A patient-specific poroelastic model of the brain was constructed in COMSOL Multiphysics and evaluated for its usability in a clinical setting. Image processing of magnetic resonance (MR) images of a standard (uninjured) brain and a computed tomography (CT) scan of a patient with a subdural hematoma was used to make an estimation of the shape patient’s pre-injury brain and obtain a deformation map describing the displacement due to the hematoma. A finite-element mesh of the normal brain was generated from a standard MRI-based brain atlas. The steady-state solution of the normal brain was similar to that found in a previous study. The steady-state solution of the deformed brain had the same pressure distribution as the normal brain, which was predicted by analysis of the equations. When the hematoma was simulated over 15000 seconds, the progression of the pressure over time seemed qualitatively plausible. The strain in the steady-state deformed brain and time-based studies generally behaved as expected, but a few regions near the surface of the brain adjacent to the hematoma had unexpectedly high values. When the magnitude of hematoma deformation was altered, it was seen that intracranial pressure, maximum pressure and strain had an exponential-recovery relationship over time for all factors. Strain rate decreased exponentially with time. The intracranial pressure, maximum pressure and strain had a linear relationship with a scale factor that was used to change to magnitude of deformation of the outer surface. Cortical cell death increased exponentially with scale factor and with time. Hematoma volume had a linear relationship with scale factor. Simulated pressure-volume curves did not have the same shape as experimental curves and the observed deformation had noticeable differences in mid-line shift when compared with the real brain. Conditions of hyper- and hypotension had big effects on the pressure, but not the strain. The results indicate that the model has the potential to be a good tool in brain injury evaluation, but more work must be done to increase accuracy and to validate the model.

An aerodynamic propeller model, which can contribute to the prediction of structural loads experienced by aircraft in different flight maneuvers is presented.The model is based on Blade Element Momentum theory and is able to predict the unsymmetrical and frequency-dependent forces and moments induced by the propeller on the airplane structure at steady and unsteady inflow-conditions.In order to validate the model, a comparison with experimental results was performed and it can be seen that the model is in agreement with the experimental data providing that the aerodynamic data used for the calculations has good accuracy. / En modell har utvecklats för att beräkna aerodynamiska krafter som orsakas av propellern vid manöverflygning. Modellen använder sig av klassiska bladelementteorin för predikering av osymmetriska stationära krafter som uppstår vid snedanblåsning av propellerskivan. Modellen kommer att användas inom ett forskningsprojekt om effektiv beräkning av aerodynamiska laster vid flygmanövrar och i vindbyar. En vidareutveckling av den klassiska metoden används för att ta fram instationära kraftbidrag i frekvensplanet i en form som är lämpligt för aeroelastiska stabilitetsanalys och beräkning av vindbylasterna.Jämförelser med omfattande experimentella resultat har genomförts för att validera modellen. Inom ramen för antaganden och noggrannheten i modellens indata kan modellens tillförlitighet bedömas som tillräckligt för ändamålet. Däremot visar sig att propellermodellen är -- som förväntat -- mindre lämpligt för att bedöma propellerlasterna utanför propellerns reguljära driftområdet.

An image matching system for object recognition in scenes of varying complexity was constructed in Matlab for evaluating the recognition quality of two types of image features: SURF (Speeded-Up Robust Features) and SIFT (Scale Invariant Feature Transform) using the affine Hough matching algorithm for finding matches between training and test images. In the experimental part of the thesis, the matching was algorithm tested for varying number of image features extracted from the train and test images, namely 1000, 2000 and 3000 interest points. These experiments were carried out against 9 objects of different complexity, including difficulties such as repeating patterns on the image, down and upscaling of the object, cluttered scenes, silhouette features, partly occluded object and multiple known objects in the scene. The work provides the directions for improvement of the given view-based recognition algorithm and suggests other possible ways to perform the object matching with higher quality.

We study the problem of packing spheres of different radii into a rigid container. The spheres are packed as densely as possible so they neither overlap nor cross the boundaries of the container. The packed spheres are then meshed in preparation for finite element analysis. The spheres are meshed individually (separately) without taking care of the contact surface between spheres or containers wall. The last step is the hydrostatic pressing of the spheres made of elastic-plastic materials and with simplified contact conditions. Such simulations are of interest to the metallurgist because they can show differences in structure between grain surfaces and centres.

