Gabriel Ziegler

Bayesian model reduction and empirical Bayes for group (DCM) studies.

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.

Estimating anatomical trajectories with Bayesian mixed-effects modeling.

We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimers Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimers Disease (AD).

Developmental cognitive neuroscience using latent change score models: A tutorial and applications

Highlights • We describe Latent change score modelling as a flexible statistical tool.• Key developmental questions can be readily formalized using LCS models.• We provide accessible open source code and software examples to fit LCS models.• White matter structural change is negatively correlated with processing speed gains.• Frontal lobe thinning in adolescence is more variable in males than females.

Efficient Gaussian Process-Based Modelling and Prediction of Image Time Series

In this work we propose a novel Gaussian process-based spatio-temporal model of time series of images. By assuming separability of spatial and temporal processes we provide a very efficient and robust formulation for the marginal likelihood computation and the posterior prediction. The model adaptively accounts for local spatial correlations of the data, and the covariance structure is effectively parameterised by the Kronecker product of covariance matrices of very small size, each encoding only a single direction in space. We provide a simple and flexible framework for within- and between-subject modelling and prediction. In particular, we introduce the Hoffman-Ribak method for efficient inference on posterior processes and its uncertainty. The proposed framework is applied in the context of longitudinal modelling in Alzheimers disease. We firstly demonstrate the advantage of our non-parametric method for modelling of within-subject structural changes. The results show that non-parametric methods demonstrably outperform conventional parametric methods. Then the framework is extended to optimize complex parametrized covariate kernels. Using Bayesian model comparison via marginal likelihood the framework enables to compare different hypotheses about individual change processes of images.

Multivariate dynamical modelling of structural change during development

ABSTRACT Here we introduce a multivariate framework for characterising longitudinal changes in structural MRI using dynamical systems. The general approach enables modelling changes of states in multiple imaging biomarkers typically observed during brain development, plasticity, ageing and degeneration, e.g. regional gray matter volume of multiple regions of interest (ROIs). Structural brain states follow intrinsic dynamics according to a linear system with additional inputs accounting for potential driving forces of brain development. In particular, the inputs to the system are specified to account for known or latent developmental growth/decline factors, e.g. due to effects of growth hormones, puberty, or sudden behavioural changes etc. Because effects of developmental factors might be region‐specific, the sensitivity of each ROI to contributions of each factor is explicitly modelled. In addition to the external effects of developmental factors on regional change, the framework enables modelling and inference about directed (potentially reciprocal) interactions between brain regions, due to competition for space, or structural connectivity, and suchlike. This approach accounts for repeated measures in typical MRI studies of development and aging. Model inversion and posterior distributions are obtained using earlier established variational methods enabling Bayesian evidence‐based comparisons between various models of structural change. Using this approach we demonstrate dynamic cortical changes during brain maturation between 6 and 22 years of age using a large openly available longitudinal paediatric dataset with 637 scans from 289 individuals. In particular, we model volumetric changes in 26 bilateral ROIs, which cover large portions of cortical and subcortical gray matter. We account for (1) puberty‐related effects on gray matter regions; (2) effects of an early transient growth process with additional time‐lag parameter; (3) sexual dimorphism by modelling parameter differences between boys and girls. There is evidence that the regional pattern of sensitivity to dynamic hidden growth factors in late childhood is similar across genders and shows a consistent anterior‐posterior gradient with strongest impact to prefrontal cortex (PFC) brain changes. Finally, we demonstrate the potential of the framework to explore the coupling of structural changes across a priori defined subnetworks using an example of previously established resting state functional connectivity. HIGHLIGHTSMultivariate approach for structural changes in development using dynamical systems.States follow a system with inputs accounting for driving forces of development.Demonstrate dynamic gray matter changes during maturation between 6 and 22 years.Account for effects of puberty and estimate a hidden growth factor affecting PFC.Explore coupled structural change within/between two resting‐state fMRI networks.

Progressive neurodegeneration following spinal cord injury: Implications for clinical trials

