**3. Conclusion**

Over the past two decades, the development of new neuroimaging techniques has produced spectacular improvements in the amount of detail with which brain activity can be monitored. As precision has rapidly been gained, though, so has the typical data set size grown steadily. The range of questions that researchers and clinicians alike have started finding an answer for with neuroimaging techniques has also dramatically expanded. All this, in turn, has created a demand for new methods of data analysis, These new methods were developed on the one hand to provide new ways to represent brain activity, and on the other hand, to make quantitative sense of the rich information embedded in very high dimensional data and to visualize them in a way that can be read and understood in a sufficiently straightforward way by researchers first and, ultimately, by clinicians.

In this chapter, we presented FH a method which effectively tackles these issues. The FH algorithm deals with the multivariate and multiscale nature of brain imaging data sets and simplifies their complexity by representing patterns in a low-dimensional space which preserves the higher dimensional information of the original pattern of connectivity. In this sense, the FH analysis may be regarded as a system-level analysis that produces a complete, holographic, representation of brain activation.

Fig. 16. The averaged Z score of number of links in the MST connecting the two clusters across subjects (N=15) for each experiment block. The two repetitive hand movements (i.e. blocks 2 and 8) resulted in higher average than the rest of the blocks. A statistical Z-test was calculated for each block with the null hypothesis that the scores in each block are a random sample from a normal distribution with mean zero. According to this test the two repetitive hand movements were found significant (p=2x10-4 and p=6.9x10-10 for blocks 2 and 8

Over the past two decades, the development of new neuroimaging techniques has produced spectacular improvements in the amount of detail with which brain activity can be monitored. As precision has rapidly been gained, though, so has the typical data set size grown steadily. The range of questions that researchers and clinicians alike have started finding an answer for with neuroimaging techniques has also dramatically expanded. All this, in turn, has created a demand for new methods of data analysis, These new methods were developed on the one hand to provide new ways to represent brain activity, and on the other hand, to make quantitative sense of the rich information embedded in very high dimensional data and to visualize them in a way that can be read and understood in a

sufficiently straightforward way by researchers first and, ultimately, by clinicians.

holographic, representation of brain activation.

In this chapter, we presented FH a method which effectively tackles these issues. The FH algorithm deals with the multivariate and multiscale nature of brain imaging data sets and simplifies their complexity by representing patterns in a low-dimensional space which preserves the higher dimensional information of the original pattern of connectivity. In this sense, the FH analysis may be regarded as a system-level analysis that produces a complete,

respectively).

**3. Conclusion** 

The method also provides an effective visualization of the system, of critical importance when dealing with highly complex systems, and is particularly helpful in the identification of clusters and their hierarchies. Even more important though is the ability of the FH analysis to reveal subtle, system-level dynamical features that are hard to detect through other methods, even at the single subject level. And that might be overlooked due to prior assumptions by hypothesis-driven methods. In fact, the FH method can capture sensitive hemodynamic variations at the single block level, without further need for averaging or for contrasts between experimental conditions. In addition the method requires far less time point to localize activations than other clustering methods, viz. ICA (Bell & Sejnowski, 1995), FCA (Windischberger et al., 2003) or TCA (Zhao et al., 2007), suggesting that the FH method may play a prominent role in the development of classification algorithms for blind identification of different conditions in extremely short time series.

It is important to portray the FH method not only as an alternative but also as a valuable complement to existing methods. For instance, its dimension reduction step could be carried out using a variety of clustering techniques. Perhaps even more cogently, there is a clear complementarily between network theory and the FH method. The application of the former that we presented, i.e. the MST, clearly represents but one out of the many possible applications. To the extremely vast field of issues that network theory allows to address in a versatile but quantitatively rigorous and qualitatively explicit way, the FH method adds a compact representation in an auxiliary field that makes functional networks more explicit, as it divorces them from the anatomical space in which they live.

