Mechanical Control of Sensory Hair-Bundle Function

Hair bundles detect sound in the auditory system, head position and rotation in the vestibular system, and fluid flow in the lateral-­‐‑line system. To do so, bundles respond to periodic, static, and hydrodynamic forces contingent upon the receptor organs in which they are situated. As the mechanosensory function of a hair bundle varies, so too do the mechanical properties of the bundle and its microenvironment. Hair bundles range in height from 1 μμm to 100 μμm and in stiffness from 100 μμN·∙m-­‐‑1 to 10,000 μμN·∙m-­‐‑1. They are composed of actin-­‐‑filled, hypertrophic microvilli—stereocilia—that number from fewer than 20 through more than 300 per bundle. In addition, bundles may or may not possess one true cilium, the kinocilium. Hair bundles differ in shape across organs and organisms: they may be isodiametric, fan-­‐‑shaped, or V-­‐‑shaped. Depending on the organ in which they occur, bundles may be free-­‐‑standing or they may be coupled to a tectorial membrane, otolithic membrane, cupula, or sallet. Because all hair bundles are comprised of similar molecular components, their distinct mechanosensory functions may instead be regulated by their mechanical loads. Dynamical-­‐‑systems analysis provides mathematical predictions of hair-­‐‑bundle behavior. One such model captures the effects of mechanical loading on bundle function in a state diagram. A mechanical-­‐‑load clamp permits exploration of this state diagram by robustly controlling the loads—constant force, load stiffness, virtual drag, and virtual mass—imposed on a hair bundle. Upon changes in these mechanical parameters, the bundle’s response characteristics alter. Subjected to particular control parameters, a bundle may oscillate spontaneously or remain quiescent. It may respond nonlinearly to periodic stimuli with high sensitivity, sharp frequency tuning, and easy entrainment; or it may respond linearly with low sensitivity, broad tuning, and reluctant entrainment. The bundle’s response to a force pulse may resemble that of an edge-­‐‑detection system or a low-­‐‑pass filter. Finally, a bundle from an amphibian vestibular organ can operate in a manner qualitatively similar to that from a mammalian auditory organ, implying an essential similarity between hair bundles. The bifurcation near which a bundle’s operating point resides controls its function: the state diagram provides a functional map of mechanosensory modalities. Auditory function is best tuned near a supercritical Hopf bifurcation, whereas vestibular function is captured by a subcritical Hopf bifurcation and a cusp bifurcation. Within the proposed region vestibular responsiveness, a hair bundle exhibits mechanical excitability analogous to the electrical excitability of neurons. This behavior implies for the first time a direct relationship between the mechanical behaviors of sensory organelles and the electrical behaviors of afferent neurons. Man-­‐‑made detectors function in limited capacities, each designed for a unique purpose. A single hair bundle, on the other hand, evolved to serve multiple purposes with the requirement of only two functional traits: adaptation and nonlinear channel gating. The remarkable conservation of these capabilities thus provides unique insight into the evolution of sensory systems

