3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Simulation of subseismic joint and fault networks using a heuristic mechanical model

Flow simulations of fractured and faulted reservoirs require representation of subseismic structures about which subsurface data are limited. We describe a method for simulating fracture growth that is mechanically based but heuristic, allowing for realistic modelling of fracture networks with reasonable run times. The method takes a triangulated meshed surface as input, together with an initial stress field. Fractures initiate and grow based on the stress field, and the growing fractures relieve the stress in the mesh. We show that a wide range of bedding-plane joint networks can be modelled simply by varying the distribution and anisotropy of the initial stress field. The results are in good qualitative agreement with natural joint patterns. We then apply the method to a set of parallel veins and demonstrate how the variations in thickness of the veins can be represented. Lastly, we apply the method to the simulation of normal fault patterns on salt domes. We derive the stress field on the bedding surface using the horizon curvature. The modelled fault network shows both radial and concentric faults. The new method provides an effective means of modelling joint and fault networks that can be imported to the flow simulator

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Towards Individualized Transcranial Electric Stimulation Therapy through Computer Simulation

Transkranielle Elektrostimulation (tES) beschreibt eine Gruppe von Hirnstimulationstechniken, die einen schwachen elektrischen Strom über zwei nicht-invasiv am Kopf angebrachten Elektroden applizieren. Handelt es sich dabei um einen Gleichstrom, spricht man von transkranieller Gleichstromstimulation, auch tDCS abgekürzt. Die allgemeine Zielstellung aller Hirnstimulationstechniken ist Hirnfunktion durch ein Verstärken oder Dämpfen von Hirnaktivität zu beeinflussen. Unter den Stimulationstechniken wird die transkranielle Gleichstromstimulation als ein adjuvantes Werkzeug zur Unterstützung der mikroskopischen Reorganisation des Gehirnes in Folge von Lernprozessen und besonders der Rehabilitationstherapie nach einem Schlaganfall untersucht. Aktuelle Herausforderungen dieser Forschung sind eine hohe Variabilität im erreichten Stimulationseffekt zwischen den Probanden sowie ein unvollständiges Verständnis des Zusammenspiels der der Stimulation zugrundeliegenden Mechanismen. Als Schlüsselkomponente für das Verständnis der Stimulationsmechanismen wird das zwischen den Elektroden im Kopf des Probanden aufgebaute elektrische Feld erachtet. Einem grundlegenden Konzept folgend wird angenommen, dass Hirnareale, die einer größeren elektrischen Feldstärke ausgesetzt sind, ebenso einen höheren Stimulationseffekt erfahren. Damit kommt der Positionierung der Elektroden eine entscheidende Rolle für die Stimulation zu. Allerdings verteilt sich das elektrische Feld wegen des heterogenen elektrischen Leitfähigkeitsprofil des menschlichen Kopfes nicht uniform im Gehirn der Probanden. Außerdem ist das Verteilungsmuster auf Grund anatomischer Unterschiede zwischen den Probanden verschieden. Die triviale Abschätzung der Ausbreitung des elektrischen Feldes anhand der bloßen Position der Stimulationselektroden ist daher nicht ausreichend genau für eine zielgerichtete Stimulation. Computerbasierte, biophysikalische Simulationen der transkraniellen Elektrostimulation ermöglichen die individuelle Approximation des Verteilungsmusters des elektrischen Feldes in Probanden basierend auf deren medizinischen Bildgebungsdaten. Sie werden daher zunehmend verwendet, um tDCS-Anwendungen zu planen und verifizieren, und stellen ein wesentliches Hilfswerkzeug auf dem Weg zu individualisierter Schlaganfall-Rehabilitationstherapie dar. Softwaresysteme, die den dahinterstehenden individualisierten Verarbeitungsprozess erleichtern und für ein breites Feld an Forschern zugänglich machen, wurden in den vergangenen Jahren für den Anwendungsfall in gesunden Erwachsenen entwickelt. Jedoch bleibt die Simulation von Patienten mit krankhaftem Hirngewebe und strukturzerstörenden Läsionen eine nicht-triviale Aufgabe. Daher befasst sich das hier vorgestellte Projekt mit dem Aufbau und der praktischen Anwendung eines Arbeitsablaufes zur Simulation transkranieller Elektrostimulation. Dabei stand die Anforderung im Vordergrund medizinische Bildgebungsdaten insbesondere neurologischer Patienten mit krankhaft verändertem Hirngewebe verarbeiten zu können. Der grundlegende