Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Summary

Multivariate techniques including principal component analysis (PCA) have been used to identify signature patterns of regional change in functional brain images. We have developed an algorithm to identify reproducible network biomarkers for the diagnosis of neurodegenerative disorders, assessment of disease progression, and objective evaluation of treatment effects in patient populations.

Abstract

The scaled subprofile model (SSM)^1-4 is a multivariate PCA-based algorithm that identifies major sources of variation in patient and control group brain image data while rejecting lesser components (Figure 1). Applied directly to voxel-by-voxel covariance data of steady-state multimodality images, an entire group image set can be reduced to a few significant linearly independent covariance patterns and corresponding subject scores. Each pattern, termed a group invariant subprofile (GIS), is an orthogonal principal component that represents a spatially distributed network of functionally interrelated brain regions. Large global mean scalar effects that can obscure smaller network-specific contributions are removed by the inherent logarithmic conversion and mean centering of the data^2,5,6. Subjects express each of these patterns to a variable degree represented by a simple scalar score that can correlate with independent clinical or psychometric descriptors^7,8. Using logistic regression analysis of subject scores (i.e. pattern expression values), linear coefficients can be derived to combine multiple principal components into single disease-related spatial covariance patterns, i.e. composite networks with improved discrimination of patients from healthy control subjects^5,6. Cross-validation within the derivation set can be performed using bootstrap resampling techniques⁹. Forward validation is easily confirmed by direct score evaluation of the derived patterns in prospective datasets¹⁰. Once validated, disease-related patterns can be used to score individual patients with respect to a fixed reference sample, often the set of healthy subjects that was used (with the disease group) in the original pattern derivation¹¹. These standardized values can in turn be used to assist in differential diagnosis^12,13 and to assess disease progression and treatment effects at the network level^7,14-16. We present an example of the application of this methodology to FDG PET data of Parkinson's Disease patients and normal controls using our in-house software to derive a characteristic covariance pattern biomarker of disease.

Introduction

Neurodegenerative disorders have been extensively studied using techniques that localize and quantify abnormalities of brain metabolism as well as non-inferential methods that study regional interactions¹⁷. Data-driven multivariate analytical strategies such as principal component analysis (PCA)^1,2,4,18 and independent component analysis (ICA)^19,20, as well as supervised techniques such as partial least squares (PLS)²¹ and ordinal trends canonical variates analysis (OrT/CVA)²² can reveal characteristic patterns or "networks" of interrelated activity. The basics of multivariate procedures, particularly the scaled subprofile model (SSM)^1,2,4-6,18 have been previously described in JoVE³. This PCA-based approach was originally developed to examine abnormal functional covariance relationships between brain regions in steady-state single volume images of cerebral blood flow and metabolism acquired in the resting state of modalities such as PET and SPECT that exhibit high signal-to-noise characteristics. Disease-specific SSM patterns are imaging biomarkers that reflect overall differences in the regional topography in patients compared to normal subjects^7,16 and may reflect a single network process or the assimilation of several complex abnormal functions²³. Metabolic covariance pattern brain networks are associated with expression values (subject scores) that can distinguish between normal and disease groups and provide network-based measures that correlate with clinical ratings of disease severity. Typically, subject scores for such patterns increase with disease progression and may even be expressed before symptom onset^14,24. Indeed, disease-related network biomarkers have been characterized for neurodegenerative disorders such as Parkinson's disease¹⁰ (PD), Huntington's disease²⁵(HD), and Alzheimer's disease⁸ (AD). Importantly, disease-related metabolic topographies have also been identified for atypical parkinsonian movement disorders such as multiple system atrophy (MSA) and progressive supranuclear palsy (PSP). These patterns have been used in concert for the differential diagnosis of individuals with clinically similar "look-alike" syndromes^12,13,26.