Objective To quantify atrophy, demyelination, and iron accumulation over 2 years following acute spinal cord injury and to identify MRI predictors of clinical outcomes and determine their suitability as surrogate markers of therapeutic intervention. Methods We assessed 156 quantitative MRI datasets from 15 patients with spinal cord injury and 18 controls at baseline and 2, 6, 12, and 24 months after injury. Clinical recovery (including neuropathic pain) was assessed at each time point. Between-group differences in linear and nonlinear trajectories of volume, myelin, and iron change were estimated. Structural changes by 6 months were used to predict clinical outcomes at 2 years. Results The majority of patients showed clinical improvement with recovery stabilizing at 2 years. Cord atrophy decelerated, while cortical white and gray matter atrophy progressed over 2 years. Myelin content in the spinal cord and cortex decreased progressively over time, while cerebellar loss decreases decelerated. As atrophy progressed in the thalamus, sustained iron accumulation was evident. Smaller cord and cranial corticospinal tract atrophy, and myelin changes within the sensorimotor cortices, by 6 months predicted recovery in lower extremity motor score at 2 years. Whereas greater cord atrophy and microstructural changes in the cerebellum, anterior cingulate cortex, and secondary sensory cortex by 6 months predicted worse sensory impairment and greater neuropathic pain intensity at 2 years. Conclusion These results draw attention to trauma-induced neuroplastic processes and highlight the intimate relationships among neurodegenerative processes in the cord and brain. These measurable changes are sufficiently large, systematic, and predictive to render them viable outcome measures for clinical trials.

Compulsivity and impulsivity are linked to distinct aberrant developmental trajectories of fronto-striatal myelination

The transition from adolescence into adulthood is a period where rapid brain development coincides with a greatly enhanced incidence of psychiatric disorder. The precise developmental brain changes that might account for this emergent psychiatric symptomatology remains obscure. Capitalising on a unique longitudinal dataset, that includes in-vivo myelin-sensitive magnetization transfer (MT) MRI, we show this transition period is characterised by brain-wide growth in MT, within both gray matter and adjacent juxta-cortical white matter. The expression of common developmental psychiatric risk symptomatology in this otherwise healthy population, namely compulsivity and impulsivity, was tied to regionally specific aberrant unfolding of these MT trajectories. This was most marked in superior frontal/cingulate cortex for compulsivity, and in inferior frontal/insular cortex for impulsivity. The findings highlight a brain developmental linkage for emergent psychiatric risk features, evident in regionally specific perturbations in the expansion of MT-related myelination.

Modelling Non-stationary and Non-separable Spatio-Temporal Changes in Neurodegeneration via Gaussian Process Convolution

Modelling longitudinal changes in organs is fundamental for the understanding of biological and pathological processes. Most of the previous works on spatio-temporal modelling of image time series relies on the assumption of stationarity of the local spatial correlation, and on the separability between spatial and temporal processes. These assumptions are often made in order to lead to computationally tractable approaches to longitudinal modelling, but inevitably lead to an oversimplification of the complex spatial and temporal dynamics underlying the biological processes. In this work we propose a novel spatio-temporal generative model of time series of images based on kernel convolutions of a white noise Gaussian process. The proposed model is parameterised by a sparse set of control points independently identified by specific spatial and temporal parameters. This formulation is highly flexible and can naturally account for spatially and temporally varying dynamics of changes. We demonstrate a preliminary application of our non-parametric method on the modelling of within-subject structural changes in the context of longitudinal analysis in Alzheimers disease. In particular we show that our method provides an accurate description of the pathological evolution of the brain, while showing high flexibility in modelling and predicting region-specific non-linearity due to accelerated structural decline in dementia.

MODELING OF HIDDEN CAUSES FOR DYNAMIC CHANGES IN STRUCTURAL INTEGRITY AND COGNITION IN SUBJECTIVE COGNITIVE DECLINE: A DELCODE PROJECT

Alzheimer’s disease) were anesthetized with intraperitoneal (i.p.) injection of propofol (150 mg/kg body weight) in combination with inhalation of 2.5% sevoflurane for 1 or 3 hrs. After awaken from anesthesia, the mice were returned to their home cages. Behavioral tests (Morris water maze, open field test, one-trial novel object recognition test, contextual and cued fear conditioning test, and elevated plus maze) were performed on various dates after anesthesia. Results:We found that anesthesia with propofol and sevoflurane caused significant deficits in spatial learning and memory, as tested using Morris Water maze 2-6 days after anesthesia exposure, in aged (17-18 months old) wild-type (WT) mice and in adult (7-8 months old) 3xTg-AD mice, but not in adult WT mice. Anesthesia resulted in long-term neurobehavioral changes in the fear conditioning task carried out 65 days after exposure to anesthesia in 3xTg-AD mice. Importantly, daily intranasal administration of insulin (1.75 U/mouse/day) for only three days prior to anesthesia completely prevented the anesthesia-induced deficits in spatial learning and memory and the long-term neurobehavioral changes tested 65 days after exposure to anesthesia in 3xTg-AD mice. Conclusions:Our results indicate that aging and Alzheimer-like brain pathology increase the vulnerability to cognitive impairment after anesthesia and that intranasal treatment with insulin can prevent anesthesia-induced cognitive impairment.