## Brain Imaging Analysis Methods

The UCLA NIC uses a variety of analysis techniques, both univariate and multivariate to interrogate imaging data. For univariate analysis of neuroimaging data, parametric statistical models are assumed at each voxel, using the General Linear Model (GLM) to describe the data in terms of experimental and confounding effects, and residual variability. For fMRI, the GLM is used in combination with a temporal model, convolving condition parameters with a Haemodynamic Response Function (HRF). Classical statistical inference is used to test hypotheses that are expressed in terms of GLM parameters. This uses an image whose voxel values are statistics, a Statistic Image. For such classical inferences, the multiple comparisons problem is addressed using continuous random field theory RFT, assuming the statistic image to be a good lattice representation of an underlying continuous stationary random field. This results in inference based on corrected p-values. Bayesian inference can be used in place of classical inference.

**Statistical Parametric Mapping (SPM):** Statistical parametric mapping is a technique used to identify functionally specialized brain responses and is the most prevalent approach to characterizing functional anatomy and disease-related changes. The characterization of a regionally specific effect rests on estimation and inference. Inferences in neuroimaging may be about differences expressed when comparing one group of subjects to another or, within subjects, changes over a sequence of observations. They may pertain to structural differences (e.g. in voxel-based morphometry) or neurophysiological indices of brain functions (e.g. fMRI and PET). Statistical parametric mapping is a univariate, voxel-based approach, employing classical inference. The SPM software is a suite of MATLAB (The MathWorks, Inc) functions and subroutines with some externally compiled C routines. SPM was written to organise and interpret functional neuroimaging data by members and collaborators of the Functional Imaging Laboratory (FIL), Wellcome Department of Imaging Neuroscience, UCL, UK. The main features of the software are: Realignment of image sequences, Automated non-linear spatial normalization, Image segmentation, Coregistration, Spatial smoothing, Specification of design matrices for GLMs, (Restricted) Maximum Likelihood estimation of GLM parameters, Formation of Statistical Parametric Maps

**FSL:** FSL is a comprehensive library of analysis tools for FMRI, MRI and DTI brain imaging data, written mainly by members of the Analysis Group, FMRIB, Oxford, UK. The main features of the software are: Model-based FMRI analysis: data preprocessing (including MCFLIRT motion correction); first-level GLM timeseries analysis; higher-level FLAME Bayesian mixed effects analysis, Model-free FMRI analysis using Probabilistic Independent Component Analysis (PICA), Generation of optimal HRF basis functions and Bayesian activation estimation, Integrated Registration and Segmentation Tool, Diffusion Toolbox – tools for low-level diffusion parameter reconstruction and probabilistic tractography, including cross-fibre modelling.

**Effective Connectivity:** While PET and fMRI can be very effective as a noninvasive method for localizing brain activation during specific tasks, functional localization does not reveal any information about the communication between active regions. Activations in specific brain areas may have very different interpretations based on the co-activation of other regions that are connected via a dynamic network of inputs and projections. Indeed, neural network information can provide critical insights into brain function especially in functional pain disorders such as IBS, where the pathophysiology of the disease remains unclear, and as such, existing pharmacological therapies are suboptimal.

Network analysis supports inferences regarding the interrelations among specified brain areas in a network, and how these may vary depending on individual characteristics, behaviors, and cognitive processes. Network analysis in our lab employs robust and sophisticated multivariate techniques including partial least squares (PLS) and structural equation modeling (SEM). These multivariate methods permit examination of integrated neural systems (SEM) as well as the identification of spatial and temporal clustering of neuroimaging data (PLS). Thus, unlike activation analyses, network analyses incorporate anatomical connections among brain regions and consider their interactions simultaneously to explicitly quantify the effect brain structures exert on one another in a network.

Effective connectivity is the process used to describe influences among brain regions. Our current model-based approaches to effective connectivity of a neural network involve (1) empirically determining the nodes of a network (via Partial Least Squares), (2) specifying the relevant functional and anatomical connectivity of the brain regions comprising the network, and (3) testing and characterizing the effective connectivity of this functional neural network (SEM).