In contrast, typical fMRI voxel-based univariate methods assess the significance of differences between patients and controls in isolated brain clusters. More recently, methods have been developed to measure functional connectivity between variously defined brain regions^27-29. This definition of functional connectivity is restricted to subject and region specific interactions and deviates from the original SSM/PCA concept that refers to the cross-sectional interconnectivity of intrinsic spatially distributed brain network regions^1,2,23,30. To their advantage, MRI platforms are easily installed, widely available, non-invasive and typically require shorter scanning time than traditional radiotracer imaging modalities such as PET or SPECT resulting in an upsurge of potential methodologies described in recent literature. However, the resulting time-dependent fMRI signals provide indirect measures of local neural activity^31,32. The generally complex analytical algorithms employed have been limited by the large size of datasets, the physiological noise inherent in fMRI signals, as well as the high variability in brain activity that exists between subjects and regions^19,23. Although interesting information regarding brain organization can be inferred from the properties of fMRI "networks", they have not been sufficiently stable to be used as reliable disease biomarkers. Furthermore, the resulting network topographies are not necessarily equivalent to those identified using established functional imaging methodologies such as SSM/PCA. For the most part, rigorous cross-validation of the resulting fMRI topographies has been lacking with few examples of successful forward application of derived patterns in prospective scan data from single cases.

An advantage of PCA covariance analysis lies in its capacity to identify the most significant sources of data variation in the first few principal components but it is ineffective if the prominent eigenvectors represent random noise factors rather than actual intrinsic network response. By selecting only the first few eigenvectors and limiting to those that show significant differences in patient versus normal control scores, we greatly reduce the influence of noise elements. However, for the basic approach described here, these measures may not be adequate to generate robust estimators in a typical fMRI dataset with the exception of the modalities described below.

Thus, because of the stable direct relationship of regional glucose metabolism and synaptic activity³³, this methodology has been applied primarily to the analysis of rest state FDG PET data. However, given that cerebral blood flow (CBF) is closely coupled to metabolic activity in the resting state^10,11,34, SPECT^35,36 and more recently arterial spin labeling (ASL) MRI perfusion imaging methods^37,38, have been used to assess abnormal metabolic activity in individual cases. That said, the derivation of reliable spatial covariance patterns with resting state fMRI (rsfMRI) is as previously noted not straightforward ^31,32. Even so, preliminary SSM/PCA analysis of rsfMRI data from PD patients and control subjects has revealed some topographical homologies between disease-related patterns identified using the two modalities, PET and amplitude of low-frequency fluctuations (ALFF) of BOLD fMRI^39,40. Lastly, we also note that this approach has been applied successfully in voxel based morphometry (VBM) structural MRI data^41,42, revealing distinctive spatial covariance patterns associated with age-related volume loss and in further comparisons of VBM and ASL patterns in the same subjects⁴³. The relationship between SSM/PCA spatial covariance topographies and analogous brain networks identified using different analytical approaches and imaging platforms is a topic of ongoing investigation.

Protocol

1. Data Collection and Preprocessing

1. The SSM/PCA method can be applied to single volume images obtained from various sources and modalities. Specifically, for on-site PET imaging of metabolism, prepare a suitable radionuclide tracer such as [¹⁸F]-fluorodeoxyglucose (FDG) and administer to each patient. Patients are usually scanned at rest with eyes open, following a fast of at least 12 hr, off medications.
2. Scan each subject for individual or group assessment. For pattern derivation, scan an equal number of gender- and age-matched patients and controls.
3. Transfer data to a workstation and convert to an appropriate format for analysis in your platform. Our windows PC based MATLAB analysis software (scanvp, ssm_pca, www.feinsteinneuroscience.org) requires ANALYZE or nifti format images (Mayo Clinic, Rochester, MN). It provides a conversion routine to transform GE Advance (Milwaukee, WI, USA) scanner and other format images to ANALYZE format.
4. Normalize each subject's image to a common stereotaxic space (e.g. Montreal Neurological Institute [MNI]) using a standard neuroimaging software package such as statistical parametric mapping (SPM) (http://www.fil.ion.ucl.ac.uk/spm) so that there is a one-to-one correspondence of voxel values between subjects (Figure 2). Masking to limit the analysis to gray matter areas (Figure 3) and log transformation are described in the next steps.

