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The emerging paradigm of Machine to Machine (M2M)-driven Internet of Things (IoT), where physical objects are not disconnected from the virtual world but aim at collectively provide contextual services, calls for enhanced and more energy-efficient resource management approaches. In this paper, the problem is addressed through a joint interest, physical and energy-aware clustering and resource management framework, capitalizing on the wireless powered communication (WPC) technique. Within the proposed framework the numerous M2M devices initially form different clusters based on the low complexity Chinese Restaurant Process (CRP), properly adapted to account for interest, physical and energy related factors. Following that, a cluster-head is selected among the members of each cluster. The proposed approach enables the devices of a cluster with the support of the cluster-head to harvest and store energy in a stable manner through Radio Frequency (RF) signals adopting the WPC paradigm, thus prolonging the operation of the overall M2M network. Each M2M device is associated with a generic utility function, which appropriately represents its degree of satisfaction in relation to the consumed transmission power. Based on the distributed nature of the M2M network, a maximization problem of each device's utility function is formulated as a non-cooperative game and its unique Nash equilibrium point is determined, in terms of devices’ optimal transmission powers. Considering the devices’ equilibrium transmission powers, the optimal charging transmission powers of the cluster-heads are derived. The performance of the proposed approach is evaluated via modeling and simulation and under various topologies and scenarios, and its operational efficiency and effectiveness is demonstrated.

We investigated the correlation of epileptic seizure onset times with long term EEG functional brain network properties. To do so, we constructed binary functional brain networks from long-term, multichannel electroencephalographic data recorded from nine patients with epilepsy. The corresponding network properties were quantified using the average network degree. It was found that the network degree (as well as other network properties such as the network efficiency and clustering coefficient) exhibited large fluctuations over time; however, it also exhibited specific periodic temporal structure over different time scales (1.5hr-24hr periods) that was consistent across subjects. We investigated the correlation of the phases of these network periodicities with the seizure onset by using circular statistics. The results showed that the instantaneous phases of the 3.5hr, 5.5hr, 12hr and 24hr network degree periodic components are not uniformly distributed, suggesting that functional network properties are related to seizure generation and occurrence.

Orthonormal function expansions have been used extensively in the context of linear and nonlinear systems identification, since they result in a significant reduction in the number of required free parameters. In particular, Laguerre basis expansions have been used in the context of biological/ physiological systems identification, due to the exponential decaying characteristics of the Laguerre orthonormal basis, the rate of which is determined by the Laguerre parameter α. A critical aspect of the Laguerre expansion technique is the selection of the model structural parameters, i.e., polynomial model order for nonlinear systems, number of Laguerre functions and value of the Laguerre parameter α. This selection is typically made by trial-and-error procedures on the basis of the model prediction error. In the present paper, we formulate the Laguerre expansion technique in a Bayesian framework. Based on this formulation, we derive analytically the posterior distribution of the α parameter and the model evidence, in order to perform model order selection. We also demonstrate the performance of the proposed method by simulated examples and compare it to alternative statistical criteria for model order selection. ©2010 IEEE.

We present a random forest (RF) classification and regression technique to predict, intraoperatively, the unified Parkinson's disease rating scale (UPDRS) improvement after deep brain stimulation (DBS). We hypothesized that a data-informed combination of features extracted from intraoperative microelectrode recordings (MERs) can predict the motor improvement of Parkinson's disease patients undergoing DBS surgery. We modified the employed RFs to account for unbalanced datasets and multiple observations per patient, and showed, for the first time, that only five neurophysiologically interpretable MER signal features are sufficient for predicting UPDRS improvement. This finding suggests that subthalamic nucleus (STN) electrophysiological signal characteristics are strongly correlated to the extent of motor behavior improvement observed in STN-DBS.

