Longitudinal growth modeling of discrete-time functions with application to DTI tract evolution in early neurodevelopment

pre-printWe present a new framework for spatiotemporal analysis of parameterized functions attributed by properties of 4D longitudinal image data. Our driving application is the measurement of temporal change in white matter diffusivity of fiber tracts. A smooth temporal modeling of change from a discrete-time set of functions is obtained with an extension of the logistic growth model to time-dependent spline functions, capturing growth with only a few descriptive parameters. An unbiased template baseline function is also jointly estimated. Solution is demonstrated via energy minimization with an extension to simultaneous modeling of trajectories for multiple subjects. The new framework is validated with synthetic data and applied to longitudinal DTI from 15 infants. Interpretation of estimated model growth parameters is facilitated by visualization in the original coordinate space of fiber tracts

Parametric regression scheme for distributions: analysis of DTI fiber tract diffusion changes in early Brain Development

pre-printTemporal modeling frameworks often operate on scalar variables by summarizing data at initial stages as statistical summaries of the underlying distributions. For instance, DTI analysis often employs summary statistics, like mean, for regions of interest and properties along fiber tracts for population studies and hypothesis testing. This reduction via discarding of variability information may introduce significant errors which propagate through the procedures. We propose a novel framework which uses distribution-valued variables to retain and utilize the local variability information. Classic linear regression is adapted to employ these variables for model estimation. The increased stability and reliability of our proposed method when compared with regression using single-valued statistical summaries, is demonstrated in a validation experiment with synthetic data. Our driving application is the modeling of age-related changes along DTI white matter tracts. Results are shown for the spatiotemporal population trajectory of genu tract estimated from 45 healthy infants and compared with a Krabbe's patient

Doctor of Philosophy

dissertationMany mental illnesses are thought to have their origins in early stages of development, encouraging increased research efforts related to early neurodevelopment. Magnetic resonance imaging (MRI) has provided us with an unprecedented view of the brain in vivo. More recently, diffusion tensor imaging (DTI/DT-MRI), a magnetic resonance imaging technique, has enabled the characterization of the microstrucutral organization of tissue in vivo. As the brain develops, the water content in the brain decreases while protein and fat content increases due to processes such as myelination and axonal organization. Changes of signal intensity in structural MRI and diffusion parameters of DTI reflect these underlying biological changes. Longitudinal neuroimaging studies provide a unique opportunity for understanding brain maturation by taking repeated scans over a time course within individuals. Despite the availability of detailed images of the brain, there has been little progress in accurate modeling of brain development or creating predictive models of structure that could help identify early signs of illness. We have developed methodologies for the nonlinear parametric modeling of longitudinal structural MRI and DTI changes over the neurodevelopmental period to address this gap. This research provides a normative model of early brain growth trajectory as is represented in structural MRI and DTI data, which will be crucial to understanding the timing and potential mechanisms of atypical development. Growth trajectories are described via intuitive parameters related to delay, rate of growth, and expected asymptotic values, all descriptive measures that can answer clinical questions related to quantitative analysis of growth patterns. We demonstrate the potential of the framework on two clinical studies: healthy controls (singletons and twins) and children at risk of autism. Our framework is designed not only to provide qualitative comparisons, but also to give researchers and clinicians quantitative parameters and a statistical testing scheme. Moreover, the method includes modeling of growth trajectories of individuals, resulting in personalized profiles. The statistical framework also allows for prediction and prediction intervals for subject-specific growth trajectories, which will be crucial for efforts to improve diagnosis for individuals and personalized treatment

Regional characterization of longitudinal DT-MRI to study white matter maturation of the early developing brain

The human brain undergoes rapid and dynamic development early in life. Assessment of brain growth patterns relevant to neurological disorders and disease requires a normative population model of growth and variability in order to evaluate deviation from typical development. In this paper, we focus on maturation of brain white matter as shown in diffusion tensor MRI (DT-MRI), measured by fractional anisotropy (FA), mean diffusivity (MD), as well as axial and radial diffusivities (AD, RD). We present a novel methodology to model temporal changes of white matter diffusion from longitudinal DT-MRI data taken at discrete time points. Our proposed framework combines nonlinear modeling of trajectories of individual subjects, population analysis, and testing for regional differences in growth pattern. We first perform deformable mapping of longitudinal DT-MRI of healthy infants imaged at birth, 1 year, and 2 years of age, into a common unbiased atlas. An existing template of labeled white matter regions is registered to this atlas to define anatomical regions of interest. Diffusivity properties of these regions, presented over time, serve as input to the longitudinal characterization of changes. We use non-linear mixed effect (NLME) modeling where temporal change is described by the Gompertz function. The Gompertz growth function uses intuitive parameters related to delay, rate of change, and expected asymptotic value; all descriptive measures which can answer clinical questions related to quantitative analysis of growth patterns. Results suggest that our proposed framework provides descriptive and quantitative information on growth trajectories that can be interpreted by clinicians using natural language terms that describe growth. Statistical analysis of regional differences between anatomical regions which are known to mature differently demonstrates the potential of the proposed method for quantitative assessment of brain growth and differences thereof. This will eventually lead to a prediction of white matter diffusion properties and associated cognitive development at later stages given imaging data at early stages

