Functional Connectivity and Similarity Analysis of Human Brain (Part-III)
Spatial Analysis of the Human Brain
Materials
This is the third article of the series, namely “Cognitive Computational Modelling for Spatio-Temporal fMRI in Ventral Temporal Cortex”. If you want to check out the whole series, go to the following link.
I will introduce the topic of functional connectivity and similarity analysis, their use case in the research of brain decoding. Let’s get started.
All related materials are hosted on my GitHub page. Don’t forget to check it out. If you are a paper lover, you can read the paper version of this series of articles that can also be found in my repo.
Before diving into analysis and code, let’s manipulate the Haxby dataset a little bit and apply ventral temporal masks to extract signals from regions of interest of the human brain. The installation and importing part is done in the previous article. If you did not check out my previous articles, I think to stop here and take a quick look. But, don’t worry. All parts are “nearly” independent from each other. Let’s start coding.
Here, we fetch the Haxby dataset. Next, we’ll understand the data structure and convert it to a NumPy array for further processing.
As we can see, there 8 categories. (We’ll ignore the “rest” category as it did not provide additional information.)
Let’s remove the “rest” condition data and explore the shape of the data as follows.
So, there are 864 samples that connected temporally, i.e., time-series data. The fMRI data in fixed time have a 40x64x64 dimension where 40 refers to the depth of the 3-D image and 64s refer to spatial dimensions. Hence, we are 4-D time-series image data. Recall that there are 6 subjects in the experiment so let’s look at all subjects as follows.
So, all subjects have 864-time series data. Please refer the part-I for a detailed description of the dataset.
Then, let’s perform masking to extract the region of interest to reduce the dimensionality of the fMRI. Masked fMRI samples represent the region where neural activity possibly occurred.
Yes, this script enables us to
- Fetch fMRI data and convert it into NumPy matrix
- Create and apply spatio-temporal masks to extract regions of interests
- Prepare the supervisions (target/labels)
So, let’s run this function and get the data.
Yes! Finally, we prepared our dataset. Now, we can perform any analysis we want. In this article, we’ll perform functional connectivity and similarity analysis of the human brain.
Functional Connectivity and Similarity Analysis
Functional connectivity is defined as the temporal dependency of neuronal activation patterns of anatomically separated brain regions and in the past years, an increasing body of neuroimaging studies has started to explore functional connectivity by measuring the level of co-activation of resting-state fMRI time-series between brain regions [23]. These functional connections are important in establishing statistical connections in brain regions. Functional connectivity can be obtained by estimating a covariance (or correlation) matrix for signals from different brain regions decomposed, for example on resting-state or naturalistic- stimuli datasets. Here, we performed functional connectivity analysis based on the correlation, precision, and partial correlation. Then, similarity analysis based on the cosine, Minkowski, and euclidean distance is performed to further extend statistical findings in masked fMRI data.
Functional Connectivity: Correlation
Functional connectivity based on pearson correlation is performed on subject 1. We can see that in the ventral temporal cortex of subject 1, there are strong correlations when the stimuli of faces are presented.
Functional Connectivity: Precision
As shown in the papers [20, 24], it is more interesting to use the inverse covariance matrix, i.e. the precision matrix. It gives only direct connections between regions, as it contains partial covariances, which are covariances between two regions conditioned on all the others. Moreover, we performed a functional connectome based on a precision score, to extract signals on RoI’s of subject 1 . Here, with the change in the connectivity measure, we see direct changes in spatial correlations in the ventral cortex of subject 1. With the precision measure, we further get an understanding of brain organization and brain networks.
Functional Connectivity: Partial Correlation
Among the range of network modeling methods, the partial correlation has shown great promise in accurately detecting true brain network connections [25]. So, we performed functional connectivity analysis based on partial correlation. Visualization of partial correlation in RoI fMRI data demonstrates that the ventral temporal cortex of subject 1 is not much correlated.
Similarity Analysis: Cosine Distance
To facilitate the geodesic understanding in the context of statistical connections in the brain, we performed cosine similarity analysis on subject 1, and the obtained matrix is visualized. The results demonstrate that there are highly overlapping regions in terms of neural activity when visual stimuli are presented.
Similarity Analysis: Minkowski Distance
To experiment with different similarity metrics, we utilized the minkowski distance that is a generalization of both the Euclidean and the Manhattan distance. Hence, it is useful in fMRI temporal similarity analysis.
Similarity Analysis: Euclidean Distance
Lastly, we performed similarity analysis based on classical euclidean distance. It is a very classical measure of the distance in terms of cartesian coordinates of the points using the Pythagorean theorem [13]. From the statistical and structural patterns exposed by functional connectivity and similarity analysis, we can conclude that the neural activity evoked in the ventral temporal cortex of the human brain is highly overlapping and distributed.
Yeah! That’s it for this article. I covered functional connectivity and similarity analysis techniques for fMRI data in depth.
Congratulations! You completed the third article and took a step through cognitive computational approaches for decoding the human brain.
In the next article, we’ll perform unsupervised representation learning to extract latency in the human brain.
Links of Articles
- Published Articles
2.
3.
4.
