Learning Common Harmonic Waves on Stiefel Manifold - A New Mathematical Approach for Brain Network Analyses

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, their spatial patterns follow large-scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanisms of neuropathological events as they spread through the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework that provides enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves. This algebra overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic differences are measured by a set of common harmonic waves learned from a population of individual Eigen-systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves, which reside at the center of the Stiefel manifold. To that end, the common harmonic waves constitute a new set of neurobiological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuropathological burden spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns than Euclidean methods

Development and applications of high speed and hyperspectral nonlinear microscopy

Nonlinear microscopy refers to a range of laser scanning microscopy techniques that are based on nonlinear optical processes such as two-photon excited fluorescence and second harmonic generation. Nonlinear microscopy techniques are powerful because they enable the visualization of highly scattering biological samples with subcellular resolution. This capability is especially valuable for in vivo and live tissue imaging since it can provide both structural and functional information about tissues in their native environment. With the use of a range of exogenous dyes and intrinsic contrast, in vivo nonlinear microscopy can be used to characterize and measure dynamic processes of tissues in their normal environment. These advances have been particularly relevant in neuroscience, where truly understanding the function of the brain requires that its neural and vascular networks be observed while undisturbed. Despite these advantages, in vivo nonlinear microscopy still faces several major challenges. First, observing dynamics that occur in large areas over short time scales, such as neuronal signaling and blood flow, is challenging because nonlinear microscopy generally requires scanning to create an image. This limits the study of dynamic behavior to either a single plane or to a small subset of regions within a volume. Second, applications that rely on the use of exogenous dyes can be limited by the need to stain tissues before imaging, the availability of dyes, and specificity that can be achieved. Usually considered a nuisance, endogenous tissue contrast from autofluorescence or structures exhibiting second harmonic generation can produce stunning images for visualizing subcellular morphology. Imaging endogenous contrast can also provide valuable information about the chemical makeup and metabolic state of the tissue. Few methods have been developed to carefully and quantitatively examine endogenous fluorescence in living tissues. In this thesis, these two challenges in nonlinear microscopy are addressed. The development of a novel hyperspectral two-photon microscopy method to acquire spectroscopic data from tissues and increase the information available from endogenous contrast is presented. This system was applied to visualize and identify sources of endogenous contrast in gastrointestinal tissues, providing robust references for the assessment of normal and diseased tissues. Secondly, three methods for high speed volumetric imaging using laser scanning nonlinear microscopy were developed to address the need for improved high-speed imaging in living tissues. A spectrally-encoded high-speed imaging method that can provide simultaneous imaging of multiple regions of the living brain in parallel is presented and used to study spontaneous changes in vascular tone in the brain. This technique is then extended for use with second harmonic generation microscopy, which has the potential to greatly increase the degree of multiplexing. Finally, a complete system design capable of volumetric scan rates >1Hz is shown, offering improved performance and versatility to image brain activity

