[Show abstract][Hide abstract] ABSTRACT: A sophisticated combination of noise reducing, segmentation and meshgeneration methods provides the reconstruction of the surface morphology fromthree dimensional computed tomography scans of archaeological data as triangularsurface meshes. The highly parallelized GPU-enabled implementation of the algo-rithm processes large data sets in only a few minutes, allowing the systematic recon-struction of various objects. Rendering of the generated triangular meshes and thecalculation of the surface area and the volume of the reconstructed items or selectedparts of interest, can be done in real time. Those items can also be exchanged byscientists around the world and can be investigated without manipulating the irre-placeable artifacts. The application of computed tomography and the developmentof archaeological adjusted post processing of the acquired volumetric data enablea non-destructive investigation of the entire object regarding shape, manufacturingtechniques or material textures. The reconstructions can also serve as a basis forvirtual exhibitions.
edited by Hans Georg Bock; Willi Jäger; Michael Winckler, 08/2013; Springer., ISBN: 978-3-642-28021-4
[Show abstract][Hide abstract] ABSTRACT: The scope of this manuscript is to investigate the role of the Forchheimer correction in the description of variable-density flow in fractured porous media. A fractured porous medium, which shall be also referred to as “the embedding medium”, represents a flow region that is made macroscopically heterogeneous by the presence of fractures. Fractures are assumed to be filled with a porous medium characterized by flow properties that differ appreciably from those of the embedding medium. The fluid, which is free to move in the pore space of the entire flow region, is a mixture of water and brine. Flow is assumed to be a consequence of the variability of the fluid mass density in response to the generally nonuniform distribution of brine, which is subject to diffusion and convection. The fractures are assumed to be thin in comparison with the characteristic sizes of the embedding medium. Within this framework, some benchmark problems are solved by adopting two approaches: (i) the fractures are treated as thin but
-dimensional flow subregions, with
being the geometric dimension of the embedding medium; (ii) the fractures are regarded as
-dimensional manifolds. In the first approach, the equations of variable-density flow are written in the same,
-dimensional form both in the fractures and in the embedding medium. In the second approach, instead, new equations are obtained by averaging the
-dimensional ones over the fracture width. The reliability of the second approach is discussed by comparing the results of the
-dimensional numerical simulations of the selected benchmark problems with those obtained by using the
-dimensional approach. Moreover, the deviations of the results determined by accounting for the Forchheimer correction to flow velocity are compared with those predicted by Darcy’s law.
[Show abstract][Hide abstract] ABSTRACT: In this article a mathematical model is introduced, which estimates the distribution of the four anaerobic digestion phases (hydrolysis, acidogenesis, acetogenesis and methanogenesis) that occur among the leach bed reactor and the anaerobic filter of a biogas plant. It is shown that only the hydrolysis takes place in the first stage (leach bed reactor), while all other anaerobic digestion phases take place in both reactor stages. It turns out that, besides the usually measured raw materials of the acetogenesis and the methanogenesis phases (organic acids), it is also necessary to analyze the process liquid for raw materials of the acidogenesis phase, i.e., sugars, fatty acids, amino acids, etc. The introduced model can be used to monitor the inhibition of the anaerobic digestion phases in reactor stages and can, thus, help to improve the control system of biogas plants.
[Show abstract][Hide abstract] ABSTRACT: Data from 24 full scale biogas plants in Germany digesting cow manure and crops were evaluated. Special emphasis was given to the effect of hydraulic retention time HRT and proportion of crops in the mixture (VS basis) p(VS,Crops)(Inp) on the methane yield from the digester [Formula: see text] and the storage tank [Formula: see text] at 37 and 22°C. The evaluation has shown model parameters for maximal methane yield of manure and crops [Formula: see text] at 270 and 420 Lkg(-1), respectively. For example, at HRT of 60days, maximum methane yield result to 249 and 388 Lkg(-1) for a crop proportion in the input of 0.0 and 1.0, respectively. The calculation of [Formula: see text] considers first order reaction rates and a temperature term f(T). Hence, at any arbitrary temperature in the range of 12°C<T<37°C the values of [Formula: see text] in the course of time can be calculated, which correspond to methane emissions for uncovered storage tanks.
[Show abstract][Hide abstract] ABSTRACT: In recent years, the combination of computational modeling and experiments has become a useful tool that is proving increasingly powerful for explaining biological complexity. As computational power is increasing, scientists are able to explore ever more complex models in finer detail and to explain very complex real world data. This work provides an overview of one-, two- and three-dimensional diffusion models for penetration into mammalian skin. Besides diffusive transport this includes also binding of substances to skin proteins and metabolism. These models are based on partial differential equations that describe the spatial evolution of the transport process through the biological barrier skin. Furthermore, the work focuses on analytical and numerical techniques for this type of equations such as discretization schemes or homogenization (upscaling) techniques. Finally, the work compares different geometry models with respect to the permeability.
