A New Proxy Measurement Algorithm with Application to the Estimation of Vertical Ground Reaction Forces Using Wearable Sensors.

Measurement of the ground reaction forces (GRF) during walking is typically limited to laboratory settings, and only short observations using wearable pressure insoles have been reported so far. In this study, a new proxy measurement method is proposed to estimate the vertical component of the GRF (vGRF) from wearable accelerometer signals. The accelerations are used as the proxy variable. An orthogonal forward regression algorithm (OFR) is employed to identify the dynamic relationships between the proxy variables and the measured vGRF using pressure-sensing insoles. The obtained model, which represents the connection between the proxy variable and the vGRF, is then used to predict the latter. The results have been validated using pressure insoles data collected from nine healthy individuals under two outdoor walking tasks in non-laboratory settings. The results show that the vGRFs can be reconstructed with high accuracy (with an average prediction error of less than 5.0%) using only one wearable sensor mounted at the waist (L5, fifth lumbar vertebra). Proxy measures with different sensor positions are also discussed. Results show that the waist acceleration-based proxy measurement is more stable with less inter-task and inter-subject variability than the proxy measures based on forehead level accelerations. The proposed proxy measure provides a promising low-cost method for monitoring ground reaction forces in real-life settings and introduces a novel generic approach for replacing the direct determination of difficult to measure variables in many applications.

Modified variational Bayes EM estimation of hidden Markov tree model of cell lineages.

MOTIVATION: Human pluripotent stem cell lines persist in culture as a heterogeneous population of SSEA3 positive and SSEA3 negative cells. Tracking individual stem cells in real time can elucidate the kinetics of cells switching between the SSEA3 positive and negative substates. However, identifying a cell's substate at all time points within a cell lineage tree is technically difficult. RESULTS: A variational Bayesian Expectation Maximization (EM) with smoothed probabilities (VBEMS) algorithm for hidden Markov trees (HMT) is proposed for incomplete tree structured data. The full posterior of the HMT parameters is determined and the underflow problems associated with previous algorithms are eliminated. Example results for the prediction of the types of cells in synthetic and real stem cell lineage trees are presented. AVAILABILITY: The Matlab code for the VBEMS algorithm is freely available at http://www.acse.dept.shef.ac.uk/repository/vbems_lineage_tree/VBEMS.ZIP CONTACT: visakan@sheffield.ac.uk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Tremor after long term lithium treatment; is it cortical myoclonus?

INTRODUCTION: Tremor is a common side effect of treatment with lithium. Its characteristics can vary and when less rhythmical, distinction from myoclonus can be difficult. METHODS: We identified 8 patients on long-term treatment with lithium that developed upper limb tremor. All patients were assessed clinically and electrophysiologically, with jerk-locked averaging (JLA) and cross-correlation (CC) analysis, and five of them underwent brain MRI examination including spectroscopy (MRS) of the cerebellum. RESULTS: Seven patients (6 female) had action and postural myoclonus and one a regular postural and kinetic tremor that persisted at rest. Mean age at presentation was 58 years (range 42-77) after lengthy exposure to lithium (range 7-40 years). During routine monitoring all patients had lithium levels within the recommended therapeutic range (0.4-1 mmol/l). There was clinical and/or radiological evidence (on cerebellar MRS) of cerebellar dysfunction in 6 patients. JLA and/or CC suggested a cortical generator of the myoclonus in seven patients. All seven were on antidepressants and three additionally on neuroleptics, four of them had gluten sensitivity and two reported alcohol abuse. CONCLUSIONS: A synergistic effect of different factors appears to be contributing to the development of cortical myoclonus after chronic exposure to lithium. We hypothesise that the cerebellum is involved in the generation of cortical myoclonus in these cases and factors aetiologically linked to cerebellar pathology like gluten sensitivity and alcohol abuse may play a role in the development of myoclonus. Despite the very limited evidence in the literature, lithium induced cortical myoclonus may not be so rare.

Real-Life Measurement of Tri-Axial Walking Ground Reaction Forces Using Optimal Network of Wearable Inertial Measurement Units.

