Laguerre Expansion Technique Research Articles

Cognitive activity significantly affects the dynamic cerebral autoregulation, but not the dynamic vasoreactivity, in healthy adults.

Neurovascular coupling (NVC) is an important mechanism for the regulation of cerebral perfusion during intensive cognitive activity. Thus, it should be examined in terms of its effects on the regulation dynamics of cerebral perfusion and its possible alterations during cognitive impairment. The dynamic dependence of continuous changes in cerebral blood velocity (CBv), which can be measured noninvasively using transcranial Doppler upon fluctuations in arterial blood pressure (ABP) and CO2 tension, using end-tidal CO2 (EtCO2) as a proxy, can be quantified via data-based dynamic modeling to yield insights into two key regulatory mechanisms: the dynamic cerebral autoregulation (dCA) and dynamic vasomotor reactivity (DVR), respectively. Using the Laguerre Expansion Technique (LET), this study extracted such models from data in supine resting vs cognitively active conditions (during attention, fluency, and memory tasks from the Addenbrooke's Cognitive Examination III, ACE-III) to elucidate possible changes in dCA and DVR due to cognitive stimulation of NVC. Healthy volunteers (n = 39) were recruited at the University of Leicester and continuous measurements of CBv, ABP, and EtCO2 were recorded. Modeling analysis of the dynamic ABP-to-CBv and CO2-to-CBv relationships showed significant changes in dCA, but not DVR, under cognitively active conditions compared to resting state. Interpretation of these changes through Principal Dynamic Mode (PDM) analysis is discussed in terms of possible associations between stronger NVC stimulation during cognitive tasks and enhanced sympathetic activation.

Special structural Gramian approximation methods for model order reduction of time‐delay systems

AbstractModel order reduction methods via low‐rank approximation of Gramians for time‐delay systems are developed in this paper. The main contribution is to achieve the balancing and truncation of the system by utilizing low‐rank decomposition of the Gramians combined with the low‐rank square root framework. Here, based on Laguerre expansion technique, the low‐rank factorization of the system Gramians is realized via a linear system with special structure, thus enabling an efficient implementation of the reduction process. Furthermore, the issue of stability preservation is briefly described. We employ the dominant subspaces projection model reduction method to mitigate the effects which may accidentally produce unstable reduced models. Finally, numerical results verify the performance of the approximation‐Gramian methods.

Nonparametric Model of Smooth Muscle Force Production During Electrical Stimulation.

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

Dynamic cerebral autoregulation in young athletes following concussion.

The purpose of this study was to examine cerebral autoregulation (CA) in young athletes experiencing concussion. The subjects were monitored and repeatedly tested 72 hours, 2 weeks and 1 month post-injury. Mean arterial blood pressure (MABP), end-tidal partial pressure of carbon dioxide (PETCO2) and cerebral blood flow velocity (CBFV) in the middle and posterior cerebral arteries were monitored during mental activation paradigms. In order to characterize CA we employed autoregressive models with exogenous inputs (ARX) and impulse response models based on the Laguerre expansion technique (LET). By extracting gain and phase estimates from the obtained models we were able to detect disruptions in CA 72 hours following concussion and a slow recovery within a time period of one month.

Towards an SEMG-based tele-operated robot for masticatory rehabilitation

This paper proposes a real-time trajectory generation for a masticatory rehabilitation robot based on surface electromyography (SEMG) signals. We used two Gough-Stewart robots. The first robot was used as a rehabilitation robot while the second robot was developed to model the human jaw system. The legs of the rehabilitation robot were controlled by the SEMG signals of a tele-operator to reproduce the masticatory motion in the human jaw, supposedly mounted on the moving platform, through predicting the location of a reference point. Actual jaw motions and the SEMG signals from the masticatory muscles were recorded and used as output and input, respectively. Three different methods, namely time-delayed neural networks, time delayed fast orthogonal search, and time-delayed Laguerre expansion technique, were employed and compared to predict the kinematic parameters. The optimal model structures as well as the input delays were obtained for each model and each subject through a genetic algorithm. Equations of motion were obtained by the virtual work method. Fuzzy method was employed to develop a fuzzy impedance controller. Moreover, a jaw model was developed to demonstrate the time-varying behavior of the muscle lengths during the rehabilitation process. The three modeling methods were capable of providing reasonably accurate estimations of the kinematic parameters, although the accuracy and training/validation speed of time-delayed fast orthogonal search were higher than those of the other two aforementioned methods. Also, during a simulation study, the fuzzy impedance scheme proved successful in controlling the moving platform for the accurate navigation of the reference point in the desired trajectory. SEMG has been widely used as a control command for prostheses and exoskeleton robots. However, in the current study by employing the proposed rehabilitation robot the complete continuous profile of the clenching motion was reproduced in the sagittal plane.

