Hydraulic conductivity fields: Gaussian or not?

Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.

Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

The origin of cyclical high- and low-Cr basalts with continental crust trace element signatures in the Kalkarindji Large Igneous Province

The 510 million year old Kalkarindji Large Igneous Province correlates in time with the first major extinction event after the Cambrian explosion of life. Large igneous provinces correlate with all major mass extinction events in the last 500 million years. The genetic link between large igneous provinces and mass extinction remains unclear. My work is a contribution towards understanding magmatic processes involved in the generation of Large Igneous Provinces. I concentrate on the origin of variation in Cr in magmas and have developed a model in which high temperature melts intrude into and assimilate large amounts of upper continental crust.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Effect of constitutive material models on seismic response of two-story reinforced concrete frame

This paper focuses on the finite element (FE) response sensitivity and reliability analyses considering smooth constitutive material models. A reinforced concrete frame is modeled for FE sensitivity analysis followed by direct differentiation method under both static and dynamic load cases. Later, the reliability analysis is performed to predict the seismic behavior of the frame. Displacement sensitivity discontinuities are observed along the pseudo-time axis using non-smooth concrete and reinforcing steel model under quasi-static loading. However, the smooth materials show continuity in response sensitivity at elastic to plastic transition points. The normalized sensitivity results are also used to measure the relative importance of the material parameters on the structural responses. In FE reliability analysis, the influence of smoothness behavior of reinforcing steel is carefully noticed. More efficient and reasonable reliability estimation can be achieved by using smooth material model compare with bilinear material constitutive model.

Genetic and environmental influences on neuroimaging phenotypes: A meta-analytical perspective on twin imaging studies

Because brain structure and function are affected in neurological and psychiatric disorders, it is important to disentangle the sources of variation in these phenotypes. Over the past 15 years, twin studies have found evidence for both genetic and environmental influences on neuroimaging phenotypes, but considerable variation across studies makes it difficult to draw clear conclusions about the relative magnitude of these influences. Here we performed the first meta-analysis of structural MRI data from 48 studies on >1,250 twin pairs, and diffusion tensor imaging data from 10 studies on 444 twin pairs. The proportion of total variance accounted for by genes (A), shared environment (C), and unshared environment (E), was calculated by averaging A, C, and E estimates across studies from independent twin cohorts and weighting by sample size. The results indicated that additive genetic estimates were significantly different from zero for all metaanalyzed phenotypes, with the exception of fractional anisotropy (FA) of the callosal splenium, and cortical thickness (CT) of the uncus, left parahippocampal gyrus, and insula. For many phenotypes there was also a significant influence of C. We now have good estimates of heritability for many regional and lobar CT measures, in addition to the global volumes. Confidence intervals are wide and number of individuals small for many of the other phenotypes. In conclusion, while our meta-analysis shows that imaging measures are strongly influenced by genes, and that novel phenotypes such as CT measures, FA measures, and brain activation measures look especially promising, replication across independent samples and demographic groups is necessary.

Relationship of a variant in the NTRK1 gene to white matter microstructure in young adults

The NTRK1 gene (also known as TRKA) encodes a high-affinity receptor for NGF, a neurotrophin involved in nervous system development and myelination. NTRK1 has been implicated in neurological function via links between the T allele at rs6336 (NTRK1-T) and schizophrenia risk. A variant in the neurotrophin gene, BDNF, was previously associated with white matter integrity in young adults, highlighting the importantce of neurotrophins to white matter development. We hypothesized that NTRK1-T would relate to lower fractional anisotropy in healthy adults. We scanned 391 healthy adult human twins and their siblings (mean age: 23.6 ± 2.2 years; 31 NTRK1-T carriers, 360 non-carriers) using 105-gradient diffusion tensor imaging at 4 tesla. We evaluated in brain white matter how NTRK1-T and NTRK1 rs4661063 allele A (rs4661063-A, which is in moderate linkage disequilibrium with rs6336) related to voxelwise fractional anisotropy-acommondiffusion tensor imaging measure of white matter microstructure. We used mixed-model regression to control for family relatedness, age, and sex. The sample was split in half to test reproducibility of results. The false discovery rate method corrected for voxelwise multiple comparisons. NTRK1-T and rs4661063-A correlated with lower white matter fractional anisotropy, independent of age and sex (multiple-comparisons corrected: false discovery rate critical p=0.038 forNTRK1-Tand0.013 for rs4661063-A). In each half-sample, theNTRK1-T effectwasreplicated in the cingulum, corpus callosum, superior and inferior longitudinal fasciculi, inferior fronto-occipital fasciculus, superior corona radiata, and uncinate fasciculus. Our results suggest that NTRK1-T is important for developing white matter microstructure.