Critical bistability and large-scale synchrony in human brain dynamics

Neurophysiological dynamics of the brain, overt behaviours, and private experiences of the mind are co-emergent and co-evolving phenomena. An adult human brain contains ~100 billion neurons that are hierarchically organized into intricate networks of functional units comprised of interconnected neurons. It has been hypothesized that neurons within a functional unit communicate with each other or neurons from other units via synchronized activity. At any moment, cascades of synchronized activity from millions of neurons propagate through networks of all sizes, and the levels of synchronization wax and wane. How to understand cognitive functions or diseases from such rich dynamics poses a great challenge. The brain criticality hypothesis proposes that the brain, like many complex systems, optimize its performance by operating near a critical point of phase transition between disorder and order, which suggests complex brain dynamics be effectively studied by combining computational and empirical approaches. Hence, the brain criticality framework requires both classic reductionist and reconstructionist approaches. Reconstructionism in the current context refers to addressing the “Wholeness” of macro-level emergence due to fundamental mechanisms such as synchrony between neurons in the brain. This thesis includes five studies and aims to advance theory, empirical evidence, and methodology in the research of neuronal criticality and large-scale synchrony in the human brain. Study I: The classic criticality theory is based on the hypothesis that the brain operates near a continuous, second order phase transition between order and disorder in resource-conserving systems. This idea, however, cannot explain why the brain, a non-conserving system, often shows bistability, a hallmark of first order, discontinuous phase transition. We used computational modeling and found that bistability may occur exclusively within the critical regime so that the first-order phase transition emerged progressively with increasing local resource demands. We observed that in human resting-state brain activity, moderate α-band (11 Hz) bistability during rest predicts cognitive performance, but excessive resting-state bistability in fast (> 80 Hz) oscillations characterizes epileptogenic zones in patients’ brain. These findings expand the framework of brain criticality and show that near-critical neuronal dynamics involve both first- and second-order phase transitions in a frequency-, neuroanatomy-, and state-dependent manner. Study II: Long-range synchrony between cortical oscillations below ~100 Hz is pervasive in brain networks, whereas oscillations and broad-band activities above ~100 Hz have been considered to be strictly local phenomena. We showed with human intracerebral recordings that high-frequency oscillations (HFOs, 100−400 Hz) may be synchronized between brain regions separated by several centimeters. We discovered subject-specific frequency peaks of HFO synchrony and found the group-level HFO synchrony to exhibit laminar-specific connectivity and robust community structures. Importantly, the HFO synchrony was both transiently enhanced and suppressed in separate sub-bands during tasks. These findings showed that HFO synchrony constitutes a functionally significant form of neuronal spike-timing relationships in brain activity and thus a new mesoscopic indication of neuronal communication per se. Studies III: Signal linear mixing in magneto- (MEG) and electro-encephalography (EEG) artificially introduces linear correlations between sources and confounds the separability of cortical current estimates. This linear mixing effect in turn introduces false positives into synchrony estimates between MEG/EEG sources. Several connectivity metrics have been proposed to supress the linear mixing effects. We show that, although these metrics can remove false positives caused by instantaneous mixing effects, all of them discover false positive ghost interactions (SIs). We also presented major difficulties and technical concerns in mapping brain functional connectivity when using the most popular pairwise correlational metrics. Study IV and V: We developed a novel approach as a solution to the SIs problem. Our approach is to bundle observed raw edges, i.e., true interactions or SIs, into hyperedges by raw edges’ adjacency in signal mixing. We showed that this bundling approach yields hyperedges with optimal separability between true interactions while suffers little loss in the true positive rate. This bundling approach thus significantly decreases the noise in connectivity graphs by minimizing the false-positive to true-positive ratio. Furthermore, we demonstrated the advantage of hyperedge bundling in visualizing connectivity graphs derived from MEG experimental data. Hence, the hyperedges represent