Dynamic modeling of SEMG–force relation in the presence of muscle fatigue during isometric contractions

Abstract Electromyogram signals contain information for predicting muscle force that can be used in human-machine interaction and medical applications such as the control of prosthetic hands. Different methods exist for estimating the SEMG–force relation. However, muscle dynamic variations during voluntary contractions due to fatigue have been neglected in the identification stage. This would make the models not applicable to normal working conditions. We developed a model based on Laguerre expansion technique, LET, to identify the dynamic SEMG–force relation and investigate the presence of fatigue through kernel analysis. Our proposed data acquisition protocol was used to induce fatigue in the muscles involved in the act of grasping, hence enabling us to study the effects of muscle fatigue. The results of LET in comparison with fast orthogonal search and parallel cascade identification, which were able to accurately identify the desired dynamics, represent an improvement of 15% and 3.8% in prediction fitness, respectively. Moreover, by extracting median frequency (MDF) of the recorded SEMG signals and tracking its changes over time, the existence of muscle fatigue was studied. The results showed that fatigue had an impact on the Brachioradialis muscle. The first and second order kernels of the LET illustrated variations in the time and frequency domains similar to that of MDF for the Brachioradialis muscle corresponding to the fatigue generation process. Employing the proposed model the dynamics of SEMG–force relation can be predicted and its variations due to muscle fatigue can also be investigated.

Model reduction of discrete-time bilinear systems by a Laguerre expansion technique

In this paper, we investigate model reduction of discrete-time bilinear control systems using a Laguerre expansion technique. The transfer function of systems is expanded under the Laguerre functions basis and we show that Laguerre coefficients take on a recursion relationship, which allows us to execute the reduction elegantly based on the recursion, instead of the cumbersome expression of Laguerre coefficients. Then reduced models are produced in the framework of two-sided projection methods and a certain number of Laguerre coefficients of the original systems are preserved implicitly, thereby resulting in a good approximation. Noting that the order of reduced models may rise rapidly, a terminal reduction method is introduced to modify our algorithm. The modified algorithm is achieved by properly defining an auxiliary system, significantly shrinking the order of reduced models. Theoretical analysis and numerical experiments show the efficiency of our approach.

System identification of point-process neural systems using probability based Volterra kernels.

Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics. A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq. The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs. The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance. The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems.

Model Order Reduction of Time-Delay Systems Using a Laguerre Expansion Technique

The demands for miniature sized circuits with higher operating speeds have increased the complexity of the circuit, while at high frequencies it is known that effects such as crosstalk, attenuation and delay can have adverse effects on signal integrity. To capture these high speed effects a very large number of system equations is normally required and hence model order reduction techniques are required to make the simulation of the circuits computationally feasible. This paper proposes a higher order Krylov subspace algorithm for model order reduction of time-delay systems based on a Laguerre expansion technique. The proposed technique consists of three sections i.e., first the delays are approximated using the recursive relation of Laguerre polynomials, then in the second part, the reduced order is estimated for the time-delay system using a delay truncation in the Laguerre domain and in the third part, a higher order Krylov technique using Laguerre expansion is computed for obtaining the reduced order time-delay system. The proposed technique is validated by means of real world numerical examples.

Nonstationary multivariate modeling of cerebral autoregulation during resting state and hypercapnia (1184.10)

We examined the time‐varying characteristics of cerebral autoregulation and hemodynamics during resting state and hypercapnia by using recursively estimated multivariate (two‐input) models which quantify the dynamic effects of mean arterial blood pressure (ABP) and end‐tidal CO2 tension (PETCO2) on middle cerebral artery blood flow velocity (CBFV). Experimental measurements of spontaneous variations of these signals were obtained from thirteen healthy subjects under normal, free‐breathing conditions. Beat‐to‐beat values of ABP and CBFV, as well as breath‐to‐breath values of PETCO2 were also obtained in 8 female subjects during baseline and sustained euoxic hypercapnia. The multiple‐input, single‐output linear models used to describe the relationship between ABP, PETCO2 and CBFV were based on the Laguerre expansion technique. In order to account for the different dynamics associated with each input, the model parameters were updated using a recursive least squares scheme with constant and adaptive multiple forgetting factors. The results reveal the presence of nonstationarities that are more pronounced in the very low frequency range. By comparing one‐input (MABP) and two‐input (MABP and PETCO2) models, our results point out that the incorporation of PETCO2 as an additional input yields less time‐varying estimates of dynamic pressure autoregulation obtained from single‐input (MABP‐CBFV) models, suggesting the important role of PETCO2 and the possible shortcomings of assessing dynamic autoregulation using such models.

