A nonlinear model of the arterial vessels within a limb segment

The relationship between the arterial blood pressure and the volume of the arteries within a segment of an extremity is nonlinear. The present paper shows how the flow and volume pulsations of the arteries within a limb segment can be simulated taking this property into account. An electrical model was constructed comprising one resistor and two voltage dependent ‘capacitors’, the latter corresponding to the pressure dependent elasticity, or compliance, of the arteries. Adequate simulations were obtained over a wide pressure range, which is impossible with linear models. The nonlinear, i.e. pressure dependent, relationship between the volume and pressure of arteries, observed under static conditions, must also be taken into consideration when studying pulsatile events with models whether mathematical or physical.     

Time adaptive denoising of single trial event-related potentials in the wavelet domain

We present a new wavelet-based method for single trial analysis of transient and time variant event-related potentials (ERPs). Expecting more accurate filter settings than achieved by other techniques (low-pass filter, a posteriori Wiener filter, time invariant wavelet filter), ERPs were initially balanced in time. By simulation, better filter performance could be established for test signals contaminated with either white noise or isospectral noise. To provide an example of real application, the method was applied to limbic P300 potentials (MTL-P300). As a result, variance of single trial MTL-P300s decreased, without restricting the corresponding mean. The proposed method can be regarded as an alternative for single-trial ERP analysis.     

Two Methods for Identifying Wiener Cascades Having Noninvertible Static Nonlinearities

Two methods are proposed for identifying the component elements of a Wiener cascade that is comprised of a dynamic linear element (L) followed by a static nonlinearity (N). Both methods avoid potential problems of instability in a procedure presented by Paulin [M. G. Paulin, Biol. Cybern. 69: 67–76, 1993], which itself is a modification of a method described earlier by Hunter and Korenberg [I. W. Hunter and M. J. Korenberg, Biol. Cybern. 55: 135–144, 1996]. The latter method is a rapidly convergent iterative procedure that produces accurate estimates of the L and N elements from short data records, provided that the static nonlinearity N is invertible. Subsequently, Paulin introduced a modification that removed this limitation and enabled identification of Wiener cascades with nonmonotonic static nonlinearities. However, Paulin presented his modification employing an autoregressive moving average (ARMA) model representation for the dynamic linear element. To remove the possibility that the estimated ARMA model could be unstable, we recast the procedure by utilizing instead a rapid method for finding an impulse response representation for the dynamic linear element. However, in this form the procedure did not have good convergence properties, so we introduced two key ideas, both of which provide effective alternatives for identifying Wiener cascades whether or not the static nonlinearities therein are invertible. The new procedures are illustrated on challenging examples involving high-degree polynomial static nonlinearities, of odd or even symmetry, a high-pass linear element, and output noise corruption of 50%. © 1999 Biomedical Engineering Society. PAC99: 8710+e, 0210Nj, 0250-r     

A Stochastic Nonlinear Autoregressive Algorithm Reflects Nonlinear Dynamics of Heart-Rate Fluctuations

Current methods for detecting nonlinear determinism in a time series require long and stationary data records, as most of them assume that the observed dynamics arise only from the internal, deterministic workings of the system, and the stochastic portion of the signal (the noise component) is assumed to be negligible. To explicitly account for the stochastic portion of the data we recently developed a method based on a stochastic nonlinear autoregressive (SNAR) algorithm. The method iteratively estimates nonlinear autoregressive models for both the deterministic and stochastic portions of the signal. Subsequently, the Lyapunov exponents (LE) are calculated for the estimated models in order to examine if nonlinear determinism is present in the deterministic portion of the fitted model. To determine if nonlinear dynamic analysis of heart-rate fluctuations can be used to assess arrhythmia susceptibility by predicting the outcome of invasive cardiac electrophysiologic study (EPS), we applied the SNAR algorithm to noninvasively measured resting sinus-rhythm heart-rate signals obtained from 16 patients. Our analysis revealed that a positive LE was highly correlated to a patient with a positive outcome of EPS. We found that the statistical accuracy of the SNAR algorithm in predicting the outcome of EPS was 88% (sensitivity=100%, specificity=75%, positive predictive value=80%, negative predictive value=100%, p=0.0019). Our results suggest that the SNAR algorithm may serve as a noninvasive probe for screening high-risk populations for malignant cardiac arrhythmias. © 2002 Biomedical Engineering Society. PAC2002: 8719Hh, 0545Tp, 8710+e     

Standardization for image characteristics in telemammography using genetic and nonlinear algorithms

As the soft copy reading and computer assisted diagnosis (CAD) in mammography become more and more important, the standardization of digital images becomes paramount. Telemammography and telemedicine requires the standardization for image characteristics, such as image resolution, bit-depth and intensity response. Soft copy reading and CAD in mammography are both dependent on the characteristics of the source of the digital data, either direct digital mammography or digitized screen-film mammography. An algorithm developed on images from one database may not perform well as on images from another database (with a different digitization). In this paper, we describe two methods based on a genetic algorithm and a nonlinear algorithm for standardization of digitized and digital mammography. The proposed standardization techniques are based on geometric and intensity transformations that are discovered using a set of calibration images. A set of transformation algorithm is used to search for the best standardization.     

