Synthetic images by subspace transforms. I. Principal components images and related filters

Comparison of fMRI analysis methods for heterogeneous BOLD responses in block design studies

A large number of fMRI studies have shown that the temporal dynamics of evoked BOLD responses can be highly heterogeneous. Failing to model heterogeneous responses in statistical analysis can lead to significant errors in signal detection and characterization and alter the neurobiological interpretation. However, to date it is not clear that, out of a large number of options, which methods are robust against variability in the temporal dynamics of BOLD responses in block-design studies. Here, we used rodent optogenetic fMRI data with heterogeneous BOLD responses and simulations guided by experimental data as a means to investigate different analysis methods' performance against heterogeneous BOLD responses. Evaluations are carried out within the general linear model (GLM) framework and consist of standard basis sets as well as independent component analysis (ICA). Analyses show that, in the presence of heterogeneous BOLD responses, conventionally used GLM with a canonical basis set leads to considerable errors in the detection and characterization of BOLD responses. Our results suggest that the 3rd and 4th order gamma basis sets, the 7th to 9th order finite impulse response (FIR) basis sets, the 5th to 9th order B-spline basis sets, and the 2nd to 5th order Fourier basis sets are optimal for good balance between detection and characterization, while the 1st order Fourier basis set (coherence analysis) used in our earlier studies show good detection capability. ICA has mostly good detection and characterization capabilities, but detects a large volume of spurious activation with the control fMRI data.

The 2D Hotelling filter - a quantitative noise-reducing principal-component filter for dynamic PET data, with applications in patient dose reduction

Background

In this paper we apply the principal-component analysis filter (Hotelling filter) to reduce noise from dynamic positron-emission tomography (PET) patient data, for a number of different radio-tracer molecules. We furthermore show how preprocessing images with this filter improves parametric images created from such dynamic sequence.

We use zero-mean unit variance normalization, prior to performing a Hotelling filter on the slices of a dynamic time-series. The Scree-plot technique was used to determine which principal components to be rejected in the filter process. This filter was applied to [¹¹C]-acetate on heart and head-neck tumors, [¹⁸F]-FDG on liver tumors and brain, and [¹¹C]-Raclopride on brain. Simulations of blood and tissue regions with noise properties matched to real PET data, was used to analyze how quantitation and resolution is affected by the Hotelling filter. Summing varying parts of a 90-frame [¹⁸F]-FDG brain scan, we created 9-frame dynamic scans with image statistics comparable to 20 MBq, 60 MBq and 200 MBq injected activity. Hotelling filter performed on slices (2D) and on volumes (3D) were compared.

Results

The 2D Hotelling filter reduces noise in the tissue uptake drastically, so that it becomes simple to manually pick out regions-of-interest from noisy data. 2D Hotelling filter introduces less bias than 3D Hotelling filter in focal Raclopride uptake. Simulations show that the Hotelling filter is sensitive to typical blood peak in PET prior to tissue uptake have commenced, introducing a negative bias in early tissue uptake. Quantitation on real dynamic data is reliable. Two examples clearly show that pre-filtering the dynamic sequence with the Hotelling filter prior to Patlak-slope calculations gives clearly improved parametric image quality. We also show that a dramatic dose reduction can be achieved for Patlak slope images without changing image quality or quantitation.

Conclusions

The 2D Hotelling-filtering of dynamic PET data is a computer-efficient method that gives visually improved differentiation of different tissues, which we have observed improve manual or automated region-of-interest delineation of dynamic data. Parametric Patlak images on Hotelling-filtered data display improved clarity, compared to non-filtered Patlak slope images without measurable loss of quantitation, and allow a dramatic decrease in patient injected dose.

Analysis of FMRI data using an integrated principal component analysis and supervised affinity propagation clustering approach

Clustering analysis is a promising data-driven method for analyzing functional magnetic resonance imaging (fMRI) time series data. The huge computational load, however, creates practical difficulties for this technique. We present a novel approach, integrating principal component analysis (PCA) and supervised affinity propagation clustering (SAPC). In this method, fMRI data are initially processed by PCA to obtain a preliminary image of brain activation. SAPC is then used to detect different brain functional activation patterns. We used a supervised Silhouette index to optimize clustering quality and automatically search for the optimal parameter p in SAPC, so that the basic affinity propagation clustering is improved by applying SAPC. Four simulation studies and tests with three in vivo fMRI datasets containing data from both block-design and event-related experiments revealed that functional brain activation was effectively detected and different response patterns were distinguished using our integrated method. In addition, the improved SAPC method was superior to the k -centers clustering and hierarchical clustering methods in both block-design and event-related fMRI data, as measured by the average squared error. These results suggest that our proposed novel integrated approach will be useful for detecting brain functional activation in both block-design and event-related experimental fMRI data.