The use of a GPGPU programming paradigm (running CUDA-enabled algorithms on GPU cards) in biomedical engineering and biology-related applications have shown promising results. GPU acceleration can be used to speedup computation-intensive models, such as the mathematical modeling of biological systems, which often requires the use of nonlinear modeling approaches with a large number of free parameters. In this context, we developed a CUDA-enabled version of a model which implements a nonlinear identification approach that combines basis expansions and polynomial-type networks, termed Laguerre-Volterra networks and can be used in diverse biological applications. The proposed software implementation uses the GPGPU programming paradigm to take advantage of the inherent parallel characteristics of the aforementioned modeling approach to execute the calculations on the GPU card of the host computer system. The initial results of the GPU-based model presented in this work, show performance improvements over the original MATLAB model.

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.

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 CO 2 upon 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.

Treating brain as a complex system is currently among the most popular approaches that are used to understand its function and explain encephalopathies. The networked epileptic brain has already been studied through various neuroimaging modalities based on estimates of functional connectivity. Here, we suggest that additional insights to epileptogenesis can be gained with an appropriate description on the network (re)organization dynamics as these are reflected in surface EEG measurements. Our approach commences with a pattern analytic step that turns a time series of connectivity patterns into a symbolic time series. The condensed dynamics are then analyzed by means of Markov chain modeling and a motif detection algorithm. Both descriptions yield novel dynamic characteristics that can capture the progression towards an epileptic crisis. Conceptually, our work adds to the emerging field of “chronnectomics”. Empirically, the obtained results based on actual experimental data are very encouraging and deserve further consideration.

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It is fairly established that dynamic recordings of functional activity maps can naturally and efficiently be represented by functional connectivity networks. In this article we study weighted and fully-connected brain networks, created from electroencephalographic (EEG) measurements that concern patients with focal and generalized epilepsy. We introduce a totally new methodology that has never been utilized before and that investigates weighted and fully-connected networks, which includes eigen-decomposition analysis, feature extraction and quantitative comparisons among entire graph datasets. Our goal is to establish epileptic seizure detection/prediction rules, by identifying repetitive EEG activity in patients before and after each seizure onset. In the present paper we treat each brain network as a weighted and full adjacency matrix, without cutting, binarizing or ignoring any values. In this way, it is the first time that the full structure of the connectivity weighing profile is exploited. Also apart from graph theory approaches, mathematical models such as eigen-decomposition analysis are used in our research, in order to study and analyze brain networks. Finally, we present and discuss the results and conclusions of our new method, which are in line with earlier EEG epilepsy findings and demonstrate a standard EEG behavior in both the postictal and preictal period.

Item does not contain fulltext Cerebral autoregulation is the intrinsic ability of the brain to maintain adequate cerebral perfusion in the presence of blood pressure changes. A large number of methods to assess the quality of cerebral autoregulation have been proposed over the last 30 years. However, no single method has been universally accepted as a gold standard. Therefore, the choice of which method to employ to quantify cerebral autoregulation remains a matter of personal choice. Nevertheless, given the concept that cerebral autoregulation represents the dynamic relationship between blood pressure (stimulus or input) and cerebral blood flow (response or output), transfer function analysis became the most popular approach adopted in studies based on spontaneous fluctuations of blood pressure. Despite its sound theoretical background, the literature shows considerable variation in implementation of transfer function analysis in practice, which has limited comparisons between studies and hindered progress towards clinical application. Therefore, the purpose of the present white paper is to improve standardisation of parameters and settings adopted for application of transfer function analysis in studies of dynamic cerebral autoregulation. The development of these recommendations was initiated by (but not confined to) theCerebral Autoregulation Research Network(CARNet -www.car-net.org).

