Can parametric statistical methods be trusted for fMRI based group studies?

The most widely used task fMRI analyses use parametric methods that depend on a variety of assumptions. While individual aspects of these fMRI models have been evaluated, they have not been evaluated in a comprehensive manner with empirical data. In this work, a total of 2 million random task fMRI group analyses have been performed using resting state fMRI data, to compute empirical familywise error rates for the software packages SPM, FSL and AFNI, as well as a standard non-parametric permutation method. While there is some variation, for a nominal familywise error rate of 5% the parametric statistical methods are shown to be conservative for voxel-wise inference and invalid for cluster-wise inference; in particular, cluster size inference with a cluster defining threshold of p = 0.01 generates familywise error rates up to 60%. We conduct a number of follow up analyses and investigations that suggest the cause of the invalid cluster inferences is spatial auto correlation functions that do not follow the assumed Gaussian shape. By comparison, the non-parametric permutation test, which is based on a small number of assumptions, is found to produce valid results for voxel as well as cluster wise inference. Using real task data, we compare the results between one parametric method and the permutation test, and find stark differences in the conclusions drawn between the two using cluster inference. These findings speak to the need of validating the statistical methods being used in the neuroimaging field

Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM

Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected $p$-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing procedure as the construction of a very large permutation testing matrix, $T$, one can exploit structural properties derived from the data and the test statistics to reduce the runtime under certain conditions. In particular, we see that $T$ is low-rank plus a low-variance residual. This makes $T$ a good candidate for low-rank matrix completion, where only a very small number of entries of $T$ ($\sim0.35\%$ of all entries in our experiments) have to be computed to obtain a good estimate. Based on this observation, we present RapidPT, an algorithm that efficiently recovers the max null distribution commonly obtained through regular permutation testing in voxel-wise analysis. We present an extensive validation on a synthetic dataset and four varying sized datasets against two baselines: Statistical NonParametric Mapping (SnPM13) and a standard permutation testing implementation (referred as NaivePT). We find that RapidPT achieves its best runtime performance on medium sized datasets ($50 \leq n \leq 200$), with speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger datasets ($n \geq 200$) RapidPT outperforms NaivePT (6x - 200x) on all datasets, and provides large speedups over SnPM13 when more than 10000 permutations (2x - 15x) are needed. The implementation is a standalone toolbox and also integrated within SnPM13, able to leverage multi-core architectures when available.Comment: 36 pages, 16 figure

True 4D Image Denoising on the GPU

The use of image denoising techniques is an important part of many medical imaging applications. One common application is to improve the image quality of low-dose (noisy) computed tomography (CT) data. While 3D image denoising previously has been applied to several volumes independently, there has not been much work done on true 4D image denoising, where the algorithm considers several volumes at the same time. The problem with 4D image denoising, compared to 2D and 3D denoising, is that the computational complexity increases exponentially. In this paper we describe a novel algorithm for true 4D image denoising, based on local adaptive filtering, and how to implement it on the graphics processing unit (GPU). The algorithm was applied to a 4D CT heart dataset of the resolution 512  × 512  × 445  × 20. The result is that the GPU can complete the denoising in about 25 minutes if spatial filtering is used and in about 8 minutes if FFT-based filtering is used. The CPU implementation requires several days of processing time for spatial filtering and about 50 minutes for FFT-based filtering. The short processing time increases the clinical value of true 4D image denoising significantly

Fast Random Permutation Tests Enable Objective Evaluation of Methods for Single Subject fMRI Analysis

Parametric statistical methods, such as Z-, t-, and F-values are traditionally employed in functional magnetic resonance imaging (fMRI) for identifying areas in the brain that are active with a certain degree of statistical significance. These parametric methods, however, have two major drawbacks. First, it is assumed that the observed data are Gaussian distributed and independent; assumptions that generally are not valid for fMRI data. Second, the statistical test distribution can be derived theoretically only for very simple linear detection statistics. With non-parametric statistical methods, the two limitations described above can be overcome. The major drawback of non-parametric methods is the computational burden with processing times ranging from hours to days, which so far have made them impractical for routine use in single subject fMRI analysis. In this work, it is shown how the computational power of cost-efficient Graphics Processing Units (GPUs) can be used to speed up random permutation tests. A test with 10 000 permutations takes less than a minute, making statistical analysis of advanced detection methods in fMRI practically feasible. To exemplify the permutation based approach, brain activity maps generated by the General Linear Model (GLM) and Canonical Correlation Analysis (CCA) are compared at the same significance level. During the development of the routines and writing of the paper, 3-4 years of processing time has been saved by using the GPU

