Hebbian mechanisms help explain development of multisensory integration in the superior colliculus: a neural network model.

The superior colliculus (SC) integrates relevant sensory information (visual, auditory, somatosensory) from several cortical and subcortical structures, to program orientation responses to external events. However, this capacity is not present at birth, and it is acquired only through interactions with cross-modal events during maturation. Mathematical models provide a quantitative framework, valuable in helping to clarify the specific neural mechanisms underlying the maturation of the multisensory integration in the SC. We extended a neural network model of the adult SC (Cuppini et al., Front Integr Neurosci 4:1-15, 2010) to describe the development of this phenomenon starting from an immature state, based on known or suspected anatomy and physiology, in which: (1) AES afferents are present but weak, (2) Responses are driven from non-AES afferents, and (3) The visual inputs have a marginal spatial tuning. Sensory experience was modeled by repeatedly presenting modality-specific and cross-modal stimuli. Synapses in the network were modified by simple Hebbian learning rules. As a consequence of this exposure, (1) Receptive fields shrink and come into spatial register, and (2) SC neurons gained the adult characteristic integrative properties: enhancement, depression, and inverse effectiveness. Importantly, the unique architecture of the model guided the development so that integration became dependent on the relationship between the cortical input and the SC. Manipulations of the statistics of the experience during the development changed the integrative profiles of the neurons, and results matched well with the results of physiological studies.

A semantic model to study neural organization of language in bilingualism.

A neural network model of object semantic representation is used to simulate learning of new words from a foreign language. The network consists of feature areas, devoted to description of object properties, and a lexical area, devoted to words representation. Neurons in the feature areas are implemented as Wilson-Cowan oscillators, to allow segmentation of different simultaneous objects via gamma-band synchronization. Excitatory synapses among neurons in the feature and lexical areas are learned, during a training phase, via a Hebbian rule. In this work, we first assume that some words in the first language (L1) and the corresponding object representations are initially learned during a preliminary training phase. Subsequently, second-language (L2) words are learned by simultaneously presenting the new word together with the L1 one. A competitive mechanism between the two words is also implemented by the use of inhibitory interneurons. Simulations show that, after a weak training, the L2 word allows retrieval of the object properties but requires engagement of the first language. Conversely, after a prolonged training, the L2 word becomes able to retrieve object per se. In this case, a conflict between words can occur, requiring a higher-level decision mechanism.

A neural network model of semantic memory linking feature-based object representation and words.

Recent theories in cognitive neuroscience suggest that semantic memory is a distributed process, which involves many cortical areas and is based on a multimodal representation of objects. The aim of this work is to extend a previous model of object representation to realize a semantic memory, in which sensory-motor representations of objects are linked with words. The model assumes that each object is described as a collection of features, coded in different cortical areas via a topological organization. Features in different objects are segmented via gamma-band synchronization of neural oscillators. The feature areas are further connected with a lexical area, devoted to the representation of words. Synapses among the feature areas, and among the lexical area and the feature areas are trained via a time-dependent Hebbian rule, during a period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from acoustic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits).

Visual and computer-based detection of slow eye movements in overnight and 24-h EOG recordings.

OBJECTIVE: The present work aimed to evaluate the performance of an automatic slow eye movement (SEM) detector in overnight and 24-h electro-oculograms (EOG) including all sleep stages (1, 2, 3, 4, REM) and wakefulness. METHODS: Ten overnight and five 24-h EOG recordings acquired in healthy subjects were inspected by three experts to score SEMs. Computerized EOG analysis to detect SEMs was performed on 30-s epochs using an algorithm based on EOG wavelet transform, recently developed by our group and initially validated by considering only pre-sleep wakefulness, stages 1 and 2. RESULTS: The validation procedure showed the algorithm could identify epochs containing SEM activity (concordance index k=0.62, 80.7% sensitivity, 63% selectivity). In particular, the experts and the algorithm identified SEM epochs mainly in pre-sleep wakefulness, stage 1, stage 2 and REM sleep. In addition, the algorithm yielded consistent indications as to the duration and position of SEM events within the epoch. CONCLUSIONS: The study confirmed SEM activity at physiological sleep onset (pre-sleep wakefulness, stage 1 and stage 2), and also identified SEMs in REM sleep. The algorithm proved reliable even in the stages not used for its training. SIGNIFICANCE: The study may enhance our understanding of SEM meaning and function. The algorithm is a reliable tool for automatic SEM detection, overcoming the inconsistency of manual scoring and reducing the time taken by experts.