Examining the development of brain structure in utero with fetal MRI, acquired as part of the Developing Human Connectome Project

The human brain is an incredibly complex organ, and the study of it traverses many scales across space and time. The development of the brain is a protracted process that begins embryonically but continues into adulthood. Although neural circuits have the capacity to adapt and are modulated throughout life, the major structural foundations are laid in utero during the fetal period, through a series of rapid but precisely timed, dynamic processes. These include neuronal proliferation, migration, differentiation, axonal pathfinding, and myelination, to name a few. The fetal origins of disease hypothesis proposed that a variety of non-communicable diseases emerging in childhood and adulthood could be traced back to a series of risk factors effecting neurodevelopment in utero (Barker 1995). Since this publication, many studies have shown that the structural scaffolding of the brain is vulnerable to external environmental influences and the perinatal developmental window is a crucial determinant of neurological health later in life. However, there remain many fundamental gaps in our understanding of it. The study of human brain development is riddled with biophysical, ethical, and technical challenges. The Developing Human Connectome Project (dHCP) was designed to tackle these specific challenges and produce high quality open-access perinatal MRI data, to enable researchers to investigate normal and abnormal neurodevelopment (Edwards et al., 2022). This thesis will focus on investigating the diffusion-weighted and anatomical (T2) imaging data acquired in the fetal period, between the second to third trimester (22 – 37 gestational weeks). The limitations of fetal MR data are ill-defined due to a lack of literature and therefore this thesis aims to explore the data through a series of critical and strategic analysis approaches that are mindful of the biophysical challenges associated with fetal imaging. A variety of analysis approaches are optimised to quantify structural brain development in utero, exploring avenues to relate the changes in MR signal to possible neurobiological correlates. In doing so, the work in this thesis aims to improve mechanistic understanding about how the human brain develops in utero, providing the clinical and medical imaging community with a normative reference point. To this aim, this thesis investigates fetal neurodevelopment with advanced in utero MRI methods, with a particular emphasis on diffusion MRI. Initially, the first chapter outlines a descriptive, average trajectory of diffusion metrics in different white matter fiber bundles across the second to third trimester. This work identified unique polynomial trajectories in diffusion metrics that characterise white matter development (Wilson et al., 2021). Guided by previous literature on the sensitivity of DWI to cellular processes, I formulated a hypothesis about the biophysical correlates of diffusion signal components that might underpin this trend in transitioning microstructure. This hypothesis accounted for the high sensitivity of the diffusion signal to a multitude of simultaneously occurring processes, such as the dissipating radial glial scaffold, commencement of pre-myelination and arborization of dendritic trees. In the next chapter, the methods were adapted to address this hypothesis by introducing another dimension, and charting changes in diffusion properties along developing fiber pathways. With this approach it was possible to identify compartment-specific microstructural maturation, refining the spatial and temporal specificity (Wilson et al., 2023). The results reveal that the dynamic fluctuations in the components of the diffusion signal correlate with observations from previous histological work. Overall, this work allowed me to consolidate my interpretation of the changing diffusion signal from the first chapter. It also serves to improve understanding about how diffusion signal properties are affected by processes in transient compartments of the fetal brain. The third chapter of this thesis addresses the hypothesis that cortical gyrification is influenced by both underlying fiber connectivity and cytoarchitecture. Using the same fetal imaging dataset, I analyse the tissue microstructural change underlying the formation of cortical folds. I investigate correlations between macrostructural surface features (curvature, sulcal depth) and tissue microstructural measures (diffusion tensor metrics, and multi-shell multi-tissue decomposition) in the subplate and cortical plate across gestational age, exploring this relationship both at the population level and within subjects. This study provides empirical evidence to support the hypotheses that microstructural properties in the subplate and cortical plate are altered with the development of sulci. The final chapter explores the data without anatomical priors, using a data-driven method to extract components that represent coordinated structural maturation. This analysis aims to examine if brain regions with coherent patterns of growth over the fetal period converge on neonatal functional networks. I extract spatially independent features from the anatomical imaging data and quantify the spatial overlap with pre-defined neonatal resting state networks. I hypothesised that coherent spatial patterns of anatomical development over the fetal period would map onto the functional networks observed in the neonatal period. Overall, this thesis provides new insight about the developmental contrast over the second to third trimester of human development, and the biophysical correlates affecting T2 and diffusion MR signal. The results highlight the utility of fetal MRI to research critical mechanisms of structural brain maturation in utero, including white matter development and cortical gyrification, bridging scales from neurobiological processes to whole brain macrostructure. their gendered constructions relating to women