Common Alzheimer's disease risk variant within the CLU gene affects white matter microstructure in young adults

There is a strong genetic risk for late-onset Alzheimer's disease (AD), but so far few gene variants have been identified that reliably contribute to that risk. A newly confirmed genetic risk allele C of the clusterin (CLU) gene variant rs11136000 is carried by ~88% of Caucasians. The C allele confers a 1.16 greater odds of developing late-onset AD than the T allele. AD patients have reductions in regional white matter integrity. We evaluated whether the CLU risk variant was similarly associated with lower white matter integrity in healthy young humans. Evidence of early brain differences would offer a target for intervention decades before symptom onset. We scanned 398 healthy young adults (mean age, 23.6 ± 2.2 years) with diffusion tensor imaging, a variation of magnetic resonance imaging sensitive to white matter integrity in the living brain. We assessed genetic associations using mixed-model regression at each point in the brain to map the profile of these associations with white matter integrity. Each C allele copy of the CLUvariant was associated with lower fractional anisotropy-a widely accepted measure of white matter integrity-in multiple brain regions, including several known to degenerate in AD. These regions included the splenium of the corpus callosum, the fornix, cingulum, and superior and inferior longitudinal fasciculi in both brain hemispheres. Young healthy carriers of the CLU gene risk variant showed a distinct profile of lower white matter integrity that may increase vulnerability to developing AD later in life.

Relation between variants in the neurotrophin receptor gene, NTRK3, and white matter integrity in healthy young adults

The NTRK3 gene (also known as TRKC) encodes a high affinity receptor for the neurotrophin 3'-nucleotidase (NT3), which is implicated in oligodendrocyte and myelin development. We previously found that white matter integrity in young adults is related to common variants in genes encoding neurotrophins and their receptors. This underscores the importance of neurotrophins for white matter development. NTRK3 variants are putative risk factors for schizophrenia, bipolar disorder, and obsessive-compulsive disorder hoarding, suggesting that some NTRK3 variants may affect the brain.To test this, we scanned 392 healthy adult twins and their siblings (mean age, 23.6. ±. 2.2. years; range: 20-29. years) with 105-gradient 4-Tesla diffusion tensor imaging (DTI). We identified 18 single nucleotide polymorphisms (SNPs) in the NTRK3 gene that have been associated with neuropsychiatric disorders. We used a multi-SNP model, adjusting for family relatedness, age, and sex, to relate these variants to voxelwise fractional anisotropy (FA) - a DTI measure of white matter integrity.FA was optimally predicted (based on the highest false discovery rate critical p), by five SNPs (rs1017412, rs2114252, rs16941261, rs3784406, and rs7176429; overall FDR critical p=. 0.028). Gene effects were widespread and included the corpus callosum genu and inferior longitudinal fasciculus - regions implicated in several neuropsychiatric disorders and previously associated with other neurotrophin-related genetic variants in an overlapping sample of subjects. NTRK3 genetic variants, and neurotrophins more generally, may influence white matter integrity in brain regions implicated in neuropsychiatric disorders.

Extending genetic linkage analysis to diffusion tensor images to map single gene effects on brain fiber architecture

We extended genetic linkage analysis - an analysis widely used in quantitative genetics - to 3D images to analyze single gene effects on brain fiber architecture. We collected 4 Tesla diffusion tensor images (DTI) and genotype data from 258 healthy adult twins and their non-twin siblings. After high-dimensional fluid registration, at each voxel we estimated the genetic linkage between the single nucleotide polymorphism (SNP), Val66Met (dbSNP number rs6265), of the BDNF gene (brain-derived neurotrophic factor) with fractional anisotropy (FA) derived from each subject's DTI scan, by fitting structural equation models (SEM) from quantitative genetics. We also examined how image filtering affects the effect sizes for genetic linkage by examining how the overall significance of voxelwise effects varied with respect to full width at half maximum (FWHM) of the Gaussian smoothing applied to the FA images. Raw FA maps with no smoothing yielded the greatest sensitivity to detect gene effects, when corrected for multiple comparisons using the false discovery rate (FDR) procedure. The BDNF polymorphism significantly contributed to the variation in FA in the posterior cingulate gyrus, where it accounted for around 90-95% of the total variance in FA. Our study generated the first maps to visualize the effect of the BDNF gene on brain fiber integrity, suggesting that common genetic variants may strongly determine white matter integrity.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