It is well known that the blood-oxygen level dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI) is influenced - in addition to neuronal activity - by fluctuations in physiological signals, including arterial CO2. For instance, even spontaneous CO2 fluctuations have been shown to influence the BOLD fMRI signal regionally. Related to this, studies of functional connectivity between different brain regions, performed when the subject is at rest, may be confounded by the effects of physiological noise. Moreover, resting functional connectivity has been shown to vary with respect to time (dynamic functional connectivity), with the sources of this variation not fully understood at present. In this context, in the present paper we examine the relation between dynamic functional connectivity patterns and the properties of the end-tidal CO2 signal (PETCO2) using resting-state fMRI measurements from 12 healthy subjects. The results demonstrate that there exists a modulatory effect of the correlation strength between PETCO2 and the BOLD signal on dynamic resting functional connectivity. The extent to which this effect was observed was found to be strongly dependent on the data analysis methodology.

Automatic detection and removal of muscle artifacts plays an important role in long-term scalp electroencephalography (EEG) monitoring, and muscle artifact detection algorithms have been intensively investigated. This paper proposes an algorithm for automatic muscle artifacts detection and removal using canonical correlation analysis (CCA) and wavelet transform (WT) in epochs from long-term EEG recordings. The proposed method first performs CCA analysis and then conducts wavelet decomposition on the canonical components within a specific frequency range and selects a subset of the wavelet coefficients for subsequent processing. A set of features, including the mean of wavelet coefficients and the canonical component autocorrelation values, are extracted from the above analysis and subsequently used as input in a random forest (RF) classifier. The RF classifier produces a similarity measure between observations and selects a subset of the most important features by comparing the original data with a set of synthetic data that is constructed based on the latter. The RF predictor output is finally used in combination with unsupervised clustering algorithms to discriminate between contaminated and non-contaminated EEG epochs. The proposed method is evaluated in epochs of 30 min from scalp EEG recordings obtained from three patients with epilepsy and yields a sensitivity of 71% and 80%, as well as a specificity of 81% and 85% for k-means and spectral clustering, respectively.

The recording of brain event-related potentials (ERPs) is a widely used technique to investigate the neural basis of sensory perception and cognitive processing in humans. A commonly used assumption, when dealing with potentially overlapping ERPs elicited by successive stimuli with interstimulus interval (ISI) smaller than the latency of the ERPs, is that their interaction is linear. These overlaps are usually dealt by using averaged waveforms, mostly to enhance the signal-to-noise ratio (SNR) and performing algebraic waveform subtractions. In this paper, we examine the hypothesis of linear interactions by providing a statistical framework that examines the presence of nonlinear additive effects between overlapping ERPs elicited by successive stimuli with short ISIs. The statistical analysis is designed for single trial rather than averaged waveforms. The results suggest that there are no nonlinear additive effects due to the time overlap per se but that, for the range of ISIs examined, the second ERP is modulated by the presence of the first stimulus irrespective of whether there is time overlap or not. In other words, two ERPs that overlap in time can still be written as an addition of two ERPs, with the second ERP being different to the first. The modulation effect on the second ERP by the first stimulus varies for different ISIs.

Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results., European Territorial Cooperation Programmes, National Funds of Greece and Cyprus

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The Electroencephalogram (EEG) is often contaminated by muscle artifacts. EEG is a widely used recording technique for the study of many brain related diseases such as epilepsy. The detection and removal of muscle artifacts from the EEG signal poses a real challenge and is crucial for the reliable interpretation of EEG-based quantitative measures. In this paper, an automatic method for detection and removal of muscle artifacts from scalp EEG recordings, based on canonical correlation analysis (CCA), is introduced. To this end we exploit the fact that the EEG signal may exhibit altered autocorrelation structure and spectral characteristics during periods when it is contaminated by muscle activity. Therefore, we design classifiers in order to automatically discriminate between contaminated and non-contaminated EEG epochs using features based on the aforementioned quantities and examine their performance on simulated data and in scalp EEG recordings obtained from patients with epilepsy.

