Nonlinear modeling of the dynamic effects of arterial pressure and CO2 variations on cerebral blood flow in healthy humans

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal CO2 fluctuations on beat-to-beat cerebral blood flow velocity variations is studied using the Laguerre-Volterra network methodology for multiple-input nonlinear systems. The observations made from experimental measurements from ten healthy human subjects reveal that, whereas pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), end-tidal CO2 fluctuations as well as nonlinear interactions between pressure and CO2 have a considerable effect in the lower frequencies (below 0.04 Hz). They also indicate that cerebral autoregulation is strongly nonlinear and dynamic (frequency-dependent). Nonlinearities are mainly active in the low-frequency range (below 0.04 Hz) and are more prominent in the dynamics of the end-tidal CO2-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of CO2 on blood flow velocity dynamics.     

On the efficacy of linear system analysis of renal autoregulationin rats

To assess the linearity of the mechanisms subserving renal blood flow autoregulation, broadband arterial pressure fluctuations at three different power levels were induced experimentally and the resulting renal blood flow responses were recorded. Linear system analysis methods were applied in both the time and frequency domain. In the frequency domain, spectral estimates employing fast Fourier transform (FFT), autoregressive moving average (ARMA), and moving average (MA) methods were used. The residuals (i.e. model prediction errors) of the MA model were smaller than the ARMA, model for all levels of arterial pressure forcings. The observed low coherence values and significant model residuals in the 0.02-0.05-Hz frequency range suggest that the tubuloglomerular feedback (TGF) active in this frequency range is a nonlinear vascular control mechanism. In addition, experimental results suggest that the operation of the TGF mechanism is more evident at low/moderate pressure fluctuations and becomes overwhelmed when the arterial pressure forcing is too high     

Soft tissue differentiation using multiband signatures of high resolution ultrasonic transmission tomography

In this paper, we are interested in soft tissue differentiation by multiband images obtained from the High-Resolution Ultrasonic Transmission Tomography (HUTT) system using a spectral target detection method based on constrained energy minimization (CEM). We have developed a new tissue differentiation method (called "CEM filter bank") consisting of multiple CEM filters specially designed for detecting multiple types of tissues. Statistical inference on the output of the CEM filter bank is used to make a decision based on the maximum statistical significance rather than the magnitude of each CEM filter output. We test and validate this method through three-dimensional interphantom/intraphantom soft tissue classification where target profiles obtained from an arbitrary single slice are used for differentiation over multiple other tomographic slices. The performance of the proposed classifier is assessed using receiver operating characteristic analysis. We also apply our method to classify tiny structures inside a bovine kidney and sheep kidneys. Using the proposed method we can detect physical objects and biological tissues such as styrofoam balls, chicken tissue, calyces, and vessel-duct successfully.     

Modeling of neural systems by use of neuronal modes

A methodology for modeling spike-output neural systems from input-output data is proposed, which makes use of “neuronal modes” (NM) and “multi-input threshold” (MT) operators. The modeling concept of NMs was introduced in a previously published paper (V.Z. Marmarelis, ibid., vol.36, p.15-24, 1989) in order to provide concise and general mathematical representations of the nonlinear dynamics involved in signal transformation and coding by a class of neural systems. The authors present and demonstrate (with computer simulations) a method by which the NMs are determined using the 1stand 2nd-order kernel estimates of the system, obtained from input-output data. The MT operator (i.e., a binary operator with multiple real-valued operands which are the outputs of the NMs) possesses an intrinsic refractory mechanism and generates the sequence of output spikes. The spike-generating characteristics of the MT operator are determined by the “trigger regions” defined on the basis of data. This approach is offered as a reasonable compromise between modeling complexity and prediction accuracy, which may provide a common methodological framework for modeling a certain class of neural systems     

Nonlinear Modeling of the Dynamic Effects of Infused Insulin on Glucose: Comparison of Compartmental With Volterra Models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted ldquominimal modelrdquo and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.     

Identification of Multi-Input Biological Systems

The Wiener theory of nonlinear system identification is extended to multi-input-output systems and experimentally applied. The experimental applicability of the method is discussed with regard to biological systems. It is shown that the method is well suited for the treatment of the idiosyncratic features of such systems: nonlinearities, short lifetimes of experimental preparations, and high noise content. A preliminary analysis is outlined, taking into account the characteristics of the system under study, which results in the determination of the parameters of the identifying experiment. An error analysis is made which can be used to increase the accuracy of the derived model within certain constraints. Several examples are given of the experimental application of the method to certain neural networks in a vertebrate retina (the catfish, Ictalurus punctatus, retina was used for these experiments). In addition to functional identification through white-noise stimulation, these same retinal neurons are identified morphologically through intracellular dye injection. The performance of the derived functional models, as compared to the physical system, is evaluated through a variety of tests and it is found to be very satisfactory.     

Nonlinear system analysis of renal autoregulation in normotensiveand hypertensive rats

The authors compared the dynamic characteristics in renal autoregulation of blood flow of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR), using both linear and nonlinear systems analysis. Linear analysis yielded only limited information about the differences in dynamics between SDR and SHR. The predictive ability, as determined by normalized mean-square errors (NMSE), of a third-order Volterra model is better than for a linear model. This decrease in NMSE with a third-order model from that of a linear model is especially evident at frequencies below 0.2 Hz. Furthermore, NMSE are significantly higher in SHR than SDR, suggesting a more complex nonlinear system in SHR. The contribution of the third-order kernel in describing the dynamics of renal autoregulation in arterial blood pressure and blood flow was found to be important. Moreover, the authors have identified the presence of nonlinear interactions between the oscillatory components of the myogenic mechanism and tubuloglomerular feedback (TGF) at the level of whole kidney blood flow in SDR. An interaction between these two mechanisms had previously been revealed for SDR only at the single nephron level. However, nonlinear interactions between the myogenic and TGF mechanisms are not detected for SHR