Assessment of Granger Causality by Nonlinear Model Identification: Application to Short-term Cardiovascular Variability

A method for assessing Granger causal relationships in bivariate time series, based on nonlinear autoregressive (NAR) and nonlinear autoregressive exogenous (NARX) models is presented. The method evaluates bilateral interactions between two time series by quantifying the predictability improvement (PI) of the output time series when the dynamics associated with the input time series are included, i.e., moving from NAR to NARX prediction. The NARX model identification was performed by the optimal parameter search (OPS) algorithm, and its results were compared to the least-squares method to determine the most appropriate method to be used for experimental data. The statistical significance of the PI was assessed using a surrogate data technique. The proposed method was tested with simulation examples involving short realizations of linear stochastic processes and nonlinear deterministic signals in which either unidirectional or bidirectional coupling and varying strengths of interactions were imposed. It was found that the OPS-based NARX model was accurate and sensitive in detecting imposed Granger causality conditions. In addition, the OPS-based NARX model was more accurate than the least squares method. Application to the systolic blood pressure and heart rate variability signals demonstrated the feasibility of the method. In particular, we found a bilateral causal relationship between the two signals as evidenced by the significant reduction in the PI values with the NARX model prediction compared to the NAR model prediction, which was also confirmed by the surrogate data analysis. Furthermore, we found significant reduction in the complexity of the dynamics of the two causal pathways of the two signals as the body position was changed from the supine to upright. The proposed is a general method, thus, it can be applied to a wide variety of physiological signals to better understand causality and coupling that may be different between normal and diseased conditions.     

Postural control strategy during standing is altered in patients with multiple sclerosis

Disturbances in balance are one of the first reported symptoms of Multiple Sclerosis (MS), yet limited research has been performed to classify the postural control deficits in this population. This study investigated the variability present in the sway patterns during quiet standing in patients with MS (PwMS) and healthy controls. Subjects were assessed (eyes open, closed) standing on a force platform. Variability of the sway patterns was quantified using a measure of amount of variability (root mean square; RMS) and two measures of temporal structure of variability (Lyapunov Exponent – LyE; Approximate Entropy – ApEn). RMS results revealed significantly higher amount of variability in the sway patterns of PwMS. PwMS also exhibit increased regularity (decreased ApEn) and decreased divergence (decreased LyE) during standing compared to healthy controls. Removing vision resulted in significantly decreased divergence (decreased LyE) in the MS subject group. These changes in the temporal structure correspond well with the theoretical model of the optimal movement variability hypothesis and the results support using variability measures to understand the mechanisms that underline postural control in PwMS and possibly other neurodegenerative disease pathologies.     

Selection of effective features for ECG beat recognition based on nonlinear correlations

Objective

The objective of this study is to develop feature selectors based on nonlinear correlations in order to select the most effective and least redundant features from an ECG beat classification system based on higher order statistics of subband components and a feed-forward back-propagation neural network, denoted as HOS-DWT-FFBNN.

Methods and materials

Three correlation-based filters (NCBFs) are proposed. Two of them, NCBF1 and NCBF2, apply feature-feature correlation to remove redundant features prior to the feature selection process based on feature-class correlation. The other, SUFCO, skips the redundancy reduction process and selects features based only on feature-class correlation. The performance of these filters is compared to another commonly used nonlinear feature selection method, Relief-F. The discriminality and redundancy of the retained features are evaluated quantitatively. The performance of the most effective NCBF is compared with that of the linear correlation-based filter (LCBF) and other representative heartbeat classifiers in the literature.

Results

The results demonstrate that the two NCBFs based on both feature-feature and feature-class correlation methods, i.e. NCBF1 and NCBF2, outperform the other two methods, i.e. SUFCO and Relief-F. An accuracy of as high as 96.34% can be attained with as few as eight features. When tested with statistical methods, the retained features selected by the NCBF1/NCBF2 approach are demonstrated to be more discriminative and less redundant when compared with those features selected by other methods. When compared with LCBF and other heartbeat classifiers in the literature, the proposed NCBF1/NCBF2 approach in conjunction with the HOS-DWT-FFBNN structure outperform them with improved performance that allows discrimination of more beat types and fewer feature dimensions.

Conclusion

This study demonstrates the effectiveness and superiority of the proposed approach for ECG beat recognition.     