Arbeitsablauf zur Simulation wurde zunächst für gesunde Erwachsene entworfen und validiert. Dies umfasste die Zusammenstellung medizinischer Bildverarbeitungsalgorithmen zu einer umfangreichen Verarbeitungskette, um elektrisch relevante Strukturen in den Magnetresonanztomographiebildern des Kopfes und des Oberkörpers der Probanden zu identifizieren und zu extrahieren. Die identifizierten Strukturen mussten in Computermodelle überführt werden und das zugrundeliegende, physikalische Problem der elektrischen Volumenleitung in biologischen Geweben mit Hilfe numerischer Simulation gelöst werden. Im Verlauf des normalen Alterns ist das Gehirn strukturellen Veränderungen unterworfen, unter denen ein Verlust des Hirnvolumens sowie die Ausbildung mikroskopischer Veränderungen seiner Nervenfaserstruktur die Bedeutendsten sind. In einem zweiten Schritt wurde der Arbeitsablauf daher erweitert, um diese Phänomene des normalen Alterns zu berücksichtigen. Die vordergründige Herausforderung in diesem Teilprojekt war die biophysikalische Modellierung der veränderten Hirnmikrostruktur, da die resultierenden Veränderungen im Leitfähigkeitsprofil des Gehirns bisher noch nicht in der Literatur quantifiziert wurden. Die Erweiterung des Simulationsablauf zeichnete sich vorrangig dadurch aus, dass mit unsicheren elektrischen Leitfähigkeitswerten gearbeitet werden konnte. Damit war es möglich den Einfluss der ungenau bestimmbaren elektrischen Leitfähigkeit der verschiedenen biologischen Strukturen des menschlichen Kopfes auf das elektrische Feld zu ermitteln. In einer Simulationsstudie, in der Bilddaten von 88 Probanden einflossen, wurde die Auswirkung der veränderten Hirnfaserstruktur auf das elektrische Feld dann systematisch untersucht. Es wurde festgestellt, dass sich diese Gewebsveränderungen hochgradig lokal und im Allgemeinen gering auswirken. Schließlich wurden in einem dritten Schritt Simulationen für Schlaganfallpatienten durchgeführt. Ihre großen, strukturzerstörenden Läsionen wurden dabei mit einem höheren Detailgrad als in bisherigen Arbeiten modelliert und physikalisch abermals mit unsicheren Leitfähigkeiten gearbeitet, was zu unsicheren elektrischen Feldabschätzungen führte. Es wurden individuell berechnete elektrische Felddaten mit der Hirnaktivierung von 18 Patienten in Verbindung gesetzt, unter Berücksichtigung der inhärenten Unsicherheit in der Bestimmung der elektrischen Felder. Das Ziel war zu ergründen, ob die Hirnstimulation einen positiven Einfluss auf die Hirnaktivität der Patienten im Kontext von Rehabilitationstherapie ausüben und so die Neuorganisierung des Gehirns nach einem Schlaganfall unterstützen kann. Während ein schwacher Zusammenhang hergestellt werden konnte, sind weitere Untersuchungen nötig, um diese Frage abschließend zu klären.:Kurzfassung Abstract Contents 1 Overview 2 Anatomical structures in magnetic resonance images 2 Anatomical structures in magnetic resonance images 2.1 Neuroanatomy 2.2 Magnetic resonance imaging 2.3 Segmentation of MR images 2.4 Image morphology 2.5 Summary 3 Magnetic resonance image processing pipeline 3.1 Introduction to human body modeling 3.2 Description of the processing pipeline 3.3 Intermediate and final outcomes in two subjects 3.4 Discussion, limitations & future work 3.5 Conclusion 4 Numerical simulation of transcranial electric stimulation 4.1 Electrostatic foundations 4.2 Discretization of electrostatic quantities 4.3 The numeric solution process 4.4 Spatial discretization by volume meshing 4.5 Summary 5 Simulation workflow 5.1 Overview of tES simulation pipelines 5.2 My implementation of a tES simulation workflow 5.3 Verification & application examples 5.4 Discussion & Conclusion 6 Transcranial direct current stimulation in the aging brain 6.1 Handling age-related brain changes in tES simulations 6.2 Procedure of the simulation study 6.3 Results of the uncertainty analysis 6.4 Findings, limitations and discussion 7 Transcranial direct current stimulation in stroke patients 7.1 Bridging the gap between simulated electric fields and brain activation in stroke patients 7.2 Methodology for relating simulated electric fields to functional MRI data 7.3 Evaluation of the simulation study and correlation analysis 7.4 Discussion & Conclusion 8 Outlooks for simulations of transcranial electric stimulation List of Figures List of Tables Glossary of Neuroscience Terms Glossary of Technical Terms BibliographyTranscranial electric current stimulation (tES) denotes a group of brain stimulation techniques that apply a weak electric current over two or more non-invasively, head-mounted