Efficient numerical strategies for an implicit volume fraction transfer scheme for single crystal plasticity including twinning and secondary plasticity on the example of magnesium

In this work an efficient algorithm for a fully implicit single crystal plasticity routine including twinning and secondary plasticity is presented and implemented for the example of magnesium. The material model uses the volume fraction transfer scheme for the evolution of twinning, that is, plastic slip in newly formed twins (“secondary plasticity”) is resolved. This is considered particularly important, if the volume fractions of some twins reach the order of magnitude of the parent phase. However the resolution of secondary plasticity also implies a large number of unknowns, which is significantly reduced by a newly proposed algorithm. For magnesium a hardening model based on basal, prismatic, pyramidal a and pyramidal c+a slip modes as well as a tension and a compression twinning mode and yields a total of 18 slip systems and 12 twinning systems. As a special feature of the proposed algorithm, the total amount of 246 unknowns, due to simultaneous slip in the parent phase and the twinned phases, is reduced to only 31 unknowns. Additionally, thermodynamic consistency is ensured by including the second law with the Clausius–Duhem equation, which considers the change of free energy upon twinning as an additional driving force for twinning. Further, the setup of the time discrete nonlinear equation system using midpoint rule, as well as the analytical solution of the algorithmic tangent are given in detail. Finally, the implemented model is tested in finite element simulations and compared to single- and polycrystal compression and tension experiments

Radiotherapy planning for glioblastoma based on a tumor growth model: Improving target volume delineation

Glioblastoma are known to infiltrate the brain parenchyma instead of forming a solid tumor mass with a defined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infiltrated by tumor cells at low density appears normal on current imaging modalities. In clinical practice, a uniform margin is applied to account for microscopic spread of disease. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth: Anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and infiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher-Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defined as an isoline of the simulated tumor cell density. A retrospective study involving 10 glioblastoma patients has been performed. To illustrate the main findings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioblastoma, and may therefore provide a tool to make target delineation more objective and automated

Betriebsstruktur und Grobfuttererzeugung ökologisch wirtschaftender Milchviehbetriebe in Deutschland

Die Erzeugung hochwertiger Grobfuttermittel spielt für die Rentabilität und Nachhaltigkeit der Milcherzeugung im ökologischen Landbau eine entscheidende Rolle. Grobfuttermittel beeinflussen die Gesundheit und Leistung des Milchviehs auf verschiedene Art und Weise. Zudem variieren die standörtlichen Bedingungen des Futterbaus sowie die avisierten Leistungsniveaus der Milchviehhaltung in der Praxis erheblich (Haas et al. 2001, Brinkmann & Winckler 2005, Müller-Lindenlauf et al. 2010). Ziel dieser Untersuchung ist es, die Variabilität der betrieblichen Konzepte der Grobfuttererzeugung überregional zu analysieren und etwaige Strategietypen zu identifizieren, die für weitergehende Analysen und Beratungsempfehlungen eine objektivierte Grundlage bieten

On a Projection Method for the Numerical Integration of Constitutive Equations Involving Large Inelastic and Incompressible Deformations

Finite deformation plasticity often involves the multiplicative split of the deformation gradient into an elastic and plastic part. Motivated by observations in physics, the plastic part is assumed to be volume preserving, i.e., the plastic part of the deformation gradient is unimodular. In order to not accumulate errors, in the best case, one fulfills this constraint exactly to obtain accurate results (see, e.g., [3]). While other approaches where pursued as well, many authors therefore adopted the use of the exponential map, which is a geometric integrator preserving the plastic incompressibility. However, it's computation is not straightforward and performing the eigenvalue decomposition and it's linearization for the exponential function is numerically elaborate. Therefore, in this work, a new approach which also exactly preserves the incompressibility constraint is developed. It makes use of a projection of all symmetric tensors onto the manifold of unimodular tensors. The proposed method is compared to models utilizing the exponential map in numerical experiments

Use of Diffusion Tensor Images in Glioma Growth Modeling for Radiotherapy Target Delineation

International audienceIn radiotherapy of gliomas, a precise de nition of the treat- ment volume is problematic, because current imaging modalities reveal only the central part of the tumor with a high cellular density, but fail to detect all regions of microscopic tumor cell spread in the adjacent brain parenchyma. Mathematical models can be used to integrate known growth characteristics of gliomas into the target delineation process. In this paper, we demonstrate the use of di usion tensor imaging (DTI) for simulating anisotropic cell migration in a glioma growth model that is based on the Fisher-Kolmogorov equation. For a clinical application of the model, it is crucial to develop a detailed understanding of its behavior, capabilities, and limitations. For that purpose, we perform a retrospective analysis of glioblastoma patients treated at our institution. We analyze the impact of di usion anisotropy on model-derived target volumes, and interpret the results in the context of the underlying im- ages. It was found that, depending on the location of the tumor relative to major ber tracts, DTI can have signi cant in uence on the shape of the radiotherapy target volume

Mobile 3D sensor for documenting maintenance processes of large complex structures

With the new handheld goSCOUT3D sensor system, the entire surface of complex industrial machinery spanning several meters can be captured three-dimensionally within a matter of minutes. In addition, a comprehensive photo collection is registered and precisely assigned to the corresponding 3D object points in one hybrid 2D/3D model. At the basis of the robust 3D digitization are the measuring principles of photogrammetric reconstruction using a high-resolution color camera and simultaneous localization and imaging using a tracking unit. Following image acquisition, the process leading to generation of the complete hybrid model is fully automated. Under continuous movement of the sensor head, up to six images per second and a total of up to several thousand images can be recorded. Those images are then aligned in 3D space and used to reconstruct the 3D model. Results regarding accuracy measurements are presented as well as application examples of digitized technical machinery under maintenance and inspection

Radiotherapy planning for glioblastoma based on a tumor growth model: implications for spatial dose redistribution

International audienceGliomas differ from many other tumors as they grow infiltratively into the brain parenchyma rather than forming a solid tumor mass with a well-defined boundary. Tumor cells can be found several centimeters away from the central tumor mass that is visible using current imaging techniques. The infiltrative growth characteristics of gliomas question the concept of a radiotherapy target volume that is irradiated to a homogeneous dose--the standard in current clinical practice. We discuss the use of the Fisher-Kolmogorov glioma growth model in radiotherapy treatment planning. The phenomenological tumor growth model assumes that tumor cells proliferate locally and migrate into neighboring brain tissue, which is mathematically described via a partial differential equation for the spatio-temporal evolution of the tumor cell density. In this model, the tumor cell density drops approximately exponentially with distance from the visible gross tumor volume, which is quantified by the infiltration length, a parameter describing the distance at which the tumor cell density drops by a factor of e. This paper discusses the implications for the prescribed dose distribution in the periphery of the tumor. In the context of the exponential cell kill model, an exponential fall-off of the cell density suggests a linear fall-off of the prescription dose with distance. We introduce the dose fall-off rate, which quantifies the steepness of the prescription dose fall-off in units of Gy mm−1. It is shown that the dose fall-off rate is given by the inverse of the product of radiosensitivity and infiltration length. For an infiltration length of 3 mm and a surviving fraction of 50% at 2 Gy, this suggests a dose fall-off of approximately 1 Gy mm−1. The concept is illustrated for two glioblastoma patients by optimizing intensity-modulated radiotherapy plans. The dose falloff rate concept reflects the idea that infiltrating gliomas lack a defined boundary and are characterized by a continuous fall-off of the density of infiltrating tumor cells. The approach can potentially be used to individualize the prescribed dose distribution if better methods to estimate radiosensitivity and infiltration length on a patient by patient basis become available