A distinctive quality of the FH method is represented by its versatility. While originally developed for cultured neural networks, the method can be applied to the analysis of essentially any type of signal, including the main tools for system-level neuroimaging, viz. EEG/MEG and fMRI. Although fewer examples of application to the latter are and further investigation of the method on different (viz. event-related) designs is needed, the proposed method shows great potential even for fMRI data in differentiating experimental conditions particularly when the corresponding signals are separated (Jacob et al., 2010). Since the outcome of the analysis is a holographic presentation in an abstract reduced space, it represents an ideal tool for multi-modal analysis of data from experiments combining EEG´s temporal precision with fMRI´s spatial one. Finally, the principles and implementation of the FH analysis are relatively simple and straightforward; taken together with the methods efficiency in delineating and tracking the time-varying unfolding of fine details of clustered activity at different spatial scales, it may represent a tool of election for brain scientists and for clinical neurologists alike.

## **4. Acknowledgment**

We are most thankful to Asaf Madi, Dror Kenett, Amir Rapson, Michal Kafri and Keren Rosenberg for fruitful discussions. This research has been supported in part by the Israel-US Binational Science Foundation – 2005385 (EBJ, TH), the Maguy-Glass chair in physics of complex systems (EBJ), the Tauber Family Funds and the Italy-Israel program in System Level Network Neuroscience at Tel Aviv University (EBJ), the National Science Foundation Grants PHY- 0216576 and 0225630 at UCSD (EBJ), the Israel Science Foundation - 1747/07 (TH) and by the U.S Department Of Defense W81XWH-11-2-0008 (TH).

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**7** 

Xin Zhou

*P.R. China* 

**Hyperpolarized Xenon Brain MRI** 

*State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics,* 

Since hyperpolarized 129Xe MRI was first demonstrated in the lung, air space imaging using hyperpolarized noble gases (129Xe and 3He) has progressed at a rapid rate (Goodson, 2002; Zhou, 2011c). Owing to high lipid solubility, absence of background signal in biological tissue, non-invasiveness, lack of radioactivity, different relaxation to oxygenated and deoxygenated blood, and larger chemical shift to the neighbor environment, hyperpolarized 129Xe magnetic resonance imaging (MRI) has a great potential as a tool for studying the brain, especially for

In this chapter, we will review the progress of recent research on hyperpolarized xenon brain MRI, and compare this novel technique with the conventional proton MRI in order to comment the possible innovation and development in the future. This chapter contains six

Xenon, with the chemical element symbol Xe and atomic number 54, is a member of the zero-valence elements that are called noble gases or inert gases. Xenon was discovered in the residue left over from evaporating components of liquid air by William Ramsay and Morris Travers in England in 1898, then was named by Ramsay from Greek word *ξένον*, with the meaning 'foreign' and 'strange'. Natural abundant xenon is made of nine stable isotopes, and more than 35 unstable isotopes have been characterized. Nuclei of two isotopes, 129Xe and 131Xe, have non-zero spin quantum number: 26.4% of 129Xe with a nuclear spin I=1/2 ; and 21.2% of 131Xe with a nuclear spin I=3/2 (133Xe is used as a radioisotope in nuclear medicine). These two isotopes are both detectable by NMR with sensitivities of 0.021 (129Xe, per nucleus relative to proton assuming thermal polarization) and 2.710-3 ( 131Xe). The highly enhanced signal of hyperpolarized xenon and extremely long relaxation time greatly simplified and enhanced NMR experiments, and it is the fundamental for possible

Xenon, chemically inert with the external electronic orbits fully occupied, is well known as a noble gas at room temperature and an atmospheric pressure. However, the liquid and solid

the assessment of cerebral blood flow (CBF) related to the brain function and activities.

**1. Introduction** 

main parts as follows:

**2. Properties of xenon** 

biological application in MRI.

*Wuhan Center for Magnetic Resonance,* 

*Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan,* 

Strogatz, S.H. Exploring complex networks. Nature, 2001; 410: 268-76.