We extracted adaptive univariate and multivariate dynamic models of cerebral hemodynamics during resting and hypercapnic conditions using a Recursive Least Squares estimation scheme with multiple adaptive forgetting factors. The time dependent relationship between mean arterial blood pressure (MABP), end-tidal CO2 tension (PETCO2) and middle cerebral artery blood flow velocity (CBFV) was assessed using Laguerre - Volterra models with time varying coefficients. The results suggest that the addition of PETCO2 as a second input yields more accurate and less nonstationary estimates, indicating that unobservable physiological variables are important in the context of nonstationary systems modeling, and particularly for assessing cerebral hemodynamics and autoregulation.

The derivation and application of a method designed to investigate the focusing properties of pulsed baseband signals of short pulsewidth (/spl sim/1 ns) in biological tissue media are reported. To this end, sources fed from TEM waveguides, concentrically placed at the periphery of a three-layer cylindrical lossy model, are assumed. A Fourier-series-based methodology, appropriate for a useful class of pulse train incident signals, is presented and utilized to study the dynamics of pulse propagation inside the tissue medium. The propagation of each spectral component of the incident field within the tissue medium is analyzed by applying an integral-equation technique and a Fourier-series representation is used in order to obtain the time dependence of the electromagnetic fields produced at any point within tissue due to the pulsed excitation of the array elements. Numerical results are computed and presented at several points in a three-layer geometry, 20 cm in diameter, irradiated by an eight-element waveguide array. Focusing at a specific point of interest within tissue is achieved by properly adjusting the time delay of the signals injected to the individual applicators of the array.

We investigated the nonstationary properties of cerebral hemodynamics by examining the relationship between mean arterial blood pressure (MABP), end-tidal CO 2 tension (P ETCO2 ) and middle cerebral artery blood flow velocity (CBFV) during resting and hypercapnic conditions. To this end, we employed univariate and multivariate time-varying Laguerre-Volterra models as well as a Recursive Least Squares estimation scheme with multiple adaptive forgetting factors. The results reveal the presence of nonstationarities mainly in the very low frequency range, which are more pronounced and irregular for the CO 2 reactivity component.

Seizure detection and prediction studies using scalp- or intracranial-EEG measurements often focus on short-length recordings around the occurrence of the seizure, normally ranging between several seconds and up to a few minutes before and after the event. The underlying assumption in these studies is the presence of a relatively constant EEG activity in the interictal period, that is presumably interrupted by the occurrence of a seizure, at the time the seizure starts or slightly earlier. In this study, we put this assumption under test, by examining long-duration scalp EEG recordings, ranging between 22 and 72 hours, of five patients with epilepsy. For each patient, we construct functional brain networks, by calculating correlations between the scalp electrodes, and examine how these networks vary in time. The results suggest not only that the network varies over time, but it does so in a periodic fashion, with periods ranging between 11 and 25 hours.

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In this work, we present how optimized treatment interruptions during chemotherapy may be used to control drug-resistance, a major challenge for clinicians worldwide. Specifically, we examine resistance in cancer and HIV/AIDS. For each disease, we use mathematical models alongside real data to represent the respective complex biological phenomena and optimal control algorithms to design optimized treatment schedules aiming at controlling disease progression and patient death. In both diseases, it is shown that the key to controlling resistance is the optimal management of the frequency and magnitude of treatment interruptions as a way to facilitate the interplay between the competitive resistant/sensitive strains.

Prophylactic cranial irradiation (PCI) is a standard treatment technique for small cell lung cancer patients. However, there is evidence that this technique may contribute to neurocognitive deficits. Therefore the study of anatomical and functional connectivity in patients undergoing PCI as well as their neurocognitive functionality, depending on the type of disease and the phase of treatment and time of clinical examination, is of considerable interest. In this context, we investigate whether there are any differentiations in brain function during resting state and task-related functional magnetic resonance imaging (fMRI) in patients with cancer before PCI compared to healthy subjects. During a finger tapping task, the brain regions that were activated bilaterally for both groups are consistent with previous studies. During rest, the Default Mode Network (DMN) was identified in both groups. The preliminary results presented herein are subject to further investigation with larger patient and control group.

