Correction of spatial distortion in magnetic resonance imaging

Dissertation to Obtain the Degree of Master in Biomedical Engineering

Single molecule simulation of diffusion and enzyme kinetics

This work presents a molecular-scale agent-based model for the simulation of enzymatic reactions at experimentally measured concentrations. The model incorporates stochasticity and spatial dependence, using diffusing and reacting particles with physical dimensions. We developed strategies to adjust and validate the enzymatic rates and diffusion coefficients to the information required by the computational agents, i.e., collision efficiency, interaction logic between agents, the time scale associated with interactions (e.g., kinetics), and agent velocity. Also, we tested the impact of molecular location (a source of biological noise) in the speed at which the reactions take place. Simulations were conducted for experimental data on the 2-hydroxymuconate tautomerase (EC 5.3.2.6, UniProt ID Q01468) and the Steroid Delta-isomerase (EC 5.3.3.1, UniProt ID P07445). Obtained results demonstrate that our approach is in accordance to existing experimental data and long-term biophysical and biochemical assumptions.

Structural Interactions in Spatial Panels

Until recently, much effort has been devoted to the estimation of panel data regression models without adequate attention being paid to the drivers of diffusion and interaction across cross section and spatial units. We discuss some new methodologies in this emerging area and demonstrate their use in measurement and inferences on cross section and spatial interactions. Specifically, we highlight the important distinction between spatial dependence driven by unobserved common factors and those based on a spatial weights matrix. We argue that, purely factor driven models of spatial dependence may be somewhat inadequate because of their connection with the exchangeability assumption. Limitations and potential enhancements of the existing methods are discussed, and several directions for new research are highlighted.

Do labour mobility and networks foster geographical knowledge diffusion? The case of European regions

The goal of this paper is twofold: first, we aim to assess the role played by inventors’ cross-regional mobility and networks of collaboration in fostering knowledge diffusion across regions and subsequent innovation. Second, we intend to evaluate the feasibility of using mobility and networks information to build cross-regional interaction matrices to be used within the spatial econometrics toolbox. To do so, we depart from a knowledge production function where regional innovation intensity is a function not only of the own regional innovation inputs but also external accessible R&D gained through interregional interactions. Differently from much of the previous literature, cross-section gravity models of mobility and networks are estimated to use the fitted values to build our ‘spatial’ weights matrices, which characterize the intensity of knowledge interactions across a panel of 269 regions covering most European countries over 6 years.

Heterogeneous 40Ar* distributions in naturally deformed muscovite: in situ UV-laser ablation evidence for micro structurally controlled intragrain diffusion

Micas are commonly used in Ar-40/Ar-39 thermochronological studies of variably deformed rocks yet the physical basis by which deformation may affect radiogenic argon retention in mica is poorly constrained. This study examines the relationship between deformation and deformation-induced microstructures on radiogenic argon retention in muscovite, A combination of furnace step-heating and high-spatial resolution in situ UV-laser ablation Ar-40/Ar-39 analyses are reported for deformed muscovites sampled from a granitic pegmatite vein within the Siviez-Mischabel Nappe, western Swiss Alps (Penninic domain, Brianconnais unit). The pegmatite forms part of the Variscan (similar to 350 Ma) Alpine basement and exhibits a prominent Alpine S-C fabric including numerous mica `fish' that developed under greenschist facies metamorphic conditions, during the dominant Tertiary Alpine tectonic phase of nappe emplacement. Furnace step-heating of milligram quantities of separated muscovite grains yields an Ar-40/Ar-39 age spectrum with two distinct staircase segments but without any statistical plateau, consistent with a previous study from the same area. A single (3 X 5 mm) muscovite porphyroclast (fish) was investigated by in situ UV-laser ablation. A histogram plot of 170 individual Ar-40/Ar-39 UV-laser ablation ages exhibit a range from 115 to 387 Ma with modes at approximately 340 and 260 Ma. A variogram statistical treatment of the (40)Ad/Ar-39 results reveals ages correlated with two directions; a highly correlated direction at 310 degrees and a lesser correlation at 0 degrees relative to the sense of shearing. Using the highly correlated direction a statistically generated (Kriging method) age contour map of the Ar-40/Ar-39 data reveals a series of elongated contours subparallel to the C-surfaces which where formed during Tertiary nappe emplacement. Similar data distributions and slightly younger apparent ages are recognized in a smaller mica fish. The observed intragrain age variations are interpreted to reflect the partial loss of radiogenic argon during Alpine (similar to 35 Ma) greenschist facies metamorphism. One-dirnensional diffusion modelling results are consistent with the idea that the zones of youngest apparent age represent incipient shear band development within the mica porphyroclasts, thus providing a network of fast diffusion pathways. During Alpine greenschist facies metamorphism the incipient shear bands enhanced the intragrain loss of radiogenic argon. The structurally controlled intragrain age variations observed in this investigation imply that deformation has a direct control on the effective length scale for argon diffusion, which is consistent with the heterogeneous nature of deformation. (C) 2001 Elsevier Science B.V. All rights reserved.

Combined analysis of grey matter voxel-based morphometry and white matter tract-based spatial statistics in late-life bipolar disorder.

