Classification of spatially unaligned fMRI scans

Abstract

The analysis of fMRI data is challenging because they consist generally of a relatively modest signal contained in a high-dimensional space: a single scan can contain millions of voxel recordings over space and time. We present a method for classification and discrimination among fMRI that is based on modeling the scans as distance matrices, where each matrix measures the divergence of spatial network signals that fluctuate over time. We used single-subject independent components analysis (ICA), decomposing an fMRI scan into a set of statistically independent spatial networks, to extract spatial networks and time courses from each subject that have unique relationship with the other components within that subject. Mathematical properties of these relationships reveal information about the infrastructure of the brain by measuring the interaction between and strength of the components. Our technique is unique, in that it does not require spatial alignment of the scans across subjects. Instead, the classifications are made solely on the temporal activity taken by the subject's unique ICs. Multiple scans are not required and multivariate classification is implementable, and the algorithm is effectively blind to the subject-uniform underlying task paradigm. Classification accuracy of up to 90% was realized on a resting-scanned schizophrenia/normal dataset and a tasked multivariate Alzheimer's/old/young dataset. We propose that the ICs represent a plausible set of imaging basis functions consistent with network-driven theories of neural activity in which the observed signal is an aggregate of independent spatial networks having possibly dependent temporal activity.

Introduction

Existing neuroimaging classification methods for functional magnetic resonance imaging (fMRI) data have shown much promise in discriminating among cerebral scans, but are limited in the types of data they can handle, and in the numbers of outcomes they can predict (Ford et al., 2003, Zhang and Samaras, 2005). In general, fMRI discrimination methods require preprocessing steps such as spatial alignment of the scans and are only infrequently suitable for multivariate classification problems (Calhoun et al., 2007) because of their utilization of bivariate classifiers. Spatial alignment algorithms often are constructed assuming a subject has a normal brain, and therefore may be less accurate when warping scans of patients with physical anomalies. Existing classification methods typically require knowledge of the task paradigm thereby limiting their application to subjects who are able and willing to perform such tasks. Here we introduce a procedure called spectral classification that is capable of multivariate discrimination among single-session fMRI scans taken during both a tasked and “mind-wandering” (task-free) state. The methods classify based on the temporal structure of the data rather than the spatial structure, thereby bypassing the need for spatial alignment of the scans. We call this method spectral classification because of its usage of spectral graph-theory measurements for discrimination. We demonstrate here a non-spatial method of classification having cross-validation accuracy rates as high as 90% for bivariate classification. Mathematically we introduce a method for comparing and classifying objects represented by distance matrices. In this paper an entire matrix describes an fMRI scan where the entries contain the “distances” between the activity of two components' timeseries; however these methods are generally applicable to any problem in which the elements are described as matrices rather than isolated points and discrimination is desired among these objects.

Temporally recorded neuroimaging data pose a unique challenge to classification because of the high-dimensional structure of the data sets. One scan can contain more than 120,000 recordings that often are highly correlated both in only four effective dimensions consisting of space and time. Because of this, practical classification procedures require an initial dimension-reduction stage where discriminating signal is extracted from the noisy data. In spatial-based discrimination methods, localized summaries of the temporal signal are used to compress the temporal dimension into a single point at every spatial location. The spatial regions containing discriminating summary statistics are extracted and used to create a classification machine. (Zhang and Samaras, 2005, Ford et al., 2003).

The summary statistics used for describing temporal activity include mean signal intensities or p-values measuring association with a known task-paradigm. These regional summary statistics are compared across subjects when training the classifier, requiring the scans be spatially aligned to a common atlas space. The most often used alignment algorithms (Woods et al., 1998) are 12-parameter affine transformations that warp a subject's brain to a common atlas space. Alignment precision is limited with normal patients by the low geometric flexibility of the algorithms, and is potentially more difficult to achieve with subjects having structural inconsistencies associated with mental disorders. For example, it is known that people with schizophrenia have significantly larger ventricles (Shenton et al., 2001) and that Alzheimer's sufferers show brain atrophy (Ridha et al., 2006); standard structural alignment tools cannot take into account the unique differences existing in these patients. Thus, spatially based discrimination methods may fail in classifications across individuals due simply to poor spatial alignment.