Nonstationary multivariate modeling of cerebral autoregulation during hypercapnia

We examined the time-varying characteristics of cerebral autoregulation and hemodynamics during a step hypercapnic stimulus by using recursively estimated multivariate (two-input) models which quantify the dynamic effects of mean arterial blood pressure (ABP) and end-tidal CO2 tension (PETCO2) on middle cerebral artery blood flow velocity (CBFV). Beat-to-beat values of ABP and CBFV, as well as breath-to-breath values of PETCO2 during baseline and sustained euoxic hypercapnia were obtained in 8 female subjects. The multiple-input, single-output models used were based on the Laguerre expansion technique, and their parameters were updated using recursive least squares with multiple forgetting factors. The results reveal the presence of nonstationarities that confirm previously reported effects of hypercapnia on autoregulation, i.e. a decrease in the MABP phase lead, and suggest that the incorporation of PETCO2 as an additional model input yields less time-varying estimates of dynamic pressure autoregulation obtained from single-input (ABP–CBFV) models.

利用Volterra-Wiener模型估算壓力反射敏感度－以EUROBAVAR資料庫為例

The short-term control of blood pressure is the arterial baroreflex and the baroreflex sensitivity (BRS) is the indicator that describes such mechanism. The BRS estimation, spontaneous BRS index, is based on beat-to-beat time series analysis of systolic blood pressure and heart rate interval underlying openloop or closed-loop linear model in time or frequency domain. However, the physiological regulatory mechanism of blood pressure is inherently nonlinear and dynamic. It would make a great improvement for accurate assessment of arterial baroreflex by a suitable dynamic nonlinear model. This paper presents a nonlinear Volterra-Wiener model and the Laguerre expansion technique to analyze the changes in systolic arterial blood pressure, as model’s input, and their corresponding changes in heart rate interval, as model ’s output. Compared with the measurements by sequence technique and alpha coefficient technique in EUROBAVAR dataset, we found that the estimates of BRS by the proposed technique were lower either in lying or in standing position and the lying/standing ratio were higher. The proposed technique improves the overestimation of spontaneous BRS index obtained by other approaches such as sequence technique or alpha coefficient technique.

Fully automated deconvolution method for on-line analysis of time-resolved fluorescence spectroscopy data based on an iterative Laguerre expansion technique

Time-resolved fluorescence spectroscopy (TRFS) is a powerful analytical tool for quantifying the biochemical composition of organic and inorganic materials. The potential of TRFS for tissue diagnosis has been recently demonstrated. To facilitate the translation of TRFS to the clinical arena, algorithms for online TRFS data analysis are essential. A fast model-free TRFS deconvolution algorithm based on the Laguerre expansion method has previously been introduced. One limitation of this method, however, is the need to heuristically select two parameters that are crucial for the accurate estimation of the fluorescence decay: the Laguerre parameter alpha and the expansion order. Here, a new implementation of the Laguerre deconvolution method is introduced, in which a nonlinear least-square optimization of the Laguerre parameter alpha is performed, and the optimal expansion order is selected based on a minimum description length criterion (MDL). In addition, estimation of the zero-time delay between the recorded instrument response and fluorescence decay is also performed based on normalized mean square error criterion (NMSE). The method is validated on experimental data from fluorescence lifetime standards, endogenous tissue fluorophores, and human tissue. The proposed automated Laguerre deconvolution method will facilitate online applications of TRFS, such as real-time clinical tissue diagnosis.

Principal dynamic mode analysis of hippocampal neuronal networks

Methods The input-output data required for training and modeling was acquired from acute slices of the rat hippocampus. A seizure-like state was induced by perfusion with low Mg2+ artificial cerebrospinal fluid. Gaussian white-noise (GWN) was applied as input to CA3 pyramidal neuron and the output was measured from the same CA3 pyramidal neuron. PDMs were computed using the Laguerre expansion technique.