Background: Previous magnetic resonance imaging (MRI) studies in young patients with bipolar disorder indicated the presence of grey matter concentration changes as well as microstructural alterations in white matter in various neocortical areas and the corpus callosum. Whether these structural changes are also present in elderly patients with bipolar disorder with long-lasting clinical evolution remains unclear. Methods: We performed a prospective MRI study of consecutive elderly, euthymic patients with bipolar disorder and healthy, elderly controls. We conducted a voxel-based morphometry (VBM) analysis and a tract-based spatial statistics (TBSS) analysis to assess fractional anisotropy and longitudinal, radial and mean diffusivity derived by diffusion tensor imaging (DTI). Results: We included 19 patients with bipolar disorder and 47 controls in our study. Fractional anisotropy was the most sensitive DTI marker and decreased significantly in the ventral part of the corpus callosum in patients with bipolar disorder. Longitudinal, radial and mean diffusivity showed no significant between-group differences. Grey matter concentration was reduced in patients with bipolar disorder in the right anterior insula, head of the caudate nucleus, nucleus accumbens, ventral putamen and frontal orbital cortex. Conversely, there was no grey matter concentration or fractional anisotropy increase in any brain region in patients with bipolar disorder compared with controls. Limitations: The major limitation of our study is the small number of patients with bipolar disorder. Conclusion: Our data document the concomitant presence of grey matter concentration decreases in the anterior limbic areas and the reduced fibre tract coherence in the corpus callosum of elderly patients with long-lasting bipolar disorder.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

A spatial accommodation by neighboring cells is required for organ initiation in Arabidopsis.

Lateral root formation in plants can be studied as the process of interaction between chemical signals and physical forces during development. Lateral root primordia grow through overlying cell layers that must accommodate this incursion. Here, we analyze responses of the endodermis, the immediate neighbor to an initiating lateral root. Endodermal cells overlying lateral root primordia lose volume, change shape, and relinquish their tight junction-like diffusion barrier to make way for the emerging lateral root primordium. Endodermal feedback is absolutely required for initiation and growth of lateral roots, and we provide evidence that this is mediated by controlled volume loss in the endodermis. We propose that turgidity and rigid cell walls, typical of plants, impose constraints that are specifically modified for a given developmental process.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Individual prediction of cognitive decline in mild cognitive impairment using support vector machine-based analysis of diffusion tensor imaging data.

Although cross-sectional diffusion tensor imaging (DTI) studies revealed significant white matter changes in mild cognitive impairment (MCI), the utility of this technique in predicting further cognitive decline is debated. Thirty-five healthy controls (HC) and 67 MCI subjects with DTI baseline data were neuropsychologically assessed at one year. Among them, there were 40 stable (sMCI; 9 single domain amnestic, 7 single domain frontal, 24 multiple domain) and 27 were progressive (pMCI; 7 single domain amnestic, 4 single domain frontal, 16 multiple domain). Fractional anisotropy (FA) and longitudinal, radial, and mean diffusivity were measured using Tract-Based Spatial Statistics. Statistics included group comparisons and individual classification of MCI cases using support vector machines (SVM). FA was significantly higher in HC compared to MCI in a distributed network including the ventral part of the corpus callosum, right temporal and frontal pathways. There were no significant group-level differences between sMCI versus pMCI or between MCI subtypes after correction for multiple comparisons. However, SVM analysis allowed for an individual classification with accuracies up to 91.4% (HC versus MCI) and 98.4% (sMCI versus pMCI). When considering the MCI subgroups separately, the minimum SVM classification accuracy for stable versus progressive cognitive decline was 97.5% in the multiple domain MCI group. SVM analysis of DTI data provided highly accurate individual classification of stable versus progressive MCI regardless of MCI subtype, indicating that this method may become an easily applicable tool for early individual detection of MCI subjects evolving to dementia.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Structured sparsity for spatially coherent fibre orientation estimation in diffusion MRI.

We propose a novel formulation to solve the problem of intra-voxel reconstruction of the fibre orientation distribution function (FOD) in each voxel of the white matter of the brain from diffusion MRI data. The majority of the state-of-the-art methods in the field perform the reconstruction on a voxel-by-voxel level, promoting sparsity of the orientation distribution. Recent methods have proposed a global denoising of the diffusion data using spatial information prior to reconstruction, while others promote spatial regularisation through an additional empirical prior on the diffusion image at each q-space point. Our approach reconciles voxelwise sparsity and spatial regularisation and defines a spatially structured FOD sparsity prior, where the structure originates from the spatial coherence of the fibre orientation between neighbour voxels. The method is shown, through both simulated and real data, to enable accurate FOD reconstruction from a much lower number of q-space samples than the state of the art, typically 15 samples, even for quite adverse noise conditions.

A missing spatial link in institutional quality

History tells that institutions evolve gradually over time, pushing new ideas across borders and cultures. Globalisation is argued to accelerate this process. We examine the spatial links of different political institutions across borders. Applying various tests for spatial proximity, we do not find evidence of contemporaneous spatial links. This result is robust to various measures of distance and of cultural proximity across countries. Instead, when we analyse long run dynamics diffusion of institutions seems to occur only gradually.