A mathematical model for the prediction of solute kinetics, osmolarity and fluid volume changes during hemodiafiltration with on-line regeneration of ultrafiltrate (HFR).

Hemodiafiltration with on-line regeneration of ultrafiltrate (HFR) is a technique indicated for the treatment of dialysis patients affected by inflammatory syndrome and malnutrition. In the present work, a mathematical model, which describes intradialytic fluid and solute kinetics during standard diffusive dialysis, has been adapted to analyze solutes and fluid dynamics during HFR. The model is an improved version of our previous ones, and represents a good compromise between simplicity and reliability. It considers the intradialytic kinetics of sodium, potassium and urea, and two body fluid compartments: intracellular and extracellular. Moreover, the model includes simple equations to predict the intradialytic time pattern of osmolarity. The model has been experimentally validated by using 9 HFR sessions on 9 patients (one per each patient), comparing the time course of plasma solutes and osmolarity measured every 30 minutes during HFR, with those predicted by the model. Predictions are performed a priori, i.e., without any parameter adjustment, but just starting from knowledge of a few quantities (plasma sodium, potassium, urea, osmolarity and body weight) at the beginning of the session. The average deviations between model and real data (sodium: 1.9 mEq/L; potassium: 0.32 mEq/L; urea: 1.04 mmol/L; osmolarity: 5.02 mosm/L) are of the same order as measurement errors and similar to those obtained using our previous models in standard and profiled hemodialysis. Moreover, the prediction on sodium concentration only scarcely worsens (from 1.9 to 2.02 mEq/L) if default values are used for the initial value of other solutes in blood (i.e., if the algorithm uses only initial body weight and initial sodium concentration in plasma). The results confirm the good predictive capacity of the model in HFR, and suggest its possible innovative use to optimize sodium balance in HFR, from knowledge of only the sodium concentration in the ultrafiltrate.

Object segmentation and reconstruction via an oscillatory neural network: interaction among learning, memory, topological organization and gamma-band synchronization.

Synchronization of neuronal activity in the gamma-band has been shown to play an important role in higher cognitive functions, by grouping together the necessary information in different cortical areas to achieve a coherent perception. In the present work, we used a neural network of Wilson-Cowan oscillators to analyze the problem of binding and segmentation of high-level objects. Binding is achieved by implementing in the network the similarity and prior knowledge Gestalt rules. Similarity law is realized via topological maps within the network. Prior knowledge originates by means of a Hebbian rule of synaptic change; objects are memorized in the network with different strengths. Segmentation is realized via a global inhibitor which allows desynchronisation among multiple objects avoiding interference. Simulation results performed with a 40x40 neural grid, using three simultaneous input objects, show that the network is able to recognize and segment objects in several different conditions (different degrees of incompleteness or distortion of input patterns), exhibiting the higher reconstruction performances the higher the strength of object memory. The presented model represents an integrated approach for investigating the relationships among learning, memory, topological organization and gamma-band synchronization.

Short-term autonomic control of the cardio-respiratory system: a summary with the help of a comprehensive mathematical model.

The system which provides short-term cardiovascular regulation has a very complex structure, resulting from the non-linear interaction among several different mechanisms: they include baroreceptors, peripheral chemoreceptors, lung-stretch receptors, a direct CNS response to hypoxia and hypercapnia, local vessel response to changes in blood gas content. Furthermore, during dynamic exercise a feedforward mechanism anticipates cardiovascular requirements, and interacts with the respiratory and muscle pumps. Aim of this work is to summarize the complexity of this system, and to point out the role of individual mechanisms and their mutual relations, with the help of a comprehensive mathematical model developed by the authors in previous years. Examples of system response are discussed during various acute cardiovascular perturbations (pressure changes, changes in blood gas content, dynamic exercise) and model results compared with existing data in the literature. These examples emphasize the great complexity, richness and variability of the autonomic cardiovascular control system. Simulations suggest that mathematical models and computer simulation techniques may represent essential tools to comprehend and deepen our understanding of complex, multifactorial systems, the behaviour of which cannot be fully revealed by simple qualitative analysis. Models play an important role in modern physiology as a repository of knowledge and to integrate disparate data inside an integrative coherent structure.

Modelling study of the acute cardiovascular response to hypocapnic hypoxia in healthy and anaemic subjects.