Time-resolved Fluorescence Spectra of Arterial Fluorescent Compounds: Reconstruction with the Laguerre Expansion Technique

Time-resolved Fluorescence Spectra of Arterial Fluorescent Compounds: Reconstruction with the Laguerre Expansion Technique

New Methods for Time-resolved Fluorescence Spectroscopy Data Analysis Based on the Laguerre Expansion Technique

A new deconvolution method for the analysis of time-resolved laser-induced fluorescence spectroscopy (TR-LIFS) data is introduced and applied for tissue diagnosis. The intrinsic TR-LIFS decays are expanded on a Laguerre basis, and the computed Laguerre expansion coefficients (LEC) are used to characterize the sample fluorescence emission. The method was applied for the diagnosis of atherosclerotic vulnerable plaques. At a first stage, using a rabbit atherosclerotic model, 73 TR-LIFS in-vivo measurements from the normal and atherosclerotic aorta segments of eight rabbits were taken. The Laguerre deconvolution technique was able to accurately deconvolve the TR-LIFS measurements. More interesting, the LEC reflected the changes in the arterial biochemical composition and provided discrimination of lesions rich in macrophages/foam-cells with high sensitivity (> 85%) and specificity (> 95%). At a second stage, 348 TR-LIFS measurements were obtained from the explanted carotid arteries of 30 patients. Lesions with significant inflammatory cells (macrophages/foam-cells and lymphocytes) were detected with high sensitivity (> 80%) and specificity (> 90%), using LEC-based classifiers. This study has demonstrated the potential of using TR-LIFS information by means of LEC for in vivo tissue diagnosis, and specifically for detecting inflammation in atherosclerotic lesions, a key marker of plaque vulnerability.

Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener-Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal). The static nonlinearity, which can be viewed as a measure of the probability of action potential firing as a function of the PDM output values, is computed as the locus of points of the latter that correspond to output action potentials. The performance of the model is assessed by computing receiver operating characteristic (ROC) curves, akin to the ones used in decision theory and quantified by computing the area under the ROC curve. Three PDMs are revealed by the analysis. The first PDM exhibits a high-pass characteristic, illustrating the importance of the velocity of slit displacement in the generation of action potentials at the mechanoreceptor output, while the second and third PDMs exhibit band-pass and low-pass characteristics, respectively. The corresponding three-input nonlinearity exhibits asymmetric behavior with respect to its arguments, suggesting directional dependence of the mechanoreceptor response on the mechanical stimulation and the PDM outputs, in agreement to our findings from a previous study (Ann Biomed Eng 27:391-402, 1999). Differences between the Type A and B neurons are observed in the zeroth-order Volterra kernels (related to the average firing), as well as in the magnitudes of the second and third PDMs that perform band-pass and low-pass processing of the input signal, respectively.

Autonomic Cardiovascular Control Following Transient Arousal From Sleep: A Time-Varying Closed-Loop Model

Recent studies suggest that exposure to repetitive episodes of hypoxia and transient arousal can lead to increased risk for cardiovascular disease in patients with obstructive sleep apnea syndrome (OSAS). To obtain an improved understanding of and to quantitatively characterize the autonomic effects of arousal from sleep, a time-varying closed-loop model was used to determine the interrelationships among respiration, heart rate and blood pressure in 8 normal adults. A recursive least squares algorithm was used in combination with the Laguerre expansion technique to estimate the time-varying impulse responses of the 4 model components. We found that during arousal: 1) respiratory-cardiac coupling gain increases in nonrapid-eye movement (NREM) but not in REM sleep; 2) in both NREM and REM sleep, baroreflex gain shows an initial increase, but this is followed by a more sustained decrease below pre-arousal baseline levels, allowing sympathetic tone to be elevated over a relatively long duration; 3) the gains of other model components show increases with arousal that are consistent with the increased sympathetic modulation of systemic vascular resistance and contractility of the heart. These findings establish a normative database against which further measurements of cardiovascular arousal responses in OSAS may be compared.

Ultrafast Method for the Analysis of Fluorescence Lifetime Imaging Microscopy Data Based on the Laguerre Expansion Technique.

We report a new deconvolution method for fluorescence lifetime imaging microscopy (FLIM) based on the Laguerre expansion technique. The performance of this method was tested on synthetic and real FLIM images. The following interesting properties of this technique were demonstrated. 1) The fluorescence intensity decay can be estimated simultaneously for all pixels, without a priori assumption of the decay functional form. 2) The computation speed is extremely fast, performing at least two orders of magnitude faster than current algorithms. 3) The estimated maps of Laguerre expansion coefficients provide a new domain for representing FLIM information. 4) The number of images required for the analysis is relatively small, allowing reduction of the acquisition time. These findings indicate that the developed Laguerre expansion technique for FLIM analysis represents a robust and extremely fast deconvolution method that enables practical applications of FLIM in medicine, biology, biochemistry, and chemistry.

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P–W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process ‘input’) and another axon (a point-process ‘output’) or some other measure of neuronal activity (a continuous ‘output’, such as population activity) with which a causal link exists.