Analysis of activity in fMRI data using affinity propagation clustering

Clustering analysis is a promising data-driven method for the analysis of functional magnetic resonance imaging (fMRI) data. The huge computation load, however, makes it difficult for the practical use. We use affinity propagation clustering (APC), a new clustering algorithm especially for large data sets to detect brain functional activation from fMRI. It considers all data points as possible exemplars through the minimisation of an energy function and message-passing architecture, and obtains the optimal set of exemplars and their corresponding clusters. Four simulation studies and three in vivo fMRI studies reveal that brain functional activation can be effectively detected and that different response patterns can be distinguished using this method. Our results demonstrate that APC is superior to the k-centres clustering, as revealed by their performance measures in the weighted Jaccard coefficient and average squared error. These results suggest that the proposed APC will be useful in detecting brain functional activation from fMRI data.

Application of the Karhunen-Loeve transform temporal image filter to reduce noise in real-time cardiac cine MRI

Real-time dynamic magnetic resonance imaging (MRI) typically sacrifices the signal-to-noise ratio (SNR) to achieve higher spatial and temporal resolution. Spatial and/or temporal filtering (e.g., low-pass filtering or averaging) of dynamic images improves the SNR at the expense of edge sharpness. We describe the application of a temporal filter for dynamic MR image series based on the Karhunen-Loeve transform (KLT) to remove random noise without blurring stationary or moving edges and requiring no training data. In this paper, we present several properties of this filter and their effects on filter performance, and propose an automatic way to find the filter cutoff based on the autocorrelation of the eigenimages. Numerical simulation and in vivo real-time cardiac cine MR image series spanning multiple cardiac cycles acquired using multi-channel sensitivity-encoded MRI, i.e., parallel imaging, are used to validate and demonstrate these properties. We found that in this application, the noise standard deviation was reduced to 42% of the original with no apparent image blurring by using the proposed filter cutoff. Greater noise reduction can be achieved by increasing the length of the image series. This advantage of KLT filtering provides flexibility in the form of another scan parameter to trade for SNR.

Analysis of fMRI data using improved self-organizing mapping and spatio-temporal metric hierarchical clustering

The self-organizing mapping (SOM) and hierarchical clustering (HC) methods are integrated to detect brain functional activation; functional magnetic resonance imaging (fMRI) data are first processed by SOM to obtain a primary merged neural nodes image, and then by HC to obtain further brain activation patterns. The conventional Euclidean distance metric was replaced by the correlation distance metric in SOM to improve clustering and merging of neural nodes. To improve the use of spatial and temporal information in fMRI data, a new spatial distance (node coordinates in the 2-D lattice) and temporal correlation (correlation degree of each time course in the exemplar matrix) are introduced in HC to merge the primary SOM results. Two simulation studies and two in vivo fMRI data that both contained block-design and event-related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods. Our results demonstrate that the improved SOM and HC methods are clearly superior to the statistical parametric mapping (SPM), independent component analysis (ICA), and conventional SOM methods in the block-design, especially in the event-related experiment, as revealed by their performance measured by receiver operating characteristic (ROC) analysis. Our results also suggest that the proposed new integrated approach could be useful in detecting block-design and event-related fMRI data.

Derivative temporal clustering analysis: detecting prolonged neuronal activity

Temporal clustering analysis (TCA) and independent component analysis (ICA) are promising data-driven techniques in functional magnetic resonance imaging (fMRI) experiments to obtain brain activation maps in conditions with unknown temporal information regarding the neuronal activity. Although comparable to ICA in detecting transient neuronal activities, TCA fails to detect prolonged plateau brain activations. To eliminate this pitfall, a novel derivative TCA (DTCA) method was introduced and its algorithms with different subtraction intervals were tested on simulated data with a pattern of prolonged plateau brain activation. It was found that the best performance of DTCA method in generating functional maps could be obtained if the subtraction interval is equal to or larger than the length of the rising time of the fMRI response. The DTCA method and its theoretical predication were further investigated and validated using in vivo fMRI data sets. By removing the limitations in the previous TCA, DTCA has shown its powerful capability in detecting prolonged plateau neuronal activities.

Background suppression in time-resolved MR angiography without mask acquisition or operator intervention

PURPOSE

To suppress static and background tissue in time-resolved MRA studies of the full thorax or abdomen without the need of a mask image or operator intervention.

MATERIALS AND METHODS

The time course of each voxel is projected onto the orthogonal complement space of a matrix that spans static and linearly enhancing signal vectors. The norm of the solution, or the projection length, acts as a confidence measure for segmenting vascular and nonvascular tissue. Voxels whose confidence measures fall below an automatically detected threshold value are considered nonvascular. These voxels undergo an increasing level of suppression as the distance of the confidence measure from the threshold grows.

RESULTS

MIPs of processed volunteer studies were compared to the original unaltered studies to assess the improvement in clarity of vascular structures. Qualitative and quantitative comparisons of full body MIPs verify excellent suppression of nonvascular tissue in time-resolved three-dimensional image volumes.