Permutation Inference for Canonical Correlation Analysis

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 reference

Generation of a whole-brain hemodynamic response function and sex-specific differences in cerebral processing of mechano-sensation in mice detected by BOLD fMRI

BOLD fMRI has become a prevalent method to study cerebral sensory processing in rodent disease models, including pain and mechanical hypersensitivity. fMRI data analysis is frequently combined with a general-linear-model (GLM) -based analysis, which uses the convolution of a hemodynamic response function (HRF) with the stimulus paradigm. However, several studies indicated that the HRF differs across species, sexes, brain structures, and experimental factors, including stimulation modalities or anesthesia, and hence might strongly affect the outcome of BOLD analyzes. While considerable work has been done in humans and rats to understand the HRF, much less is known in mice. As a prerequisite to investigate mechano-sensory processing and BOLD fMRI data in male and female mice, we (1) designed a rotating stimulator that allows application of two different mechanical modalities, including innocuous von Frey and noxious pinprick stimuli and (2) determined and statistically compared HRFs across 30 brain structures and experimental conditions, including sex and, stimulus modalities. We found that mechanical stimulation lead to brain-wide BOLD signal changes thereby allowing extraction of HRFs from multiple brain structures. However, we did not find differences in HRFs across all brain structures and experimental conditions. Hence, we computed a whole-brain mouse HRF, which is based on 88 functional scans from 30 mice. A comparison of this mouse-specific HRF with our previously reported rat-derived HRF showed significantly slower kinetics in mice. Finally, we detected pronounced differences in cerebral BOLD activation between male and female mice with mechanical stimulation, thereby exposing divergent processing of noxious and innocuous stimuli in both sexes

The speed of visual processing of complex objects in the human brain. Sensitivity to image properties, the influence of aging, optical factors and individual differences.

Visual processing of complex objects is a feat that the brain accomplishes with remarkable speed – generally in the order of a few hundred milliseconds. Our knowledge with regards to what visual information the brain uses to categorise objects, and how early the first object-sensitive responses occur in the brain, remains fragmented. It seems that neuronal processing speed slows down with age due to a variety of physiological changes occurring in the aging brain, including myelin degeneration, a decrease in the selectivity of neuronal responses and a reduced efficiency of cortical networks. There are also considerable individual differences in age-related alterations of processing speed, the origins of which remain unclear. Neural processing speed in humans can be studied using electroencephalogram (EEG), which records the activity of neurons contained in Event-Related-Potentials (ERPs) with millisecond precision. Research presented in this thesis had several goals. First, it aimed to measure the sensitivity of object-related ERPs to visual information contained in the Fourier phase and amplitude spectra of images. The second goal was to measure age-related changes in ERP visual processing speed and to find out if their individual variability is due to individual differences in optical factors, such as senile miosis (reduction in pupil size with age), which affects retinal illuminance. The final aim was to quantify the onsets of ERP sensitivity to objects (in particular faces) in the human brain. To answer these questions, parametric experimental designs, novel approaches to EEG data pre-processing and analyses on a single-subject and group basis, robust statistics and large samples of subjects were employed. The results show that object-related ERPs are highly sensitive to phase spectrum and minimally to amplitude spectrum. Furthermore, when age-related changes in the whole shape of ERP waveform between 0-500 ms were considered, a 1 ms/year delay in visual processing speed has been revealed. This delay could not be explained by individual variability in pupil size or retinal illuminance. In addition, a new benchmark for the onset of ERP sensitivity to faces has been found at ~90 ms post-stimulus in a sample of 120 subjects age 18-81. The onsets did not change with age and aging started to affect object-related ERP activity ~125-130 ms after stimulus presentation. Taken together, this thesis presents novel findings with regards to the speed of visual processing in the human brain and outlines a range of robust methods for application in ERP vision research