Functional magnetic resonance imaging (fMRI) has emerged as the method of choice to non-invasively investigate brain function in humans. Though brain is known to act as a nonlinear system, here has not been much effort to explore the applicability of nonlinear analysis techniques to fMRI data. Also, recent trends have suggested that functional localization as a model of brain function is incomplete and efforts are being made to develop models based on networks of regions to understand brain function. Therefore this thesis attempts to introduce the twin concepts of nonlinear dynamics and network analysis into a broad spectrum of fMRI data analysis techniques. First, we characterized the nonlinear univariate dynamics of fMRI noise using the concept of embedding to explain the origin of tissue-specific differences of baseline activity in the brain. The embedding concept was extended to the multivariate case to study nonlinear functional connectivity in the distributed motor network during resting state and continuous motor task. The results showed that the nonlinear method may be more sensitive to the desired gray matter signal. Subsequently, the scope of connectivity was extended to include directional interactions using Granger causality. An integrated approach was developed to alleviate the confounding effect of the spatial variability of the hemodynamic response and graph theory was employed to characterize the network topology. This methodology proved effective in characterizing the dynamics of cortical networks during motor fatigue. The nonlinear extension of Granger causality showed that it was more robust in the presence of confounds such as baseline drifts. Finally, we utilized the integration of the spatial correlation function to study connectivity in local brain networks. We showed that our method is robust and can reveal interesting information including the default mode network during resting state. Application of this technique to anesthesia data showed dose dependent suppression of local connectivity in the default mode network, particularly in the frontal areas. Given the body of evidence emerging from our studies, nonlinear and network characterization of fMRI data seems to provide novel insights into brain function.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 135-144).

Made available in DSpace on 2015-12-10T14:23:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-24. Added 1 bitstream(s) on 2015-12-10T14:29:45Z : No. of bitstreams: 1 000851910.pdf: 2512713 bytes, checksum: 213411a21fdec9803efc190d0200efae (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Introdução. A demanda espontânea é considerada um problema na gestão dos serviços de atenção primária à saúde e na garantia do acesso oportuno. Adicionalmente, o Brasil passa por processo de transição demográfica e epidemiológica que modifica o uso dos serviços. Assim, a carga de morbimortalidade é deslocada dos grupos mais jovens para os mais idosos e a predominância da mortalidade dá lugar à morbidade. Desta maneira, esse estudo propõe: 1. Classificar e quantificar o padrão de comportamento da ocorrência das morbidades diagnosticadas nos atendimentos não agendados de idosos em uma Unidade de Saúde da Família; 2. Mostrar a adequação da análise não linear em fenômeno social humano. Método. Estudo de abordagem quantitativa, observacional, ecológico de tendência temporal. Utilizouse a Dinâmica Simbólica e a Quantificação da Recorrência para análise não linear das séries históricas (categórica e temporais) construídas. As morbidades identificadas no atendimento não agendado de idosos em uma unidade de saúde da família do interior paulista, no período de maio/2012 a maio/2014, foram convertidas em séries históricas. Resultados. A morbidade musculoesquelética apresenta uma tendência de comportamento aleatório, porém é a mais prevalente. A morbidade respiratória apresenta tendência de comportamento periódico, enquanto a morbidade circulatória e as crônicas prevalentes (hipertensão arterial sistêmica e diabetes mellitus) apresentam tendência caótica. A análise não linear demonstrou-se mais adequada que a estatística clássica na avaliação da dinâmica do fenômeno investigado / Introduction. The unscheduled encounters represent a significant problem for primary care clinics management and to provide timely access. Additionally, Brazil has undergone a demographic and epidemiological transition process that modifies the use of health services. Thus, the burden of morbidity and mortality is shifted from younger to older groups and the prevalence of morbidity replaces mortality. We propose: 1. To classify the behavior pattern of morbidities diagnosed in the unplanned appointments resulting from the elderly in a service provider; 2. To show the adequacy of nonlinear analysis in human social phenomenon. Method. It is a quantitative research, observational, ecological design to temporal trend. We used the Symbolic Dynamic and Recurrence quantification analysis to analyze the time-series. The morbidities diagnosed in the unplanned appointments from elderly were transformed into time series. The data was collect in a Primary Care Unit locate in the country of São Paulo State, between May/2012 to May/2014. Results. Musculoskeletal discords has a tendency to random behavior, however, it is the most prevalent. The circulatory morbidity and prevalent chronic (Hypertension and Diabetes Mellitus) present chaotic trend and the linear respiratory diseases were linear. The nonlinear analysis was more appropriate than the classic statistic in assessing the dynamic of investigated phenomenon