We suggest a multi-process dynamic model and a sequential bayesian forecasting method of tumor-specific growth. The mixture model uses prior information obtained from the general population and becomes more individualized as more observations from the tumor are sequentially taken into account. In this study we propose utilizing all available tumor-specific information up to date to approximate the unknown multi-scale process of tumor growth over time, in a stochastic context. The validation of our approach was performed with experimental data from mice and the results show that after few observations from a tumor are obtained and included in the model, the latter becomes more individualized, in the sense that its parameters are adjusted in order to reect the growth of each individual tumor, yielding more precise estimates of its size.

This study deals with the planning of anti-cancer therapy in mice with drug-resistance using mathematical modeling and optimal control. By making use of experimental data in order to develop our mathematical models, we herein propose a promising methodology by which cancer progression in mice with resistance to docetaxel, a widely-used anti-cancer drug, can be controlled. We leverage experimental findings on the reduced fitness of drug-resistant cells, in terms of their ability to compete for nutrients with the sensitive cells, in order to control total cancer growth; during therapy, growth of sensitive cells is inhibited, however during a drug-free period the sensitive cells have an advantage and prevail. Using optimal control, we demonstrate that the optimal planning of the frequency and magnitude of treatment interruptions is key to the control of cancer progression in subjects with resistance and should be further investigated in an experimental setting.

Extracellular recordings in the area of the subthalamic nucleus (STN) of Parkinson's disease patients undergoing deep brain stimulation comprise fast events, Action Potentials and slower events, known as Local Field Potentials (LFP). The LFP is believed to represent the synchronized input into the observed area, as opposed to the spike data, which represents the output. We have shown before that there is an input-output relationship between these two components in the STN. In the present paper, we extend these observations by using LFP-driven Volterra models and the Laguerre expansion technique to estimate nonlinear dynamic models which are able to predict the recorded spiking activity. To this end, we rigorously examine the optimal model order. The improved performance of the second-order Volterra models indicates that there is a nonlinear relationship between the LFP and the spiking activity. To obtain a more compact and readily interpretable model, the most significant dynamic components of the identified Volterra models are extracted using principal dynamic mode analysis.

Purpose: To demonstrate the feasibility of measuring the temporal dynamics of cerebral lactate concentration and examine these dynamics in human subjects using magnetic resonance spectroscopy (MRS) during hypoxia. Materials and Methods: A respiratory protocol consisting of 10-minute baseline normoxia, 20-minute inspiratory hypoxia, and ending with 10-minute normoxic recovery was used, throughout which lactate-edited MRS was performed. This was repeated four times in three subjects. A separate session was performed to measure blood lactate. Impulse response functions using end-tidal oxygen and blood lactate as system inputs and cerebral lactate as the system output were examined to describe the dynamics of the cerebral lactate response to a hypoxic challenge. Results: The average lactate increase was 20% 6 15% during the last half of the hypoxic challenge. Significant changes in cerebral lactate concentration were observed after 400 seconds. The average relative increase in blood lactate was 188% 6 95%. The temporal dynamics of cerebral lactate concentration was reproducibly demonstrated with 200-second time bins of MRS data (coefficient of variation 0.063 6 0.035 between time bins in normoxia). The across-subject coefficient of variation was 0.333. Conclusion: The methods for measuring the dynamics of the cerebral lactate response developed here would be useful to further investigate the brain’s response to hypoxia.

We consider a linear dynamic model for tumor growth evolution. A number of temporal statistical models for tumor growth exist in the literature. In the majority of these cases the employed models are formulated in a deterministic context, providing no information on their uncertainty. Some of these are theoretically well defined and very useful in practice, e.g. to define general optimal treatment protocols through nonlinear constrained optimization. Nevertheless a challenging task is the estimation of the model parameters for a specific individual since, especially in humans, it is not feasible to collect a large number of tumor size values with respect to time, as the tumor is removed immediately after diagnosis in most cases. Therefore, we suggest a probabilistic model for personalized sequential tumor growth prediction, given only a few observed data and an a priori information regarding the average response to a specific type of cancer of the population to which the subject belongs. We validated the proposed model with experimental data from mice and the results are promising.

