Predict the slow oscillation of the single-vessel resting-state fMRI signal of rats and humans with echo state networks
Filip Sobczak1, Yi He1, and Xin Yu1

1MPI for Biological Cybernetics, Tübingen, Germany


Single-vessel fMRI has enabled the detection of slow fluctuations (<0.1Hz) of the hemodynamic fMRI signal from individual vessels in both rat and human brains. The Echo State Network (ESN) has been used to encode the slowly changing temporal dynamics of individual vessels by training the network to predict the oscillatory signals from individual vessels 10 seconds ahead in time. Distinct network reservoirs are optimized for human and animal vascular signals, showing high correlation for the ESN-predictive signal with the original fresh data. This work establishes ESN-based signal prediction for the slow-oscillatory brain fMRI signal in real-time.


Resting-state fMRI signal has been shown to be closely coupled to brain-wide neuronal signal fluctuations, presenting large-scale functional connectivity1,2,3. The resting-state fMRI signal fluctuation demonstrates <0.1 Hz oscillatory patterns at varied brain states4. Here, we hypothesize that the spectral feature of the slow oscillatory pattern can be encoded by an artificial neural network system in a supervised learning process, and that the temporal dynamic pattern of the fMRI signal fluctuation can be predicted by the trained neural network.

Recently, a single-vessel fMRI method has been developed to characterize the resting-state fMRI signal fluctuation from individual vessels5,6. The single-vessel fMRI with simultaneous GCaMP-mediated calcium recordings revealed that (i) single venules are the main contributors of cortical slow fluctuations observed in whole-brain BOLD measurements and (ii) vascular fluctuations closely follow changes in neural activity. Here, we built up an Echo State Network7 (ESN) system to process single-vessel fMRI signal fluctuations and predict the <0.1 Hz slow oscillatory temporal dynamics with 10 seconds lead time.


Rat data acquisition

All images in rats were acquired with a 14.1T/26em horizontal bore magnet (Magnex) interfaced to an Avanee Ill console (Bruker) using the bSSFP8 method. A transceiver surface coil with a 6-mm diameter was used to acquire images. bSSFP was implemented with the following parameters: TE:3.9 ms;TR,7.8 ms; flip angle (FA),12°;matrix, 128x128;slice thickness,400 IJm; in-plane resolution,100x100 1Jm2,resulting in one slice repetition time of 1 s. The duration of each trial of resting state fMRI was 15 minutes, and data from 6 rats has been acquired.

Human data acquisition

All measurements were performed on a 3T Siemens Prisma with a 20-channel receive head coil. 6 healthy adult subjects were scanned using an EPI sequence with the following parameters: TR, 1000 ms; TE, 29 ms; FA. 60°; GRAPPA factor 3; partial Fourier 6/8; matrix, 121 x 119; in-plane resolution, 840 1-1m x 840 IJm; 9 slices with a thickness of 1.5 mm. The duration of each trial of rs-fMRI was 15 minutes with eyes closed.

Data preprocessing

Locations of single vessels penetrating the rat somatosensory cortex were found using a high-resolution anatomical image – the A-V map (Fig. 1,2-A)5. Independent component analysis9 has been employed for every trial to find a component exhibiting a strong slow fluctuation and its corresponding spatial map highlighting the dominating vascular contribution (Fig. 1,2-B,C). These two analysis steps combined allowed to extract time courses only from venules displaying strong slow fluctuations (Fig. 1,2-D). In the case of human data the ICA step alone has been sufficient. After normalizing the data, the signals have been bandpass filtered in either 0.01-0.05 Hz (rat) or 0.01-0.1 Hz (human) frequency ranges to extract the slowly changing feature.


The slow fluctuations have been encoded using ESNs – artificial neural networks trained using a supervised learning scheme. This has been done by forcing the ESNs to predict the extracted features (network output) shifted by 10 seconds with regard to the normalized raw data (network input) (Fig. 3). Every ESN performs the encoding by projecting the temporal structure of input data onto a high-dimensional space, in which features are analyzed by a simple linear decoder to generate the prediction. To find the networks achieving best predictions of vascular dynamics random search optimization10 has been employed.


Surrogate data11, artificial signals that preserve the autocorrelation structure and mean of their source data, have been generated based on real vascular time courses. These served as controls verifying the degree of encoding performed by the chosen ESNs.


