Dissociating tinnitus patients from healthy controls using resting-state cyclicity analysis and clustering.

Chronic tinnitus is a common and sometimes debilitating condition that lacks scientific consensus on physiological models of how the condition arises as well as any known cure. In this study, we applied a novel cyclicity analysis, which studies patterns of leader-follower relationships between two signals, to resting-state functional magnetic resonance imaging (rs-fMRI) data of brain regions acquired from subjects with and without tinnitus. Using the output from the cyclicity analysis, we were able to differentiate between these two groups with 58-67% accuracy by using a partial least squares discriminant analysis. Stability testing yielded a 70% classification accuracy for identifying individual subjects' data across sessions 1 week apart. Additional analysis revealed that the pairs of brain regions that contributed most to the dissociation between tinnitus and controls were those connected to the amygdala. In the controls, there were consistent temporal patterns across frontal, parietal, and limbic regions and amygdalar activity, whereas in tinnitus subjects, this pattern was much more variable. Our findings demonstrate a proof-of-principle for the use of cyclicity analysis of rs-fMRI data to better understand functional brain connectivity and to use it as a tool for the differentiation of patients and controls who may differ on specific traits.

Comparing Cyclicity Analysis With Pre-established Functional Connectivity Methods to Identify Individuals and Subject Groups Using Resting State fMRI.

The resting state fMRI time series appears to have cyclic patterns, which indicates presence of cyclic interactions between different brain regions. Such interactions are not easily captured by pre-established resting state functional connectivity methods including zero-lag correlation, lagged correlation, and dynamic time warping distance. These methods formulate the functional interaction between different brain regions as similar temporal patterns within the time series. To use information related to temporal ordering, cyclicity analysis has been introduced to capture pairwise interactions between multiple time series. In this study, we compared the efficacy of cyclicity analysis with aforementioned similarity-based techniques in representing individual-level and group-level information. Additionally, we investigated how filtering and global signal regression interacted with these techniques. We obtained and analyzed fMRI data from patients with tinnitus and neurotypical controls at two different days, a week apart. For both patient and control groups, we found that the features generated by cyclicity and correlation (zero-lag and lagged) analyses were more reliable than the features generated by dynamic time warping distance in identifying individuals across visits. The reliability of all features, except those generated by dynamic time warping, improved as the global signal was regressed. Nevertheless, removing fluctuations >0.1 Hz deteriorated the reliability of all features. These observations underscore the importance of choosing appropriate preprocessing steps while evaluating different analytical methods in describing resting state functional interactivity. Further, using different machine learning techniques including support vector machines, discriminant analyses, and convolutional neural networks, our results revealed that the manifestation of the group-level information within all features was not sufficient enough to dissociate tinnitus patients from controls with high sensitivity and specificity. This necessitates further investigation regarding the representation of group-level information within different features to better identify tinnitus-related alternation in the functional organization of the brain. Our study adds to the growing body of research on developing diagnostic tools to identify neurological disorders, such as tinnitus, using resting state fMRI data.

Euler integration over definable functions.

We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks.

Whispering gallery modes inside asymmetric resonant cavities.

Two dimensional resonators with a smooth strictly convex boundary are known to possess a whispering gallery region supporting modes concentrated near the boundary. A new class of asymmetric resonant cavities is introduced, where a whispering gallery-like region is found deep inside the resonator. The construction of such resonators is a novel application of the geometric control methods. The results of numerical simulations and experiments are presented.