Doctor of Philosophy

dissertationMagnetic Resonance (MR) is a relatively risk-free and flexible imaging modality that is widely used for studying the brain. Biophysical and chemical properties of brain tissue are captured by intensity measurements in T1W (T1-Weighted) and T2W (T2-Weighted) MR scans. Rapid maturational processes taking place in the infant brain manifest as changes in co{\tiny }ntrast between white matter and gray matter tissue classes in these scans. However, studies based on MR image appearance face severe limitations due to the uncalibrated nature of MR intensity and its variability with respect to changing conditions of scan. In this work, we develop a method for studying the intensity variations between brain white matter and gray matter that are observed during infant brain development. This method is referred to by the acronym WIVID (White-gray Intensity Variation in Infant Development). WIVID is computed by measuring the Hellinger Distance of separation between intensity distributions of WM (White Matter) and GM (Gray Matter) tissue classes. The WIVID measure is shown to be relatively stable to interscan variations compared with raw signal intensity and does not require intensity normalization. In addition to quantification of tissue appearance changes using the WIVID measure, we test and implement a statistical framework for modeling temporal changes in this measure. WIVID contrast values are extracted from MR scans belonging to large-scale, longitudinal, infant brain imaging studies and modeled using the NLME (Nonlinear Mixed Effects) method. This framework generates a normative model of WIVID contrast changes with time, which captures brain appearance changes during neurodevelopment. Parameters from the estimated trajectories of WIVID contrast change are analyzed across brain lobes and image modalities. Parameters associated with the normative model of WIVID contrast change reflect established patterns of region-specific and modality-specific maturational sequences. We also detect differences in WIVID contrast change trajectories between distinct population groups. These groups are categorized based on sex and risk/diagnosis for ASD (Autism Spectrum Disorder). As a result of this work, the usage of the proposed WIVID contrast measure as a novel neuroimaging biomarker for characterizing tissue appearance is validated, and the clinical potential of the developed framework is demonstrated

Bayesian Analysis of Varying Coefficient Models and Applications

The varying coefficient models have been very important analytic tools to study the dynamic pattern in biomedicine fields. Since nonparametric varying coefficient models make few assumptions on the specification of the model, the 'curse of dimensionality' is an very important issue. Nonparametric Bayesian methods combat the curse of dimensionality through specifying a sparseness-favoring structure. This is accomplished through the Bayesian penalty for model complexity (Jeffreys and Berger, 1992) and is aided through centering on a base Bayesian parametric model. This dissertation presents three novel semiparametric Bayesian methods for the analysis of longitudinal data, diffusion tensor imaging data, and longitudinal circumplex data. In longitudinal data analysis, we propose a semiparametric Bayes approach to allow the impact of the predictors to vary across subjects, which allows flexibly local borrowing of information across subjects. Local hypothesis testing and confidence bands are developed for the identification of time windows for significant predictor impact, adjusting for multiple comparisons. The methods are assessed using simulation studies and applied to a yeast cell-cycle gene expression data set. In analyzing diffusion tensor imaging data, we propose a semiparametric Bayesian local functional model to connect multiple diffusion properties along white matter fiber bundles with a set of covariates of interest. An LPP2 prior facilitates global and local borrowing of information among subjects, while an infinite factor model flexibly represents low-dimensional structure. Local hypothesis testing and confidence bands are developed to identify fiber segments for significant association of covariates with multiple diffusion properties, controlling for multiple comparisons. The method is assessed by a simulation study and illustrated via two fiber tract data sets for neurodevelopment. In analyzing longitudinal circumplex data, we propose a semiparametric Bayesian infinite state-space circumplex model to capture the dynamic transition pattern of affective experience, where affects are characterized as an ordering on the circumference of a circle. A sticky infinite state hidden Markov model via hierarchical Dirichlet proces is used to address the time related state-switching structure and the self-transition feature. The method is assessed by a simulation study and an emotion data set for the dynamics of emotion regulation