2. Perform Multivariate SSM/PCA

Operations for multivariate SSM/PCA (Figure 4) can be performed by external software. The steps itemized below reflect the procedures performed for the most part automatically by our in-house routines (Figure 5) (scanvp/ssmpca, www.feinsteinneuroscience.org also available as an SPM toolbox ssm_pca).

1. Mask data using an available 0/1 image to remove unwanted areas of the voxel space such as white matter and ventricles. Using the ssmpca routine, the user is given an option to select the default or other external mask (Figure 3) or to have the program automatically create a mask by removing values lower than a selected fixed percent of each subject's data maximum. Individual subject masks are then multiplied to determine a composite mask. The areas within the mask define a common non-zero voxel space for the analysis.
2. Convert each subject's 3D masked image voxel data to one continuous row vector by appending sequential scan lines from consecutive planes (Figure 4a). Form a group data matrix (D) so that each subject's data corresponds to a specific row of the matrix. Each column then represents a particular voxel across subjects. Ideally, for biomarker derivation, the matrix will be composed of an equal number of rows of normal control subject data and disease subject data.
3. Transform each data entry to logarithmic form.
4. Center the data matrix by subtracting each row average or subject mean from the row elements. The average of all centered rows represents a characteristic group mean log image termed a group mean profile (GMP, Figure 4a). Subtract the column means that are the elements of the GMP from the corresponding matrix column elements. Each row of the double centered matrix represents a 'residual' image termed a subject residual profile (SRP) whose elements represent deviations from both the subject s and voxel v group means (Figure 4b).
   SRP_sv = logD_sv - mean_s - GMP_v
5. Construct the subject-by-subject covariance matrix C of the composite double centered data matrix by computing the non-normalized covariance between each subject pair i, j of SRP matrix rows evaluated as a product of corresponding voxel elements summed over all voxels v (Figure 4b).
   C_ij =∑_v (SRP_iv x SRP_jv)
6. Apply PCA to the subject-by-subject covariance matrix C. The results will be a set of subject score eigenvectors with associated eigenvalues. Weight each vector by multiplying by the square root of its corresponding eigenvalue. The set of score eigenvectors is represented by the columns of the resulting matrix S in Figure 4c.
7. Voxel eigenvectors for the same set of eigenvalues can be determined by applying PCA to the column by column covariance matrix or by this alternative computationally less demanding procedure depicted in (Figure 4c). Left multiply the previously derived score vector matrix by the transpose SRP matrix to derive an array P of voxel pattern eigenvectors in descending order of eigenvalues (Figure 4c, Figure 6, Figure 7a).
   P = SRP^T x S
   Each column vector represents a principal component (PC) image pattern of the SSM/PCA analysis attributed to a percent of the total variance accounted for (vaf) corresponding to the relative size of its eigenvalue.

