RESUMO
Continuous glucose monitoring is increasingly used in the management of diabetes. Subcutaneous glucose profiles are characterised by a strong non-stationarity, which limits the application of correlation-spectral analysis. We derived an index of linear predictability by calculating the autocorrelation function of time series increments and applied detrended fluctuation analysis to assess the non-stationarity of the profiles. Time series from volunteers with both type 1 and type 2 diabetes and from control subjects were analysed. The results suggest that in control subjects, blood glucose variation is relatively uncorrelated, and this variation could be modelled as a random walk with no retention of 'memory' of previous values. In diabetes, variation is both greater and smoother, with retention of inter-dependence between neighbouring values. Essential components for adequate longer term prediction were identified via a decomposition of time series into a slow trend and responses to external stimuli. Implications for diabetes management are discussed.
Assuntos
Glucose/metabolismo , Modelos Biológicos , Monitorização Fisiológica/estatística & dados numéricos , Tela Subcutânea/metabolismo , Adulto , Idoso , Glicemia/análise , Estudos de Casos e Controles , Diabetes Mellitus Tipo 1/sangue , Diabetes Mellitus Tipo 1/metabolismo , Diabetes Mellitus Tipo 2/sangue , Diabetes Mellitus Tipo 2/metabolismo , Feminino , Humanos , Modelos Lineares , Masculino , Pessoa de Meia-Idade , Processos Estocásticos , Adulto JovemRESUMO
We discuss open problems related to the stochastic modeling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short time scales via an analysis of HRV within the framework of a random walk approach. Our experiments show that HRV on timescales of less than a minute takes the form of free diffusion, close to Brownian motion, which can be described as a non-stationary process with stationary increments. Secondly, we consider the inverse problem of modeling the state of the control system so as to reproduce the experimentally observed HRV statistics of. We discuss some simple toy models and identify open problems for the modelling of heart dynamics.
RESUMO
Continuous and pulsed forms of control of a multistable system are compared directly, both theoretically and numerically, taking as an example the switching of a periodically driven class-B laser between its stable and unstable pulsing regimes. It is shown that continuous control is the more energy efficient. This result is illuminated by making use of the close correspondence that exists between the problems of energy-optimal control and the stability of a steady state.
Assuntos
Lasers , Modelos Teóricos , Dinâmica não LinearRESUMO
Noise-induced failures in the stabilization of an unstable orbit in the one-dimensional logistic map are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and analysis of the optimal path and the optimal fluctuational force corresponding to the stabilization failure. The problem of controlling noise-induced large fluctuations is discussed, and methods of control have been developed.