Advanced drug delivery reviews 11/2012; · 11.96 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work investigates in vitro finite dose skin absorption of the model compounds flufenamic acid and caffeine experimentally and mathematically. The mass balance in different skin compartments (donor, stratum corneum (SC), deeper skin layers (DSL), lateral skin parts and acceptor) is analyzed as a function of time. For both substances high amounts were found in the lateral skin compartment after 6 hours of incubation, which emphasizes not to elide these parts in the modeling. Here, three different mathematical models were investigated and tested with the experimental data: a pharmacokinetic model (PK), a detailed microscopic two-dimensional diffusion model (MICRO) and a macroscopic homogenized diffusion model (MACRO). While the PK model was fitted to the experimental data, the MICRO and the MACRO models employed input parameters derived from infinite dose studies to predict the underlying diffusion process. All models could satisfyingly predict or describe the experimental data. The PK model and MACRO model also feature the lateral parts.
Journal of Controlled Release 10/2012; · 7.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: SpineLab is a software tool developed for reconstructing neuronal feature skeletons from three-dimensional single- or multi-photon image stacks. These images often suffer from limited resolution and a low signal-to-noise ratio, making the extraction of morphometric information difficult. To overcome this limitation, we have developed a software tool that offers the possibility to create feature skeletons in various modes-automatically as well as with manual interaction. We have named this novel tool SpineLab. In a first step, an investigator adjusts a set of parameters for automatic analysis in an interactive manner, i.e., with online visual feedback, followed by a second step, in which the neuronal feature skeleton can be modified by hand. We validate the ability of SpineLab to reconstruct the entire dendritic tree of identified GFP-expressing neurons and evaluate the accuracy of dendritic spine detection. We report that SpineLab is capable of significantly facilitating the reconstruction of dendrites and spines. Moreover, the automatic approach appears sufficient to detect spine density changes in time-lapse imaging experiments. Taken together, we conclude that SpineLab is an ideal software tool for partially automatic reconstruction of neural cell morphology.
Journal of Biomedical Optics 07/2012; 17(7):076007. · 2.88 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We represent a biological tissue by a multi-constituent, fiber-reinforced material, in which we consider two phases: fluid, and a fiber-reinforced solid. Among the various processes that may occur in such a system, we study growth, mass transfer, and remodeling. To us, mass transfer is the reciprocal exchange of constituents between the phases, growth is the variation of mass of the system in response to interactions with the surrounding environment, and remodeling is the evolution of its internal structure. We embrace the theory according to which these events, which lead to a structural reorganization of the system and anelastic deformations, require the introduction of balance laws, which complete the physical picture offered by the standard ones. The former are said to be non-standard. Our purposes are to determine the rates of anelastic deformation related to mass transfer and growth, and to study fiber reorientation in the case of a statistical distribution of fibers. In particular, we discuss the use of the non-standard balance laws in modeling transfer of mass, and compare our results with a formulation in which such balance laws are not introduced.
International Journal of Non-linear Mechanics - INT J NON-LINEAR MECH. 03/2012;
[Show abstract][Hide abstract] ABSTRACT: We consider a standard Adaptive Edge Finite Element Method (AEFEM) based on arbitrary order Nédélec edge elements, for three-dimensional indefinite time-harmonic Maxwell equations. We prove that the AEFEM gives a contraction for the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. Using the geometric decay, we show that the AEFEM yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom. The main technical contribution of the paper is the establishment of a quasi-orthogonality and a localized a posteriori error estimator.
Mathematics of Computation 01/2012; 81. · 1.37 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work presents an extension of grid generation techniques for finite-volume discretizations of density-driven flow in fractured porous media, in which fractures are considered as low-dimensional manifolds and are resolved by sides of grid elements. The proposed technique introduces additional degrees of freedom for the unknowns assigned to the fractures and thus allows to reconstruct jumps of the solution over a fracture. Through the concept of degenerated elements, the proposed technique can be used for arbitrary junctions of fractures but is sufficiently simple regarding the implementation and allows for the application of conventional numerical solvers. Numerical experiments presented at the end of the paper demonstrate the applicability of this technique in two and three dimensions for complicated fracture networks.
Computing and Visualization in Science 01/2012; 15(4).