CONCLUSION

Contrast increased by an average factor of 13 in five volunteer studies, quantitatively emphasizing the improvement in MIP processing achieved by this method. Improvement in the clarity of vascular structures in subvolume MIPs is also demonstrated to emphasize the significant increase in ease with which regions of interest can be identified.

An integrated neighborhood correlation and hierarchical clustering approach of functional MRI

Clustering analysis is a promising data-driven method for the analysis of functional magnetic resonance imaging (fMRI) time series, however, the huge computation load makes it difficult for practical use. In this paper, neighborhood correlation (NC) and hierarchical clustering (HC) methods are integrated as a new approach where fMRI data are processed first by NC to get a preliminary image of brain activations, and then by HC to remove some noises. In HC, to better use spatial and temporal information in fMRI data, a new spatio-temporal measure is introduced. A simulation study and an application to visual fMRI data show that the brain activations can be effectively detected and that different response patterns can be discriminated. These results suggest that the proposed new integrated approach could be useful in detecting weak fMRI signals.

A multivariate approach for processing magnetization effects in triggered event-related functional magnetic resonance imaging time series

Triggered event-related functional magnetic resonance imaging requires sparse intervals of temporally resolved functional data acquisitions, whose initiation corresponds to the occurrence of an event, typically an epileptic spike in the electroencephalographic trace. However, conventional fMRI time series are greatly affected by non-steady-state magnetization effects, which obscure initial blood oxygen level-dependent (BOLD) signals. Here, conventional echo-planar imaging and a post-processing solution based on principal component analysis were employed to remove the dominant eigenimages of the time series, to filter out the global signal changes induced by magnetization decay and to recover BOLD signals starting with the first functional volume. This approach was compared with a physical solution using radiofrequency preparation, which nullifies magnetization effects. As an application of the method, the detectability of the initial transient BOLD response in the auditory cortex, which is elicited by the onset of acoustic scanner noise, was used to demonstrate that post-processing-based removal of magnetization effects allows to detect brain activity patterns identical with those obtained using the radiofrequency preparation. Using the auditory responses as an ideal experimental model of triggered brain activity, our results suggest that reducing the initial magnetization effects by removing a few principal components from fMRI data may be potentially useful in the analysis of triggered event-related echo-planar time series. The implications of this study are discussed with special caution to remaining technical limitations and the additional neurophysiological issues of the triggered acquisition.

Functional magnetic resonance imaging activation detection: fuzzy cluster analysis in wavelet and multiwavelet domains

PURPOSE

To present novel feature spaces, based on multiscale decompositions obtained by scalar wavelet and multiwavelet transforms, to remedy problems associated with high dimension of functional magnetic resonance imaging (fMRI) time series (when they are used directly in clustering algorithms) and their poor signal-to-noise ratio (SNR) that limits accurate classification of fMRI time series according to their activation contents.

MATERIALS AND METHODS

Using randomization, the proposed method finds wavelet/multiwavelet coefficients that represent the activation content of fMRI time series and combines them to define new feature spaces. Using simulated and experimental fMRI data sets, the proposed feature spaces are compared to the cross-correlation (CC) feature space and their performances are evaluated. In these studies, the false positive detection rate is controlled using randomization. To compare different methods, several points of the receiver operating characteristics (ROC) curves, using simulated data, are estimated and compared.

RESULTS

The proposed features suppress the effects of confounding signals and improve activation detection sensitivity. Experimental results show improved sensitivity and robustness of the proposed method compared to the conventional CC analysis.

CONCLUSION

More accurate and sensitive activation detection can be achieved using the proposed feature spaces compared to CC feature space. Multiwavelet features show superior detection sensitivity compared to the scalar wavelet features.

Models of Brain Function in Neuroimaging

Inferences about brain function, using neuroimaging data, rest on models of how the data were caused. These models can be quite diverse, ranging from conceptual models of functional anatomy to nonlinear mathematical models of hemodynamics. However, they all have to be internally consistent because they model the same thing. This consistency encompasses many levels of description and places constraints on the statistical models, adopted for data analysis, and the experimental designs they embody. The aim of this review is to introduce the key models used in imaging neuroscience and how they relate to each other. We start with anatomical models of functional brain architectures, which motivate some of the fundaments of neuroimaging. We then turn to basic statistical models (e.g., the general linear model) used for making classical and Bayesian inferences about where neuronal responses are expressed. By incorporating biophysical constraints, these basic models can be finessed and, in a dynamic setting, rendered causal. This allows us to infer how interactions among brain regions are mediated.

