Comments on a Monte Carlo approach to the analysis of functional neuroimaging data

Statistical framework and noise sensitivity of the amplitude radial correlation contrast method

A statistical framework for the amplitude radial correlation contrast (RCC) method, which integrates a conventional pixel threshold approach with cluster-size statistics, is presented. The RCC method uses functional MRI (fMRI) data to group neighboring voxels in terms of their degree of temporal cross correlation and compares coherences in different brain states (e.g., stimulation OFF vs. ON). By defining the RCC correlation map as the difference between two RCC images, the map distribution of two OFF states is shown to be normal, enabling the definition of the pixel cutoff. The empirical cluster-size null distribution obtained after the application of the pixel cutoff is used to define a cluster-size cutoff that allows 5% false positives. Assuming that the fMRI signal equals the task-induced response plus noise, an analytical expression of amplitude-RCC dependency on noise is obtained and used to define the pixel threshold. In vivo and ex vivo data obtained during rat forepaw electric stimulation are used to fine-tune this threshold. Calculating the spatial coherences within in vivo and ex vivo images shows enhanced coherence in the in vivo data, but no dependency on the anesthesia method, magnetic field strength, or depth of anesthesia, strengthening the generality of the proposed cutoffs.

A Monte Carlo analysis technique applied to cerebral perfusion SPECT scans

OBJECTIVE

Voxel-based techniques are used to provide objective analyses of SPECT scans. The aim of this study was to develop a voxel-based analysis technique that uses a Monte Carlo method of statistical inference and assess this analysis technique for application to cerebral perfusion SPECT scans.

METHODS

Assessment of the validity of this non-parametric, Monte Carlo method of statistical inference has been performed for a range of study designs, image characteristics and analysis parameters using phantom SPECT and Gaussian images. The Monte Carlo method of statistical inference and the voxel-based analysis technique were clinically evaluated for the analysis of individual cerebral perfusion SPECT scans using control subject data. In addition, a comparison has been performed with an existing analysis package that uses a theoretical parametric method of statistical inference (statistical parametric mapping).

RESULTS

The Monte Carlo method was found to provide accurate statistical inference for phantom SPECT and Gaussian images independent of degrees of freedom, acquired counts, image smoothness and voxel significance level threshold. The clinical evaluation of the analysis of individual cerebral perfusion SPECT scans demonstrated satisfactory statistical inference and characterization of perfusion deficits.

CONCLUSION

An analysis method incorporating a Monte Carlo method of statistical inference has been successfully applied for the analysis of cerebral perfusion SPECT scans.

Quantile estimation to derive optimized test thresholds for random field statistics

We present a numerical method to estimate the true threshold values in random fields needed to determine the significance of apparent signals observed in noisy images. To accomplish this, a quantile estimation algorithm is applied to derive the threshold with a predefined confidence interval from a large number of simulated random fields. Also, a computationally efficient method for generating a random field simulation is presented using resampling techniques. Applying these techniques, thresholds have been determined for a large variety of parameter settings (smoothness, voxel size, brain shape, type of statistics). By means of interpolation techniques, thresholds for additional arbitrary settings can be quickly derived without the need to run individual simulations. Compared to the parametric approach of Worsley et al. (1996) (Worsley, K.J., Marrett, S., Neelin P., Vandal, A.C., Friston, K.J., Evans, A.C., 1996. A unified statistical approach for determining significant signals in images of cerebral activation. Hum. Brain Mapp. 4, 58-73) and Friston et al. (1991) (Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S. 1991. Comparing functional (PET) images: the assessment of significant change. J. Cereb. Blood Flow Metab. 11(4), 690-699), and to the Bonferroni approach, these optimized thresholds lead to higher levels of significance (i.e., lower p values) with a specific amount of activation especially with fields of moderate smoothness (i.e., with a relative full width half maximum between 2 and 6). Alternatively, the threshold for a specified level of significance can be lowered. This improved statistical sensitivity is illustrated by the analysis of an actual event related functional magnetic resonance data set, and its limitations are tested by determining the false positive rate with experimental MR noise data. The grid of estimated threshold values as well as the interpolation algorithm to derive thresholds for arbitrary parameter settings are made available over the internet (http://neuro2.med.uni-magdeburg.de/quantile_estimation).

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.

Serial MRI findings in patient with chronic cryptococcus meningo-encephalitis

We describe the serial changes of magnetic resonance imaging (MRI) in a patient with chronic cryptococcus meningo-encephalitis. In the subacute phase, MRI revealed a focal lesion with hyperintensity on T2-weighted image (WI) in the left thalamus. At 11 months after the onset, MRI showed a focal lesion with hyperintensity on T2-WI in the right pons that was enhanced with gadolinium (Gd). At 13 months after the onset, the lesion in the left thalamus became rim enhanced with Gd. After antifungal therapy (amphotericin B and 5-flucytosine), the rim enhancement in the left thalamus and the high signal intensity area in the right pons decreased. Cryptococcoma should be in the differential from other ring enhancing lesions.

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.

Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference.

Statistical limitations in functional neuroimaging. II. Signal detection and statistical inference

The field of functional neuroimaging (FNI) methodology has developed into a mature but evolving area of knowledge and its applications have been extensive. A general problem in the analysis of FNI data is finding a signal embedded in noise. This is sometimes called signal detection. Signal detection theory focuses in general on issues relating to the optimization of conditions for separating the signal from noise. When methods from probability theory and mathematical statistics are directly applied in this procedure it is also called statistical inference. In this paper we briefly discuss some aspects of signal detection theory relevant to FNI and, in addition, some common approaches to statistical inference used in FNI. Low-pass filtering in relation to functional-anatomical variability and some effects of filtering on signal detection of interest to FNI are discussed. Also, some general aspects of hypothesis testing and statistical inference are discussed. This includes the need for characterizing the signal in data when the null hypothesis is rejected, the problem of multiple comparisons that is central to FNI data analysis, omnibus tests and some issues related to statistical power in the context of FNI. In turn, random field, scale space, non-parametric and Monte Carlo approaches are reviewed, representing the most common approaches to statistical inference used in FNI. Complementary to these issues an overview and discussion of non-inferential descriptive methods, common statistical models and the problem of model selection is given in a companion paper. In general, model selection is an important prelude to subsequent statistical inference. The emphasis in both papers is on the assumptions and inherent limitations of the methods presented. Most of the methods described here generally serve their purposes well when the inherent assumptions and limitations are taken into account. Significant differences in results between different methods are most apparent in extreme parameter ranges, for example at low effective degrees of freedom or at small spatial autocorrelation. In such situations or in situations when assumptions and approximations are seriously violated it is of central importance to choose the most suitable method in order to obtain valid results.