3. Pattern Biomarker Derivation

1. Examine the results of the preceding analysis to determine PC patterns that are associated with high vaf values. Within our routine, voxel pattern vectors are Z-transformed so that their values represent positive and negative standard deviations from their mean value. They are then reshaped into image format prior to display (Figure 7a).
2. In some cases patterns with known regional deviations associated with the disease can be visually identified. The mathematical formulation considers positive and negative forms of the derived PCs as equivalent solutions in which case both the PCs and their associated scores may be multiplied by minus one to conform to a physically correct interpretation.
3. Scores corresponding to each PC pattern are displayed as bar graphs and scatter plots (Figure 7). An optional ROC plot can be generated (Figure 7d) . To identify a disease-specific pattern, notice the differentiation of subject scores between patients and controls reflected by the p-values of the corresponding two-sample t-tests and AUC values. Limit the analysis to those PCs associated with a high vaf and high differentiation for some fixed cutoff values (e.g., p < 0.05 and vaf > 5%). Typically, only one or two PCs satisfy this criterion for PET data.
4. There are various other ways for PC selection that can be considered⁴⁴. The scree plot of sequential eigenvalues (Figure 6) may give a sharp cutoff value represented by a bend in the curve and a sharp reduction in the slope of the curve where eigenvalues begin to degenerate. Another approach is to include all PCs that account for the top 50% of the variance. A widely accepted procedure is to compute the Akaike Information Criterion (AIC)⁴⁵ to determine which combination of PCs define the model with the lowest AIC value that can distinguish between patients and controls.
5. The selected PC(s) can be vector normalized and linearly combined to yield a single disease-related pattern. Our software optionally uses the MATLAB function glmfit to determine coefficients based on logistic or other regression models applied to subject scores. Although differentiation of patient and control groups usually improves with the additional PCs considered in the derivation group, the resultant patterns are a composite representation that may not correspond to a single physical network or may incorporate outlier deviations (Figures 7a and 7c).
6. Further validation is required for reliability and prospective significance. Bootstrap resampling can be performed as discussed below⁸ to identify the most reliable voxels within the original derivation dataset associated with the least standard deviation in repeated pattern derivation. Forward validation is performed to test for the sensitivity and specificity of independent group discrimination by deriving scores for prospective groups of patients and controls using the single-subject score evaluation method (Figure 4d) described in the next segment of the protocol.

4. Single-subject Prospective Score Evaluation using a Predetermined Biomarker

1. Once a significant SSM-GIS biomarker pattern has been identified, a score for its expression in a prospective subject can be evaluated from that individual's scan using a simple computation of the internal vector product of the subject's SRP vector and the GIS pattern vector (Figure 4d, Figure 7d).
   SCORE = SRPs • Pattern
2. The previous operation is automated by our TPR routine. However, to independently derive the subject SRPs vector use the associated intrinsic GIS mask on the log transformed data and subtract both the subject mean and the corresponding voxel values of the prederived reference group GMP as in step 2.4. This insures that scores can be compared to the predetermined reference range. Scores for a new group can be similarly evaluated as a set of prospective single subject scores. For use with a different reference group or setting, GMP can be recalibrated while the pattern is unchanged.

Results

A simple application of multivariate SSM/PCA analysis to derive a neuroimaging biomarker pattern for PD is illustrated below. PET FDG images of ten clinically diagnosed PD patients (6M/4F, 59y ± 7y sd) of variable diseased duration (9y ± 5y sd) and ten age and gender matched normal controls (6M/4F, 58y ±7y sd) were analyzed using our ssmpca routine. The twenty corresponding spatially pre-normalized images were initially selected under the categories disease subjects or controls along with the default mask (

Discussion

The SSM/PCA model originally presented by Moeller et al.⁴ has evolved^1-3 into a straightforward and robust technique for the analysis of neuroimaging data. However, there have been ambiguities in the application of this methodology that we have attempted to clarify here and in previous publications^5-7,10. Some of these issues have been addressed in the text but are reemphasized here because of their importance. As detailed in the Introduction, SSM/PCA is primarily effective in re...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Image Acquisition
PET Scanner	GE Medical Systems	GE Advance	Any PET, PET/CT and PET/MRI Scanners from GE, Siemens and Philips
PC Workstations	Lenovo	Any	http://www.lenovo.com/us/en/
Radiopharmaceuticals
[18F]-fluorodeoxyglucose	Feinstein Institute for Medical Research	Routine Production	Also distributed by Cardinal Health http://www.cardinal.com/
Software
ScanVP	Feinstein Institute for Medical Research	Version 5.9.1, Version 6.2, To be released	www.feinsteinneuroscience.org
SPM	The UCL Institute of Neurology	spm99-spm8	http://www.fil.ion.ucl.ac.uk/spm
Windows	Microsoft	Any
Matlab	Mathworks	Matlab Version 7.0, 7.3	http://www.mathworks.com/
JMP	SAS	Version 5	http://www.jmp.com/