Comparison of Two Exploratory Data Analysis Methods for fMRI: Unsupervised Clustering Versus Independent Component Analysis

Exploratory data-driven methods such as unsupervised clustering and independent component analysis (ICA) are considered to be hypothesis-generating procedures, and are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). In this paper, we present a comparison between unsupervised clustering and ICA in a systematic fMRI study. The comparative results were evaluated by 1) task-related activation maps, 2) associated time-courses, and 3) receiver operating characteristic analysis. For the fMRI data, a comparative quantitative evaluation between the three clustering techniques, self-organizing map, "neural gas" network, and fuzzy clustering based on deterministic annealing, and the three ICA methods, FastICA, Infomax and topographic ICA was performed. The ICA methods proved to extract features relatively well for a small number of independent components but are limited to the linear mixture assumption. The unsupervised Clustering outperforms ICA in terms of classification results but requires a longer processing time than the ICA methods.

Model-free functional MRI analysis based on unsupervised clustering

Conventional model-based or statistical analysis methods for functional MRI (fMRI) are easy to implement, and are effective in analyzing data with simple paradigms. However, they are not applicable in situations in which patterns of neural response are complicated and when fMRI response is unknown. In this paper the "neural gas" network is adapted and rigourosly studied for analyzing fMRI data. The algorithm supports spatial connectivity aiding in the identification of activation sites in functional brain imaging. A comparison of this new method with Kohonen's self-organizing map and with a fuzzy clustering scheme based on deterministic annealing is done in a systematic fMRI study showing comparative quantitative evaluations. The most important findings in this paper are: (1) both "neural gas" and the fuzzy clustering technique outperform Kohonen's map in terms of identifying signal components with high correlation to the fMRI stimulus, (2) the "neural gas" outperforms the two other methods with respect to the quantization error, and (3) Kohonen's map outperforms the two other methods in terms of computational expense. The applicability of the new algorithm is demonstrated on experimental data.

Detection and quantification of a wide range of fMRI temporal responses using a physiologically-motivated basis set

The temporal dynamics of fMRI responses can span a broad range, indicating a rich underlying physiology, but also posing a significant challenge for detection. For instance, in human auditory cortex, prolonged sound stimuli ( approximately 30 sec) can evoke responses ranging from sustained to highly phasic (i.e., characterized by prominent peaks just after sound onset and offset). In the present study, we developed a method capable of detecting a wide variety of responses, while simultaneously extracting information about individual response components, which may have different neurophysiological underpinnings. Specifically, we implemented the general linear model using a novel set of basis functions chosen to reflect temporal features of cortical fMRI responses. This physiologically-motivated basis set (the "OSORU" basis set) was tested against (1) the commonly employed "sustained-only" basis "set" (i.e., a single smoothed "boxcar" function), and (2) a sinusoidal basis set, which is capable of detecting a broad range of responses, but lacks a direct relationship to individual response components. On data that included many different temporal responses, the OSORU basis set performed far better overall than the sustained-only set, and as well or better than the sinusoidal basis set. The OSORU basis set also proved effective in exploring brain physiology. As an example, we demonstrate that the OSORU basis functions can be used to spatially map the relative amount of transient vs. sustained activity within auditory cortex. The OSORU basis set provides a powerful means for response detection and quantification that should be broadly applicable to any brain system and to both human and non-human species.

Clustered components analysis for functional MRI

A common method of increasing hemodynamic response (SNR) in functional magnetic resonance imaging (fMRI) is to average signal timecourses across voxels. This technique is potentially problematic because the hemodynamic response may vary across the brain. Such averaging may destroy significant features in the temporal evolution of the fMRI response that stem from either differences in vascular coupling to neural tissue or actual differences in the neural response between two averaged voxels. Two novel techniques are presented in this paper in order to aid in an improved SNR estimate of the hemodynamic response while preserving statistically significant voxel-wise differences. The first technique is signal subspace estimation for periodic stimulus paradigms that involves a simple thresholding method. This increases SNR via dimensionality reduction. The second technique that we call clustered components analysis is a novel amplitude-independent clustering method based upon an explicit statistical data model. It includes an unsupervised method for estimating the number of clusters. Our methods are applied to simulated data for verification and comparison to other techniques. A human experiment was also designed to stimulate different functional cortices. Our methods separated hemodynamic response signals into clusters that tended to be classified according to tissue characteristics.

Cluster analysis of fMRI data using dendrogram sharpening

The major disadvantage of hierarchical clustering in fMRI data analysis is that an appropriate clustering threshold needs to be specified. Upon grouping data into a hierarchical tree, clusters are identified either by specifying their number or by choosing an appropriate inconsistency coefficient. Since the number of clusters present in the data is not known beforehand, even a slight variation of the inconsistency coefficient can significantly affect the results. To address these limitations, the dendrogram sharpening method, combined with a hierarchical clustering algorithm, is used in this work to identify modality regions, which are, in essence, areas of activation in the human brain during an fMRI experiment. The objective of the algorithm is to remove data from the low-density regions in order to obtain a clearer representation of the data structure. Once cluster cores are identified, the classification algorithm is run on voxels, set aside during sharpening, attempting to reassign them to the detected groups. When applied to a paced motor paradigm, task-related activations in the motor cortex are detected. In order to evaluate the performance of the algorithm, the obtained clusters are compared to standard activation maps where the expected hemodynamic response function is specified as a regressor. The obtained patterns of both methods have a high concordance (correlation coefficient = 0.91). Furthermore, the dependence of the clustering results on the sharpening parameters is investigated and recommendations on the appropriate choice of these variables are offered. Hum. Brain Mapping 20:201-219, 2003.