Using a neural network for mining interpretable relationships of West Nile risk factors

The West Nile Virus (WNV) is an infectious disease spreading rapidly throughout the United States, causing illness among thousands of birds, animals, and humans. Yet, we only have a rudimentary understanding of how the mosquito-borne virus operates in complex avian-human environmental systems. The four broad categories of risk factors underlying WNV incidences are: environmental (temperature, precipitation, wetlands), socioeconomic (housing age), built-environment (catch basins, ditches), and existing mosquito abatement policies. This research first built a model incorporating the non-linear relationship between WNV incidences and hypothesized risk factors and second, identified important factor(s) whose management would result in effective disease prevention and containment. The research was conducted in the Metropolitan area of Minnesota, which had experienced significant WNV outbreaks from 2002. Computational neural network (CNN) modeling was used to understand the occurrence of WNV infected dead birds because of their ability to capture complex relationships with higher accuracy than linear models. Further a detailed interpretation technique, based on weights and biases of the network, provided a means for extracting relationships between risk factors and disease occurrence. Five risk factors: proximity to bogs, lakes, temperature, housing age, and developed medium density land cover class, were selected by the model. The detailed interpretation indicated that temperature, age of houses, and developed medium density land cover were positively related, and distance to bogs and lakes were negatively related to the incidence of WNV. This paper provides both applied and methodological contributions to the field of health geography. The relationships between the risk factors and disease occurrence could contribute to vector control strategies such as targeted insecticide spraying near bogs and lakes, mosquito control treatments for older houses, and extensive mapping, inspection, and treatments of catch basins. The proposed interpretation technique expanded the role of CNN models in health sciences as both predictive and explanatory tools.     

群体药代动力学参数估计的SAEM算法

目的 建立在群体药代动力学参数估计问题中的SAEM算法.方法 本文基于房室模型的非线性混合效应模型,根据SAEM算法讨论群体药代动力学模型的参数估计问题,给出算法过程,并应用于计算机模拟C-肽释放实例分析.结果 计算机模拟证实了该方法的有效性,通过研究C-肽释放实例分析也表明SAEM算法估计群体药代动力学参数误差较小.结论利用SAEM算法估计群体药代动力学参数是一个比较好的方法.     

Linear and nonlinear effects in the interactions of motor units and muscle spindle afferents

Summary Successive motor unit (MU) twitches often do not sum linearly. Also, muscle spindle (MS) afferents may react nonlinearly to MU contractions occurring at short intervals. Little data is presently available on the interactions between two (or more) MUs regarding their effects on tension output and MS responses. We have studied these effects in cat Mm. gastrocnemius medialis (MG), soleus and semitendinosus. In adult anaesthetized cats, MUs of the muscle under study were electrically stimulated via their ventral root axons with random sequences of brief pulses having mean rates between 6 and 12 pulses per second. Isometric tension fluctuations were recorded from the muscle under study, and discharge patterns of MS afferents (Ia and group II) were recorded from dorsal root filaments. A crosscorrelation analysis was performed to display linear and nonlinear effects evoked by selected time constellations of MU activations. 1) 18 (67%) of 27 MG MUs showed marked potentiation of the second of two twitches in response to pairs of stimuli separated by 5 to about 25 ms. The remainder of these and 16 of the soleus MUs did not exhibit conspicuous nonlinearities. — 2) MS responses to such pairs of MU activations usually showed a prolonged spindle pause. — 3) About 28% of 36pairs of MG MUs produced twitch tension less than expected for linear summation if activated nearly simultaneously. — 4) If two MUs both produced a spindle pause and possibly a relaxation discharge in an MS afferent, the near-synchronous activation of the units produced respective discharge variations that were less than expected for linear summation. If one MU produced an early discharge, contraction of another MU would often prevent it. — These results are discussed in regard to mechanisms of tremor suppression.     

刺激作用下大规模神经元群的随机非线性演化模型及动态神经编码

在前期研究工作的基础上，我们考虑外刺激作用下神经振子群对信息的处理及神经编码的动态演化。通过对模型的数值分析，得到了在三维空间用于描述神经元群内神经元放电过程时的数密度随时间演化的图像，即神经编码的动态演化。数值分析的结果表明该模型能够用来描述大量相互作用神经元在刺激下神经编码的演化过程，研究证明只有在适当的刺激强度下神经元之间的耦合强度与耦合结构才能发生改变，从而体现了神经元的可塑性变化。     

Nonparametric Block-Structured Modeling of Lung Tissue Strip Mechanics

Very large amplitude pseudorandom uniaxial perturbations containing frequencies between 0.125 and 12.5 Hz were applied to five dog lung tissue strips. Three different nonlinear block-structured models in nonparametric form were fit to the data. These models consisted of (1) a static nonlinear block followed by a dynamic linear block (Hammerstein model); (2) the same blocks in reverse order (Wiener model); and (3) the blocks in parallel (parallel model). Both the Hammerstein and Wiener models performed well for a given input perturbation, each accounting for greater than 99% of the measured stress signal variance. However, the Wiener and parallel model parameters showed some dependence on the strain amplitude and the mean stress. In contrast, a single Hammerstein model accounted for the data at all strain amplitudes and operating stresses. A Hammerstein model featuring a fifth-order polynomial static nonlinearity and a linear impulse response function of 1 s duration accounted for the most output variance (99.84% ± 0.13%, mean ± standard deviations for perturbations of 50% strain at 1.5 kPa stress). The static nonlinear behavior of the Hammerstein model also matched the quasistatic stress–strain behavior obtained at the same strain amplitude and operating stress. These results show that the static nonlinear behavior of the dog lung tissue strip is separable from its linear dynamic behavior. © 1998 Biomedical Engineering Society. PAC98: 8745Bp, 8710+e