801 research outputs found

    Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: application to cardiac electromechanics

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    The accurate robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. We present a novel method that combines rescaled localized Radial Basis Function (RBF) interpolation with Singular Value Decomposition (SVD) to preserve the positivity of the determinant of the deformation gradient tensor. The method involves decomposing the evaluations of the tensor at the quadrature nodes of the source mesh into rotation matrices and diagonal matrices of singular values; computing the RBF interpolation of the quaternion representation of rotation matrices and the singular value logarithms; reassembling the deformation gradient tensors at quadrature nodes of the destination mesh, to be used in the assembly of the electrophysiology model equations. The proposed method overcomes limitations of existing interpolation methods, including nested intergrid interpolation and RBF interpolation of the displacement field, that may lead to the loss of physical meaningfulness of the mathematical formulation and then to solver failures at the algebraic level, due to negative determinant values. The proposed method enables the transfer of solution variables between finite element spaces of different degrees and shapes and without stringent conformity requirements between different meshes, enhancing the flexibility and accuracy of electromechanical simulations. Numerical results confirm that the proposed method enables the transfer of the deformation gradient tensor, allowing to successfully run simulations in cases where existing methods fail. This work provides an efficient and robust method for the intergrid transfer of the deformation gradient tensor, enabling independent tailoring of mesh discretizations to the particular characteristics of the physical components concurring to the of the multiphysics model.Comment: 24 pages; 11 figure

    Design of decorative 3D models: from geodesic ornaments to tangible assemblies

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    L'obiettivo di questa tesi è sviluppare strumenti utili per creare opere d'arte decorative digitali in 3D. Uno dei processi decorativi più comunemente usati prevede la creazione di pattern decorativi, al fine di abbellire gli oggetti. Questi pattern possono essere dipinti sull'oggetto di base o realizzati con l'applicazione di piccoli elementi decorativi. Tuttavia, la loro realizzazione nei media digitali non è banale. Da un lato, gli utenti esperti possono eseguire manualmente la pittura delle texture o scolpire ogni decorazione, ma questo processo può richiedere ore per produrre un singolo pezzo e deve essere ripetuto da zero per ogni modello da decorare. D'altra parte, gli approcci automatici allo stato dell'arte si basano sull'approssimazione di questi processi con texturing basato su esempi o texturing procedurale, o con sistemi di riproiezione 3D. Tuttavia, questi approcci possono introdurre importanti limiti nei modelli utilizzabili e nella qualità dei risultati. Il nostro lavoro sfrutta invece i recenti progressi e miglioramenti delle prestazioni nel campo dell'elaborazione geometrica per creare modelli decorativi direttamente sulle superfici. Presentiamo una pipeline per i pattern 2D e una per quelli 3D, e dimostriamo come ognuna di esse possa ricreare una vasta gamma di risultati con minime modifiche dei parametri. Inoltre, studiamo la possibilità di creare modelli decorativi tangibili. I pattern 3D generati possono essere stampati in 3D e applicati a oggetti realmente esistenti precedentemente scansionati. Discutiamo anche la creazione di modelli con mattoncini da costruzione, e la possibilità di mescolare mattoncini standard e mattoncini custom stampati in 3D. Ciò consente una rappresentazione precisa indipendentemente da quanto la voxelizzazione sia approssimativa. I principali contributi di questa tesi sono l'implementazione di due diverse pipeline decorative, un approccio euristico alla costruzione con mattoncini e un dataset per testare quest'ultimo.The aim of this thesis is to develop effective tools to create digital decorative 3D artworks. Real-world art often involves the use of decorative patterns to enrich objects. These patterns can be painted on the base or might be realized with the application of small decorative elements. However, their creation in digital media is not trivial. On the one hand, users can manually perform texture paint or sculpt each decoration, in a process that can take hours to produce a single piece and needs to be repeated from the ground up for every model that needs to be decorated. On the other hand, automatic approaches in state of the art rely on approximating these processes with procedural or by-example texturing or with 3D reprojection. However, these approaches can introduce significant limitations in the models that can be used and in the quality of the results. Instead, our work exploits the recent advances and performance improvements in the geometry processing field to create decorative patterns directly on surfaces. We present a pipeline for 2D and one for 3D patterns and demonstrate how each of them can recreate a variety of results with minimal tweaking of the parameters. Furthermore, we investigate the possibility of creating decorative tangible models. The 3D patterns we generate can be 3D printed and applied to previously scanned real-world objects. We also discuss the creation of models with standard building bricks and the possibility of mixing standard and custom 3D-printed bricks. This allows for a precise representation regardless of the coarseness of the voxelization. The main contributions of this thesis are the implementation of two different decorative pipelines, a heuristic approach to brick construction, and a dataset to test the latter