Fuzzy cluster analysis of high-field functional MRI data

Functional magnetic resonance imaging (fMRI) based on blood-oxygen level dependent (BOLD) contrast today is an established brain research method and quickly gains acceptance for complementary clinical diagnosis. However, neither the basic mechanisms like coupling between neuronal activation and haemodynamic response are known exactly, nor can the various artifacts be predicted or controlled. Thus, modeling functional signal changes is non-trivial and exploratory data analysis (EDA) may be rather useful. In particular, identification and separation of artifacts as well as quantification of expected, i.e. stimulus correlated, and novel information on brain activity is important for both, new insights in neuroscience and future developments in functional MRI of the human brain. After an introduction on fuzzy clustering and very high-field fMRI we present several examples where fuzzy cluster analysis (FCA) of fMRI time series helps to identify and locally separate various artifacts. We also present and discuss applications and limitations of fuzzy cluster analysis in very high-field functional MRI: differentiate temporal patterns in MRI using (a) a test object with static and dynamic parts, (b) artifacts due to gross head motion artifacts. Using a synthetic fMRI data set we quantitatively examine the influences of relevant FCA parameters on clustering results in terms of receiver-operator characteristics (ROC) and compare them with a commonly used model-based correlation analysis (CA) approach. The application of FCA in analyzing in vivo fMRI data is shown for (a) a motor paradigm, (b) data from multi-echo imaging, and (c) a fMRI study using mental rotation of three-dimensional cubes. We found that differentiation of true "neural" from false "vascular" activation is possible based on echo time dependence and specific activation levels, as well as based on their signal time-course. Exploratory data analysis methods in general and fuzzy cluster analysis in particular may help to identify artifacts and add novel and unexpected information valuable for interpretation, classification and characterization of functional MRI data which can be used to design new data acquisition schemes, stimulus presentations, neuro(physio)logical paradigms, as well as to improve quantitative biophysical models.

Human motor cortex activity during mental rotation

The functional role of human premotor and primary motor cortex during mental rotation has been studied using functional MRI at 3 T. Fourteen young, male subjects performed a mental rotation task in which they had to decide whether two visually presented cubes could be identical. Exploratory Fuzzy Cluster Analysis was applied to identify brain regions with stimulus-related time courses. This revealed one dominant cluster which included the parietal cortex, premotor cortex, and dorsolateral prefrontal cortex that showed signal enhancement during the whole stimulus presentation period, reflecting cognitive processing. A second cluster, encompassing the contralateral primary motor cortex, showed activation exclusively after the button press response. This clear separation was possible in 3 subjects only, however. Based on these exploratory results, the hypothesis that primary motor cortex activity was related to button pressing only was tested using a parametric approach via a random-effects group analysis over all 14 subjects in SPM99. The results confirmed that the stimulus response via button pressing causes activation in the primary motor cortex and supplementary motor area while parietal cortex and mesial regions rostral to the supplementary motor area are recruited for the actual mental rotation process.

Performance evaluation of principal component analysis in dynamic FDG-PET studies of recurrent colorectal cancer

Performance evaluation of principal component analysis (PCA) of dynamic F-18-FDG-PET studies of patients with recurrent colorectal cancer. Principal component images (PCI) of 17 iteratively reconstructed data sets were visually and quantitatively evaluated. The F-18-FDG compartment model parameters were estimated using polynomial regression. All structures were present in PCI1. PCI2 was correlated with the vascular component and PCI3 with the tumor. The vessel density in the tumor was estimated with a correlation coefficient equal to 0.834. PCA supports the visual interpretation of dynamic F-18-FDG-PET studies, facilitates the application of compartment modeling and is a promising quantification technique.

The evaluation of preprocessing choices in single-subject BOLD fMRI using NPAIRS performance metrics

This work proposes an alternative to simulation-based receiver operating characteristic (ROC) analysis for assessment of fMRI data analysis methodologies. Specifically, we apply the rapidly developing nonparametric prediction, activation, influence, and reproducibility resampling (NPAIRS) framework to obtain cross-validation-based model performance estimates of prediction accuracy and global reproducibility for various degrees of model complexity. We rely on the concept of an analysis chain meta-model in which all parameters of the preprocessing steps along with the final statistical model are treated as estimated model parameters. Our ROC analog, then, consists of plotting prediction vs. reproducibility results as curves of model complexity for competing meta-models. Two theoretical underpinnings are crucial to utilizing this new validation technique. First, we explore the relationship between global signal-to-noise and our reproducibility estimates as derived previously. Second, we submit our model complexity curves in the prediction versus reproducibility space as reflecting classic bias-variance tradeoffs. Among the particular analysis chains considered, we found little impact in performance metrics with alignment, some benefit with temporal detrending, and greatest improvement with spatial smoothing.

