Multiple-input nonlinear modelling of cerebral haemodynamics using spontaneous arterial blood pressure, end-tidal CO2 and heart rate measurements.

In order to examine the effect of changes in heart rate (HR) upon cerebral perfusion and autoregulation, we include the HR signal recorded from 18 control subjects as a third input in a two-input model of cerebral haemodynamics that has been used previously to quantify the dynamic effects of changes in arterial blood pressure and end-tidal CO2upon cerebral blood flow velocity (CBFV) measured at the middle cerebral arteries via transcranial Doppler ultrasound. It is shown that the inclusion of HR as a third input reduces the output prediction error in a statistically significant manner, which implies that there is a functional connection between HR changes and CBFV. The inclusion of nonlinearities in the model causes further statistically significant reduction of the output prediction error. To achieve this task, we employ the concept of principal dynamic modes (PDMs) that yields dynamic nonlinear models of multi-input systems using relatively short data records. The obtained PDMs suggest model-driven quantitative hypotheses for the role of sympathetic and parasympathetic activity (corresponding to distinct PDMs) in the underlying physiological mechanisms by virtue of their relative contributions to the model output. These relative PDM contributions are subject-specific and, therefore, may be used to assess personalized characteristics for diagnostic purposes.

Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Linear Analysis.

Compartmental and data-based modeling of cerebral hemodynamics are alternative approaches that utilize distinct model forms and have been employed in the quantitative study of cerebral hemodynamics. This paper examines the relation between a compartmental equivalent-circuit and a data-based input-output model of dynamic cerebral autoregulation (DCA) and CO2-vasomotor reactivity (DVR). The compartmental model is constructed as an equivalent-circuit utilizing putative first principles and previously proposed hypothesis-based models. The linear input-output dynamics of this compartmental model are compared with data-based estimates of the DCA-DVR process. This comparative study indicates that there are some qualitative similarities between the two-input compartmental model and experimental results.

Model-based physiomarkers of cerebral hemodynamics in patients with mild cognitive impairment.

In our previous studies, we have introduced model-based "functional biomarkers" or "physiomarkers" of cerebral hemodynamics that hold promise for improved diagnosis of early-stage Alzheimer's disease (AD). The advocated methodology utilizes subject-specific data-based dynamic nonlinear models of cerebral hemodynamics to compute indices (serving as possible diagnostic physiomarkers) that quantify the state of cerebral blood flow autoregulation to pressure-changes (CFAP) and cerebral CO2 vasomotor reactivity (CVMR) in each subject. The model is estimated from beat-to-beat measurements of mean arterial blood pressure, mean cerebral blood flow velocity and end-tidal CO2, which can be made reliably and non-invasively under resting conditions. In a previous study, it was found that a CVMR index quantifying the impairment in CO2 vasomotor reactivity correlates with clinical indications of early AD, offering the prospect of a potentially useful diagnostic tool. In this paper, we explore the use of the same model-based indices for patients with amnestic Mild Cognitive Impairment (MCI), a preclinical stage of AD, relative to a control subjects and clinical cognitive assessments. It was found that the model-based CVMR values were lower for MCI patients relative to the control subjects.

On parsing the neural code in the prefrontal cortex of primates using principal dynamic modes.

Nonlinear modeling of multi-input multi-output (MIMO) neuronal systems using Principal Dynamic Modes (PDMs) provides a novel method for analyzing the functional connectivity between neuronal groups. This paper presents the PDM-based modeling methodology and initial results from actual multi-unit recordings in the prefrontal cortex of non-human primates. We used the PDMs to analyze the dynamic transformations of spike train activity from Layer 2 (input) to Layer 5 (output) of the prefrontal cortex in primates performing a Delayed-Match-to-Sample task. The PDM-based models reduce the complexity of representing large-scale neural MIMO systems that involve large numbers of neurons, and also offer the prospect of improved biological/physiological interpretation of the obtained models. PDM analysis of neuronal connectivity in this system revealed "input-output channels of communication" corresponding to specific bands of neural rhythms that quantify the relative importance of these frequency-specific PDMs across a variety of different tasks. We found that behavioral performance during the Delayed-Match-to-Sample task (correct vs. incorrect outcome) was associated with differential activation of frequency-specific PDMs in the prefrontal cortex.

Model-based quantification of cerebral hemodynamics as a physiomarker for Alzheimer's disease?