The present study analyses the cardiovascular response to acute hypocapnic hypoxia (simulating the effect of respiration at high altitude) both in healthy, unacclimatised subjects and in subjects with moderate anaemia, by means of a mathematical model of short-term cardiovascular regulation. During severe hypoxia, cardiac output and heart rate (HR) exhibit a significant increase compared with the basal level (cardiac output: +90%; HR: +64%). Systemic arterial pressure remains quite constant or shows a mild increase. Coronary blood flow increases dramatically (+200%), thus maintaining a constant oxygen delivery to the heart. However, blood oxygen utilisation in the heart augments, to fulfil the increased power of the cardiac pump during hypoxia. Cerebral blood flow rises only at very severe hypoxia but, owing to the vasoconstrictory effect of hypocapnia, its increase (+80%) is insufficient to maintain oxygen delivery to the brain. The model suggests that a critical level for the aerobic metabolism in these organs (heart and brain) is reached at an oxygen partial pressure in arterial blood (PaO2) of approximately 25 mmHg. Moderate anaemia during normoxia is compensated by an increase in cardiac output (+22%), a decrease in total peripheral resistance (-30%) and an increase in O2 extraction from blood (+40%). As cardiovascular regulation mechanisms are already recruited in anaemic subjects at rest, their action soon becomes exhausted during hypocapnic hypoxia. Critical levels for vital functions are already reached at a PaO2 of approximately 45 mmHg.

Effects of cardiovascular parameter changes on heart rate variability: analysis by a mathematical model of short-term cardiovascular regulation.

A mathematical model of short-term cardiovascular regulation is used to investigate how heart period power spectrum reflects alterations in cardiovascular parameters. The model includes the pulsating heart, the systemic and pulmonary circulation, the mechanical effects of respiration on hemodynamics, two groups of receptors (arterial baroreceptors and lung-stretch receptors), the sympathetic and vagal efferent branches, several distinct effectors, and a very low frequency vasomotor noise. All parameters in the model are assigned on the basis of the physiological literature. With basal parameter values, the simulated heart period (HP) power spectrum exhibits a high frequency (HF) peak, synchronous with respiration (0.2 Hz) and a smaller low frequency (LF) component around 0.1 Hz. Model results stress that the features of the HP spectrum are influenced by several factors, other than strength and integrity of autonomic nervous system. In particular, sensitivity analyses reveal that alterations in total peripheral resistance and in left ventricle contractility affect HP spectrum markedly, by causing a change in the working point of the autonomic control mechanisms. The model may be useful in the physiopathological interpretation of heart rate variability, to relate changes in HP spectrum with autonomic and/or cardiovascular perturbations.

A wavelet based analysis of energy redistribution in scalp EEG during epileptic seizures.

In this work, wavelet decomposition and multiresolution analysis are used to explore the changes in scalp EEG signals during epileptic seizures. EEG tracings, which include non-epileptic periods, the beginning of seizure and the peak of seizure, have been decomposed in five details using order 10 Daubechies orthonormal wavelets. Energy has then been computed, at each detail, from square wavelet coefficients, in order to unmask the presence of brief episodes of energy relocation among different scales. Results reveal the existence of significant changes in energy distribution at seizure onset; this redistribution, however, exhibits significant differences from one patient to another, and also among different channels in the same patient. Some channels exhibit a significant energy increase at low scales (high frequencies greater than 20 Hz) at seizure onset, whereas energy drops at higher scales. Other channels, however, exhibit energy increase at high scales (frequency less than 15 Hz) revealing a predominance of low-frequency activity. These two patterns may be simultaneously present at seizure onset and may change with different spatial evolution during the subsequent seizure progression. Wavelet analysis appears as a powerful tool for extracting features relative to seizure, and to study their propagation among different regions in the scalp.

Comparative bioavailability study of a generic sustained release diclofenac sodium tablet.

The bioavailability of a generic diclofenac sodium sustained release tablet preparation (Zolterol, SR) was compared with the innovator product, Voltaren, SR. Twelve healthy adult male volunteers participated in the study, which was conducted according to a randomized, two-way crossover design with a wash out period of one week. The bioavailability of diclofenac was compared using the parameters area under the plasma concentration-time curve (AUC(0-infinity)), peak plasma concentration (Cmax) and time to reach peak plasma concentration (Tmax). No statistically significant difference was observed for both logarithmically transformed AUC(0-infinity), Cmax values and Tmax value of the two preparations.

Cardiovascular response to dynamic aerobic exercise: a mathematical model.