A known task function is often correlated regionally with timeseries to identify regions closely associated with a task. Improved alignment methods notwithstanding, localized low-order summary statistics of the regional BOLD signal may not capture higher-order discriminating information contained in the temporal domain. If functional anatomy is similar among patient groups, then the temporal information of the scans offer a new dimension with potentially discriminative information. If the group differences exist not in the spatially localized signal summary but in the native temporal activity taken by the brain, classification methods relying on summary statistics could fail to distinguish between groups. A method that instead reduced the often-redundant spatial dimension while keeping intact the temporal structure would capitalize on signal differences existing in the temporal domain rather than spatial. The method proposed here is agnostic to the task function and yields similar accuracy results discriminating among identically tasked scans and untasked scans in two datasets tested here.

Because of the limitations of spatial discrimination methods, there is a need for a classification method that is both insensitive to spatial alignment and independent of low order statistical summaries. Using unaligned scans our method classifies on temporal activity patterns between independent components within a subject. The blind source separation method of independent components analysis (ICA) is capable of decomposing a sequence of three-dimensional images into sources consisting of statistically independent spatial maps acting over time according to possibly dependent activity patterns. When applied to fMRI data, ICA decomposes a four-dimensional single fMRI scan into a set of statistically independent spatial components (Hyvärinen and Oja, 2000). These spatially independent components have corresponding time courses that show statistical dependence with the time courses of other components. The strength of the relationship between components is indicated by coupling, or correlated intensities over time.

It is not known which if any of the spatial components identified by ICA represent functional neural networks, however it has previously been shown that ICA-methods yield identifiable stable neurological patterns. Damoiseaux et al. (2006) were able to identify 10 consistent resting state networks common across their population that appear to correspond to identifiable phenomena such as motor function, visual processing, executive functioning, auditory processing, memory, and even the default-mode network, however the identification of these components is not required with our approach to classification yet remains a hidden layer that might be useful for neuroscientific interpretation. The general goal of our work is to develop a classification method that is independent of any trained user interaction making the tool more practically applicable and less sensitive to experimenter bias. One consequence of this, as implemented here, is that the classification itself may be based on signals that are not directly interpretable as neural in nature. For example, it is possible that group specific artifacts, such as head motion, might be contributing to the classifier. For the moment, we note that even in the face of this potential limitation, the classifier appears quite robust. In the future, we intend to use automated means to detect and reject identifiable artifacts (such as motion). Because the time courses alone are used for discrimination our method does not require us to associate the spatial components with a known biological process to classify a scan; rather, we are concerned with the temporal structure that these components take, how similar they are with other components in that subject, and how this dependency varies across subjects and groups.

In the classification method described here, inter-subject component comparisons do not require multiple scans or knowledge of the underlying task paradigm. We describe here the application of our methods using two separate datasets. The first consists of blocked-task designed scans from normal old, normal young, and Alzheimer's patients, while the second dataset consists of resting-state scans of Schizophrenia subjects and normal controls. We estimated the classification testing accuracy using cross-validation (C.V.) and the out-of-bag error from the random forests (R.F.) (Breiman, 2001) classifier, where the accuracy is an estimate of how well the classifier would do if given a new scan from a previously unseen subject.

Random forests is a decision-tree machine learning method that creates many classification trees by resampling from both the observations and classifiers at each node and subsequently making decision rules to minimize the misclassification rate of the sampled data within each tree. Many decision trees are constructed and combined to create a “forest” that decides an observation's class by voting over the decisions made by each tree. The tree is then tested on observations that weren't selected in the initial sampling, to give the “out-of-bag” error which is usually an unbiased estimate of the testing error.