    Zero-Level-Set Encoder for Neural Distance Fields

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    Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., to compute a signed distance or occupancy value at a specific spatial position. Previous methods tend to rely on the auto-decoder paradigm, which often requires densely-sampled and accurate signed distances to be known during training and testing, as well as an additional optimization loop during inference. This introduces a lot of computational overhead, in addition to having to compute signed distances analytically, even during testing. In this paper, we present a novel encoder-decoder neural network for embedding 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. Furthermore, the network is trained to solve the Eikonal equation and only requires knowledge of the zero-level set for training and inference. Additional volumetric samples can be generated on-the-fly, and incorporated in an unsupervised manner. This means that in contrast to most previous work, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. In other words, our network computes approximate solutions to the boundary-valued Eikonal equation. It also requires only a single forward pass during inference, instead of the common latent code optimization. We further propose a modification of the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surface-meshes and non-manifold geometry. We finally demonstrate the efficacy, generalizability and scalability of our method on datasets consisting of deforming 3D shapes, single class encoding and multiclass encoding, showcasing a wide range of possible applications

    Inverse dynamics of underactuated flexible mechanical systems governed by quasi-linear hyperbolic partial differential equations

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    Diese Arbeit befasst sich mit der inversen Dynamik unteraktuierter, flexibler, mechanischer Systeme, welche durch quasi-lineare hyperbolische partielle Differentialgleichungen beschrieben werden können. Diese Gleichungnen, sind zeitlich veränderlichen Dirichlet-Randbedingungen unterworfen, welche durch unbekannte, räumlich disjunkte, also nicht kollokierte Neumann-Randbedingungen erzwungen werden. Die zugrundeliegenden Gleichungen werden zunächst abstrakt hergeleitet, bevor verschiedene mechanische Systeme vorgestellt werden können, die mit der eingangs postulierten Formulierung übereinstimmen. Hierzu werden geometrisch exakte Theorien hergeleitet, welche in der Lage sind große Bewegungen schlanker Strukturen wie Seile und Balken, aber auch ganz allgemein, dreidimensionaler Festkörper zu beschreiben. In der Regel werden Anfangs-Randwertprobleme, die in der nichtlinearen Strukturdynamik auftreten, durch Anwendung einer sequentiellen Diskretisierung in Raum und Zeit gelöst. Diese Verfahren basieren für gewöhnlich auf einer räumlichen Diskretisierung mit finiten Elementen, gefolgt von einer geeigneten zeitlichen Diskretisierung, welche meist auf finiten Differenzen beruht. Ein kurzer Überblick über derartige sequentielle Integrationsverfahren für das vorliegende Anfangs-Randwertproblem wird zunächst anhand der direkten Formulierung des Problems gegeben werden. D.h. es wird zunächst das reine Neumann-Randproblem betrachtet, bevor anschließend ganz allgemein, verschiedene Möglichkeiten zur Einbindung etwaiger Dirichlet-Randbedingungen diskutiert werden. Darauf aufbauend wird das Problem der inversen Dynamik im Kontext räumlich diskreter mechanischer Systeme, welche rheonom-holonomen Servo-Bindungen unterliegen, eingeführt. Eine ausführliche Untersuchung dieser Art von gebundenen Systemen soll die grundlegenden Unterschiede zwischen Servo-Bindungen und klassischen Kontakt-Bindungen herausarbeiten. Die daraus resultierenden Folgen für die Entwicklung geeigneter numerisch stabiler Integrationsverfahren können dabei ebenfalls angesprochen werden, bevor zahlreich ausgewählte Beispiele vorgestellt werden können. Aufgrund der sehr eingeschränkten Anwendbarkeit der sequentiellen Lösung der inversen Dynamik in Raum und Zeit, wird eine eingehende Analyse des vorliegenden Anfangs-Randwertproblems unternommen. Vor allem durch die Freilegung der hyperbolischen Struktur der zugrundeliegenden partiellen Differentialgleichungen werden sich weitere Einblicke in das vorliegende Problem erhofft. Die Erforschung der daraus resultierenden Mechanismen der Wellenausbreitung in kontinuierlichen Strukturen öffnet die Tür zur Entwicklung numerisch stabiler Integrationsverfahren für die inverse Dynamik. So kann unter anderem eine Methode vorgestellt werden, die auf der Integration der partiellen Differentialgleichungen entlang charakteristischer Mannigfaltigkeiten beruht. Dies regt zu der Entwicklung neuartiger Galerkinverfahren an, die ebenfalls in dieser Arbeit vorgestellt werden können. Diese neu entwickelten Methoden können anschlie\ss end auf die Steuerung verschiedener mechanischer Systeme angewendet werden. Darüber hinaus können die neuartigen Integrationsverfahren auch auf flexible Mehrkörpersysteme übertragen werden. Angeführt seien hier beispielsweise die kooperative Steuerung eines an mehreren flexiblen Seilen aufgehängten starren Körpers oder die Steuerung des Endeffektors eines flexiblen mehrgliedrigen Schwenkarms. Ausgewählte numerische Beispiele verdeutlichen die Relevanz der hier vorgeschlagenen, in Raum und Zeit simultanen Integration des vorliegenden Anfangs-Randwertproblems