Previous studies have found that Alzheimer's disease (AD) impairs cerebral vascular function, even at early stages of the disease. This offers the prospect of a useful diagnostic method for AD, if cerebral vascular dysfunction can be quantified reliably within practical clinical constraints. We present a recently developed methodology that utilizes a data-based dynamic nonlinear closed-loop model of cerebral hemodynamics to compute "physiomarkers" quantifying the state of cerebral flow autoregulation to pressure-changes (CA) and cerebral CO2 vasomotor reactivity (CVMR) in each subject. This model is estimated from beat-to-beat measurements of mean arterial blood pressure, mean cerebral blood flow velocity and end-tidal CO2, which can be made reliably and non-invasively under resting conditions. This model may also take an open-loop form and comparisons are made with the closed-loop counterpart. The proposed model-based physiomarkers take the form of two indices that quantify the gain of the CA and CVMR processes in each subject. It was found in an initial set of clinical data that the CVMR index delineates AD patients from control subjects and, therefore, may prove useful in the improved diagnosis of early-stage AD.

Closed-loop dynamic modeling of cerebral hemodynamics.

The dynamics of cerebral hemodynamics have been studied extensively because of their fundamental physiological and clinical importance. In particular, the dynamic processes of cerebral flow autoregulation (CFA) and CO2 vasomotor reactivity have attracted broad attention because of their involvement in a host of pathologies and clinical conditions (e.g., hypertension, syncope, stroke, traumatic brain injury, vascular dementia, Alzheimer's disease, mild cognitive impairment etc.). This raises the prospect of useful diagnostic methods being developed on the basis of quantitative models of cerebral hemodynamics, if cerebral vascular dysfunction can be quantified reliably from data collected within practical clinical constraints. This paper presents a modeling method that utilizes beat-to-beat measurements of mean arterial blood pressure, cerebral blood flow velocity and end-tidal CO2 (collected non-invasively under resting conditions) to quantify the dynamics of CFA and cerebral vasomotor reactivity (CVMR). The unique and novel aspect of this dynamic model is that it is nonlinear and operates in a closed-loop configuration.

Design of optimal stimulation patterns for neuronal ensembles based on Volterra-type hierarchical modeling.

This paper presents a general methodology for the optimal design of stimulation patterns applied to neuronal ensembles in order to elicit a desired effect. The methodology follows a variant of the hierarchical Volterra modeling approach that utilizes input-output data to construct predictive models that describe the effects of interactions among multiple input events in an ascending order of interaction complexity. The illustrative example presented in this paper concerns the multi-unit activity of CA1 neurons in the hippocampus of a rodent performing a learned delayed-nonmatch-to-sample (DNMS) task. The multi-unit activity of the hippocampal CA1 neurons is recorded via chronically implanted multi-electrode arrays during this task. The obtained model quantifies the likelihood of having correct performance of the specific task for a given multi-unit (spatiotemporal) activity pattern of a CA1 neuronal ensemble during the 'sample presentation' phase of the DNMS task. The model can be used to determine computationally (off-line) the 'optimal' multi-unit stimulation pattern that maximizes the likelihood of inducing the correct performance of the DNMS task. Our working hypothesis is that application of this optimal stimulation pattern will enhance performance of the DNMS task due to enhancement of memory formation and storage during the 'sample presentation' phase of the task.

Dynamic nonlinear modeling of interactions between neuronal ensembles using principal dynamic modes.

We present a novel methodology for modeling the interactions between neuronal ensembles that utilizes the concept of Principal Dynamic Modes (PDM) and their associated nonlinear functions (ANF). This new approach seeks to reduce the complexity of the multi-input/multi-output (MIMO) model of the interactions between neuronal ensembles--an issue of critical practical importance in scaling up the MIMO models to incorporate hundreds (or even thousands) of input-output neurons. Global PDMs were extracted from the data using estimated first-order and second-order kernels and singular value decomposition (SVD). These global PDMs represent an efficient "coordinate system" for the representation of the MIMO model. The ANFs of the PDMs are estimated from the histograms of the combinations of PDM output values that lead to output spikes. For initial testing and validation of this approach, we applied it to a set of data collected at the pre-frontal cortex of a non-human primate during a behavioral task (Delayed Match-to-Sample). Recorded spike trains from Layer-2 neurons were viewed as the "inputs" and from Layer-5 neurons as the outputs. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The results indicate that this methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance.

Diagnostic biomarkers for Alzheimer's disease using dynamic nonlinear models based on Principal Dynamic Modes.