An original mathematical model of the cardiovascular response to dynamic exercise is presented. It includes the pulsating heart, the pulmonary and systemic circulation, a separate description of the vascular bed in active tissues, the local metabolic vasodilation in these tissues and the mechanical effects of muscular contractions on venous return. Moreover, the model provides a description of the ventilatory response to exercise and various neural regulatory mechanisms working on cardiovascular parameters. These mechanisms embrace the so-called central command, the arterial baroreflex and the lung inflation reflex. All parameters in the model have been given in accordance with physiological data from the literature. In this work, the model has been used to simulate the steady-state value of the main cardiorespiratory quantities at different levels of aerobic exercise and the temporal pattern in the transient phase from rest to moderate exercise. Results suggest that, with suitable parameter values the model is able accurately to simulate the cardiorespiratory response in the overall range of aerobic exercise. This response is characterised by a moderate hypertension (10-30%) and by a conspicuous increase in systemic conductance (80-130%), heart rate (64-150%) and cardiac output (100-200%). The transient pattern exhibits three distinct phases (lasting approximately 5s, 15s and 2 min), that reflect the temporal heterogeneity of the mechanisms involved. The model may be useful to improve understanding of exercise physiology and as an educational tool to analyse the complexity of cardiovascular and respiratory regulation.

A mathematical model of CO2 effect on cardiovascular regulation.

The effect of changes in arterial CO2 tension on the cardiovascular system is analyzed by means of a mathematical model. The model is an extension of a previous one that already incorporated the main reflex and local mechanisms triggered by O2 changes. The new aspects covered by the model are the O2-CO2 interaction at the peripheral chemoreceptors, the effect of local CO2 changes on peripheral resistances, the direct central neural system (CNS) response to CO2, and the control of central chemoreceptors on ventilation and tidal volume. A statistical comparison between model simulation results and various experimental data has been performed. This comparison suggests that the model is able to simulate the acute cardiovascular response to changes in blood gas content in a variety of conditions (normoxic hypercapnia, hypercapnia during artificial ventilation, hypocapnic hypoxia, and hypercapnic hypoxia). The model ascribes the observed responses to the complex superimposition of many mechanisms simultaneously working (baroreflex, peripheral chemoreflex, CNS response, lung-stretch receptors, local gas tension effect), which may be differently activated depending on the specific stimulus under study. However, although some experiments can be reproduced using a single basal set of parameters, reproduction of other experiments requires a different combination of the mechanism strengths (particularly, a different strength of the local CO2 mechanism on peripheral resistances and of the CNS response to CO2). Starting from these results, some assumptions to explain the striking differences reported in the literature are presented. The model may represent a valid support for the interpretation of physiological data on acute cardiovascular regulation and may favor the synthesis of contradictory results into a single theoretical setting.

Role of tissue hypoxia in cerebrovascular regulation: a mathematical modeling study.

This paper presents a mathematical model of cerebrovascular regulation, in which emphasis is given to the role of tissue hypoxia on cerebral blood flow (CBF). In the model. three different mechanisms are assumed to work on smooth muscle tension at the level of large and small pial arteries: CO2 reactivity, tissue hypoxia, and a third mechanism necessary to provide good reproduction of autoregulation to cerebral perfusion pressure (CPP) changes. Using a single set of parameters for the mechanism gains, assigned via a best fitting procedure, the model is able to reproduce the pattern of pial artery caliber and CBF under a large variety of physiological stimuli, either acting separately (hypoxia, CPP changes, CO2 pressure changes) or combination (hypercapnia+hypoxia; hypercapnia+hypotension). Furthermore, the model can explain the increase in CBF and the vasoconstriction of small pial arteries observed experimentally during hemodilution, ascribing it to the decrease in blood viscosity and to the antagonistic action of the flow-dependent mechanism (responsible for vasoconstriction) and of hypoxia (responsible for vasodilation). Finally, the interaction between hypoxia and intracranial pressure (ICP) has been analyzed. This interaction turns out quite complex, leading to different ICP time patterns depending on the status of the cerebrospinal fluid outflow pathways and of intracranial compliance.

An integrated model of the human ventilatory control system: the response to hypercapnia.