    Crack propagation in anisotropic brittle materials: from a phase-field model to a shape optimization approach

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    The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a length-scale parameter that smooths the sharp discontinuity, which influences the diffuse band and results in mesh-sensitive fracture propagation results. Recently, a novel approach based on the optimization on Riemannian shape spaces has been proposed, where the crack path is realized by techniques from shape optimization. This approach requires the shape derivative, which is derived in a continuous sense and used for a gradient-based algorithm to minimize the energy of the system. Due to the continuous derivation of the shape derivative, this approach yields mesh-independent results. In this paper, the novel approach based on shape optimization is presented, followed by an assessment of the predicted crack path in anisotropic brittle material using numerical calculations from a phase-field model

    Applications of Deep Learning to Differential Equation Models in Oncology

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    The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly differential equation-based models, have had great success in various biological applications, including modelling bacterial growth, disease propagation, and tumour spread. However, these approaches can be somewhat limited due to their reliance on known parameter values, initial conditions, and boundary conditions, which can dull their applicability. Furthermore, their forms are directly tied to mechanistic phenomena, making these models highly explainable, but also requiring a comprehensive understanding of the underlying dynamics before modelling the system. On the other hand, machine learning models typically require less prior knowledge of the system but require a significant amount of data for training. Although machine learning models can be more flexible, they tend to be black boxes, making them difficult to interpret. Hybrid models, which combine conventional and machine learning approaches, have the potential to achieve the best of both worlds. These models can provide explainable outcomes while relying on minimal assumptions or data. An example of this is physics-informed neural networks, a novel deep learning approach that incorporates information from partial differential equations into the optimization of a neural network. This hybrid approach offers significant potential in various contexts where differential equation models are known, but data is scarce or challenging to work with. Precision oncology is one such field. This thesis employs hybrid conventional/machine learning models to address problems in cancer medicine, specifically aiming to advance personalized medicine approaches. It contains three projects. In the first, a hybrid approach is used to make patient-specific characterizations of brain tumours using medical imaging data. In the second project, a hybrid approach is employed to create subject-specific projections of drug-carrying cancer nanoparticle accumulation and intratumoral interstitial fluid pressure. In the final project, a hybrid approach is utilized to optimize radiation therapy scheduling for tumours with heterogeneous cell populations and cancer stem cells. Overall, this thesis showcases several examples of how quantitative tools, particularly those involving both conventional and machine learning approaches, can be employed to tackle challenges in oncology. It further supports the notion that the continued integration of quantitative tools in medicine is a key strategy in addressing problems and open questions in healthcare

    Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations

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    Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3+13+1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta (IMEX) methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit RK commonly employed for the MHD and Einstein equations. Finally, we analyze their performance in several numerical tests.Comment: 18 + 6. Updated manuscript matching published version + additional appendix "Comparing the convergence order of IMEX and semi-implicit schemes