Nonlinear structural and material properties and models: The pulmonary trunk

General models are developed for static and dynamic geometric and material passive responses. The models are applied to data obtained from the main pulmonary arteries of calves and dogs. The structural model predicts distortions by simultaneous stretching and bending in a concise manner. Parameters are obtained by a fiveelement material model. This latter predicts static and dynamic, nonlinear, frequency-dependent, viscoelastic responses observed in biomaterials over the entire strain range irrespective of the nature of loading. Validity and baseline parameter values are investigated for the inactivated state, developed by poisoning the smooth muscle with potassium cyanide. Complexities, related to nonlinear (strain-dependent) and colloidal (thixotropic) properties of tissues, are analyzed. These properties enter into functional responses in a complex manner that can modify substantially concepts of material components and vary appreciably between physiologic circumstances and laboratory evaluations. We propose that, in general, evaluations of material responses must account for these properties.     

Flexible effects of quantified cigarette-smoke delivery on EEG dimensional complexity

A quantified smoke delivery system (QSDS) was used to experimentally control the administration of inhaled cigarette smoke to 28 male smokers. One puff (2 s, 35 cc) was taken every 30 s on a cigarette (nicotine yield 1.0 mg) until the char line reached 3 mm from the filter wrap. The smoke was inhaled for 5 s. Resting eyes-closed and eyes-open EEG was recorded from F3, F4, P3, and P4 before and after quantified smoke delivery (QSD). EEG dimensional complexity (DC _x, a measure derived from chaos theory) was computed using the Takens-Ellner method. QSD appeared to have a flexible effect on EEGDC _x, primarily lowering it in subjects whose pre-smoking level was high, not affecting it in subjects whose pre-smoking level was intermediate, and tending to raise it in subjects whose pre-smoking level was low. This replicates previous results obtained with ad libitum smoking, suggesting the hypothesis that smoking may have an optimizing effect on the complexity of brain dynamics.     

STATISTICAL INFERENCE FOR RELATIVE POTENCY IN BIVARIATE DOSE-RESPONSE ASSAYS WITH CORRELATED RESPONSES

ABSTRACT

The analysis of dose-response assays measuring two correlated responses is considered. Attention is given to statistical inference for the potency ratio. Results from a simulation study suggest that a post hoc adjustment for the correlation in parameter estimates obtained from univariate fits provides nearly as much power to detect differences in potency as a bivariate response model fit.     

Statistical considerations for crosssectional data relating to tracheal reconstruction over time

Complementary statistical analyses are performed on data concerning tracheal reconstruction in rats. The principal response criterion is vessel area as defined by the area of a graft onto the trachea covered by blood vessels. Postoperatively, this vessel area changes in a nonlinear fashion over time. Starting at 0% immediately postoperation, the vessel area increases to a peak and then sharply decreases to a certain level at which it remains. A total of 64 independently observed cross-sectional pairs (postop day, vessel area) are distributed among four treated groups. Analysis consists of two-way analysis of variance and piecewise linear regression under the usual assumptions of normality and variance homogeneity. Other analyses that relax these assumptions are also considered; treatment differences are established by nonparametric tests, and a quasi-likelihood analysis of the piecewise linear regression model is applied under the assumption of a binomial-like variance function. The resulting fit of the normal-theory-based piecewise linear model is compared to that of a nonlinear model whose shape is that of a gamma function integrand.     

Reliability of center of pressure measures for assessing the development of sitting postural control through the stages of sitting

Cerebral palsy (CP) impairs an individual’s ability to move and control one’s posture. Unfortunately, the signs and symptoms of CP may not be apparent before age two. Evaluating sitting posture is a potential way to assess the developing mechanisms that contribute to CP. The purpose of this project was to determine the reliability of linear and nonlinear measures, including inter- and intrastage reliability, when used to analyze the center of pressure (COP) time series during the stages of sitting development in children with typical development (TD) and with/at-risk for cerebral palsy (CP). We hypothesized that nonlinear tools would be more reliable than linear tools in assessing childrens’ sitting development, and reliability would increase with development. COP data was recorded for three trials at eight sessions. Linear parameters used were root mean square, range of sway for the anterior-posterior (AP) and medial-lateral (ML) directions, and sway path. Nonlinear parameters used were Approximate Entropy, the largest Lyapunov Exponent, and Correlation Dimension for the AP and ML direction. Participants consisted of 33 children with TD and 26 children with/at-risk for CP. Our results determined that COP is a moderately reliable method for assessing the development of sitting postural control in stages in both groups. Thus, clinicians may be able to use measures from COP data across stages to assess the efficacy of therapeutic interventions that are intended to improve sitting postural abilities in children with/at-risk for CP.