Synopsis

In order to understand the sources of dynamic EPI signals under complex stimuli or in the resting state, local signal transfer functions were computed from natural stimulation data sets, and the coherence vector was mapped and color coded analogously to conventional methods for structural connectivity maps. As expected, signal propagation is frequency dependent, whereas high frequencies are caused by cardiovascular pulsations, but low frequencies are less well understood. We conclude that the observed frequency dependence of this local signal transfer model might aid the understanding of the foundation of functional connectivity analysis and the meaning of observed complex patterns such as the resting states.

Introduction

Functional MR imaging provides spatiotemporal (3D & time) data sets whose full complexity under various tasks or even during ‘rest’ we are just starting to appreciate. In addition, EPI-based fMRI experiments increasingly move from tightly controlled designs to experiments that probe the brain under natural, complex stimuli or behavior, such as virtual reality or watching movies. In order to understand brain activity in these experiments, it is even more important to be able to disentangle the various contributions to the spatiotemporal EPI signals¹. Towards this end, here we performed an analysis of local signal propagation^2,3 between neighboring MRI voxels by means of transfer functions and coherences. This method might aid the detection of local EPI signal properties of relevance for global connectivity studies⁴ by mapping frequency-dependent EPI signal sources, for example vascular vs. BOLD sources.

Methods

Theory: The linear relationship, including arbitrary lag times, between an output signal y(t) and an input signal x(t) can be written in frequency space under steady-state conditions by the transfer or frequency response function H(ω), which relates the Fourier transforms X(ω) and Y(ω) to each other, i.e.,

Y(ω) = H(ω)X(ω) .

Here, the signals consists of time series of EPI data, independent of their origin (vascular, BOLD, flow, etc.) With the cross- and auto-power spectra P_XY(ω) = X^*(ω)Y(ω), P_XX(ω) = |X(ω)|², P_YY(ω) = |Y(ω)|², the coherence between the signals is

C_XY(ω) = |P_XY(ω)|²/(P_XX(ω)P_YY(ω)) = |H(ω)|² P_XX(ω)/P_YY(ω).

The application to spatiotemporal data is shown schematically in Figure 1, which also includes further model assumptions.

Data: Four natural stimulation (audio version of a feature film) dynamic EPI scans from a publicly available data base⁵ were used, covering parts of frontal and occipital cortex and regions in between. The data was acquired on a 7 Tesla MRI scanner and sampled every 2 s for 15 min at 1.4 mm isotropic resolution.

Analysis: Local coherences of the EPI signal were obtained from high-pass filtered data (cutoff period 1 min to remove trends^6,7), using standard spectral estimation methods as they are provided by Matlab’s cpsd function. For each voxel, three nearest neighbor coherences were taken into account (to avoid redundancy) and a coherence vector formed from these. The vector magnitude was represented as maximum intensity projections (MIPs), and the principal direction (largest of the three components) color coded analogously to methods used for structural connectivity maps⁸.

Results

Signal propagation is visible at the main cerebral arteries, in smaller arteries, next to or in gray cortical matter, in cerebrospinal fluid, and in some extracerebral areas, but mostly absent in white matter (Figures 2, 3). This signal propagation is frequency dependent: For high frequencies (corresponding periods below 12.5 s), mainly the main arteries are visible, for lower frequencies (periods between 12.5 and 60 s), smaller arteries and probably some gray matter areas are added while the main blood vessels appear diminished but not completely suppressed. The gray matter of the basal ganglia and thalamus does not show pronounced signal transfer in this model. There are also artifacts caused but not limited to eye and head motion. The model’s sensitivity becomes apparent when applied to data sets that underwent widely used standard fMRI pre-processing: Re-sampling data to higher resolution and distortion correction cause artifacts, shown in Figure 2D.

Discussion

The cardiac pulse affects mainly the highest frequencies of the EPI signal. This pulse sensitivity has been observed before in complementary local methods tailored to pulsatile signals in EPI data^9-11. Low-frequency fluctuations visible in signal transfer¹² seemingly affect smaller vessels and gray matter, but their origin (autoregulation/neuronal processes or their interaction¹³) and their exact source (arterioles/veins/capillary bed) remain open without further analysis or experiments. The possible value of color coding the direction of the coherence vector still needs to be evaluated. In order to avoid some of the present model assumptions (Figure 1), partial coherences^14,15 could be used, and for more than three directions.

Conclusion

The observed frequency dependence of a local signal transfer model for spatiotemporal MR data might aid the understanding of the foundation of applications such as functional connectivity analysis and the meaning of observed complex patterns such as the resting states. The proposed model might be the starting point for a more refined analysis, with possible value towards the interpretation^16-18 of the growing number of clinical and more complex MRI experiments or the application of network control theory to the human brain¹⁹. In addition, vectorizing³ local neuronal connectivity is a first step towards tracking of functional connections in gray matter analogous to tracking structural connections in white matter, and thus again a step towards a global mapping of brain dynamics.

Acknowledgements

We would like to thank M. Hanke and A. Brechmann for personal support.

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