    Surface-Based tools for Characterizing the Human Brain Cortical Morphology

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    Tesis por compendio de publicacionesThe cortex of the human brain is highly convoluted. These characteristic convolutions present advantages over lissencephalic brains. For instance, gyrification allows an expansion of cortical surface area without significantly increasing the cranial volume, thus facilitating the pass of the head through the birth channel. Studying the human brain’s cortical morphology and the processes leading to the cortical folds has been critical for an increased understanding of the pathological processes driving psychiatric disorders such as schizophrenia, bipolar disorders, autism, or major depression. Furthermore, charting the normal developmental changes in cortical morphology during adolescence or aging can be of great importance for detecting deviances that may be precursors for pathology. However, the exact mechanisms that push cortical folding remain largely unknown. The accurate characterization of the neurodevelopment processes is challenging. Multiple mechanisms co-occur at a molecular or cellular level and can only be studied through the analysis of ex-vivo samples, usually of animal models. Magnetic Resonance Imaging can partially fill the breach, allowing the portrayal of the macroscopic processes surfacing on in-vivo samples. Different metrics have been defined to measure cortical structure to describe the brain’s morphological changes and infer the associated microstructural events. Metrics such as cortical thickness, surface area, or cortical volume help establish a relation between the measured voxels on a magnetic resonance image and the underlying biological processes. However, the existing methods present limitations or room for improvement. Methods extracting the lines representing the gyral and sulcal morphology tend to over- or underestimate the total length. These lines can provide important information about how sulcal and gyral regions function differently due to their distinctive ontogenesis. Nevertheless, some methods label every small fold on the cortical surface as a sulcal fundus, thus losing the perspective of lines that travel through the deeper zones of a sulcal basin. On the other hand, some methods are too restrictive, labeling sulcal fundi only for a bunch of primary folds. To overcome this issue, we have proposed a Laplacian-collapse-based algorithm that can delineate the lines traversing the top regions of the gyri and the fundi of the sulci avoiding anastomotic sulci. For this, the cortex, represented as a 3D surface, is segmented into gyral and sulcal surfaces attending to the curvature and depth at every point of the mesh. Each resulting surface is spatially filtered, smoothing the boundaries. Then, a Laplacian-collapse-based algorithm is applied to obtain a thinned representation of the morphology of each structure. These thin curves are processed to detect where the extremities or endpoints lie. Finally, sulcal fundi and gyral crown lines are obtained by eroding the surfaces while preserving the structure topology and connectivity between the endpoints. The assessment of the presented algorithm showed that the labeled sulcal lines were close to the proposed ground truth length values while crossing through the deeper (and more curved) regions. The tool also obtained reproducibility scores better or similar to those of previous algorithms. A second limitation of the existing metrics concerns the measurement of sulcal width. This metric, understood as the physical distance between the points on opposite sulcal banks, can come in handy in detecting cortical flattening or complementing the information provided by cortical thickness, gyrification index, or such features. Nevertheless, existing methods only provided averaged measurements for different predefined sulcal regions, greatly restricting the possibilities of sulcal width and ignoring the intra-region variability. Regarding this, we developed a method that estimates the distance from each sulcal point in the cortex to its corresponding opposite, thus providing a per-vertex map of the physical sulcal distances. For this, the cortical surface is sampled at different depth levels, detecting the points where the sulcal banks change. The points corresponding to each sulcal wall are matched with the closest point on a different one. The distance between those points is the sulcal width. The algorithm was validated against a simulated sulcus that resembles a simple fold. Then the tool was used on a real dataset and compared against two widely-used sulcal width estimation methods, averaging the proposed algorithm’s values into the same region definition those reference tools use. The resulting values were similar for the proposed and the reference methods, thus demonstrating the algorithm’s accuracy. Finally, both algorithms were tested on a real aging population dataset to prove the methods’ potential in a use-case scenario. The main idea was to elucidate fine-grained morphological changes in the human cortex with aging by conducting three analyses: a comparison of the age-dependencies of cortical thickness in gyral and sulcal lines, an analysis of how the sulcal and gyral length changes with age, and a vertex-wise study of sulcal width and cortical thickness. These analyses showed a general flattening of the cortex with aging, with interesting findings such as a differential age-dependency of thickness thinning in the sulcal and gyral regions. By demonstrating that our method can detect this difference, our results can pave the way for future in vivo studies focusing on macro- and microscopic changes specific to gyri or sulci. Our method can generate new brain-based biomarkers specific to sulci and gyri, and these can be used on large samples to establish normative models to which patients can be compared. In parallel, the vertex-wise analyses show that sulcal width is very sensitive to changes during aging, independent of cortical thickness. This corroborates the concept of sulcal width as a metric that explains, in the least, the unique variance of morphology not fully captured by existing metrics. Our method allows for sulcal width vertex-wise analyses that were not possible previously, potentially changing our understanding of how changes in sulcal width shape cortical morphology. In conclusion, this thesis presents two new tools, open source and publicly available, for estimating cortical surface-based morphometrics. The methods have been validated and assessed against existing algorithms. They have also been tested on a real dataset, providing new, exciting insights into cortical morphology and showing their potential for defining innovative biomarkers.Programa de Doctorado en Ciencia y Tecnología Biomédica por la Universidad Carlos III de MadridPresidente: Juan Domingo Gispert López.- Secretario: Norberto Malpica González de Vega.- Vocal: Gemma Cristina Monté Rubi

