Laguerre Expansion Technique Research Articles

Elucidating nonlinear baroreflex and respiratory contributions to heart rate variability in obstructive sleep apnea syndrome.

Using a Volterra-Wiener model and the Laguerre expansion technique, we estimated in a previous study the parameters that characterize linear and the second order effects of respiration ("RSA") and arterial blood pressure ("ABR") on heart rate. RSA and ABR gains were significantly lower in Obstructive Sleep Apnea (OSA) patients than in normal subjects. During sleep, ABR gain increased in normals but remained unchanged in OSA. In the present work, we investigated the physiological interpretation of the nonlinear components of the described model of heart rate variability, by means of simulation on the computed linear and nonlinear kernels. Our results indicate that the 2ndorder kernels reflect specific characteristics of the RSA and ABR mechanisms, such as a RSA frequency response dependence upon tidal volume, saturation in the ABR-Blood Pressure relation, and respiratory modulation of ABR.

Nonparametric Analysis Of Time-Resolved Fluorescence Data Based On The Laguerre Expansion Technique.

To estimate the intrinsic fluorescence intensity decay of a compound, the excitation light pulse must be deconvolved from the measured fluorescence pulse trace. The most commonly used deconvolution method is the multiexponential least-square iterative reconvolution (LSIR) technique. A variant of LSIR in which the intrinsic fluorescence intensity decay is expressed as an expansion on the discrete time Laguerre basis, was recently introduced. In this study, the performance of the Laguerre deconvolution technique was successfully tested with simulated and fluorescence standard data. It was also demonstrated that the Laguerre deconvolution presents a number of advantages over the classical multiexponential LSIR, including less expensive computational resolution, and the property to generate a unique set of expansion coefficients highly correlated with the intrinsic lifetimes. A novel method for concentration estimation based on the analysis of the Laguerre expansion coefficients was also proposed and successfully applied to different fluorescence standard mixtures, performing even better (error<2%) than more traditional methods of spectral analysis, such as PCR (error<7%) and PLS (error<10%). These findings suggest that the use of Laguerre expansion coefficients represents an alternative nonparametric approach to characterize and discriminate biological systems, in terms of their spectral and lifetime characteristics.

Time-resolved fluorescence spectra of arterial fluorescent compounds: reconstruction with the Laguerre expansion technique.

The time-resolved fluorescence spectra of the main arterial fluorescent compounds were retrieved using a new algorithm based on the Laguerre expansion of kernels technique. Samples of elastin, collagen and cholesterol were excited with a pulsed nitrogen laser and the emission was measured at 29 discrete wavelengths between 370 and 510 nm. The expansion of the fluorescence impulse response function on the Laguerre basis of functions was optimized to reproduce the observed fluorescence emission. Collagen lifetime (5.3 ns at 390 nm) was substantially larger than that of elastin (2.3 ns) and cholesterol (1.3 ns). Two decay components were identified in the emission decay of the compounds. For collagen, the decay components were markedly wavelength dependent and hydration dependent such that the emission decay became shorter at higher emission wavelengths and with hydration. The decay characteristics of elastin and cholesterol were relatively unchanged with wavelength and with hydration. The observed variations in the time-resolved spectra of elastin, collagen and cholesterol were consistent with the existence of several fluorophores with different emission characteristics. Because the compounds are present in different proportions in healthy and atherosclerotic arterial walls, characteristic differences in their time-resolved emission spectra could be exploited to assess optically the severity of atherosclerotic lesions.

Nonparametric characterization of human breast tissue by the Laguerre expansion of the kernels technique applied on propagating femtosecond laser pulses through biopsy samples

Ultrafast laser pulses transmitted through excised human breast tissue have been detected by a streak camera. Experimental data of the temporal spread of the ultrafast pulse during the transmission through the tissue have been analyzed using the Laguerre expansion technique. This method treats the medium of propagation as a “black box system” and using data sets of incident–transmitted pulse, it relates to this system a set of coefficients as well the first-order system kernels. This analysis could present an alternative method of tissue characterization when, due to the limited optical thickness of small biopsy samples, the photon diffusion approximation cannot be used successfully.

Nonlinear analysis of renal autoregulation in rats using principal dynamic modes.