2. On the Way (Coming soon…)
- Placeholder for Part-V
Further Reading
The following list of references is utilized in my research for both machine learning and neuroscience sides. I highly recommend copy-and-paste the references and review them in brief.
References
[1] J. L. Ba, J. R. Kiros, and G. E. Hinton. Layer normalization, 2016.
[2] L. Buitinck, G. Louppe, M. Blondel, F. Pedregosa, A. Mueller, O. Grisel, V. Niculae, P. Prettenhofer, A. Gramfort, J. Grobler, R. Layton, J. VanderPlas, A. Joly, B. Holt, 10 and G. Varoquaux. API design for machine learning software: experiences from the scikit-learn project. In ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pages 108–122, 2013.
[3] X. Chu, Z. Tian, Y. Wang, B. Zhang, H. Ren, X. Wei, H. Xia, and C. Shen. Twins: Revisiting the design of spatial attention in vision transformers, 2021.
[4] K. Crammer, O. Dekel, J. Keshet, S. Shalev-Shwartz, and Y. Singer. Online passive aggressive algorithms. 2006.
[5] K. J. Friston. Statistical parametric mapping. 1994.
[6] C. G. Gross, C. d. Rocha-Miranda, and D. Bender. Visual properties of neurons in inferotemporal cortex of the macaque. Journal of neurophysiology, 35(1):96–111, 1972.
[7] S. J. Hanson, T. Matsuka, and J. V. Haxby. Combinatorial codes in ventral temporal lobe for object recognition.
[8] J. Haxby, M. Gobbini, M. Furey, A. Ishai, J. Schouten, and P. Pietrini. ”visual object recognition”, 2018.
[9] R. A. Heckemann, J. V. Hajnal, P. Aljabar, D. Rueckert, and A. Hammers. Automatic anatomical brain mri segmentation combining label propagation and decision fusion. NeuroImage, 33(1):115–126, 2006.
[10] D. Hendrycks and K. Gimpel. Gaussian error linear units (gelus), 2020.
[11] S. Huang, W. Shao, M.-L. Wang, and D.-Q. Zhang. fmribased decoding of visual information from human brain activity: A brief review. International Journal of Automation and Computing, pages 1–15, 2021.
[12] R. Koster, M. J. Chadwick, Y. Chen, D. Berron, A. Banino, E. Duzel, D. Hassabis, and D. Kumaran. Big-loop recurrence ¨ within the hippocampal system supports integration of information across episodes. Neuron, 99(6):1342–1354, 2018.
[13] E. Maor. The Pythagorean theorem: a 4,000-year history. Princeton University Press, 2019.
[14] K. A. Norman, S. M. Polyn, G. J. Detre, and J. V. Haxby. Beyond mind-reading: multi-voxel pattern analysis of fmri data. Trends in cognitive sciences, 10(9):424–430, 2006.
[15] A. J. O’toole, F. Jiang, H. Abdi, and J. V. Haxby. Partially distributed representations of objects and faces in ventral temporal cortex. Journal of cognitive neuroscience, 17(4):580–590, 2005.
[16] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825–2830, 2011.
[17] R. A. Poldrack. Region of interest analysis for fmri. Social cognitive and affective neuroscience, 2(1):67–70, 2007.
[18] M. Poustchi-Amin, S. A. Mirowitz, J. J. Brown, R. C. McKinstry, and T. Li. Principles and applications of echo-planar imaging: a review for the general radiologist. Radiographics, 21(3):767–779, 2001.
[19] R. P. Reddy, A. R. Mathulla, and J. Rajeswaran. A pilot study of perspective taking and emotional contagion in mental health professionals: Glass brain view of empathy. Indian Journal of Psychological Medicine, page 0253717620973380, 2021.
[20] S. M. Smith, K. L. Miller, G. Salimi-Khorshidi, M. Webster, C. F. Beckmann, T. E. Nichols, J. D. Ramsey, and M. W. Woolrich. Network modelling methods for fmri. Neuroimage, 54(2):875–891, 2011.
[21] K. Tanaka. Inferotemporal cortex and object vision. Annual review of neuroscience, 19(1):109–139, 1996.
[22] M. S. Treder. Mvpa-light: a classification and regression toolbox for multi-dimensional data. Frontiers in Neuroscience, 14:289, 2020.
[23] M. P. Van Den Heuvel and H. E. H. Pol. Exploring the brain network: a review on resting-state fmri functional connectivity. European neuropsychopharmacology, 20(8):519–534, 2010.
[24] G. Varoquaux, A. Gramfort, J. B. Poline, and B. Thirion. Brain covariance selection: better individual functional connectivity models using population prior. arXiv preprint arXiv:1008.5071, 2010.
[25] Y. Wang, J. Kang, P. B. Kemmer, and Y. Guo. An efficient and reliable statistical method for estimating functional connectivity in large scale brain networks using partial correlation. Frontiers in neuroscience, 10:123, 2016.
[26] S. Wold, K. Esbensen, and P. Geladi. Principal component analysis. Chemometrics and intelligent laboratory systems, 2(1–3):37–52, 1987.
[27] S. Wold, K. Esbensen, and P. Geladi. Principal component analysis. Chemometrics and intelligent laboratory systems, 2(1–3):37–52, 1987.