Sensitive and robust diagnostic biomarkers for Alzheimer's disease (AD) were sought using dynamic nonlinear models of the causal interrelationships among time-series (beat-to-beat) data of arterial blood pressure, end-tidal CO(2) and cerebral blood flow velocity collected in human subjects (4 AD patients and 4 control subjects). These models were based on Principal Dynamic Modes (PDM) and yielded a reliable biomarker for AD diagnosis in the form of the "Effective CO(2) Reactivity Index" (ECRI). The results from this initial set of subjects corroborated the efficacy of the ECRI biomarker for accurate AD diagnosis.

Improving bioassay sensitivity for neurotoxins detection using volterra based third order nonlinear analysis.

Based on a novel analytical method for analyzing short-term plasticity (STP) of the CA1 hippocampal region in vitro, a screening tool for the detection and classification of unknown chemical compounds affecting the nervous system was recently introduced [1], [2]. The recorded signal consisted of evoked population spike in response to Poisson distributed random train impulse stimuli. The developed analytical approach used the first order Volterra kernel and the Laguerre coefficients of the second order Volterra model as classification features [3]. The biosensor showed encouraging results, and was able to classify out of sample compounds correctly [2]. We have taken an exploratory step to investigate the advantage of introducing a third order model [4]. DAP5, an NMDA channel blocker, did not show major changes in the second order kernel and in its corresponding Laguerre coefficients. Data were reanalyzed using a third order model. DAP5 showed discernable changes in the third order kernel as well as in the some of the corresponding Laguerre coefficients. Hence, the third order Volterra based model has the potential to improve the sensitivity and the discriminatory power of the proposed bioassay.

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.

A modeling paradigm incorporating parametric and non-parametric methods.

A novel parametric/non-parametric modeling paradigm was defined and used in characterization of synaptic transmission. In this paradigm, parametric and nonparametric techniques were incorporated in a complementary manner. Non-parametric method was used to generalize experimental data and extract system input/output properties. It provided a quantitative and intuitive way to validate a parametric model with respect to general, complete input patterns. Biological processes or mechanisms missed by the conventional parametric modeling approach were revealed and subsequently included into the modified parametric model.

Modeling of nonlinear physiological systems with fast and slow dynamics. II. Application to cerebral autoregulation.

Dynamic autoregulation of cerebral hemodynamics in healthy humans is studied using the novel methodology of the Laguerre-Volterra network for systems with fast and slow dynamics (Mitsis, G. D., and V. Z. Marmarelis, Ann. Biomed. Eng. 30:272-281, 2002). Since cerebral autoregulation is mediated by various physiological mechanisms with significantly different time constants, it is used to demonstrate the efficacy of the new method. Results are presented in the time and frequency domains and reveal that cerebral autoregulation is a nonlinear and dynamic (frequency-dependent) system with considerable nonstationarities. Quantification of the latter reveals greater variability in specific frequency bands for each subject in the low and middle frequency range (below 0.1 Hz). The nonlinear dynamics are prominent also in the low and middle frequency ranges, where the frequency response of the system exhibits reduced gain.

Modeling of nonlinear physiological systems with fast and slow dynamics. I. Methodology.

Effective modeling of nonlinear dynamic systems can be achieved by employing Laguerre expansions and feedforward artificial neural networks in the form of the Laguerre-Volterra network (LVN). This paper presents a different formulation of the LVN that can be employed to model nonlinear systems displaying complex dynamics effectively. This is achieved by using two different filter banks, instead of one as in the original definition of the LVN, in the input stage and selecting their structural parameters in an appropriate way. Results from simulated systems show that this method can yield accurate nonlinear models of Volterra systems, even when considerable noise is present, separating at the same time the fast from the slow components of these systems effectively.

A novel network for nonlinear modeling of neural systems with arbitrary point-process inputs.

This paper address the issue of nonlinear model estimation for neural systems with arbitrary point-process inputs using a novel network that is composed of a pre-processing stage of a Laguerre filter bank followed by a single hidden layer with polynomial activation functions. The nonlinear modeling problem for neural systems has been attempted thus far only with Poisson point-process inputs and using cross-correlation methods to estimate low-order nonlinearities. The specific contribution of this paper is the use of the described novel network to achieve practical estimation of the requisite nonlinear model in the case of arbitrary (i.e. non-Poisson) point-process inputs and high-order nonlinearities. The success of this approach has critical implications for the study of neuronal ensembles, for which nonlinear modeling has been hindered by the requirement of Poisson process inputs and by the presence of high-order nonlinearities. The proposed methodology yields accurate models even for short input-output data records and in the presence of considerable noise. The efficacy of this approach is demonstrated with computer-simulated examples having continuous output and point-process output, and with real data from the dentate gyrus of the hippocampus.

