principles, therapy guidance, simulations and applications

In the past two decades, high-intensity focused ultrasound (HIFU) in combination with diagnostic ultrasound (USgFUS) or magnetic resonance imaging (MRgFUS) opened new ways of therapeutic access to a multitude of pathologic conditions. The therapeutic potential of HIFU lies in the fact that it enables the localized deposition of high-energy doses deep within the human body without harming the surrounding tissue. The addition of diagnostic ultrasound or in particular MRI with HIFU allows for planning, control and direct monitoring of the treatment process. The clinical and preclinical applications of HIFU range from the thermal treatment of benign and malign lesions, targeted drug delivery, to the treatment of thrombi (sonothrombolysis). Especially the therapy of prostate cancer under US-guidance and the ablation of benign uterine fibroids under MRI monitoring are now therapy options available to a larger number of patients. The main challenges for an abdominal application of HIFU are posed by partial or full occlusion of the target site by bones or air filled structures (e.g. colon), as well as organ motion. In non-trivial cases, the implementation of computer based modeling, simulation and optimization is desirable. This article describes the principles of HIFU, ultrasound and MRI therapy guidance, therapy planning and simulation, and gives an overview of the current and potential future applications.

The virtual liver: a multidisciplinary, multilevel challenge for systems biology

The liver is the central metabolic organ in human physiology, with functions that are fundamentally important to the detoxification of xenobiotics (drugs), the maintenance of homeostasis of numerous blood metabolites, and the production of mediators of the acute phase response. Liver toxicity, whether actual or implied is the reason for the failure of a significant proportion of many promising novel medicines that consequently never reach the market, and diseases such as atherosclerosis, diabetes, and fatty liver diseases, that are a major burden on current health resources, are directly linked to functional and structural disorders of the liver. This article presents the concepts and approaches underpinning one of the most exciting and ambitious modeling projects in the field of systems biology and systems medicine. This major multidisciplinary research program is aimed at developing a whole‐organ model of the human liver, representing its central physiological functions under normal and pathological conditions The model will be composed of a larger battery of interconnected submodels representing liver anatomy and physiology, integrating processes across hierarchical levels in space, time, and structural organization. In this article, we outline the general architecture of the liver model and present first step taken to reach this ambitious goal. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1158

Anisotropic nonlinear diffusion in flow visualization

Vector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data in an intuitively understandable and precise way. Here a new approach based on anisotropic nonlinear diffusion is introduced. It enables an easy perception of flow data and serves as an appropriate scale space method for the visualization of complicated flow patterns. The approach is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. An initial noisy image is smoothed along streamlines, whereas the image is sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem. It is discretized only in the final implementational step. Therefore, many important qualitative aspects can already be discussed on a continuous level. Applications are shown in 2D and 3D and the provisions for flow segmentation are outlined.

Numerical simulation of radio frequency ablation with state dependent material parameters in three space dimensions

We present a model for the numerical simulation of radio frequency (RF) ablation of tumors with mono- or bipolar probes. This model includes the electrostatic equation and a variant of the well-known bio-heat transfer equation for the distribution of the electric potential and the induced heat. The equations are nonlinearly coupled by material parameters that change with temperature, dehydration and damage of the tissue. A fixed point iteration scheme for the nonlinear model and the spatial discretization with finite elements are presented. Moreover, we incorporate the effect of evaporation of water from the cells at high temperatures using a predictor-corrector like approach. The comparison of the approach to a real ablation concludes the paper.

A LEVEL SET METHOD FOR ANISOTROPIC GEOMETRIC DIFFUSION IN 3D IMAGE PROCESSING

A new morphological multiscale method in three-dimensional (3D) image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth the level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic curvature evolution, where time serves as the multiscale parameter. Thereby the diffusion tensor depends on a regularized shape operator of the evolving level sets. As one suitable regularization, local L2 projection onto quadratic polynomials is considered. The method is compared to a related parametric surface approach, and a geometric interpretation of the evolution and its invariance properties is given. A spatial finite element discretization on hexahedral meshes and a semi-implicit, regularized backward Euler discretization in time are the building blocks of the easy-to-code algorithm. Different a...

STOCHASTIC COLLOCATION FOR OPTIMAL CONTROL PROBLEMS WITH STOCHASTIC PDE CONSTRAINTS

We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). Thereby the constraining SPDE depends on data which is not deterministic but random. Assuming a deter- ministic control, randomness within the states of the input data will propagate to the states of the system. For the solution of SPDEs there has recently been an increasing effort in the development of efficient numerical schemes based upon the mathematical concept of generalized polynomial chaos. Modal-based stochastic Galerkin and nodal-based stochastic collocation versions of this methodol- ogy exist, both of which rely on a certain level of smoothness of the solution in the random space to yield accelerated convergence rates. In this paper we apply the stochastic collocation method to develop a gradient descent as well as a sequential quadratic program (SQP) for the minimization of objective functions constrained by an SPDE. The stochastic function involves several higher-order moments of the random states of the system as well as classical regularization of the control. In particular we discuss several objective functions of tracking type. Numerical examples are presented to demonstrate the performance of our new stochastic collocation minimization approach.

A phase field model for continuous clustering on vector fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn-Hilliard (1958) model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional, where time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns, during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution, a shear-layer-type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. We discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross-streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.

Flow Field Clustering via Algebraic Multigrid

We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite element technique. The entries of the corresponding stiffness matrix represent the anisotropically weighted couplings of adjacent nodes of the domain mesh. We use an algebraic multigrid algorithm to generate a hierarchy of fine to coarse descriptions for the above coupling data. This hierarchy comprises a set of coarse grid nodes, a multiscale of basis functions and their corresponding supports. We use these supports to obtain a multilevel decomposition of the flow structure. Standard streamline icons are used to visualize this decomposition at any user-selected level of detail. The method provides a single framework for vector field decomposition independent on the domain dimension or mesh type. Applications are shown in 2D, for flow fields on curved surfaces, and for 3D volumetric flow fields.

Spatio-temporal simulation of first pass drug perfusion in the liver.

The liver is the central organ for detoxification of xenobiotics in the body. In pharmacokinetic modeling, hepatic metabolization capacity is typically quantified as hepatic clearance computed as degradation in well-stirred compartments. This is an accurate mechanistic description once a quasi-equilibrium between blood and surrounding tissue is established. However, this model structure cannot be used to simulate spatio-temporal distribution during the first instants after drug injection. In this paper, we introduce a new spatially resolved model to simulate first pass perfusion of compounds within the naive liver. The model is based on vascular structures obtained from computed tomography as well as physiologically based mass transfer descriptions obtained from pharmacokinetic modeling. The physiological architecture of hepatic tissue in our model is governed by both vascular geometry and the composition of the connecting hepatic tissue. In particular, we here consider locally distributed mass flow in liver tissue instead of considering well-stirred compartments. Experimentally, the model structure corresponds to an isolated perfused liver and provides an ideal platform to address first pass effects and questions of hepatic heterogeneity. The model was evaluated for three exemplary compounds covering key aspects of perfusion, distribution and metabolization within the liver. As pathophysiological states we considered the influence of steatosis and carbon tetrachloride-induced liver necrosis on total hepatic distribution and metabolic capacity. Notably, we found that our computational predictions are in qualitative agreement with previously published experimental data. The simulation results provide an unprecedented level of detail in compound concentration profiles during first pass perfusion, both spatio-temporally in liver tissue itself and temporally in the outflowing blood. We expect our model to be the foundation of further spatially resolved models of the liver in the future.