well the true cortical interactions that are detectable and dissociable in MEG/EEG sources. Taken together, these studies have advanced theory, empirical evidence, and methodology in the research of neuronal criticality and large-scale synchrony in the human brain. Study I provided modeling and empirical evidence for linking bistable criticality and the classic criticality hypothesis into a unified framework. Study II was the first to reveal HFO phase synchrony in large-scale neocortical networks, which was a fundamental discovery of long-range neuronal interactions on fast time-scale per se. Study III raised awareness of the ghost interaction (SI) problem for a critical view on reliable interpretation of MEG/EEG connectivity, and for the development of novel approaches to address the SI problem. Study IV offered a practical solution to the SI problem and opened a new avenue for mapping reliable MEG/EEG connectivity. Study V described the technical details of the hyperedge bundling approach, shared the source code and specified the simulation parameters used in Study IV.Ihmisaivojen neurofysiologinen dynamiikka, ihmisen käyttäytyminen, sekä yksityiset mielen kokemukset syntyvät ja kehittyvät rinnakkaisina ilmiöinä. Ihmisen aivot koostuvat ~100 miljardista hierarkisesti järjestäytyneestä hermosolusta, jotka toisiinsa kytkeytyneinä muodostavat monimutkaisen verkoston toiminnallisia yksiköitä. Hermosolujen aktiivisuuden synkronoitumisen on esitetty mahdollistavan neuronien välisen kommunikoinnin toiminnallisten yksiköiden sisällä sekä niiden välillä. Hetkenä minä hyvänsä, synkronoidun aktiivisuuden kaskadit etenevät aivojen erikokoisissa verkostoissa jatkuvasti heikentyen ja voimistuen. Kognitiivisten funktioiden ja erilaisten aivosairauksien ymmärtäminen tulkitsemalla aivojen rikasta dynamiikkaa on suuri haaste. Kriittiset aivot -hypoteesi ehdottaa aivojen, kuten monien muidenkin kompleksisten systeemien, optimoivan suorituskykyään operoimalla lähellä kriittistä pistettä järjestyksen ja epäjärjestyksen välissä, puoltaen sitä, että aivojen kompleksisia dynamiikoita voitaisiin tutkia yhdistämällä laskennallisia ja empiirisiä lähestymistapoja. Aivojen kriittisyyden viitekehys edellyttää perinteistä reduktionismia ja rekonstruktionismia. Erityisesti, rekonstruktionismi tähtää kuvaamaan aivojen makrotason “yhteneväisyyden” syntymistä perustavanlaatuisten mekaniikoiden, kuten aivojen toiminnallisten yksiköiden välisen synkronian avulla. Tämä väitöskirja sisältää viisi tutkimusta, jotka edistävät teoriaa, empiirisiä todisteita ja metodologiaa aivojen kriittisyyden ja laajamittaisen synkronian tutkimuksessa. Tutkimus I tarjosi mallinnuksia ja empiirisiä todisteita bistabiilin kriittisyyden ja klassisen kriittisyyden hypoteesien yhdistämiseksi yhdeksi viitekehykseksi. Tutkimus II oli ensimmäinen laatuaan paljastaen korkeataajuisten oskillaatioiden (high-frequency oscillation, HFO) vaihesynkronian laajamittaisissa neokortikaalisissa verkostoissa, mikä oli perustavanlaatuinen löytö pitkän matkan neuronaalisista vuorovaikutuksista nopeilla aikaskaaloilla. Tutkimus III lisäsi tietoisuutta aave-vuorovaikutuksien (spurious interactions, SI) ongelmasta MEG/EEG kytkeytyvyyden luotettavassa tulkinnassa sekä uudenlaisten menetelmien kehityksessä SI-ongelman ratkaisemiseksi. Tutkimus IV tarjosi käytännöllisen “hyperedge bundling” -ratkaisun SI-ongelmaan ja avasi uudenlaisen tien luotettavaan MEG/EEG kytkeytyvyyden kartoittamiseen. Tutkimus V kuvasi teknisiä yksityiskohtia hyperedge bundling -menetelmästä, jakoi menetelmän lähdekoodin ja täsmensi tutkimuksessa IV käytettyjä simulaatioparametreja. Yhdessä nämä tutkimukset ovat edistäneet teoriaa, empiirisiä todisteita ja metodologiaa neuronaalisen kriittisyyden sekä laajamittaisen synkronian hyödyntämisessä ihmisaivojen tutkimuksessa

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin

Nonlinear Modeling of Power Electronics-based Power Systems for Control Design and Harmonic Studies

The massive integration of power electronics devices in the modern electric grid marked a turning point in the concept of stability, power quality and control in power systems. The evolution of the grid toward a converter-dominated network motivates a deep renovation of the classical power system theory developed for machine-dominated networks. The high degree of controllability of power electronics converters, furthermore, paves the way to the investigation of advanced control strategies to enhance the grid stability, resiliency and sustainability. This doctoral dissertation explores four cardinal topics in the field of power electronics-based power systems: dynamic modeling, stability analysis, converters control, and power quality with particular focus on harmonic distortion. In all four research areas, a particular attention is given to the implications of the nonlinearity of the converter models on the power system