This article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0-0.5 Hz) blood pressure-flow data generated by pseudorandom forcing and collected in normotensive and hypertensive rats for two levels of pressure forcing (as measured by the standard deviation of the pressure fluctuation). The PDMs are computed from first-order and second-order kernel estimates obtained from the data via the Laguerre expansion technique. The results demonstrate that two PDMs suffice for obtaining a satisfactory nonlinear dynamic model of renal autoregulation under these conditions, for both normotensive and hypertensive rats. Furthermore, the two PDMs appear to correspond to the two main autoregulatory mechanisms: the first to the myogenic and the second to the tubuloglomerular feedback (TGF) mechanism. This allows the study of the separate contributions of the two mechanisms to the autoregulatory response dynamics, as well as the effects of the level of pressure forcing and hypertension on the two distinct autoregulatory mechanisms. It is shown that the myogenic mechanism has a larger contribution and is affected only slightly, while the TGF mechanism is affected considerably by increasing pressure forcing or hypertension (the emergence of a second resonant peak and the decreased relative contribution to the response flow signal).

Sensitivity Analysis of Kernel Estimates: Implications in Nonlinear Physiological System Identification

Many techniques have been developed for the estimation of the Volterra/Wiener kernels of nonlinear systems, and have found extensive application in the study of various physiological systems. To date, however, we are not aware of methods for estimating the reliability of these kernels from single data records. In this study, we develop a formal analysis of variance for least-squares based nonlinear system identification algorithms. Expressions are developed for the variance of the estimated kernel coefficients and are used to place confidence bounds around both kernel estimates and output predictions. Specific bounds are developed for two such identification algorithms: Korenberg's fast orthogonal algorithm and the Laguerre expansion technique. Simulations, employing a model representative of the peripheral auditory system, are used to validate the theoretical derivations, and to explore their sensitivity to assumptions regarding the system and data. The simulations show excellent agreement between the variances of kernel coefficients and output predictions as estimated from the results of a single trial compared to the same quantities computed from an ensemble of 1000 Monte Carlo runs. These techniques were validated with white and nonwhite Gaussian inputs and with white Gaussian and nonwhite non-Gaussian measurement noise on the output, provided that the output noise source was independent of the test input.

Comparative nonlinear modeling of renal autoregulation in rats: Volterra approach versus artificial neural networks

Volterra models have been increasingly popular in modeling studies of nonlinear physiological systems. In this paper, feedforward artificial neural networks with two types of activation functions (sigmoidal and polynomial) are utilized for modeling the nonlinear dynamic relation between renal blood pressure and flow data, and their performance is compared to Volterra models obtained by use of the leading kernel estimation method based on Laguerre expansions. The results for the two types of artificial neural networks (sigmoidal and polynomial) and the Volterra models are comparable in terms of normalized mean-square error (NMSE) of the respective output prediction for independent testing data. However, the Volterra models obtained via the Laguerre expansion technique achieve this prediction NMSE with approximately half the number of free parameters relative to either neural-network model. Nonetheless, both approaches are deemed effective in modeling nonlinear dynamic systems and their cooperative use is recommended in general, since they may exhibit different strengths and weaknesses depending on the specific characteristics of each application.

Volterra models and three-layer perceptrons

This paper proposes the use of a class of feedforward artificial neural networks with polynomial activation functions (distinct for each hidden unit) for practical modeling of high-order Volterra systems. Discrete-time Volterra models (DVMs) are often used in the study of nonlinear physical and physiological systems using stimulus-response data. However, their practical use has been hindered by computational limitations that confine them to low-order nonlinearities (i.e., only estimation of low-order kernels is practically feasible). Since three-layer perceptrons (TLPs) can be used to represent input-output nonlinear mappings of arbitrary order, this paper explores the basic relations between DVMs and TLPs with tapped-delay inputs in the context of nonlinear system modeling. A variant of TLP with polynomial activation functions-termed "separable Volterra networks" (SVNs)-is found particularly useful in deriving explicit relations with DVM and in obtaining practicable models of highly nonlinear systems from stimulus-response data. The conditions under which the two approaches yield equivalent representations of the input-output relation are explored, and the feasibility of DVM estimation via equivalent SVN training using backpropagation is demonstrated by computer-simulated examples and compared with results from the Laguerre expansion technique (LET). The use of SVN models allows practicable modeling of high-order nonlinear systems, thus removing the main practical limitation of the DVM approach.

Circulatory effects of ventilator rate and PEEP in unparalysed preterm infants : Sandie Bohin, Alan C. Fenton, David H. Evans, Kent L. Woods and David J. Field, Neonatal Unit, Leicester Royal Infirmary, Leicester LE1 5 WW, UK

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.