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‘Small-world’ neuronal networks are characterized by strong clustering in combination with short path length, and assist the progress of synchronization and conceivably seizure procreation. In this article we aim to investigate if the brain networks display ‘small-world’ features during seizures, by using graph-theoretic measures as well as scalp EEG recordings from patients with focal and generalized epilepsy. Specifically, we used linear cross-correlation to characterize patterns between nodes in scalp EEG recordings of 5 patients for 3 periods of interest: before, during and after seizure onset. For each period we reconstruct graphs from the linear cross-correlation calculations and use different network measures to characterize the graphs such as clustering coefficient, characteristic path length, betweenness centrality and network small-world-ness. In three (out of five) patients, our results suggest that shortly after seizure onset and in the early postictal period the brain network changes towards a more small-world structure, in agreement with earlier graph-theoretic based results related to epilepsy. However, for one patient the opposite was observed: small-worldness decreased after seizure onset. Finally, for one patient we could observe no differences in the network properties before and after the onset. These preliminary results suggest the potential use of graph-theoretic measures to quantify brain dynamics before and during seizures after further refinements.

This paper presents our work on the application of mathematical modeling and optimal control techniques in the modeling of tumor progression and optimal treatment planning. We present a pharmacokinetic-pharmacodynamic approach to the modeling of tumor progression in mice. Specifically, we describe colon cancer progression in both untreated mice as well as mice treated with anti-cancer agents. We also a present pharmacokinetic model to describe the drug kinetics in the body as well as toxicity models to describe the severity of side-effects. Lastly, we propose a promising methodology by which cancer progression in mice with drug-resistance can be controlled. By using optimal control, we demonstrate that the optimal planning of the frequency and magnitude of treatment breaks is key to cancer control in subjects with resistance and should be further investigated in an experimental setting, which is currently underway.

We present a computational scheme to obtain adaptive non-linear, multiple-input models of the Volterra-Wiener class, by utilizing Laguerre expansions of Volterra kernels in a recursive least-squares formulation. Function expansions have been proven successful in systems identification as they result in a significant reduction of the required free parameters, which is a major limiting factor particularly for nonlinear systems, whereby this number depends exponentially on the nonlinear system order. We apply this scheme in order to obtain adaptive estimates for a two-input model of cerebral hemodynamics, where the two inputs are arterial blood pressure (ABP) and end-tidal CO 2 (P ETCO2 ) variations and the output is cerebral blood flow velocity (CBFV) variations, by utilizing long-duration (40 min) experimental measurements of spontaneous variations of these signals in healthy humans. Maintenance of a relatively steady cerebral blood flow, despite changes in arterial pressure, is critical in order to meet the high metabolic demands of the brain. This is achieved by the synergistic action of various physiological factors, which may vary over different time-scales and also exhibit nonstationarities. We quantify these nonstationarities for the two main physiological determinants of cerebral blood flow variability (i.e., arterial pressure and arterial CO 2 ) by considering one- (ABP) and two-input (ABP and P ETCO2 ) models. The results illustrate the presence of nonstationarities which are frequency-dependent and also that incorporation of P ETCO2 as an additional input, results in estimates of dynamic pressure autoregulation that are more consistent with respect to time.

We present a computational scheme to obtain adaptive non-linear, multiple-input models of the Volterra-Wiener class, by utilizing function expansions of the Volterra kernels in a recursive least-squares formulation. Function expansions have been proven successful in linear and nonlinear systems identification as they result in a significant reduction of the required free parameters, which is a major limiting factor particularly for nonlinear systems, whereby this number depends exponentially on the nonlinear system order. We illustrate the performance of the proposed scheme by presenting results for a simulated linear two-input system with time-varying characteristics.