Statistical and heuristic image noise extraction (SHINE): a new method for processing Poisson noise in scintigraphic images

Poisson noise is one of the factors degrading scintigraphic images, especially at low count level, due to the statistical nature of photon detection. We have developed an original procedure, named statistical and heuristic image noise extraction (SHINE), to reduce the Poisson noise contained in the scintigraphic images, preserving the resolution, the contrast and the texture. The SHINE procedure consists in dividing the image into 4 x 4 blocks and performing a correspondence analysis on these blocks. Each block is then reconstructed using its own significant factors which are selected using an original statistical variance test. The SHINE procedure has been validated using a line numerical phantom and a hot spots and cold spots real phantom. The reference images are the noise-free simulated images for the numerical phantom and an extremely high counts image for the real phantom. The SHINE procedure has then been applied to the Jaszczak phantom and clinical data including planar bone scintigraphy, planar Sestamibi scintigraphy and Tl-201 myocardial SPECT. The SHINE procedure reduces the mean normalized error between the noisy images and the corresponding reference images. This reduction is constant and does not change with the count level. The SNR in a SHINE processed image is close to that of the corresponding raw image with twice the number of counts. The visual results with the Jaszczak phantom SPECT have shown that SHINE preserves the contrast and the resolution of the slices well. Clinical examples have shown no visual difference between the SHINE images and the corresponding raw images obtained with twice the acquisition duration. SHINE is an entirely automatic procedure which enables halving the acquisition time or the injected dose in scintigraphic acquisitions. It can be applied to all scintigraphic images, including PET data, and to all low-count photon images.

Feature-space clustering for fMRI meta-analysis

Clustering functional magnetic resonance imaging (fMRI) time series has emerged in recent years as a possible alternative to parametric modeling approaches. Most of the work so far has been concerned with clustering raw time series. In this contribution we investigate the applicability of a clustering method applied to features extracted from the data. This approach is extremely versatile and encompasses previously published results [Goutte et al., 1999] as special cases. A typical application is in data reduction: as the increase in temporal resolution of fMRI experiments routinely yields fMRI sequences containing several hundreds of images, it is sometimes necessary to invoke feature extraction to reduce the dimensionality of the data space. A second interesting application is in the meta-analysis of fMRI experiment, where features are obtained from a possibly large number of single-voxel analyses. In particular this allows the checking of the differences and agreements between different methods of analysis. Both approaches are illustrated on a fMRI data set involving visual stimulation, and we show that the feature space clustering approach yields nontrivial results and, in particular, shows interesting differences between individual voxel analysis performed with traditional methods.

Contextual clustering for analysis of functional MRI data

We present a contextual clustering procedure for statistical parametric maps (SPM) calculated from time varying three-dimensional images. The algorithm can be used for the detection of neural activations from functional magnetic resonance images (fMRI). An important characteristic of SPM is that the intensity distribution of background (nonactive area) is known whereas the distributions of activation areas are not. The developed contextual clustering algorithm divides an SPM into background and activation areas so that the probability of detecting false activations by chance is controlled, i.e., hypothesis testing is performed. Unlike the much used voxel-by-voxel testing, neighborhood information is utilized, an important difference. This is achieved by using a Markov random field prior and iterated conditional modes (ICM) algorithm. However, unlike in the conventional use of ICM algorithm, the classification is based only on the distribution of background. The results from our simulations and human fMRI experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel-by-voxel thresholding technique. The algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications.

Separation of arteries and veins in 3D MR angiography using correlation analysis

Multiphase contrast-enhanced 3D MR angiography (MRA) data sets allow the separate visualization of the arterial and venous pulmonary vasculature. However, due to short arterial-to-venous bolus transit times in the lung, the generation of pure venograms without arterial overlay is difficult. To suppress arterial signal in venograms, early arterial phase data are typically subtracted from peak venous phase images. In this study, a correlation algorithm is used to postprocess the multiphase 3D MRA data sets. The cross-correlation between a measured arterial or venous reference function and the local signal-time course is computed which highlights image locations with a similar signal-time curve as the reference function and suppresses constant signal. Conventional maximum intensity projections (MIP) are generated from the arterial and venous correlation maps. In a study with five volunteers, an increase in SNR by a factor of 2.1 (1.8) of arterial (venous) correlation MIP images over subtraction MIP images was observed.

Comparison of two exploratory data analysis methods for fMRI: fuzzy clustering vs. principal component analysis

Exploratory data-driven methods such as Fuzzy clustering analysis (FCA) and Principal component analysis (PCA) may be considered as hypothesis-generating procedures that are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). Here, a comparison between FCA and PCA is presented in a systematic fMRI study, with MR data acquired under the null condition, i.e., no activation, with different noise contributions and simulated, varying "activation." The contrast-to-noise (CNR) ratio ranged between 1-10. We found that if fMRI data are corrupted by scanner noise only, FCA and PCA show comparable performance. In the presence of other sources of signal variation (e.g., physiological noise), FCA outperforms PCA in the entire CNR range of interest in fMRI, particularly for low CNR values. The comparison method that we introduced may be used to assess other exploratory approaches such as independent component analysis or neural network-based techniques.