Numerical simulations play an important role to uncover the dynamic behaviour at the cellular and network levels and accelerate the work in the field of Neuroscience. The modern computational technologies have made it possible to simulate a huge network of neurons which was possible only in theory two decades ago. The simulations of networks of thousand of neurons are carried out on the parallel machine Cray XE6 system, based on the AMD Opteron 12-core which shows good scaling properties. These models can be beneficial for the generation of global behaviour which could not be produced by fewer cells. For example, the effect of inhibition in a striatal network of MSNs is only seen if the number of cells and the synapses are increased sufficiently. The simulated responses of cells are greatly influenced by the numerical scheme. This has been demonstrated using gap junctions between striatal fast spiking inter-neurons. Implicit numerical schemes need to be used in order to get stable and accurate results. The simulations are carried out using serial and parallel implementations on the GENESIS and PGENESIS simulator respectively. The limitations of the simulators have been highlighted by performing several simulation experiments. After exploiting the shortcomings presented in this work, it would be possible to use the insight to investigate biologically relevant questions. / Numeriska simuleringar har en stor betydelse när man vill undersöka och förstå dynamiska fenomen på cell- och nätverksnivå. Detta är mycket viktigt för hela neuroområdet. Dagens beräkningsteknologier har gjort det möjligt att simulera stora nätverk av neuroner, vilket knappast var realistiskt för 10-20 år sedan. Simuleringar av nätverk som består av tusentals neuroner kan göras lokalt på KTH på en parallelldator som heter Cray XE6 och som är baserad på AMD Opteron 12-core,med goda skalningsegenskaper. Sådana nätverkssimuleringar är nödvändiga för att undersöka det globala beteendet i nätverket vilket inte kan produceras med färre antal celler. Ett exempel på en nätverkseffekt som endast kan ses i en storskalig modell är hur inhibitionen mellan s.k. medium spiny neurons (MSNs) i det striatal nätverket fungerar. Eftersom inhibitionen mellan varje cellpar är mycket svag behövs input från många celler för att nätverket skall påverkas. Simuleringsresultaten påverkas signifikant av vilken numerisk metod som används. Detta demonstreras med ett striatalt nätverk innehållande s.k. gap junctions (elektriska synapser) mellan striatala fast-spiking interneurons (FS). Implicita numeriska metoder blir nödvändiga för att få stabila och riktiga resultat. Simuleringar görs både seriellt och parallellt med hjälp m.h.a. Genesis simulatorn (PGenesis för parallella implementationer), vilket är en standardsimulator för biofysikaliskt detaljerade neuronmodeller. För att utvärdera Genesis simulatorn och dess svagheter har flera simuleringsexperiment utförts. Insikter från dessa simuleringar, vilka diskuteras i detta arbete, kan hjälpa till att lägga en grund för framtida användning av Genesis för storskaliga simuleringar.

Some cases of infant skull fracture fall under the category of forensic study where it is not obvious whether the head trauma happened due to an accident or abuse. To be able to determine the cause of the head trauma with sufficient accuracy, biomechanical analysis using finite element modeling of the infant cranium has been established. By simulating the trauma, one may be able to obtain the fracture propagation of the skull and from it determine if the scenario narrative is plausible. Geometry of skull, sutures, scalp and brain of a 2 month old infant head was obtained using CT images and meshed using voxel hexahedral meshing. Simulation of an impact to the head from a fall of 0.82 m height, to a rigid floor, was carried out in the non-linear finite element program LS-Dyna. Two scenarios were simulated: an impact to the occipitalparietal bones and an impact to the right parietal bone. The fracture propagation was obtained using the Chang-Chang Composite Failure Model as a constitutive model for the skull bones. The amount of material parameters gathered in the present study to predict fracture of the infant skull has not been obtained before, to the best knowledge of author. Validation of the models’ ability to show relatively correct fracture propagation was carried out by comparing the obtained fracture pattern from the parietal-occipital impact against published fracture patterns of infant PMHS skulls from a free fall onto a hard surface. The fracture pattern was found to be in good compliance with the published data. The fracture pattern in the parietal bone from the impact was compared against a fracture pattern from a previously constructed model at STH. The patterns of the models show some similarities but improvements to the model and further validations need to be carried out. / Några skallskador hos spädbarn ger grund till kriminaltekniska studier där det inte är självklart om skallskadan skett på grund av en olycka eller misshandel. För att kunna fastställa orsaken till skallskadan med tillräcklig noggrannhet har biomekaniska analyser med finita element modeler av barns huvud genomförts. Genom att simulera traumat kan man kunna få sprickpropagering I skallbenet och från den avgöra om scenariot är rimligt. Geometrin för skallen, suturer, hårbotten och hjärnan hos ett 2 månader gammalt spädbarns huvud erhölls genom CT-bilder och Voxel hexahedermeshning. Simulering av påverkan på huvudet från ett fall på 0,82 m höjd mot ett hart golv simulerades i det icke-linjära finita element programmet LS-Dyna. Två scenarier simulerades: ett islag mot nack-hjässbenet och ett mot det högra hjässbenet. Sprickpropagering simulerades med en Chang-Chang Composite konstitutiv frakturmodell för skallbenet. Den omfattande mängd materialparametrar som sammanfattades i denna studie för att prediktera skallbensfrakturer hos spädbarnets har, enligt författarens kännedom, inte erhållits tidigare. Validering av modellernas förmåga att visa relativt korrekt sprickpropagering genomfördes genom att jämföra det erhållna frakturmönstret från simuleringarna med publicerade frakturmönster från spädbarn för fritt fall mot en hård yta mot nack-hjässbenet. Frakturmönstret befanns vara i god överensstämmelse med publicerade data. Brottmönstret i hjässbenet jämfördes med frakturmönstret från en tidigare konstruerad modell på KTH. Brottmönstren från modellerna visar vissa likheter men förbättringar av modellen och ytterligare valideringar måste genomföras.