Laser induced fluorescence attenuation spectroscopy: detection of hypoxia.

The development of a new laser-induced fluorescence (LIF) spectroscopy technique for the measurement of the attenuation spectrum of tissue is described. The technique, termed laser-induced fluorescence attenuation spectroscopy (LIFAS), has been applied to study the effects of hypoxia on the in vivo optical properties of renal and myocardial tissue in the 350-600-nm band. Excimer laser (Xe-Cl) is used to excite a small volume of the tissue (rabbit model, N = 20) and induce autofluorescence. The emitted LIF is monitored fiberoptically at two locations that are unevenly displaced about the fluorescing volume. The optical attenuation of the tissue is calculated from the dual LIF measurements by assuming an exponential decay of the fluorescence with distance. The results indicate that hypoxia modulates the attenuation spectrum leading to characteristic changes in its shape. Primarily, the spectral profile becomes more concave between 455 nm and 505 nm and two spectral peaks at about 540 and 580 nm disappear leaving in their place a single peak at about 555 nm. The attenuation spectra of normoxic and hypoxic tissue are used to train partial least squares multivariate model for spectral classification. The model detected acute renal and myocardial hypoxia with an accuracy greater than 90% (range: 90%-96%) and 74% (range: 74%-90%), respectively.

Application of a novel modeling method to the nonstationary properties of potentiation in the rabbit hippocampus.

This paper presents the first application of a novel methodology for nonstationary nonlinear modeling to neurobiological data consisting of extracellular population field potentials recorded from the dendritic layer of the dentate gyrus of the rabbit hippocampus under conditions of stimulus-induced potentiation. The experimental stimulus was a Poisson random sequence with a mean rate of 5 impulses/s applied to the perforant path, which was sufficient to induce a progressive potentiation of perforant path-evoked granule cell response. The modeling method utilizes a novel artificial neural network architecture, which is based on the general time-varying Volterra model. The artificial neural network is composed of parallel subnets of three-layer perceptrons with polynomial activation functions, with the output of each subnet modulated by an appropriate time function that models the system nonstationarities and gives the summative output its time-varying characteristics. For the specific application presented herein these time functions are sigmoidal functions with trainable slopes and inflection points. A possible mapping between the nonstationary components of the model and the mechanisms underlying potentiation changes in the hippocampus is discussed.

Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor.

The nonlinear dynamics of the mechanoelectrical transduction in an arthropod mechanoreceptor (cuticular slit sense organ of the spider Cupiennius salei) were studied using Volterra kernel measurements and the recently proposed method of principal dynamic modes. Since mechanoreceptors must operate with sufficient gain sensitivity to rapidly varying displacement stimuli over a broad bandwidth and for a wide range of amplitudes, the experimental data were generated by applying pseudorandom broadband mechanical displacements of various mean levels to the cuticular slits. The recorded response data were intracellular current and potential. The purpose of this paper is to demonstrate the use of the principal dynamic mode (PDM) methodology in elucidating the nonlinear dynamics of a spider mechanoreceptor. The results obtained demonstrate that two PDMs suffice to provide a complete nonlinear dynamic model of this insect mechanoreceptor. The first PDM resembles the first-order kernel and has a low pass characteristic (position dependent), while the second PDM has a high-pass characteristic (velocity-dependent) and resides entirely in the second-order kernel (nonlinear adaptation). This study may serve as an example of the proper use of this new methodology for the analysis of nonlinear physiological systems.

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).

Modeling of nonlinear nonstationary dynamic systems with a novel class of artificial neural networks.

This paper introduces a novel neural-network architecture that can be used to model time-varying Volterra systems from input-output data. The Volterra systems constitute a very broad class of stable nonlinear dynamic systems that can be extended to cover nonstationary (time-varying) cases. This novel architecture is composed of parallel subnets of three-layer perceptrons with polynomial activation functions, with the output of each subnet modulated by an appropriate time function that gives the summative output its time-varying characteristics. The paper shows the equivalence between this network architecture and the class of time-varying Volterra systems, and demonstrates the range of applicability of this approach with computer-simulated examples and real data. Although certain types of nonstationarities may not be amenable to this approach, it is hoped that this methodology will provide the practical tools for modeling some broad classes of nonlinear, nonstationary systems from input-output data, thus advancing the state of the art in a problem area that is widely viewed as a daunting challenge.