Fractal Dimension Analysis of the Oscillated Blood Flow with a Vibrating Flow Pump

Abstract: To analyze the hemodynamic parameters during circulation with oscillated blood flow, nonlinear mathematical analyzing techniques, including fractal theory, were utilized. Vibrating flow pumps (VFP) were implanted as a left heart bypass, and the ascending aorta was clamped to constitute the total left heart circulation with oscillated blood flow in acute animal experiments using 7 adult goats. Using nonlinear mathematical analyzing techniques, reconstructed attractors of the arterial blood pressure waveform in the phase space during natural circulation and oscillated circulation were analyzed.
Using the Grassberger-Procaccia correlation dimension analyzing technique, fractal dimension analysis of the reconstructed attractor was performed. During VFP bypass, lower fractal dimensions of the reconstructed attractor were shown compared with those during natural heart circulation. The results suggest that lower dimensional chaotic dynamics contributed to the circulation with oscillated blood flow.     

A chaos-based model for low complexity predictive coding scheme for compression and transmission of electroencephalogram data

A method for low complexity, low bit rate transmission of EEG (electroencephalogram) data, based on chaotic principles, is presented. The EEG data is assumed to be generated by a non-linear dynamical system of E dimensions. The E dynamical variables are reconstructed from the one-dimensional time series by the process of time-delay embedding. A model of the form X[n+1]=F(X[n], X[n−1],...X[n−p]) is fitted for the data in the E-dimensional space and this model is used as predictor in the predictive coding scheme for transmission. This model is able to give a reduction of nearly 50% of the dynamic range of the error signal to be transmitted, with a reduced complexity, when compared to the conventionally used linear prediction method. This implies that a reduced bit rate of transmission with a reduced complexity can be obtained. The effects of variation of model parameters on the complexity and bit rate are discussed.     

Linear and non-linear analysis of the surface electrocardiogram during human ventricular fibrillation shows evidence of order in the underlying mechanism

Ventricular fibrillation (VF) is a poorly understood yet potentially lethal cardiac arrhythmia. The electrocardiogram (ECG) time series of VF is investigated by comparison of the linear and non-linear features of VF time series and surrogates in which internal correlations have been destroyed. From 40 ECG time series of human VF and 40 surrogate time series, three quantities are evaluated: the percentage of the linear time-frequency distribution (TFD) exceeding a threshold, the non-linear coarse-grained correlation dimension (Dcg), and the percentage of diagonal lines in the non-linear recurrence plot longer than 10 elements (D10). It is found that the mean (SD) percent threshold TFD and Dcg are higher for the surrogates (6.7% (1.3) and 5.3 (0.6)) than the VF time series (5.6% (0.7) and 3.8 (0.9)), whereas the mean D10 is higher for the VF time series (49% (13)) than the surrogates (32% (7)). All of these differences are significant (p < 0.0001) and indicate greater order in the VF time series than in the surrogates. It is therefore shown that both linear and non-linear signal analysis demonstrate order in the ECG time series of VF.     

Microemboli detection using ultrasound backscatter

Microemboli detection and characterisation have recently received great attention due to its clinical importance in the management of cerebrovascular disease. The new method presented in this paper is directly based on the idea that the ultrasound (US) backscattered signal from flowing blood is chaotic (El-Brawany and Nassiri 2002). The detection technique involves building a nonlinear model of the deterministic characteristics of the chaotic backscatter signal from blood, and the use of this model to look at the prediction error as a primary decision-making criterion for the microemboli detector. A complementary feature to the prediction error, namely, the degree of coherence between the US excitation pulse and the prediction error signal is used to enhance the detection process. The detector has been built using a feed-forward neural network with error back-propagation. The detection technique is tested successfully using a vascular flow phantom with solid spheres and bubbles of known sizes introduced in the flow circuit to mimic solid and gaseous emboli. Receiver operating characteristic (ROC) curve is used to assess the performance of the detection process. The total classification rate ranges from 88% to 96%.     