Genetics of brain fiber architecture and intellectual performance

The study is the first to analyze genetic and environmental factors that affect brain fiber architecture and its genetic linkage with cognitive function. We assessed white matter integrity voxelwise using diffusion tensor imaging at high magnetic field (4 Tesla), in 92 identical and fraternal twins. White matter integrity, quantified using fractional anisotropy (FA), was used to fit structural equation models (SEM) at each point in the brain, generating three-dimensional maps of heritability. We visualized the anatomical profile of correlations between white matter integrity and full-scale, verbal, and performance intelligence quotients (FIQ, VIQ, and PIQ). White matter integrity (FA) was under strong genetic control and was highly heritable in bilateral frontal (a 2 = 0.55, p = 0.04, left; a 2 = 0.74, p = 0.006, right), bilateral parietal (a 2 = 0.85, p < 0.001, left; a 2 = 0.84, p < 0.001, right), and left occipital (a 2 = 0.76, p = 0.003) lobes, and was correlated with FIQ and PIQ in the cingulum, optic radiations, superior fronto- occipital fasciculus, internal capsule, callosal isthmus, and the corona radiata (p = 0.04 for FIQ and p = 0.01 for PIQ, corrected for multiple comparisons). In a cross-trait mapping approach, common genetic factors mediated the correlation between IQ and white matter integrity, suggesting a common physiological mechanism for both, and common genetic determination. These genetic brain maps reveal heritable aspects of white matter integrity and should expedite the discovery of single-nucleotide polymorphisms affecting fiber connectivity and cognition.

BDNF gene effects on brain circuitry replicated in 455 twins

Brain-derived neurotrophic factor (BDNF) plays a key role in learning and memory, but its effects on the fiber architecture of the living brain are unknown. We genotyped 455 healthy adult twins and their non-twin siblings (188 males/267 females; age: 23.7 ± 2.1. years, mean ± SD) and scanned them with high angular resolution diffusion tensor imaging (DTI), to assess how the BDNF Val66Met polymorphism affects white matter microstructure. By applying genetic association analysis to every 3D point in the brain images, we found that the Val-BDNF genetic variant was associated with lower white matter integrity in the splenium of the corpus callosum, left optic radiation, inferior fronto-occipital fasciculus, and superior corona radiata. Normal BDNF variation influenced the association between subjects' performance intellectual ability (as measured by Object Assembly subtest) and fiber integrity (as measured by fractional anisotropy; FA) in the callosal splenium, and pons. BDNF gene may affect the intellectual performance by modulating the white matter development. This combination of genetic association analysis and large-scale diffusion imaging directly relates a specific gene to the fiber microstructure of the living brain and to human intelligence.

Genetics of white matter development: A DTI study of 705 twins and their siblings aged 12 to 29

White matter microstructure is under strong genetic control, yet it is largely unknown how genetic influences change from childhood into adulthood. In one of the largest brain mapping studies ever performed, we determined whether the genetic control over white matter architecture depends on age, sex, socioeconomic status (SES), and intelligence quotient (IQ). We assessed white matter integrity voxelwise using diffusion tensor imaging at high magnetic field (4-Tesla), in 705 twins and their siblings (age range 12-29; 290. M/415. F). White matter integrity was quantified using a widely accepted measure, fractional anisotropy (FA). We fitted gene-environment interaction models pointwise, to visualize brain regions where age, sex, SES and IQ modulate heritability of fiber integrity. We hypothesized that environmental factors would start to outweigh genetic factors during late childhood and adolescence. Genetic influences were greater in adolescence versus adulthood, and greater in males than in females. Socioeconomic status significantly interacted with genes that affect fiber integrity: heritability was higher in those with higher SES. In people with above-average IQ, genetic factors explained over 80% of the observed FA variability in the thalamus, genu, posterior internal capsule, and superior corona radiata. In those with below-average IQ, however, only around 40% FA variability in the same regions was attributable to genetic factors. Genes affect fiber integrity, but their effects vary with age, sex, SES and IQ. Gene-environment interactions are vital to consider in the search for specific genetic polymorphisms that affect brain integrity and connectivity.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.