Orientador: Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T23:11:17Z (GMT). No. of bitstreams: 1 Monteiro_Evandro_D.pdf: 681089 bytes, checksum: 5ec4729a2d7b386329193adf424f6b42 (MD5) Previous issue date: 2011 / Resumo: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: The complete abstract is available with the full electronic digital thesis or dissertations / Doutorado / Matematica / Doutor em Matemática

Indiana University-Purdue University Indianapolis (IUPUI) / Physical and biological phenomena that involve oscillations on multiple time scales attract attention of mathematicians because resulting equations include a small parameter that allows for decomposing a three- or higher-dimensional dynamical system into fast/slow subsystems of lower dimensionality and analyzing them independently using geometric singular perturbation theory and other techniques. However, in most life sciences applications observed dynamics is extremely complex, no small parameter exists and this approach fails. Nevertheless, it is still desirable to gain insight into behavior of these mathematical models using the only viable alternative – ad hoc computational analysis. Current dissertation is devoted to this latter approach. Neural networks in the region of the brain called basal ganglia (BG) are capable of producing rich activity patterns. For example, burst firing, i.e. a train of action potentials followed by a period of quiescence in neurons of the subthalamic nucleus (STN) in BG was shown to be related to involuntary shaking of limbs in Parkinson’s disease called tremor. The origin of tremor remains unknown; however, a few hypotheses of tremor-generation were proposed recently. The first project of this dissertation examines the BG-thalamo-cortical loop hypothesis for tremor generation by building physiologically-relevant mathematical model of tremor-related circuits with negative delayed feedback. The dynamics of the model is explored under variation of connection strength and delay parameters in the feedback loop using computational methods and data analysis techniques. The model is shown to qualitatively reproduce the transition from irregular physiological activity to pathological synchronous dynamics with varying parameters that are affected in Parkinson’s disease. Thus, the proposed model provides an explanation for the basal ganglia-thalamo-cortical loop mechanism of tremor generation. Besides tremor-related bursting activity BG structures in Parkinson’s disease also show increased synchronized activity in the beta-band (10-30Hz) that ultimately causes other parkinsonian symptoms like slowness of movement, rigidity etc. Suppression of excessively synchronous beta-band oscillatory activity is believed to suppress hypokinetic motor symptoms in Parkinson’s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronized dynamics used to study the delayed feedback stimulation. The second project of this dissertation explores the action of delayed feedback stimulation on partially synchronous oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces the fine temporal structure of the synchronous dynamics observed experimentally. Modeling results suggest that delayed feedback DBS in Parkinson’s disease may boost rather than suppresses synchronization and is therefore unlikely to be clinically successful. Single neuron dynamics may also have important physiological meaning. For instance, bistability – coexistence of two stable solutions observed experimentally in many neurons is thought to be involved in some short-term memory tasks. Bistability that occurs at the depolarization block, i.e. a silent depolarized state a neuron enters with excessive excitatory input was proposed to play a role in improving robustness of oscillations in pacemaker-type neurons. The third project of this dissertation studies what parameters control bistability at the depolarization block in the three-dimensional conductance-based neuronal model by comparing the reduced dopaminergic neuron model to the Hodgkin-Huxley model of the squid giant axon. Bifurcation analysis and parameter variations revealed that bistability is mainly characterized by the inactivation of the Na+ current, while the activation characteristics of the Na+ and the delayed rectifier K+ currents do not account for the difference in bistability in the two models.

Abstract The dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type. A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function. A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point.