Neural basis of acquired amusia and its recovery

In acquired amusia, the healthy music processing system in the brain is disrupted due to focal brain damage. This creates an exceptional opportunity to investigate the critical neural architectures of music processing. Yet, the neural basis of acquired amusia has remained largely unexplored. In this multimodal magnetic resonance imaging (MRI) study of stroke patients with a 6-month follow-up, we systematically explored the neural basis of music processing by determining the lesions patterns, structural grey and white matter changes, and brain activation and functional network connectivity changes associated with acquired amusia and its recovery. We found that damage to the right temporal areas, insula, and putamen forms the crucial neural substrate for acquired amusia after stroke. Longitudinally, persistent amusia was associated with further atrophy in the right superior temporal regions, located more anteriorly for rhythm-amusia and more posteriorly for pitchamusia. In addition, persistent amusia was associated with structural damage and later degeneration in multiple right frontotemporal and frontal pathways as well as interhemispheric connections. Interestingly, rhythm-amusia was associated with additional deficits in left frontal connectivity. During listening to instrumental music, acquired amusics exhibited dysfunction of multiple frontal and temporal brain regions included in the large-scale music network. Interestingly, amusics showed less activation deficits during listening to vocal music, as compared to instrumental music, suggesting less defective processing of singing. Recovery from acquired amusia was related to increased activation in the right frontal and parietal areas as well as increased functional connectivity in the right and left frontoparietal networks. Overall, the results provide a comprehensive neuroanatomical and functional picture of acquired amusia and highlight the neural structures crucial for normal music perception.Aivoinfarktin ja -verenvuodon jälkeinen musiikin käsittelyn häiriö ja siitä kuntoutuminen Hankinnaisessa amusiassa aivojen musiikinkäsittelyjärjestelmän normaali toiminta häiriintyy aivojen paikallisen vaurioitumisen takia. Tämä luo poikkeuksellisen mahdollisuuden tutkia musiikin käsittelylle tärkeitä aivorakenteita. Hankinnaisen amusian aivoperusta on kuitenkin suurelta osin vielä täysin tuntematonta. Tässä aivoverenkiertohäiriön (AVH) sairastaneiden potilaiden 6 kuukauden seurantatutkimuksessa selvitimme magneettikuvantamisen avulla musiikin käsittelyn aivoperustaa tutkimalla, minkä aivoalueiden vauriot, mitkä harmaan ja valkean aineen rakenteelliset muutokset ja millaiset aivojen toiminnalliset muutokset liittyvät hankinnaiseen amusiaan ja siitä kuntoutumiseen. Tuloksemme osoittivat, että AVH:n jälkeinen amusia syntyy oikean ohimolohkon yläosan, aivosaaren ja tyvitumakealueen vauriosta. Pysyvään amusiaan liittyi lisäksi harmaan aineen atrofiaa oikeassa ohimolohkossa. Rytmin havaitsemiseen liittyvässä amusiassa atrofia painottui ohimolohkon etuosaan ja äänenkorkeuden havaitsemiseen liittyvässä amusiassa ohimolohkon takaosaan. Lisäksi, pysyvään amusiaan liittyi laaja oikean aivopuoliskon ja aivopuoliskon välisten radastojen vaurio ja atrofia. Amusia aiheutti myös laajamittaisia aivojen toimintahäiriöitä musiikin kuuntelun aikana. Mielenkiintoista on, että toimintahäiriöt olivat suurempia kuunneltaessa instrumentaalimusiikkia kuin laulettua musiikkia. Amusiasta kuntoutuminen oli yhteydessä toiminnallisten yhteyksien vahvistumiseen oikean sekä vasemman aivopuoliskon otsa- ja päälakilohkojen välillä. Tulokset antavat kattavan kuvan amusiaan johtavista aivovaurioista sekä siihen liittyvistä rakenteellisista ja toiminnallisista muutoksista. Lisäksi tulokset valottavat musiikin käsittelylle keskeisen tärkeitä aivorakenteita

FTIR difference and resonance raman spectroscopy of rhodopsins with applications to optogenetics

Thesis (Ph. D.)--Boston UniversityThe major aim of this thesis is to investigate the molecular basis for the function of several types of rhodopsins with special emphasis on their application to the new field of optogenetics. Rhodopsins are transmembrane biophotonic proteins with 7 a-helices and a retinal chromophore. Studies included Archaerhodopsin 3 (AR3), a light driven proton pump similar to the extensively studied bacteriorhodopsin (BR); channelrhodopsins 1 and 2, light-activated ion channels; sensory rhodopsin II (SRII), a light-sensing protein that modulates phototaxis used in archaebacteria; and squid rhodopsins (sRho), the major photopigment in squid vision and a model for human melanopsin, which controls circadian rythms. The primary techniques used in these studies were FTIR difference spectroscopy and resonance Raman spectroscopy. These techniques, in combination with site directed mutagenesis and other biochemical methodologies produced new knowledge regarding the structural changes of the retinal chromophore, the location and function of internal water molecules as well as specific amino acids and peptide backbone. Specialized techniques were developed that allowed rhodopsins to be studied in intact membrane environments and in some cases in vivo measurements were made on rhodopsin heterologously expressed in E. coli thus allowing the effects of interacting proteins and membrane potential to be investigated. Evidence was found that the local environment of one or more internal water molecules in SRII is altered by interaction with its cognate transducer, Htrii, and is also affected by the local lipid environment. In the case of AR3, many of the broad IR continuum absorption changes below 3000 cm-1, assigned to networks of water molecules involved in proton transport through cytoplasmic and extracellular portions in BR, were found to be very similar to BR. Bands assigned to water molecules near the Schiff base postulated to be involved in proton transport were, however, shifted or absent. Structural changes of internal water molecules and possible bands associated with the interaction with ,8-arrestins were also detected in photoactivated squid rhodopsin when transformed to the acid Meta intermediate. Near-IR confocal resonance Raman measurements were performed both on AR3 reconstituted into E. coli polar lipids and in vivo in E. coli expressing AR3 in the absence and presence of a negative transmembrane potential. On the basis of these measurements, a model is proposed which provides a possible explanation for the observed fluorescence dependence of AR3 and other microbial rhodopsins on transmembrane potential