Model-free functional MRI analysis using Kohonen clustering neural network and fuzzy C-means

Conventional model-based or statistical analysis methods for functional MRI (fMRI) suffer from the limitation of the assumed paradigm and biased results. Temporal clustering methods, such as fuzzy clustering, can eliminate these problems but are difficult to find activation occupying a small area, sensitive to noise and initial values, and computationally demanding. To overcome these adversities, a cascade clustering method combining a Kohonen clustering network and fuzzy, means is developed. Receiver operating characteristic (ROC) analysis is used to compare this method with correlation coefficient analysis and t test on a series of testing phantoms. Results shown that this method can efficiently and stably identify the actual functional response with typical signal change to noise ratio, from a small activation area occupying only 0.2% of head size, with phase delay, and from other noise sources such as head motion. With the ability of finding activities of small sizes stably this method can not only identify the functional responses and the active regions more precisely, but also discriminate responses from different signal sources, such as large venous vessels or different types of activation patterns in human studies involving motor cortex activation. Even when the experimental paradigm is unknown in a blind test such that model-based methods are inapplicable, this method can identify the activation patterns and regions correctly.

Assessment of cluster homogeneity in fMRI data using Kendall's coefficient of concordance

In fMRI both model-led and exploratory data-driven methods are used to identify groups of voxels according to their correlation either with an external reference or with some similarity measure. Here we present a technique to assess intragroup homogeneity using Kendall's coefficient of concordance W once groups have been identified. We show that the time-courses belonging to the group may be ranked according to their contribution to the overall concordance and describe an algorithm for group purification. We suggest the use of W as a cluster validation index in exploratory data analysis approaches, such as fuzzy or hard clustering, principal component analysis, independent component analysis and Kohonen maps.

Experimental comparison of data transformation procedures for analysis of principal components

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

Plurality and resemblance in fMRI data analysis

We apply nine analytic methods employed currently in imaging neuroscience to simulated and actual BOLD fMRI signals and compare their performances under each signal type. Starting with baseline time series generated by a resting subject during a null hypothesis study, we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple, convolved with spatially varying hemodynamic responses, and highly spatially interactive. We then apply these same nine methods to BOLD fMRI time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study. Paired comparisons of results across methods include a voxel-specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces. Receiver-operating characteristic curves show considerable model differences in ranges less than 10% significance level (false positives) and greater than 80% power (true positives). Concordance and resemblance measures reveal significant differences between activity surfaces in both data sets. These measures can assist researchers by identifying groups of models producing similar and dissimilar results, and thereby help to validate, consolidate, and simplify reports of statistical findings. A pluralistic strategy for fMRI data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain. Results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain-behavior relationships that may remain hidden if only a single method is employed.

Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework

Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio-temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates.

A hierarchical clustering method for analyzing functional MR images

We introduce a novel method for detecting anatomic and functional structures in fMRI. The main idea is to divide the data hierarchically into smaller groups using k-means clustering. The separation is halted if the clusters contain no further structure that is verified by several independent tests. The resulting cluster centers are then used for computing the final results in one step. The procedure is flexible, fast to compute, and the numbers of clusters in the data are obtained in a data-driven manner. Applying the algorithm to synthetic fMRI data yields perfect separation of "anatomic," i.e., time-invariant, and "functional," i.e., time-varying, information for a standard off-on paradigm and a typical functional contrast-to-noise ratio of two and higher. In addition, an EPI-fMRI data set of the human motor cortex was analyzed to demonstrate the performance of this novel approach in vivo.

Fuzzy clustering of gradient-echo functional MRI in the human visual cortex. Part II: quantification

Fuzzy cluster analysis (FCA) is a new exploratory method for analyzing fMRI data. Using simulated functional MRI (fMRI) data, the performance of FCA, as implemented in the software package Evident, was tested and a quantitative comparison with correlation analysis is presented. Furthermore, the fMRI model fit allows separation and quantification of flow and blood oxygen level dependent (BOLD) contributions in the human visual cortex. In gradient-recalled echo fMRI at 1.5 T (TR = 60 ms, TE = 42 ms, radiofrequency excitation flip angle [theta] = 10 degrees-60 degrees) total signal enhancement in the human visual cortex, ie, flow-enhanced BOLD plus inflow contributions, on average varies from 5% to 10% in or close to the visual cortex (average cerebral blood volume [CBV] = 4%) and from 100% to 20% in areas containing medium-sized vessels (ie, average CBV = 12% per voxel), respectively. Inflow enhancement, however, is restricted to intravascular space (= CBV) and increases with increasing radiofrequency (RF) flip angle, whereas BOLD contributions may be obtained from a region up to three times larger and, applying an unspoiled gradient-echo (GRE) sequence, also show a flip angle dependency with a minimum at approximately 30 degrees. This result suggests that a localized hemodynamic response from the microvasculature at 1.5 T may be extracted via fuzzy clustering. In summary, fuzzy clustering of fMRI data, as realized in the Evident software, is a robust and efficient method to (a) separate functional brain activation from noise or other sources resulting in time-dependent signal changes as proven by simulated fMRI data analysis and in vivo data from the visual cortex, and (b) allows separation of different levels of activation even if the temporal pattern is indistinguishable. Combining fuzzy cluster separation of brain activation with appropriate model calculations allows quantification of flow and (flow-enhanced) BOLD contributions in areas with different vascularization.