Monitoring natural human gait in real-life environment is essential in many applications including the quantification of disease progression, and monitoring the effects of treatment and alteration of performance biomarkers in professional sports. Nevertheless, reliable and practical techniques and technologies necessary for continuous real-life monitoring of gait is still not available. This paper explores in detail the correlations between the acceleration of different body segments and walking ground reaction forces GRF(t) in three dimensions and proposes three sensory systems, with one, two, and three inertial measurement units (IMUs), to estimate GRF(t) in the vertical (V), medial-lateral (ML), and anterior-posterior (AP) directions. The nonlinear autoregressive moving average model with exogenous inputs (NARMAX) non-linear system identification method was utilized to identify the optimal location for IMUs on the body for each system. A simple linear model was then proposed to estimate GRF(t) based on the correlation of segmental accelerations with each other. It was found that, for the three-IMU system, the proposed model estimated GRF(t) with average peak-to-peak normalized root mean square error (NRMSE) of 7%, 16%, and 18% in V, AP, and ML directions, respectively. With a simple subject-specific training at the beginning, these errors were reduced to 7%, 13%, and 13% in V, AP, and ML directions, respectively. These results were found favorably comparable with the results of the benchmark NARMAX model, with subject-specific training, with 0% (V), 4% (AP), and 1% (ML) NRMSE difference.

The cortical focus in childhood absence epilepsy; evidence from nonlinear analysis of scalp EEG recordings.

OBJECTIVE: To determine the origin and dynamic characteristics of the generalised hyper-synchronous spike and wave (SW) discharges in childhood absence epilepsy (CAE). METHODS: We applied nonlinear methods, the error reduction ratio (ERR) causality test and cross-frequency analysis, with a nonlinear autoregressive exogenous (NARX) model, to electroencephalograms (EEGs) from CAE, selected with stringent electro-clinical criteria (17 cases, 42 absences). We analysed the pre-ictal and ictal strength of association between homologous and heterologous EEG derivations and estimated the direction of synchronisation and corresponding time lags. RESULTS: A frontal/fronto-central onset of the absences is detected in 13 of the 17 cases with the highest ictal strength of association between homologous frontal followed by centro-temporal and fronto-central areas. Delays consistently in excess of 4 ms occur at the very onset between these regions, swiftly followed by the emergence of "isochronous" (0-2 ms) synchronisation but dynamic time lag changes occur during SW discharges. CONCLUSIONS: In absences an initial cortico-cortical spread leads to dynamic lag changes to include periods of isochronous interhemispheric synchronisation, which we hypothesize is mediated by the thalamus. SIGNIFICANCE: Absences from CAE show ictal epileptic network dynamics remarkably similar to those observed in WAG/Rij rats which guided the formulation of the cortical focus theory.

A Pilot Study Investigating a Novel Non-Linear Measure of Eyes Open versus Eyes Closed EEG Synchronization in People with Alzheimer's Disease and Healthy Controls

BACKGROUND: The incidence of Alzheimer disease (AD) is increasing with the ageing population. The development of low cost non-invasive diagnostic aids for AD is a research priority. This pilot study investigated whether an approach based on a novel dynamic quantitative parametric EEG method could detect abnormalities in people with AD. METHODS: 20 patients with probable AD, 20 matched healthy controls (HC) and 4 patients with probable fronto temporal dementia (FTD) were included. All had detailed neuropsychology along with structural, resting state fMRI and EEG. EEG data were analyzed using the Error Reduction Ratio-causality (ERR-causality) test that can capture both linear and nonlinear interactions between different EEG recording areas. The 95% confidence intervals of EEG levels of bi-centroparietal synchronization were estimated for eyes open (EO) and eyes closed (EC) states. RESULTS: In the EC state, AD patients and HC had very similar levels of bi-centro parietal synchronization; but in the EO resting state, patients with AD had significantly higher levels of synchronization (AD = 0.44; interquartile range (IQR) 0.41 vs. HC = 0.15; IQR 0.17, p < 0.0001). The EO/EC synchronization ratio, a measure of the dynamic changes between the two states, also showed significant differences between these two groups (AD ratio 0.78 versus HC ratio 0.37 p < 0.0001). EO synchronization was also significantly different between AD and FTD (FTD = 0.075; IQR 0.03, p < 0.0001). However, the EO/EC ratio was not informative in the FTD group due to very low levels of synchronization in both states (EO and EC). CONCLUSION: In this pilot work, resting state quantitative EEG shows significant differences between healthy controls and patients with AD. This approach has the potential to develop into a useful non-invasive and economical diagnostic aid in AD.

Markov Chain Monte Carlo Algorithm based metabolic flux distribution analysis on Corynebacterium glutamicum.

MOTIVATION: Metabolic flux analysis via a (13)C tracer experiment has been achieved using a Monte Carlo method with the assumption of system noise as Gaussian noise. However, an unbiased flux analysis requires the estimation of fluxes and metabolites jointly without the restriction on the assumption of Gaussian noise. The flux distributions under such a framework can be freely obtained with various system noise and uncertainty models. RESULTS: In this paper, a stochastic generative model of the metabolic system is developed. Following this, the Markov Chain Monte Carlo (MCMC) approach is applied to flux distribution analysis. The disturbances and uncertainties in the system are simplified as truncated Gaussian multiplicative models. The performance in a real metabolic system is illustrated by the application to the central metabolism of Corynebacterium glutamicum. The flux distributions are illustrated and analyzed in order to understand the underlying flux activities in the system. AVAILABILITY: Algorithms are available upon request.