The ESNs were trained for human and rat data respectively and their performances have been evaluated by computing Pearson correlation coefficients between network-predictive outputs and fresh target output data (Fig. 4,5-A). In both human and rat cases the predictions of real data obtained significantly higher scores than those of controls (Fig. 4,5-B). The optimized ESN reservoir from one rat can be used to predict slow fMRI signal fluctuations of other rats (Fig. 4E). Also, an ESN trained on human vessels has been employed in a preliminary effort to classify signals extracted from V1 cortex ROIs obtained from the Human Connectome Project12 data, showing different slow oscillatory features over the 250 human subjects (Fig. 6).

In summary, we have established an ESN system to predict the slow oscillatory temporal dynamic pattern of single-vessel fMRI signal fluctuation. This ESN system could even be applied to classify the different slow oscillatory temporal dynamics in the HCP data.


This research was supported by the Internal funding from Max Planck Society and the Graduate Training Center of neuroscience, International Max Planck Research School.


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Figure 1. Extraction of single venules exhibiting strong slow fluctuations – rat. A. The A-V map enables the localization of single venules (dark dots) in rat somatosensory cortex. B. An ICA spatial map highlights the presence of slow fluctuations predominantly in veins. C. Time course of the slowly changing ICA component shaping vascular dynamics and its power spectral density estimate (PSD). D. Examples of extracted vascular time courses selected for further processing (marked as red dots on the A-V map) along with their PSDs. The ICA component is present in the signals, but individual differences are clearly visible.

Figure 2. Extraction of single venules exhibiting strong slow fluctuations – human. A. The mean of a human single-vessel EPI time series enables the localization of single veins (black regions) in the V1 cortex. B-D. Human equivalent of the single-vessel extraction process described for rat in Fig.1B-D. A clear difference in power distribution across species is visible in the PSDs. A wider range of frequencies contribute strongly to time courses extracted from human vessels. The PSD curves extend up to the 0.1 Hz mark as compared to the 0.05 Hz in the rat case.

Figure 3. Echo State Network training and optimization. A. ESN optimization using random search. Values for network's hyperparameters are drawn randomly from pre-specified ranges to generate an ESN instance to be trained on time courses from 3 trials and evaluated on vessels from a 4th trial (rat case). From a 1000 tested ESNs the best 100 are cross-validated on all 3+1 trial combinations to select a single, best performing network. B. Normalized raw time courses serve as inputs of the network. The target outputs are the same signals, bandpass filtered and shifted in time by 10 seconds.

Figure 4. ESN prediction of the spontaneous slow fluctuation of rat vascular dynamics. A. Prediction scores of all the signals extracted from a single rat (blue dots) ordered by trials. Real data are matched with controls for every trial (red dots). B,F. Significantly higher mean scores of real data as compared to controls (pB=0.004, pF=0.00004). E. Mean prediction scores for trials extracted from different rats (blue) and their control counterparts (red). C,D,G. Highest score prediction plots of: (C) training rat; (D) training rat controls; (G) real veins of two other rats; (black – raw data, blue – target prediction, red – network output)

Figure 5. ESN prediction of the spontaneous slow fluctuation of human vascular dynamics. A. Prediction scores of all the signals extracted from 6 subjects (blue dots). Real data are matched with controls for every subject (red dots). B. Significantly higher mean prediction scores of real data as compared to controls (p=0.000153). C. Lags at which the correlation between targets and network outputs was the highest. Distribution centered around 0 indicates that the prediction wasn’t simply the filtered and shifted input. D,E. Highest score prediction plots of: (D) real signals; (E) controls; (black – raw data, blue – target prediction, red – network output)

Figure 6. ESN categorization of V1 temporal patterns. Slow fluctuations (<0.1 Hz) of 2000 single-hemisphere V1 ROIs extracted from 250 subjects from HCP have been predicted by the ESN trained on V1 single-vessel signals of 6 subjects (A). By looking at PSDs of ROIs scoring at the top (blue) and bottom (red) 5%, a clear distinction in their frequency distributions emerges. This combined with the different lag histograms of all (E) and top 5% (F) predictions indicates a possibility of utilizing the trained ESN to identify specific brain states. C,G. Plots of two predictions that obtained the highest scores.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)