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High spatial resolution functional MRI (fMRI) and advanced multivariate analysis techniques are promising tools for studying the cortical basis of human cognitive processes at the level of columns and layers. However the true spatial specificity of high-resolution fMRI has not been quantified, and the basis for decoding from fine scale structures using large voxels and relatively low magnetic field strength is unknown. It is also not yet known what method and voxel size is optimal for decoding and what voxel size is optimal for high-resolution imaging. In this thesis we present four studies that answer part of these questions using a model-based approach of imaging cortical columns.
We started our investigation of model-based analysis of high-resolution fMRI of cortical columns by addressing the specific problem of how it is possible to decode information thought to be mediated by cortical columns using large voxels at low field strength. Multivariate machine learning algorithms applied to human functional MRI (fMRI) data can decode information conveyed by cortical columns, despite the voxel-size being large relative to the width of columns. Several mechanisms have been proposed to underlie decoding of stimulus orientation or the stimulated eye. These include: (I) aliasing of high spatial-frequency components, including the main frequency component of the columnar organization, (II) contributions from local irregularities in the columnar organization, (III) contributions from large-scale non-columnar organizations, (IV) functionally selective veins with biased draining regions, and (V) complex spatio-temporal filtering of neuronal activity by fMRI voxels. Here we sought to assess the plausibility of two of the suggested mechanisms: (I) aliasing and (II) local irregularities, using a naive model of BOLD as blurring and MRI voxel sampling. To this end, we formulated a mathematical model that encompasses both the processes of imaging ocular dominance (OD) columns and the subsequent linear classification analysis. Through numerical simulations of the model, we evaluated the distribution of functional differential contrasts that can be expected when considering the pattern of cortical columns, the hemodynamic point spread function, the voxel size, and the noise. We found that with data acquisition parameters used at 3 Tesla, sub-voxel supra-Nyquist frequencies, including frequencies near the main frequency of the OD organization (0.5 cycles per mm), cannot contribute to the differential contrast. The differential functional contrast of local origin is dominated by low-amplitude contributions from low frequencies, associated with irregularities of the cortical pattern. Realizations of the model with parameters that reflected a best-case scenario and the reported BOLD point-spread at 3 Tesla (3.5 mm) predicted decoding performances lower than those that have been previously obtained at this magnetic field strength. We conclude that low frequency components that underlie local irregularities in the columnar organization are likely to play a role in decoding. We further expect that fMRI-based decoding relies, in part, on signal contributions from large-scale, non-columnar functional organizations, and from complex spatio-temporal filtering of neuronal activity by fMRI voxels, involving biased venous responses. Our model can potentially be used for evaluating and optimizing data-acquisition parameters for decoding information conveyed by cortical columns.
Having developed a model of imaging ODCs we then used this model to estimate the spatial specificity of BOLD fMRI, specifically at high field (7 T). Previous attempts at characterizing the spatial specificity of the blood oxygenation level dependent functional MRI (BOLD fMRI) response by estimating its point-spread function (PSF) have conventionally relied on spatial representations of visual stimuli in area V1. Consequently, their estimates were confounded by the width and scatter of receptive fields of V1 neurons. Here, we circumvent these limits by instead using the inherent cortical spatial organization of ocular dominance columns (ODCs) to determine the PSF for both Gradient Echo (GE) and Spin Echo (SE) BOLD imaging at 7 Tesla. By applying Markov Chain Monte Carlo sampling on a probabilistic generative model of imaging ODCs, we quantified the PSFs that best predict the spatial structure and magnitude of differential ODCs’ responses. Prior distributions for the ODC model parameters were determined by analyzing published data of cytochrome oxidase patterns from post-mortem histology of human V1 and of neurophysiological ocular dominance indices. The most probable PSF full-widths at half-maximum were 0.82 mm (SE) and 1.02 mm (GE). Our results provide a quantitative basis for the spatial specificity of BOLD fMRI at ultra-high fields, which can be used for planning and interpretation of high-resolution differential fMRI of fine-scale cortical organizations.