Metabolic flux estimation--a self-adaptive evolutionary algorithm with singular value decomposition.

Metabolic flux analysis is important for metabolic system regulation and intracellular pathway identification. A popular approach for intracellular flux estimation involves using 13C tracer experiments to label states that can be measured by nuclear magnetic resonance spectrometry or gas chromatography mass spectrometry. However, the bilinear balance equations derived from 13C tracer experiments and the noisy measurements require a nonlinear optimization approach to obtain the optimal solution. In this paper, the flux quantification problem is formulated as an error-minimization problem with equality and inequality constraints through the 13C balance and stoichiometric equations. The stoichiometric constraints are transformed to a null space by singular value decomposition. Self-adaptive evolutionary algorithms are then introduced for flux quantification. The performance of the evolutionary algorithm is compared with ordinary least squares estimation by the simulation of the central pentose phosphate pathway. The proposed algorithm is also applied to the central metabolism of Corynebacterium glutamicum under lysine-producing conditions. A comparison between the results from the proposed algorithm and data from the literature is given. The complexity of a metabolic system with bidirectional reactions is also investigated by analyzing the fluctuations in the flux estimates when available measurements are varied.

Generalized multiscale radial basis function networks.

A novel modelling framework is proposed for constructing parsimonious and flexible multiscale radial basis function networks (RBF). Unlike a conventional standard single scale RBF network, where all the basis functions have a common kernel width, the new network structure adopts multiscale Gaussian functions as the bases, where each selected centre has multiple kernel widths, to provide more flexible representations with better generalization properties for general nonlinear dynamical systems. As a direct extension of the traditional single scale Gaussian networks, the new multiscale network is easy to implement and is quick to learn using standard learning algorithms. A k-means clustering algorithm and an improved orthogonal least squares (OLS) algorithm are used to determine the unknown parameters in the network model including the centres and widths of the basis functions, and the weights between the basis functions. It is demonstrated that the new network can lead to a parsimonious model with much better generalization property compared with the traditional single width RBF networks.

Feature subset selection and ranking for data dimensionality reduction.

A new unsupervised forward orthogonal search (FOS) algorithm is introduced for feature selection and ranking. In the new algorithm, features are selected in a stepwise way, one at a time, by estimating the capability of each specified candidate feature subset to represent the overall features in the measurement space. A squared correlation function is employed as the criterion to measure the dependency between features and this makes the new algorithm easy to implement. The forward orthogonalization strategy, which combines good effectiveness with high efficiency, enables the new algorithm to produce efficient feature subsets with a clear physical interpretation.

Sparse model identification using a forward orthogonal regression algorithm aided by mutual information.

A sparse representation, with satisfactory approximation accuracy, is usually desirable in any nonlinear system identification and signal processing problem. A new forward orthogonal regression algorithm, with mutual information interference, is proposed for sparse model selection and parameter estimation. The new algorithm can be used to construct parsimonious linear-in-the-parameters models.

Fly Photoreceptors Encode Phase Congruency.

More than five decades ago it was postulated that sensory neurons detect and selectively enhance behaviourally relevant features of natural signals. Although we now know that sensory neurons are tuned to efficiently encode natural stimuli, until now it was not clear what statistical features of the stimuli they encode and how. Here we reverse-engineer the neural code of Drosophila photoreceptors and show for the first time that photoreceptors exploit nonlinear dynamics to selectively enhance and encode phase-related features of temporal stimuli, such as local phase congruency, which are invariant to changes in illumination and contrast. We demonstrate that to mitigate for the inherent sensitivity to noise of the local phase congruency measure, the nonlinear coding mechanisms of the fly photoreceptors are tuned to suppress random phase signals, which explains why photoreceptor responses to naturalistic stimuli are significantly different from their responses to white noise stimuli.

Reproducibility of parameters of postocclusive reactive hyperemia measured by diffuse optical tomography.