This work presents a mathematical model of the human respiratory control system, based on physiological knowledge. It includes three compartments for gas storage and exchange (lungs, brain tissue and other body tissues), and various kinds of feedback mechanisms. These comprehend peripheral chemoreceptors in the carotid body, central chemoreceptors in the medulla and a central ventilatory depression. The latter acts by reducing the response of the central neural system to the afferent peripheral chemoreceptor activity during prolonged hypoxia of the brain tissue. Furthermore, the model considers local blood flow adjustments in response to O2 and CO2 arterial pressure changes. In this study, the model has been validated by simulating the response to square changes in alveolar PCO2, performed at different constant levels of alveolar PO2. A good agreement with data reported in the literature has been checked. Subsequently, a sensitivity analysis on the role of the main feedback mechanisms on ventilation response to CO2 has been performed. The results suggest that the ventilatory response to CO2 challenges during hyperoxia can be almost completely ascribed to the central chemoreflex, while, during normoxia, the peripheral chemoreceptors provide a modest contribution too. By contrast, the response to hypercapnic stimuli during hypoxia involves a complex superimposition among different factors with disparate dynamics. Hence, results suggest that the ventilatory response to hypercapnia during hypoxia is more complex than that provided by simple empirical models, and that discrimination between the central and peripheral components based on time constants may be misleading.

An integrated model of the human ventilatory control system: the response to hypoxia.

The mathematical model of the respiratory control system described in a previous companion paper is used to analyse the ventilatory response to hypoxic stimuli. Simulation of long-lasting isocapnic hypoxia at normal alveolar PCO2 (40 mmHg=5.33 kPa) shows the occurrence of a biphasic response, characterized by an initial peak and a subsequent hypoxic ventilatory decline (HVD). The latter is about as great as 2/3 of the initial peak and can be mainly ascribed to prolonged neural hypoxia. If isocapnic hypoxia is performed during hypercapnia (PACO2=48 mmHg =6.4 kPa), the ventilatory response is stronger and HVD is minimal (about 1/10-1/5 of the initial peak). During poikilocapnic hypoxia, ventilation exhibits smaller changes compared with the isocapnic case, with a rapid return toward baseline within a few minutes. Moreover, a significant undershoot occurs at the termination of the hypoxic period. This undershoot may lead to apnea and to a transient destabilization of the control system if the peripheral chemoreflex gain and time delay are twofold greater than basal.

Acute cardiovascular response to isocapnic hypoxia. I. A mathematical model.

A mathematical model of the acute cardiovascular response to isocapnic hypoxia is presented. It includes a pulsating heart, the systemic and pulmonary circulation, a separate description of the vascular bed in organs with the higher metabolic need, and the local effect of O(2) on these organs. Moreover, the model also includes the action of several reflex regulatory mechanisms: the peripheral chemoreceptors, the lung stretch receptors, the arterial baroreceptors, and the hypoxic response of the central nervous system. All parameters in the model are given in accordance with the physiological literature. The simulated overall response to a deep hypoxia (28 mmHg) agrees with the experimental data quite well, showing a biphasic pattern. The early phase (8-10 s), caused by activation of peripheral chemoreceptors, exhibits a moderate increase in mean systemic arterial pressure, a decrease in heart rate, a quite constant cardiac output, and a redistribution of blood flow to the organs with higher metabolic need at the expense of other organs. The later phase (20 s) is characterized by the activation of lung stretch receptors and by the central nervous system hypoxic response. During this phase, cardiac output and heart rate increase together, and blood flow is restored to normal levels also in organs with lower metabolic need. The model may be used to gain a deeper understanding of the role of each mechanism in the overall cardiovascular response to hypoxia.

Acute cardiovascular response to isocapnic hypoxia. II. Model validation.

The role of the different mechanisms involved in the cardiovascular response to hypoxia [chemoreceptors, baroreceptors, lung stretch receptors, and central nervous system (CNS) hypoxic response] is analyzed in different physiological conditions by means of a mathematical model. The results reveal the following: 1) The model is able to reproduce the cardiovascular response to hypoxia very well between 100 and 28 mmHg PO(2). 2) Sensitivity analysis of the impact of each individual mechanism underlines the role of the baroreflex in avoiding excessive derangement of systemic arterial pressure and cardiac output during severe hypoxia and suggests the existence of significant redundancy among the other regulatory factors. 3) Simulation of chronic sinoaortic denervation (i.e., simultaneous exclusion of baroreceptors, chemoreceptors, and lung stretch receptors) shows that the CNS hypoxic response alone is able to maintain quite normal cardiovascular adjustments to hypoxia; however, suppression of the CNS hypoxic response, as might occur during anesthesia, led to a significant arterial hypotension. 4) Simulations of experiments with controlled ventilation show a significant decrease in heart rate that can only partly be ascribed to inactivation of lung stretch receptors. 5) Simulations performed by maintaining constant cardiac output suggest that during severe hypoxia the chemoreflex can produce a significant decrease in systemic blood volume. In all the previous cases, model predictions exhibit a satisfactory agreement with physiological data.