    Inkjet printing digital image generation and compensation for surface chemistry effects

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    Additive manufacturing (AM) of electronic materials using digital inkjet printing (DIJP) is of research interests nowadays because of its potential benefits in the semiconductor industry. Current trends in manufacturing electronics feature DIJP as a key technology to enable the production of customised and microscale functional devices. However, the fabrication of microelectronic components at large scale demands fast printing of tight features with high dimensional accuracy on substrates with varied surface topography which push inkjet printing process to its limits. To understand the DIJP droplet deposition on such substrates, generally requires computational fluid dynamics modelling which is limited in its physics approximation of surface interactions. Otherwise, a kind of “trial and error” approach to determining how the ink spreads, coalesce and solidifies over the substrate is used, often a very time-consuming process. Consequently, this thesis aims to develop new modelling techniques to predict fast and accurately the surface morphology of inkjet-printed features, enabling the optimisation of DIJP control parameters and the compensation of images for better dimensional accuracy of printed electronics devices. This investigation explored three categories of modelling techniques to predict the surface morphology of inkjet-printed features: physics-based, data-driven and hybrid physics-based and data-driven. Two physics-based numerical models were developed to reproduce the inkjet printing droplet deposition and solidification processes using a lattice Boltzmann (LB) multiphase flow model and a finite element (FE) chemo-mechanical model, respectively. The LB model was limited to the simulation of single tracks and small square films and the FE model was mainly employed for the distortion prediction of multilayer objects. Alternatively, two data-driven models were implemented to reconstruct the surface morphology of single tracks and free-form films using images from experiments: image analysis (IA) and shape from shading (SFS). IA assumed volume conservation and minimal energy drop shape to reconstruct the surface while SFS resolved the height of the image using a reflection model. Finally, a hybrid physics-based and data-driven approach was generated which incorporates the uncertainty of droplet landing position and footprint, hydrostatic analytical models, empirical correlations derived from experiments, and relationships derived from physics-based models to predict fast and accurately any free-form layer pattern as a function of physical properties, printing parameters and wetting characteristics. Depending on the selection of the modelling technique to predict the deformed geometry, further considerations were required. For the purely physics-based and data-driven models, a surrogate model using response surface equations was employed to create a transfer function between printing parameters, substrate wetting characteristics and the resulting surface morphology. The development of a transfer function significantly decreased the computational time required by purely physics-based models and enabled the parameter optimisation using a multi-objective genetic algorithm approach to attain the best film dimensional accuracy. Additionally, for multilayer printing applications, a layer compensation approach was achieved utilizing a convolutional neural network trained by the predicted (deformed) geometry to reduce the out of plane error to target shape. The optimal combination of printing parameters and input image compensation helped with the generation of fine features that are traditionally difficult for inkjet, improved resolution of edges and corners by reducing the amount of overflow from material, accounted for varied topography and capillary effects thereof on the substrate surface and considered the effect of multiple layers built up on each other. This study revealed for the first time to the best of our knowledge the role of the droplet location and footprint diameter uncertainty in the stability and uniformity of printed features. Using a droplet overlap map which was proposed as a universal technique to assess the effect of printing parameters on pattern geometry, it was shown that reliable limits for break-up and bulging of printed features were obtained. Considering droplet position and diameter size uncertainties, predicted optimal printing parameters improved the quality of printed films on substrates with different wettability. Finally, a stability diagram illustrating the onset of bulging and separation for lines and films as well as the optimal drop spacing, printing frequency and stand-off distance was generated to inform visually the results. This investigation has developed a predictive physics-based model of the surface morphology of DIJP features on heterogeneous substrates and a methodology to find the printing parameters and compensate the layer geometry required for optimum part dimensional accuracy. The simplicity of the proposed technique makes it a promising tool for model driven inkjet printing process optimization, including real time process control and paves the way for better quality devices in the printed electronics industry
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