Our BOLD fMRI PSF findings show that the PSF is considerably smaller than what was reported previously. This in turn raised the question of the role of the imaging PSF, which now has become relevant. Next, we show that the commonly used magnitude point-spread function fails to accurately represent the true effects of k-space sampling and signal decay, and propose an alternative model that accounts more accurately for these effects. The effects of k-space sampling and signal decay on the effective spatial resolution of MRI and functional MRI (fMRI) are commonly assessed by means of the magnitude point-spread function (PSF), defined as the absolute values (magnitudes) of the complex MR imaging PSF. It is commonly assumed that this magnitude PSF signifies blurring, which can be quantified by its full-width at half-maximum (FWHM). Here we show that the magnitude PSF fails to accurately represent the true effects of k-space sampling and signal decay. Firstly, a substantial part of the width of the magnitude PSF is due to MRI sampling per se. This part is independent of any signal decay and its effect depends on the spatial frequency composition of the imaged object. Therefore, it cannot always be expected to introduce blurring. Secondly, MRI reconstruction is typically followed by taking the absolute values (magnitude image) of the reconstructed complex image. This introduces a non-linear stage into the process of image formation. The complex imaging PSF does not fully describe this process, since it does not reflect the stage of taking the magnitude image. Its corresponding magnitude PSF fails to correctly describe this process, since convolving the original pattern with the magnitude PSF is different from the true process of taking the absolute following a convolution with the complex imaging PSF. Lastly, signal decay can have not only a blurring, but also a high-pass filtering effect. This cannot be reflected by the strictly positive width of the magnitude PSF. As an alternative, we propose to model the imaging process by decomposing it into a signal decay-independent MR sampling part and an approximation of the signal decay effect. We approximate the latter as a convolution with a Gaussian PSF or, if the effect is that of high-pass filtering, as reversing the effect of a convolution with a Gaussian PSF. We show that for typical high-resolution fMRI at 7 Tesla, signal decay in Spin-Echo has a moderate blurring effect (FWHM = 0.89 voxels, corresponds to 0.44 mm for 0.5 mm wide voxels). In contrast, Gradient-Echo acts as a moderate high-pass filter that can be interpreted as reversing a Gaussian blurring with FWHM = 0.59 voxels (0.30 mm for 0.5 mm wide voxels). Our improved approximations and findings hold not only for Gradient-Echo and Spin-Echo fMRI but also for GRASE and VASO fMRI. Our findings support the correct planning, interpretation, and modeling of high-resolution fMRI.
In our first study we used our model to analyze imaging of cortical columns under a very specific scenario. We studied a best case scenario for decoding the stimulated eye from ODCs imaged at 3T using large voxels. In order to do so, we formalized available knowledge about fMRI of cortical columns. In particular, the ability of fMRI to resolve cortical columnar organization depends on several interdependent factors, e.g. the spatial scale of the columnar pattern, the point-spread of the BOLD response, voxel size and the signal-to-noise ratio. In our fourth study we aim to analyze how these factors contribute and combine in imaging of arbitrary cortical columnar patterns at varying field strengths and voxel sizes. In addition, we compared different pattern imaging approaches. We show how detection, decoding and reconstruction of a fine scale organization depend on the parameters of the model, and we predict optimal voxel sizes for each approach under various scenario. The capacity of fMRI to resolve cortical columnar organizations depends on several factors, e.g. the spatial scale of the columnar pattern, the point-spread of the fMRI response, the voxel size, and the SNR considering thermal and physiological noise. How these factors combine, and what is the voxel size that optimizes fMRI of cortical columns remain unknown. Here we combine current knowledge into a quantitative model of fMRI of patterns of cortical columns. We compare different approaches for imaging patterns of cortical columns, including univariate and multivariate based detection, multi-voxel pattern analysis (MVPA) based decoding, and reconstruction of the pattern of cortical columns. We present the dependence of their performance on the parameters of the imaged pattern and the data acquisition, and predict voxel sizes that optimize fMRI under various scenarios. To this end, we modeled differential imaging of realistic patterns of cortical columns with different spatial scales and degrees of irregularity. We quantified the capacity to detect and decode stimulus-specific responses by analyzing the distribution of voxel-wise differential responses relative to noise. We quantified the accuracy with which the spatial pattern of cortical columns can be reconstructed as the correlation between the underlying columnar pattern and the imaged pattern. For regular patterns, optimal voxel widths for detection, decoding and reconstruction were close to half the main cycle length of the organization. Optimal voxel widths for irregular patterns were less dependent on the main cycle length, and differed between univariate detection, multivariate detection and decoding, and reconstruction. We compared the effects of different factors of Gradient Echo fMRI at 3 Tesla (T), Gradient Echo fMRI at 7T and Spin-Echo fMRI at 7T, and found that for all measures (detection, decoding, and reconstruction), the width of the fMRI point-spread has the most significant effect. In contrast, different response amplitudes and noise characteristics played a comparatively minor role. We recommend specific voxel widths for optimal univariate detection, for multivariate detection and decoding, and for reconstruction under these three data-acquisition scenarios. Our study supports the planning, optimization, and interpretation of fMRI of cortical columns and the decoding of information conveyed by these columns. |
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