The application of near-infrared spectroscopy (NIRS) to assess microvascular function has shown promising results. An important limitation when using a single source-detector pair, however, is the lack of depth sensitivity. Diffuse optical tomography (DOT) overcomes this limitation using an array of sources and detectors that allow the reconstruction of volumetric hemodynamic changes. This study compares the key parameters of postocclusive reactive hyperemia measured in the forearm using standard NIRS and DOT. We show that while the mean parameter values are similar for the two techniques, DOT achieves much better reproducibility, as measured by the intraclass correlation coefficient (ICC). We show that DOT achieves high reproducibility for muscle oxygen consumption (ICC: 0.99), time to maximal HbO2 (ICC: 0.94), maximal HbO2 (ICC: 0.99), and time to maximal HbT (ICC: 0.99). Absolute reproducibility as measured by the standard error of measurement is consistently smaller and close to zero (ideal value) across all parameters measured by DOT compared to NIRS. We conclude that DOT provides a more robust characterization of the reactive hyperemic response and show how the availability of volumetric hemodynamic changes allows the identification of areas of temporal consistency, which could help characterize more precisely the microvasculature.

A new class of wavelet networks for nonlinear system identification.

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.

A nonlinear generalization of spectral Granger causality.

Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous (ARX) inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this study, it is shown that the classical Geweke's spectral causality measure can be explicitly linked with the output spectra of corresponding restricted and unrestricted time-domain models. The latter representation is then generalized to nonlinear bivariate signals and for the first time nonlinear causality analysis in the frequency domain. This is achieved by using the nonlinear ARX (NARX) modeling of signals, and decomposition of the recently defined output frequency response function which is related to the NARX model.

A nonlinear causality measure in the frequency domain: nonlinear partial directed coherence with applications to EEG.

BACKGROUND: Frequency domain Granger causality measures have been proposed and widely applied in analyzing rhythmic neurophysiological and biomedical signals. Almost all these measures are based on linear time domain regression models, and therefore can only detect linear causal effects in the frequency domain. NEW METHOD: A frequency domain causality measure, the partial directed coherence, is explicitly linked with the frequency response function concept of linear systems. By modeling the nonlinear relationships between time series using nonlinear models and employing corresponding frequency-domain analysis techniques (i.e., generalized frequency response functions), a new nonlinear partial directed coherence method is derived. RESULTS: The advantages of the new method are illustrated via a numerical example of a nonlinear physical system and an application to electroencephalogram signals from a patient with childhood absence epilepsy. COMPARISON WITH EXISTING METHODS: The new method detects both linear and nonlinear casual effects between bivariate signals in the frequency domain, while the existing measures can only detect linear effects. CONCLUSIONS: The proposed new method has important advantages over the classical linear measures, because detecting nonlinear dependencies has become more and more important in characterizing functional couplings in neuronal and biological systems.

Quantitative EEG analysis using error reduction ratio-causality test; validation on simulated and real EEG data.

OBJECTIVE: To introduce a new method of quantitative EEG analysis in the time domain, the error reduction ratio (ERR)-causality test. To compare performance against cross-correlation and coherence with phase measures. METHODS: A simulation example was used as a gold standard to assess the performance of ERR-causality, against cross-correlation and coherence. The methods were then applied to real EEG data. RESULTS: Analysis of both simulated and real EEG data demonstrates that ERR-causality successfully detects dynamically evolving changes between two signals, with very high time resolution, dependent on the sampling rate of the data. Our method can properly detect both linear and non-linear effects, encountered during analysis of focal and generalised seizures. CONCLUSIONS: We introduce a new quantitative EEG method of analysis. It detects real time levels of synchronisation in the linear and non-linear domains. It computes directionality of information flow with corresponding time lags. SIGNIFICANCE: This novel dynamic real time EEG signal analysis unveils hidden neural network interactions with a very high time resolution. These interactions cannot be adequately resolved by the traditional methods of coherence and cross-correlation, which provide limited results in the presence of non-linear effects and lack fidelity for changes appearing over small periods of time.

Reduced-order modeling of light transport in tissue for real-time monitoring of brain hemodynamics using diffuse optical tomography.

This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3 s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach.

Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach.

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

A data-driven framework for identifying nonlinear dynamic models of genetic parts.

A key challenge in synthetic biology is the development of effective methodologies for characterization of component genetic parts in a form suitable for dynamic analysis and design. In this investigation we propose the use of a nonlinear dynamic modeling framework that is popular in the field of control engineering but is novel to the field of synthetic biology: Nonlinear AutoRegressive Moving Average model with eXogenous inputs (NARMAX). The framework is applied to the identification of a genetic part BBa_T9002 as a case study. A concise model is developed that exhibits accurate representation of the system dynamics and a structure that is compact and consistent across cell populations. A comparison is made with a biochemical model, derived from a simple enzymatic reaction scheme. The NARMAX model is shown to be comparably simple but exhibits much greater prediction accuracy on the experimental data. These results indicate that the data-driven NARMAX framework is an attractive technique for dynamic modeling of genetic parts.