**Partial Least Squares (PLS):** As used in neuroimaging, partial least squares can be used to describe the relation between a set of measures (such as design contrasts, behavioral scores, or seed activity) and a set of functional brain images (McIntosh et al., 1996). It is similar to eigenimage, principal component and independent analyses in the use of singular-value decomposition (a mathematical technique) to summarize large data sets into a smaller number of components (Moeller et al., 1987; Friston et al., 1993; Lobaugh et al., 2001). However, PLS differs in that the singular-value decomposition is applied not to the raw data, but to the covariance or correlation matrix relating the raw data (e.g. functional brain activity) to the set of measure(s). PLS requires neither large samples nor statistical independence among measures, making it ideal for neuroimaging data (McIntosh et al., 1996).

**Partial Least Squares:** PLS is a family of robust multivariate techniques that will be applied to ascertain distributed patterns of activity that a) contribute to task or group differentiation (task-PLS); b) predict individual characteristics; and c) identify particular patterns of functional connectivity (seed-PLS). PLS permits hypothesis testing regarding the nodes comprising a proposed functional neural network. PLS does not require large samples nor statistical independence among measures, making it ideal for neuroimaging data. Task-PLS will be implemented to identify task and group-related distributed patterns of activity (networks). Behavior-PLS can be implemented to examine the relationships between subjective measures and brain network activity. Seed-PLS identifies patterns of functional connectivity between a “seed” brain region and other brain regions that may vary among tasks/groups. Seed-PLS can be used in conjunction with the task-PLS to more fully identify neural networks underlying brain processes.

**Structural Equation Modeling:** Structural equation modeling permits hypothesis testing about the causal influences (effective connectivity) among brain structures in a hypothesized brain network. This multivariate model testing approach requires prior specification of a neural network model to be tested. Brain regions or nodes for a network are selected based on a combination of univariate analysis (mean changes in rCBF, SPM contrasts), objective statistical criteria (PLS analysis) and a priori network hypotheses as previously described. Connectivity between brain regions in the network is derived from known neuroanatomical connections. In specifying an anatomical model, a compromise is commonly reached between anatomical accuracy and interpretability (finding a mathematical solution). SEM determines the weights or path coefficients for each anatomical connection within a given network. These estimates reflect the direct proportional influence one brain region has on another through their direct anatomical connection, controlling for all other regions in the model. Path coefficients can be compared across tasks to determine if interactions in functional networks differ across task. Group- or condition-dependent changes can be assessed statistically using multi-group or stacked SEM models approaches.

**Multivariate Pattern Classification Analyses:** Multivariate pattern classification analyses is being applied to identify patterns in the brain that discriminate or predict responders to the non-responders to pharmacological and treatment with CBT, hypnois, and mediatation and to functionally link alterations in brain architecture and resting state networks with measureable clinical and biological parameters enabling identification of distinct brain endophenotypes which characterize subpopulations of patients with different pathophysiology and treatment responses.

Our current methods are described in a previously publish paper from our group (Anderson et al., 2011). Using the selected features from initial ICA to reduce the dimensions of the brain biomarker data, a random forests classifier (Breiman, 2001) will can be trained and tested on the features concatenated with the behavioral, genetic, physiological and clinical parameters. A random forest classifier is the machine learning algorithm of choice due to its resiliency to overtraining in problems with limited numbers of observations. This classifier also has the added benefit of producing decision trees that indicate how the classifier actually operates, instead of a black box tool such as SVM where the actual decision boundaries are hyperplanes in a high-dimensional space. Other classification techniques applied include classification and regression trees (CART) and Partial Least Squares analyses.