Fuzzy clustering of gradient-echo functional MRI in the human visual cortex. Part I: reproducibility

Reproducibility of human functional MRI (fMRI) studies is essential for clinical and neuroresearch applications of this new human brain mapping method. Based on a recently presented study on reproducibility of gradient-echo fMRI in the human visual cortex (Moser et al. Magn Reson Imaging 1996; 14:567-579), comparing the performance of three different threshold strategies for correlation analysis, we demonstrate that (a) fuzzy clustering is a robust, model-independent method to extract functional information in time and space; (b) intertrial reproducibility of cortical activation is significantly improved by the capability of fuzzy clustering to separate signal contributions from larger vessels, running perpendicular to the slice orientation, from activation apparently close to the primary visual cortex; and (c) for repeated single subject studies, SDs of <20% for signal enhancement in approximately 80% of the studies and SDs of <30% for activated area size in approximately 65% of the studies are obtained. This, however, depends also on signal-to-noise ratio, (motion) artifacts, and subject cooperation.

Fuzzy C-means clustering and principal component analysis of time series from near-infrared imaging of forearm ischemia

Fuzzy C-means clustering and principal components analysis were used to analyze a temporal series of near-IR images taken of a human forearm during periods of venous outflow restriction and complete forearm ischemia. The principal component eigen-time course analysis provided no useful information and the principal component eigen-image analysis gave results that correlated poorly with anatomical features. The fuzzy C-means clustering analysis, on the other hand, showed distinct regional differences in the hemodynamic response and scattering properties of the tissue, which correlated well with the anatomical features of the forearm.

Quantification of intensity variations in functional MR images using rotated principal components

In functional MRI (fMRI), the changes in cerebral haemodynamics related to stimulated neural brain activity are measured using standard clinical MR equipment. Small intensity variations in fMRI data have to be detected and distinguished from non-neural effects by careful image analysis. Based on multivariate statistics we describe an algorithm involving oblique rotation of the most significant principal components for an estimation of the temporal and spatial distribution of the stimulated neural activity over the whole image matrix. This algorithm takes advantage of strong local signal variations. A mathematical phantom was designed to generate simulated data for the evaluation of the method. In simulation experiments, the potential of the method to quantify small intensity changes, especially when processing data sets containing multiple sources of signal variations, was demonstrated. In vivo fMRI data collected in both visual and motor stimulation experiments were analysed, showing a proper location of the activated cortical regions within well known neural centres and an accurate extraction of the activation time profile. The suggested method yields accurate absolute quantification of in vivo brain activity without the need of extensive prior knowledge and user interaction.

Linear dimension reduction of sequences of medical images: III. Factor analysis in signal space

A method is presented for improving the precision of factor analysis by utilizing physiological information. The first step is an optimal linear dimension reduction, whereby the data are projected onto a low-dimensional signal space. Then principal component analysis is performed in the signal space rather than in the entire data space. This improves the precision of the principal components. Unlike ordinary principal component analysis, the present method is not degraded when the time intervals are subdivided, provided that the signal space is correct. Alternatively, but with identical results, the covariance matrix can be calculated from the whole data space. The covariance matrix is then transformed and principal component analysis is performed in either a low-rank matrix or a low-dimensional submatrix instead of in the whole covariance matrix. Factor analysis using the intersection method with a theory space may be improved by employing the present method. In simulations based on a [11C]flumazenil study with 27 frames, the proposed method required only 58 per cent of the radioactivity to produce the same precision as the intersection method and only 27 per cent when compared to ordinary principal component analysis.

Efficient calculation of the principal components of imaging data

Principal components analysis (PCA) of images is important in many applications such as positron emission tomography and functional magnetic resonance imaging. PCA is difficult for image data because the correlation matrix is very large. We present a direct method of calculating the PCA of the voxels from the small matrix expressing the correlations between images, instead of the larger matrix representing the correlations between voxels. The method is fast and accurate. It is faster and requires less memory than a singular value decomposition, although it is less accurate. It is much faster and more accurate than iterative and other approximate methods developed for this problem.