The focus of this report will be on independence complexes constructed from independent sets of members of sequences graphs. For such independence complexes, we will study generating functions and closed formulae for the Euler characteristics and f-polynomials, as well as homology groups of different degrees. All of these can be computed by hand, although this quickly becomes tedious as well as really difficult to do, hence recursive methods will be used instead. the generating functions, bounded formulae and recursive equations will be compared to known number sequences, and where possible bijections to other problems will be establised. For the independence complexes of each graphs sequence, formulae will be given for where the homology groups are nonzero, as well as in some cases formulae for the exact dimensions of the homology groups for each complex.

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Two topics in temporal graphical probabilistic models are studied. The topics are treated in separate papers, both with applications in finance. The first paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model and some toy examples with promising results. The second paper treats probabilistic graphical models in continuous time —a class of models with the ability to express causality. Tools for inference in these models are developed and employed in the design of a causality measure. The framework is used to analyze tick-by-tick data from the foreign exchange market. / Två teman inom temporala grafiska modeller betraktas. De behandlas i separata artiklar, båda med tillämpningar inom finans. Den första artikeln studerar inferens i dynamiska Bayesianska nätverk med Monte Carlo-metoder. En ny metod för att simulera slumptal föreslås. Metoden delar upp tillståndsrummet i underrum. Detta gör att simuleringarna kan utföras parallellt med oberoende och distinkta simuleringstekniker på underrummen. Metodiken demonstreras på en volatilitesmodell och ett par leksaksmodeller med lovande resultat. Den andra artikeln behandlar probabilistiska grafiska modeller i kontinuerlig tid. Dessa modeller har förmåga att uttrycka kausalitet. Verktyg för inferens i dessa modeller utvecklas och används för att designa ett kausalitets-mått. Ramverket tillämpas genom att analysera tick-data från valutamarknaden. / <p>QC 20150218</p>

A finite element based numerical method for the two-dimensional elliptic interface problems is presented. Due to presence of these interfaces the problem will contain discontinuities in the coefficients and singularities in the right hand side that are represented by delta functionals along the interface. As a result, the solution to the interface problem and its derivatives may have jump discontinuities. The introduced method is specifically designed to handle this features of the solution using non-body fitted grids, i.e. the grids are not aligned with the interfaces. The main idea is to modify the standard basis function in the vicinity of the interface such that the jump conditions are well approximated. The resulting finite element space is, in general, non-conforming. The interface itself is represented by a set of Lagrangian markers together with a parametric description connecting them. To illustrate the abilities of the method, numerical tests are presented. For all the considered test problems, the introduced method has been shown to have super-linear or second order of convergence. Our approach is also compared with the standard finite element method. Finally, the method is applied to the interface Stokes problem, where the interface represents an elastic stretched band immersed in fluid. Since we assume the fluid to be homogeneous, the Stokes equations are reduced to a sequence of three Poisson problems that are solved with our method. The numerical results agree well with those found in the literature. / QC 20101118