**Resting State Analysis:** Functional imaging studies of FGIDs to date have focused on task-related brain activity (e.g. onset and offset of a rectal balloon distension or visual signal that a stimulus will occur). A very different approach to characterize brain activity from fMRI can be found in the recently developed methods for analysis of task-independent, spontaneous brain activity acquired during a resting state. In these studies, the subject typically lies quietly, usually with the eyes closed, while a short functional brain scan is performed. Independent components analysis, seed based functional connectivity analyses, or similar approaches are used identify brain regions that show correlated spontaneous low frequency BOLD signal fluctuations. This pattern of intercorrelations over time can then be attributed to discrete, functionally connected brain networks. While it is now accepted that reliable intrinsic functional brain networks exist, the significance of such networks remains an area of active investigation. It has been proposed that the intrinsic brain networks may represent endophenotypes associated with disease vulnerability or alternatively that alterations in these networks are a consequence of disease and may be amenable to therapy. Abnormalities have been noted within intrinsic brain networks neuropsychiatric disorders and to a lesser extent in chronic pain conditions, and therefore it is likely this type of analysis has considerable promise for FGIDs which are characterized by pain and co-morbid mood disorders.

**Model-Based Approach:** Proposing an a priori model for effective connectivity analyses is particularly challenging and requires an extensive knowledge of the literature._ Information on anatomical connectivity is often diffuse and cannot be easily translated in terms of functional interactions. Our approach is to consult with neuroanatomists and review anatomical tracing studies in human and nonhuman primates.

**Structural Equation Modeling:** Structural equation modeling (SEM) can be used to determine how regions of the brain influence each other during a specific task, given an a priori specified model. Traditionally used in the social and behavioral sciences, structural equation modeling is a collection of statistical tools used to represent dependency (arguably causal relations) in multivariate data. Based upon theory, structural equation modeling specifies a set of relationships between multiple independent and dependent variables (continuous or discrete) using a system of structural (regression) equations (linear or nonlinear) that represent causal processes. These relationships or processes are typically represented pictorially to enhance understanding of the theory under study. This model or the entire system of variables is then simultaneously tested to determine the extent to which it is consistent with the data.

**Connectivity and Computation Statistics:** NIC investigators aim to map the neural networks relevant for stress, pain and emotion as well as those with particular relevance for brain gut interactions. An important goal is to provide critical insights into brain systems that underlie symptom generation in primarily symptom based disorders, such as common persistent pain disorders (irritable bowel syndrome, painful bladder syndrome/interstitial cystitis). In these disorders it is essential to identify brain networks that may play a role in generating symptom-specific anxiety, autonomic dysregulation, and modulation of pain sensitivity as a means of developing more effective therapeutic interventions in the future.

Network analysis in the NIC employs robust and sophisticated multivariate techniques including partial least squares (PLS), and structural equation modeling (SEM). These multivariate methods permit examination of integrated neural systems (SEM) as well as the identification of spatial and temporal clustering of neuroimaging data (PLS). Thus, unlike simple activation analyses, network analyses incorporate anatomical connections among brain regions and consider their interactions simultaneously to explicitly quantify the effect brain structures exert on one another in a network (effective connectivity). Using autoregressive models (Granger causality) latent variable models, and temporal SEM, NIC investigators are attempting to delineate the dynamic components of functional neural networks including the homeostatic afferent (and emotional arousal circuitry.

NIC investigators have recently begun application of pattern classification and machine learning methods such as support vector machines and multidimensional scaling. Pattern classification methods (including PLS) can be used to link individual brain activation patterns to experimental conditions, and may be successful at predicting disease diagnosis based on specific activation patterns. We are working on a disease classifier for IBS based genetic, neuroimaging, psychophysiological, and psychological patient attributes.

Current directions included improvement of experimental paradigm for specific functional network isolation and application of repetitive TMS to perturb neural networks and infer causal brain behavior relationships.

Applying network analyses, we have shown:

- inhibitory cortico-limbic circuitry is associated with 1. more effective descending pain inhibition
- sex-differences in the brain response of patients with functional gastrointestinal pain during expectation and delivery of aversive visceral stimuli due to alterations in the emotional-arousal circuitry rather than homeostatic-afferent circuitry
- group differences in the neural networks associated with variants of the function polymorphism in the promoter region of the serotonin transporter gene (5-HTTLPR) and the effects of acute lowering of 5-HT levels on engagement of a central arousal network involved in central pain amplification