Diffusion Tensor Imaging Biomarkers of Brain Development and Disease

<p>Understanding the structure of the brain has been a major goal of neuroscience research over the past century, driven in part by the understanding that brain structure closely follows function. Normative brain maps, or atlases, can be used to understand normal brain structure, and to identify structural differences resulting from disease. Recently, diffusion tensor magnetic resonance imaging has emerged as a powerful tool for brain atlasing; however, its utility is hindered by image resolution and signal limitations. These limitations can be overcome by imaging fixed ex-vivo specimens stained with MRI contrast agents, a technique known as diffusion tensor magnetic resonance histology (DT-MRH). DT-MRH represents a unique, quantitative tool for mapping the brain with unprecedented structural detail. This technique has engendered a new generation of 3D, digital brain atlases, capable of representing complex dynamic processes such as neurodevelopment. This dissertation explores the use of DT-MRH for quantitative brain atlasing in an animal model and initial work in the human brain. </p><p>Chapter 1 describes the advantages of the DT-MRH technique, and the motivations for generating a quantitative atlas of rat postnatal neurodevelopment. The second chapter covers optimization of the DT-MRH hardware and pulse sequence design for imaging the developing rat brain. Chapter 3 details the acquisition and curation of rat neurodevelopmental atlas data. Chapter 4 describes the creation and implementation of an ontology-based segmentation scheme for tracking changes in the developing brain. Chapters 5 and 6 pertain to analyses of volumetric changes and diffusion tensor parameter changes throughout rat postnatal neurodevelopment, respectively. Together, the first six chapters demonstrate many of the unique and scientifically valuable features of DT-MRH brain atlases in a popular animal model.</p><p>The final two chapters are concerned with translating the DT-MRH technique for use in human and non-human primate brain atlasing. Chapter 7 explores the validity of assumptions imposed by DT-MRH in the primate brain. Specifically, it analyzes computer models and experimental data to determine the extent to which intravoxel diffusion complexity exists in the rhesus macaque brain, a close model for the human brain. Finally, Chapter 8 presents conclusions and future directions for DT-MRH brain atlasing, and includes initial work in creating DT-MRH atlases of the human brain. In conclusion, this work demonstrates the utility of a DT-MRH brain atlasing with an atlas of rat postnatal neurodevelopment, and lays the foundation for creating a DT-MRH atlas of the human brain.</p>Dissertatio

Neurodevelopment under the prism of environmental challenges

Prenatal development affects adult health. Exposures to a variety of prenatal environ-mental factors have important effects on fetal development and, in turn, are extensively associated with neurobehavioral, structural and functional phenotypes after birth. Developmental processes are in part promoted by orchestrated levels of glucocorticoids, which are steroid hormones involved in fetal organ maturation. Glucocorticoids also mediate the hormonal stress response of the organism as part of the hypothalamic-pituitary-adrenal axis. During pregnancy levels of glucocorticoids outside of the normal range, either due to maternal pathology including stress-related psychiatric disorders or to antenatal synthetic glucocorticoid treatments, have been associated with altered brain structural and neurobehavioral phenotypes after birth. Interestingly, developmental time-windows seem to interplay with the exposure to influence the direction of post-natal phenotypes. Exposures later in gestation are mainly associated with adverse out-comes while exposures earlier in gestation are additionally associated with potentially beneficial outcomes. While many studies have investigated the effects of glucocorticoids on late developmental time-windows, so far little evidence is available on their effects on early human cortical development and especially during the neurogenic period, which is when neurons are produced. Thus, the potential cellular and molecular underpinnings of the timing dependent divergent effects of glucocorticoids on postnatal phenotypes are not known. To investigate these processes in a complex model of early human neurodevelopment that is reactive to environmental stimuli, I used induced Pluripotent Stem Cells-derived 3-dimensional cerebral organoids and combined them with in vivo mouse neurodevelopment. I found that application of glucocorticoids during neurogenesis increases neurogenic processes that are enriched in species with a gyrified brain, like humans, while are rare in species with a smooth brain, like rodents. These processes contribute to the increased neuronal production and cortical expansion seen in gyrencephalic species. More specifically, at the molecular level this effect is mediated by the glucocorticoid receptor, a transcription factor, which in turn activates ZBTB16 by altering its methylation landscape in specific DNA regulatory elements. Subsequently ZBTB16, a transcription factor itself, increases the expression of PAX6, a key driver of neurogenesis, by activating its promoter. This results in increased numbers of progenitor cells expressing PAX6 and EOMES (a marker of more mature progenitors) in the basal regions of the germinal zones in both organoids and mice. PAX6- and EOMES- positive progenitors are enriched in gyrified species while they are rare in species with smooth brains. The increased numbers of these highly proliferative and neurogenic progenitors lead to an extended neurogenic period and ultimately to increased production of deep layer neurons (BCL11B- positive). Finally, the altered cellular architecture due to glucocorticoids and ZBTB16 potentially mediates beneficial postnatal outcomes as indicated by causal associations with higher educational attainment and increased postnatal cortical thick-ness. This work highlights the importance of early neurodevelopment and specifically of the neurogenic period as a sensitive time-window for glucocorticoid effects. In addition, the molecular and cellular mechanisms as well as the pathways identified could have pro-found implications for our understanding of glucocorticoid effects during early brain development that potentially mediate postnatal outcomes