[Show abstract][Hide abstract] ABSTRACT: Acetoclastic methanogenesis in the second stage of a two-phase biogas reactor is investigated. A mathematical model coupling chemical reactions with transport of process liquid and with the variation of population of the microorganisms living on the plastic tower packing of the reactor is proposed. The evolution of the liquid is described by an advection-diffusion-reaction equation, while a monod-type kinetic is used for the reactions. Moreover, a new inhibition factor MO(max) is introduced, which hinders the growth of microorganisms when the plastic tower packing is overpopulated. After estimating the reaction parameters, the acetate outflow measured experimentally is in good agreement with that predicted by simulations. For coupling liquid transport with reaction processes, a spatial discretization of the reactor is performed. This yields essential information about the distribution of acetate and the production of methane in the reactor. This information allows for defining a measure of the effectiveness of the reactor.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider the fast computation of integral terms arising in simulations of structured populations modeled by integro-differential equations. This is of enormous relevance for demographic studies in which populations are structured by a large number of variables (often called i-states) like age, gender, income etc. This holds equally for applications in ecology and biotechnology. In this paper we will concentrate on an example describing microbial growth. For this class of problems we apply the panel clustering method that has str almost linear complexity for many integral kernels that are of interest in the field of biology. We further present the primitive function method as an improved version of the panel clustering for the case that the kernel function is non-smooth on hypersurfaces. We compare these methods with a conventional numerical integration algorithm, all used in-side standard discretization schemes for the complete system of integro-differential equations.
Mathematical Models and Methods in Applied Sciences 11/2011; 16(12). · 1.87 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a numerical technique for the simulation of salinity- as well as thermohaline-driven flows in fractured porous
media. In this technique, the fractures are represented by low-dimensional manifolds, on which a low-dimensional variant of
the PDEs of variable-density flow is formulated. The latter is obtained from the full-dimensional model by the average-along-the-vertical.
The discretization of the resulting coupled system of the full- and low-dimensional PDEs is based on a finite-volume method.
This requires a special construction of the discretization grid which can be obtained by the algorithm presented in this work.
This technique allows to reconstruct in particular the jumps of the solution at the fracture. Its precision is demonstrated
in the numerical comparisons with the results obtained in the simulations where the fractures are represented by the full-dimensional
[Show abstract][Hide abstract] ABSTRACT: Modeling biophysical processes in general requires knowledge about underlying biological parameters. The quality of simulation results is strongly influenced by the accuracy of these parameters, hence the identification of parameter values that the model includes is a major part of simulating biophysical processes. In many cases, secondary data can be gathered by experimental setups, which are exploitable by mathematical inverse modeling techniques. Here we describe a method for parameter identification of diffusion properties of calcium in the nuclei of rat hippocampal neurons. The method is based on a Gauss-Newton method for solving a least-squares minimization problem and was formulated in such a way that it is ideally implementable in the simulation platform uG. Making use of independently published space- and time-dependent calcium imaging data, generated from laser-assisted calcium uncaging experiments, here we could identify the diffusion properties of nuclear calcium and were able to validate a previously published model that describes nuclear calcium dynamics as a diffusion process.
[Show abstract][Hide abstract] ABSTRACT: The scheme of inertia based anisotropic diffusion is a very powerful noise reducing and structure preserving image processing operator. This paper presents an implementation of this time consuming filter process on a cluster of Nvidia Tesla high performance computing processors, which can be applied to very large amounts of data in only a few minutes. Applying the inertia based diffusion filter to high resolution image stacks of neuron cells provides fully automatic geometric reconstructions of these images on a scale of <1μm. Such a high throughput and automatic image processing tool has great impact on various research areas, in particular the fast growing field of computational neuroscience, where one encounters increasing amount of microscopy data that needs to be processed.
Computing and Visualization in Science 04/2011; 14(4).
[Show abstract][Hide abstract] ABSTRACT: A simulation environment for the numerical calculation of permeation processes through human skin has been developed. In geometry models that represent the actual cell morphology of stratum corneum (SC) and deeper skin layers, the diffusive transport is simulated by a finite volume method. As reference elements for the corneocyte cells and lipid matrix, both three-dimensional tetrakaidecahedra and cuboids as well as two-dimensional brick-and-mortar models have been investigated. The central finding is that permeability and lag time of the different membranes can be represented in a closed form depending on model parameters and geometry. This allows a comparison of the models in terms of their barrier effectiveness at comparable cell sizes. The influence of the cell shape on the barrier properties has been numerically demonstrated and quantified. It is shown that tetrakaidecahedra in addition to an almost optimal surface-to-volume ratio also has a very favorable barrier-to-volume ratio. A simulation experiment was successfully validated with two representative test substances, the hydrophilic caffeine and the lipophilic flufenamic acid, which were applied in an aqueous vehicle with a constant dose. The input parameters for the simulation were determined in a companion study by experimental collaborators.
[Show abstract][Hide abstract] ABSTRACT: Research highlights
▶ Applying the method of asymptotic expansion to membranes of tetrakaidekahedral cells. ▶ Resulting effective diffusion tensor is of diagonal shape. ▶ Providing closed form expressions for the description of lateral and transversal diffusity.