electrodes. When employing a direct-current, this method is denoted transcranial direct current stimulation (tDCS). The general aim of all tES techniques is the modulation of brain function by an up- or downregulation of brain activity. Among these, transcranial direct current stimulation is investigated as an adjuvant tool to promote processes of the microscopic reorganization of the brain as a consequence of learning and, more specifically, rehabilitation therapy after a stroke. Current challenges of this research are a high variability in the achieved stimulation effects across subjects and an incomplete understanding of the interplay between its underlying mechanisms. A key component to understanding the stimulation mechanism is considered the electric field, which is exerted by the electrodes and distributes in the subjects' heads. A principle concept assumes that brain areas exposed to a higher electric field strength likewise experience a higher stimulation. This attributes the positioning of the electrodes a decisive role for the stimulation. However, the electric field distributes non-uniformly across subjects' brains due to the heterogeneous electrical conductivity profile of the human head. Moreover, the distribution pattern is variable between subjects due to their individual anatomy. A trivial estimation of the distribution of the electric field solely based on the position of the stimulating electrodes is, therefore, not precise enough for a well-targeted stimulation. Computer-based biophysical simulations of transcranial electric stimulation enable the individual approximation of the distribution pattern of the electric field in subjects based on their medical imaging data. They are, thus, increasingly employed for the planning and verification of tDCS applications and constitute an essential tool on the way to individualized stroke rehabilitation therapy. Software pipelines facilitating the underlying individualized processing for a wide range of researchers have been developed for use in healthy adults over the past years, but, to date, the simulation of patients with abnormal brain tissue and structure disrupting lesions remains a non-trivial task. Therefore, the presented project was dedicated to establishing and practically applying a tES simulation workflow. The processing of medical imaging data of neurological patients with abnormal brain tissue was a central requirement in this process. The basic simulation workflow was first designed and validated for the simulation of healthy adults. This comprised compiling medical image processing algorithms into a comprehensive workflow to identify and extract electrically relevant physiological structures of the human head and upper torso from magnetic resonance images. The identified structures had to be converted to computational models. The underlying physical problem of electric volume conduction in biological tissue was solved by means of numeric simulation. Over the course of normal aging, the brain is subjected to structural alterations, among which a loss of brain volume and the development of microscopic alterations of its fiber structure are the most relevant. In a second step, the workflow was, thus, extended to incorporate these phenomena of normal aging. The main challenge in this subproject was the biophysical modeling of the altered brain microstructure as the resulting alterations to the conductivity profile of the brain were so far not quantified in the literature. Therefore, the augmentation of the workflow most notably included the modeling of uncertain electrical properties. With this, the influence of the uncertain electrical conductivity of the biological structures of the human head on the electric field could be assessed. In a simulation study, including imaging data of 88 subjects, the influence of the altered brain fiber structure on the electric field was then systematically investigated. These tissue alterations were found to exhibit a highly localized and generally low impact. Finally, in a third step, tDCS simulations of stroke patients were conducted. Their large, structure-disrupting lesions were modeled in a more detailed manner than in previous stroke simulation studies, and they were physically, again, modeled by uncertain electrical conductivity resulting in uncertain electric field estimates. Individually simulated electric fields were related to the brain activation of 18 patients, considering the inherently uncertain electric field estimations. The goal was to clarify whether the stimulation exerts a positive