孕大鼠和胎鼠心脏系统混沌特征分析

应用计算机化大鼠心电信号采集和处理系统,引导妊娠第21dSD大鼠和胚胎宫内心电,记录母胎鼠心动周期信号混沌图形参数和数值参数,探讨正常妊娠大鼠母胎心脏系统混沌特征,分析母胎鼠自主神经系统发育的差异性。结果显示,(1)正常胎鼠与孕鼠比较,频率和电压较低,差异均有显著性(P<0.01);(2)正常胎鼠和孕鼠心动周期信号功率谱具有类似于人的心动周期信号功率谱三峰特征;正常胎鼠和孕鼠比较,第二峰、第三峰明显较低;(3)正常胎鼠与孕鼠比较,相对分散度、李雅普诺夫指数和分维数均显著较低,差异均有显著性(P<0.01)。本研究表明,正常胎鼠心动周期信号变化的复杂性低于孕鼠,胎鼠心脏混沌程度低于孕鼠,胎鼠自主神经系统发育尚不成熟。     

混沌理论在边缘性人格障碍患者认知心理治疗中的应用

心理结构符合混沌运动特点,本研究将混沌理论的多项特点应用于边缘性人格障碍患者的认知心理治疗中,经过关注情绪、建立非线性思维、通过非线性思维调控情绪、处理空虚感及关注人格未来发展等治疗步骤的实施,达到缓解边缘性人格障碍患者的临床症状、促使人格朝着健康方向发展的目的 。     

Longitudinal associations among family environment,neural cognitive control,and social competence among adolescents

During adolescence, prefrontal cortex regions, important in cognitive control, undergo maturation to adapt to changing environmental demands. Ways through which social-ecological factors contribute to adolescent neural cognitive control have not been thoroughly examined. We hypothesize that household chaos is a context that may modulate the associations among parental control, adolescent neural cognitive control, and developmental changes in social competence. The sample involved 167 adolescents (ages 13–14 at Time 1, 53% male). Parental control and household chaos were measured using adolescents’ questionnaire data, and cognitive control was assessed via behavioral performance and brain imaging at Time 1. Adolescent social competence was reported by adolescents at Time 1 and at Time 2 (one year later). Structural equation modeling analyses indicated that higher parental control predicted better neural cognitive control only among adolescents living in low-chaos households. The association between poor neural cognitive control at Time 1 and social competence at Time 2 (after controlling for social competence at Time 1) was significant only among adolescents living in high-chaos households. Household chaos may undermine the positive association of parental control with adolescent neural cognitive control and exacerbate the detrimental association of poor neural cognitive control with disrupted social competence development.     

The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks

In a previous paper we introduced the notion of frustrated chaos occurring in Hopfield networks [Neural Networks 11 (1998) 1017]. It is a dynamical regime which appears in a network when the global structure is such that local connectivity patterns responsible for stable oscillatory behaviors are intertwined, leading to mutually competing attractors and unpredictable itinerancy among brief appearance of these attractors. Frustration destabilizes the network and provokes an erratic ‘wavering’ among the orbits that characterize the same network when it is connected in a non-frustrated way. In this paper, through a detailed study of the bifurcation diagram given for some connection weights, we will show that this frustrated chaos belongs to the family of intermittency type of chaos, first described by Berge et al. [Order within chaos (1984)] and Pomeau and Manneville [Commun. Math. Phys. 74 (1980) 189]. Indeed, the transition to chaos is a critical one, and all along the bifurcation diagram, in any chaotic window, the duration of the intermittent cycles, between two chaotic bursts, grows as an invert ratio of the connection weight. Specific to this regime are the intermittent cycles easily identifiable as the non-frustrated regimes obtained by altering the values of these same connection weights. We will more specifically show that anywhere in the bifurcation diagram, a chaotic window always lies between two oscillatory regimes, and that the resulting chaos is a merging of, among others, the cycles at both ends. The strength (i.e. the duration of its oscillatory phase before the chaotic burst) of the first cycle decreases while the regime tends to stabilize into the second cycle (with the strength of this second cycle increasing) that will finally get the control. Since in our study, the bifurcation diagram concerns the same connection weights responsible for the learning mechanism of the Hopfield network, we will discuss the relations existing between bifurcation, learning and control of chaos. We will show that, in some cases, the addition of a slower Hebbian learning mechanism onto the Hopfield networks makes the resulting global dynamics to drive the network into a stable oscillatory regime, through a succession of intermittent and quasiperiodic regimes. Finally, we will present a series of possible logical steps to manually construct a frustrated network.