influence on brain function in the context of rehabilitation therapy supporting brain reorganization following a stroke. While a weak correlation could be established, further investigation will be necessary to answer that research question.:Kurzfassung Abstract Contents 1 Overview 2 Anatomical structures in magnetic resonance images 2 Anatomical structures in magnetic resonance images 2.1 Neuroanatomy 2.2 Magnetic resonance imaging 2.3 Segmentation of MR images 2.4 Image morphology 2.5 Summary 3 Magnetic resonance image processing pipeline 3.1 Introduction to human body modeling 3.2 Description of the processing pipeline 3.3 Intermediate and final outcomes in two subjects 3.4 Discussion, limitations & future work 3.5 Conclusion 4 Numerical simulation of transcranial electric stimulation 4.1 Electrostatic foundations 4.2 Discretization of electrostatic quantities 4.3 The numeric solution process 4.4 Spatial discretization by volume meshing 4.5 Summary 5 Simulation workflow 5.1 Overview of tES simulation pipelines 5.2 My implementation of a tES simulation workflow 5.3 Verification & application examples 5.4 Discussion & Conclusion 6 Transcranial direct current stimulation in the aging brain 6.1 Handling age-related brain changes in tES simulations 6.2 Procedure of the simulation study 6.3 Results of the uncertainty analysis 6.4 Findings, limitations and discussion 7 Transcranial direct current stimulation in stroke patients 7.1 Bridging the gap between simulated electric fields and brain activation in stroke patients 7.2 Methodology for relating simulated electric fields to functional MRI data 7.3 Evaluation of the simulation study and correlation analysis 7.4 Discussion & Conclusion 8 Outlooks for simulations of transcranial electric stimulation List of Figures List of Tables Glossary of Neuroscience Terms Glossary of Technical Terms Bibliograph

Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to yield a coarse classical mesh. The use of a special control mapping allows to fine-tune properties of the coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a 'scaffolding' to generate a boundary-conforming mesh out of a fine background mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of memory storage. Additionally, the adaptation at run-time is extremely cheap compared to computing the flow solution. Furthermore, this method circumvents the need for expensive re-meshing and projections of solutions making it efficient and accurate. It is incorporated into a space-time finite element framework. We present time-dependent test cases of non-Newtonian fluids in 2D and 3D for complex screw designs. They demonstrate the potential of the method also for arbitrarily complex industrial applications

Quantification of Turbulence Statistics for the Near-Wall Region in Unstructured Pebble Beds Using Direct Numerical Simulation

The aim of this study was to employing high-fidelity computational fluid dynamics to investi-gate and quantify the turbulent flow effects for incompressible, isothermal fluid flows, in the near wall region of unstructured, randomly packed spheres. The flow domain treated in this study is a replication of an experimental setup and analogous to those encountered in pebble bed based high-temperature reactors. A new meshing strategy and meshing assumptions have been employed to decrease the mesh size and these were validated with the experimental results. Quantifying turbulent flow effects sever a dual purpose: One, it assists lower-fidelity engineering tool development, such as those incorporating Reynolds averaged Navier-Stokes based methodologies, and two deepens our fundamental understanding of the physics involved for in-compressible flows over complex geometries. Nek5000, an open source spectral element computational fluid dynamics code, developed by Argonne National Lab was used to conduct this study. The code was used to perform a series of direct numerical simulations on the experimental geometry at low to moderate Reynolds numbers, matching the experimental flow parameters, to validate the model. This was done for a the full and section of the geometry to investigate the cross flow dependence in the problem. Presented results include the comparison between experimental and numerical findings, the development of a high-fidelity database of the experimental geometry at low and moderate Reynolds number, identification of possible flow phenomena present in random packed spheres as well as the calculation of the first and second order statistics in the near wall domain of random packed spheres